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miv72 [106K]
3 years ago
12

Nine less than four times a number is the same as nineteen

Mathematics
2 answers:
BaLLatris [955]3 years ago
5 0

Answer:

x= 7, the number is 7

Step-by-step explanation:

4x-9= 19

  • Add 9 to both sides

4x=28

  • Divide each side by 4

x=7

Lemur [1.5K]3 years ago
5 0

Answer:

4x - 9 = 19

Step-by-step explanation:

We can represent 4 times any numbers as 4x.

Then they want 9 less than 4x. This means that they want 4x but 9 units shorter. So to make 4x 9 units shorter, you would take away 9 from 4x which is represented as 4x - 9. A common mistake is writing this as 9 - 4x.

They also want 4x - 9 to be the same, or equal to, 19. So to equate both expression, you would add the equals sign between both expressions.

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In slope intercept form, write the equation for the line that passes through the point (2,3) and the point (7,13).
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First, Use the slope equation to find the slope of the line passing thru these two points:

m=rise/run

Here, the rise is 13-3, or 10, and the run is 7-2, or 5.  Thus, the slope, m, is 10/5, or 2:  m=2.

We want the slope-intercept form, so let's begin with its general form:

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Substituting these values into y=2x+b:    3 = 2(2) + b, or b= 3 -4, or b = -1.

Then the equation of this line, in slope-intercept form, is y = 2x - 1.

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What other points are on the line of direct variation through (5, 12)? Check all that apply. (0, 0) (2.5, 6) (3, 10) (7.5, 18) (
aalyn [17]

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form y/x=k or y=kx

in this problem we have

the point (5,12) is on the line of direct variation

so

Find the constant of proportionality k

y/x=k-------> substitute ------> k=12/5

the equation is

y=\frac{12}{5}x

Remember that

If a point is on the line of direct variation

then

the point must satisfy the equation of direct variation

we're proceeding to verify each point

<u>case A)</u> point (0,0)

x=0\ y=0

Substitute the value of x and y in the direct variation equation

0=\frac{12}{5}*0

0=0 -------> is true

therefore

the point (0,0) is on the line of direct variation

<u>case B)</u> point (2.5,6)

x=2.5\ y=6

Substitute the value of x and y in the direct variation equation

6=\frac{12}{5}*2.5

6=6 -------> is true

therefore

the point (2.5,6) is on the line of direct variation

<u>case C)</u> point (3,10)

x=3\ y=10

Substitute the value of x and y in the direct variation equation

10=\frac{12}{5}*3

10=7.2 -------> is not  true

therefore

the point (3,10) is not on the line of direct variation

<u>case D)</u> point (7.5,18)

x=7.5\ y=18

Substitute the value of x and y in the direct variation equation

18=\frac{12}{5}*7.5

18=18 -------> is true

therefore

the point (7.5,18) is on the line of direct variation

<u>case E)</u> point (12.5,24)

x=12.5\ y=24

Substitute the value of x and y in the direct variation equation

24=\frac{12}{5}*12.5

18=30 -------> is not true

therefore

the point  (12.5,24) is not on the line of direct variation

<u>case F)</u> point (15,36)

x=15\ y=36

Substitute the value of x and y in the direct variation equation

36=\frac{12}{5}*15

36=36 -------> is true

therefore

the point (15,36) is on the line of direct variation

therefore

<u>the answer is</u>

(0,0)

(2.5,6)

(7.5,18)

(15,36)


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