Sam and Liam raced each other up and then down the hill. Sam's average speed up the hill was 1 mph, and his average speed down the hill was 9 mph. Lian ran up the hill and down the hill with the same speed, 2 mph. if the path from the bottom to the top of the hill is 1 mile long, how much time did it take each of the boys to finish?

Answers

Answer 1

Answer:

[tex]\begin{gathered} \text{Lian - 1 hour} \\ \text{Sam - 1}\frac{1}{9}\text{ hours} \end{gathered}[/tex]

Explanation:

Here, we want to calculate the time taken for each of the boys to finish the race

From what we have, the total distance traveled is 2 miles (1 mile up , 1 mile down)

The general formula to get time from speed and distance is:

[tex]\text{time = }\frac{dis\tan ce}{\text{speed}}[/tex]

Kindly understand that the journey is in two phases, the leg up and the leg down. The time spent on each will be summed to give the total time spent on the race

Let us start with Lian. We have it as:

[tex]\frac{1}{2}\text{ + }\frac{1}{2}\text{ = 1}[/tex]

Lian took one hour

For Sam, we have it that:

[tex]\frac{1}{9}+\text{ }\frac{1}{1}\text{ = }\frac{1\text{ + 9}}{9}\text{ = }\frac{10}{9}\text{ = 1}\frac{1}{9}\text{ hours}[/tex]


Related Questions

Question is in the photo. Disregard checked answer I just guessed don’t know if it’s right or wrong

Answers

Answer:

0, 3, and 6

Explanation:

Given the second derivative of the function, f(x) below:

[tex]f^{\prime}^{\prime}(x)=x^2(x-3)(x-6)[/tex]

To find the x-coordinate of the point of inflection, set the second derivative of the function equal to zeroand solve for x:

[tex]\begin{gathered} x^2(x-3)(x-6)=0 \\ \implies x^2=0,x-3=0,x-6=0 \\ \implies x=0,3,6 \end{gathered}[/tex]

The x-coordinates of the point of inflection are 0, 3, and 6.

3.) If f(x)=-|x| is graphed on a regular coordinate grid, does the graph form an acute, right, or obtuse angle at its vertex? a. Acute b. Right c. Obtuse d. There is no vertex

Answers

The given function is an absolute value function with vertex at the origin (0,0).

It is important to know that an absolute value function has a v-form where the lines are perpendicular because the lines have opposite slopes.

Hence, the right answer is B there is a right angle between the lines.

Find the common difference for the arithmetic sequence.-49, -42, -35, -28...

Answers

The set of numbers shown is a sequence, an arithmetic sequence. The common difference is the number which you must add to an existing term in order to get the next one. That means the common difference is what was added to -49 in order to arrive at -42. Lets calculate the common difference, d;

[tex]\begin{gathered} -49+d=-42 \\ \text{Add 49 to both sides of the equation (so as to eliminate it from the left side} \\ -49+49+d=-42+49 \\ 0+d=49-42 \\ d=7 \end{gathered}[/tex]

Arrange the systems of equations in order from least to greatest based on the number of solution for each system. NEED FAST HELP

Answers

On solving equations in the box 1:

-5x+y=10 -> 1

-25x+5y=50 ->2

div by -5 on equation 2.

so we get as 5x-y=-10 ->3

so solving 1 and 3 we get the equations cancel each other.so x and y are not true.They dont have any solutions.

On solving the equations in the box 2:

3x -7y =9 -->1

-4x +5y =1 -->2

so lets multiply equation 1 by 4 and euqation 2 by 3 so we get

12x-28y=36

-12x+15y=3

on solving we get -13y=39

y=-3 ,we can get x value by putting y value in any of the above equations.

3x-7(-3)=9

3x+21=9

3x=-12

x=-12/3

x=-4 so we get x=-4 and y=-3

On solving the equations in the box 3:

y=6x-2

by re-arranging we get -6x+y=-2 ---> 1

y=6x-4

on re arranging we get -6x+y=-4 ----->2

multiplying equation 2 by -1

so we get 6x-y=4 ---> 3

on solving 1 and 3 we get them cancel eachother so they have no solutions.

so finally analyzing all the boxes we can conclude that box 2 more number of solutions

Which equation models this situation?The sum of 22 and a number is 41.A. 22 + 41 = × B. 22 - × = 41C. 41 + × = 22D. 22 + × = 41

Answers

The sum of 22 and a number is 41.

Let x represent the number.

To represent the statement above as an equation, we have:

22 + x = 41

ANSWER:

D. 22 + x = 41

(8.76*10*9)(6.52*10*-3) /13.27*10*5 =

Answers

[tex]\begin{gathered} \frac{(8.76X10^9)(6.52X10^{-3})^{}}{13.27X10^5}^{} \\ =\frac{57.1152X10^{9+(-3)}}{13.27X10^5} \\ =4.3X10^{6-5} \\ =4.3X10^1 \end{gathered}[/tex]

Find the missing side using Pythagorean theorem, than find the surface area

Answers

Given:

Consider the triangular part in the given figure.

To find the third side of right triangle. Use pythagorean theorem,

[tex]\begin{gathered} x^2=3^2+4^2 \\ x^2=9+16 \\ x^2=5^2 \\ x=5 \end{gathered}[/tex]

The missing side of triangle is 5 cm.

Now to find the surface area of triangular prism.

Note that the height of the right triangle is 4 cm and base is 3 cm.

[tex]s_1=3,s_2=4,s_3=5,l=6,h=4,b=3[/tex]

First calculate the area of each side,

[tex]\begin{gathered} \text{Area of one triangle=}\frac{1}{2}(4\times3)=6 \\ \text{Area of second triangle}=\frac{1}{2}(4\times3)=6 \\ \text{One rectangle =4}\times6=24 \\ \text{second rectangle}=3\times6=18 \\ \text{Third rectangle =}5\times6=30 \end{gathered}[/tex]

So, the surface area is,

[tex]SA=6+6+24+18+30=84[/tex]

Answer: surface area is 84 square cm.

Answer the questions by drawing on the coordinate plane below. You may need to print the test and graphthe images by hand.

Answers

From the figure, we have the following coordinates of the vertices :

[tex]\begin{gathered} Q(-4,2) \\ R(-1,1) \\ S(-2,4) \end{gathered}[/tex]

a. Rotation of 180 degrees about the origin has a rule of :

[tex](x,y)\rightarrow(-x,-y)[/tex]

The sign of the coordinates will change from positive to negative or negative to positive.

The new coordinates will be :

[tex]\begin{gathered} Q(-4,2)\rightarrow Q^{\prime}(4,-2) \\ R(-1,1)\rightarrow R^{\prime}(1,-1) \\ S(-2,4)\rightarrow S^{\prime}(2,-4) \end{gathered}[/tex]

The graph will be :

b. Reflection across the x-axis has a rule of :

[tex](x,y)\rightarrow(x,-y)[/tex]

Only the y coordinate will change its sign.

So from the coordinates we got in a.

[tex]\begin{gathered} Q^{\prime}(4,-2)\rightarrow Q^{\doubleprime}(4,2) \\ R^{\prime}(1,-1)\rightarrow R^{\doubleprime}^{\prime}(1,1) \\ S^{\prime}(2,-4)\rightarrow S^{\doubleprime}(2,4) \end{gathered}[/tex]

The graph will be :

round 1,587,966 to nearest ten thousand.


Answers

Answer:

Step-by-step explanation:

1,590,000

12, 10, 23 15, 6.2, 6.24.6, 8.2, 3.812, 5, 7which could be the length of three sides of a triangle ?

Answers

We would apply the traingle inequality theorem which states that the sum of the length of two sides of a triangle is greater than the length of the third side. Thus,

For the first option

12 + 10 = 22 and it is less than 23. It can't form the length of the three sides of a triangle

For the second option

6.2 + 6.2 = 12.4 and it is less than 15. It can't form the length of the three sides of a triangle

For the third option,

4.6 + 3.8 = 8.4 and it is greater than 8.2. It can form the length of the three sides of a triangle

For the fourth option

5 + 7 = 12 and it is equal to 12. It can't form the length of the three sides of a triangle

Thus, the correct option is 4.6, 8.2, 3.8

What is the equation of the line that passes through (-1,8 and (1, -4)?

Answers

Using slope-intercept form, an equation of a line can be written as

[tex]y=mx+c[/tex]

Find the slope using the two-point formula.

[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{-4-8}{1-(-1)} \\ =\frac{-12}{2} \\ =-6 \end{gathered}[/tex]

Substitute -6 for m into y = mx + c.

[tex]y=-6x+c[/tex]

Now, to find the y-intercept,c, substitute any given point into the equation.

[tex]\begin{gathered} 8=-6(-1)+c \\ 8=6+c \\ c=2 \end{gathered}[/tex]

Thus, y = -6x + 2, which is the required equation of the line passing through (-1,8) and (1,-4).

determine if the triangles are congruent byASA,SSS,SAS,AAS,HL or not congruent

Answers

Consider the given triangles.

Two triangles are said to be congruent, if all the sides are equal or all the angles are equal.

There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.

SSS - All the sides are equal.

SAS - Two sides and included angle are equal.

ASA - Two angles and included sides are equal.

AAS - Two angles and non included angle are equal.

HL (right angled trianles) - the same length of hypotenuse and the same length for one of the other two legs.

In the given traingles, it is given that,

SIde, EN = PR

Side EM = PQ

Therefore, we can say that the traingles are not congruent.

Find the a1 and d for the arithmetic where Sn=187, n=17, and a17 = -13

Answers

The sum of n terms is:

[tex]S_n=\frac{n}{2}(2a_1+(n-1)d)[/tex]

For n = 17, a17 = -13 and Sn = 187, then:

[tex]\begin{gathered} 187=\frac{17}{2}(2a_1+(17-1)d) \\ 187\cdot\frac{2}{17}=2a_1+16d \\ 22\text{ = }2a_1+16d \end{gathered}[/tex]

Arithmetic sequence formula:

[tex]a_n=a_1+(n-1)d[/tex]

Replacing with n = 17 and a17 = -13:

[tex]\begin{gathered} -13=a_1+(17-1)d_{} \\ -13=a_1+16d \end{gathered}[/tex]

Subtracting this equation to the previous one

[tex]\begin{gathered} 22-(-13)=2a_1-a_1+16d-16d_{}_{}_{} \\ 35=a_1 \end{gathered}[/tex]

Then d is equal to:

-13 - 35 = 16d

-48/16 = d

-3 = d

lf the sum of two angles is 180, which condition MUST be true?

Answers

By definition, if the sum of two angles is 180 degrees then they are called supplementary.

Answer: That the angles are supplementary. Two angles are supplementary if the sum of their measures is 180.

Step-by-step explanation:

Can three segments with lengths 8,15, and 6 make a triangle? Explain your answer.

Answers

Answer:

No

Explanation:

Given three segments with lengths 8, 15, and 6

We check if the sum of two sides is greater than the third.

[tex]8+6=14[/tex]

Since 14 is less than 15, the three segments cannot make a triangle.

2 WRITE THE RULE FOR THE TRANSLATION. (x Y Y D A c

Answers

This figure was translated 1 unit to the right and 4 units down, so the rule of translation will be:

(x + 1, y - 4)

by the following expression using distributive property of division (30x-15)/3

Answers

we have the following:

[tex]\begin{gathered} \frac{30x-15}{3}​=\frac{30x}{3}-\frac{15}{3} \\ 10x-5 \end{gathered}[/tex]

therefore, the answer is 10 x - 5

Which representation shows a nonproportional relationship between x and y? 6 4 2 1 FA 11 3 y = -X -9-8-7-6-5-4-3-2-1 334 5 6 7 8 9 5 19 9 y у у -4 -1.6 -5 -1 B - 2 -0.8 -3 -0.2 1 0.4 2. 1.8

Answers

proportional relationships have constant ratios.

the graph is a line, so it is a proportional relationship. (A)

the function is in the form y=kx (proportional function) (C)

Find the ratio of the tables: (B)

[tex]m=\frac{-0.8-(-1.6)}{-2-(-4)}=0.4=\frac{0.4-(-0.8)}{1-(-2)}=\frac{1.2-0.4}{3-1}=[/tex]

D

[tex]m=\frac{-0.2-(-1)}{-3-(-5)}=0.4=\frac{1.8-(-0.2)}{2-(-3)}=\frac{3-1.8}{5-2}[/tex]

All represent a proportional relationship

Complete the equation for the piece wise function graphed below.

Answers

Answer:

[tex]f(x)=\mleft\{\begin{aligned}-0.5x+3,if-6\le x\le-2 \\ -3,if-2Explanation:

For the value of x such that: -6≤x≤-2

We have the endpoints (-6,0) and (-2, -2).

We determine the equation in the slope-intercept form, y=mx+b.

[tex]\begin{gathered} \text{Slope,m}=\frac{0-(-2)}{-6-(-2)} \\ =\frac{2}{-6+2} \\ =\frac{2}{-4} \\ m=-0.5 \end{gathered}[/tex]

The equation then becomes:

[tex]y=-0.5x+b[/tex]

Using the point (-6,0)

[tex]\begin{gathered} 0=-0.5(6)+b \\ b=3 \end{gathered}[/tex]

Therefore: f(x)=-0.5x+3, -6≤x≤-2

Next, f(x)=-3 for -2

Finally, for 1The endpoints are (1,-4) and (6,1)

[tex]\text{Slope,m}=\frac{-4-1}{1-6}=\frac{-5}{-5}=1[/tex]

Using the point (1,-4)

[tex]\begin{gathered} y=mx+b \\ -4=1(1)+b \\ b=-4-1=-5 \end{gathered}[/tex]

Therefore, f(x)=x-5, for 1

The completed function will now be:

[tex]f(x)=\mleft\{\begin{aligned}-0.5x+3,-6\le x\le-2 \\ -3,-2

If the average-size man with a parachute jumps from an airplane, he will fall12.5(0.2^t– 1) + 21t feet in t seconds. How long will it take him to fall 170 feet?(Round your answers to two decimal places.)=_______sec

Answers

The equation relating time and fall height is given by

[tex]h(t)=12.5(0.2^t-1)+21t[/tex]

We want to find out how long will it take him to fall 170 feet?

Let us substitute h(t) = 170

[tex]170=12.5(0.2^t-1)+21t[/tex]

Now let's solve the equation

[tex]\begin{gathered} 170=12.5(0.2^t-1)+21t \\ 170=2.5^t-12.5+21t \\ 170+12.5=2.5^t+21t \\ 182.5=2.5^t+21t \end{gathered}[/tex]

Taking log on both sides

[tex]\ln (182.5)=\ln (2.5^t)+\ln (21t)_{}[/tex]

Using a given zero to a polynomial as a product of linear factors complex zeros

Answers

When we have a polynomial of higher degree bu we know some of its zeros, we can use synthetic division to factor the polynomial and solve the remaining factors.

We have apolynomial of fourth degree, and we know that 1 is a zero with multiplicity two, that is, the polynomial have two factors (x - 1), so it can be rewritten as:

[tex]x^4-6x^3+22x^2-30x+13=(ax^2+bx+c)(x-1)(x-1)=(ax^2+bx+c)(x-1)^2[/tex]

To find out the quadratic fator, we can do the synthetic division by 1 twice.

To do this, e start by writing 1 and the coefficients of the polynomial:

1 | 1 -6 22 -30 13

|

| 1

The leading coefficient was also copied to the last row. Now, we will do the following repeatedly:

- multiply the number on the last row of the column we are by the divisor "1" and put the result under the next coefficient (the column to the right).

- add the two rows of this next coefficient and put the result in the last row.

- repeat

So:

1 | 1 -6 22 -30 13

| 1

| 1 -5

1 | 1 -6 22 -30 13

| 1 -5

| 1 -5 17

1 | 1 -6 22 -30 13

| 1 -5 17

| 1 -5 17 -13

1 | 1 -6 22 -30 13

| 1 -5 17 -13

| 1 -5 17 -13 0

Now, the 4 first numbers in the last row are the coefficients of the polynomial that is the result, and the last is the remainder, which is zero because 1 is a zero of the original polynomial.

Now, we can rewrite the polynomial as:

[tex]x^4-6x^3+22x^2-30x+13=(x^3-5x^2+17x-13)(x-1)[/tex]

Now, we take this third degree polynomial and divide again by 1:

1 | 1 -5 17 -13

|

| 1

1 | 1 -5 17 -13

| 1

| 1 -4

1 | 1 -5 17 -13

| 1 -4

| 1 -4 13

1 | 1 -5 17 -13

| 1 -4 13

| 1 -4 13 0

Now, we can rewrite the third degree polynomial as:

[tex]x^3-5x^2+17x-13=(x^2-4x+13)(x-1)[/tex]

So, the original becomes:

[tex]x^4-6x^3+22x^2-30x+13=(x^2-4x+13)(x-1)^2[/tex]

Now, to finish the factoring, we can find the zeros of the quadratic factor, which we can do by using the quadratic formula:

[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}=\frac{-(-4)\pm\sqrt[]{(-4)^2-4(1)(13)}}{2(1)}=\frac{-4\pm\sqrt[]{16-52}}{2} \\ x=\frac{-4\pm\sqrt[]{-36}}{2}=\frac{-4\pm6i}{2}=-2\pm3i \\ x_1=-2-3i \\ x_2=-2+3i \end{gathered}[/tex]

So, we can write the quadratic factor as:

[tex]x^2-4x+13=(x-(-2-3i))(x-(-2+3i))=(x+2+3i)(x+2-3i)[/tex]

So, the original polynomial as a product of linear factors is:

[tex]f(x)=(x+2+3i)((x+2-3i)(x-1)^2[/tex]

Marcos is building a dog run for his new puppy. He has enough money to buy 75 feet of fencing. He wants to fence in a rectangulararea and it should be at least twice as long as it is wide. Which system of inequalities represents the possible lengths L and widths Wfor his dog run?

Answers

Let the length of the fence be L

Let the wide of the fence be W

Since, he can afford 75 feet fencing

Therefore, the perimeter of the fence = 75

Perimeter = 2( L + W)

The length of the fence should be twice as long as the wide

W = 2L

P = 75

2(L + 2L) < = 75

for the given function, state the amplitude and the minimum output for the function.

Answers

Explanation:

Let the following function:

[tex]f(x)=A\cos(Bx\text{ -C})\text{ + D}[/tex]

by definition, the amplitude of this function is the absolute value of A.

Now, consider the following function:

[tex]f(t)=3\cos(\frac{6}{5}t)[/tex]

then, by definition, the amplitude of this function would be:

[tex]|3|\text{ = 3}[/tex]

now, to find the minimum output of the given function we can use the first derivative criterion:

Notice that the critical points would be:

[tex]t=\frac{5\pi}{3}n,\text{ t=}\frac{5\pi}{6}+\frac{5\pi}{3}n[/tex]

now, the domain of f(x) is:

[tex]\text{ -}\infty\text{ < t <}\infty[/tex]

thus, the interval where the function is decreasing is:

[tex]\frac{5\pi}{3}n\text{ < t < }\frac{5\pi}{6}+\text{ }\frac{5\pi}{3}n[/tex]

and the interval where the function is increasing is:

[tex]\frac{5\pi}{6}+\frac{5\pi}{3}n\text{ < t < }\frac{5\pi}{3}n\text{ + }\frac{5\pi}{3}[/tex]

thus, we can conclude that the minimum output occurs when

[tex]t=\text{ }\frac{5\pi}{6}+\frac{5\pi}{3}n[/tex]

and this output would be - 3.

Then, the correct answer is:

Answer:

When triangles ABC is reflected across line AB, the image is triangle ABD. Why is angle ACD congruent to angle ADB?

Answers

When we reflect the triangle ABC across AB, segments AD and AC are equal in length. Therefore, triangle ADC is an Isosceles triangle as it has two sides of the same measure.

Then, AC and AD are the legs of an Isosceles triangle; thus, angles The answer is An isosceles triangle has a pair of congruent angles.

a. Deshaun's test score average increased by 8 points this semester. Write a signed number to represent this change in average. b. Ali lost 75 dollars from his pocket. Write a signed number to represent this change.

Answers

We have the following:

"Deshaun's test score average increased by 8 points this semester. Write a signed number to represent this change in average."

Because it is an increase, the sign is positive

The answer is +8

Ali lost 75 dollars from his pocket. Write a signed number to represent this change.​

Because it is a loss, the sign is negative

The answer is -75

What’s the exponential function of g?X 0,1,2,3,4 g(x) 1,3,9,27,81

Answers

In order to find the exponential function g(x), let's use the model below for an exponential function:

[tex]g(x)=a\cdot b^x[/tex]

Using the points (0, 1) and (1, 3), we have:

[tex]\begin{gathered} (0,1)\colon \\ 1=a\cdot b^0 \\ a=1 \\ \\ (1,3)\colon \\ 3=1\cdot b^1 \\ b=3 \end{gathered}[/tex]

Therefore the equation is g(x) = 3^x.

Gretchen's gross annual salary is $34,788. What is the maximum amount of rent shecan afford to pay per month? Round answer to the nearest whole number.

Answers

Given:

Grethen's gross annual salary = $34, 788

The maximum amount of rent she can afford to pay per month can be found using the formula:

[tex]\text{Max amount of rent she can pay = }\frac{Gross\text{ annual salary}}{Number\text{ of months in a year}}[/tex]

Applying the formula:

[tex]\begin{gathered} \text{Max amount of rent she can pay= }\frac{34788}{12} \\ =\text{ \$2899} \end{gathered}[/tex]

Hence, the maximum amount of rent she can afford to pay per month is $2899

Answer: $2899

keisha eric and carlos served a total of 120 orders monday at the school cafeteria. eric served 3 times as many orders as carlos. keisha served 10 more orders than carlos. how many orders did they each serve

Answers

Let the number of orders served by Carlos be x, so

Eric = 3x

Keisha = 10 + x

then, we have:

[tex]\text{Carlos + Eric+ Keisha = 120 }[/tex]

so

[tex]\begin{gathered} x+3x+10+x=120 \\ 5x+10=120 \\ 5x+10-10=120-10 \\ 5x=110 \\ \frac{5x}{5}=\frac{110}{5} \\ x=22 \end{gathered}[/tex]

therefore, the answer is:

Carlos = 22 orders

Eric = 3(22) = 66 orders

Keisha = 10 + 22 = 32 orders

On each right triangle ,find the tangent of each angle that is not the right angle.Number 2.

Answers

Given the triangle ABC, you know that:

[tex]\begin{gathered} AB=10 \\ AC=6 \\ BC=8 \end{gathered}[/tex]

You can identify that the small square in the vertex C of the triangle is a Right Angle (an angle that measures 90 degrees). Therefore, you have to find the tangent of the other two angles:

[tex]\begin{gathered} \angle A \\ \angle B \end{gathered}[/tex]

By definition:

[tex]tan\theta=\frac{opposite}{adjacent}[/tex]

Then:

- For angle A, you can identify that:

[tex]\begin{gathered} \theta=A \\ opposite=BC=8 \\ adjacent=AC=6 \end{gathered}[/tex]

Therefore:

[tex]\begin{gathered} tan(A)=\frac{8}{6} \\ \\ tan(A)=\frac{4}{3} \end{gathered}[/tex]

- For angle B:

[tex]\begin{gathered} \theta=B \\ opposite=AC=6 \\ adjacent=BC=8 \end{gathered}[/tex]

Therefore, you get:

[tex]\begin{gathered} tan(B)=\frac{6}{8} \\ \\ tan(B)=\frac{3}{4} \end{gathered}[/tex]

Hence, the answer is:

[tex]\begin{gathered} tan(A)=\frac{4}{3} \\ \\ tan(B)=\frac{3}{4} \end{gathered}[/tex]

What is the intermediate step in the form (x + a)2 = b as a result of completing thesquare for the following equation?6x2 +962 - 13 = -132.Submit Answerattempt 1 out of 2

Answers

First step is to separate the terms with variables from the constant terms.

Add 13 to both sides of the equation :

[tex]\begin{gathered} 6x^2+96x-13=-13 \\ 6x^2+96x-\cancel{13}+\cancel{13}=-13+13 \\ 6x^2+96x=0 \end{gathered}[/tex]

Divide both sides by 6 :

[tex]\begin{gathered} 6x^2+96x=0 \\ x^2+16x=0 \end{gathered}[/tex]

Next step, completing the square by adding this term to both sides of the equation :

[tex](\frac{b}{2a})^2[/tex]

From the equation,

a = 1

b = 16

So it follows that :

[tex](\frac{b}{2a})^2=(\frac{16}{2\times1})^2=(8)^2[/tex]

Adding this to both sides of the equation :

[tex]\begin{gathered} x^2+16x=0 \\ x^2+16x+8^2=8^2 \end{gathered}[/tex]

And you will get a perfect square trinomial on the left side of the equation in the form :

[tex]x^2+bx+c^2[/tex]

It can be factored as :

[tex]x^2+bx+c^2=(x+c)^2[/tex]

So the equation will be :

[tex]\begin{gathered} x^2+16x+8^2=8^2 \\ (x+8)^2=8^2 \\ (x+8)^2=64 \end{gathered}[/tex]

The answer is :

[tex](x+8)^2=64[/tex]

Other Questions
I need help will this besin A =a/c or the followingsin A =b/csin A =b/asin A =c/bsin A =c/asin A =a/csin A =a/b the table below shows Luke's golf score each week he participated in a golf tournament used to line of best fit to estimate Lux score for week 12 What would make the following equation true? -4+_____=2m+(3m-4)A: -5mB: -4mC: -1mD: 6mE: 5m group of college students bought a couch for $80. However, five of them failed to pay their share so the others had to each pay $8 more. How many students were in the original group? Edlyn could hear her named being called out for the third time as she mentally rehearsed the Thanksgiving poem. Mrs. Barth had given Edlyn the opportunity to recite the Thanksgiving poem in front of her favorite poet, who was sitting among the panel of judges. At first, Edlyn was thrilled with this idea, but now, moments before the event, she was trembling with anxiety. Seeing her miserable condition, Edlyn's friend Veronica hugged her and whispered comforting words in her ears. Hearing her friend's supportive words and seeing her confident smile, Edlyn's nervousness faded away and she felt ready to be on stage.Which is the best summary of the paragraph? A. Edlyn feels nervous about reciting a Thanksgiving poem in front of her favorite author. Her friend Veronica comforts her, and Edlyn feels more confident about performing on stage. B. Edlyn panics because she hears her name being called out for the third time on stage for the recitation of the Thanksgiving poem. In the end, Edlyn decides not to go as she feels too nervous. C. Edlyn finds out that her favorite poet is going to be among the panel of judges. To impress him, Edlyn decides to recite a Thanksgiving poem in front of him and the entire school. D. Edlyn trembles with anxiety as she realizes she has to recite the Thanksgiving poem she wrote in front of her favorite poet. Edlyn's friend Veronica sees this and wonders how she can comfort her friend. Find the amount of aluminum needed to make this bucket. Include the base.90cm at top 30.6 cm on the side24 cm in the middle52cm at the bottom Part A: complete the statement below about inscribed quadrilateralsPart B: select all of the statements that are true Find the length of ZX to the nearest tenth of a foot. simplify the following expreission(2m^3 -5m+3m^2) + (4+5m^2-2m) please help ASAP!!!!! There is a population of 9,000 bacteria in a colony. If the number of bacteria doubles every 245 hours, what will the population be 980 hours from now? a 20-acre Orchard is planted with apple and peach trees at most $10,000 going to be spent on planting cost planting cost for apple trees $400 per acre in for peach trees $1,000 per acre choose the best graph that shows the area of each crop that can be planted If The last frame before the shuttle begins to move is 140 and the shuttle travels 56 meters in 243 frames. (a) If each frame is 24 seconds what is the time elapsed?(b) Assuming constant acceleration, at what rate is the shuttle accelerating?(c) If the shuttle continued to move with thisacceleration, what speed would it reach 76s after launch?(d) If the shuttle traveled directly upwards, what would its altitude be at 76 s? A movie club surveyed 150 high school students. The students were asked how often they go to the movies and whether they prefer action movies or comedies.Thelr responses are summarized in the following table.Twice a month Three times a monthAction4527Comedy 6612or lessor more(a) What percentage of the students go to the movies three times a month or more?(b) What percentage of the students prefer action movies ?(a) 0965?(b) 1%Submit AContinue2021 McGraw Hill LLC. All Rights Reserved. Terms of Use Privacy Center Boyle's Law says that the volume of a gas varies inversely with the pressure. When the volume of a certain gas is 2 L, the pressure is 1165 kPa (kilopascals),What is the volume when the pressure is 466 kPa ? I dont understand what it means to divide You can pick any question to solve. I really need help though...If you solve all of it, I'll give you 115 points. ive got this due tomorrow and i literally CANNOT find the answer keys so imma need help in these three Directions: Solve each equation. Check your solution(s) then indicate whether or not the solutions are extraneous. When you throw a penny and a nickel what is the probability of both the coins landing tails