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3 years ago

Calculate the slope of the line through the points M(-2, -1) and N(0, -13).

Mathematics

1 answer:

galina1969 [7]3 years ago

6 0

Answer:-6

Step-by-step explanation:

to solve for slope, you have to do (y1-y2)/(x1-x2)

in this problem, that turns into (-1-(-13))/(-2-0)

which is (-1+13)/(-2-0) which is 12/-2 which is -6, your answer

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1/4x – 2 = 3/8 Please show an equation and work. :)

Julli [10]

1/4x - 2 = 3/8

First, to start solving this, we can rearrange our fraction. Let's take 1/4x and change it to x/4. Why? Well, a variable can also be considered as the number 1.
$\frac{x}{4} - 2 = \frac{3}{8}$

Second, now we can continue solving for our variable (x). Let's add 2 to each side.
$\frac{x}{4} = \frac{3}{8} + 2$

Third, let's simplify 3/8 + 2. (3/8 + 2 = 2.375 =19/8)
$\frac{x}{4} = \frac{19}{8}$

Fourth, continue trying to get the variable by itself. Multiply each side by 4.
$x = \frac{19}{8} \times 4$

Fifth, let's simplify 19/8 × 4. This is simple. Leave the denominator be and just do 19 × 4, which equals 76.
$x = \frac{76}{8}$

Sixth, our final step is to simplify our fraction. To do so, we will need to list the factors of the numerator and denominator and find the greatest common factor (GCF).

Factors of 76: 1, 2, 4, 19, 38, 76
Factors of 8: 1, 2, 4, 8

Since 4 is our first common factor, it is considered our GCF.

Seventh, now let's divide. Divide both the numerator and denominator by the GCF (4) to create our new simplified fraction.
$76 \div 4 = 19 \\ 8 \div 4 = 2$

Answer in fraction form: $\fbox {x = 19/2}$
Answer in decimal form: $\fbox {x = 9.5}$

8 0

3 years ago

What are the sine and cosine ratios for a 30°–60°–90° triangle with a hypotenuse of 6, when θ = 60°?

Margaret [11]

Answer:

There are two ways to do this problem algebraically or trigonometrically.

Algebraically/geometrically

The ratios of the sides of a 30/60/90 tri. are x, x√3, 2x (short leg, long leg, hyp). Therefore, if the long leg is 6 'units'. then 6 = x√3. x = 6√3.

The hyp is 2x then the hypotenuse is 2(6√3) = 12√3, rationalizing is 12√3/3 = 4√3

Using Trig.

We can use sinx = y/r = opp/hyp. The long leg of 6 is opposite 60 degrees (pi/3).

Therefore, sin(pi/3) = 6/r =

r = 6/sin(pi/3) = 6/(√3/2) = 12/√3, when you rationalize you get 12√3/3 = 4√3

4 0

2 years ago

A rental company charges $15 plus $4 per hour to rent a bicycle. If Margie does not want to spend more than $27 for her rental,

serious [3.7K]

15 + 4(h) = 27
27 - 15 = 12
12/4 = 12
Margie can rent the bicycle for 4 hours.

8 0

3 years ago

3 less than a number p is 25

Goryan [66]

Answer:

The number is 28

Step-by-step explanation:

<u>Step 1: Make an expression </u>

$p - 3 = 25$

<u>Step 2: Add 3 to both sides </u>

$p - 3 + 3 = 25 + 3$

$p = 28$

Answer: The number is 28

5 0

3 years ago

18 and 19 please ;D!!

frosja888 [35]

Answer:

18.

∠2 = 40

∠3 = 140

∠4 =140

19.

∠1 = 134

∠2 = 46

∠3 = 134

∠4 = 46

Step-by-step explanation:

18. Using vertical angle theorem, 1 is equal to 2 and 3 is equal to 4. Therefore 2 is equal to 40 degrees. Then since 2 and 3 are supplementary adjacent angles or a linear pair, they equal 180 when combined. 180-40 equals 140. 3 and 4 are also vertical angles so 3 = 4 and they are both 140.

19. Angles 1 & 3 and 2 & 4 are vertical angles because they are directly across from each other and share the same bisectors. You can use what you know about special angle pairs to find the measure of each angle because since 1 & 3 are vertical angles and 2 & 4 are also vertical angles, 1 is equal to 3 and 2 is equal to 4. So, since the angle formed at the right is angle 2, we can confirm that angle 4 is equal to it and therefore angles 2 and 4 are 46 degrees. Then since angles 1 & 2 and 3 & 4 are linear pairs, we can say that angle 1 + angle 2 is equal to 180 and the same for angles 3 & 4. So subtract 180 - 46 and you get 134. Therefore angles 1 and 3 are equal to 134 degrees.

4 0

3 years ago