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3 years ago

Solve inequality -7(y+6)+33<3(5-y)

Mathematics

1 answer:

AysviL [449]3 years ago

6 0

So firstly, you want to foil -7(y+6) and 3(5-y): $-7y-42+33$

Next, combine like terms: $-7y-9$

Next, add 7y on both sides: $-9$

Next, subtract 15 on both sides: $-24$

Lastly, divide both sides by 4, and your answer will be -6 < y

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Find the perimeter of quadrilateral PQRS with the vertices P(2,4), Q(2,3), R(-2,-2), and S(-2,3).

storchak [24]

Answer:

$P=16.53\ units$

Step-by-step explanation:

we know that

The perimeter of quadrilateral PQRS is equal to the sum of its four length sides

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

the vertices P(2,4), Q(2,3), R(-2,-2), and S(-2,3)

step 1

Find the distance PQ

P(2,4), Q(2,3)

substitute in the formula

$d=\sqrt{(3-4)^{2}+(2-2)^{2}}$

$d=\sqrt{(-1)^{2}+(0)^{2}}$

$d=\sqrt{1}$

$dPQ=1\ unit$

step 2

Find the distance QR

Q(2,3), R(-2,-2)

substitute in the formula

$d=\sqrt{(-2-3)^{2}+(-2-2)^{2}}$

$d=\sqrt{(-5)^{2}+(-4)^{2}}$

$dQR=\sqrt{41}\ units$

step 3

Find the distance RS

R(-2,-2), and S(-2,3)

substitute in the formula

$d=\sqrt{(3+2)^{2}+(-2+2)^{2}}$

$d=\sqrt{(5)^{2}+(0)^{2}}$

$dRS=5\ units$

step 4

Find the distance PS

P(2,4), S(-2,3)

substitute in the formula

$d=\sqrt{(3-4)^{2}+(-2-2)^{2}}$

$d=\sqrt{(-1)^{2}+(-4)^{2}}$

$dPS=\sqrt{17}\ units$

step 5

Find the perimeter

$P=PQ+QR+RS+PS$

substitute the values

$P=1+\sqrt{41}+5+\sqrt{17}$

$P=6+\sqrt{41}+\sqrt{17}$

$P=16.53\ units$

5 0

3 years ago

16x -7<-71<br><br><br> Please Help

saw5 [17]

Answer:

x<-4

Step-by-step explanation:

$16x - 7 < - 71 \\ 16x < - 71 + 7 \\ 16x < - 64 \\ x < - 4$

4 0

3 years ago

A quantity of 230 grams of coffee is added to a jar containing 2.3 kg of coffee. What is the weight of the coffee after the addi

12345 [234]

Answer:

2.530 kg

Step-by-step explanation:

230g = 0.23 kg

2.3+0.23=2.53kg

6 0

3 years ago

Matthew bought a pair of shoes for 810 after getting a discount of 10 what is the market price of the shoe

qaws [65]

Answer:

$900

Step-by-step explanation:

If the $810 is the price after 10% discount that means

$810 is 90% of the original price

So we divide 810 / 90% or 810 / 0.9

to get $900 as final price

5 0

3 years ago

John puts the base of a 13 foot ladder 4 feet from the wall of his house. How far up the wall does the ladder reach? Round your

antiseptic1488 [7]

Answer:

12.04 feet

Step-by-step explanation:

Applying Pythagoras theorem,

$a^{2}= b^{2} + c^{2}$

$13^{2} =4^{2} + c^{2}$

$c^{2} = 145$

c= $\sqrt{145}$

c=12.04

7 0

3 years ago