Use the inverse variation equation to fill in the table.

p =
8.31
V

Volume
(Liters) Pressure
(kilopascals)
83.1 a
b 0.4
415.5 c


a =
4.17
⇒ 0.1, b =
⇒ 20.775, c =
8.31
⇒ 0.02

Answer:

1/2 log2

Step-by-step explanation:

I hope you understand

Answer:

[tex]x & = \dfrac{1}{2} \ln 2[/tex]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=x^2+4x\\g(x)=1+e^{2x}\end{cases}[/tex]

Function composition is an operation that takes two functions and produces a third function.

Therefore, the given composite function fg(x) means to substitute the function g(x) in place of the x in function f(x):

[tex]\begin{aligned}f[g(x)] & = [g(x)]^2 + 4[g(x)]\\& = \left(1+e^{2x}\right)^2+4\left(1+e^{2x}\right)\\& = 1+2e^{2x}+(e^{2x})^2+4+4e^{2x}\\& = e^{4x}+6e^{2x}+5\end{aligned}[/tex]

[tex]\textsf{Let }u=e^{2x}[/tex]

[tex]\implies e^{4x}+6x^{2x}+5=u^2+6u+5[/tex]

Set the composite function to 21 and factor:

[tex]\begin{aligned}f[g(x)] & = 21\\\implies u^2+6u+5 & = 21\\u^2+6u-16 & = 0\\u^2+8u-2u-16 & = 0\\u(u+8)-2(u+8) & = 0\\(u-2)(u+8) & = 0\\\end{aligned}[/tex]

Apply the zero-product property:

[tex]\implies (u-2)=0 \implies u=2[/tex]

[tex]\implies (u+8)=0 \implies u=-8[/tex]

[tex]\textsf{Substitute back in }u=e^{2x}:[/tex]

[tex]\implies e^{2x}=2[/tex]

[tex]\implies e^{2x}=-8[/tex]

As we cannot take logs of negative numbers, the only solution is:

[tex]\begin{aligned}e^{2x} & = 2\\\ln e^{2x} & = \ln 2\\2x \ln e & = \ln 2\\2x(1) & = \ln 2\\2x & = \ln 2\\\implies x & = \dfrac{1}{2} \ln 2\end{aligned}[/tex]

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Answer:

BAC=BDC(BDX)=30°

Step-by-step explanation:

We know that BD=OD.

But OD=OB= Radius of the circle.

Therefore

BD=OD=OB

BDO is equilateral triangle.

Angle DBO= 60°

Now let us take the intersecting point of CD and AB as X.

In triangle BDX,

BXD= 90°(BXD+BXC=180°, BXD+90°=180°, BXD=90°)

BXD+DBX+BDX=180°{Angle Sum Property}

90°+60°+BDX= 180°

BDX= 30°

We also know that,

BDC(BDX)= BAC (Angles lie on the same arc{BC} are equal in measure.

Therefore,

BAC=BDC(BDX)=30°

Using a system of equations, the correct statement is given as follows:

B. The equation that represents this situation is 10 + x = -18. The second number is -28.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

The numbers are x and y, and their sum is -18, hence:

x + y = -18.

The number y is 10, hence:

x + 10 = -18.

x = -18 - 10 = -28.

Which means that option B is correct.

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Ten gave the check of $5768 to the bank for payment.

Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, so a borrower will never have to pay interest on the interest already accumulated because a creditor will only pay interest on the principal amount.

Formula for simple interest is;-

Simple interest = (principal amount×rate of interest×time duration in years)/100

S.I = (P×R×T)/100

Calculation of the total amount paid by Ted to the bank-

The principal amount is  $5,600.

The rate of interest is 9%.

Time duration is 4 months equals 4/12 = 1/3 years.

S.I = (5,600×9×1)/(3×100)

S.I  = 168

The simple interest on amount is $168.

Thus, the total amount is S.I + principal amount

Total amount = 168 + 5600

                      = 5768

Therefore, the total amount paid by the Ted to the bank is $5768.

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The Intervals of increasing and decreasing are written in terms of the 'x' value, and you will use the symbol for  'x' with the 'y' coordinate from the vertex.

The increasing and decreasing  intervals are written in the terms of the 'x' value of the function

They are represented thus;

Increasing interval =  f (x) ≤ f (y)

Decreasing interval = f (x) ≥ f (y)

Thus, the Intervals of increasing and decreasing are written in terms of the 'x' value, and you will use the symbol for  'x' with the 'y' coordinate from the vertex.

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Answer:

y=7x

Step-by-step explanation:

The equation of the with a slope of m and a y-intercept of b is y=mx+b.

Answer:

A.) x = 3

Step-by-step explanation:

This equation is an example of a perfect square quadratic. This means that the quadratic can be simplified into two of the same factors.  

How can you factor the equation? The simplest way is to ask yourself, which two numbers multiply to 9 while also adding to -6? The two numbers which satisfy this question are -3 and -3. Knowing this, you can construct your factors, simplify, and then solve for "x".

x² - 6x + 9 = 0                    <----- Expanded equation

(x - 3)(x - 3) = 0                  <----- Factored equation

(x - 3)² = 0                          <----- Combine both factors

x - 3 = 0                             <----- Take square root of both sides

x = 3                                 <----- Add 3 to both sides

Hello !

Answer:

When x = -3 or x = 3

Step-by-step explanation:

[tex] \frac{ {x}^{2} - 9}{ {x}^{2} + 6x + 8} = 0[/tex]

[tex]\Leftrightarrow \frac{ {x}^{2} - 9 }{ {x}^{2} + 6x + 8} \times ( {x}^{2} + 6x + 8) = 0 \times ( {x}^{2} + 6x + 8)[/tex]

[tex]\Leftrightarrow {x}^{2} - 9 = 0[/tex]

[tex]\Leftrightarrow(x - 3)(x + 3) = 0[/tex]

[tex]\Leftrightarrow \: x - 3= 0 \: or \: x + 3 = 0[/tex]

[tex]\Leftrightarrow \: x = 3 \: or \: x = - 3[/tex]

[tex]\boxed{S = {-3 \: \: or \: \: 3}}[/tex]

Answer:

The answer is B.

Step-by-step explanation:

I learned this last year.

Answer:

[tex](x+5)^{3}[/tex]

Step-by-step explanation:

Hope this helps

The expression for the word problem is ( x + 5 )².

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The given word problem is the cube of the sum of a number and 5. The expression will be formed as below:-

Let the unknown number be x.

E = ( x + 5 )²

Therefore, the expression for the word problem is ( x + 5 )².

The complete question is given below:-

The cube of the sum of a number and 5. Write the mathematical expression.

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Answer:

The answer is 6 and -6

Step-by-step explanation:

The given equation is
[tex]x^2 - kx + 9 = 0 ... (1)[/tex]

where a = 1. b = -k, c = a

since the equation (1) has equal roots

[tex]\Rightarrow b^2 - 4ac = 0 \newline\\\Rightarrow (-k)^2 - 4(1)(9) = 0\\ \newline\\\Rightarrow (k)^2 - 36 = 0 \newline\\\Rightarrow k^2 = 36 \newline\\\Rightarrow k = \pm 6[/tex]

Hence volume of k = 6, -6

The midpoint of the segment is (-15/2, -15/2)

The complete question is in the attached image

The points are given as:

(-8, -7) and (-7, -8)

The midpoint is calculated as:

(x,y) = 1/2 * (x1 + x2, y1 + y2)

So, we have:

(x,y) = 1/2 * (-8 - 7, -7 - 8)

Evaluate the difference

(x,y) = 1/2 * (-15, -15)

Evaluate the product

(x,y) = (-15/2, -15/2)

Hence, the midpoint of the segment is (-15/2, -15/2)

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Answer:

45 dandelion × 15 rows= 675

Answer:  < -4/5,  3/5>

This is equivalent to writing < -0.8, 0.6 >

======================================================

Explanation:

Draw an xy grid and plot the point (-4,3) on it. Draw a segment from the origin to this point. Then draw a vertical line until reaching the x axis. See the diagram below.

We have a right triangle with legs of 4 and 3. The hypotenuse is [tex]\sqrt{4^2+3^2} = \sqrt{16+9} = \sqrt{25} = 5[/tex] through use of the pythagorean theorem.

We have a 3-4-5 right triangle.

Therefore, the vector is 5 units long. This is the magnitude of the vector.

Divide each component by the magnitude so that the resulting vector is a unit vector pointing in this same direction.

Therefore, we go from < -4, 3 > to < -4/5,  3/5 >

This is equivalent to < -0.8, 0.6 > since -4/5 = -0.8 and 3/5 = 0.6

Side note: Unit vectors are useful in computer graphics.

Answer:

- x + 1

Step-by-step explanation:

(x² + 2x + 3) - (x² + 3x + 2) ← multiply terms inside parenthesis by - 1

= x² + 2x + 3 - x² - 3x - 2 ← collect like terms

= - x + 1

Options A,B and D. The correction about the area of the triangle are

Firstly this is an equilateral triangle

3 of the sides have the length of 8.7cm

b = half of 8.7

= 4.35cm

To get A we have

a² + b² = c²

a² + 4.35² = 5²

When we solve this out we would have

a² = 25 - 18.9225

a ≈ 2.5 cm.

Hence we have proved that the first option is correct.

For B,

In an equilateral triangles, each of the angles = 60 degrees

60/2 = 30 is the angle that is made from the base

a / 4.35 = tan 30

then a = 4.35 tan 30

This would also give us an approximate of 2.5

For D

The calculations we have done based on the statements in A and B shows that D is correct as 2.5.

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Answer:

1

Step-by-step explanation:

any number (except zero) raised to the 0th power is equal to 1.

Answer:

1

Step-by-step explanation:

(10 - 11)⁰ = ( -1)⁰ = 1

We have a⁰ = 1

Answer:

by sss

Step-by-step explanation:

The property of congruence:

ΔABC ≅ ΔDCB by the SSS criterion.

The correct option is the SSS postulate.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Given information:

AB ≅ DC and AC ≅ DB.

The proof is given described as:

In triangle ABC and triangle DCB,

The two sides are congruent,

AB ≅ DC and AC ≅ DB ( As per the information provided).

And as per the diagram and reflexive property of congruence,

BC ≅ BC.

Therefore, ΔABC ≅ ΔDCB by the SSS criterion.

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Answer:

15556913140

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

In option c, the first block is divided into 3 pieces where 2 parts are shaded whereas the second block is divided into 6 pieces where 3 parts are shaded

For both to be equivalent, both of them should be the same

2/3 = x/6

x = 4

4 pieces should be shaded in in the second block to be equal to the first one, in the diagram only 3 parts are shaded thus the answer is c

Answer:

-∞ < x < 4

Step-by-step explanation:

→ The graph touches the y axis at 4, therefore 4 part of the range. As h ( x  ) has a vertical asymptote it will never touch the line x = 1, therefore -∞.

The number which would correspond to the position of the word; $BAB$ is; $2×1×2$ = 4.

As evident in the task content, by observation, if follows that since; $AAA$ is Word $1 and $CCC$ is Word $27$.

Then, it can be inferred that A = 1 , B = 2 and C = 3.

On this note, the number which would correspond to the position of the word; $BAB$ is; $2×1×2$ = 4.

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Answer:

B) 18%

Step-by-step explanation:

100% - 36% - 29% - 17% = 18%

Answer:

the answer would be B) 18%

The parameter to be tested is z.

We would set up the hypothesis test.

For the null hypothesis,

µ ≥ 4.2

For the alternative hypothesis,

µ < 4.2

It is a left tailed test.

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 4.2

x = 4.3

σ = 0.4

n = 37

z = (4.3 - 4.2)/(0.4/√37) = 1.53

Looking at the normal distribution table, the probability corresponding to the z score is 0.933

The p value gotten is to the right of the normal curve. Since it is a left tailed test, we need the p value to the left of the curve. Therefore,

p = 1 - 0.933 = 0.067

Since alpha, 0.05 < than the p value, 0.067, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, there is no significant evidence that mean GPA of these graduates does not exceed 4.30

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Step-by-step explanation:

IR = 9√3

E = 60°

I = 30°

R = 90°

• Find ER.

ER/sin(I) = IR/sin(E)

ER/sin(30°) = 9√3/sin(60°)

ER/(1/2) = 9√3/(1/2 √3)

ER/(1/2) = (9√3 . 2)/√3

ER/(1/2) = 18√3/√3

ER/(1/2) = 18 → IR/sin(E)

ER = 18 . 1/2

ER = 9 is the answer

• Find IE (There are 2 ways).

First, using a Sinus Rule.

IE/sin(R) = IR/sin(E)

IE/sin(90°) = 9√3/sin(60°)

IE/1 = 9√3/(1/2 √3)

IE = (9√3 . 2)/√3

IE = (18√3)/√3

IE = 18 is the answer

Second, using a Pythagoras Theorem.

IE = √(IR² + ER²)

IE = √((9√3)² + 9²)

IE = √(81.3 + 81)

IE = √(243 + 81)

IE = √324

IE = 18 is the answer

Plug the second equation (the one already solved for y) into the first equation

2x - (2x + 3) = 7

2x - 2x - 3 = 7

-3 = 7

Since the 2x's canceled out and left a false statement, this system of equations has no solution.

Hope this helps!

Answer:

The linear equation for tip barista gets in a day is f(n)=0.5n+20.

Step-by-step explanation:

It is given, at a noon a barista notice that she has $20 in tip jar, if she makes an average of $0.50 from each customer,

It is required to find how much will she have in her tip jar if she serves n more customers during her shift. m=0.5. Bases on this write the equation for n more customers.

Step 1 of 1

It is given, at a noon a barista notice that she has $20 in tip jar, if she makes an average of $0.50 from each customer,

To solve this let f(n) is the total tip barista has in her tip jar after a day.

When n is equal to 0 , that barista has $20,

Then if barista make 0.5 from each customer, then for the linear function m=0.5,

Bases on this write the equation for n more customers,

[tex]$$f(n)=0.5 n+20 .$$[/tex]

Answer: 10

Step-by-step explanation:

By the geometric mean theorem,

[tex]\frac{BD}{5}=\frac{20}{BD}\\\\(BD)^2 = 100\\\\BD=10[/tex]

The length of side BD, given that AD = 5 and CD = 20 is 10 (Option A)

Since the triangles are similar, we can obtain the length of side BD as illustrated below:

CD / BD = BD / AD

20 / BD = BD / 5

Cross multiply

BD × BD = 20 × 5

BD² = 100

Take the square root of both sides

BD = √100

BD = 10

Thus, the length of side BD is 10

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Answer:

x = - 5 , x = [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

the values of x that make f(x) zero are the zeros

to find the zeros let f(x) = 0 , that is

3x² + 13x - 10 = 0

consider the factors of the product of  the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 3 × - 10 = - 30 and sum = + 13

the factors are + 15 and - 2

use these factors to split the x- term

3x² + 15x - 2x - 10 = 0 ( factor the first/second and third/fourth terms )

3x(x + 5) - 2(x + 5) = 0 ← factor out (x + 5) from each term

(x + 5)(3x - 2) = 0

equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

3x - 2 = 0 ⇒ 3x = 2 ⇒ x = [tex]\frac{2}{3}[/tex]

Answer:

This is always true so there are infinite solutions

Step-by-step explanation:

2(x+4)=4x+3-2x+5

To find the solution, the first step is to distribute

2x+8 =4x+3-2x+5

Combine like terms

2x+8= 2x+8

Subtract 2x from each side

2x+8 -2x = 2x+8-2x

8 = 8

This is always true so there are infinite solutions