Write an inequality to represent the phrase: The sum of a number an 6 is no less than 31

poizon [28]

Part A
The given line passes through (-2,2) and it is parallel to the line

$4x - 3y - 7 = 0$

We need to determine the slope of this line by writing it in slope -intercept form.

$3y = 4x - 7$

$y = \frac{4}{3} x - \frac{7}{3}$
The slope of this line is
$\frac{4}{3}$

The line parallel to this line also has slope

$m = \frac{4}{3}$

The equation is

$y = \frac{4}{3} x + c$

We substitute (-2,2)

$2 = \frac{4}{3}( - 2) + c$

$c = 2 + \frac{8}{3} = \frac{14}{3}$

The required equation is

$y = \frac{4}{3} x + \frac{14}{3}$

PART B

The given line is

$4x - 3y - 7 = 0$

The slope of this line is
$\frac{4}{3}$

The slope of the line perpendicular to it is

$m = - \frac{3}{4}$

The equation of the line is

$y = - \frac{ 3}{4} x + c$

We substitute the point, (-2,2)

$2= - \frac{ 3}{4} ( - 2) + c$

$2= \frac{ 3}{2} + c$

$c = 2 - \frac{3}{2} = \frac{1}{2}$

The equation of the perpendicular line is

$y= - \frac{ 3}{4} x + \frac{1}{2}$

6 0

3 years ago

Find the sum of first 100 even numbers.

alexdok [17]

Answer:

10100

Step-by-step explanation:

the sum of the first 100 even integers is equal to 10100.

7 0

3 years ago

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The equation y 10x describes the amount of money Sandra earns, where x is the number of hours she

tester [92]

Answer:

a) $10 per hour

b) Sandra

Step-by-step explanation:

Complete Question:

The equation y 10x describes the amount of money Sandra earns, where x is the number of hours she works and y is the amount of money she earns

The table shows the amount of money Susan cams for different numbers of hours worked

Susan's Earnings

Time (h) Money Earned

5 40

8 64

10 80

(a) How much money does Sandra eam per hour? Show your work

(b) Who earns more per hour? Justify your answer

Answer:

a)

y = 10x is sandra's equation. To find her hourly rate, we need to find how much she earns in "1" hour. Since x is hours, we plug in x = 1 and find y (which is her pay).

y = 10x

y = 10(1)

y = 10

$10 is Sandra's hourly rate.

b)

To find who earns more per hour, we need to find the hourly rate of Susan as well from the table. Then compare.

5 hours = $40 so per hour is 40/5 = 8

8 hours is 64, so per hour 64/8 = 8

10 hours is 80, so 80/10 = 8

The table is justified at $8 per hour.

We know Sandra earns $10/hr and Susan earns $8 per hour. So Sandra earns more per hour.

4 0

3 years ago

3)

Cerrena [4.2K]

Answer:

$500

Step-by-step explanation:

$25 = 5% of x

0.05x = 25

x = 25/0.05

x = 500

Answer: $500

4 0

3 years ago

4x + 1 = 2x – 5 can someone help me. Whoever gets it right gets it right gets brainliest

castortr0y [4]

Answer:

x=-3

Step-by-step explanation:

subtract "2x" to "4x + 1" and that'll leave -5 by itself and leave 2x+1 on the left and -5 on the right then subtract -1 to -5 and it'll add up to -6 then after that you'd divide 2x to -6 and get -3 and it'll leave 'x' by itself so therefore X = -3

3 0

3 years ago

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