What is the slope and y-intercept of the linear function? f(x)= 2/3x + 12

Please help! I'll mark brainiest

vovikov84 [41]

Answer: x = 14

Step-by-step explanation: 14 minus 12 is 2

6 0

3 years ago

You have two cards with a sum of (-12) in your hands. what two cards could you have?

Readme [11.4K]

Your two cards could be a negative six and a positive two.

4 0

3 years ago

If triangle CAT is similar to triangle DOG, which of the following statements is incorrect?

jeyben [28]

Answer:

1. triangle TCA ~ triangle GOD

4. If TC/GD=3/2, then m<T/m<G=3/2.

Step-by-step explanation:

The statements of the question are

1. triangle TCA ~ triangle GOD

2. AT: OG= AC:OD

3. If TC/GD=3/2, then AC/OD=3/2.

4. If TC/GD=3/2, then m<T/m<G=3/2.

5. If the scale factor of triangle CAT to triangle DOG is 3 to 2, then the scale factor of triangle DOG to triangle CAT is 2 to 3.

6. If AC is twice as long as AT, then OD is twice as long as OG

Verify each statement

1) triangle TCA ~ triangle GOD

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

triangle CAT ~ triangle DOG -----> is given

so

Reorder

Corresponding sides are named using pairs of letters in the same position on either side of the congruence statement

triangle TCA ~ triangle GDO

therefore

The statement is not correct

2). AT: OG= AC:OD

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

triangle CAT ~ triangle DOG -----> is given

so

Applying proportion

$\frac{AT}{OG}=\frac{AC}{OD}=\frac{TC}{GD}$

The statement is true

3). If TC/GD=3/2, then AC/OD=3/2.

we have that

$\frac{AT}{OG}=\frac{AC}{OD}=\frac{TC}{GD}$ ---> see part 2)

so

$\frac{TC}{GD}=\frac{AC}{OD}$

therefore

The statement is true

4). If TC/GD=3/2, then m<T/m<G=3/2

Remember that

In two similar triangles, corresponding angles are congruent

so

$m\angle T=m\angle G$

$m\angle T/m\angle G=1$

therefore

The statement is false

5). If the scale factor of triangle CAT to triangle DOG is 3 to 2, then the scale factor of triangle DOG to triangle CAT is 2 to 3

we know that

If the scale factor of triangle CAT to triangle DOG is a/b. then the scale factor of triangle DOG to triangle CAT is b/a

The scale factor will be the reciprocal

therefore

The statement is true

6). If AC is twice as long as AT, then OD is twice as long as OG

we know that

$\frac{AT}{OG}=\frac{AC}{OD}$

Reorder

$\frac{AT}{AC}=\frac{OG}{OD}$

If AC is twice as long as AT ----> AC=2AT

If OD is twice as long as OG ----> OD=2OG

substitute

$\frac{AT}{2AT}=\frac{OG}{2OG}$

simplify

$\frac{1}{2}=\frac{1}{2}$ ----> is true

therefore

The statement is true

5 0

2 years ago

A cylindrical tank holds 20,000 gallons of water, which can be drained from the bottom of the tank in 20 minutes. The function g

IgorLugansk [536]

You didn't include the function.

If the function is, V = 20,000 (1 - t/20)^2, as you can see, for t = 20, V = 0

Then I am going to show you the work with that function, and you can use the same procedure with your own fucntion.

The rate of change of the volume is the derivative of the function with respect to the time.

[dV/dt] = 20,000 *2 [1 -t/20] * [-1/20] = - 2000 [1 - t/20] = 2000[t/20 - 1]

At t = 3

dV/dt = 2000[3/20 - 1] = -1700 gallons / min

The negative sign mean decreasing.

The answer is - 1700 gallons / min

Now, for the same function, if the time is t = 2, you would obtain one of the results of the list of options.

dV/dt = 20,000 [2/20 - 1] = -1800 gallons/minute, which is the option D of the list.

3 0

3 years ago

Find the midpoint between 3+8i and 2-i

exis [7]

Answer:

(5/2) +(7/2)i

Step-by-step explanation:

The midpoint is the average value:

((3 +8i)+(2 -i))/2 = (5 +7i)/2 = (5/2) +(7/2)i

7 0

3 years ago