MATHEMATICS MIDDLE SCHOOL

What is the slope of the line that passes through the pair of points (-10,14) and (-6,12).

Answers

Answer 1

Answer:

Step-by-step explanation:

(-10,14) and (-6,12)

y2 = 12, y1 = 14, x2 = -6, x1 = -10

Slope m = (y2 - y1)/(x2 - x1)

m = (12 - 14)/(-6 + 10)

m = -2/4

m = -1/2

The equation of line

y - y1 = m(x - x1)

y - 14 = -1/2(x + 10)

y - 14 = -x/2 - 5

y = -x/2 - 5 + 14

y = -x/2 + 9

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Karli and her friend can paint 6/7 of a picture in 3/14 of an hour. How many pictures can they paint in a full hour?

Answers

The number of pictures which Karli and her friend can paint in a full hour is equal to 4 pictures.

What is algebra ?

Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as division , multiplication , etc.

It is given that Karli and her friend can paint 6/7 of a picture in 3/14 of an hour.

Let's assume they can paint x number of pictures in a full hour.

So , the fraction by dividing 6/7 by 3/14 can be written equal to x .

i.e.,

$(6/7)/(3/14)$ = x

We need to do the cross product here :

$(3)/(14)$ × x = $(6)/(7)$

x = ( $(6)/(7)$ ) ÷ ( $(3)/(14)$ )

We know that when dividing two fractions we need to change the division sign to multiplication sign by inverse the fraction value right to the division sign i.e.,

x = ( $(6)/(7)$ ) × ( $(14)/(3)$ )

x = 84 / 21

x = 4

Therefore , the number of pictures which Karli and her friend can paint in a full hour is equal to 4 pictures.

Learn more about algebra here :

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Answer:

4 pictures

Step-by-step explanation:

(6/7)/(3/14)=x/1

cross product

3/14*x=6/7*1

3/14x=6/7

x=(6/7)/(3/14)

x=(6/7)(14/3)

x=(6/1)(2/3)

x=12/3

x=4

Which addition exercise must you make a new ten to solve

Answers

the ten cubes or ten hole ,block

Which three ordered pairs complete the table to give solutions of the equation y = x – 7?  A.(3, –10), (0, –7), and (3, 4)
B.(–3, –10), (0, –7), and (3, –4)
C.(–3, –4), (0, –7), and (3, –4)
D.(–3, 4), (0, –7), and (3, –4)

Answers

The answer is B.(–3, –10), (0, –7), and (3, –4)
y = x - 7

According to the table:
- When x = -3, then y = -3 - 7 = -10. So the pair is (-3, -10)
- When x = 0, then y = 0 - 7 = -7. So the pair is (0, -7)
- When x = 3, then y = 3 - 7 = -4. So the pair is (3, -4)

A quadratic function has zeros of -2 and 14. Find its axis of symmetry.

Answers

Answer:

The axis of symmetry is 6

Step-by-step explanation:

The axis of symmetry is halfway between the zeros

Add the zeros and divide by 2

(-2+14)/2 = (12/2) =6

The axis of symmetry is 6

Find the measures of the angles in ∆ABC if m∠A : m∠B : m∠C = 2:3:4.

Answers

Answer:

A=40, B=60, C=80

Step-by-step explanation:

180/7 to find what "1" would be in the ratio then multiply 20*2, 20*3, 20*4.

Final answer:

The measures of the angles in a triangle with the ratio 2:3:4, namely ∆ABC, are 40°, 60°, and 80° respectively.

Explanation:

To determine the measures of the angles in ∆ABC given that m∠A: m∠B: m∠C = 2:3:4, you first need to understand that the sum of the interior angles in a triangle equals 180°.

We will begin by assigning values to the angles as per the given ratios.

Therefore, we'll say m∠A = 2x, m∠B = 3x, and m∠C = 4x.

Based on the rule that the angles of a triangle add up to 180°, we get the equation 2x + 3x + 4x = 180.

Simplifying that, we get 9x = 180.

To find the value for 'x', divide both sides of the equation by 9. This results to x = 20.

To get the measures of the angles, you then multiply the values of 'x' with the ratios.

Hence, m∠A = 2 * 20 = 40°, m∠B = 3 * 20 = 60°, and m∠C = 4 * 20 = 80°.