Find the surface area and volume of each figure. Round each answer to the nearest hundredth.

you answer is b) -x^2-4x+7

Answer:

B

Step-by-step explanation:

4x² - 7x + 9 - (5x² - 3x + 2) ← distribute by - 1

= 4x² - 7x + 9 - 5x² + 3x - 2 ← collect like terms

= (4x² - 5x² ) + (- 7x + 3x ) + (9 - 2)

= - x² - 4x + 7 → B

Answer:

The constant of proportionality is y/x so the rate us 35

Step-by-step explanation:

By solving a system of equations, we determined the quadratic function h(x) = 33.5x^2 + 14x + 53.5 and found that the height of the ball after 3 seconds is 229.5 feet.

Certainly! Let's go through the step-by-step calculation to find the quadratic function representing the height of the ball and then determine the height after 3 seconds.

Given information:

h(1) = 91 feet

h(2) = 164 feet

We need to find the coefficients a, b, and c in the quadratic function h(x) = ax^2 + bx + c.

Step 1: Setting up Equations

We have two equations based on the given information:

a + b + c = 91 (since h(1) = a(1)^2 + b(1) + c = a + b + c = 91)

4a + 2b + c = 164 (since h(2) = a(2)^2 + b(2) + c = 4a + 2b + c = 164)

Step 2: Solving the System of Equations

We can solve the system of equations to find the values of a, b, and c.

Subtracting the first equation from the second gives: 3a + b = 73.

Let's multiply the first equation by 3 and subtract it from the second:

3(3a + b) - (a + b + c) = 3(73) - 91

Simplifying, we get 6a - c = 110.

Step 3: Substituting into the First Equation

Substitute 6a - c = 110 into the first equation:

6a - c + c = 110 + 91

Solving, 6a = 201, which implies a = 33.5.

Step 4: Finding b and c

Substitute a back into the first equation to find b + c = 91 - 33.5, and then b and c are determined as b = 14 and c = 53.5.

Step 5: Quadratic Function

Now, we have the quadratic function h(x) = 33.5x^2 + 14x + 53.5.

Step 6: Finding h(3)

Finally, substitute x = 3 into the quadratic function:

h(3) = 33.5(3)^2 + 14(3) + 53.5

Solving this yields h(3) = 229.5 feet.

Final Answer:

The height of the ball after 3 seconds is 229.5 feet.

ANSWER

The correct answer is A

EXPLANATION

If the two functions are inverses , then

[tex]f(g(x)) = g(f(x)) = x[/tex]

Given

[tex]f(x) = 5x - 11[/tex]

and

[tex]g(x) = \frac{1}{5}x + 11[/tex]

[tex]f(g(x)) = f( \frac{1}{5} x + 11)[/tex]

This implies that,

[tex]f(g(x)) = 5(\frac{1}{5} x + 11) - 11[/tex]

Expand to get;

[tex]f(g(x)) =x + 55 - 11[/tex]

[tex]f(g(x)) =x +44[/tex]

Since

[tex]f(g(x)) \ne \: x[/tex]

The two functions are not inverses

The correct answer is A

Answer:

Correct choice is A.

Step-by-step explanation:

Given functions are [tex]f\left(x\right)=5x-11[/tex] and [tex]g\left(x\right)=\frac{1}{5}x+11[/tex].

Then [tex]f\left(g\left(x\right)\right)=f\left(\frac{1}{5}x+11\right)=5\left(\frac{1}{5}x+11\right)-11=x+55-11=x+44[/tex]

By definition of inverse we says that if f(x) and g(x) are inverse of each other then f(g(x)) must be equal to x.

But in above calculation we can see that f(g(x)) is not equal to x.

Hence correct choice is A.

A. n+4=5  

Hope this helps

Answer:

Volume of prism is 60 cm^3.

Step-by-step explanation:

The volume of prism can be found using formula:

V= B*h

Where B= base area and h= height.

In the question, we are given Base area B= 10cm^2 and height h= 6cm.

Putting values in the formula:

V= B8h

V= 10* 6

V = 60 cm^3

So, volume of prism is 60 cm^3.

ANSWER

Katnis is right

EXPLANATION

We use the Remainder Theorem to check if she is right.

According to the Remainder Theorem, if the polynomial function,

[tex]p(x) = {x}^{3} + 2 {x}^{2} - 3x - 4[/tex]

is divided by x+1, then the remainder is given by

[tex]p( - 1)[/tex]

We substitute x=-1 into the function to obtain,

[tex]p( - 1) = {( - 1)}^{3} + 2 { ( - 1)}^{2} - 3( - 1) - 4[/tex]

We simplify to get:

[tex]p( - 1) = - 1+ 2 (1) + 3 - 4[/tex]

[tex]p( - 1) = 4- 4[/tex]

[tex]p( - 1) = 0[/tex]

Katnis is right because the remainder is zero

Answer: A.4 units

Step-by-step explanation:

We know that if a figure is dilated by a scale factor of k , then the measure of the corresponding image (l') of a line segment having measure 'l' is given by :-

[tex]l'=kl[/tex]

Given : Square RSTU dilates by a factor of 1\2 with respect to the origin to create square R'S'T'U'.

The measure of line segment R'S' = 2 units

The scale factor : [tex]k=\dfrac{1}{2}[/tex]

Using the above equation , we have

[tex]R'S'=\dfrac{1}{2}RS\\\\\Rightarrow\ RS= 2\times R'S'\\\\\Rightarrow\ RS= 2\times2=4[/tex]

Hence, RS = 4 units.

Consider a striking deviation as an outlier (Something that stands out in a pattern, EX: 2, 3, 4, 4, 4, 5, 5, 10 where the outlier would be 10.) Because there are no outliers (Or, Striking deviations), we can conclude that the answer would be D: No striking deviation.

The answer is B. I think. Hope that helps!

Answer:

The answer is B,

26-12.81=13.19

13.19-10=3.19

3.19/0.42 is a little greater than 7

[tex]63:21=3:1[/tex]

Hope this helps.

r3t40

the answer is even is the right answer

ANSWER

even

EXPLANATION

The given function is

[tex]f(x) = |x| + {x}^{2} + 0.001[/tex]

If f(x) is even then f(-x) =f(x).

[tex]f( - x) = | - x| + {( - x)}^{2} + 0.001[/tex]

[tex]f( - x) = | x| + {x}^{2} + 0.001[/tex]

We can see that:

[tex]f( - x) = f(x)[/tex]

Hence the given function is even.

Answer:

a

Step-by-step explanation:

it is 189ft² just trust me

Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation of a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have the center (0, -1) and the radius r = 5   (look at the picture).

Substitute:

[tex](x-0)^2+(y-(-1))^2=5^2\\\\x^2+(y+1)^2=25[/tex]

use (a + b)² = a² + 2ab + b²

[tex]x^2+y^2+2y+1=25[/tex]             subtract 25 from both sides

[tex]x^2+y^2+2y-24=0[/tex]

Answer:

13

Step-by-step explanation:

(x + 3)^3/2 = 64

√(x + 3)^3 = 64

(x + 3)^3 = 64^2

(x + 3)^3 = (4^3)^2

(x + 3)^3 = (4^2)^3

Same exponent

So

x + 3 = 4^2

x + 3 = 16

x = 13

ANSWER

A. No because f(c)=-30

EXPLANATION

The given polynomial is

[tex]f(x) =2x^3-9x^2+13x-6[/tex]

If x+1 is a factor , then f(-1) must evaluate to zero.

[tex]f( - 1) =2( - 1)^3-9( - 1)^2+13( - 1)-6[/tex]

[tex]f( - 1) =2( - 1)-9( 1)+13( - 1)-6[/tex]

[tex]f( - 1) = - 2-9 - 13-6[/tex]

[tex]f( - 1) = -11 - 19[/tex]

[tex]f( - 1) = - 30[/tex]

Since f(-1) is not equal to zero, x+1 is not a factor of

[tex]f(x) =2x^3-9x^2+13x-6[/tex]

Answer:

A

Step-by-step explanation:

Solving for x:

-3x + 8 ≥ 14

-3x ≥ 6

x ≤ -2

Notice the sign gets reversed when you divide or multiply by a negative number.

The only option less than -2 is -3, A.

Here's a tip: on multiple choice questions, sometimes it's faster to try each answer instead of solving the equation.  This can save time on tests like the SAT or ACT.

Let's try it:

-3(-3) + 8 = 9 + 8 = 17

-3(-1) + 8 = 3 + 8 = 11

-3(0) + 8 = 0 + 8 = 8

-3(3) + 8 = -9 + 8 = -1

So you can see the answer is A.

Answer:

x^2+5x-6

a = 1  b = 5 and c = -6

Using the quadratic formula:

x = [-5 +- sq root (25 -4 * 1 *-6) ] / 2 * 1

x = [-5 +- sq root (49)] / 2

x = [-5 +- 7] / 2

x1 = 1

x2 = -6

Step-by-step explanation:

Answer:

x>8

Step-by-step explanation:

The number has to be bigger than 8 in order to be at least fifteen, so x is greater than 8

Step-by-step Answer:

Since there are no repetitions in the five letters of the word ZEBRA, the number of permutations is 5! = 120 = 5*4*3*2*1.

Answer:

The probability is 0.953

Step-by-step explanation:

We know that the mean [tex]\mu[/tex] is:

[tex]\mu=10:30\ p.m[/tex]

The standard deviation [tex]\sigma[/tex] is:

[tex]\sigma=0:15\ minutes[/tex]

The Z-score is:

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

We seek to find

[tex]P(10:00\ p.m.<x<11:00\ p.m.)[/tex]

The Z-score is:

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

[tex]Z=\frac{10:00-10:30}{0:15}[/tex]

[tex]Z=\frac{-0:30}{0:15}[/tex]

[tex]Z=-2[/tex]

The score of Z =-2 means that 10:00 p.m. is -2 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the condition of 2 deviations from the mean has percentage of 2.35%

and

[tex]Z=\frac{x-\mu}{\sigma}[/tex]

[tex]Z=\frac{11:00-10:30}{0:15}[/tex]

[tex]Z=\frac{0:30}{0:15}[/tex]

[tex]Z=2[/tex]

The score of Z =2 means that 11:00 p.m. is 2 standard deviations from the mean. Then by the rule of the 8 parts of the normal curve, the area that satisfies the condition of 2 deviations from the mean has percentage of 2.35%

[tex]P(10:00\ p.m.<x<11:00\ p.m.)=100\%-2.35\%-2.35\%[/tex]

[tex]P(10:00\ p.m.<x<11:00\ p.m.)=95.3\%[/tex]

[tex]P(10:00\ p.m.<x<11:00\ p.m.)=0.953[/tex]

the probability is 0.4772, or 47.72%.

To find the probability that Flight 202's arrival time is between 10:00 p.m. and 11:00 p.m., we need to standardize the times and use the properties of the normal distribution. The mean arrival time is 10:30 p.m., and the standard deviation is 15 minutes.

First, convert the times to minutes past 10:00 p.m.: 10:30 p.m. is 30 minutes past, and 11:00 p.m. is 60 minutes past. Now, standardize these times using the formula for z-scores:

Using the z-table or a standard normal distribution calculator, we find the area under the curve to the left of z = 0 is 0.5, and to the left of z = 2 is approximately 0.9772. Therefore, the probability that the arrival time is between 10:00 PM and 11:00 PM is the difference of these probabilities:

P(10:00 PM < X < 11:00 PM) = P(Z < 2) - P(Z < 0) = 0.9772 - 0.5 = 0.4772

So, the probability is 0.4772, or 47.72%.

Hello! :)

Since there is one value of y for every value of x in ( − 4 , 3 ) , ( − 2 , 3 ) , ( − 1 , 2 ) , ( 2 , 5 ) , ( 3 , 2 ) ( - 4 , 3 ) , ( - 2 , 3 ) , ( - 1 , 2 ) , ( 2 , 5 ) , ( 3 , 2 ) , this relation is a function. The relation is a function.

Hope I helped and wasn’t too late in answering!

Have fun and good luck!

~ Destiny ^_^

the correct answer is a) Function 1 only.

To determine which relations are functions from the given sets, we need to check if each element of the domain (the first number in each ordered pair) is mapped to only one element in the range (the second number in each ordered pair).

Set 1: {(-4, 3), (-2, 3), (-1, 2), (2, 5), (3, 2)}

Set 2: {(-4, 1), (-2, 3), (-2, 1), (-1, 5), (3, 2)}

Set 3: {(-4, 1), (-2, 3), (-1, 2), (3, 5), (3, 2)}

Set 4: {(-4, 1), (-2, 3), (-1, 1), (-1, 5), (3, 2)}

Analyzing each set:

Set 1 is a function because each domain value is unique and pairs with only one range value.

Set 2 is not a function because the domain value -2 is mapped to two different range values (3 and 1).

Set 3 is also not a function because the domain value 3 is mapped to two different range values (5 and 2).

Set 4 is not a function because the domain value -1 is mapped to two different range values (1 and 5).

Therefore, the correct answer is a) Function 1 only.

ANSWER

No, there is no constant ratio.

EXPLANATION

We want to determine whether the sequence

4, 16, 36, 64

is geometric.

We need to find out if there is a common ratio between the consecutive terms.

[tex] \frac{16}{4} = 4[/tex]

[tex] \frac{36}{16} = \frac{9}{4} [/tex]

[tex] \frac{64}{36} = \frac{16}{9} [/tex]

Since the ratio is not the same for the consecutive terms, the sequence is not geometric.

4, 16, 36, 64 is a geometric sequence with a common ratio of 4.

Yes, 4, 16, 36, 64 is a geometric sequence.

Answer:

graph?

Step-by-step explanation:

Answer:CUB

Step-by-step explanation:

Answer:

[tex]\frac{(3x)^{12} }{(3x)^{4} } =(3x)^{8}[/tex]

Step-by-step explanation:

As we are dividing by powers, we can just subtract the powers as they have the same base. As 12-4=8 the answer would be

[tex]\frac{(3x)^{12} }{(3x)^{4} } =(3x)^{8}[/tex]

Answer:

[tex] (3 x )^ 8 [/tex]

Step-by-step explanation:

We are given the following expression which we are to multiply or divide as indicated:

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

We know that if the bases are same and they are divided, then the exponent of the denominator is subtracted from the exponent of the numerator. So we get:

[tex] ( 3 x ) ^ { 1 2 - 4 } =( 3 x )^ 8 [/tex]

The area of the two smaller squares are shown as 25 and 144, add them together to get 25 + 144 = 169.

The area of the larger square is shown as 169, which is the same as the sum of the two smaller ones.

The answer is Yes.

yes the sum of the smaller squares is equal to the largest one. 25 + 144 = 169

The area of the largest squares is 169, so the area of the smaller squares is equal to the largest square.

Answer:

The maximum area is equal to [tex]20,000\ ft^{2}[/tex]

Step-by-step explanation:

Let

x ----> the length of the rectangular yard

y ----> the width of the rectangular yard

we know that

The perimeter is equal to

[tex]400=x+2y[/tex] --> remember that the fourth side will be against her deck

isolate the variable y

[tex]y=200-0.5x[/tex] -----> equation A

The area of the rectangular yard is equal to

[tex]A=xy[/tex] ----> equation B

substitute equation A in equation B

[tex]A=x(200-0.5x)\\ \\A=200x-0.5x^{2}[/tex]

The quadratic function is a vertical parabola open downward

The vertex is a maximum

The x-coordinate of the vertex represent the length of the rectangular yard for an maximum area

The y-coordinate of the vertex represent the maximum area of the rectangular yard

Using a graphing tool

The vertex is the point (200,20,000)

see the attached figure

therefore

The length of the rectangular yard is 200 ft

The width of the rectangular yard is [tex]y=200-0.5(200)=100\ ft[/tex]

The maximum area is equal to [tex]20,000\ ft^{2}[/tex]

The answer is D. -2x+5.

If we simplify the left side of the equation first given, we come to the expression -2x-10.

If we solve for D., we get the same results. Thus, because an equation with all the same variable terms and constants have infinite solutions, the answer is D.

Hope this helps!

Answer:

The correct option is D) -2(x+5)

Step-by-step explanation:

Consider the provided equation.

-5(x+2)+3x=

The above equation is linear equation having one variable.

For an linear equation ax=b

a=0, b=0 in that situation the equation is in the form of 0x=0 for all value of x. Then there are infinitely many solutions.

Now solve the expression on the left side

-5(x+2)+3x

-5x-10+3x

-2x-10

-2(x+5)

Now for 0x=0 form the expression on the right side must be same as the expression on the left side for the provided equation.

Consider the options.

Option A) -5(x-3)+2x

Solve the above expression.

-5x-15+2x

-3x-15

-2(x+5)≠-3x-15

Thus the option is not correct.

Option B) -5x-10

Solve the above expression.

-5x-10

-5(x+2)

-2(x+5)≠-5(x+2)

Thus the option is not correct.

Option C) x-2x+2+3x

Solve the above expression.

x-2x+2+3x

2x+2

2(x+1)

-2(x+5)≠2(x+1)

Thus the option is not correct.

Option D) -2(x+5)

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

Hence, the correct option is D) -2(x+5)

Answer:

8/15 chance

Step-by-step explanation:

To calculate the probability of forming an all-female group of three students from a class of 15 students, we find the total combinations of choosing three females and divide by the combinations of choosing any three students, resulting in a probability of 56/455.

The question involves calculating the probability that a group of three randomly selected students will consist of all females from a class of 15 students (8 females and 7 males). This is a problem of combinatorics and probability. We use combinations to determine the number of ways to choose three female students out of eight and divide that by the number of ways to choose any three students out of the fifteen.

First, we find the number of ways to choose three females: C(8,3) = 8! / (3! * (8-3)!) = 56. Then, we find the total number of ways to choose any three students: C(15,3) = 15! / (3! * (12!)) = 455. Therefore, the probability of choosing all females is 56/455.