The tennis coach at Riverside High School is purchasing equipment for the team. He has a budget of no more than $300 to purchase racquets and tennis balls. He wants to buy a large case of tennis balls costing $20 and several racquets that cost $40 each. Write an inequality statement that represents his purchase. What does the variable represent in your inequality? Solve the inequality.​

Given:

The function is

[tex]f(x)=x^3-7x^2+10x[/tex]

To find:

The end behavior of its graph.

Solution:

We have,

[tex]f(x)=x^3-7x^2+10x[/tex]

Here, leading coefficient is 1 which is positive and degree of function is 3 which is odd.

For odd degree and positive leading coefficient, the end behavior is

[tex]f(x)\to \infty\text{ as }x\to \infty[/tex]

[tex]f(x)\to -\infty\text{ as }x\to -\infty[/tex]

Using this, we get

[tex]\text{As }x\to \infty, y\to \infty[/tex]

[tex]\text{As }x\to -\infty, y\to -\infty[/tex]

Therefore, the correct statements are A and D.

We want to study the end behavior of the given polynomial.

The two correct statements are A and D.

The polynomial is:

f(x)  = x^3 - 7*x^2 + 10*x.

We can see that the degree of this polynomial is odd, this means that the behavior on the negative side is opposite to the one in the positive side.

In this case, the leading coefficient is one, so it is positive. This will mean that, for large positive values of x, f(x) will be positive.

For large (in absolute value) negative values of x, f(x) will be negative.

Then the end behavior is given by:

So the two correct statements are A and D.

If you want to learn more, you can read:

https://brainly.com/question/22723521

Step-by-step explanation:

1.

(80-4)²÷8

(76)²÷8

5776÷8

722

2.

92.3-(3.2÷0.4)*2³

92.3-8*2³

92.3-8*8

92.3-64

28.3

3.

[(2³*2.5÷1/2)]+120

(8*5)+120

40+120

160

4.

(2*10⁰)÷1/3+8

(2*1)÷1/3+8

2÷1/3+8

6+8

14

Wishing Success

Answer:

S/A/H/a=8

Step-by-step explanation:

Answer: variables

Letters can represent any number, therefore it varies, thus the name “variable”

Answer:

Average rate of change = -4

Step-by-step explanation:

Given:

f(x) = x² + 7x + 10

-8 ≤ x ≤ -3 or [-8, -3] in interval notation

Average rate of change of the function can be solved using the formula:

[tex]\mathrm{Average\:rate\:of\:change} = \dfrac{ f \left( b \right) -f \left( a \right) }{ b-a }[/tex]

[tex]\mathrm{Average\:rate\:of\:change} = \dfrac{ f \left( -3 \right) -f \left( -8 \right) }{ -3 - (-8) }[/tex]

[tex]\mathrm{Average\:rate\:of\:change} = \dfrac{ f \left( -3 \right) -f \left( -8 \right) }{ -3 + 8 }[/tex]

[tex]\mathrm{Average\:rate\:of\:change} = \dfrac{ f \left( -3 \right) -f \left( -8 \right) }{ 5 }[/tex]

Substitute x = -3 to the given function for f(-3) and x = -8 for f(-8)

[tex]\mathrm{Average\:rate\:of\:change} = \dfrac{ f \left( -3 \right) -f \left( -8 \right) }{ 5 }[/tex][tex]\mathrm{Average\:rate\:of\:change} = \dfrac{ { \left[( -3 \right) }^{ 2 } +7 \left( -3 \right) +10]- { \left[( -8 \right) }^{ 2 } +7 \left( -8 \right) +10] }{ 5 }[/tex]

[tex]\mathrm{Average\:rate\:of\:change} = \dfrac{ [9-21+10]-[64-56+10] }{ 5 }[/tex]

[tex]\mathrm{Average\:rate\:of\:change} = \dfrac{ [-2]-[18] }{ 5 }[/tex]

[tex]\mathrm{Average\:rate\:of\:change} = \dfrac{ - 20 }{ 5 }[/tex]

[tex]\mathrm{Average\:rate\:of\:change} = {-4 }[/tex]

Answer:

3a. 7.2

3b. 0.9

4a. 7.2

4b. 2.4

5a. 104

5b. 260

hope this helps, everything in bold is the correct answer,

have an awesome day, -TJ

Answer:

3.a. 36

b. 4.5

4.a. 7.2

b. 2.4

5.a. 104

b. 260

Step-by-step explanation:

100/20 = 5

18 x 5 = 90 (100%)

18 x 2 = 36

18/4 = 4.5

14.4/2 = 7.2

7.2/3 = 2.4

52 x 2 = 104 (100%)

(195/3) 4 = 65 x 4

65 x 4 = 260 (100%)

Answer:

my anawer na po eh 19 marong gento=eh

Option three [tex]\rm log3+log(x+4)[/tex] is the equivalent to the logarithm expression [tex]\rm log3(x+4)[/tex]

It is given that logarithm expression is  [tex]\rm log3(x+4)[/tex]

It is required to simplify the above equation.

It is another way to represent the power of numbers and we say that 'b' is the logarithm of 'c' with base 'a' if and only if 'a' to the power 'b' equals 'c'.

[tex]\rm a^b=c\\\rm log_ac=b[/tex]

We have logarithm expression:

[tex]\rm log3(x+4)[/tex]

We know the log property that we can split a logarithm into two logarithms if it contains the product of two numbers ie.

[tex]\rm logxy=logx+logy[/tex]

By using this property we get:

[tex]\rm =log3(x+4)\\\rm = log3+log(x+4)[/tex]

Because 3 and (x+4) are two different numbers, not (x+4).

Thus, option three [tex]\rm log3+log(x+4)[/tex] is the equivalent to the logarithm expression [tex]\rm log3(x+4)[/tex]

Learn more about the Logarithm here:

brainly.com/question/163125

Answer:

Step-by-step explanation:

optin three is the answer i have took the test                                                     (Which expression is equivalent to log3(x + 4)?

log3 – log(x + 4)

log12 + logx

log3 + log(x + 4)

StartFraction log 3 Over log (x + 4) EndFraction)

Answer:

16

Step-by-step explanation: parenthesis first (2+2)=4

then division 8/2=4

then multiply 4x4=16

Answer:

16

Step-by-step explanation:

8÷2(2+2)

(2+2)

8÷2(4)

8÷2

4(4)

16

Answer:

Today: Monday, 12 October 2020

Hour: 09.08 WIB (in Indonesian)

_________________________

3x + 5 = 20

3x = 20 - 5

3x = 15

x = 15/3

x = 5

Answer:

the answer is 5

Step-by-step explanation:

you subtract 5 from both sides and you get 3x=15 you divide and you get 5

Answer:

its c

Step-by-step explanation:

A x B = ab

A x C = ac

A x D = ad

(ab-ac-ad)

Let the width be "x" cm.

Then the length is "x+12" cm

And the area = x(x+12) = x^2+12x cm^2

----------------------------

Change the dimensions:

width = "x-2" cm

length = "x+10" cm

New area = (x-2)(x+10) = x^2 + 8x - 20 cm^2

------------------

Equations :

Old area - New area = 108 cm^2

x^2+12x -(x^2 + 8x - 20) = 108

4x + 20 = 108

4x = 88

x = 22 cm (original width)

x+12 = 24 cm (original length)

Answer:

$13,000

Step-by-step explanation:

Given:

Seema bought a refrigerator for {14300 including a GST of 10%.

To FInd:

The price of the refrigerator before GST was added is

Solve:

[tex]\\[/tex]100/100+10×14300

=100/110×14300

=$13,000

Hence, The price of the refrigerator before GST was added is $13,000.

~Learn with Lenvy~

Answer:

x=12

Step-by-step explanation:

AB/FE=BC/EC

x/6= 5+5/5

x/6=10/5

x=6(2)

x=12

~

Answer:

-124

Step-by-step explanation:

3x + 2y = 14 (×3) → 9x + 6y = 42

- → x = -18

5x + 3y = 12 (×2) → 10x + 6y = 24

3(-18) + 2y = 14

-54 + 2y = 14 → 2y = 14 + 54 = 68 → y = 68/2 = 34

5x - y = 5(-18) - 34 = -90 - 34 = -124

Answer:

After 11 weeks she has 5 dollars left in her bank account

Step-by-step explanation

I divided 225 ÷ 5 without going to the end of the operation so the rest was 5 dollars.

Answer:

nonlinear

Step-by-step explanation:

[tex]x(x + 3) = {x}^{2} + 3 \\ \: it \: will \: be \: a \: parabola \: because \: of \: the \: {x}^{2} [/tex]

x = -2
y = 3

[tex]-4x-2y=2\\ -4x+y=11[/tex]

Subtract the two equations

[tex]-4x-2y-(-4x+y)=2-11[/tex]

Remove parentheses

[tex]-4x-2y+4x-y=2-11[/tex]

Cancel one variable

[tex]-2y-y=2-11[/tex]

Combine like terms

[tex]-3y=2-11[/tex]

Calculate the sum or difference

[tex]-3y=-9[/tex]

Divide both sides of the equation by the coefficient of variable

[tex]y=\frac{-9}{-3}[/tex]

Determine the sign for multiplication or division

[tex]y=\frac{9}{3}[/tex]

Cross out the common factor

[tex]y=3[/tex]

Substitute into one of the equations

[tex]-4x+3=11[/tex]

Rearrange variables to the left side of the equation

[tex]-4x=11-3[/tex]

Calculate the sum or difference

[tex]-4x=8[/tex]

Divide both sides of the equation by the coefficient of variable

[tex]x=-\frac{8}{4}[/tex]

Cross out the common factor

[tex]x=-2[/tex]

The solution of the system is

[tex]x=-2\\ y=3[/tex]

I hope this helps you

:)

Answer:

The formula for circumference of s circle is pi x diameter.

If the circumference is 28 we can divide it by pi to get the Diameter.

28/ pi = 8.9126768131461388030574907488608042739297 rounded to 8.91 (2dp)

The radius is half of the diameter, so this means 8.91 / 2 = 4.46 ft (rounded to 2dp)

Answer:

true

Step-by-step explanation:

Answer: True

Step-by-step explanation:

[tex]\tan ^2\left(x\right)\cos ^2\left(x\right)=1-\cos ^2\left(x\right)[/tex]

[tex]\mathrm{Manipulating\:left\:side}[/tex]

[tex]\tan ^2\left(x\right)\cos ^2\left(x\right)[/tex]

[tex]\mathrm{Use \ the \ basic \ trigonometric \ identity \ \:tan\left(x\right)=\frac{sin\left(x\right)}{cos\left(x\right)}}[/tex]

[tex]=\cos ^2\left(x\right)\left(\frac{\sin \left(x\right)}{\cos \left(x\right)}\right)^2[/tex]

[tex]=\frac{\sin ^2\left(x\right)}{\cos ^2\left(x\right)}\cos ^2\left(x\right)[/tex]

[tex]=\frac{\sin ^2\left(x\right)\cos ^2\left(x\right)}{\cos ^2\left(x\right)}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:\cos ^2\left(x\right)[/tex]

[tex]=\sin ^2\left(x\right)[/tex]

[tex]\mathrm{Use \ the \ Pythagorean \ identity \ \cos ^2\left(x\right)-\sin ^2\left(x\right)=1 \rightarrow \sin ^2\left(x\right)=1-\cos ^2\left(x\right)}}[/tex]

[tex]=1-\cos ^2\left(x\right)[/tex]

[tex]1-\cos ^2\left(x\right) =1-\cos ^2\left(x\right)[/tex]

Left side = right side

Therefore, the identity is true

Answer:

Dilation is a transformation, that stretches or shrinks the original figure presented on the grid based on the scale factor. Included here are umpteen printable worksheets to help 8th grade and high school students hone in on finding the scale factor, identifying the dilation type, determining the new coordinates and drawing the dilated shapes with the center as origin.

Step-by-step explanation:

Answer:

Step-by-step explanation:

I'm assuming problem 6 is the graph on the right.

If so, then the slope is 1/2

Start at a point like (0,-1) which is the y intercept. Move up 1 and to the right 2 to arrive at (2,0) which is the x intercept.

The movement pattern "up 1, right 2" determines the slope directly

slope = rise/run = 1/2

rise = 1 = go up 1

run = 2 = go to the right 2

------------------------------

You could also pick two points from the blue line, then use the slope formula. If we picked (0,-1) and (2,0), then

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

m = (0-(-1))/(2-0)

m = (0+1)/(2-0)

m = 1/2

Answer:

Associative Property of Multiplication

Step-by-step explanation:

Even though the Associative Property usually means adding or subtracting, under these circumstances, it can be used with multiplication.

Answer:

Measure of the shortest side is 5 cm

Measure of the longest side is 12 cm

Step-by-step explanation:

Given:

Perimeter of ∆ = 27 cm

Side lengths of ∆: x, 2x, and 3x - 3

Required:

Measure of the shortest side and measure of the longest side.

SOLUTION:

Sum of all sides of the ∆ = Perimeter

[tex] x + 2x + (3x - 3) = 27 [/tex]

Solve for x

[tex] x + 2x + 3x - 3 = 27 [/tex]

Collect like terms

[tex] 6x - 3 = 27 [/tex]

Add 3 to both sides

[tex] 6x = 27 + 3 [/tex]

[tex] 6x = 30 [/tex]

Divide both sides by 6

[tex] x = \frac{30}{6} [/tex]

[tex] x = 5 [/tex]

Length of each side of the ∆:

x = 5 cm

2x = 2(5) = 10 cm

3x - 3 = 3(5) - 3 = 15 - 3 = 12 cm

Measure of the shortest side is 5 cm

Measure of the longest side is 12 cm

Answer:

1 gallon every 6 days

Step-by-step explanation:

To obtain a whole-number ratio, we multiply the 1/2 gallon by two. Since we are doing that, we should multiply the 3 days by two also.

Answer: it’s $305,000

Step-by-step explanation:

correct on ED2022

Answer:

B

Step-by-step explanation:

I just got it right

Answer: its 5w

Step-by-step explanation: