Twelve less than the product of three and a number is less than 21.

Answers

Answer 1

Answer:

the answer is 11

11x3= 33

33-12=21

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For $7.52, you purchased 8 pens and highlighters from a local bookstore. Each highlighter costs $1.09 and each pen costs $.69. How many pens did you buy.

Answers

p=number of pens
h=number of highlighters

p+h=8

1.09h+0.69p=752

p+h=8
minus h from both sides
p=8-h

sub that for p

1.09h+0.69(8-h)=7.52
1.09h+5.52-0.69h=7.52
0.4h+5.52=7.52
minus 5.52 from both sides
0.4h=2
divide both sides by 0.4
h=5

sub back

h=8-p
5=8-p
minus 8 frm both sides
-3=-p
mltiply both sides by -1
3=p

3 pens you bought

Let p be the number of pens purchased and h be the number of highlighters purchased.
p + h = 8 ..........(1)
h = 8 - p ...........(2)
0.69p + 1.09h = 7.52 ........(3)
Plugging the value for h from (2) into equation (3) we get:
0.69p + 1.09(8 - p) = 7.52 .....(4)
Expanding the bracket in (4) gives:
0.69p + 8.72 - 1.09p = 7.52
Therefore
-0.4p = -1.2
p = -1.2/-0.4 = 3
The answer is 3 pens.

What is the solution of the system? Use substitution. 4x – y = 5
3x – 7 = 2
A) (3, 7)
B) (7, -7)
C) (-3, 7)
D) (3/4, 2/5)

Answers

We need to solve 3x-7=2 for x

Let's start by adding 7 to both sides

3x-7+7=2+7

3x=9

Now just divide both sides by 3 so we can find the value for x

3x/3=9/3

x=3

Now substitute 3 for x in 4x-y=5 so we can find the value for y

4x-7=5

4(3)-y=5

-y+12=5

Add -12

-y+12-12=5-12

-y=-7

Now divide both sides by -1 so we can find the positive value for y

-y/-1=-7/-1

y=7

The answer is A

(3,7)

Good luck:0

Given points A(2, 3) and B(-2,5), explain how you could use the Distance Formula and an indirect argument to show that point C(O, 3) is NOT the midpoint of AB.

Answers

Answer:

Therefore C is not the midpoint of AB.

Step-by-step explanation:

Midpoint: The midpoint is a point from which the distance between the endpoints of a line segment is always equal.

Distance formula:

The distance between the points (x₁,y₁) and (x₂,y₂) is

$√((x_2-x_1)^2+(y_2-y_1))$

Given points are A(2,3) and B(-2,5).

If C(0,3) is the midpoint of the line segment AB,then AC=BC.

The distance between AC is

$√((0-2)^2+(3-3)^2)$

$=√(2^2)$

=2 units

The distance between AC is

$√((0-(-2))^2+(3-5)^2)$

$=√(2^2+2^2)$

$=4√(2)$ units.

Since AC ≠ BC

Therefore C is not the midpoint of AB.

The distances (y), in miles, of two cars from their starting points at certain times (x), in hours, are shown by the equations below:Car A
y = 45x + 20

Car B
y = 35x + 60

WILL UPVOTE
After how many hours will the two cars be at the same distance from their starting point and what will that distance be?

3 hours, 200 miles

3 hours, 180 miles

4 hours, 200 miles

4 hours, 180 miles

Answers

If you would like to find the amount of hours and the distance, you can calculate this using the following steps:

y = y
45x + 20 = 35x + 60
45x - 35x = 60 - 20
10x = 40
x = 40 / 10
x = 4 hours

y = 45x + 20 = 45 * 4 + 20 = 200 miles
y = 35x + 60 = 35 * 4 + 60 = 200 miles

The correct result would be 4 hours, 200 miles.

Answer:

4 hours, 200 miles

Step-by-step explanation:

If P(x,y) is the point on the unit circle defined by real number theta , then csc theta= _____.x/y
y/x
1/x
1/y

Answers

csc thta =r/ y=1 /sin theta
see attachment below

Answer:1/y

Step-by-step explanation:

Select all that apply.Debra usually works 16 hours a week, but this week she worked 22 hours. What is the change in her hours?

an increase of 6 hours
an increase of 37.5%
an increase of 27.3%
a decrease of 6 hours

Answers

If you would like to know the change in Debra's hours, you can calculate this using the following steps:

x% of 16 hours is 22 hours
x% * 16 = 22
x/100 * 16 = 22
x = 22 * 100 / 16
x = 137.5%

137.5% - 100% = 37.5%

22 hours - 16 hours = 6 hours

The correct result would be: an increase of 6 hours, and an increase of 37.5%.

Answer:

a decrease of 6 hours

an increase of 37.5%

Step-by-step explanation:

Hope it helps :b

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