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3 years ago

What is the solution to the system of equations?

Mathematics

2 answers:

o-na [289]3 years ago

7 0

Answer:

x = -5

y = 4

Step-by-step explanation:

3x + 4y = 1 /*(-4)

4x + 5y = 0 /*3

---------------------

-12x - 16y = -4

12x + 15y = 0 +

---------------------

-y = -4

y = 4

---------------------

12x = -15y

12x = -60

x = -5

---------------------

Sonja [21]3 years ago

3 0

Answer: x = - 5

y = 4

Step-by-step explanation:

The given system of linear equations is expressed as

3x + 4y = 1- - - - - - - - - - - - -1

4x + 5y = 0- - - - - - - - - - - -2

We would eliminate x by multiplying equation 1 by 4 and equation 2 by 3. It becomes

12x + 16y = 4- - - - - - - - - - -3

12x + 15y = 0- - - - - - - - - - - -4

Subtracting equation 4 from equation 3, it becomes

y = 4

Substituting y = 4 into equation 1, it becomes

3x + 4 × 4 = 1

3x + 16 = 1

Subtracting 16 from the left hand side and the right hand side of the equation, it becomes

3x + 16 - 16 = 1 - 16

3x = - 15

Dividing the left hand side and the right hand side of the equation by 3, it becomes

3x/3 = - 15/3

x = - 5

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Oksanka [162]

Answer:

Step-by-step explanation:

Let's solve your equation step-by-step.

11=−d+15

Step 1: Flip the equation.

−d+15=11

Step 2: Subtract 15 from both sides.

−d+15−15=11−15

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Step 3: Divide both sides by -1.

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4 0

3 years ago

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Tamara wants to calculate the height of a tree outside her home. Using her clinometer, she measures the angle from 35 feet away

serg [7]

Answer:

71.32 feet

Step-by-step explanation:

We set up a trigonometric function to get height of tree

Distance ,x = 35 feet away from tree base

Angle = 62⁰ at eye level

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= Y = tan(62⁰) x 35

Y = 1.881 x 35

Y = 65.82 feet

We add Tamara's height to the total height of the tree

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= 71.32 feet is the height of the tree

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3 years ago

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UkoKoshka [18]

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3 years ago

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If 2^n + 1 is an odd prime for some integer n, prove that n is a power of 2. (H

vovikov84 [41]

Step-by-step explanation:

We will prove by contradiction. Assume that $2^n + 1$ is an odd prime but n is not a power of 2. Then, there exists an odd prime number p such that $p\mid n$ . Then, for some integer $k\geq 1$ ,

$n=p\times k.$

Therefore

$2^n + 1=2^{p\times k} + 1=(2^{k})^p + 1^p.$

Here we will use the formula for the sum of odd powers, which states that, for $a,b\in \mathbb{R}$ and an odd positive number $n$ ,

$a^n+b^n=(a+b)(a^{n-1}-a^{n-2}b+a^{n-3}b^2-...+b^{n-1})$

Applying this formula in 1) we obtain that

$2^n + 1=2^{p\times k} + 1=(2^{k})^p + 1^p=(2^k+1)(2^{k(p-1)}-2^{k(p-2)}+...-2^{k}+1)$ .

Then, as $2^k+1>1$ we have that $2^n+1$ is not a prime number, which is a contradiction.

In conclusion, if $2^n+1$ is an odd prime, then n must be a power of 2.

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3 years ago

Based on executing the test in Question 5, what would you conclude, given a margin of error of 5%? Group of answer choices We re

Harman [31]

People often draw hypothesis in research. Based on executing the test in Question 5, We reject the null hypothesis; the mean delivery time is different for every day of the week.

<h3>Why do we reject the null hypothesis?</h3>

Note that if the p-value of an experiment (Like the one above) is less than or found to be equal to the significance level of your test, one can reject the null hypothesis.

By that, we known that the data is in favors the alternative hypothesis. Hence the results gotten by you are statistically significant. If your p-value is found to be greater than your significance level, you then fail to reject the null hypothesis.

Learn more about hypothesis from

brainly.com/question/11555274

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2 years ago