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2 years ago

The first three steps in determining the solution set of the system of equations algebraically are shown.

Mathematics

1 answer:

Ivenika [448]2 years ago

3 0

(2,-1), (-4,17).

Step-by-step explanation:

Equate the equation A and equation B

Convert the quadratic equation in factored form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Complete the square. Remember to balance the equation by adding the same constants to each side.

Rewrite as perfect squares

Square root both sides

Find the values of y

Substitute the value of x in the equation B

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The first side of a triangle is 7cm less than twice the second side. The third side is 4cm longer than the first side. The perim

Vinil7 [7]

Given:

First side(A): 2B - 7

Second side(B): B

Third side(C): B + 4

Plug in values:

A + B + C = 80

2B - 7 + B + B + 4 = 80

If you look at the coefficients only, you can rewrite the equation like this:

2B + B + B - 7 + 4 = 80

This means that 4B - 7 + 4 = 80

=4B - 3 = 80

= 4B = 80 + 3

B = 83/4, so you can either write B as 83/4 or as 20.75.

Checking your work:

A: 2(20.75) - 7 = 34.5

B: 20.75

C: 4 + 20.75 = 24.75

34.5 + 20.75 + 24.75 = 80cm.

Hope this helped.

3 0

2 years ago

What is 1 2/3+3 3/4=

STALIN [3.7K]

Answer:

5 5/12

Step-by-step explanation:

2/3 + 3/4 = 1 5/12 + 3+1

= 5 5/12

7 0

3 years ago

Read 2 more answers

(a) Find the size of each of two samples (assume that they are of equal size) needed to estimate the difference between the prop

zalisa [80]

Answer:

(a) The sample sizes are 6787.

(b) The sample sizes are 6666.

Step-by-step explanation:

(a)

The information provided is:

Confidence level = 98%

MOE = 0.02

n₁ = n₂ = n

$\hat p_{1} = \hat p_{2} = \hat p = 0.50\ (\text{Assume})$

Compute the sample sizes as follows:

$MOE=z_{\alpha/2}\times\sqrt{\frac{2\times\hat p(1-\hat p)}{n}$

$n=\frac{2\times\hat p(1-\hat p)\times (z_{\alpha/2})^{2}}{MOE^{2}}$

$=\frac{2\times0.50(1-0.50)\times (2.33)^{2}}{0.02^{2}}\\\\=6786.125\\\\\approx 6787$

Thus, the sample sizes are 6787.

(b)

Now it is provided that:

$\hat p_{1}=0.45\\\hat p_{2}=0.58$

Compute the sample size as follows:

$MOE=z_{\alpha/2}\times\sqrt{\frac{\hat p_{1}(1-\hat p_{1})+\hat p_{2}(1-\hat p_{2})}{n}$

$n=\frac{(z_{\alpha/2})^{2}\times [\hat p_{1}(1-\hat p_{1})+\hat p_{2}(1-\hat p_{2})]}{MOE^{2}}$

$=\frac{2.33^{2}\times [0.45(1-0.45)+0.58(1-0.58)]}{0.02^{2}}\\\\=6665.331975\\\\\approx 6666$

Thus, the sample sizes are 6666.

7 0

2 years ago

Please please help me

Anarel [89]

so you are going to use the Pythagorean theorem on the smaller triangle to find the connecting side's length

${5}^{2} = {3}^{2} ( {b}^{2} ) \\ b = 4$

now you can find the bigger triangle's hypotenuse

${6}^{2} + {4}^{2} = {c}^{2} \\$

c=4

8 0

2 years ago

The sum of the interior angles of a polygon is 1080 degrees. How many sides does the polygon have?

postnew [5]

9514 1404 393

Answer:

Step-by-step explanation:

The formula for the number of degrees in the sum of the interior angles of an n-sided polygon is ...

sum of angles = 180°(n -2)

Filling in the given value and solving for n, we get ...

1080 = 180(n -2)

6 = n -2 . . . . . . divide by 180

8 = n . . . . . . . . add 2

The polygon has 8 sides.

4 0

2 years ago