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2 years ago

Give work for equations following: -x+2y<-4 2x+3y>6 thanks sooooo much!!!!

Mathematics

1 answer:

Schach [20]2 years ago

3 0

Answer: See below

Step-by-step explanation:

A) $-x+2y < -4$

$-x+2y-2y < -4-2y$

$-x < -4-2y$

Multiply both sides by -1 and reverse the inequality:

$\left(-x\right)\left(-1\right) > -4\left(-1\right)-2y\left(-1\right)$

$x > 4+2y$

B) $2x+3y > 6$

$2x+3y-3y > 6-3y$

$2x > 6-3y$

$\frac{2x}{2} > \frac{6}{2}-\frac{3y}{2}$

$x > \frac{6-3y}{2}\\x > 3-\frac{3y}{2}$

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George bought 7.5 cases of pancake mix for his diner. A case contains 12 1.3-pound boxes. How many pounds of pancake mix did Geo

Ilya [14]

In order to get the answer to this problem, first we have to find out how many pounds does one case of pancake mix have. We know that one box has 1.3 pounds of pancake mix. We also know that one case has 12 boxes. So first, we multiply 1.3 to 12. The answer we will get is 15.6. One case of pancake mix has a total of 15.6 pounds of pancake mix. Now we also know there are 7.5 cases that George bought. So in order to get the total pounds George bought, we multiply 15.6 to 7.5. So all in all, George bought 117 pounds of Pancake Mix.

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3 years ago

Read 2 more answers

What is the equation of the circle with center (−3, 1) that passes through the point (−5, 3)?

Mariulka [41]

Answer:

( x + 3)^2 + ( y - 1)^2 = 8

Step-by-step explanation:

The equation of a circle with a center and a point

( x - a) ^2 + ( y - b) ^2 = r^2

( x , y) - any point on the circle

( a, b) - center of the circle

r^2 - radius of the circle

( -3 , 1) - center - ( a, b)

a = -3

b = 1

( -5 , 3) - point - ( x, y)

x = -5

y = 3

Step 1: substitute the center into the equation

( x -(-3)^2 + ( y - 1)^2 = r^2

( x + 3)^2 + ( y - 1)^2 = r^2

Step 2 : sub the point into the equation

( x + 3)^2 + ( y - 1)^2 = r^2

( -5 + 3)^2 + ( 3 - 1)^2 = r^2

(-2)^2 + 2^2 = r^2

4 + 4 = r^2

8 = r^2

Step 3 : sub the radius into the equation

( x + 3)^2 + ( y - 1)^2 = r^2

( x + 3)^2 + (y - 1)^2 = 8

Therefore, the equation of the circle is

( x + 3)^2 + (y - 1)^2 = 8

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3 years ago

Ryan uses 2 gallons of water to fill up 10 water balloons. Each balloon

Nutka1998 [239]

5 because your dividing 10 and 2.

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3 years ago

Match the correct equation for the variable n with * for number of times compound interest is figured. quarterly d.___ semi-annu

Dvinal [7]

Answer:

quarterly N = 4

semi-annually N = 2

Monthly N = 12

annually N = 1

Step-by-step explanation:

Given the following compound interest times :

N = number of times interest is compounded per period :

A period is regarded as a whole year.

Interest compounded;

QUARTERLY = Every 4 months per period = 12/3= 4

SEMI ANNUALLY = Every 6 months per period = 12/6 = 2

MONTHLY = Every month = 12 / 1 = 12

ANNUALLY = Every 12 months = 12 /12 = 1

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2 years ago

In a certain lottery, you must select 5 numbers (in any order) out of 26 correctly to win. a. How many ways can 5 numbers be

Step2247 [10]

Answer:

a. 7893600

$b.\ \dfrac{1}{26}$

Step-by-step explanation:

Given that there are 26 numbers out of which 5 numbers are to be chosen.

Here repetition is not allowed.

For each of the 5 cases, the total number of possibilities will keep on decreasing by 1.

1st case, number of possibilities = 26

2nd case, number of possibilities = 25

3rd case, number of possibilities = 24

4th case, number of possibilities = 23

5th case, number of possibilities = 22

a. Total number of possibilities = 26 $\times$ 25 $\times$ 24 $\times$ 23 $\times$ 22 = <em>7893600</em>

b. Probability of winning by choosing one number:

Formula for probability of an event E can be observed as: $P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

Number of favorable cases = 1

Total number of cases = 26

So, required probability:

$P(E) = \dfrac{1}{26}$

So, the answers are:

a. 7893600

$b.\ \dfrac{1}{26}$

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3 years ago