Peta attempted to solve the following equation. Explain Peta's error.
x (x - 5) = 20
x = 20 and x - 5 = 20
x = 20 and x = 25

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:

[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]

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.

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)

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.

Answer:

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

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:

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

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:

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:

The horizontal cross-sections of the pyramid and the cone at the same height must have the same area.

Step-by-step explanation:

We are given that a pyramid and a cone are both 10 centimeters tall and have the same volume and we are to determine a statement which must be true for both the solids.

The horizontal cross-sections of the pyramid and cone at the same height must have the same area.

This is because

Answer:

Tbase area is same for both pyramid and cone

And cross section at same height the cross sectional area is same

Step-by-step explanation:

Points to remember

Volume of pyramid = (a²h)/3

Where a -  side of base

h - height of pyramid

Volume of cone = (πr²h)/3

Where r - Radius of cone and

h - Height of cone

To find the correct answer

We have height of pyramid and cone is 10 cm

(a²h)/3 = (πr²h)/3

(a² * 10)/3 = (πr² * 10)/3

10a² = 10πr²

From this we get base area is same for both pyramid and cone

And cross section at same height the cross sectional area is same

5 1/2 weeks. you divide 85 1/4 by 15 1/2 to get the answer

Ryan will take 5 weeks and 5 days to complete the tree house.

'The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.'

According to the given problem,

Time taken by Ryan to complete building the tree house = 85[tex]\frac{1}{4}[/tex] hours

                                                                                               = [tex]\frac{341}{4}[/tex] hours

Hours he work on the tree house = 15[tex]\frac{1}{2}[/tex] hours

                                                        = [tex]\frac{31}{2}[/tex]

Weeks taken by Ryan to complete building = [tex]\frac{341}{4}[/tex] ÷ [tex]\frac{31}{2}[/tex]

                                                                        = 5.5 weeks

                                                                        = 5 weeks 5 days

Hence, we can conclude that Ryan is going to take 5 weeks and 5 days to complete building the tree house.

Learn more about Unitary Method here: https://brainly.com/question/24406804

#SPJ2

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:

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:

a

Step-by-step explanation:

it is 189ft² just trust me

Answer:

a

Step-by-step explanation:

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

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

A. n+4=5  

Hope this helps

Answer:

acute

Step-by-step explanation:

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

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

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: 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.

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]

Answer:

6. an odd-degree polynomial function.

    f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞

7. Length =x+10=8+10=18 inches

   Width=x=8 inches

Step by step explanation;

6. The graph represent an odd-degree polynomial function.

The graph enters the graphing box from the bottom and goes up leaving through the top of the graphing box.This is a positive polynomial whose limiting behavior is given by;

f(x)⇒-∞ as x⇒-∞ and f(x)⇒∞ as x⇒∞

7.

The area of a rectangle is given by l×w, where l is length and w is the width

Let=w=x  , l=x+10  and A=144 in² then;

l×w=144

(x+10) × x = 144

x²+10x =144......................complete squares on both sides

x²+10x+25=144+25

x²+10x+25=144+25................factorize

(x+5)²=169.......................square root the right-hand side

x+5= ±√169

x+5=±13.

x+5=13⇒⇒⇒x=8

x+5=-13⇒⇒⇒x= --18

x=8 inches....................value of width should be positive

Length =x+10=8+10=18 inches

Width=x=8 inches

Answer:

6. Since, by given graph,

The end behavior of the function f(x),

[tex]f(x)\rightarrow -\infty\text{ if }x\rightarrow -\infty[/tex]

[tex]f(x)\rightarrow +\infty\text{ if }x\rightarrow +\infty[/tex]

Thus, the function f(x) must has odd number of roots ( where the graph of a function intersects the x-axis )

⇒ The function must has odd number of solutions,

Again by the graph,

Graph of the function intersects the x-axis 5 times ( it touches the origin so it have the repeated root of x = 0 ),

Hence, the total number of real solution of f(x) is 5.

7. Let x represents the width of the rectangle( in inches ),

Given,

The length is 10 inches longer than the width,

⇒ Length of the rectangle = ( x + 10 ) inches

Thus, the area of the rectangle,

A = length × width = x(x+10)

According to the question,

A = 144 in²

⇒ x(x+ 10) = 144

[tex]x^2+10x=144[/tex]

[tex]x^2+10x-144=0[/tex]

[tex]x^2+18x-8x-144=0[/tex]  ( Middle term splitting )

[tex]x(x+18)-8(x+18)=0[/tex]

[tex](x+18)(x-8)=0[/tex]

⇒ x = -18 or x = 8    ( By zero test property )

The width can not be negative,

Hence, the width of the rectangle would be 8 inches.

Answer:

graph?

Step-by-step explanation:

Answer:CUB

Step-by-step explanation:

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

Answer:

The direction that the paraboa y=-4x^2-8x-13 open is

Down

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

Hope this helps.

r3t40