Michael, whose eyes are five feet off the ground, is standing 26 feet away from the base of a building, and he looks up at a 65° angle of elevation to a point on the edge of building’s roof. To the nearest foot, how tall is the building?

Answer:

He is 200 meters south of his house.

Step-by-step explanation:

Say north is positive and south is negative, but your answer will be the absolute value. He goes 250m North. He then goes 450m south which would translate into a problem as 250-450=|-200|=200. In simpler terms think of the road as a number line where north is positive and south is negative and your house is zero, you want the distance on the line from zero.

Answer:

We know that a₁ = 2 and that you have to add 4 to the previous term to get the term you are looking for so the answer is:

a₁ = 2

aₙ = aₙ₋₁ + 4

Answer:

When x=-3 ,  y= -16

when x=-2 , y= -10

when x=-1 , y= -6

when x=0 , y=-4

when x=1 y=-2

when x=2, y= 2

when x= 3, y= 8

Step-by-step explanation:

Equation: y= x^2+x-4

All you have to do is plug in the values of x given in the table inorder to find the y values.

Answer:

When x=-3 ,  y= -16

when x=-2 , y= -10

when x=-1 , y= -6

when x=0 , y=-4

when x=1 y=-2

when x=2, y= 2

when x= 3, y= 8

Just plug in each x value to the equation

Answer:

(B) 2

Step-by-step explanation:

=> [tex]\frac{\sqrt{32}+ \sqrt{48} }{\sqrt{8}+\sqrt{12} }[/tex]

=> [tex]\frac{4\sqrt{2}+4\sqrt{3} }{2\sqrt{2}+2\sqrt{3} }[/tex]

=> [tex]\frac{4(\sqrt{2}+\sqrt{3}) }{2(\sqrt{2}+\sqrt{3)} }[/tex]

Cancelling [tex]\sqrt{2}+\sqrt{3}[/tex]

=> [tex]\frac{4}{2}[/tex]

=> 2

Answer:

5/2

Step-by-step explanation:

You slope is always mx

In point-slope form, your mx is just in factored form. All you need to do is distribute to find m.

Answer:

x = -9

Step-by-step explanation:

-7x = 63

Divide -7 into both sides.

-7x/-7 = 63/-7

x = 63/-7

x = -9

Put x as -9 in the function to check.

h(x) = -7x

h(-9) = -7(-9)

h(-9) = 63

Answer:

x = -9

Step-by-step explanation:

h(x)=−7x ; h(x)=63

Set the two equal

-7x = 63

Divide by -7

-7x/-7 = 63/-7

x = -9

Answer:

0.06 l

Step-by-step explanation:

Volume of cube = 3 x 4 x 5 = 60 cm cubed.

1 cm cubed = 0.001 liters

So 60 cm cubed = 0.06 liters.

Hope this helps

Answer:

I hope this is helpful (2x-3)(3x+5)

Step-by-step explanation:

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

6x2-9x+10x-15

6x2+x-15

Answer:

your answer is 3x+5

Step-by-step explanation:

on edge 2021

Answer:

A

Step-by-step explanation:

Answer:

b)

Step-by-step explanation:

the easy way of doing this in my opinion is just to multiply the options by their corresponding values so in this case 3x10=30 and 5x14=70 then add those together and it equals 100 points with a total of 24 questions

Answer:

d.

Step-by-step explanation:

i looked at the graph!

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The length of the base is 3 feet and the height of the triangle is 6 feet.

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees. The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the triangle in a two-dimensional plane is called the area of the triangle.

Given that the height of a triangle is 3 feet greater than the base. The area of the triangle is 54 square feet.

The dimensions of the triangle will be calculated as,

A = (1/2)  x b x h

A = (1/2) x b x ( b + 3 )

54 = ( 1 / 2 ) x ( b² + 3b )

108 =  ( b² + 3b )

( b² + 3b - 108) = 0

( b² + 12b -3b -108 ) = 0

(b - 3 ) ( b+ 12 ) = 0

b = 3 and b = -12 ignore negative value.

The height will be calculated as,

h = b + 3

h = 3 + 3

h = 6 feet

Therefore, the length of the base is 3 feet and the height of the triangle is 6 feet.

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Answer:

6/8

Step-by-step explanation:

3/4

Multiply by 2/2

3/4 *2/2 = 6/8

Answer:

True

Step-by-step explanation:

The distance between the given points is [tex]\sqrt{(x_{1}-1 )^{2}-(y_{1}-2 )^{2} }[/tex].

The given points are  (1, 2) and [tex](x_{1} , y_{1})[/tex] .

We to find the distance between the given points.

The formula to find the distance between points is [tex]\sqrt{(x_{1}-x_{2} )^{2}-(y_{1}-y_{2} )^{2} }[/tex].

Now, [tex]\sqrt{(x_{1}-1 )^{2}-(y_{1}-2 )^{2} }[/tex]

Therefore, the distance between the given points is [tex]\sqrt{(x_{1}-1 )^{2}-(y_{1}-2 )^{2} }[/tex].

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Answer:

B. 116

Step-by-step explanation:

Answer:

D) 102

Step-by-step explanation:

Angle ABC is an inscribed angle.

Inscribed angle = 1/2 * Intercepted Arc

The intercepted arc is arc CD + arc DA, which would be 128 + 76 = 204

m<ABC = 1/2(204)

m<ABC = 102 degrees

You answer is D) 102

Answer:

A

Step-by-Step Explanation:

We want to find the limit:

[tex]\displaystyle{\lim_{x\to\frac{\pi}{2}}(2e^x\cos(x))}[/tex]

Use direct substitution.

Hence:

[tex]\displaystyle{\Rightarrow 2e^\frac{\pi}{2}\cos(\frac{\pi}{2}})[/tex]

Recall the unit circle. cos(π/2) is simply 0. Hence:

[tex]\displaystyle{\Rightarrow 2e^\frac{\pi}{2}(0)=0[/tex]

Therefore:

[tex]\displaystyle{\lim_{x\to\frac{\pi}{2}}(2e^x\cos(x))}=0[/tex]

So, our answer is A.

Answer:

Step-by-step explanation:

Consider that by changing the the variable x with x-c represents a horizontal shift of c units. If c>0 then it is a right shift and it is a left shift otherwise. When we multiply the variable by a number d (i.e dx) we are applying an horizontal compression/stretching. If d>1 it compresses it, and if 0<d<1 it stretches it. By multipyling the variable x by a negative sign, we are reflecting with respect the x -axis. Finally when we add a number to the function, we are applying a vertical shift.

original function x.

1. (x-7): horizontal shift of 7 units to the right.

2. 1/3(x-7): Horizontal stretching by factor 1/3.

3.-1/3(x-7): Reflection with respect the x-axis

4.-1/3(x-7)+2: Vertical shift of two units up.

Answer:

17p

Step-by-step explanation:

9p+8p=17p

Answer:

Step-by-step explanation:

Hello

(fog)(x)=f(g(x))=10(x-6)/10+6=x-6+6=x

(gof)(x)=(10x-6+6)/10=10x/10=x

So YES the functions are inverse

hope this helps

Answer:

The center of the circle is at  the point (-3, -2) on the plane

Step-by-step explanation:

The first four steps in the completing of the squares to find the standard equation of a circle are correct. Let's start from there and actually complete the squares correctly:

[tex](x^2+6\,x+9)+(y^2+4\,y+4)=3+9+4\\(x+3)^2+(y+2)^2=16\\(x+3)^2+(y+2)^2=4^2[/tex]

Therefore, this is a circle centered at x = -3 [based on the horizontal translation defined by (x+3)], and at y = -2 [based on the vertical translation defined by (y+2)], and the circle has radius 4 based on the numerical constant squared on the right side of the equal sign.

Answer:

true it's A....

Answer:

A

Step-by-step explanation:

64x³ + 125

∛(64x³ + 125)

= 4x + 5

The expression is a sum of cubes.

Answer:

The answer is 5

Step-by-step explanation:

hope this helped you

Today Britney beat 5 levels of a video game if she played at the same playing proportion with time as yesterday.

proportion or rate of work done is the ratio of the total work done in a given time divided by the given time. It is the measure of the proportion of doing work per unit time.

proportion of work done = Total work done / Given time

Yesterday ,Britney played 3 levels in time  27 minutes

Work done(levels cleared) = 3 levels

Time taken  = 27 minutes

Yesterday the proportion or rate of playing game = 3 levels / 27 minutes = ( 1/ 9) levels/ min

Today, Britney is allowed to play  for 45 minutes at the same proportion rate she played yesterday

Then, the  work done or level beat today = rate of playing game × time

                                                                    = (1/9)×45 = 5 games

Therefore, Britney cleared 5 games today if she played at same rate as she did yesterday

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Answer:

[tex]9^8[/tex]

Step-by-step explanation:

[tex]9^8=43046721[/tex]

[tex]ln(9^x)=xln(9)[/tex]

so we search [tex]x=ln(43046721)/ln(9)[/tex]

hope this helps

Answer:

9^8=43046721

Step-by-step explanation:

The exponent 9 of a number is found by multiplying that number by itself 9 times.

Answer:

palindromes

Step-by-step explanation:

palindromes are spelled the same forward and backward, thus have vertical symmetry.

Answer:

Step-by-step explanation:

The general form of a quadratic equation with roots a and b is expressed as shown;

x²-(sum of root) x + (product of roots) = 0

x² - (a+b)x + ab = 0 ... 1

Given the sum of roots a+b = -7

Product of roots ab = -2

Substituting this values in equation 1 above wil give;

x²-(-7)x+(-2) = 0

x²+7x-2 = 0

The resulting quadratic polynomial is x²+7x-2 = 0

Answer:

220 products need to be sold to break it even.

Step-by-step explanation:

550 + 3.00x = 5.50x

550 = 2.50x

220 = x

Answer:

The magnitude of the boat's velocity is 5.66 m/s

Step-by-step explanation:

Given;

Radius of curvature of the circular path, r = 40 m

speed of the boat, v = 0.8 t m/s

The magnitude of the boat's velocity when it has traveled 20 m is ?

a = dv / dt,

v = 0.8 t (differentiate with respect to t)

dv / dt = 0.8 = a

thus, a = 0.8 m/s²

If the boat starts from rest, initial velocity, u = 0

Apply kinematic equation, to solve for the boat velocity at 20 m

v² = u² + 2as

v² = 0 + 2 x 0.8 x 20

v² = 0 + 32

v² = 32

v = √32

v = 5.66 m/s

Therefore, the magnitude of the boat's velocity when it has traveled 20 m is 5.66 m/s

Answer:

12

Step-by-step explanation:

X=12

Because chords are the same size

Answer:16.6 is the correct answer.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The original amount will be the coefficient of (1 + 0.04)^r which is $728.00.