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3 years ago

{y=2x+3 {y=-x-9 solve each system of equations by substitution

Mathematics

1 answer:

azamat3 years ago

3 0

Substitute y = 2x + 3 into y = -x - 9

2x + 3 = -x - 9

Solve for x in 2x + 3 = - - 9

x = -4

Substitute x = -4 into y = 2x + 3

y = -5

Therefore,

x = -4

y = -5

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One of the roots of the quadratic equation dx^2+cx+p=0 is twice the other, find the relationship between d, c and p

scZoUnD [109]

Answer:

$c^2 = 9dp$

Step-by-step explanation:

Given

$dx^2 + cx + p = 0$

Let the roots be $\alpha$ and $\beta$

So:

$\alpha = 2\beta$

Required

Determine the relationship between d, c and p

$dx^2 + cx + p = 0$

Divide through by d

$\frac{dx^2}{d} + \frac{cx}{d} + \frac{p}{d} = 0$

$x^2 + \frac{c}{d}x + \frac{p}{d} = 0$

A quadratic equation has the form:

$x^2 - (\alpha + \beta)x + \alpha \beta = 0$

So:

$x^2 - (2\beta+ \beta)x + \beta*\beta = 0$

$x^2 - (3\beta)x + \beta^2 = 0$

So, we have:

$\frac{c}{d} = -3\beta$ -- (1)

and

$\frac{p}{d} = \beta^2$ -- (2)

Make $\beta$ the subject in (1)

$\frac{c}{d} = -3\beta$

$\beta = -\frac{c}{3d}$

Substitute $\beta = -\frac{c}{3d}$ in (2)

$\frac{p}{d} = (-\frac{c}{3d})^2$

$\frac{p}{d} = \frac{c^2}{9d^2}$

Multiply both sides by d

$d * \frac{p}{d} = \frac{c^2}{9d^2}*d$

$p = \frac{c^2}{9d}$

Cross Multiply

$9dp = c^2$

$c^2 = 9dp$

Hence, the relationship between d, c and p is: $c^2 = 9dp$

8 0

3 years ago

Find the margin of error for the given values of c, o, and n.

Alika [10]

Using the z-distribution, it is found that the margin of error is of 0.059.

We are given the standard deviation for the population, hence the z-distribution is used.

<h3>What is the margin of error for a z-confidence interval?</h3>

It is given by:

$M = z\frac{\sigma}{\sqrt{n}}$

In which:

z is the critical value.

$\sigma$ is the population standard deviation.

n is the sample size.

In this problem, the parameters are:

$\sigma = 0.25, n = 49$ .

Confidence level of 0.90, hence, using a z-distribution calculator, the critical value is z = 1.645.

Then:

$M = z\frac{\sigma}{\sqrt{n}}$

$M = 1.645\frac{0.25}{\sqrt{49}}$

$M = 0.059$

The margin of error is of 0.059.

You can learn more about the z-distribution at brainly.com/question/12517818

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2 years ago

Is - 5 a solution to the equation 6x + 5 = 5x + 8 + 2x BRAINLIEST

s344n2d4d5 [400]

No: 6(-5) +5 = 5(-5) +8 + 2(-5)
-30 + 5 = =25 + 8 - 10
-25 ≠ -27

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3 years ago

How many quarts of water does Paul need to add to keep the

gladu [14]

Answer:

Step-by-step explanation:

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qwelly [4]

Answer:

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3 years ago