PLEASE HELP ME ASAp!!!!!!

To solve for the distance from the base of the cliff, the time to hit the ground is calculated from the initial vertical velocity and the height of the cliff. The horizontal distance is then found by multiplying the time by the horizontal component of the initial velocity.

To determine how far from the base of the cliff a bullet strikes the ground, we use the concepts of projectile motion. The initial velocity components are [tex]v_{0x} = 800 \cos(30^{\circ}) m/s[/tex] (horizontal component) and v_{0y} = [tex]800 \sin(30^{\circ}) m/s[/tex](vertical component downwards). The time it takes for the bullet to hit the ground can be found using the equation for vertical motion: y =[tex]v_{0y}t + \frac{1}{2}gt^2[/tex], where y is the height of the cliff, g is the acceleration due to gravity [tex](-9.8 m/s^2[/tex] since the bullet is moving downwards), and t is the time. Solving for t we get two possible times, but we choose the positive one. Once we have t, we can find the horizontal distance using x = v_{0x}t. Using these calculations, the appropriate distance from the base of the cliff can be determined.

Answer:

Estimate

Step-by-step explanation:

Estimation is the process by which we deduce a close value to the required value through the method of approximation.

A graph is one of the tools used for finding the exact value of a limit. It can help us to approximate a limit by allowing us to estimate the finite value we're approaching as we get closer asymptotically to some independent variable values.

When working with graphs, the best we can do is estimate the value of limits in an appropriate step or procedure.

Therefore, the great fall back plan hen working with graph is to estimate.

Answer: Create a t-chart to graph the coordinates

Answer:

The linear equation that represent this problem is [tex]y=50x-2,500[/tex]

Step-by-step explanation:

Let

x -----> the number of people

y ----> the profit in dollars

we have

For x=100, y=2,500

and

For x=80, y=1,500

Find the slope m

we have

(80,1,500) and (100,2,500)

The slope is equal to

[tex]m=(2,500-1,500)/(100-80)\\ \\m=50\frac{\$}{people}[/tex]

Find the equation of the line into point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=50[/tex] and point (100,2,500)

substitute

[tex]y-2,500=50(x-100)[/tex] ----> equation in slope point form

Convert to slope intercept form

[tex]y=50x-5,000+2,500[/tex]

[tex]y=50x-2,500[/tex]

Answer: a.) 3

Step-by-step explanation:

Using the common convention that the horizontal axis represents variable x and the vertical axis represents variable y, then x-intercept or horizontal intercept is a point where the graph of the function intersects the x-axis of the coordinate system. As such, these points satisfy y = 0 where the line crosses the x-axis.

Then replacing this value in the equation

2x-3y = 6

2x - 3*0 = 6

2x = 6

x = 6/2 = 3

The x-intercept is 3

Answer: a.) 3

[tex]\textit{\textbf{Spymore}}[/tex]

Answer:

a 3

Step-by-step explanation:

Given

2x - 3y = 6

To find the x- intercept substitute y = 0 into the equation and solve for x

2x - 3(0) = 6

2x = 6 ( divide both sides by 2 )

x = 3 ← x- intercept

Answer:

624 people

(I put two ways to look at the problem.)

Step-by-step explanation:

What is describe here is an exponential function of the form:

[tex]P=P_0 e^{kt}[/tex]

[tex]t[/tex] is the number of years after 1761.

[tex]P_0[/tex] is the initial population.

So t=0 represents year 1761.

t=1 represents year 1762

t=2 represents year 1763

....

t=20 represents year 1781.

So we have the doubling time is 5 years.  This means the population will be twice what it was in 5 years.  Let's plug this into:

[tex]P=P_0e^{kt}[/tex]

[tex]2P_0=P_0e^{k\cdot 5}[/tex]

Divide both sides by [tex]P_0[/tex]:

[tex]2=e^{5k}[/tex]

Convert to logarithm form:

[tex]5k=\ln(2)[/tex]

Multiply both sides by 1/5:

[tex]k=\frac{1}{5}\ln(2)[/tex]

[tex]k=\ln(2^{\frac{1}{5}})[/tex] By power rule.

So in the next sentence they actually give us the initial population and we just found k so this is our function for P:

[tex]P=39e^{\ln(2^{\frac{1}{5}})t}[/tex]

So now we plug in 20 to find how many residents there were in 1761:

[tex]P=39e^{\ln(2^{\frac{1}{5}})(20)}[/tex]

This is surely going to the calculator:

[tex]P=624[/tex]

Now if you don't like that, let's try this:

Year 0 we have 39 people.

Year 5 we have 39(2)=78 people.

Year 10 we have 78(2)=156 people.

Year 15 we have 156(2)=312 people.

Year 20 we have 312(2)=624 people.

Answer:

[tex]\large\boxed{(2,2)}[/tex]

Step-by-step explanation:

In this question, we're trying to find the midpoint of the line segment "ST"

In order to find the midpoint, we're going to need to sue the midpoint formula.

Mid point formula:

[tex]m=({\frac{x1+x2}{2}},\frac{y1+y2}{2})[/tex]

You would plug the numbers into the right spot. Plugging the first "x" coordinate to x1 and etc.

Your equation should look like this:

[tex]m=({\frac{-2+6}{2}},\frac{-4+8}{2})[/tex]

Now you will solve:

[tex]m=({\frac{-2+6}{2}},\frac{-4+8}{2})\\\\\text{Lets add all the numbers}\\\\m=({\frac{4}{2}},\frac{4}{2})\\\\\text{Now, you would simply divide the fractions}\\\\m=(2,2)[/tex]

When you're done solving, you should get (2,2)

This means that the midpoint of ST is (2,2)

The formula for midpoint is ([tex]\frac{x_{1}+x_{2}}{2}[/tex], [tex]\frac{y_{1}+y_{2}}{2}[/tex])

In this case:

[tex]x_{1} =-2\\x_{2} =6\\y_{1} =-4\\y_{2} =8[/tex]

^^^Plug in these number into the formula given above...

([tex]\frac{-2 + 6}{2}[/tex], [tex]\frac{-4 + 8}{2}[/tex])

([tex]\frac{4}{2}[/tex], [tex]\frac{4}{2}[/tex])

Simplify the fractions:

(2, 2)

^^^This is the coordinate of the midpoint

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

[tex]a_n=9(4^{n-1})[/tex]

Step-by-step explanation:

we know that

In a Geometric Sequence each term is found by multiplying the previous term by a constant, called the common ratio (r)

In this problem we have

[tex]a_2=36\\ a_5=2,304[/tex]

Remember that

[tex]a_2=a_1(r)[/tex] -----> [tex]36=a_1(r)[/tex] -----> equation A

[tex]a_5=a_4(r)[/tex]

[tex]a_5=a_3(r^{2})[/tex]

[tex]a_5=a_2(r^{3})[/tex]

Substitute the values of a_5 and a_2 and solve for r

[tex]2,304=36(r^{3})[/tex]

[tex]r^{3}=2,304/36[/tex]

[tex]r^{3}=64[/tex]

[tex]r=4[/tex]

Find the value of a_1 in equation A

[tex]36=a_1(4)[/tex]

[tex]a_1=9[/tex]

therefore

The explicit rule for the nth term is

[tex]a_n=a_1(r^{n-1})[/tex]

substitute

[tex]a_n=9(4^{n-1})[/tex]

Answer:

an=9(4^n-1)

Step-by-step explanation:

so, we know his average speed is 1¾ of a mile in 1 hour, so how long is it to cover 9⅝ miles then?

[tex]\bf \begin{array}{ccll} miles&hour\\ \cline{1-2} 1\frac{3}{4}&1\\\\ 9\frac{5}{8}&x \end{array}\implies \cfrac{~~1\frac{3}{4}~~}{9\frac{5}{8}}=\cfrac{1}{x}\implies \cfrac{~~\frac{1\cdot 4+3}{4}~~}{\frac{9\cdot 8+5}{8}}=\cfrac{1}{x}\implies \cfrac{~~\frac{7}{4}~~}{\frac{77}{8}}=\cfrac{1}{x}[/tex]

[tex]\bf \cfrac{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 4 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{2}{~~\begin{matrix} 8 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{\underset{11}{~~\begin{matrix} 77 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}} =\cfrac{1}{x}\implies \cfrac{2}{11}=\cfrac{1}{x}\implies 2x=11\implies x=\cfrac{11}{2}\implies x=5\frac{1}{2}[/tex]

The required time is 5.5 hours.

Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1.

It is given that,

Speed=[tex]1\frac{3}{4}[/tex] mile per hour.

Distane:=[tex]9\frac{5}{8}[/tex] mile

[tex]Time=\frac{Distance}{Speed}[/tex]

Now, substituting the given values into the above formula we get,

[tex]T=\frac{\frac{77}{8} }{\frac{7}{4} }\\ =\frac{77\times4}{8\times 7} \\=\frac{11}{2}\\ T=5.5 hour[/tex]

Learn more about the time:https://brainly.com/question/19668173

Answer:

True.

Step-by-step explanation:

If the sides of one triangle are lengths 2,4 and 6 and another triangle has sides of lengths 3,6 and 9 then the triangles are similar.

Answer:

5

Step-by-step explanation:

The radius is a distance on a circle from the center to a point on the circle.

We have both of these points describe here in this definition.  Using the distance formula will give us the radius.

[tex]\sqrt{(x \text{ difference })^2+(y \text{ difference})^2[/tex]

The difference between 1 and -3 is 1-(-3)=4.

The difference between 5 and 2 is 5-2=3.

[tex]\sqrt{4^2+3^2}[/tex]

[tex]\sqrt{16+9}[/tex]

[tex]\sqrt{25}[/tex]

[tex]5[/tex]

Answer:

A. good

Step-by-step explanation:

it is in the range of 660-749.

Answer:

"Good"

Step-by-step explanation:

"Good" is appropriate, because the score 726 is between 660 and 749.

Answer:

Option 2

Step-by-step explanation:

Given

B = (-6,1)

B' = (-3,-2)

Step 1: Substitute the original and translated coordinates into (x,y) => (x+a,y+b)

B(-6,1) => B'(-6+a , 1+b) = B'(-3,-2)

Step 2: Write two equations

-6+a = -3 => a = -3+6 = 3

1+b=-2 => b = -2-1 = -3

Hence, we can conclude that Indira wrote the equations wrong which was her first error.

Therefore, Option 2 is correct ..

Answer:

B. You had a math test on Thursday

Step-by-step explanation:

B is most likely the answer because you would have a math test regardless of the weather. Teachers do stuff like that. Also I just took this quiz on APEX.

Answer:

Question 1

Part A: The total length of sides 1, 2, and 3 is (8y² + 8y - 10)

Part B: The length of the fourth side is 22y³ + 2y² + 2y - 7

Part C: Yes the answers for Part A and Part B show that the polynomials are closed under addition and subtraction

Question 2

Part A: The expression of the area of the square is 4x² - 20x + 25

Part B: The degree and classification of the expression obtained in part A

are second degree and trinomial

Part C: The polynomials are closed under multiplication

Question 3

Part A: The function of the area of the circle of spilled oil is 49 πt²

Part B: The area of the spilled oil after 8 minutes is 9847.04 units²

Step-by-step explanation:

* Lets explain how to solve the problems

# Question 1

∵ The length of the three sides of a quadrilateral are

- Side 1: 4y + 2y² - 3

- Side 2: -4 + 2y² + 2y

- Side 3: 4y² - 3 + 2y

- The perimeter of the quadrilateral is 22y³ + 10y² + 10y − 17

* Part A:

- To find the total length of sides 1, 2, and 3 of the quadrilateral

  add them

∴ s1 + s2 + s3 = (4y + 2y² - 3) + (-4 + 2y² + 2y) + (4y² - 3 + 2y)

- Collect the like terms

∴ S1 + S2 + S3 = (2y² + 2y² + 4y²) + (4y + 2y + 2y) + (-3 + -4 + -3)

∴ S1 + S2 + S3 = 8y² + 8y + (-10) = 8y² + 8y - 10

* The total length of sides 1, 2, and 3 is (8y² + 8y - 10)

* Part B:

∵ The perimeter of the quadrilateral is the sum of its 4 sides

∴ The length of its fourth side is the difference between its

   perimeter and the sum of the other 3 sides

∵ The perimeter of the quadrilateral is 22y³ + 10y² + 10y − 17

∵ The sum of the three sides is (8y² + 8y - 10)

∴ The length of the 4th side = (22y³ + 10y² + 10y − 17) - (8y² + 8y - 10)

- Remember that (-)(+) = (-) and (-)(-) = (+)

∴ S4 = 22y³ + 10y² + 10y - 17 - 8y² - 8y + 10

- Collect the like terms

∴ S4 = (22y³) + (10y² - 8y²) + (10y - 8y) + (-17 + 10)

∴ S4 = 22y³ + 2y² + 2y + (-7) = 22y³ + 2y² + 2y - 7

* The length of the fourth side is 22y³ + 2y² + 2y - 7

* Part C:

- Polynomials will be closed under an operation if the operation

 produces another polynomial

∵ In part A there are 3 polynomials add to each other and the answer

  is also polynomial

∴ The polynomials are closed under addition

∵ In part B there are 2 polynomial one subtracted from the other and

  the answer is also polynomial

∴ The polynomials are closed under subtraction

* Yes  the answers for Part A and Part B show that the polynomials

  are closed under addition and subtraction

# Question 2

∵ The side of a square measure (2x - 5) units

* Part A:

∵ The are of the square = S × S, where S is the length of its side

∵ S = 2x - 5

∴ The area of the square = (2x - 5) × (2x - 5)

- Multiply the two brackets using the foil method

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

∴ (2x - 5)(2x - 5) = 4x² + (-10x) + (-10x) + 25

- Add the like terms

∴ (2x - 5)(2x - 5) = 4x² + (-20x) + 25 = 4x² - 20x + 25

∴ The area of the square = 4x² - 20x + 25

* The expression of the area of the square is 4x² - 20x + 25

* Part B:

∵ The greatest power in the expression obtained in Part A is 2

∴ Its degree is second

∵ The expression obtained in part A has three terms

∴ The expression obtained in Part A is trinomial

* The degree and classification of the expression obtained in Part A

  are second degree and trinomial

* Part C:

- Polynomials will be closed under an operation if the operation

 produces another polynomial

∵ (2x - 5) is polynomial

∵ (4x² - 20x + 25) is polynomial

∴ The product of two polynomials give a polynomial

∴ The polynomials are closed under multiplication

# Question 3

∵ n(t) = 7t, where t represents time in minutes and n represents how

  far the oil is spreading

∵ The area of the pattern can be expressed as A(n) = πn²

* Part A:

- To find the area of the circle of spilled oil as a function of time, then

  find the composite function A[n(t)]

- That means replace n in A(n) by the function n(t)

∵ n(t) = 7t

∴ A[n(t)] = A(7t)

∵ A(n) = πn²

- Replace n by 7t

∴ A(7t) = π (7t)² = 49 πt²

∴ A[n(t)] = 49 πt²

* The function of the area of the circle of spilled oil is 49 πt²

* Part B:

∵ The area of the circle of spilled oil in t minutes = 49 πt²

- To find the area of the circle of spilled oil after 8 minutes substitute

  t by 8

∴ Area of the spilled oil after 8 minutes = 49 π (8)²

∵ π = 3.14

∴ Area of the spilled oil after 8 minutes = 49(3.14)(64) = 9847.04

* The area of the spilled oil after 8 minutes is 9847.04 units²

Answer:

The graph is stretched by a factor of 2, moves 2 units to the left, and 1 unit up.

Step-by-step explanation:

The base of the quadratic function is

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

We can transform this function to look narrower or wider.

Looking narrower is termed a stretch.

This happens when a>1

Looking wider is termed a compression.

This happens when 0<a<1

We can also

[tex]g(x) = a {(x + h)}^{2} + k[/tex]

+h moves the parent graph to the left by h units

-h moves the parent graph to the left by h units.

+ k moves the parent function up by k units

- k moves the parent function down by k units.

The change that occurs to

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

given

[tex]f(x) = 2( {x + 2)}^{2} + 1[/tex]

is that, the graph is stretched by a factor of 2, moves 2 units to the left, and 1 unit up

Therefore the last choice is the correct answer.

Answer:

The correct option is B....

Step-by-step explanation:

The  given equation is:

x + 2y = 12  -----equation 1

- x= -y-6. -------equation 2

lets take equation 2:

-x=-y-6

Take minus as common on R.H.S

-x= -(y+6)

x=y+6  (Lets call it equation 3)

Substitute the value of x in the first equation:

x+2y=12

y+6+2y=12

Combine the like terms:

y+2y = 12-6

3y=6

Divide both the sides by 3

3y/3=6/3

y=2

Now substitute the value of y in equation 3:

x=y+6

x=2+6

x=8

Thus the solution set is (x,y){(8,2)}.

The correct option is B....

Answer:

B. (8,2)

Step-by-step explanation:

Apex

Hope this helps Have a nice day

Answer:

[tex]\frac{1}{x+4}[/tex]

Step-by-step explanation:

because you want to do [tex]\frac{x}{x+4}[/tex] divided by 4 which would end up being [tex]\frac{x}{x(x+4)}[/tex] then you cancel out the x and you are left with [tex]\frac{1}{x+4}[/tex]

For this case we must find an expression equivalent to:

[tex]\frac {\frac {x} {x + 4}} {x}[/tex]

Applying double C we have:

[tex]\frac {x} {x (x + 4)} =[/tex]

We simplify common terms of the numerator and denominator:

[tex]\frac {1} {x + 4}[/tex]

Finally we have:

[tex]\frac {1} {x + 4}[/tex]

Answer:

[tex]\frac {1} {x + 4}[/tex]

Step-by-step explanation:

both are obtuse angles

and

angle 2 = angle 3

they are also alternative interior angles

Answer:

A

Step-by-step explanation:

let y = f(x) and rearrange making x the subject, that is

y = x - 1 ( add 1 to both sides )

y + 1 = x

change y back into terms of x, hence

[tex]f^{-1}[/tex] (x ) = x + 1 → A

the correct (answer)

is A f1(x)=x+1

Answer:

RS/VU=ST/UT and ∠S≅∠U

Step-by-step explanation:

we know that

The Side-Angle-Side Similarity Theorem states that: If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar

In this problem the included angle is

∠S≅∠U

therefore

side RS must be proportional to side VU  and side ST must be proportional to side UT

so

RS/VU=ST/UT

Verify

substitute the given values

12/6=16/8

2=2 -----> is true

therefore

The two sides are proportional

Answer:

The answer is -3x^2+2x+7 ....

Step-by-step explanation:

(3x2 + 2x - 9) - (6x2 - 16)

Open the parenthesis

Keep in mind that when you will open the parenthesis the signs of 2nd bracket will be multiplied by negative sign

3x^2+2x-9-6x^2+16

Arrange the terms:

3x^2-6x^2+2x+16-9

Solve the like terms:

= -3x^2+2x+7

Thus the answer is -3x^2+2x+7 ....

= (3x²+2x-9) - (6x²-16)

= 3x² + 2x - 9 - 6x² +16

= -3x² +2x + 7

While opening the brackets, make sure you change the signs accordingly. If there is a "-" sign outside the bracket then while opening the brackets, terms inside change their signs, which means "+" becomes "-" and vice versa.

Answer:

[tex](x-1)^2+(y-4)^2=4[/tex].

Step-by-step explanation:

So the standard form of a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex] where (h,k) is the center and r is the radius.

You are given (h,k)=(1,4) and r=2.

So we are going to plug in 1 for h, 4 for k, and 2 for r:

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

[tex](x-1)^2+(y-4)^2=2^2[/tex]

[tex](x-1)^2+(y-4)^2=4[/tex].

Answer:

(x-1)^2 + (y+4)^2 = 4

Step-by-step explanation:

APEXXXX

He afford 5 games at bowling alley C.

Comparing Numbers means identifying a number that is smaller or greater than the rest. We can compare numbers using different methods such as on a number line, by counting, or by counting the number of digits, using place values of the numbers, etc.

According to the topic , we know

4 games at bowling alley B need to speed [tex]4 \times 5.25 = 21 > 20[/tex]

5 games at bowling alley C need to speed [tex]5 \times 3.75 =18.75 < 20[/tex]

5 games at bowling alley A need to speed [tex]5 \times 4.25 = 21.25 > 20[/tex]

6 games at bowling alley D need to speed [tex]6 \times 3.50 = 21 > 20[/tex]

So, the answer is 5 games at bowling alley C.

Option B is correct.

He afford 5 games at bowling alley C.

Find out more information about comparison of numbers here

brainly.com/question/13505153

#SPJ2

Answer:

the only answers are 8 and 5

Answer:

36

Step-by-step explanation:

We have to compute 4 distances and then add them up.

It may help to draw this first to see which distances to compute.

So I'm going to start with computing the distance from (0,0) to (5,12), then from (5,12) to (9,9), then from (9,9) to (12,5), and then finally from (12,5) to (0,0).

So distance from (0,0) to (5,12)

d=sqrt((5-0)^2+(12-0)^2)=sqrt(25+144)=sqrt(169)=13

Distance from (5,12) to (9,9)

d=sqrt((9-5)^2+(12-9)^2)=sqrt(4^2+3^2)=sqrt(16+9)=sqrt(25)=5

Distance from (9,9) to (12,5)

d=sqrt((12-9)^2+(9-5)^2)=sqrt(3^2+4^2)=sqrt(9+16)=sqrt(25)=5

Distance from (12,5) to (0,0)

d=sqrt((12-0)^2+(5-0)^2)=sqrt(12^2+5^2)=sqrt(144+25)=sqrt(169)=13.

Up all of our distances 13+5+5+13=(13+13)+(5+5)=26+10=36

Answer:

c. 36

Step-by-step explanation:

that is what that one says up there

Answer: Z=30.8 when X=14 and Z=16.7 when Y=7

Step-by-step explanation:

Z is directly proportional to X: Z=K*X, Where K is a constant

Z is inversely proportional to Y:[tex]Z=\frac{K_{1} }{Y}[/tex] where [tex]K_{1}[/tex] is another constant.

When Z=19.5 ,   X=9 , Using this condition we find K value  

19.5=K*9 so, K=[tex]K=\frac{19.5}{9}[/tex]=2,2

When Z=19.5 ,   Y=6 , Using this condition we find [tex]K_{1}[/tex] value  

19.5=[tex]\frac{K_{1} }{6}[/tex] so, [tex]K_{1}[/tex]=19.5*6=117

So, When X=14,  Z= 2.2*14=30.8

When Y=7  Z= [tex]\frac{117}{7}[/tex]=16.7

Answer:

A line where you put it in the middle of the shape and see if it's symmetrical or the same. You fold the shape and if one side matches to other, that is symmetrical. That is the line of symmetry.

A line of symmetry divides a figure into two parts such that each part is the mirror image of the other. In other words, if we flip one side of the figure over the line of symmetry, it should match up exactly with the other side.

Answer:

The correct answer is second option  option

9¹/⁸ ˣ

Step-by-step explanation:

Points to remember

Identities

ᵃ√x = = x¹/ᵃ

√x = x¹/²

(xᵃ)ᵇ = xᵃᵇ

To find the correct option

It s given that,

(⁴√9)¹/² ˣ

By using the above identities we can write,

(⁴√9)¹/²ˣ = (9¹/⁴)¹/²ˣ     [ since ⁴√9 = 9¹/⁴]

 = 9⁽¹/⁴ * ¹/²⁾ ˣ

 = 9¹/⁸ ˣ

Therefore the correct answer is second option  option

9¹/⁸ ˣ

Answer:

the answer you picked is the right one.

Answer: 11.18

Step-by-step explanation:

You’re substituting 5 for x in the equations...

Sqrt[x^2+4x^2]

Sqrt[5^2+4(5)^2]

Sqrt[25+4(25)]

Sqrt[25+100]

Sqrt[125]

In the provided equation, substituting x with 5 and simplifying gives us the square root of 425, which is approximately 20.6. Therefore, the estimated length of the ladder when the base is 5 ft from the wall is about 20.6 feet.

In this problem, the length of the ladder should be the square root of the sum (x)^2 and (4x)^2. In this equation, you're given that the base of the ladder is 5 feet from the wall, represented by 'x'. First substitute x with 5 into the equation: √[(5)^2 + (4*5)^2]. This simplifies to √[25 + 400] = √425. The square root of 425 is about 20.6. Therefore, if you round it to the nearest tenth, the desired length of the ladder when the base is positioned 5 ft from the wall is approximately 20.6 feet.

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