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ss7ja [257]
3 years ago
10

Line MN passes through points M4, 3) and M7, 12). If the equation of the line is written in slope-intercept form, y-mx+ b, what

is the value of b?
Mathematics
1 answer:
Butoxors [25]3 years ago
4 0

Answer:

<h2>b = -9</h2>

Step-by-step explanation:

The slope-intercept form of an equation of a line:

y=mx+b

m - slope

b - y-intercept

The formula of a slope:

m=\dfrac{y_2-y_1}{x_2-x_1}

We have the points M(4, 3) and N(7, 12). Substitute:

m=\dfrac{12-3}{7-4}=\dfrac{9}{3}=3

Therefore we have the equation:

y=3x+b

Put the coordinates of the point M to the equation:

3=3(4)+b

3=12+b            <em>subtract 12 from both sides</em>

-9=b

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The denominator of a fraction is two more than the numerator. If both numerator and denominator are decreased by six, the simpli
ira [324]

Answer:

\dfrac{40}{42}

Step-by-step explanation:

Let the numerator of the fraction=x

Since the denominator of a fraction is two more than the numerator.

Denominator=x+2

The fraction is therefore:

\dfrac{x}{x+2}

If both numerator and denominator are decreased by six, the fraction becomes:

\dfrac{x-6}{x+2-6}

The simplified result is \dfrac{17}{18}

Therefore:

\dfrac{x-6}{x+2-6}=\dfrac{17}{18}\\$Next, we solve for x\\Cross multiply\\18(x-6)=17(x+2-6)\\18(x-6)=17(x-4)\\Expand the bracket\\18x-108=17x-68\\Collect like terms\\18x-17x=-68+108\\x=40

Substituting x=40 into the initial fraction

\dfrac{x}{x+2}=\dfrac{40}{40+2}=\dfrac{40}{42}

Therefore, the original fraction is \dfrac{40}{42}

4 0
3 years ago
Cuál es el máximo común divisor de<br>25:<br>30:​
Minchanka [31]

Answer:

5

Step-by-step explanation:

8 0
3 years ago
Emergency I need help I don't understand this​
lora16 [44]

Answer:

108 is your answer.

Step-by-step explanation:

1 x + 2x + 3x = 180

10 x = 180

x = 180/ 10

x = 18

Then

18 X 6 = 108

I HOPE IT WILL HELP YOU.

Have a great day.

it's me Sopnila.

❤❤❤

8 0
3 years ago
Read 2 more answers
On Monday, 341 students went on a trip to the zoo. All 6 buses were filled and 5 students had to travel in cars. How many studen
Otrada [13]

Answer:

If 4 students travelled in cars, then 341 - 5 = 336students travelled by bus.

 There were 5 buses.  336÷ 6 = 56

 There were 56 students on each bus.

3 0
3 years ago
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Help with A and B plzzzz
Digiron [165]

a.) The height of the closet is 96 inches, and you want to have 4 rows, so you divide the total height 96 by 4

96 ÷ 4 = 24

So each cube organizer can be a height of 24 inches since it divides out evenly


b.) Each shoe box is 4 1/2 inches, because there are 3 boxes that are stacked on top of each other, you can multiply 4 1/2 by 3, or you can do 4 1/2 + 4 1/2 + 4 1/2.

4 1/2 + 4 1/2 + 4 1/2 = 12 3/2 = 13 1/2

The total height of the 3 boxes is 13 1/2


6 0
3 years ago
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