(15 − 8)9
-------------
[(5 + 2)3]2

The simplified expression is:

Answer:

[tex]f(x)=162^\frac{x}{4}[/tex]

[tex]f(x)=[3\sqrt[4]{2}]^{x}[/tex]

[tex]f(x)=[3(2^{\frac{1}{4}})]^{x}[/tex]

Step-by-step explanation:

we have

[tex]f(x)=\sqrt[4]{162^{x}}[/tex]

Remember that

[tex]\sqrt[n]{a^{m}}=a^{m/n}[/tex]

[tex](a^{m})^{n}=a^{m*n}[/tex]

so

1) [tex]\sqrt[4]{162^{x}}=162^\frac{x}{4}[/tex]

2) The number 162  decompose in prime factors is

[tex]162=(2)(3^4)[/tex]

substitute

[tex]f(x)=\sqrt[4]{[(2)(3^4)]^{x}}={[(2)(3^4)]^{x/4}={{[(2)(3^4)]^{(1/4)}}^x=[3\sqrt[4]{2}]^{x}[/tex]

3) [tex]f(x)=[3\sqrt[4]{2}]^{x}=[3(2^{\frac{1}{4}})]^{x}[/tex]

therefore

[tex]f(x)=162^\frac{x}{4}[/tex]

[tex]f(x)=[3\sqrt[4]{2}]^{x}[/tex]

[tex]f(x)=[3(2^{\frac{1}{4}})]^{x}[/tex]

Answer:

A.B. E.

Step-by-step explanation:

Answer:

As you remember from pre-algebra a coordinate plane is a two-dimensional number line where the vertical line is called the y-axis and the horizontal is called the x-axis. These lines are perpendicular and intersect at their zero points. This point is called the origin.

Step-by-step explanation:

Answer:

mhmmmmm

i need help on this too

Since it is in a 180 degrees... Flat line then we will 50 minus 180= 130.

this is your answer. D.) y=130

Answer:

42

Step-by-step explanation:

if you divide 546 with 13 it will give you 42 mostly because 546 is the total of miles that he drove so if you dive by how many days he has been driving you will get your answer.

Troy drove 546 miles over 13 days, resulting in an average of 42 miles driven each day after dividing the total miles by the number of days.

To find out how many miles Troy drove each day, we need to divide the total number of miles driven by the number of days. Troy drove a total of 546 miles over the course of 13 days.

Divide the total miles (546) by the number of days (13).

The calculation is:

546 miles / 13 days = 42 miles per day.

Therefore, Troy drove 42 miles each day.

Answer:

b

Step-by-step explanation:

Answer:

Answer:

true

Step-by-step explanation:

Because as it go's down the other go's up

Step-by-step explanation:

Converting all the numbers to decimals,

1) -0.5

2) 1/2 = 0.5

3) 0.7

4) -4/4 = -1

We see that order of numbers from least to greatest is -1 < -0.5 < 0.5 < 0.7

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Answer:

Find the area of two sides (Length*Height)*2 sides.

Find the area of adjacent sides (Width*Height)*2 sides.

Find the area of ends (Length*Width)*2 ends.

Add the three areas together to find the surface area.

Example: The surface area of a rectangular prism 5 cm long, 3 cm.

Answer:

The way to do this is multiplying all the 3 dimensional sides Then adding them.

Step-by-step explanation:

What i mean by this is by, Multiplying the Length and height together .

Next is Multiplying the Width and Height together

Next would to multiply the Length And Width together.

Lastly would to add all your solutions together.

If you have any questions feel free to ask in the comments.

Answer:  6m

Step-by-step explanation:

GCF is Greatest Common Factor.

In other words, what is the biggest factor they have in common?

You can factor both terms down to their primes and compare them:

               24m                                     18m

                 ∧                                          ∧

             4    6    m                               2   9    m

            ∧     ∧    ↓                               ↓   ∧    ↓  

          2  2   2 3  m                             2  3 3   m  

24m: 2 · 2 · 2 · 3 · m

18m:  2 · 3 · 3 · m

What do they have in common?

24m: 2 · 2 · 2 · 3 · m         Common is 6m, leftover is 4

18m:  2 · 3 · 3 · m              Common is 6m, leftover is 3

I showed the leftover because you need that to find the LCM

Answer:

two solutions

Step-by-step explanation:

it could be 5 or -5

Answer:

EXAMPLE I Round 47 to the nearest ten. Here is a part of a number line; 47 is between 40 and 50. Since 47 is closer to 50, we round up to 50. 42 is between 40 and 50.;it5

For trapezoids ABCD and A'B'C'D' on a coordinate plane, side AD's length is 8 units, A'D's length is 4 units and also the scale factor is 1/2.

The question asks for facts about the dilation of trapezoid ABCD to create trapezoid A'B'C'D' on a coordinate plane. First, we are to compare the length of side AD with side A'D'. The coordinates of AD are (-4, 0) and (4, 0), so the length is 4 - (-4) = 8 units. For A'D', using coordinates (-2, 0) and (2, 0), the length is 2 - (-2) = 4 units. This confirms that:

The length of side AD is 8 units.

The length of side A'D' is 4 units.

Next, to determine whether the image is larger than the pre-image, we examine the scale factor. As the original trapezoid has been halved in size, the scale factor is indeed 1/2. Therefore, the image is not larger; it is smaller. Hence, this option is not true.

Examining the slopes of sides CD and C'D', we can use the coordinates (2, 4) to (4, 0) and (1, 2) to (2, 0) respectively to calculate the slope. The slope of CD is (0-4)/(4-2) = -4/2 = -2, and for C'D' it is (0-2)/(2-1) = -2/1 = -2. Both slopes are indeed the same, and thus, we confirm:

Sides CD and C'D' both have the same slope, -2 not 2 as stated in the options.

The final option about the scale factor being 1/2 is true and confirms:

The scale factor is 1/2.

The true statements are:

- The length of side AD is 8 units.

- The length of side A'D' is 4 units.

- The scale factor is 1/2.

To determine which statements are true about the trapezoids, let's analyze the given information:

1. The length of side AD is 8 units.

  - To find the length of side AD, we can use the distance formula between points A and D.

  - Distance formula: [tex]\(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)[/tex]

  - [tex]\(AD = \sqrt{(4 - (-4))^2 + (0 - 0)^2} = \sqrt{8^2} = 8\)[/tex]

  - This statement is true.

2. The length of side A'D' is 4 units.

  - To find the length of side A'D', we can use the distance formula between points A' and D'.

  - Distance formula: [tex]\(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)[/tex]

  -[tex]\(A'D' = \sqrt{(2 - (-2))^2 + (0 - 0)^2} = \sqrt{4^2} = 4\)[/tex]

  - This statement is true.

3. The image is larger than the pre-image.

  - We can compare the lengths of corresponding sides.

  - The length of side AD is 8 units, while the length of side A'D' is 4 units.

  - Since the lengths of corresponding sides are not proportional, the image is not larger than the pre-image.

  - This statement is false.

4. Sides CD and C'D' both have the same slope, 2.

  - The slopes of sides CD and C'D' can be calculated using the coordinates of the points.

  - Slope formula:[tex]\(m = \frac{y_2 - y_1}{x_2 - x_1}\)[/tex]

  - For side CD: [tex]\(m_{CD} = \frac{4 - 4}{2 - (-2)} = \frac{0}{4} = 0\)[/tex]

  - For side C'D':[tex]\(m_{C'D'} = \frac{2 - 0}{1 - (-1)} = \frac{2}{2} = 1\)[/tex]

  - Since the slopes are not the same, this statement is false.

5. The scale factor is 1/2.

  - To find the scale factor, we can compare the corresponding side lengths of the pre-image and the image.

  - The length of side AD is 8 units, and the length of side A'D' is 4 units.

  - The scale factor is the ratio of corresponding side lengths: [tex]\(\frac{4}{8} = \frac{1}{2}\)[/tex]

  - This statement is true.

Answer:

Step-by-step explanation:

y = 4x + 1

We can see that for each value of x substituted into this equation will give us a value for y .

For example , if we take x to be 4 , and put the value in this equation we get 4(4) + 1 = y

We get y = 17

Algebraic expression for three times the sum of a and b, then the expression would be; 3(a+b).

Simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.

Algebraic expression for three times the sum of a and b, then the expression;

Now put a + b in brackets because your multiplying a and b three times;

= 3(a+b)

Algebraic expression for three times the sum of a and b, then the expression would be; 3(a+b).

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Answer:you do 15 divided by 8

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

x^3-2x^2-5x+6

Answer:

its b

Step-by-step explanation:

Answer:

5 inches

Step-by-step explanation:

a^2 + b^2 = c^2

12^2 + b^2 = 13^2

144 + b^2 = 169

b^2 = 25

b = 5

Jeremiah should start his cut 5 inches from P.

In the figure PQRS,

QR= 12 in. & PS = 13 in.

∠Q=∠R=90°

Now, Jeremiah will make exactly one straight cut from the top edge of the cardboard to point S in order to cut the cardboard into a rectangle.

Let, Jeremiah cut PQ at point M, where SM⊥PQ

∴ ∠SMP = 90°, so ΔSMP is a right angle triangle.

After draw SM, SMQR will a rectangle.

Then, SM = QR = 12 in.

By pythagoras theorem,

PS²= SM²+PM²

⇒ PM²= PS²-SM²

⇒ PM²= 13²-12²

⇒ PM²= 169-144

⇒ PM = √ (25)

⇒ PM = 5   (Negative value is not possible)

So, PM = 5 inches

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Answer:

7.5 inches

Step-by-step explanation:

take the 5 away from the 20, you have 15 inches left. Isosceles triangles have two equal sides; 15 divided into two equally is 7.5

Answer:

20 - 2n

Step-by-step explanation:

The sequence is arithmetic since the difference between consecutive terms is constant, that is

d = 16 - 18 = 14 - 16 = 12 - 14 = - 2

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 18 and d = - 2, thus

[tex]a_{n}[/tex] = 18 - 2(n - 1) = 18 - 2n + 2 = 20 - 2n

[tex]a_{n}[/tex] = 20 - 2n

If we know that [tex]x_{1} = 18[/tex] and [tex]r = -2[/tex], then the n-th term of the number sequence is [tex]f(n) = 18 -2\cdot (n-1)[/tex].

This sequence is an example of an arithmetic sequence, since each consecutive pair of elements has one and only one difference, that is to say:

[tex]r = x_{i+1}-x_{i}[/tex], [tex]\forall\,i\in \mathbb{N}[/tex] (1)

The expression for any arithmetic sequence is described by the following formula:

[tex]f(n) = x_{1} + r\cdot (n-1)[/tex], [tex]n \ge 1[/tex] (2)

Where:

If we know that [tex]x_{1} = 18[/tex] and [tex]r = -2[/tex], then the n-th term of the number sequence is [tex]f(n) = 18 -2\cdot (n-1)[/tex].

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Answer:

C.

Step-by-step explanation:

The area of the triangle is

[tex]\text{Area}=\dfrac{1}{2}\cdot \text{Base}\cdot \text{Height}[/tex]

You know that

Area - irrational number

[tex]\dfrac{1}{2}[/tex] - rational number (rational numbers are those that can be written as a fraction)

Base = 18 inches - rational number (actually, 18 is a natural number and each natural number is rational)

Height - unknown

You can rewrite previous formula as

[tex]\text{Area}=\dfrac{1}{2}\cdot 18\cdot \text{Height}\\ \\\text{Area}=9\cdot \text{Height}[/tex]

Now consider all options:

A. If height is a whole number then area is a whole number as a product of two whole numbers. False

B. If height is a rational number, then area is rational number as a product of two rational numbers. False

C. If height is a irrational number, then area is irrational number as a product of rational and irrational numbers. True

D. If height is a non-real complex number, then area is non-real complex number as a product of rational and non-real complex numbers. False

Option C. An irrational number.

The area of a triangle is given by the formula A = 1/2 × base × height. In this problem, the base of the triangle is 18 inches. Since the problem states that the area is an irrational number, we need to determine what the height (or altitude) of the triangle must be.

To have an irrational area, either the base or the height (or both) must be irrational. Given that the base is a whole number (18 inches), the height must be an irrational number to produce an irrational value for the area. We can set up the formula as follows:

A = 1/2 × 18 × h, where h is the height.

For A to be irrational, h must be an irrational number.

Therefore, the best answer to fill in the blank is:

Step-by-step explanation:

We need to write the following ratios with its simplest form.

1. [tex]\dfrac{21}{28}[/tex]    

Factors of 21 = 3, 7

Factors of 28 = 2, 7, 2  

[tex]\dfrac{21}{28}=\dfrac{3}{4}[/tex]  

2. [tex]\dfrac{96}{32}[/tex]    

Factors of 96 =  1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

Factors of 32 =  1, 2, 4, 8, 16, 32

[tex]\dfrac{96}{32}=\dfrac{3}{1}[/tex]

3. [tex]\dfrac{22}{33}[/tex]    

Factors of 22 = 1, 2, 11, 22

Factors of 33 =  1, 3, 11, 33

[tex]\dfrac{22}{33}=\dfrac{2}{3}[/tex]

4. [tex]\dfrac{12}{36}[/tex]    

Factors of 12 = 1, 2, 3, 4, 6, 12

Factors of 36 =  1, 2, 3, 4, 6, 9, 12, 18, 36

[tex]\dfrac{12}{36}=\dfrac{1}{3}[/tex]

5. [tex]\dfrac{72}{56}[/tex]    

Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56

[tex]\dfrac{72}{56}=\dfrac{9}{7}[/tex]

6. [tex]\dfrac{54}{63}[/tex]    

Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54

Factors of 63 = 1, 3, 7, 9, 21, 63

[tex]\dfrac{54}{63}=\dfrac{6}{7}[/tex]

Hence, this is the required solution.

Answer:

Option D: 1/3

Step-by-step explanation:

Let

x ------> the entire Stefanie's allowance

we know that

She spends on clothes (1/2)x

She spends on movies (1/6)x

To find out how much more does she spend on clothes that he does on movies, subtract the amount she spends on movies from the amount she spend on clothes

[tex]\frac{1}{2}x-\frac{1}{6}x=\frac{2}{6}x[/tex]

Simplify

[tex]\frac{1}{3}x[/tex]

therefore

She spends 1/3 more on clothes that he does on movies

Answer:

Step-by-step explanation:

This would be called the range.

Answer: Range describes the set of all possible output values for a function.

Step-by-step explanation:

Since we denote values for dependent variable as output values.

Thus , we call Range is the  set of all possible output values for a function.

Therefore, the term describes the set of all possible output values for a function : Range

Answer:

Step-by-step explanation:

11:45 + 1 hour = 12:45

12:45 + 1 hour = 1:45

1:45 + 30 minutes = 2:15

The nth term of this number sequence 18, 16, 14, 12,... will be -2n + 20.

First term = 18

Second term = 16

Common difference = 16 - 18 = -2

It should be noted that the formula for finding the next term of an arithmetic sequence will be:

= a + (n - 1)d

= 18 + (n - 1) × -2

= 18 - 2n + 2

= -2n + 20

Therefore, the nth term of this number sequence 18, 16, 14, 12,... will be -2n + 20.

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Answer:

Option A is the correct answer.

Step-by-step explanation:

Here we need to factorize  x²+3x−18

The coefficient of x is 3 and the constant is -18

Which means

           The sum of factors is 3

           The product of factors is -18

The factors satisfying are  6 and -3

Here the factors are given in the type (x+)(x−)

     So the value after plus is 6 and value after - is 3

Option A is the correct answer.            

Answer:

6 and 3

Step-by-step explanation:

Final answer:

The expression that represents the mass of two grains of salt, approximately one microgram or 0.000001g, in scientific notation is 1 x 10-6g.

Explanation:

The expression that represents the mass of two grains of salt, approximately one microgram or 0.000001g, in scientific notation is 1 x 10-6g.

Scientific notation is a way to express numbers that are extremely large or small in a more manageable format. In scientific notation, a number is written as a coefficient multiplied by a power of 10. The coefficient must be greater than or equal to 1 and less than 10, and the power of 10 represents how many places the decimal point needs to be moved to get the original number.

Option C) [tex]y=2x+10[/tex] is correct

Equation of a line passing through points [tex]\boldsymbol{\left ( x_1,y_1 \right ),\left ( x_2,y_2 \right )}[/tex] is given by [tex]\boldsymbol{y-y_1=\left ( \frac{y_2-y_1}{x_2-x_1} \right )\left ( x-x_1 \right )}[/tex]

Given points are as follows:

[tex]\left ( x_1,y_1 \right )=\left ( -7,-4 \right )\\\left ( x_2,y_2 \right )=\left ( -6,-2 \right )[/tex]

Equation of a line is [tex]y+4=\left ( \frac{-2+4}{-6+7} \right )\left (x+7\right )[/tex]

[tex]y+4=2\left ( x+7 \right )[/tex]

[tex]y+4=2x+14[/tex]

      [tex]\boldsymbol{y=2x+10}[/tex]

So, option C) is correct.

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Final answer:

To find the equation of a line in slope-intercept form, we need to determine the slope and the y-intercept of the line. Using the formula for slope, we find that the slope is 2. Then, using one of the points and the slope, we find the y-intercept to be 10. Therefore, the equation of the line is y = 2x + 10.

Explanation:

To find the equation of a line in slope-intercept form, we need to determine the slope and the y-intercept of the line. The slope can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

Given the points (-7, -4) and (-6, -2), the slope is:

slope = (-2 - (-4)) / (-6 - (-7))

slope = 2 / 1

slope = 2

Now that we have the slope, we can use one of the points and the slope to find the y-intercept. Let's use the point (-7, -4) and the slope of 2:

y = mx + b

-4 = 2(-7) + b

-4 = -14 + b

b = -4 + 14

b = 10

Therefore, the equation of the line in slope-intercept form is y = 2x + 10.

Answer: 1050 miles in 5 hours

Step-By-Step explanation: there are 20 1/20 per hour

10 1/2 x 20 = 210 miles per hour

210 * 5 =1050 miles in 5 hours

[tex]\text{Hello there!}\\\\\text{We're trying to find how many miles he can drive in 5 hours}\\\\\text{We know that he drives 10.5 miles in 1/20 of an hour}\\\\\text{We need to find how much he drives in an hour, so you have to}\\\text{multiply 10.5 by 20}\\\\10.5\cdot20=210\\\\\text{In 1 hour, he drives 210 miles}\\\\\text{Now, multiply 210 by 5 to see how much he drives in 5 hours}\\ \\210\cdot5=1050\\\\\large\boxed{\text{John drives 1,050 mile in 5 hours}}[/tex]