4. You read an article in your local newspaper about a discussion between the owner of a popular business and a group
of community members. The business owner keeps a flag raised on an outdoor flagpole during nighttime hours, but
the community members are calling for the flag to be properly illuminated at night. The business owner says that the
flag cannot be illuminated because the only power source available for the spotlights is solar power, but there is too
much shade on the ground for solar-powered spotlights to charge sufficiently during the day.
You realize that you can offer a solution to the problem by suggesting that the solar-powered spotlights be mounted
on the roof of the building where it can be charged by sufficient sunlight. You decide to contact the business owner to
suggest angling the spotlight down to the raised flag from the roof instead of angling it up to the raised flag from the
ground. The business owner informs you that the flagpole is located 55 feet from the building. If the building is 45 feet
high and the flagpole is 25 feet high, at what angle should you tell the business owner to angle a spotlight mounted on
the roof? Please show all your work.
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Answer:

20% antifreeze solution = 18 gal

15% antifreeze solution = 12 gal

Step-by-step explanation:

Let

20% antifreeze solution = x

15% antifreeze solution = y

x + y = 30

0.20x + 0.15y = 30 * 0.18

0.20x + 0.15y = 5.4

x + y = 30 (1)

0.20x + 0.15y = 5.4 (2)

From (1)

x = 30 - y

Substitute x = 30 - y into (2)

0.20x + 0.15y = 5.4 (2)

0.20(30 - y) + 0.15y = 5.4

6 - 0.20y + 0.15y = 5.4

- 0.20y + 0.15y = 5.4 - 6

-0.05y = -0.6

y = -0.6/-0.05

y = 12 gal

Substitute y = 12 into (1)

x + y = 30 (1)

x + 12 = 30

x = 30 - 12

x = 18 gal

20% antifreeze solution = 18 gal

15% antifreeze solution = 12 gal

Answer:

what are you trying to find the slope?

Step-by-step explanation:

Answer:

calculando la circunferencia

Answer:

$67

Step-by-step explanation:

So 5x12+7=C

PEDMAS so:

5x12 = 60

60+7 = 67

67 = C

Answer:

the answer to that is -1i

Step-by-step explanation:

cause if you add negative and positve you get to subtract it and get the sign of the highest number

Answer:

$145.5

Step-by-step explanation:

Period, t = August 8.to November 8 = 3 months

Simple interest formula :

A = P(1 + rt)

A = final amount =. 7200

7200 = P(1 + (0.0825 * 3/12))

7200 = P(1 + 0.020625)

7200 = P(1.020625)

7200 = 1.020625P

P = 7200 / 1.020625

P = 7054.5009

Bank discount :

A - P

7200 - 7054.5009

= $145.4991

= $145.5

Answer:

x = 5 (please read the step by step explanation)

Step-by-step explanation:

So, I'm just going to solve for x because the instructions aren't too clear. I believe there is supposed to be an image attached to it, but seeing as I don't have that, I'll just solve for x and you can plug in with the values.

15x = 12x + 15

Same to both sides:

3x = 15

Isolate x:

x = 5

Just plug in those values and you'll be good to go! Have a good day!

Answer:

m = -100

Step-by-step explanation:

(1/5)m -12 = -32

add 12 on both sides

(1/5)m = -20

multiply both sides by 5

m = -100

Answer:

m = -100

Step-by-step explanation:

So in order to solve this equation we are going to have to convert 1/5m to a decimal, this will make it easier to solve the equation:

1/5m = 0.2m

Next we are going to take our 0.2m and place it within the equation where 1/5m is:

⅕m - 12 = -32  or 0.2m - 12 = -32

So now we are going to add 12 to both sides of the equal sign in the equation to segregate the 0.2m within the equation:

0.2m - 12 = -32  or 0.2m + (-12 + 12) = (-32 + 12)

making the equation look like this:

0.2m = -20

now we are going to divide 0.2 from both 0.2m and -20 to get the value of m:

0.2m/0.2 = -20/0.2

Thus getting the answer:

m = -100

So how do we know that -100 is the value of m? well we check our work of course by substituting -100 in place of m!

⅕(-100) - 12 = -32  or 0.2(-100) - 12 = 32

0.2(-100) - 12 = 32

-20 - 12 = -32

-32 = -32

Answer:

$5,048.98

Step-by-step explanation:

took the test

Answer:

Step-by-step explanation:

C - 3(2^x).

Answer:

what is

Step-by-step explanation:

the the 3 4 4

Answer:

x=18

Step-by-step explanation:

S=(n-2)180

S=(5-2)180

S=3x180

S=540

540=(9x-6)+(3x+23)+95+((7x-4)+90

540=19x+198

540-198=19x

342=19x

342/19=x

x=18

Answer:

[tex]\displaystyle m=-2[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (4, -2)

Point (-1, 8)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer:

26. ∠ABC=44

27. ∠ABC=86

28. ∠ABC=116

Step-by-step explanation:

Since BD bisects ∠ABC in each diagram, ∠ABD=∠DBC.

26.

∠ABD=∠DBC

5x+2=7x-6

2x=8

x=4

∠ABC=∠ABD+∠DBC

=5(4)+2+7(4)-6

=20+2+28-6

=44

27.

∠ABD=∠DBC

11x-12=8x+3

3x=15

x=5

∠ABC=∠ABD+∠DBC

=11(5)-12+8(5)+3

=55-12+40+3

=86

28.

∠ABD=∠DBC

9x-23=5x+13

4x=36

x=9

∠ABC=∠ABD+∠DBC

=9(9)-23+5(9)+13

=81-23+45+13

=116

Answer:

5

Step-by-step explanation:

The ones place is the one most to the right that isn't after a decimal point.

Answer:

5, since it is all the way to the right

Step-by-step explanation:

if you ever have a big number, the number in thes ones place is ALWAYS on the far right, except if its a decimal !

i hope this helps !! :D

Answer:

The factors are [tex]2v+3,2v+3[/tex].

The factors are not [tex]4v+3,4v+3[/tex]

Step-by-step explanation:

Equation is [tex]4v^2=-12v-9[/tex].

This equation can be written as follows:

[tex]4v^2+12v+9=0[/tex]

Here,

[tex]12v=6v+6v[/tex]

Therefore,

[tex]4v^2+6v+6v+9=0\\2v(2v+3)+3(2v+3)=0\\(2v+3)(2v+3)=0[/tex]

So, the factors are [tex]2v+3,2v+3[/tex].

The factors are not [tex]4v+3,4v+3[/tex]

standard form is y=mx+b

to get there lets simplify the equation

y+2=(2/7)(x-1)   original in point slope form

y+2=(2/7)x-2/7      distribute 2/7

y=(2/7)x-16/7         subtract 2 from both sides, 2=14/7

answer: [tex]y=\frac{2}{7}-16/7[/tex]

Answer:

He made 35% of his shots he did not make 65& of his shots

Step-by-step explanation:

7/20=35%, 20/7=65%

Answer: yes you are correct

Step-by-step explanation: just took the test

Answer:

Indeed you are(For anyone else, make sure to see that your bottom point is not filled in. The Top point is black and filled and the bottom is not)

Step-by-step explanation:

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

When the parabola has a y^2 term it opens horizontally. (Positive and negative values of y give the same value of x.)

When the parabola has an x^2 term it opens vertically. (Positive and negative values of x give the same value of y.)

The sign is negative when the opening is down or to the left.

__

The opening directions are shown in the attachment.

Answer:

look below

Step-by-step explanation:

i did it

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Surface areas and Volumes.

Since, we know that the lateral area of a Right circular cone is given as,

AL = πrl

here, l = slant height , r = radius of the circular base.

so now, we have to find first slant height to get the lateral surface area,

[tex]l \: = \sqrt{ {r}^{2} + {h}^{2} } [/tex]

here, r = 8 cm and h = 15,

hence,

[tex]l \: = \sqrt{64 + 225} = \sqrt{289} = 17cm[/tex]

hence, now we apply the formula,

AL = π(8) (17) cm^2

===> AL = 136 π cm^2

Answer:Rotation is rotating an object about a fixed point without changing its size or shape. Translation is sliding a figure in any direction without changing its size, shape or orientation.

Step-by-step explanation:

Answer:

y< −x/3 −2

Step-by-step explanation:

I hope this is what you need if not let me know and ill edit the answer

Answer:

y = 1/2x

Step-by-step explanation:

y - 2 = 1/2 (x-4)

y = 1/2x - 2 + 2

y = 1/2x

(The y - intercept is 0 because -2 and 2 cancels each other out)

Hope this helps :)

Let me know if there are any mistake!!

The slope intercept form of the equation y - 2 = 1/2 (x - 4) will be

⇒ y = 1/2x

What is equation of line?

The equation of line in slope intercept form is defined as;

y = mx + b

Where, 'm' is slope of line and 'b' is y-intercept.

Given that;

The equation of line is;

y - 2 = 1/2 ( x - 4 )

Now,

We can change the equation of line in slope intercept form as,

y - 2 = 1/2 ( x - 4)

Solve as;

y - 2 = 1/2 x - 1/2 × 4

y - 2 = 1/2 x - 2

Add 2 both side,

y - 2 + 2 = 1/2 x - 2 + 2

y = 1/2 x

Thus, The slope intercept form of the equation y - 2 = 1/2 (x - 4) will be;

⇒ y = 1/2x

Learn more about the equation of line visit:

https://brainly.com/question/18555692

#SPJ5

It be 12 cause from the smaller one 2*4 would = to 8 and 5*4 also = to 20 so 3*4 = to 12.

50(30%) = 15

50 - 15 = 35

35 (6%) = 2.1

35 + 2.1 = $37.10

the total cost of his order is $37.10 !!

Answer:

b is the independent variable

c is the dependent variable

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

-23.48

Step-by-step explanation:

Hoped this helped!!

Answer: B

Step-by-step explanation: An isosceles right triangle is an isosceles triangle and a right triangle. This means that it has two congruent sides and one right angle. Therefore, the two congruent sides must be the legs.