All categories

3 years ago

Find the values of x and y. (image below)

Mathematics

1 answer:

DanielleElmas [232]3 years ago

5 0

Opposite angles have the same measures. This allows you to set and solve the following equations:

$\begin{cases} 26-6x = 20-8x \\ 5y = 9y-76 \end{cases}$

To solve both equations, let's move all the terms involving the variables on the left hand side, and all constant terms on the right hand side:

$\begin{cases} -6x+8x = 20-26 \\ 5y-9y = -76 \end{cases}$

Sum like terms:

$\begin{cases} 2x = -6 \\ -4y = -76 \end{cases}$

Divide the first equation by 2 and the second by -4:

$\begin{cases} x = -3 \\ y = 19 \end{cases}$

You might be interested in

Evaluate the expression 7x2y, when x = 4 and y = 2. (3 points)

nordsb [41]

Hey there!

If x = 4 and y = 2, then substitute them into the equation

7(4)(2)(2)

7(4) = 28

28(2)(2)

28(2) = 56

56(2) = 112

Answer: 112

Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

6 0

4 years ago

Read 2 more answers

he American Heart Association is about to conduct an anti-smoking campaign and wants to know the fraction of Americans over 45 w

Sonja [21]

Answer:

The 85% confidence interval is (0.2187, 0.2613).

Step-by-step explanation:

We have a large sample of size n = 830 Americans over 45. We have observed that 631 people don't smoke. Let p be the population proportion of Americans over 45 who smoke. An point estimate of p is $\hat{p} = 199/830 = 0.24$ and an estimate of the standard deviation of $\hat{p}$ is $\sqrt{\hat{p}(1-\hat{p})/n} = \sqrt{(0.24)(0.76)/830}$ = 0.0148. Therefore, because we have a large sample, the 85% confidence interval for the population proportion is given by $\hat{p}\pm z_{\alpha/2}\sqrt{\hat{p}(1-\hat{p})/n} = 0.24\pm z_{0.15/2}0.0148 = 0.24\pm z_{0.075}0.0148$ where $z_{0.075}$ is the 7.5th quantile of the standard normal distribution, i.e., -1.4395. Therefore the 85% confidence interval is $0.24\pm (1.4395)(0.0148)$ or equivalently (0.2187, 0.2613).

7 0

3 years ago

Use the quadratic formula to solve the equation -3x2-x-3=0

Novosadov [1.4K]

Answer:

$x=\frac{1+\sqrt{35}i}{-6}\,\, and\,\, x=\frac{1-\sqrt{35}i}{-6}\\$

Step-by-step explanation:

the quadratic formula is:

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

a= -2, b = -1 and c =-3

Putting values in the formula

$x=\frac{-(-1)\pm\sqrt{(-1)^2-4(-3)(-3)}}{2(-3)}\\x=\frac{1\pm\sqrt{-35}}{-6}\\x=\frac{1+\sqrt{-35}}{-6}\,\, and\,\, x=\frac{1-\sqrt{-35}}{-6}\\We\,\, know \,\,that \,\,\sqrt{-1} = i \\x=\frac{1+\sqrt{35}i}{-6}\,\, and\,\, x=\frac{1-\sqrt{35}i}{-6}\\$

So, $x=\frac{1+\sqrt{35}i}{-6}\,\, and\,\, x=\frac{1-\sqrt{35}i}{-6}\\$

5 0

3 years ago

Read 2 more answers

Find the measures of the following angles.

makvit [3.9K]

Answer:

1: 36° 2: 122° 3: 122° 4: 38°

Step-by-step explanation:

First start out by getting 2 and 3. so 58+angle 3 has to sum to 180° since they are supplementary and are a straight line. So 180-58=122. Angle 2 is the same since theyre vertical. then since a triangle has 180° total, you subtract from 180 to find the final angle measurement.

5 0

3 years ago

Simply using exponents 4^2 / 3^6

Juliette [100K]

Answer:45.5625

Step-by-step explanation:4 x 4= 16 and 3 x 3 x 3 x 3 x 3 x 3= 729

16/729

6 0

3 years ago

Read 2 more answers