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mamaluj [8]
3 years ago
15

In AOPQ, m2O = (2x – 5)º, m P = (3x – 8)°, and mZQ = (10x – 17). What is the value of x?

Mathematics
1 answer:
Misha Larkins [42]3 years ago
3 0

9514 1404 393

Answer:

  x = 14

Step-by-step explanation:

The sum of angles in a triangle is 180°:

  ∠O +∠P +∠Q = 180°

  (2x -5)° +(3x -8)° +(10x -17)° = 180°

  15x -30 = 180 . . . . . divide by °, collect terms

  x -2 = 12 . . . . . . . . . divide by 15

  x = 14 . . . . . . . . . . . .add 2

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A rectangular prism has a length of 312 inches, a width of 5 inches, and a height of 112 inches. What is the volume of the prism
NeTakaya
The correct question is
<span>A rectangular prism has a length of 3 1/2 inches, a width of 5 inches, and a height of 1 1/2 inches. What is the volume of the prism? Enter your answer in the box as a simplified mixed number or a decimal.</span>

we know that
length=3 1/2 in--------> (3*2+1)/2=7/2 in
width= 5 in
height=1 1/2 in--------> (1*2+1)/2=3/2 in

[volume of the prism]=[length]*[width]*[<span>height]
</span>[volume of the prism]=[7/2]*[5]*[3/2]=105/4 in³-------> 26.25=26 1/4 in³

the answer is 26 1/4 in³


7 0
3 years ago
suppose we want to choose 6 letters without replacement from 13 distinct letters. A) how many ways can this be done if order doe
kiruha [24]

Answer: A) 1716   B) 1235520

Step-by-step explanation:

  • If order doesn't matter , then we use combinations, where the number of combinations of selecting r things from n is given by :-

^nC_r=\dfrac{n!}{r!(n-r)!}

  • If order matters , then we use permutations, where the number of permutations of selecting r things from n is given by :-

^nP_r=\dfrac{n!}{(n-r)!}

Given, Total distinct letters = 13

To choose = 6 letters

A) Number of ways to choose (if order does not matter)=^{13}C_6

=\dfrac{13!}{6!7!}=\dfrac{13\times12\times11\times10\times9\times8\times7!}{(720)\times 7!}\\\\= $$1716

B) Number of ways to choose (if order matters)=^{13}P_6

=\dfrac{13!}{7!}=\dfrac{13\times12\times11\times10\times9\times8\times7!} 7!}\\\\= $$1235520

Hence, A) 1716   B) 1235520

5 0
4 years ago
Cindy has a rectangular patio that is 20 feet wide and 40 feet long. She plans to expand her patio by increasing both dimension
xenn [34]

Answer: 200

Step-by-step explanation:divide both by 2 then multiply

4 0
3 years ago
Please help please help please PLZZZ HELP
Sergeeva-Olga [200]

Answer:

The y-intercept is -4

y= -2/3 + (-4)

5 0
3 years ago
Solve: 2 x + 5y + 5 = 0 <br> 2y=3x+17. <br> Find x and y
Yanka [14]

Answer:

x = -5 and y = 1

Step-by-step explanation:

a) 2x + 5y +5 = 0

a) 2x + 5y = -5

b) 2y = 3x + 17

b) y = 3/2x + 17/2

a) 2x + 5(3/2x + 17/2) = -5

a) 2x + 15/2x + 85/2) = -5

a) 19/2x = -5 - 85/2

a) 19/2x = -95/2

a) x = (-95/2) / (19/2)

x = -5

b) 2y = 3(-5) + 17

b) y = 2/2

y = 1

7 0
2 years ago
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