Mathematics, 07.12.2020 14:00, ashleyaparicio7116

Please help asap with this question!! :)

Answers: 3

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answered: Deuce9024

Step-by-step explanation:

3x + 9x +12 = 180 {linear pairr}

12x + 12 =180

12x = 180 - 12

12x = 168

x = 168/12

x = 14

3x = 3*14 = 42

4y - 10 + 3x = 180 {linear pair}

4y - 10 + 42 = 180

4y + 32 =180

4y = 180 - 32

4y = 148

y = 148/4

y = 37

answered: vallhernandez13

x = 14, y = 37

Step-by-step explanation:

The angle vertically opposite (4y-10) is also a corresponding angle to (9x + 12) so that means that angles (4y-10) and (9x+12) are equal.

4y-10 = 9x+12 Equation 1

You also know that (4y-10) and 3x add up to 180° since they both lie on a straight line.

4y-10+3x = 180 Equation 2

From the above equation, I'm going to isolate (4y-10) so that I know a value that I can substitute in Equation 1.

4y-10 = 180-3x Equation 3

Substitute 4y-10 = 180-3x into Equation 1.

4y-10 = 9x+12

180-3x = 9x+12

Put the like terms together.

180-12 = 9x+3x

Evaluate.

12x = 168

Find x.

x = 168 ÷ 12

x = 14

Subsitite x = 14 into Equation 3.

4y-10 = 180-3x

= 180-3(14)

= 180-42

= 138

Isolate 4y.

4y = 138+10

= 148

Find y.

y = 148 ÷ 4

y = 37

answered: Guest

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

$x^2-2x+y^2-6y=26$

we now create space between the x and y terms with parenthesis.

$(x^2-2x)+(y^2-6y)=26$

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

$\frac{-2}{2} =(-1)^{2} =1$

$\frac{-6}{2} =(-3)^{2} =9$

we add the squares to both sides.

$(x^2-2x+1)+(y^2-6y+9)=26+1+9$

simplify.

$(x^2-2x+1)+(y^2-6y+9)=36$

and write the quadratics in factored form.

$(x-1)^{2} +(y-3)^{2} =36$

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

answered: Guest

$2^{2x+11}=3^{x-31}$

take the logarithm of both sides (the base of the log doesn't matter):

$\ln2^{2x+11}=\ln3^{x-31}$

apply the exponent property - this says that $\ln a^b=b\ln a$ :

$(2x+11)\ln2=(x-31)\ln3$

distribute the log terms on both sides:

$(2\ln2)x+11\ln2=(\ln3)x-31\ln3$

group like terms together:

$(2\ln2-\ln3)x=-11\ln2-31\ln3$

divide through both sides by the coefficient on $x$ :

$x=-\dfrac{11\ln2+31\ln3}{2\ln2-\ln3}$

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

$x=-\dfrac{\ln2^{11}+\ln3^{31}}{\ln2^2-\ln3}$

$x=-\dfrac{\ln2^{11}3^{31}}{\ln\frac43}$

$x=-\log_{4/3}2^{11}3^{31}$

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