let abcd be a parallelogram. prove: abcd is a rectangle iff ac = bd

Answers

Answer 1

We have shown that a parallelogram ABCD is a rectangle if and only if AC = BD.

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

To prove that a parallelogram ABCD is a rectangle if and only if AC = BD, we need to show two things:

If ABCD is a rectangle, then AC = BD.

If AC = BD, then ABCD is a rectangle.

Proof:

1. Assume that ABCD is a rectangle. This means that all angles of the parallelogram are right angles. Let's draw diagonal AC and BD, which divide the rectangle into four right triangles (ABC, BCD, ACD, and ABD). Since the opposite sides of a parallelogram are congruent, we have AB = CD and AD = BC. Therefore, triangles ABD and ACD are congruent (by side-angle-side) and have the same hypotenuse AD. This means that their legs are congruent: AB = CD and BD = AC. Since AB = CD, we have AC + BD = AD + AD = 2AD. But since ABCD is a rectangle, we know that AC = AD and BD = AD. Therefore, AC + BD = 2AD = 2AC = 2BD. So AC = BD.

2. Now assume that AC = BD. We need to prove that ABCD is a rectangle. Let's draw diagonal AC and BD again. Since AC = BD, the two diagonals divide the parallelogram into four congruent triangles (ABC, ACD, BCD, and ABD). Therefore, each of these triangles has a right angle, since the sum of their angles is 180 degrees. Since angle BCD and angle ACD are adjacent angles around a straight line, they add up to 180 degrees, so they are also right angles.

Therefore, we have shown that a parallelogram ABCD is a rectangle if and only if AC = BD.

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Related Questions

i suck at math and i’m tired of it, please help + 100 points

Answers

Answer:

C

Step-by-step explanation:

K^2 + 4

Answer:k^2+4

Step-by-step explanation:

Grace had her photo printed in two different sizes. If her wallet is in the shape of a rectangle 11cm long and 10cm wide, can the smaller photo fit into her wallet?

Answers

As the Smaller photo: 10 cm  x 10 cm which equals to the dimension of wallet. Thus, the smaller photo will fit into Grace's wallet.

Explain about the features of rectangle:

A quadrilateral featuring four right angles is a rectangle. As a result, a rectangle's angles are all equal (360°/4 = 90°). A rectangle also has parallel and equal opposite sides, and its diagonals cut it in half.

The three characteristics of a rectangle are as follows:

A rectangle has only 90° angles.In a rectangle, the opposing sides are equal and A rectangle's parallel diagonals cut each other in half.

Given data:

Dimensions of  photo:

Smaller photo: 10 cm  x 10 cm larger photo: 11 cm x 11cm

Dimensions of rectangle wallet :

length = 11 cmwidth = 10cm

The dimension of the smaller photo must be less than equal to width of the wallet to get fit inside it.

As the Smaller photo: 10 cm  x 10 cm which equals to the dimension of wallet. Thus, the smaller photo will fit into Grace's wallet.

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Complete question:

Grace had her photo printed in two different sizes. One is 11cm x 11 cm and second is 10cm x 10 cm  If her wallet is in the shape of a rectangle 11cm long and 10cm wide, can the smaller photo fit into her wallet?

give a combinatorial proof for the identity 1 + 2 + 3 ⋯ +n=(n +1/2).

Answers

Answer: Brainliest?

Step-by-step explanation:

To prove the identity 1 + 2 + 3 + ... + n = (n+1)/2 combinatorially, we can use a simple argument involving counting the number of ways to arrange a certain set of objects.

Consider a set of (n+1) objects, consisting of n white balls and 1 black ball. We want to count the number of ways to arrange these objects in a row. Let's call this number N.

On the one hand, we can count N directly by considering the number of choices we have for the first ball, then the number of choices we have for the second ball, and so on, until we have made n choices for the n white balls, leaving only the black ball to be placed in the last position. Using the multiplication principle, we see that N is equal to the product of n consecutive integers, which we can write as:

N = n(n-1)(n-2)...(3)(2)(1)

On the other hand, we can count N indirectly by considering the number of ways to divide the (n+1) objects into two groups: the black ball by itself, and the remaining n white balls. Since there are (n+1) objects in total, there are (n+1) ways to choose which object will be the black ball. Once we have made this choice, the remaining n white balls can be arranged in any order, giving us n! possible arrangements. Thus, the total number of arrangements is:

N = (n+1) n!

Now, these two expressions for N must be equal, since they are both counting the same thing. Equating them, we get:

n(n-1)(n-2)...(3)(2)(1) = (n+1) n!

Simplifying, we obtain:

1 + 2 + 3 + ... + n = n(n+1)/2

which is the desired identity.

[tex]f (x) = 2x^{3} - x^{2} - 22x - 24[/tex] synthetic division

Possible zeros:
Zeros:
Linear Factors:

Answers

The possible zeros of the polynomial are -2, -3/2 and  4.

What are the zeros of the function?

The zeros of the function is calculated as follows;

The zeros of the function are the values of x that will make the function equal to zero.

let x = -2

f(x) = 2x³ - x² - 22x - 24

f(-2) = 2(-2)³ - (-2)² - 22(-2) - 24

f(-2) = -16 - 4 + 44 - 24

f(-2) = 0

So, x + 2 is a factor of the polynomial, and other zeros of the polynomial is calculated as;

                           

                       2x² - 5x - 12

                    ----------------------------------

         x + 2    √ 2x³ - x² - 22x  - 24

                  - (2x³ +  4x²)

                    ------------------------------------

                              -5x² - 22x -24

                            - (-5x² - 10x)

                       -------------------------------------

                                       -12x - 24

                                    - (-12x - 24)

                               -------------------------

                                              0

 2x² - 5x - 12 , so will factorize this quotient as follows;

= 2x² - 8x + 3x - 12

= 2x(x - 4) + 3(x - 4)

= (2x + 3)(x - 4)

2x + 3 = 0

or

x - 4 = 0

x = -3/2 or 4

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Find (x-y) if X=5/3 y=-1/6

Answers

Answer: (x - y) = 13/6

Step-by-step explanation: To find the value of (x-y), we need to substitute the given values of x and y and then perform the subtraction.

So,

(x - y) = (5/3 - (-1/6))

We can simplify this expression by first converting the negative fraction to its equivalent positive fraction and then finding the common denominator.

(x - y) = (5/3 + 1/6) = ((10+3)/6) = 13/6

Therefore, (x - y) = 13/6.

Share Prompt

Answer:

11/6

Step-by-step explanation:

Use substitution.

x = 5/3

y = -1/6

Sub these values into (x-y):

[(5/3) - (-1/6)]

*Make sure to use brackets when subbing in values especially when there are negative signs or exponents

5/3 + 1/6 ⇒ two negatives become a positive

10/6 + 1/6 ⇒ make a common LCD

= 11/6

calculate the probability that an electron will be found a between x=0.1 and 0.2 nm in a box of length l=10nm when its wavefunction is =2/l^1/2sin(2pix/l). t

Answers

The probability of finding an electron between x = 0.1 nm and x = 0.2 nm is 0.1 nm.

The probability density function for finding an electron between two points in space is given by the square of the absolute value of the wave function, integrated over the given range.

Let's start by finding the normalization constant A for the given wave function:

∫|Ψ|^2 dx = 1

∫(2/√l)sin(2πx/l) dx = 1

Using integration by parts, we get:

A = √(l/2)

Now, the probability of finding the electron between x = 0.1 nm and x = 0.2 nm is given by:

P = ∫0.2nm 0.1nm |Ψ|^2 dx

P = A^2 ∫0.2nm 0.1nm (sin(2πx/l))^2 dx

P = (l/2) ∫0.2nm 0.1nm (sin(2πx/l))^2 dx

P = (10/2) ∫0.2nm 0.1nm (sin(2πx/10))^2 dx

P = 2 ∫0.2nm 0.1nm (sin(πx/5))^2 dx

Using the identity sin^2θ = (1/2)(1 - cos(2θ)), we can simplify this expression:

P = 2 ∫0.2nm 0.1nm (1/2)(1 - cos(2πx/5)) dx

P = ∫0.2nm 0.1nm (1 - cos(2πx/5)) dx

P = (∫0.2nm 0.1nm dx) - (∫0.2nm 0.1nm cos(2πx/5) dx)

The first integral is simply the length of the given interval:

∫0.2nm 0.1nm dx = 0.1nm

For the second integral, we can use the fact that the integral of cos(mx) from 0 to 2π is zero, unless m is equal to zero. In this case, m = 5, so we get:

∫0.2nm 0.1nm cos(2πx/5) dx = 0

Therefore, the probability of finding the electron between x = 0.1 nm and x = 0.2 nm is:

P = 0.1nm

So the probability of finding an electron between x = 0.1 nm and x = 0.2 nm is 0.1 nm.

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Recall that an angle making a full rotation measures 360 degrees or 2 radians. a. If an angle has a measure of 110 degrees, what is the measure of that angle in radians? radians Preview b. Write a formula that expresses the radian angle measure of an angle, in terms of the degree measure of that angle

Answers

The measure of the angle in radians is approximately 1.9099 radians and Where radian_angle represents the angle's measure in radians, degree_angle represents the angle's measure in degrees, and π (pi) is approximately 3.1416


a. To convert an angle of 110 degrees to radians, we can use the following conversion formula:

[tex]radians = \frac{(degrees × π) }{180}[/tex]

Step 1: Plug in the given angle (110 degrees) into the formula:
[tex]radians= \frac{110×π}{180}[/tex]

Step 2: Calculate the value:
[tex]radians= \frac{(110)(3.1416)}{180} = \frac{343.7756}{180} = 1.9000[/tex]

So, the measure of the angle in radians is approximately 1.9099 radians.

b. To write a general formula that expresses the radian angle measure of an angle, in terms of the degree measure of that angle, you can use the following formula:
[tex]radian angle= \frac{degree angle x π}{180}[/tex]

Where radian_angle represents the angle's measure in radians, degree_angle represents the angle's measure in degrees, and π (pi) is approximately 3.1416.

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if n=29, ¯ x =50, and s=2, find the margin of error at a 95onfidence level using the critical value rounded to three decimal places.

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At a 95% confidence level, the margin of error is approximately 0.762 (rounded to three decimal places).

To find the margin of error at a 95% confidence level, we need to first find the critical value associated with a sample size of 29 and a confidence level of 95%.

Using a t-distribution with n-1 degrees of freedom, we can find the critical value using a t-table or calculator. For n=29 and a confidence level of 95%, the critical value is approximately 2.045 (rounded to three decimal places).

The formula for the margin of error is:

Margin of error = critical value * (standard deviation / sqrt(sample size))

Plugging in the values we have:

Margin of error = 2.045 * (2 / sqrt(29))
Margin of error ≈ 0.762

Therefore, at a 95% confidence level, the margin of error is approximately 0.762 (rounded to three decimal places).

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Use the Power Rule to compute the derivative. (Use symbolic notation and fractions where needed.) Compute f'(x) using the limit definition. f(x) = x2 + 16x (Use symbolic notation and fractions where needed.) f'(x) = Calculate the derivative by expanding or simplifying the function. Q(r) = (1 - 4r)(6r + 5) (Use symbolic notation and fractions where needed.) Calculate the derivative. (Use symbolic notation and fractions where needed. (12x5/4 + 3x-312 + 5x) = Calculate the derivative. (Use symbolic notation and fractions where needed.) (9y? + 30x415) = Calculate the derivative of the function. h(t) = 9/0 - 0 (Express numbers in exact form. Use symbolic notation and fractions where needed.) k' (t) = Calculate the derivative of the function. h(t) = 9/1- (Express numbers in exact form. Use symbolic notation and fractions where needed.) h(t)= Calculate the derivative of the function. h(t) = 9/1 - M (Express numbers in exact form. Use symbolic notation and fractions where needed.) privacy policy terms of use contact us help

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Therefore, the derivative (Use symbolic notation and fractions where needed). [tex]f'(x)=4x^3[/tex].

Using the Power Rule to compute the derivative:

[tex]f(x) = x^2 + 16x[/tex]

[tex]f'(x) = d/dx (x^2 + 16x)[/tex]

[tex]= d/dx (x^2) + d/dx (16x)[/tex](using the linearity property)

[tex]= 2x + 16[/tex] (using the Power Rule)

Therefore, [tex]f'(x) = 2x + 16.[/tex]

Computing f'(x) using the limit definition:

[tex]f(x) = x^2 + 16x[/tex]

[tex]f'(x) = lim(h - > 0) [(f(x+h) - f(x))/h][/tex]

[tex]= lim(h - > 0) [(x+h)^2 + 16(x+h) - (x^2 + 16x))/h][/tex]

[tex]= lim(h - > 0) [x^2 + 2xh + h^2 + 16x + 16h - x^2 - 16x]/h[/tex]

[tex]= 2x + 16[/tex]

Therefore, [tex]f'(x) = 2x + 16.[/tex]

Calculating the derivative using the product rule:

[tex]Q(r) = (1 - 4r)(6r + 5)[/tex]

[tex]Q'(r) = d/dx [(1 - 4r)(6r + 5)][/tex]

[tex]= (d/dx (1 - 4r))(6r + 5) + (1 - 4r)(d/dx (6r + 5))[/tex] (using the product rule)

[tex]= (-4)(6r + 5) + (1 - 4r)(6)[/tex] (taking the derivatives of the individual factors)

[tex]= -24r - 20 + 6 - 24r[/tex]

[tex]= -48r - 14[/tex]

Therefore, Q'(r) = -48r - 14.

Calculating the derivative:

[tex]f(x) = 12x^{(5/4)} + 3x^{(-3/12)}+ 5x[/tex]

[tex]f'(x) = d/dx (12x^{(5/4)} + 3x^{(-3/12)} + 5x)[/tex]

[tex]= 12(d/dx x^{(5/4))} + 3(d/dx x^{(-3/12))} + 5(d/dx x)[/tex] (using the linearity property)

[tex]= 12(5/4)x^{(1/4)} - 3(3/12)x^{(-15/12)} + 5[/tex](using the Power Rule and the Chain Rule)

[tex]= 15x^{(1/4)} - 9x^{(-5/4)} + 5[/tex]

Therefore,[tex]f'(x) = 15x^{(1/4)} - 9x^{(-5/4)} + 5.[/tex]

Calculating the derivative:

[tex]f(x) = 9y^2 + 30x^4/15[/tex]

[tex]f'(x) = d/dx (9y^2 + 30x^4/15)[/tex]

[tex]= 0 + 4x^3[/tex] (taking the derivative of the second term and simplifying)

[tex]= 4x^3[/tex]

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A chord of a circle is l cm long. The distance of the chord to the centre of the circle is h cm and the radius of the circle is r cm. Express r in terms of l and h.

Answers

The value of r in terms of l and h is,

⇒ r = √((l/2)² + h²)

Now, We can use the Pythagorean theorem to relate r, l, and h as,

Since, The chord of the circle divides the circle into two segments, each with a height of h.

Let's call the segments are A and B.

Then, the length of the chord (l) is equal to the sum of the bases of segments A and B.

Therefore, the length of each base is,

(l/2).

Hence, We can use the Pythagorean theorem to relate r, l/2, and h for one of the segments as;

⇒ r² = (l/2)² + h²

⇒ r = √((l/2)² + h²)

Thus, The value of r in terms of l and h is,

⇒ r = √((l/2)² + h²)

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using the mmoles listed in the lab manual, how many grams of trans-cinnamic acid should you use?

Answers

We can use 740.8 grams of trans-cinnamic acid based on the m moles listed in the lab manual.  The lab manual, you would first need to know the molar mass of trans-cinnamic

To determine how many grams of trans-cinnamic acid should be used based on the m moles listed in the lab manual, we would first need to know the molar mass of trans-cinnamic acid. The molar mass of trans-cinnamic acid is 148.16 g/mol.

Next, you would need to determine the number of m moles of trans-cinnamic acid that the lab manual specifies. Let's say, for example, that the lab manual specifies using 5 m moles of trans-cinnamic acid.

To convert m moles to grams, you would use the following formula:

mass (g) = mmoles x molar mass

So, to find the mass of 5 m moles of trans-cinnamic acid:

mass (g) = 5 x 148.16
mass (g) = 740.8

Therefore, you would use 740.8 grams of trans-cinnamic acid based on the m moles listed in the lab manual.

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(a) You are given the point (1, π/2) in polar coordinates. (i) Find another pair of polar coordinates for this point such that r > 0 and 2π < θ < 4π. (ii) Find another pair of polar coordinates for this point such that r < 0 and 0 < θ < 2π (b) You are given the point (-2, π/4) in polar coordinates. (i) Find another pair of polar coordinates for this point such that r > 0 and 2π < θ < 4π. (ii) Find another pair of polar coordinates for this point such that r < 0 and-2x < θ < 0. r2 (c) You are given the point (3,2) in polar coordinates. (i) Find another pair of polar coordinates for this point such that r > 0 and 2π < θ < 4T. (ii) Find another pair of polar coordinates for this point such that r < 0 and 0 θ < 2π.

Answers

(a) (i) Another pair of polar coordinates for (1, π/2) with r > 0 and 2π < θ < 4π is (1, 5π/2).
(ii) Another pair of polar coordinates for (1, π/2) with r < 0 and 0 < θ < 2π is (-1, π/2).

(b) (i) Another pair of polar coordinates for (-2, π/4) with r > 0 and 2π < θ < 4π is (2, 9π/4).
(ii) Since there is a typo in the question, I assume you meant 0 < θ < 2π. In this case, another pair of polar coordinates for (-2, π/4) with r < 0 and 0 < θ < 2π is (-2, π/4).

(c) (i) Assuming the correct range for θ is 2π < θ < 4π, another pair of polar coordinates for (3, 2) with r > 0 and 2π < θ < 4π is (3, 2 + 2π).
(ii) Another pair of polar coordinates for (3, 2) with r < 0 and 0 < θ < 2π is (-3, 2 + π).

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(a) (i) Another pair of polar coordinates for (1, π/2) with r > 0 and 2π < θ < 4π is (1, 5π/2).
(ii) Another pair of polar coordinates for (1, π/2) with r < 0 and 0 < θ < 2π is (-1, π/2).

(b) (i) Another pair of polar coordinates for (-2, π/4) with r > 0 and 2π < θ < 4π is (2, 9π/4).
(ii) Since there is a typo in the question, I assume you meant 0 < θ < 2π. In this case, another pair of polar coordinates for (-2, π/4) with r < 0 and 0 < θ < 2π is (-2, π/4).

(c) (i) Assuming the correct range for θ is 2π < θ < 4π, another pair of polar coordinates for (3, 2) with r > 0 and 2π < θ < 4π is (3, 2 + 2π).
(ii) Another pair of polar coordinates for (3, 2) with r < 0 and 0 < θ < 2π is (-3, 2 + π).

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Let f(x) = 4(1/4) ^x+2 What is f(1)? Answer in fraction form. Provide your answer below: f(1) = __

Answers

The value of function f(1) = 1/16.

What is function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f(x).

To find f(1), we substitute x = 1 into the given expression for f(x):

f(1) = 4(1/4)⁽¹⁺²⁾ = 4(1/4)³ = 4(1/64) = 1/16

Therefore, f(1) = 1/16.

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URGENT MUST BE ANSWERED NOW !! PLEASE AND THANK YOU (image included)

Mitch uses 1/4 of his supply of apples to make apple crisp and 3/8 of his supply of apples to make pies. If Mitch uses 10 pounds of apples, how many pounds of apples are in his supply?

Answers

Answer:

16 lbs

Step-by-step explanation:

total of apples = 1/4 + 3/8 = 2/8 + 3/8 = 5/8

then 10 x 8/5 = 16

I need help with this please, i’ve been stuck on this over a hour now.

Answers

The height of the tree to the nearest hundredth is 29.65 ft.

How to find the side of a right triangle?

The measure of the distance from the tree and the angle of elevation from the ground to the top of the tree is represented as follows:

Therefore, the height of the tree to the nearest hundredth can ne found as follows:

Therefore, using trigonometric ratios,

tan 56° = opposite / adjacent

tan 56° = h / 20

cross multiply

h = 20 tan 56°

h = 20 × 1.48256096851

h = 29.6512193703

h = 29.65 ft

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An object is 25.0 cm from the center of a spherical silvered-glass Christmas tree ornament 6.20 cm in diameter. What is the position of its image (counting from the ornament surface)? Follow the sign rules. Express your answer with the appropriate units. What is the magnification of its image?

Answers

The image magnification is about 0.133 times the size of the object and is inverted.

What is magnification?

Magnification is the ratio of the size of the image to the size of the object. In optics, it is often used to describe how much larger or smaller an image appears compared to the object being viewed. It is calculated by dividing the height or size of the image by the height or size of the object. Magnification can be positive or negative, depending on whether the image is upright or inverted, respectively.

According to the given information

We can use the mirror equation to find the position of the image:

1/f = 1/do + 1/di

where f is the focal length, do is the object distance, and di are the image distance.

Since the ornament is a spherical mirror, the focal length is half the radius of curvature, which is equal to half the diameter of the ornament:

f = R/2 = 6.20 cm/2 = 3.10 cm

The object distance is given as 25.0 cm.

Substituting into the mirror equation and solving for di, we get:

1/3.10 = 1/25.0 + 1/di

di = 3.33 cm

The image is formed 3.33 cm from the center of the ornament, which is 0.23 cm beyond the surface of the ornament (since the ornament has a radius of 3.10 cm).

The magnification of the image can be found using the:

m = -di/do

where the negative sign indicates that the image is inverted.

Substituting the values we found, we get:

m = -(3.33 cm)/(25.0 cm) = -0.133

So the image is about 0.133 times the size of the object and is inverted.

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how many terms of the series Σ[infinity] 2/n^6 n=1 are needed so that the remainder is less than 0.0005? [Give the smallest integer value of n for which this is true.]

Answers

The number of terms the series needed so that the remainder is less than 0.0005 is 14. The smallest integer value of n for which this is true is 14.

To find the number of terms needed for the remainder to be less than 0.0005, we need to use the remainder formula for an infinite series:
Rn = Sn - S
where Rn is the remainder after adding n terms, Sn is the sum of the first n terms, and S is the sum of the infinite series.

For this series, S can be found using the formula for the sum of a p-series:
S = Σ[infinity] 2/n^6 n=1 = π^6/945

Now we need to find the smallest value of n for which Rn < 0.0005. We can rewrite the remainder formula as:
Rn = Σ[infinity] 2/n^6 - Σ[n] 2/n^6

Simplifying the first term using the formula for the sum of a p-series, we get:
Σ[infinity] 2/n^6 = π^6/945

Substituting this into the remainder formula, we get:
Rn = π^6/945 - Σ[n] 2/n^6

We want Rn < 0.0005, so we can set up the inequality:
π^6/945 - Σ[n] 2/n^6 < 0.0005

Solving for n using a calculator or computer program, we get:
n ≥ 14

Therefore, we need at least 14 terms of the series Σ[infinity] 2/n^6 n=1 to ensure that the remainder is less than 0.0005, and the smallest integer value of n for which this is true is 14.

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Can someone pls answers this??? asapp

Answers

The correct statement regarding the rate of change of the exponential function is given as follows:

The bacterial culture loses 1/2 of it's size every 1/6 seconds.

How to obtain the half life of the exponential function?

The exponential function that gives the bacteria's population after t seconds is given as follows:

B(t) = 9300(1/64)^t.

The rate of change of the exponential function is given as follows:

1/64.

Hence the half-life of the population is obtained as follows:

(1/64)^t = 1/2

(1/2^6)^t = (1/2)

2^(-6t) = 2^(-1)

6t = 1

t = 1/6.

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please i need the answer ill give brainliest

Answers

The simplified expression is [tex]\frac{2x}{x-1}[/tex].

How to simplify any expression?

Expression  - An expression or algebraic expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them.

To simplify the expression, we can factor out a 4x from the numerator and a 2 from the denominator, which gives:

[tex]=\frac{4x^2+4x}{2x^2-2}\\\\ = \frac{4x(x+1)}{2(x^2-1)} \\\\ = \frac{2\cdot 2x(x+1)}{2(x-1)(x+1)} \\\\ = \frac{2x}{x-1}[/tex]

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15 minutes to read 9 pages; 50 minutes to read 30 pages
what is the answer

Answers

Answer:

It takes about 1 hour to read 30 pages at an average reading speed

Step-by-step explanation:

42
At the end of a baseball game, the players were given the choice of having a bottle of
water or a box of juice. Of all of the players, 12 chose a bottle of water, which was
3
4 of the total number of players. Write and solve an equation to determine p,
the total number of players at the baseball game.
Show your work.

Answers

The equation to determine p, which is the total number of player at the basketball game, is 12 = p x 3 / 4 .

The number of players at the basketball game is 16 players .

How to find the number of players ?

The equation to find the number of players is;

Players who chose water = total players x proportion of players who chose water

12 = p x 3 / 4

This means that solving for p gives :

12 = p x 3 / 4

12 ÷ 3 / 4 = p

p = 12 ÷  3 / 4

p = 12 / 0.75

p = 16 players

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Help, will give brainliest.

Answers

Answer: this is how to do it

Step-by-step explanation: x=−3.

x=−4, y=−6

xy-3x=40, x=5

x(y-3)=40

y-3=(40/x)

y=(40/x)+3

y=(40/5)+3

y=8+3

y=11

Find N such that x+N=5.4 and x/n=5.4 are equivalent equations

Answers

Answer: 0.84375

Step-by-step explanation:

1. x = 5.4n

2. 5.4n + n = 5.4

3. n(6.4) = 5.4

4. n = 0.84375

DOUBLE CHECK

x = 5.4(0.84375)

x = 4.55625

4.55625 + 0.84375 = 5.4

0.84375 = 5.4 - 4.55625

0.84375 = 0.84375

The solution is, : for 0.84375 = N such that x+N=5.4 and x/n=5.4 are equivalent equations.

What is equation?

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

Here, we have,

the given equations are:

1. x = 5.4n

2. 5.4n + n = 5.4

3. n(6.4) = 5.4

4. n = 0.84375

DOUBLE CHECK

x = 5.4(0.84375)

x = 4.55625

4.55625 + 0.84375 = 5.4

0.84375 = 5.4 - 4.55625

0.84375 = 0.84375

Hence, The solution is, : for 0.84375 = N such that x+N=5.4 and x/n=5.4 are equivalent equations.

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determine whether the sets s1 and s2 span the same subspace of r3. s1 = {(1, 2, −1), (0, 1, 1), (2, 5, −1)} s2 = {(−2, −6, 0), (1, 1, −2)}

Answers

Therefore, s1 and s2 do not span the same subspace of R3.

To determine whether the sets s1 and s2 span the same subspace of R3, we need to check if one set can be obtained as a linear combination of the other set.

We can start by checking if the vectors in s2 can be obtained as a linear combination of the vectors in s1. We can set up the following system of equations:

[tex]a(1, 2, -1) + b (0, 1, 1) + c(2, 5, -1) = (-2, -6, 0)[/tex]

[tex]d(1, 2, -1) + e(0, 1, 1) + f(2, 5, -1) = (1, 1, -2)[/tex]

We can write this system in matrix form as follows:

[tex]\left[\begin{array}{ccc}1&0&2|-2\\2&1&5|-6\\-1&1&-1|0\end{array}\right]*\left[\begin{array}{ccc}1&0&2|1\\2&1&5|1\\-1&1&-1|-2\end{array}\right][/tex]

We can row reduce this augmented matrix to find the solutions for the system of equations:

[tex]\left[\begin{array}{ccc}1&0&2|-2\\0&1&1|2\\0&0&0|0\end{array}\right]*\left[\begin{array}{ccc}1&0&2|1\\2&1&5|1\\0&0&0|0\end{array}\right][/tex]

The matrix on the left represents the coefficients for the linear combinations of the vectors in s1 that would give us the vectors in s2. Since the matrix has a row of zeros, this means that we can't obtain the vectors in s2 as a linear combination of the vectors in s1.

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suppose x and y are independent random variables with expected values e[x] = 0, e[y] = 0, and var(x) = 1, var(y) = 1. what is var(x-y)?

Answers

The required variance for the question is var (x - y) is 2.

We are given that x and y are independent random variables with E[x] = 0, E[y] = 0, Var(x) = 1, and Var(y) = 1. We need to find Var(x - y).Step 1: Understand the properties of variance.
The variance of a difference between two random variables can be expressed as Var(x - y) = Var(x) + Var(y) - 2 * Cov(x, y), where Cov(x, y) is the covariance between x and y.Step 2: Identify the covariance for independent random variables.
Since x and y are independent random variables, their covariance is zero. Therefore, Cov(x, y) = 0.Step 3: Calculate Var(x - y).
Using the formula from Step 1 and the covariance from Step 2, we get:
Var(x - y) = Var(x) + Var(y) - 2 * Cov(x, y)
Var(x - y) = 1 + 1 - 2 * 0 (substituting Var(x) = 1, Var(y) = 1, and Cov(x, y) = 0)
Var(x - y) = 1 + 1
Var(x - y) = 2So, the variance of x - y is 2.

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. If the rank of a 7 x 6 matrix A is 4, what is the dimension of the solution space of Az = 0. A. 1 B. 2 C. 3 D. 4 E. none of the above. 8.

Answers

The dimension of the solution space is 2. Therefore, the answer is (B) 2.

How to find the dimension of the solution space?

The rank of a matrix A is defined as the maximum number of linearly independent rows or columns in A.

Therefore, if the rank of a 7 x 6 matrix A is 4, it means that there are 4 linearly independent rows or columns in A, and the other 3 rows or columns can be expressed as linear combinations of the 4 independent ones.

The equation Az = 0 represents a homogeneous system of linear equations, where z is a column vector of unknowns.

The dimension of the solution space of this system is equal to the number of unknowns minus the rank of the coefficient matrix A.

In this case, A has 6 columns and rank 4, so the number of unknowns is 6 and the dimension of the solution space is 6 - 4 = 2. Therefore, the answer is (B) 2.

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Question 14
Which explicit formula describes the pattern in this table?
d
2
3
5
10
C
6.28
9.42
15.70
31.40
Od 3.14x C
O 3.14x C-d
O 31.4 x 10 C
OC 3.14 x d
1 pts

Answers

The explicit formula is C = 3.14 × d.

What is the explicit formula?

The formal equations for L-functions in mathematics are Riemann's zeta function and links between sums over an L-function's complex number zeroes and sums over prime powers.

Here, we have

Given:

d    C

2    6.28

3    9.42

5    15.70

10   31.40

We have to find the explicit formula that describes the given pattern.

We concluded from the given table that

when d = 2

we get

c = 3.14 × 2 = 6.28

When d = 3

We get

c = 3.14 × 3 = 9.42

When d = 5

We get

c = 3.14 × 5 =  15.70

When d = 10

we get

c = 3.14 × 10 = 31.40

Hence, the explicit formula is C = 3.14 × d.

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Find the circumference of a circle with diameter 66cm(Take π=22/7)​

Answers

Answer:207

Step-by-step explanation: circumference = to 2πr or πd
substitute the diameter into the equation πd (22/7)(66) and you get 207.4285...

determine the form of a particular solution for the differential equation. (Do not evaluate coefficients.) 27. y" +9y = 4t sin 3t 28. y" - 6y' +9y = 5te3 29. y" + 3y' - Ty = t4e 30. y" - 2y' + y = 7e' cost 31. y" + 2y' + 2y = 8t'e sint 32. y" - y' - 12y = 2tºe -34

Answers

A particular solution will have the form (At^2 + Bt + C)e^(-3t), where A, B, and C are undetermined coefficients.

To determine the form of a particular solution for each differential equation, we need to consider the form of the nonhomogeneous term and choose a solution that has the same form, but with undetermined coefficients.

27. The nonhomogeneous term is 4t sin 3t, which is a product of a polynomial and a sine function. Therefore, a particular solution will have the form At^2 sin 3t + Bt cos 3t, where A and B are undetermined coefficients.

28. The nonhomogeneous term is 5te3, which is a product of a polynomial and an exponential function. Therefore, a particular solution will have the form (At^2 + Bt + C)e3t, where A, B, and C are undetermined coefficients.

29. The nonhomogeneous term is t4e, which is a product of a polynomial and an exponential function. Therefore, a particular solution will have the form (At^5 + Bt^4 + Ct^3 + Dt^2 + Et + F)e^t, where A, B, C, D, E, and F are undetermined coefficients.

30. The nonhomogeneous term is 7e^t cos t, which is a product of an exponential and a cosine function. Therefore, a particular solution will have the form (Acos t + Bsin t)e^t, where A and B are undetermined coefficients.

31. The nonhomogeneous term is 8t'e sin t, which is a product of a polynomial and a sine function. Therefore, a particular solution will have the form (At^2 + Bt + C)cos t + (Dt^2 + Et + F)sin t, where A, B, C, D, E, and F are undetermined coefficients.

32. The nonhomogeneous term is 2t^2 e^(-3t), which is a product of a polynomial and an exponential function. Therefore, a particular solution will have the form (At^2 + Bt + C)e^(-3t), where A, B, and C are undetermined coefficients.

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evaluate the iterated integral. 8 6 2z 0 ln(x) 0 xe−y dy dx dz

Answers

To evaluate the iterated integral ∫∫∫ 2z ln(x) xe^(-y) dy dx dz over the limits 0 ≤ y ≤ 6, 0 ≤ x ≤ 8, and 0 ≤ z ≤ 1, we begin by integrating the innermost integral with respect to y first, then the middle integral with respect to x, and finally the outermost integral with respect to z.

So, integrating with respect to y first, we get:
∫∫∫ 2z ln(x) xe^(-y) dy dx dz = ∫∫∫ 2z ln(x) (-e^(-y) + C) dx dz
where C is the constant of integration.
Next, integrating with respect to x, we get:
∫∫∫ 2z ln(x) (-e^(-y) + C) dx dz = ∫∫ 2z (-ln(x)e^(-y) + Cx) |_0^8 dz
= ∫∫ 16z(ln(8)e^(-y) - C) dz
= 16(ln(8)e^(-y) - C)z^2/2 |_0^1
= 8(ln(8)e^(-y) - C)
Finally, integrating with respect to z, we get:
∫∫ 8(ln(8)e^(-y) - C) dz = (8/2)(ln(8)e^(-y) - C)(1^2 - 0^2)
= 4(ln(8)e^(-y) - C)
Therefore, the value of the iterated integral over the given limits is 4(ln(8)e^(-6) - C), where C is a constant of integration.

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