Use this information for problems 1 and 2. When full, one of the pools at Sapphire Island will hold 43,000 gallons of
water. The pool currently holds 20,000 gallons of water and is being filled at a rate of 130 gallons per minute.
Write an equation that can be used to find h, the number of hours it will take to fill the pool from its current level,

Answer:

53.67⁰

Step-by-step explanation:

Give the height of the fence to be 2.4 m tall

Height of the tree = 16m

Horizintal distance from the fence to the tree = 10m

Check the diagram in the attachment.

From the attachment, we will need to first calculate the height AB

AC = AB+BC

Given AC = height of the r=tree = 16m

BC is the height of the fence = 2.4m

16 = AB + 2.4

AB = 16-2.4

AB = 13.6m

Using the SOH CAH TOA trig identity on right angled triangle AEB with AB as the opposite and AB and the adjacent as BE

Using TOA;

tan ∝ = opposite/adjacent = AB/BE

∝ is the angle of elevation of the top of the tree from the top of the fence​.

tan∝ = 13.6/10

tan∝ = 1.36

∝ = tan⁻¹1.36

∝ = 53.67⁰

Hence the angle of elevation of the top of the tree from the top of the fence​ is 53.67⁰

Answer:

1

Step-by-step explanation:

Any number that is raised to the power of 0 is 1.

1^0 = 1

323^0 = 1

k^0 = 1

Hope that helped!!! k

The Distributive property states that when we have the statement a(b + c), we can "distribute" the a by multiplying a times both terms that are inside the parenthses.

So in this problem, 2(5 + 7) can be simplified by distributing the

2 through both terms that are inside the set of parenthses.

So we have (2 · 5) + (2 · 7).

Answer:

Distributive Property

Step-by-step explanation:

You are distributing the 2 to the 5 and 7. which goes from 2(5+7) to 10+14.  

Answer: 0.02291666

Step-by-step explanation:

divide 55 by 60 (minutes)

then by 60 again (seconds)

multiply by 1.5

there you go

The person travelled for 0.0229167 miles.

To calculate the distance, we have to multiply the speed by the time taken.

Distance = Speed × Time

Speed = 55 miles per hour.

Time taken = 1.5 seconds = 0.0004167 hours

Note that 3600 seconds = 1 hour

Therefore, 1.5 seconds = 0.0004167 hours

Then, the distance will be:

= Speed × Time

= 55 × 0.0004167

= 0.0229167 miles

The person travelled for 0.0229167 miles.

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Answer:

[tex] Volume = 7440.16 ft^3 [/tex]

Step-by-step explanation:

Volume of the composite object = volume of cylinder - volume of rectangular prism

Volume of the composite object = πr²h - whl

where,

π = 3.14

r = 14 ft

h = 14 ft

w = 6 ft

l = 14 ft

[tex] Volume = (3.14*14^2*14) - (6*14*14) [/tex]

[tex] Volume = 8616.16 - 1176 [/tex]

[tex] Volume = 7440.16 ft^3 [/tex]

Answer:

12 and 16 or 12:16

Step-by-step explanation:

The ratio is 3:4.  You need the ratio to equal 28.  If you multiply 4 by each one, you get:

3 times 4= 12

4 times 4= 16

12+16=28

Answer:

m = -5

Step-by-step explanation:

m = (y₂ - y₁) / (x₂ - x₁)

m = (11 - 6) / (-18 - ( -17))

m = 5 / (-18 + 17)

m = 5 / -1

m = -5

Answer:

89.76 yd^2

Step-by-step explanation:

The area is given by

A = bh

A = 10.2 * 8.8

A =89.76 yd^2

I'm assuming you were given these four values

50.1,  -50/2, -50.1, sqrt(50)

where 'sqrt' stands for 'square root', and the slash symbol means divide or fraction.

If my assumption is correct, then the term that does not belong is sqrt(50). This is because the other values are all rational. We can express them as a fraction of two whole numbers

But we can't do the same with sqrt(50). It is irrational. Note how 50 is not a perfect square. Your calculator will show that sqrt(50) = 7.07106781186548 and that decimal sequence goes on forever without any pattern. If you were given sqrt(49), then it would work because sqrt(49) = 7 = 7/1.

Answer:

x=17/3

Step-by-step explanation:

divide both sides by 3 to isolate x

Answer:

[tex]\huge \boxed{\mathrm{99.98 \ cm}}[/tex]

Step-by-step explanation:

A quadrant is quarter of a circle.

The perimeter of a quarter of a circle is [tex]\frac{2\pi r}{4} +2r[/tex].

The radius [tex]r[/tex] is 28 cm.

[tex]\frac{2\pi (28)}{4} +2(28)= 99.982297...[/tex]

The perimeter of the quadrant with radius 28 cm is approximately 99.98 cm.

Answer:

[tex]\huge\boxed{Perimeter = 99.98\ cm}[/tex]

Step-by-step explanation:

Quadrant is one - fourth of a circle

Perimeter of quadrant = [tex]\frac{2\pi r }{4} + 2r[/tex]

Where r = 28 cm

=> P = [tex]\frac{2(3.14)(28)}{4} + 2(28)[/tex]

=> P = [tex](3.14)(14) + 56[/tex]

=> P = [tex]43.98 + 56[/tex]

=> P = 99.98 cm

29 + 36 = 65 total pushups per day.

Multiply pushups per day by 7 days per week:

65 x 7 = 455 total pushups per week

Multiply pushups per week by number of weeks:

455 x 4 weeks = 1,820 total pushups.

Answer:

46

y = 3 /5x +26

y =?

X= 12

y=3 /5x + 26

y= 3 / 5 × 12 + 26

y = 3 / 60 + 26

y = 20 + 26

y = 46 ans

Answer:

Therefore, Melissa will be charged $72 for busing work ATM 24 times in a month

Step-by-step explanation:

Melissa was charged $3 each time she used the ATM at work

She used the work ATM 24 times in a month.

Charge per usage= $3

Number of times of usage= 24

By how much did her bank account change from using the ATM at work

Total charges = charge per usage × Number of times of usage

= 3 × 24

= 72

Total charges = $72

Therefore, Melissa will be charged $72 for busing work ATM 24 times in a month

Answer:

Original Medicare comes in two parts. Medicare Part A covers hospital services, skilled nursing facility care, hospice, and some home health care. Medicare Part B covers medical services, including doctor visits, preventive screenings, certain vaccinations, lab tests, and durable medical equipment.

Answer:

- 0.25

Step-by-step explanation:

Common ratio

[tex]r = \frac{succeeding \: term}{preceding \: term} \\ = \frac{80}{ - 320} \\ = - \frac{1}{4} \\ = - 0.25[/tex]

Given that :-

Geometric sequence → -320,80,-20,5

To find :-

Common ratio .

Solution :-

Common ratio = ar/a

→ Here a = -320

→ ar = 80

→ Common ratio = 80/-320

Let's check it →

Taking a = 80 and ar = -20

→ Common ratio = -20/80

So common ratio will be -1/4

Answer:

(6+a)/3

Step-by-step explanation:

(6+a)/5-3

5-3=2

(6+a)/2

Answer:

6

Step-by-step explanation:

-3+10-1

10-4

=6

hope this helps

Answer:

6

Step-by-step explanation:

You can add -3 and -1 to make -4 and subtract from 10.

-3-1+10= 6

Answer:

Step-by-step explanation:

[tex] \sf{15 - 2(3 - 2x) = 46}[/tex]

Distribute 2 through the parentheses

⇒[tex] \sf{15 - 6 + 4x = 46}[/tex]

Subtract 6 from 15

⇒[tex] \sf{9 + 4x = 46}[/tex]

Move 9 to right hand side and change its sign

⇒[tex] \sf{4x = 46 - 9}[/tex]

Subtract 9 from 46

⇒[tex] \sf{4x = 37}[/tex]

Divide both sides of the equation by 4

⇒[tex] \sf{ \frac{4x}{4} = \frac{37}{4} }[/tex]

Calculate

⇒[tex] \sf{x = 9.25}[/tex]

Hope I helped!

Best regards!!

The solution of the given equation 15 - 2(3 - 2x) = 46 is x = 37/4.

In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equal sign = .

Now the given equation is,

15 - 2(3 - 2x) = 46

Let us first expand the brackets ,

15 - 6 + 4x = 46

Now solving them we get,

9 + 4x = 46

Substracting by 9 both the sides of the equation we get,

⇒4x = 37

Dividing the equation by 4 we get

⇒x = 37/4

Hence,The solution of the given equation 15 - 2(3 - 2x) = 46 is x = 37/4.

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Answer:

f(g(x))= 1-2(x^2-5+3)

Step-by-step explanation:

To do this you would plug in x^2-5+3 into the x for the g(x) so you would get f(g(x))= 1-2(x^2-5+3)

Answer:

4x^2+6x-1

Step-by-step explanation:

the question asks for f(g(x)). this means you have to plug in the value of g(x) into the "x" of f(x). (you should always work inside out.)

if you do that, you get this equation : (-2x+1)^2-5(-2x+1)+3 (i changed the 1-2x into -2x+1) because you plug in the g(x) (in this case, -2x+1) into the x's in the f(x) equation.

first you foil the (-2x+1)^2 and get 4x^2-4x+1.

then you distribute -5(-2x+1) and get +10x-5

and you bring down the 3.

so you have 4x^2-4x+1+10x-5+3 and you combine your like terms and get

4x^2+6x-1

which is your answer!

Answer:

36 square units.

C

Step-by-step explanation:

Please refer to the provided graph.

So we want to figure out the area of the rectangle. To do so, we simply need to figure out the base and height of the rectangle. We can then multiply them together to acquire the area.

From the graph, we can see that if we find the length of SR and SP, we can use the the base and height, respectively.

Now, we just have to find there lengths. Technically, we could just count. However, I'm going to use the distance formula.

the distance formula is:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Find the length of SR:

Point S is (-2,-1) while Point R is (4,-1). Let (-2,-1) be x₁ and y₁ and (4,-1) be x₂ and y₂. Therefore:

[tex]d=\sqrt{(4-(-2))^2+(-1-(-1))^2}\\d=\sqrt{(6^2)+(0)^2} \\d=\sqrt{36}=6[/tex]

So, SR is 6.

Now, find the length of SP:

Point S is (-2,-1) while Point P is (-2,5). Let Let (-2,-1) be x₁ and y₁ and (-2,5) be x₂ and y₂. Therefore:

[tex]d=\sqrt{(-2-(-2))^2+(5-(-1))^2}\\d=\sqrt{0^2+6^2}\\ d=\sqrt{36}=6[/tex]

Therefore, SP is also 6.

Now, the area for a rectangle is:

[tex]A=bh[/tex]

Plug in 6 for the base and 6 for the height:

[tex]A=6(6)\\A=36\text{ units}^2[/tex]

Answer:

5x -3y = 15

Step-by-step explanation:

First find the slope of the line through ( -3,2) and (2,-1)

m = (y2-y1)/(x2-x1)

   =( -1-2)/(2--3)

   = -3/(2+3)

    = -3/5

We want a line that is perpendicular so the slopes will multiply to -1

m * -3/5 = -1

Multiply each side by -5/3

m * -3/5 * -5/3 = -1 *-5/3

m = 5/3

The slope of the perpendicular line is 5/3

We have a slope and a point

Using point slope form

y-y1 = m(x-x1)

y-0 = 5/3( x-3)

y = 5/3( x-3)

Distribute

y = 5/3x -5

Multiply each side by 3

3*y = 3(5/3x -5)

3y = 5x - 15

Subtract 5x from each side

-5x+3y = -15

Multiply each side by -1

5x -3y = 15

Answer:

D. 5x − 3y = 15

May I have brainliest please? :)

Answer:

[-10, 3]

Step-by-step explanation:

Hello!

To find the range of a graph you look at the lowest point and the highest point

The highest point is 3

The lowest point is -10

The range is [-10, 3]

Hope this helps!

Answer:

-10, 3

Step-by-step explanation:

high: 3

low: -10

the order of the 2 coordinates goes left or right, then up or down

( plz mark me as brainliest, that would be most appreciated! )

Answer: The best answers are :

Step-by-step explanation:

I hope it helps :)

Answer:

a and c

Step-by-step explanation:

Answer:

top answer is -23

bottom answer is -2

Answer:

Children = 51

Adults = 42

Students= 84

Step-by-step explanation:

Children = $2

Students = $3

Adults = $4

Total sales = $522

Total people who attended = 177

Adults =a

Students = s= 2a

Children = c

c+s+a = 177 (1)

2c+3s+4a=522 (2)

Substitute s=2a into the equations

c + 2a + a = 177

c + 3a = 177 (3)

2c + 3(2a) + 4a = 522

2c + 6a + 4a = 522

2c + 10a = 522 (4)

c + 3a = 177 (3)

2c + 10a = 522 (4)

Multiply (3) by 2

2c + 6a = 354 (3b)

2c + 10a = 522

Subtract (3b) from (4)

10a - 6a = 522 - 354

4a = 168

Divide both sides by 4

a= 168/4

= 42

a= 42

s= 2a

= 2(42)

= 84

s= 84

Substitute the value of s and a into (1)

c+s+a = 177 (1)

c + 84 + 42 = 177

c + 126 = 177

c = 177 - 126

= 51

c=51

Children = 51

Adults = 42

Students= 84

Answer:

1,1.1,1.25,1.5,1.7,9

Answer:

|-12+3|=9

Step-by-step explanation:

Hello, -12+3=-9 and then we have to take the absolute value of -9, which is 9.

Thank you

Answer:

9

Step-by-step explanation:

|-12+3|

|-9|

9

First write 40% as the decimal .40.

The word "of" tells us to multiply.

So we have (.40)(20) which is 8.

So 40% of 20 is 8.

Answer:

8

Step-by-step explanation:

40% of 20

= 40 × 20/100

= 800/100

= 8/1

= 8

Thus, 40% of 20 is 8

Answer:

27

Step-by-step explanation:

375 7579 779