the sum of two numbers,x and y is 12. the difference of x and two times y is 6. what are the values of x and y?

What is the equation for the translation of X^2+y^2=9 four units to the right and three units down

icang [17]

We know that
X²+y²=9 -------> X²+y²=3²
is the equation of a circle with center (0,0) and radius r=3 units
so
the translation of four units to the right and three units down is equals to move the center (0,0)--------> (0+4,0-3)------> (4.-3)

the new center of the circle is (4,-3)
the new equation is
(x-4)²+(y+3)²=3²

see the attached figure

4 0

3 years ago

If QS bisects PQT, SQT=(8x- 25),PQT=(9x+34), and SQR=112, find each measure.

Goryan [66]

The values of the angles are; x = 12°, m∠PQS = 71°, m∠PQT = 142° and m∠TQR = 41°

<h3>What are the measure of the each angle?</h3>

The required angles; x, m∠PQS, m∠PQT, and m∠TQR

The given parameters are bisects ∠PQT

m∠SQT = (8·x - 25)°

m∠PQT = (9·x + 34)°

m∠SQR = 112°

We have;

m∠PQT = m∠SQT + m∠PQS (Angle addition postulate)

m∠SQT ≅ m∠PQS (Angles formed by angle bisector are congruent)

m∠SQT = m∠PQS by Definition of congruency

m∠PQT = 2 × m∠SQT

Therefore;

(9·x + 34)° = 2 × (8·x - 25)° = (16·x - 50)°

Collecting like terms gives:

(34 + 50)° = 16·x - 9·x = 7·x

7·x = 84°

x = 84°/7 = 12°

x = 12°

m∠SQT = (8·x - 25)°

Therefore;

m∠SQT = (8 × 12 - 25)° = 71°

m∠SQT = 71°

m∠PQT = 2 × m∠SQT

∴ m∠PQT = 2 × 71° = 142°

m∠PQT = 142°

m∠PQS = m∠SQT (Angles formed by the same bisector )

∴ m∠PQS = m∠SQT = 71°

m∠PQS = 71°

m∠SQR = m∠SQT + m∠TQR (Angle addition postulate)

m∠SQT = 71°

∴ m∠SQR = 112° = 71° + m∠TQR

m∠TQR = 112° - 71° = 41°

m∠TQR = 41°

Learn more about angles here:

brainly.com/question/2882938

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4 0

2 years ago

The attic of a house has the shape of a triangular prism. The triangular end of the attic has a base that is 12 feet across and

Liono4ka [1.6K]

1440ft3 would be your beloved answer

6 0

3 years ago

Which statement is true about the parts of this expression?

olganol [36]

A) The constant is 7.5. FALSE. 7.5 is a coefficient, not a constant.

B) The coefficients are 7.5 and -9. FALSE. The coefficients are 7.5, -1/9 and 2. 50, being a constant, could be regarded as a coefficient in this case.

C) The variables are x and y. FALSE. There are three variables: x, y and z.

D) The like terms are 7.5y and 2y. TRUE. The variable (y) is the same in each term.

4 0

3 years ago

Read 2 more answers

Which ordered pair is a solution of the equation 2x − y = 9?

Elodia [21]

You can try by plugging each ordered pair and seeing if the equation comes out true.

(5, 1)

2 * 5 - 1 = 9

That's correct so C is the correct answer.

6 0

3 years ago

Read 2 more answers