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Sergio [31]
2 years ago
15

Write an equation of the direct variation that includes the point (9, –12).

Mathematics
1 answer:
Crank2 years ago
5 0
For direct variation:
y = kx
-12 = 9k
k = -12/9 = -4/3
Therefore, the required equation is y = -4/3 x
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A sum of $4000 is invested at 5.5% interest per year. Find the amount of time needed to double the money if it’s compounded mont
musickatia [10]

9514 1404 393

Answer:

  C)  12y 8m

Step-by-step explanation:

The amount of principal P at compound monthly at interest rate r per year is given by ...

  A = P(1 +r/12)^(12t) . . . . after t years

Here, we want to find t, so ...

  A/P = (1 +r/12)^(12t)

  log(A/P) = (12t)·log(1 +r/12)

  t = log(A/P)/(12·log(1 +r/12))

Filling in the given values, we find t to be ...

  t = log(8000/4000)/(12·log(1 +0.055/12)) ≈ 12.6315 ≈ 12 years 7.6 months

It will take about 12 years 8 months to double the money.

8 0
3 years ago
To make a certain shade of orange calvin uses a rate of 2 ounces of yellow paint to 5 ounces of red paint if he uses 200 ounces
ycow [4]
Answer: 80 ounces of yellow paint

Working:
As we know 2 ounces of yellow paint to 5 ounces of red paint, we can make a ratio:

2:5

Then we look at the question which says 200 ounces of red paint, so we replace the 5 ounces of red paint in the ratio with 200.

2:200

Then we figure out how much the 5 has been multiplied by to get to 200. We do this by doing

200 divide 5 = 40

Therefore we times the 2 ounces of yellow paint by 40 which gets us:

80:200

We can think of it as a fraction too to confirm our answer:

Simplify 80 / 200

We get 2 / 5.

If you need me to further explain something please just ask :)
4 0
2 years ago
Ethan drove 100 miles and used 4 gallons of gasoline. Abby drove 225 miles and used 10 gallons of gasoline. Who got better gas m
olchik [2.2K]

Answer:

Ethan

Step-by-step explanation:

Divide the miles by the gallons of gas

8 0
3 years ago
Read 2 more answers
3(x−0.2)=1.8+x find x
bonufazy [111]

Answer:

x=6/5

Step-by-step explanation:

8 0
3 years ago
What is the surface area of this composite solid?______________ square feet 242 319 363 517
jeka57 [31]

Answer:

<h2>The right answer is 415.4 cubic feet.</h2>

Step-by-step explanation:

As you can observe in the image attached, the composite figure is formed by a square prism and a pyramid on top.

We need to find the volum of each part separately.

<h3> Square prism.</h3>

V_{prims}=11 \times 11 \times 2=242 \ ft^{3}

<h3>Square pyramid.</h3>

First, we need to find the height of the pyramid. We already know the height of each triangular face of the pyramid, which divides equally the side.

Let's use Pythagorean's Theorem to find the height of the pyramid.

7^{2}=h^{2} +(5.5)^{2}\\  49-30.25=h^{2}\\ h=\sqrt{18.75} \approx 4.3

The height is 4.3 feet, approximately.

Now, we find the volume of the pyramid

V_{pyramid}=\frac{1}{3}(11 \times 11 \times 4.3) \approx 173.4ft^{3}

The sum of both figures represents the total volume of the composite figure

V_{total}=242+173.4=415.4ft^{3}

Therefore, the right answer is 415.4 cubic feet.

3 0
3 years ago
Read 2 more answers
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