The two triangles formed by the flagpole and the man shown below are similar.

What is the height of the flagpole?
57 feet
51 feet
8.5 feet
42.5 feet

Answer:

Step-by-step explanation:

Grove City = 45,032

Franklin = 41,064

Franklin < Grove City

5 thousands > 1 thousand

Answer:-15/28

Step-by-step explanation:

2/1*x5/7x-3/8=-30/56 ÷2=-15/28

Answer:

r = 4

General Formulas and Concepts:

Pre-Alg

Step-by-step explanation:

Step 1: Define equation

-5 + 22 = r - 4 + 3r + 5

Step 2: Solve for r

Step 3: Check

Plug in r to verify it's a solution.

m<7=120'

Step-by-step explanation:

m<2 = m<6 because m and l are parallel and m<6 =m<7 because they are vertically opposite angles (v.o.a)

Answer:

m<7=120

Step-by-step explanation:

2 and 7 are alternate exterior angles and because l and m are parallel lines then m<2=m<7

Answer:

[tex]m=-\frac{3}{2}[/tex]

Step-by-step explanation:

First, look at the graph and pick out two points that we can use for the slope equation. I see (0,2) and (-2,5) as two possibilities. Now, we just plug them into the slope equation. Remember that the slope equation is

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

(the '2' and '1' are subscripts, not exponents)

Let's call our first point (0,2) x1 and y1. (-2,5) can be the second point.

If we plug this into the equation:

[tex]m=\frac{5-2}{-2-0}[/tex]

Now we just simplify and get

[tex]m=\frac{3}{-2}[/tex]

Our slope is [tex]-\frac{3}{2}[/tex].

I hope this helps!

Answer:

8

Step-by-step explanation:

we can say that AD is congruent to DC

so your equation for x is: 4x - 1 = 2x

solve this to get x = 0.5

plug x into and equation and multiply you answer by 2 to find the hypotenuse of triangle ABC and DEF

4(0.5) - 1 = 1

hypotenuse: 1 x 2 = 2

since we know x is 0.5, plug this into 4x + 1 to find the length of the leg FE,

4(0.5) + 1 = 3

In the diagram, it shows that the legs of triangle are congruent

this means that FE, ED, BA, and BC are all congruent

since we know FE is 3, we know that all the other sides are 3 as well

this means that the perimeter of the triangle is: leg + leg + hypotenuse

so 3 + 3 + 2

the perimeter is 8

Answer:

Step-by-step explanation:

[tex]X + Y \geq 15\\\\10X + 5Y \leq 100[/tex]

we want to put it into terms of Y

[tex]y \geq 15 - x\\and\\5y \leq 100 - 10x\\y \leq 20 - 2x[/tex]

the graph is in the attached image. Any point in the shaded overlap region where x is greater than or equal to 0 (assuming you cannot have negative coins) works, e.g. (2, 14)

The solution of the inequalities is required.

One of the solutions is [tex](5,10)[/tex]

Number of dimes is [tex]x[/tex]

Number of nickels is [tex]y[/tex]

Minimum number of coins is 15.

So, [tex]x+y\geq 15[/tex]

Maximum total value of the coins is $1

So, [tex]0.1x+0.05\leq 1[/tex]

The equations are

[tex]x+y=15[/tex]

[tex]0.1x+0.05y=1[/tex]

Points of the first equation

[tex](0,15)[/tex] and [tex](15,0)[/tex]

Graph the points and draw a line through them.

Points of the second equation

[tex]x=0[/tex]

[tex]y=\dfrac{1}{0.05}=20[/tex]

[tex]y=0[/tex]

[tex]x=\dfrac{1}{0.1}=10[/tex]

[tex](0,20)[/tex] and [tex](10,0)[/tex]

Graph the points and draw a line through them.

The shaded regions can be determined by substituting the point in the equations.

One of the solutions is [tex](5,10)[/tex]

This means there are 5 dimes and 10 nickels.

[tex]5+10=15\geq 15[/tex]

[tex]0.1\times 5+0.05\times 10=1\leq 1[/tex]

Hence, one of the solutions is [tex](5,10)[/tex].

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Answer:

i believe its the rise and the run of the slope.

Step-by-step explanation:

i believe its something similar to this photo

Answer:

D

Step-by-step explanation:

let the number of songs Byron have be s songs.

s + 26 = 75

Answer:

D

Step-by-step explanation:

s= number of songs played.

s+26=75

s-26=75-26

s=49

Answer:

X=17

Step-by-step explanation:

73+x=90 90-73=17

The expected number of times the mosquito will visit 0 before the first time she visits 4 is 3/4 by using concept of probability and geometric series.

Given that repeatedly throwing a fair tetrahedral die, trying to get a 4 (success) before getting a number from 1 to 3 (failure), which follows a geometric distribution.

To find the expected number of visits to 0 before reaching 4, analyze two cases:

By the given data, the probabilities of two cases are:

P(success) p = 1/4,

P(failure)=3/4.

The expected count of failures, X, can be found in terms of success probability p as

[tex]E[X]=\sum_{x=0}^{+\infty}[x(1-p)^xp][/tex]

On substituting p = 1/4 gives:

[tex]E(X) = 0(1/4)+1(3/4)(1/4)+2(3/4)^2(1/4)+3(3/4)^3(1/4)+.........[/tex]

On taking (1/4) gives

[tex]E(X) = 1/4[3/4+(3/4)^2+(3/4)^3+......+\infty]----(1)[/tex]

Consider [tex]3/4+(3/4)^2+(3/4)^3+......+\infty[/tex]

This forms a geometric series tends to infinity and the sum is given by :

[tex]S_\infty = a/(1-r)[/tex]

Here: a= 3/4

r = 3/4

Plugging these values into formula gives:

[tex]3/4+(3/4)^2+(3/4)^3+......+\infty = S_\infty[/tex]

[tex]S_\infty= 3/4/(1-3/4)[/tex]

On subtracting the denominator gives:

= 3/4/(1/4)

On taking reciprocal gives:

= 3/4 * 4

On simplifying gives:

= 3

Substituting these value into given equation 1 gives:

E(X) = 1/4*[3]

On multiplying gives:

E(X) = 3/4.

Therefore, the  expected number of times the mosquito will visit 0 before the first time she visits 4 is 3/4 by using concept of probability and geometric series.

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Answer: D

Step-by-step explanation:

I solved it:)

Answer:

x=-4

Step-by-step explanation:

Both points are on same line x=-4

Answer:

x = ± [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

[tex]|a|= \left \{ {a,if{a\geq 0} \atop-a, if {a<0}} \right.[/tex]

~~~~~~~~~~~~

7 | 3x | + 2 = 16

7 | 3x | = 14

| 3x | = 2

1). 3x = 2

x = [tex]\frac{2}{3}[/tex]

2). - 3x = 2

x = - [tex]\frac{2}{3}[/tex]

Answer:

c = 6P

Step-by-step explanation:

equation format: c = mP

c = the total cost Donna pays

m = the cost per pound of chocolate(6)

P = the amount of pounds Donna buys

Since we know the cost per pound is $6, we can input it into the equation format:

c = 6P

Now we have an equation that represents the total cost (c) that Donna pays for P pounds.

Let C = total cost that Donna pays.

Donna buys P pound at $6 per pound tells me to multiply.

C = 6P.

Understand?

Answer: 6 1/2

Step-by-step explanation:

six and 1 half of a hour

Answer:

ACD

Step-by-step explanation:

VNQLW3M2L,Q;KJ52KQ

Answer:

Step-by-step explanation:

Volume of the cuboid = Length * Width * Height

Given

Length = 4cm

Width = (x+1)cm

Height = (x-11)cm

Volume of the cuboid = 4(x+1)(x+11)

Volume of the cuboid = 4(x^2+11x+x+11)

Volume of the cuboid = 4(x^2+12x+11)

Volume of the cuboid = 4x*2+48x+44

925 = 4x*2+48x+44

4x*2+48x+44-925 = 0

4x*2+48x-881 = 0

Divide through by 4

x^2 + 12x - 220.25 = 0

Factorize using the general formula;

x = -12±√12²-4(-220.25)/2

x = -12±√144+881/2

x = -12±√1025/2

x = -12±32/2

x = 12+32/2

x = 20/2

x = 10

Hence the dimension of the cuboid is 4cm, (10+1)cm and (10+11)cm

Dimension is 4cm by 11cm by 21cm

Answer: No

Step-by-step explanation:

The range and the Domain aren’t equal

Answer:

20 mobile sets.

Step-by-step explanation:

Every mobile set costs:

40000 / 8

= 5000 Rs.

Therefore, for 100,000 Rs, the number of mobile sets that can be purchased is:

100,000 / 5000

= 20 mobile sets.

Hope this helped!

speed =  [tex]\frac{distance}{time}[/tex]

speed = [tex]\frac{100}{2.5}[/tex]

speed = 40 feet per second

Answer:

(4,3)

Step-by-step explanation:

2y = x + 2

x - 3y = -5

Rearrange the second equation to equal y.

x - 3y = -5

x + 5 = 3y

(x+5)/3 = y

Substitute into the first equation.

2y = x +2

2[(x+5)/3] = x + 2

(2x + 10)/3 = x + 2

2x + 10 = 3(x + 2)

2x + 10 = 3x + 6

10 - 6 = 3x - 2x

4 = x

Therefore, the correct ordered pair is (4,3) since x is equal to 4.

Answer:

C

Step-by-step explanation:

If you  find the difference between 45 and 31, you find the increase. Take that and make it a percentage of 68. I hope this helped! Have a great day.

Answer:

The solutions to the system of equations will be:

[tex]y=6,\:x=0[/tex]

Step-by-step explanation:

Given the equation

[tex]-6y+11x=-36[/tex]

[tex]-4y+7x=-24[/tex]

solving the system of equations

[tex]\begin{bmatrix}-6y+11x=-36\\ -4y+7x=-24\end{bmatrix}[/tex]

[tex]\mathrm{Multiply\:}-6y+11x=-36\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-12y+22x=-72[/tex]

[tex]\mathrm{Multiply\:}-4y+7x=-24\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:-12y+21x=-72[/tex]

[tex]\begin{bmatrix}-12y+22x=-72\\ -12y+21x=-72\end{bmatrix}[/tex]

[tex]-12y+21x=-72[/tex]

[tex]-[/tex]

[tex]\underline{-12y+22x=-72}[/tex]

[tex]-x=0[/tex]

[tex]\begin{bmatrix}-12y+22x=-72\\ -x=0\end{bmatrix}[/tex]

solving for x

[tex]-x=0[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-1[/tex]

[tex]\frac{-x}{-1}=\frac{0}{-1}[/tex]

[tex]x=0[/tex]

[tex]\mathrm{For\:}-12y+22x=-72\mathrm{\:plug\:in\:}x=0[/tex]

[tex]-12y+22\cdot \:0=-72[/tex]

[tex]-12y+0=-72[/tex]

[tex]-12y=-72[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-12[/tex]

[tex]\frac{-12y}{-12}=\frac{-72}{-12}[/tex]

[tex]y=6[/tex]

Therefore, the solutions to the system of equations will be:

[tex]y=6,\:x=0[/tex]

Answer:

The distance between their tops is 130 feet

Step-by-step explanation:

The given parameters are;

The height of A, [tex]h_A[/tex] = 2 × The height of B - 10

The distance between the two buildings, d = 120 feet

The height of B, [tex]h_B[/tex] = 60 feet

Therefore, we have;

The height of A, [tex]h_A[/tex]  = 2 × The height of B - 10 = 2 × 60 - 10 = 110 feet

The height of A, [tex]h_A[/tex] = 110 feet

By Pythagoras theorem, the distance between their tops = √(([tex]h_A[/tex] - [tex]h_B[/tex])² + d²)

Substituting the values gives;

The distance between their tops = √((110 - 60)² + 120²) = 130

The distance between their tops = 130 feet.

Answer:

1

Step-by-step explanation:

Given table:

     x      -1    1   3   5

     y      -2   0   2  4

Unknown:

Slope of the line  = ?

Solution:

Each x and y pair on the table lies on the line. Therefore, we can use them to find the slope;

  Slope  = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]  

 let us take;

x₁ = -1        x₂ = 3

y₁ = -2        y₂ = 2

Insert the parameters and solve;

   Slope = [tex]\frac{2 - (-2)}{3- (-1)}[/tex]   = [tex]\frac{4}{4}[/tex]   = 1

The slope of the line is 1

Answer:

b

Step-by-step explanation:

Answer:

4 x 10⁵

so that i think will be OD)