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2 years ago

Will give brainliest

Mathematics

2 answers:

kow [346]2 years ago

5 0

Answer:

PR= 8

ST=5

Step-by-step explanation:

PQ and PR are congruent so

2x=8

x=4

2*4=8

PR=8

ST and TU are congruent so

5z=2z+3

3z=3

z=1

5*1=5

ST=5

12345 [234]2 years ago

3 0

Answer:

PR=8

ST=5

Step-by-step explanation:

QS=SR (marked)

a²=b²+c² (TRIANGLE PQS)

PQ²=PS²+QS²

8²=PS²+SR² (PQ=8, QS=SR)

64=PS²+SR²

a²=b²+c² (TRIANGLE PRS)

PR²=PS²+SR²

(2x)²=64

2x=8

x=4

PR=2x=2(4)=8

a²=b²+c² (TRIANGLE VUT)

VT²=TU²+UV²

VT²=(2z+3)²+UV²

VT²=4z²+12z+9+UV²

a²=b²+c² (TRIANGLE VST)

VT²=VS²+ST²

VT²=VS²+25z²

4z²+12z+9+UV²=VS²+25z²

21z²-12z-9=0

7z²-4-3=0

(7z+3)(z-1)=0

z=-3/7 or z=1

cant be neg, z=1

ST=5(1)=5

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Caroline has some dimes and some quarters. She has a maximum of 15 coins worth at least $2.85 combined. If Caroline has 3 dimes,

gayaneshka [121]

Answer:

11, 12.

Step-by-step explanation:

Let q represent number of quarters.

We have been given that Caroline has a maximum of 15 coins worth at least $2.85 combined. We are also told that Caroline has 3 dimes. This means that total coins are less than or equal to 15.

We can represent this information in an inequality as:

$q+3\leq 15...(1)$

We are also told that the coins worth at least $2.85 combined. This means that the worth of all coins is greater than or equal to 2.85.

We know that each dime is worth $0.10 and each quarter is worth $0.25.

$0.25q+3(0.10)\geq 2.85...(2)$

Now, let us solve our system of inequalities.

From 1st inequality, we will get:

$q+3-3\leq 15-3$

$q\leq 12$

From 2nd inequality, we will get:

$0.25q+0.30\geq 2.85$

$0.25q+0.30-0.30\geq 2.85-0.30$

$0.25q\geq 2.55$

$\frac{0.25q}{0.25}\geq \frac{2.55}{0.25}$

$q\geq 10.2$

Upon combining our both inequalities, we will get:

$10.2\leq q\leq 12$

This means that numbers of quarters would be greater than or equal to 10.2 and less than or equal to 12.

Since we cannot have 0.2 of a coin, therefore, Caroline could have 11 or 12 quarters.

6 0

2 years ago

8. There are 10 balls in a bag numbered from 1 to 10. Three balls are selected at random without replacement.

PIT_PIT [208]

Answer:

a. 720

b. 0.3

Step-by-step explanation:

Three balls are selected at random without replacement.

First ball can be selected in 10 ways

Second ball can be selected in 9 ways

Third ball can be selected in 8 ways

Thus, there are 10×9×8 =720 different ways of selecting three balls.

There are three cases that satisfy this condition

first ball picked is 5, the others are not
first ball is not 5, second is 5, third is not
first and second ball is not five, third ball is 5

Each probabilities are:

$\frac{1}{10} * \frac{9}{9} *\frac{8}{8} =\frac{1}{10}$
$\frac{9}{10} *\frac{1}{9} *\frac{8}{8} =\frac{1}{10}$
$\frac{9}{10} *\frac{8}{9} *\frac{1}{8} =\frac{1}{10}$

Thus, one of the balls selected is the number 5 is then $\frac{1}{10} + \frac{1}{10} + \frac{1}{10} = \frac{3}{10}$

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2 years ago

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sveticcg [70]

17 is a prime number so the simplest form is 17/100

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3 years ago

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WARRIOR [948]

Answer:

Step-by-step explanation:

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2 years ago

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dolphi86 [110]

Answer:

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Step-by-step explanation:

A. S/5; when S=20, the number of socks in each group is 4.

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2 years ago