All categories

3 years ago

∠A and ∠B are supplementary. m∠A = (6x + 5), m∠B = (2x + 15). Find the measure of each angle.

Mathematics

1 answer:

Anastaziya [24]3 years ago

4 0

Answer:

125 and 55

Step-by-step explanation:

180=8x+20

160=8x

x=20

6(20)+5 2(20)+15=

120+5=125 degrees 40+15=55 degrees

You might be interested in

A general contractor is constructing a building that requires a concrete foundation that is to be 20 feet by 12 feet and 4 inche

ikadub [295]

First we calculate the volume of the foundation:

Volume (V) = 20 ft * 12 ft * 4 in (1 ft / 12 in)

V = 80 ft^3

Since the cost is in cubic yard (yard^3) so convert:

V = 80 ft^3 * (1 yard^3 / 27 ft^3) = 2.963 yard^3

So the total cost is:

cost = ($125 / yard^3) * 2.963 yard^3

7 0

3 years ago

Read 2 more answers

David bought a used car for $3,000 and later sold it for $1,000. What was the approximate percent decrease in the price of the c

Cloud [144]

The approximate decrease is around 66 percent.

8 0

3 years ago

Read 2 more answers

Luke has a credit line of $8,500 on his credit card. He had a previous balance of $4,236.87 and

Molodets [167]

Subtract the payment from the previous balance:

4236.87 - 3200 = 1036.87

Now add his total purchases:

1036.87 + 989.42 = 2026.29

This is the total amount he owes, now subtract that from his credit line:

8500 - 2026.29 = 6473.71

His available credit is $6,473.71

8 0

3 years ago

Read 2 more answers

Prime factorization

MAVERICK [17]

Answer:

Step-by-step explanation:

31 is a prime number meaning the only factors it has are 1 and itself, 31. If we take its factors 1 and 31 and multiply them together, we get 31.

3 0

3 years ago

Find the center that eliminates the linear terms in the translation of 4x^2 - y^2 + 24x + 4y + 28 = 0.(-3, 2)(-3,- 2)(4, 0)

baherus [9]

Step 1

Given;

$4x^2-y^2+24x+4y+28=0$

Required; To find the center that eliminates the linear terms

Step 2

$\begin{gathered} 4x^2-y^2+24x+4y=-28 \\ 4x^2+24x-y^2+4y=-28 \\ Complete\text{ the square }; \\ 4x^2+24x \\ \text{use the form ax}^2+bx\text{ +c} \\ \text{where} \\ a=4 \\ b=24 \\ c=0 \end{gathered}$ $\begin{gathered} consider\text{ the vertex }form\text{ of a }parabola \\ a(x+d)^2+e \\ d=\frac{b}{2a} \\ d=\frac{24}{2\times4} \\ d=\frac{24}{8} \\ d=3 \end{gathered}$ $\begin{gathered} Find\text{ the value of e using }e=c-\frac{b^2}{4a} \\ e=0-\frac{24^2}{4\times4} \\ e=0-\frac{576}{16}=-36 \end{gathered}$

Step 3

Substitute a,d,e into the vertex form

$\begin{gathered} a(x+d)^2+e \\ 4(x+_{}3)^2-36 \end{gathered}$ $\begin{gathered} 4(x+3)^2-36-y^2+4y=-28 \\ 4(x+3)^2-y^2+4y=\text{ -28+36} \\ \\ \end{gathered}$

Step 4

Completing the square for -y²+4y

$\begin{gathered} \text{use the form ax}^2+bx\text{ +c} \\ \text{where} \\ a=-1 \\ b=4 \\ c=0 \end{gathered}$ $\begin{gathered} consider\text{ the vertex }form\text{ of a }parabola \\ a(x+d)^2+e \\ d=\frac{b}{2a} \\ d=\text{ }\frac{4}{2\times-1} \\ d=\frac{4}{-2} \\ d=-2 \end{gathered}$ $\begin{gathered} Find\text{ the value of e using }e=c-\frac{b^2}{4a} \\ e=0-\frac{4^2}{4\times(-1)} \\ \\ e=0-\frac{16}{-4} \\ e=4 \end{gathered}$

Step 5

Substitute a,d,e into the vertex form

$\begin{gathered} a(y+d)^2+e \\ =-1(y+(-2))^2+4 \\ =-(y-2)^2+4 \end{gathered}$

Step 6

$\begin{gathered} 4(x+3)^2-y^2+4y=\text{ -28+36} \\ 4(x+3)^2-(y-2)^2+4=-28+36 \\ 4(x+3)^2-(y-2)^2=-28+36-4 \\ 4(x+3)^2-(y-2)^2=4 \\ \frac{4(x+3)^2}{4}-\frac{(y-2)^2}{4}=\frac{4}{4} \\ (x+3)^2-\frac{(y-2)^2}{2^2}=1 \end{gathered}$

Step 7

$\begin{gathered} \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1 \\ \text{This is the }form\text{ of a hyperbola.} \\ \text{From here } \\ a=1 \\ b=2 \\ k=2 \\ h=-3 \end{gathered}$

Hence the answer is (-3,2)

4 0

1 year ago