What is the equation in point−slope form of the line passing through (−2, −5) and (2, 3)?(A. y+2 = -2(x+5); B. y-2 = 2(x-3); C. y-3 = 2(x-2); D. y+3 = -2(x+2))

Answers

Answer 1

Answer: Hi,

m = (y-y₀)/(x-x₀)
m = (-5-3)/(-2-2)
m = -8/-4
m = 2

For point (2,3) ⇒ x₀ = 2 and y₀ = 3

y-y₀ = m(x-x₀)
y-3 = 2(x-2)

For point (-2,-5) ⇒ x = -2 and y = -5

-5-3 = 2(-2-2)
-8 = 2(-4)
-8 = -8 ⇒ True

Answer:

C. The equation is y-3 = 2(x-2)

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A pile of sand has a weight of 90kg.The same is put into a small bag, a medium bag and a large bag in the ratio of 2:3:7.Work out the weight of sand in each bag

Answers

Remark

This requires some sort of constant that each of the ratio members is multiplied by.

Call the constant x

Equation

2x + 3x + 7x = 90 Add the left hand side

Solution

12x = 90 Divide by 13

x = 90 /12

x = 7,5

Answer

2x = 2 * 7.5

2x = 15

3x = 22.5

7x = 52.5

Sum = 90 as it should be

Variable y varies directly with variable x, and y = 6 when x = 9. What is the value of x when y = 18?

Answers

Well, 18 is 6 x 3

Since y was multiplied by 3, we can multiply x by 3 to get its value

9 x 3 = 27

(9)(6)=(x)(18)
54=18x
3=x
hope this helps!

Triangle ABC is similar to triangle QRS by the AA Similarity Postulate.Also, m∠A = 45° and m∠S = 75°.

What is m∠B?

_________ °

Answers

Answer:

Measure of ∠B is 60°

Step-by-step explanation:

Given triangle ABC is similar to triangle QRS.

m∠A = 45° and m∠S = 75°

we have to find the measure of ∠B.

As triangles are similar then corresponding angles are congruent.

⇒ ∠A≅∠Q, ∠B≅∠R, ∠C≅∠S

hence, m∠C=m∠S=75°

By angle sum property

m∠A+m∠B+m∠C=180°

⇒ 45°+m∠B+75°=180°

⇒ m∠B+120°=180°

⇒ m∠B=60°

hence, measure of ∠B is 60°

Angle B is 60 degrees

without using your calculator or computer graphing tool. match each function rule with its graph. In each case, write a sentence explaining the type of variation that relates (x) and (y) for example Y is proportional to ..... with constant of proportionality....?

Answers

Well I know that c. goes with I. just because I saw so many x^3 graphs.

For a. the parent function is x^2, so 0.5x^2 should look about the same as x^2, so the answer is VI.

The graphs that match the function given are:

(a) VI, (b) III, (c) I, (d) II, (e) V, (f) IV

Consider the equations of the graphs given :

(a) y = 0.5 x²

This is a quadratic equation and thus will be a parabola.

This matches VI.

y is directly proportional to the square of x.

(b) y = 5/x²

Here negative values of y are not possible since x is squared.

Also, the values of y will be equal to a and -a.

This matches III.

y is inversely proportional to the square of x.

Here negative values of x will have the y values also negative.

Also, the value increases when x increases.

This matches I.

y is directly proportional to the cube of x.

(d) y = 1/x³

y value for x = -a is the negative of the y value for x = a.

Also, as x increases y decreases.

The function is not defined at 0.

This matches II.

y is inversely proportional to the cube of x.

(e) y = 3√x

Here since x is inside the cube, not defined for negative values of x.

As x increases, y also increases.

This matches V.

y is directly proportional to the square root of x.

(f) y = (0.5)ˣ

For negative values o x, the value of y will be high and for positive values of x, the value of y will be lower.

This matches IV.

y is exponentially related to x.

Learn more about Functions here :

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If 3a - 2 = 10, what is the value of 8a + 1?

Answers

Answer:

8a+1=33

Step-by-step explanation:

you can solve 3a-2=10 by simplifying to 3a=12, so a=4. Then you replace the a in 8a+1 with 4 to get 32+1, which is 33

Answer:

Step-by-step explanation:

3a-2= 10

3a=12

a=4

in this equation a=4 so you substitute that value into the other equation

8(4) +1=33

(-6x+3)-(-6x+8)
jrye ga ue,j

Answers

Answer:

(-6x + 3) - (-6x + 8) simplifies to 11.

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