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What are the measures of angles P and S? ∠P = 20°; ∠S = 160° ∠P = 40°; ∠S = 140° ∠P = 140°; ∠S = 40° ∠P = 160°; ∠S = 20°

strojnjashka [21]

*see attachement for diagram

Answer:

∠P = 140°; ∠S = 40°

Step-by-step explanation:

The figure given is a parallelogram.

Consecutive angles (adjacent angles) of a parallelogram are supplementary.

Therefore:

(x + 15)° + (6x - 10)° = 180°

Solve for x

x + 15 + 6x - 10 = 180

Add like terms

7x + 5 = 180

7x = 180 - 5

7x = 175

x = 175/7

x = 25

✔️m<P = m<R = 6x - 10 (opposite angles of a parallelogram are congruent)

m<P = 6x - 10

Plug in the value of x

m<P = 6(25) - 10 = 140°

✔️m<S = m<Q = x + 15 (opposite angles of a parallelogram are congruent)

m<S = x + 15 = 25 + 15 = 40°

5 0

2 years ago

Is 3pi/2pi a rational number or an irrational number? Explain your reasoning

Vadim26 [7]

Answer:

It is rational

Step-by-step explanation:

The pi terms cancel out when you divide. This is due to the rule x/x = 1 where x is any number you want except x cannot be zero. So replace x with pi and we have pi/pi = 1

Therefore,

(3pi)/(2pi) = (3/2)*(pi/pi)

(3pi)/(2pi) = (3/2)*1 .... use the rule mentioned above

(3pi)/(2pi) = 3/2

we get a fraction or a ratio of two whole numbers, so this proves that the given expression is rational.

7 0

2 years ago

3/4 as a percentage............

Charra [1.4K]

75%.

3/4 is .75. Drag the decimal to the right two times and it is 75%.

3 0

2 years ago

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Which is the completely factored form of 12x3 – 60x2 + 4x – 20?

Natalija [7]

Answer:

$4(x-5)(3{x}^{2}+1)$

Step-by-step explanation:

1) Find the Greatest Common Factor (GCF).

1 - What is the largest number that divides evenly into $12x^3,-60x^2,4x,$ and $-20$ ?

It is $4.$

2 - What is the highest degree of $x$ that divides evenly into $12x^3,-60x^2,4x,$ and $-20$ ?

It is 1, since $x$ is not in every term.

3 - Multiplying the results above,

The GCF is 4.

2) Factor out the GCF. (Write the GCF first. Then, in parentheses, divide each term by the GCF.)

$4(\frac{12{x}^{3}}{4}+\frac{-60{x}^{2}}{4}+\frac{4x}{4}-\frac{20}{4})$

3) Simplify each term in parentheses.

$4(3{x}^{3}-15{x}^{2}+x-5)$

4) Factor out common terms in the first two terms, then in the last two terms.

$4(3{x}^{2}(x-5)+(x-5))$

5) Factor out the common term $x-5$ .

$4(x-5)(3{x}^{2}+1)$

5 0

1 year ago

I really need help with this question

Sergeu [11.5K]

Answer:

39

Step-by-step explanation:

I assume the father's age is a 2-digit number. He is not 9 years old or younger, and he is not 100 years old or older.

The sum of the digits of a two-digit number goes up by 1 from one number to the next unless the number ends in 9.

For example, from 17 to 18, the sum of the digits goes from 8 to 9.

If the number ends in 9, for example, 29, the digits add to 11. Then the next number is 30, and now the sum of the digits is 3, which is less than 11.

The father's age now is a number whose sum of digits is not only greater than the sum of the digits next year, but it is 3 times greater.

Let's look at 2-digit number and the next number and the sum of their digits.

19, 20; sums: 10, 2; 10/2 = 5, not 3

29, 30; sums: 11, 3; 11/3 ≠ 3

39, 40; sums: 12, 4; 12/4 = 3

Answer: The father is 39 years old.

5 0

2 years ago

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