If the opposite corners of the rectangle ABCD are A (5, 3) and C (10, 1) and the equation of side BC is x-2y=8, find the equations of the other three sides. You must show your work and explain why you are doing it. (Note: opposite side of a rectangle are parallel and consecutive sides are
perpendicular)

Tables and figures must all be labelled with numbered captions that clearly identify and describe them.

x = 61

Left hand triangle containing 1 angle of 74

Label the other angle opposite the marked side also as 74

Find the third angle. Call it y.

y + 74 + 74 = 180           Combine like terms

y + 148 = 180                 Subtract 148 from both sides.

y = 180 - 148

y = 32

Now work with the triangle on the right.

label the angle making up the right angle = z

32 + z = 90                             These two angles are complementary = 90

32 - 32 + z = 90 - 32              Subtract 32 from both sides

z = 58                                      Use 58 wherever you see z

x + x + z = 180                         Substitute

2x + 58 = 180                          Subtract 58 from both sides

2x = 122                                  Divide by 2

x = 61

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The longest side of the triangle has a length of 11 cm.

Given that the sum of the lengths of the triangle is equal to 30 cm, and the sides are:

(x + 6)

(x + 4)

2x

Create an equation to find the value of x:

(x + 6) + (x + 4) + 2x = 30

x + 6 + x + 4 + 2x = 30

Combine like terms

4x + 10 = 30

4x = 30 - 10

4x = 20

4x/4 = 20/4

x = 5

Find the length of each of the sides of the triangle:

(x + 6) = 5 + 6 = 11 cm

(x + 4) = 5 + 4 = 9 cm

2x = 2(5) = 10 cm

The longest side is 11 cm.

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The interval of convergence for this series is [tex]$x \in \left(-1, 1\right)$[/tex].

What is Power Series Representation for the Function ?

To find a power series representation for a function, we need to express the function as an infinite series of the form

                      [tex]$$f(x) = \sum_{n=0}^{\infty} a_n (x-x_0)^n$$[/tex]

where [tex]$x_0$[/tex] is the center of the series, and the [tex]$a_n$[/tex] are the coefficients of the series. To determine the interval of convergence for the series, we need to find the values of [tex]$x$[/tex] for which the series converges.

To find the power series representation for a given function, we can use the process of Taylor series expansion. This involves finding the derivative of the function at the point [tex]$x_0$[/tex], and using the derivative to find the coefficients of the series.

For example, suppose we want to find a power series representation for the function [tex]$f(x) = \frac{1}{1-x}$[/tex]  centered at [tex]$x_0 = 0$[/tex]. We can use the process of Taylor series expansion to find the power series representation as follows:

[tex]$$f(x) = \frac{1}{1-x} = \frac{1}{1-0} + \frac{0-1}{(1-0)^2}x + \frac{2 \cdot 0 - 1 \cdot 1}{(1-0)^3}x^2 + \dotsb$$[/tex]

Simplifying this expression, we get

[tex]$$f(x) = 1 + x + x^2 + x^3 + \dotsb$$[/tex]

This is the power series representation of [tex]$f(x)$[/tex] centered at [tex]$x_0 = 0$[/tex].

To determine the interval of convergence for this series, we can use the ratio test. If we let [tex]$a_n = 1$[/tex] for all [tex]$n$[/tex], then the series becomes

[tex]$$\sum_{n=0}^{\infty} a_n (x-x_0)^n = \sum_{n=0}^{\infty} x^n$$[/tex]

If we take the limit of the absolute value of the ratio of successive terms, we get,

[tex]$$\lim_{n \to \infty} \left| \frac{x^{n+1}}{x^n} \right| = \left| x \right|$$[/tex]

If [tex]$|x| < 1$[/tex], then the series converges. If [tex]$|x| > 1$[/tex], then the series diverges. If [tex]$|x| = 1$[/tex], then the test is inconclusive and we need to use another method to determine convergence.

Therefore, the interval of convergence for this series is [tex]$x \in \left(-1, 1\right)$[/tex].

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The graph of a quadratic function is called a parabola

The complete table is

x = -6, -3, 0, 3 6

y = -12  -3 0 -3 -12

From the question, we have the following equation that can be used in our computation:

y=-1/3 x²

From the table of values , we have the following x values

x = -6, -3, 0, 3 and 6

Substitute x = -6, -3, 0, 3 and 6 in y=-1/3 x²

So, we have the following representation

y = -1/3 (-6)² = -12

y = -1/3 (-3)² = -3

y = -1/3 (0)² = 0

y = -1/3 (3)² = -3

y = -1/3 (6)² = -12

So, the complete table of values is

x = -6, -3, 0, 3 6

y = -12  -3 0 -3 -12

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45 years will take for 15 grams of strontium to decay to 5 grams

What is strontium?

The chemical element strontium has the atomic number 38 and the symbol Sr. Strontium is a soft, silver-white, yellowish metallic element that is an alkaline earth metal and has a strong reactivity to chemicals. When the metal is exposed to air, a thick layer of dark oxide forms.

Equation Given.

[tex]P = Po e^{-0.0244t}[/tex]

given P = 5 gram

          [tex]P_o = 15 gram[/tex]

Hence ,time taken

[tex]5 = 15 e^{-0.0244t}[/tex]

[tex]\frac{5}{15} = e^{-0.0244t}[/tex]

Taking log both side,

[tex]ln(\frac{1}{3} )=ln (e^{-0.0244t})\\\\-1.098 = -0.0244t\\\\t=\frac{1.098}{0.0244}\\\\t=45years[/tex]

Hence, 45 years will take for 15 grams of strontium to decay to 5 grams.

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Answer:

To rent a car from this company, Aaliyah will be charged a base rate of $71.87 per day, plus $0.09 for every mile she drives. In total, she plans to drive 475 miles, so she will be charged an additional $0.09 * 475 = $42.75 for the miles she drives.

The total cost of renting the car for one day will therefore be $71.87 + $42.75 = $114.62.

Aaliyah has a budget of $320, so she can afford to rent a car for a maximum of $320 / $114.62 = 2.79 days. However, since she can only rent the car for whole number of days, the maximum number of days she can afford is 2 days.

The inequality that can be used to determine the maximum number of days Aaliyah can afford to rent while staying within her budget is:

dd <= 2

Where dd is the number of days she plans to rent the car for. This inequality states that the maximum number of days Aaliyah can afford is 2.

Answer:

D

Step-by-step explanation:

5/3 x - 2/3 x = -4

3/3 x = -4

x = -4

Answer:

A = principal +interest

P = Principal Amount

r = rate

t = time

A = P(1 + rt)

5 000 = P[(1 + 0.05(821/364.25)]

5 000 = P(1 + 0.05(2.254)

5 000 = P(1 + 0.1127)

5 000 = 1.1127P

P = 4 493.5742

Therefore, you need to deposit an amount of $4 493.5742 to have $5 000 in 821 days.

Step-by-step explanation:

The equation 3x - 6 = x + 6 - 5x has one solution, which is x = 12/7.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given equation is,

3x - 6 = x + 6 - 5x

To determine the solutions, solve the equation,

3x - 6 = 6 - 4x

7x = 12

x = 12/ 7

The equation has one solution, which is 12/7.

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The value of a + b must be between 5 and 11. If the value of a 3 or 4, and b will be 4 or 5.

An unknown in mathematics is a number that we are unsure of. In algebra, where they are also known as variables and denoted by symbols like x, y, and z, they are frequently utilised.

In science, a letter from the Roman or Greek alphabet stands in for an undetermined value. They are most frequently employed in physics, where equations are used to explain how different physical qualities relate to one another.

Given that

2 < a < 5, and 3 < b < 6

a is greater than 2 and lesser than 5 , so the value will be 4 or 3.

b is greater than 3 and lesser than 6, so the value will be 4 or 5.

a + b is

3 + 4 = 7 or 4 + 5 = 9

so the product of sum will be 7 or 9, it is between 5 and 11

Therefore,  a + b must be between 5 and 11.

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The angle relationships formed in the diagram are as follows;

When parallel lines are cut by a transversal, angle relationships can be formed such as corresponding angles, alternate interior angles, alternate exterior angles, vertically opposite angles, linear angles, etc.

Therefore, let's find the angles relationship formed in the diagram as follows:

∠1 and ∠5 are corresponding angles.

∠4 and ∠7 are corresponding angles

Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line.

∠3 and ∠5 are alternate interior angles.

Alternate interior angles are the angles formed when a transversal intersects two coplanar lines.

∠1 and ∠8 are alternate exterior angles.

∠2 and ∠7 are alternate exterior angles.

Alternate exterior angles are the pair of angles that are formed on the outer side of the parallel lines but on the opposite side of the transversal.

∠3 and ∠6 are same interior angles. Same interior angles are supplementary angles.

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Answer:

So, a+2a=180°

Simplify.

3a=180°

To isolate a , divide both sides of the equation by 3 .

3a3=180°3    a=60°

The measure of the second angle is,

2a=2×60°       =120°

So, the measures of the two supplementary angles are 60° and 120° .

Answer:

3.5

Step-by-step explanation:

The ball reaches the ground when [tex]h(t)=0[/tex].

[tex]-16t^2+54t+7=0 \\ \\ 16t^2-54t-7=0 \\ \\ (8t+1)(2t-7)=0 \\ \\ t=-1/8, t=7/2 \\ \\ t>0 \implies t=3.5[/tex]

Quadratic function has minimum value which is -8.

correct option: 1

A variable with the largest power of two in a quadratic equation is called a variable. Quad, which signifies square, is the root of the term quadratic. The phrase must be two times its own strength, neither higher nor lower.

Given that they are the x values for which f(x) = 0, the roots of the function f(x) = ax² + bx + c correspond to the solutions of the quadratic equation ax² + bx + c = 0.

The term ax² is known as the quadratic term (hence the function's name), the word bx is known as the linear term, and the value c is known as the constant term.

Here, the given function,

f(x) = x² - 2x - 7 .......... (i)

now, differentiate with respect to x

d/dx {f(x)} = d/dx ( x²) - d/dx (2x) - d/dx (7)

or, f'(x) = 2x - 2 ............. (ii)

Now, put f'(x) = 0

so, 0 = 2x - 2

or, 2x - 2 = 0

or, 2x = 2

or, x = 1

From equation (ii)

f'(x) = 2x - 2

now, differentiate with respect to x

f''(x) = 2 > 0

So, it implies that, the function has minimum value at x = 1

Now, putting x = 1 in equation (i), we get -

f(1) = (1)² - 2×(1) - 7

f(1) = - 8

Function has minimum value is: - 8.

Thus, correct option is : (1)

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Answer:

True.

Step-by-step explanation:

Whether you do a rotation 180 degrees clockwise( [tex]R__(-180,O)[/tex]), or a rotation 180 degrees counterclockwise ([tex]R__(180,O)[/tex]), the image will always end up in the coordinate diagonal from the pre-image.

Answer:

y = (1/2)x + 2

Step-by-step explanation:

Go from point (-2,1) to (0, 2).

Start at point (-2, 1). First, go up 1 unit. That is a rise of 1.

Now go 2 units right. That is a run of 2.

slope = rise/run = 1/2 = m

The graph intersects the y-axis at 2, so the y-intercept = b= 2.

y = mx + b

y = (1/2)x + 2

a) If we select without taking the order into consideration there are  2380.

b) If we take the order into consideration, we have 57120 ways

We talk about the selection when we are talking about how a material can be chosen in the midst of many other materials that we have. In this case we are told that we want to choose 4 objects, without replacement, from 17 distinct objects.

If the order is not important then we need to do a combination and we have;

n!/r! (n - r)!

17!/4!(17 - 4)!

17 * 16 * 15 * 14 * 13!/4! * 13!

= 57120/24

= 2380

If we are looking at the order we have;

n!/(n-r)!

17!/(17 - 4)!

17 * 16 * 15 * 14 * 13!/13!

= 17 * 16 * 15 * 14

= 57120

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The domain and the range of the graphed function are given as follows:

The domain of a function is composed by the set that contains all possible values assumed by the input of the function. Hence, considering the graph of the function, the domain is given by the values of x of the graph.

Thus the domain of this function is given as follows:

D: (-9, -1] U (0, 4].

As there is an interval between -1 and 0 for which the function is not defined, and open circle defines that the interval is open at x = -9 and at x = 0.

The range of a function is composed by the set that contains all possible values assumed by the output of the function. Hence, considering the graph of the function, the range is given by the values of y of the graph.

Then the range of the function is given as follows:

R: (-6, 8.6].

Open interval due to the open circle at y = -6, closed at the value between 8 and 10 which is of 8.6.

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The values of x that can't be equal for the expression are 0 and 5

From the question, we have the following parameters that can be used in our computation:

(5x-2)/(x^2-5x)

This means that we set the denominator to 0

So, we have

x^2 - 5x = 0

Factorize

(x - 5)x = 0

So, we have

x - 5 = 0 and x = 0

Solve for x

x = 5 and x = 0

Hence, the solution is x = 5 and x = 0

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A horizontal line indicates that the thing is travelling steadily. A line that slopes downhill indicates that an object is slowing down.

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Answer:

106*

Step-by-step explanation:

a triangle is 180*

to find angle BCA, you do 180 - (64+42)

that =74*

a straight line is also 180* so you do 180 - BCA

180-74=106

106

Given line:

Plot two points and connect.

One point is the y-intercept:

Another point with an even value of x as its slope is a fraction with denominator of 2:

Plot these two points and connect.

See below graph.

Answer:  The measure of the three angles is 23, 67, and 90.

Step-by-step explanation:

The sum of three angles is equal to 180. We set the equation as:

x + 23 + 90 = 180

       x + 113 = 180

                x = 67

The measure of the three angles is 23, 67, and 90.

Answer:

Look below

Step-by-step explanation:

Example for A

1/5 y= 3/5 x

1/5 y= 3/5 x +4

Example for B

0x=0y

0x=0y+3

Answer for C

add statement for the y not to be equal to 0

Answer:you need to show the diagram in order for me to

Step-by-step explanation:

If we add a vector I{k+1} to the collection of 21, 22, ... I{k}, the collection will no longer be linearly independent and yes, we will still have a linearly independent collection of vectors if we delete a vector {say 2k}.

linearly independent vectors : In the theory of vector spaces, a set of vectors is said to be linearly dependent if there is a nontrivial linear combination of the vectors that equals the zero vector. If no such linear combination exists, then the vectors are said to be linearly independent. These concepts are central to the definition of dimension

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is a linearly independent vectors in a vector space V.

If we add a vector I{k+1} to the collection of 21, 22, ... I{k}, the collection will no longer be linearly independent.

If we delete a vector {say 2k}, from the collection, yes, we will still have a linearly independent collection of vectors

Therefore, if we add a vector I{k+1} to the collection of 21, 22, ... I{k}, the collection will no longer be linearly independent and yes, we will still have a linearly independent collection of vectors if we delete a vector {say 2k}.

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Answer:

15%

Step-by-step explanation:

18/120 = 0.15

0.15*100 = 15%

...

The solution is 15 %

The percentage of discount on the normal price of the jacket is given by the equation A = 15 %

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the percentage of discount be represented as A

Now , the equation will be

The normal price of the jacket = $ 120

The discounted price of the jacket = $ 18

So ,

Discounted price of the jacket = A % of normal price of the jacket

Substituting the values in the equation , we get

18 = A % x 120

On simplifying the equation , we get

( A / 100 ) x 120 = 18

Divide by 120 on both sides of the equation , we get

A / 100 = 18/120

A / 100 = 0.15

Multiply by 100 on both sides of the equation , we get

A = 15 %

Therefore , the value of A is 15 %

Hence , the discounted percentage is 15 %

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Answer:

[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} n&A \\\cline{1-2}\vphantom{\dfrac12} 1& \$4376.10\\\vphantom{\dfrac12} 2& \$4442.10\\\vphantom{\dfrac12} 4& \$4476.86\\\vphantom{\dfrac12} 12& \$4500.73\\\vphantom{\dfrac12} 365& \$4512.49\\\vphantom{\dfrac12} \sf Continuous& \$4512.89 \\\cline{1-2} \end{array}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the formula to create an equation for A in terms of n:

[tex]\implies A=2100\left(1+\dfrac{0.085}{n}\right)^{9n}[/tex]

Substitute each value of n into the equation:

[tex]\begin{aligned}n=1 \implies A&=2100\left(1+\dfrac{0.085}{1}\right)^{9 \times 1}\\&=2100\left(1.085\right)^{9}\\&=\$4376.10\end{aligned}[/tex]

[tex]\begin{aligned}n=2 \implies A&=2100\left(1+\dfrac{0.085}{2}\right)^{9 \times 2}\\&=2100\left(1.0425\right)^{18}\\&=\$4442.10\end{aligned}[/tex]

[tex]\begin{aligned}n=4 \implies A&=2100\left(1+\dfrac{0.085}{4}\right)^{9 \times 4}\\&=2100\left(1.02125\right)^{36}\\&=\$4476.86\end{aligned}[/tex]

[tex]\begin{aligned}n=12 \implies A&=2100\left(1+\dfrac{0.085}{12}\right)^{9 \times 12}\\&=2100\left(1.00708333...\right)^{108}\\&=\$4500.73\end{aligned}[/tex]

[tex]\begin{aligned}n=365 \implies A&=2100\left(1+\dfrac{0.085}{365}\right)^{9 \times 365}\\&=2100\left(1.00023287...\right)^{3285}\\&=\$4512.49\end{aligned}[/tex]

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]

[tex]\implies A=2100e^{0.085 \times 9}[/tex]

[tex]\implies A=2100e^{0.765}[/tex]

[tex]\implies A=2100(2.14899437...)[/tex]

[tex]\implies A=\$4512.89[/tex]

Input the calculated values into the table:

[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} n&A \\\cline{1-2}\vphantom{\dfrac12} 1& \$4376.10\\\vphantom{\dfrac12} 2& \$4442.10\\\vphantom{\dfrac12} 4& \$4476.86\\\vphantom{\dfrac12} 12& \$4500.73\\\vphantom{\dfrac12} 365& \$4512.49\\\vphantom{\dfrac12} \sf Continuous& \$4512.89 \\\cline{1-2} \end{array}[/tex]

Answer:

Somoeone can talk here boring

Answer:

this a quesy=tion?

Step-by-step explanation: