State the value of 'x' in this equation, and explain why you know this to be true without doing any calculations.

[tex]5^x = 5^9[/tex]

An expression is defined as a set of numbers, variables, and mathematical operations. The simplified version of the given expression is (3√2-2)√x³.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression [tex]\sqrt{32x^3} - \sqrt{16x^3} + \sqrt{4x^3} -\sqrt{2x^3}[/tex] can be simplified as shown below.

[tex]\sqrt{32x^3} - \sqrt{16x^3} + \sqrt{4x^3} -\sqrt{2x^3}\\\\=\sqrt{x^3}(\sqrt{32}-\sqrt{16}+\sqrt{4}-\sqrt{2}})\\\\= \sqrt{x^3} (4\sqrt{2}-4+2-\sqrt2)\\\\= \sqrt{x^3} (3\sqrt{2}-2)[/tex]

Hence, The simplified version of the given expression is (3√2-2)√x³.

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1) Given

2) Segment addition postulate

3) Substitution property

4) Segment addition postulate

5) Transitive property of equality

Graph C represents the following system of inequalities. For clarification refer to the attachment.

Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.

Given relations;

x < - 2x + 4

y < x + 3

x < 3

Hence graph C represents the following system of inequalities.

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Answer:

The table on the far left is a linear function.

Step-by-step explanation:

The table on the far left is the function

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

Answer:

every second it travels 1/5 of a mile after 3 seconds you are 3/5 miles away

Hope This helps!

Answer:

32

Step-by-step explanation:

the pattern of sticks from the first 3 diagrams is

7 , 12 , 17 ,..

note the pattern increases by 5 each time , then continue by adding 5 to the previous value.

4th = 17 + 5 = 22

5th = 22 + 5 = 27

6th = 27 + 5 = 32

Answer:

Vertical is the answer

Answer:

Is the second expression written correctly?  It reduces to y>-2, since no x is in the equation.

Step-by-step explanation:

We can graph the two equations.  See attached image.  If y>2 is the correct expression, all points to the right.

If the equation was meant to read y=-3x+1, then graph the revised expression.

Gene earns 2% interest after depositing $150 into his account , Option D.

A function is a law that relates an independent variable and a dependent variable with each other.

The function given is

f(x) = 0.02 x +150

Option D , Gene earns 2% interest after depositing $150 into his account

So this verbal description matches the function given as it represents , the total account balance of Gene .

Therefore Option D is the correct answer.

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By the Pythagorean theorem,

[tex]a^{2}+12^{2}=13^{2}\\\\a^{2}+144=169\\\\a^{2}=25\\ \\ a=\boxed{5}[/tex]

Answer: 113 inches cubed

Step-by-step explanation:

Volume of a sphere = 4/3 Pi r^3

Radius = 3 inches

Volume = 113 inches cubed

Hope I helped!

The range:
[tex]{x|70\leq x\leq 82[/tex]

According to the given synthetic division, the statements that are true are; Options A, C and E

In the synthetic calculation we use the coefficient of the dividend

with the factors of the function.

Therefore;

3 , -13 , 4 are the coefficient of the dividend 3x² - 13x + 4

Therefore, the divisor is 4 and as such x = 4 is a root of f(x) = 3x² - 13x + 4

Also, it means that (x - 4) is a factor of the dividend F(x) = 2x² - 2x - 12

- The quotient is the last line of the synthetic division. Thus, the coefficients of quotient are 3, -1.

- The quotient is 1 degree less than the dividend and so the degree of the dividend is 2.

- The degree of the quotient is 1 and so the he quotient is 3x - 1.

Thus, options A, C and E are correct

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Answer:

3125

Step-by-step explanation:

And

The value of a₃₂ is 7 , Option A is the correct answer.

Matrix is an array or an arrangement of numbers or expression in rows and column format.

The matrix is given

For a matrix of size mxn , m is the row and n is the column of the matrix.

a₃₂ = This term means 3rd row and 2nd column of the matrix

which is 7

Therefore the value of a₃₂ is 7 , Option A is the correct answer.

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Step-by-step explanation:

2y+9= 4

2y=-5

y=-5/2

y= -2and 1/2

Answer:

The answer is 105.

Step-by-step explanation:

Answer:

128, -256, -1024

Step-by-step explanation:

multiply 32 by 4, multiply 128 by -2, multiply -256 by 4

Even numbers = 2x +2

Consecutive even numbers = 2x+4

then

(2x+2) + (2x+4)= 38

2x + 2 + 2x + 4 = 38

2x + 2x + 2 + 4 = 38

    4x + 6 = 38

                   4x = 38 - 6

                     x = 32 :4

                    x = 8

2x+ 2 = 2(8)+2 = 16 + 2 = 18

2x+4 = 2(8) +4 = 16 + 4 = 20

The smallest number is 18

[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

Answer:

18 is the smaller number

Step-by-step explanation:

Let us take X for the first even number (it will also be the smallest)

x, x+1, x+2, so on..

the consecutive even number of x+2 is the next even number after x.

so you now get this equation...

x+(x+2) = 38

2x + 2 = 38

2x = 36

x=18

Step-by-step explanation:

Did you mean.

[tex] \text{what \: is \: the \:sin \: of } \: - \frac{4\pi}{3} \: ?[/tex]

[tex] \: [/tex]

[tex] = \sin( - \frac{4\pi}{3} ) [/tex]

[tex] = \sin( - \frac{4 \times 180 \degree}{3} ) [/tex]

[tex] = \sin( - \frac{4 \times \cancel{180} \degree}{ \cancel3} ) [/tex]

[tex] = \sin( - 4 \times 60 \degree) [/tex]

[tex] = \sin( - 240 \degree) [/tex]

[tex] = \sin(0 - 240 \degree) [/tex]

[tex] = \sin(360 \degree - 240 \degree) [/tex]

[tex] = \sin(120 \degree) [/tex]

[tex] = \frac{1}{2} \sqrt{3} \: \: \text{is \: the \: answer}[/tex]

Answer:

infinity 2 is the slope for these point .

Step-by-step explanation:

given points are

(-2,-5) and (3,5)

comparison to

(x1,y1) and (x2,y2)

here ,

[tex]slope = \frac{y2 - y1}{x2 - x1} [/tex]

slope= 5-(-5)/3-(-2)

slope =10/5

slope=2

glad to help you this may help you :)

Answer:

5.8

Step-by-step explanation:

The system of equation has an infinitely many solutions

The equations are given as:

2x + y = -3

-2y = 6 + 4x

Express 2x + y = -3 in slope-intercept form

y = - 3 -2x

Divide through by -2 in -2y = 6 + 4x

y = -3 - 2x

So, we have:

y = - 3 -2x  and y = -3 - 2x

Both equations are the same.

This means that the system of equation has an infinitely many solutions

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The weight of the smallest rectangular block is 1400 pounds.

The density refers to the heaviness of an object. It is the ratio of mass to volume.

Then we have

Density = Mass / Volume

A sculptor is planning to order a rectangular block of composite stone to sculpt a lion.

The sculptor anticipates that the lion will be 5 feet long, about 2 feet wide and at the tallest part of the lion's body, have a height of 3.5 feet.

The composite stone weighs 40 pounds per cubic foot.

To the nearest cubic foot, estimate the weight of the smallest rectangular block that the sculptor must purchase in order to create his statue.

Then the weight of the smallest rectangular block will be

Mass = density x volume

The volume will be

V = 5 x 2 x 3.5

V = 35 cubic feet

Then the weight will be

Mass = 40 x 35

Mass = 1400 pounds

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Answer:

Option C is equal to 7^1/3

Hey there ! please refer to the attachment .

I hope its help you !

A data set having two values that have the highest and equal frequencies will have a bimodal distribution. Hence, option D is the right choice.

Thus, a data set having two values that have the highest and equal frequencies will have a bimodal distribution. Hence, option D is the right choice.

The given question is incomplete. The complete question is:

"Sometimes, a data set has two values that have the highest and equal frequencies. In this case, the distribution of the data can best be described as:

A. Symmetric distribution

B. Negatively skewed distribution

C. Positively skewed distribution

D. Bimodal distribution."

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Answer:

$864.94

Step-by-step explanation:

So the amount of money over time can be given with an exponential function y=a(b)^x or more specifically y=a(1+r)^x    where r is the growth rate (interest rate)

So the equation can be written as

[tex]m= P(1.04)^t[/tex]    where m represents the amount of money over time, P represents the principle amount, and t represents time in years. Since we're given the amount of interest paid and not the total amount which includes the initial amount borrowed you have to subtract P from the equation. This will give us the equation that we'll use to find the initial amount

[tex]I = P(1.04)^t-P[/tex]  where I represents the interest paid.

plug the values into the equation

[tex]108 = P(1.04)^3-P\\108 = P(1.124864) - P\\108 = 0.124864P\\\\864.941 = P[/tex]

The circumference of the base of the cone is 8π - x since the base is equal to go the arc length of the remainder of the circle.

The radius r as a function of x will be:

8π - x = 2πr

r = (8π - x)/2π

r = 4 - x/2π

The height has a function of x will be:

r² + h² = 16

h² = 16 - r²

where r = 4 - x/2π

h = √16 - ✓(4 - x/2π)²

h = 4✓(4 - x/2π)²

The volume V of the cone as a function of x will be:

= 1/3 πr²h

= π/3(4 - x/2π)² 4✓(4 - x/2π)²

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Answer:

The horizontal asymptote is y=1 and

The vertical asymptote is x=5