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3 years ago

a direct variation function contains the points ( -8, -6 ) and (12,9 ) . Which equation represents the function ?

Mathematics

1 answer:

9966 [12]3 years ago

8 0

Answer:

y = $\frac{3}{4}$ x

Step-by-step explanation:

Given that the quantities vary directly then the equation relating them is

y = kx ← k is the constant of variation

To find k use either of the 2 given points

Using (12, 9), that is x = 12 when y = 9, then

k = $\frac{y}{x}$ = $\frac{9}{12}$ = $\frac{3}{4}$

y = $\frac{3}{4}$ x ← equation of variation

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Solve the system of equations by using substitution. x+8y=-2 x-3y=20

zysi [14]

Answer:

(14, -2)

Step-by-step explanation:

To solve by using substitution, begin by solving for a variable in the first equation. Let's solve for x:

$x+8y=-2\\x=-2-8y$

Now we know what x equals. Let's substitute this into the second equation:

$x-3y=20\\(-2-8y)-3y=20$

We can then simplify:

$-2-8y-3y=20$ Given equation

$-2-11y=20$ Combine y terms

$-11y=22$ Add 2

$y=-2$ Divide by -11

So, we now know the value of y = -2.

To find the value of X, we can substitute the value of Y into one of the equations. Let's use the first one:

$x+8y=-2$

$x+8(-2)=-2$ Substitute for y

$x-16=-2$ Distribute 8

$x=14$ Add 16

So, we now know the value of x = 14.

Therefore, we know a solution to the system of equations is (14, -2).

4 0

3 years ago

What is the volume of a sphere with a radius of 7 cm? Sphere V = 4 3 πr3 1. Substitute the radius into the formula: V = 4 3 π

netineya [11]

Answer:

1436.75504 or 1372/3π cm^3

Step-by-step explanation:

The volume of a sphere can be found using:

V = 4/3 πr^3

We know the radius is 7, so we can substitute 7 in for r

V = 4/3 π7^3

Evaluate the exponent

V = 4/3 π 343

If we want the answer in terms of pi, multiply the two other numbers, that are not pi: 4/3 and 343.

v= (4/3*343)π

v=1372/3π

If we want an exact answer, multiply 1372/3 and pi

v=1436.75504

So, the volume is 1436.75504 or 1372/3 π cm^3

4 0

3 years ago

Read 2 more answers

NO LINKS!!!! Find the equation of the circle below

inysia [295]

Answer:

$(x+3)^2+(y-2)^2=9$

Step-by-step explanation:

Equation of a circle

$(x-a)^2+(y-b)^2=r^2$

where:

(a, b) is the center
r is the radius

From inspection of the diagram, the center of the circle appears to be at point (-3, 2), although this is not very clear. Therefore, a = -3 and b = 2.

Substitute these values into the general form of the equation of a circle:

$\implies (x-(-3))^2+(y-2)^2=r^2$

$\implies (x+3)^2+(y-2)^2=r^2$

Again, from inspection of the diagram, the maximum vertical point of the circle appears to be at y = 5. Therefore, to calculate the radius, subtract the y-value of the center point from the y-value of the maximum vertical point:

⇒ radius (r) = 5 - 2 = 3

Substitute the found value of r into the equation:

$\implies (x+3)^2+(y-2)^2=3^2$