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Veseljchak [2.6K]
2 years ago
9

Put the following equation of a line into slope-intercept form, simplifying all fractions 2x + 6y = 36​

Mathematics
1 answer:
joja [24]2 years ago
6 0

Answer:

y=-\frac{1}{3} x+6

Step-by-step explanation:

Slope intercept form is y=mx+b. So, you solve for y by putting x to the other side and dividing by 6. In order it looks something like:

2x+6y=36
2x -2x +6y = 36 =2x
6y=36-2x

y=6-2/6x
y=6-1/3x

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Compound interest <br> Plz help!!!
liraira [26]

Answer:

a) A(t) = 17500(1.0053)^{12t}

b) The balance after 8 years will be of $29,069.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

A(t) = P(1 + \frac{r}{n})^{nt}

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

a)

Loan of $17,500 means that P = 17500

6.4% interest rate means that r = 0.064

Compounded monthly means that n = 12. So

A(t) = P(1 + \frac{r}{n})^{nt}

A(t) = 17500(1 + \frac{0.064}{12})^{12t}

A(t) = 17500(1.0053)^{12t}

b)

This is A(8). Then

A(8) = 17500(1.0053)^{12*8} = 29069

The balance after 8 years will be of $29,069.

8 0
2 years ago
In the illustration below, the three cube-shaped tanks are identical. The spheres in any given tank
fredd [130]

Answer:

1) Volume occupied by the spheres are equal therefore the three tanks contains the same volume of water

2) Amount \ of \, water \ remaining \ in \, the \ tank \ is \  \frac{x^3(6-\pi) }{6}

Step-by-step explanation:

1) Here we have;

First tank A

Volume of tank = x³

The  volume of the sphere = \frac{4}{3} \pi r^3

However, the diameter of the sphere = x therefore;

r = x/2 and the volume of the sphere is thus;

volume of the sphere = \frac{4}{3} \pi \frac{x^3}{8}= \frac{1}{6} \pi x^3

For tank B

Volume of tank = x³

The  volume of the spheres = 8 \times \frac{4}{3} \pi r^3

However, the diameter of the spheres 2·D = x therefore;

r = x/4 and the volume of the sphere is thus;

volume of the spheres = 8 \times \frac{4}{3} \pi (\frac{x}{4})^3= \frac{x^3 \times \pi }{6}

For tank C

Volume of tank = x³

The  volume of the spheres = 64 \times \frac{4}{3} \pi r^3

However, the diameter of the spheres 4·D = x therefore;

r = x/8 and the volume of the sphere is thus;

volume of the spheres = 64 \times \frac{4}{3} \pi (\frac{x}{8})^3= \frac{x^3 \times \pi }{6}

Volume occupied by the spheres are equal therefore the three tanks contains the same volume of water

2) For the 4th tank, we have;

number of spheres on side of the tank, n is given thus;

n³ = 512

∴ n = ∛512 = 8

Hence we have;

Volume of tank = x³

The  volume of the spheres = 512 \times \frac{4}{3} \pi r^3

However, the diameter of the spheres 8·D = x therefore;

r = x/16 and the volume of the sphere is thus;

volume of the spheres = 512\times \frac{4}{3} \pi (\frac{x}{16})^3= \frac{x^3 \times \pi }{6}

Amount of water remaining in the tank is given by the following expression;

Amount of water remaining in the tank = Volume of tank - volume of spheres

Amount of water remaining in the tank = x^3 - \frac{x^3 \times \pi }{6} = \frac{x^3(6-\pi) }{6}

Amount \ of \ water \, remaining \, in \, the \ tank =  \frac{x^3(6-\pi) }{6}.

5 0
3 years ago
Jeff hikes 1/2 mile every 15 minutes, or 1/4 hour. Lisa hikes 1/3 mile every 10 minutes, or 1/6 hour. How far do they each hike
inessss [21]

Answer:

they each hike 2 miles

Step-by-step explanation:

Jeff: 15=1/2

        *4    *4

      60 min=2 miles

Lisa:  10=1/3

          *6   *6

        60 = 2

6 0
3 years ago
Carlos needs 1.7 meters of wire for one project and 0.8 meters of wire for another project shade the model to represent the tota
vesna_86 [32]

Answer:

Step-by-step explanation:

Given that ;

Carlos needs 1.7 meters of wire for one project    &

0.8 meters of wire for another project

we are to shade the model to represent the total amount of wire Carlos needs .

NOW;

For both projects ; Carlos needs ( 1.7 + 0.8) meters of wire =  2.5 meters of wire

In  the  attached files below. the first picture shows the diagram attached to the question and the second one shows the shading of the model which represent the total amount of wire Carlos needs.

7 0
3 years ago
Given DB=42 AD=26 and SAE=52
blsea [12.9K]

Answer:

AC=42

EB=21

BC=26

thats all i know, sorry hope u figure it out

Step-by-step explanation:

4 0
3 years ago
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