The polynomial function f(x) = 3x5 – 2x2 7x models the motion of a roller coaster. the roots of the function represent when the roller coaster is at ground level. which answer choice represents all potential values of when the roller coaster is at ground level? begin by factoring x to create a constant term. 0, plus-or-minus one-seventh, plus-or-minus1, plus-or-minus three-sevenths, plus-or-minus3 0, plus-or-minus one-third, plus-or-minus1, plus-or-minus seven-thirds, plus-or-minus7 plus-or-minus one-seventh, plus-or-minus1, plus-or-minus three-sevenths, plus-or-minus3 plus-or-minus one-third, plus-or-minus1, plus-or-minus seven-thirds, plus-or-minus7

The -5⁻³ matches with -1/125, (-5⁻³)⁻¹ matches with -125, and (-5⁻³)⁰ matches with 1.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

5⁻³ = 1/5³ = 1/125

-5⁻³ = -1/5³ = -1/125

(-5⁻³)⁻¹ = (-1/5³)⁻¹ = (-1/125)⁻¹ = -125

(-5⁻³)⁰ = 1   [tex]\rm (a^0 = 1)[/tex]

Thus, the -5⁻³ matches with -1/125, (-5⁻³)⁻¹ matches with -125, and (-5⁻³)⁰ matches with 1.

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Answer:

[tex]\sf{1)\ 5^{-3}={\dfrac{1}{5^3}={\dfrac{1}{125}[/tex]

[tex]\sf{2)\ -5^{-3}={\dfrac{1}{-5^3}=-{\dfrac{1}{125}[/tex]

[tex]\sf{3)\ \left(-5^{-3}\right)^{-1}=\left(-5^{-3\times-1}\right)=-5^{3}=-125}[/tex]

[tex]\sf{4)\ \left(-5^{-3}\right)^{0}=1[/tex]

Step-by-step explanation:

Exponent Property Rules:

⟹ Zero Exponent Property - ex: x⁰ = 1

An integer (excluding 0) with an exponent of zero equals one.

⟹ Negative Exponent Property - ex: x⁻ⁿ = [tex]{\dfrac{1}{x^n}[/tex]

Any number raised to a negative power is equivalent to the reciprocal of the number's positive exponent.

⟹ Power of Product Property - ex: (xy)ⁿ = xⁿ × yⁿ

To find the power of a product, multiply the power of each factor.

[tex]\sf{1)\ 5^{-3}={\dfrac{1}{5^3}={\dfrac{1}{125}[/tex]

[tex]\sf{2)\ -5^{-3}={\dfrac{1}{-5^3}=-{\dfrac{1}{125}[/tex]

[tex]\sf{3)\ \left(-5^{-3}\right)^{-1}=\left(-5^{-3\times-1}\right)=-5^{3}=-125}[/tex]

[tex]\sf{4)\ \left(-5^{-3}\right)^{0}=1[/tex]

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Answer:

6000 pounds or lbs.

Step-by-step explanation:

A ton=2000 lbs.

Hope this helps! ;-)

3x + 2y=-10 equation 1

y=-x -4 equation 2

use the substitution method of elimination to get the answer to the question.

*using substitution

substitute equation 2 in one and we get

3x +2(-x-4)=-10

3x- 2x-8=-10

x=-2 and y=-2

Answer:

B

Answer:  Choice A

(-2, -2)

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

Explanation:

I'll use the substitution method to solve this system.

Replace y in the first equation with -x-4. This is because y = -x-4 is mentioned in the second equation.

So,

3x + 2y = -10

3x + 2( y ) = -10

3x + 2( -x-4 ) = -10 .... substitution

3x - 2x - 8 = -10

x - 8 = -10

x = -10+8

x = -2

Then use this to find y

y = -x-4

y = -(x) - 4

y = -(-2) - 4

y = 2 - 4

y = -2

We have x = -2 and y = -2 pair up together

They form the ordered pair solution (x, y) = (-2, -2)

This shows why Choice A is the answer.

Another way to see this is to graph each equation given using a tool like Desmos. It's a free graphing app.

See below.

The two lines intersect at (-2, -2) which is the solution.

Answer:

(f ∘ f)(–1) = –1

Step-by-step explanation:

To solve a composite function, rewrite using brackets and solve from inside to outside.

(f ∘ f)(x) is the same as:    f[f(x)]

Given that x = –1 in (f ∘ f)(–1), we are solving for:

f[f(–1)] = ?

Solve for f(–1) inside the square brackets first.

f(x) = x³

f(–1) = (–1)³    Simplify.

f(–1) = –1       Solved the inside.

Substitute f(–1) = –1 into the square brackets.

f[f(–1)] = f[–1]

Now, we can solve the outside.

Solve with the equation of the function, x³.

f[–1] = x³

f[–1] = [–1]³     Substitute x = –1.

f[–1] = (–1)³     Simplify.

f[–1] = –1        Final answer

Answer:

Complete the following statements.

The functions f and g have the same axis of symmetry.

The y-intercept of f is greater than the y-intercept of g.

Over the interval [-6, -3], the average rate of change of f is less than the average rate of change of g.

Answer:

x=3, Aly is correct.

Step-by-step explanation:

a. angle YWZ

b. ZY = 9

c. the triangles are congruent so 7x-20=2x-5, 5x=15, and x=3

original equation

[tex]\frac{x}{2}-\frac{3x}{4}+\frac{x}{6}=-\frac{2}{3}[/tex]

multiply by lcd

[tex]12(\frac{x}{2})-12(\frac{3x}{4})+12(\frac{x}{6}) =-12(\frac{2}{3})\\\\6x-9x+2x=-8[/tex]

isolate for x

[tex]-1x=-8\\\\x=8[/tex]

verify

[tex]\frac{8}{2}-\frac{3(8)}{4}+\frac{8}{6}=-\frac{2}{3}\\\\4-6+\frac{4}{3}=-\frac{2}{3}\\\\4-2+\frac{4}{3}=-\frac{2}{3}\\\\-\frac{2}{3}=-\frac{2}{3}\\\\LS=RS[/tex]

Answer: 996 free ride passes were given away

Step-by-step explanation:

If each child was given 3 free ride passes, then you have to do 332 x 3 which is 996

Answer:

60 ft

Step-by-step explanation:

3 times 20 is 60 ft so there is your answer

Answer:

C

Step-by-step explanation:

Diameter is 3 feet, and the radius is half the diameter.

Circumference

Distance travelled in 20 rotations

Answer:

  200 miles

Step-by-step explanation:

Each inch represents 50 miles, so 4 times 1 inch will represent 4 times 50 miles.

  4(1 in) ⇔ 4(50 mi)

  4 in ⇔ 200 mi

It is about 200 miles from Chelsea to New York City according to the map.

Answer:

G = 1.60 x 1.5, G = 1.5 x 1.60, and G ÷ 1.5 = 1.60

Step-by-step explanation:

^ ^

Answer & step-by-step explanation:

An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign. As you can clearly see here, there is no equal sign connecting anything here, thus, it is an expression.

Because for it to be called an equation you need to have the equal symbol (=) comparing two epressions.

Example of expression:

 2x - 4y + 14

Example of equation:

   -3y - 2 = -2x - 8

⇔ -3y = -2x + 6

⇔ -y = -[tex]\frac{2}{3}[/tex]x + 2

⇔ y = [tex]\frac{2}{3}[/tex]x - 2

The answer is:

(-2/9, 35/9) in rounded decimal form is (-0.22, 3.89)

x = - 2 / 9 which in decimal form as well as rounded is -0.22

y = 35 / 9 which in decimal form as well as rounded is 3.89

Hope this helps...

Answer:

x = 10.9 cm

Step-by-step explanation:

Formula for a cone

Here, we are given :

Solving

Answer:

x ≈ 3.6 cm

Step-by-step explanation:

the volume (V) of a cone is calculated as

V = πr²h ( r is the radius and h the perpendicular height )

here diameter = 7 , so r = 7 ÷ 2 = 3.5 , V = 140 and h = x , then

π × 3.5² × x = 140

π × 12.25x = 140 ( divide both sides by 12.25π )

x = [tex]\frac{140}{12.25\pi }[/tex] ≈ 3.6 cm ( to 1 dec. place )

ANWER:

rounded o the nearesr tens is 88.6

Answer:

88

Step-by-step explanation:

Because 6 is greater than 5 it will rounded off and 87.6 = 88

The roots of the equation [tex]x^{2}[/tex]-15x +2 =0 are 14.865 and 0.135

Completing the square method is one of the methods to find the roots of the given quadratic equation.

Given equation is:

[tex]x^{2}[/tex]-15x +2 =0

Using Completing the Square method we have

[tex]x^{2}[/tex]-15x +2 + [tex](\frac{15}{2})^{2}[/tex] - [tex](\frac{15}{2})^{2}[/tex] =0

Now,

[tex]x^{2}[/tex]-15x + [tex](\frac{15}{2})^{2}[/tex] - [tex](\frac{15}{2})^{2}[/tex] +2=0

or, [tex][x-(\frac{15}{2})]^{2}[/tex] - 225/4 +2 =0

or,  [tex][x-(\frac{15}{2})]^{2}[/tex] -217*4 =0

or,  [tex][x-(\frac{15}{2})]^{2}[/tex] = 217/4

or,  [tex]x[/tex] = [tex]\pm \frac{14.73}{2} + \frac{15}{2}[/tex]

or, [tex]x_1[/tex]= 14.865, [tex]x_2[/tex]= 0.135

Thus, the roots of the quadratic equation are: 14.865 and 0.135

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Step-by-step explanation:

1 min 4 cals

60 cals how many mins?

1min. 60cals

____. × _______ = 15 mins

4cals. ?mins

we simplify the matter by simplifying 60 with 4 and striking out cals... then we will have 15 on the top right and then we multiply 1 and 15 together at the end we add the mark of the answer which is (min).

Answer:

4

Step-by-step explanation:

Mean is another way to say the average of a set of numbers. To find the average you need to add all the numbers in the set together, and then divide by the amount of numbers that where given.

In this case:

6 + 8 + 2 + 0 + 4 + 5 + 3 = 28

there are 7 numbers given in the set, so you divide 28 by 7 to get your mean.

28 / 7 = 4

Answer:

4

Step-by-step explanation:

To find the mean of a set of numbers, you add up all the numbers and then divide them by the amount of numbers there are.

So, let's add up these numbers.

6 + 8 + 2 + 0 + 4 + 5 + 3 = 28

Now, there are a total of 7 numbers, so we divide 28 by 7.

28 / 7 = 4

Therefore, the mean of this data set is 4. I hope this helps! Have a lovely day!!

The number of months in which Rita has a budget to buy a camera is 8 and a half months if Rita wants to save her babysitting money to buy a $249.99 camera.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Rita wants to save her babysitting money to buy a $249.99 camera. she makes $64.33 a month, and her fixed expenses are $34.50 a month.

Let x be the number of months in which Rita has a budget to buy a camera.

The linear equation in one variable can be framed as follows:

(64.33 - 34.50)x = 249.99

29.83x = 249.99

x = 8.38 = 8.5

Thus, the number of months in which Rita has a budget to buy a camera is 8 and a half months if Rita wants to save her babysitting money to buy a $249.99 camera.

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Answer:

22 pounds of watermelon

Step-by-step explanation:

First find cost per pound
19.60/8=2.45
$2.45 per pound
Then divide $53.90 by $2.45 to determine how many pounds you can buy
53.90/2.45=22
22 pounds of watermelon

Answer:

d

Step-by-step explanation:

Answer:

[tex]x\approx-0.7149[/tex]

Step-by-step explanation:

[tex]\displaystyle 6^{x+2}=10\\\\\log_6(6^{x+2})=\log_6(10)\\\\x+2=\frac{\log(10)}{\log(6)}\\\\x+2\approx1.2851\\\\x\approx-0.7149[/tex]

Recall that the change of base formula is [tex]\displaystyle \log_a(b)=\frac{\log(b)}{\log(a)}[/tex]

Answer:

here is the required answer hope it help u

Step-by-step explanation:

−2(−5n+6)+5(2−7n)

10n-12+10-35n

-25n-2

Answer

whats the question

Step-by-step explanation:

The slope and length of segment DE in the given triangle are: 0.5, and 1.6 units respectively.

The slope of lines that are parallel to each other are always the same.

Segment DE is parallel to segment BC in triangle ABC.

Since slope of BC is 0.5, slope of DE would also be: 0.5.

Since E and D are the the midpoints of AC and AB respectively, it means that:

Length of DE = 1/2(length of BC)

Length of DE = 1/2(3.2)

Length of DE = 1.6 units

Therefore, slope of DE is: 0.5

Length of DE is: 1.5 units.

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Answer:

C. Slope = 0.5, length = 1.6 units.

Hope this helps!

Step-by-step explanation:

Answer:

Down below

Step-by-step explanation:

150 - (2 + x)^3

150 - (2 + 2)^3

150 - (4)^3

150 - 64

= 86

I would check my math but I believe this is correct.

Answer:

86

150-(2+x)^3

⇒ x = 2

2 + 2 = 4

4^3(4 • 4 • 4) = 64

150 - 64 = 86

Answer:

/TS/=12cm

/QP/=

/QR/²=16²+12²

/QR/²=256+144

/QR/²=400

/QR/=√400

/QR/=20

/QP/=20/2=10

let /PT/ be x

hyp²=opp²+adj²

16²=20²+x²

x²=400-256

x²=144

x=√144

x=12.

Step-by-step explanation:

speed = distance/time

we know the speed and the time (11:45am to 1:45pm = 2 hours).

distance = speed × time = 56 m/h × 2 h = 112 miles

Answer:

Solve for x , 1x − 2+1x + 2=4(x − 2)(x + 2) .

1x − 2+1x + 2=4(x − 2)(x + 2)

(x − 2)(x + 2)(x − 2)+(x − 2)(x + 2)(x + 2)=4(x − 2)(x + 2)(x − 2)(x + 2)

(x−2)+(x+2)=4

2x=4

x=2

But 2 is excluded from the domain of the original equation because it would make the denominator of one of the fractions zero--and division by zero is not allowed!  .  Therefore, it cannot be a root of the original equation.  So, 2 is an extraneous solution. So, the equation has no solutions.

Step-by-step explanation:

An equal when substitute x = 4, the solution is not extraneous the solution x = 4 is valid for the original equation.

The equation is: √(2x - 7) = 1

Step 1: Square both sides of the equation to remove the square root:

(√(2x - 7))² = 1²

Simplify:

2x - 7 = 1

Step 2: Add 7 to both sides to isolate the term with "x":

2x - 7 + 7 = 1 + 7

Simplify:

2x = 8

Step 3: Divide both sides by 2 to solve for x:

2x / 2 = 8 / 2

Simplify:

x = 4

Now, we have found that the solution for x is 4.

To check if the solution is extraneous, we need to substitute the value of x back into the original equation and see if both sides are still equal:

Original equation: √(2x - 7) = 1

Substitute x = 4:

√(2(4) - 7) = 1

Simplify:

√(8 - 7) = 1

√1 = 1

1 = 1

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