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3 years ago

7x+8y=−46 2y − 6=0 What is the solution (x,y) to the system of equations above?

Mathematics

1 answer:

yarga [219]3 years ago

8 0

Answer:

(-10, 3)

Step-by-step explanation:

You can do it algebraically (substitution or elimination) or graphically. I will be using substitution to solve this.

Step 1: Rewrite 2nd equation

2y = 6

y = 3

Step 2: Plug in <em>y</em>

7x + 8(3) = -46

7x + 24 = -46

7x = -70

x = -10

Put it in coordinates and we have our final answer!

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Here are two expressions whose product is a new expression, :

Vera_Pavlovna [14]

Answer:

1. Fill in the box with 1

2. Fill in the box with -2

Step-by-step explanation:

Expression:

$(-2x^3 + [\ ]x)(x^{[\ ]}+1.5) = A$

Solving (1): Fill in the box to make it a polynomial.

To make it a polynomial, we simply fill in the box with a positive integer (say 1)

Fill in the box with 1

$(-2x^3 + [1]x)(x^{[1]}+1.5) = A$

Remove the square brackets

$(-2x^3 + x)(x^1+1.5) = A$

$(-2x^3 + x)(x+1.5) = A$

Open bracket

$-2x^4 - 3x^3 + x^2 + 1.5x = A$

Reorder

$A = -2x^4 - 3x^3 + x^2 + 1.5x$

The above expression is a polynomial.

This will work for any positive integer filled in the box

Solving (2): Fill in the box to make it not a polynomial.

The powers of a polynomial are greater than or equal to 0.

So, when the boxes are filled with a negative integer (say -2), the expression will cease to be a polynomial

Fill in the box with -2

$(-2x^3 + [-2]x)(x^{[-2]}+1.5) = A$

Remove the square brackets

$(-2x^3 - 2x)(x^{-2}+1.5) = A$

Reorder

$A = (-2x^3 - 2x)(x^{-2}+1.5)$

Open brackets

$A = -2x-3x^3-2x^{-1}-3x$

Collect Like Terms

$A = -3x^3-2x-3x-2x^{-1}$

$A = -3x^3-5x-2x^{-1}$

Notice that the least power of x is -1.

Hence, this is not a polynomial.

3 0

3 years ago

What ordered pairs name the origin

Elis [28]

The ordered pair of the origin is (0,0)

4 0

3 years ago

Jing participates in a trivia contest. He completes each question in 1/2 minute.

jolli1 [7]

Answer:

300 seconds

Step-by-step explanation:

First, you have to know how much half a minute is. Half a minute is 30 seconds.

Second, you multiply 30 by 10 because he answered 10 questions.

30 * 10 = 300

So your answer is 300 seconds

Lastly, have a great day! :)

7 0

3 years ago

The weights of 67 randomly selected axles were found to have a variance of 3.85. Construct the 80% confidence interval for the p

VLD [36.1K]

Answer:

$3.13$

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 67

Variance = 3.85

We have to find 80% confidence interval for the population variance of the weights.

Degree of freedom = 67 - 1 = 66

Level of significance = 0.2

Chi square critical value for lower tail =

$\chi^2_{1-\frac{\alpha}{2}}= 51.770$

Chi square critical value for upper tail =

$\chi^2_{\frac{\alpha}{2}}= 81.085$

80% confidence interval:

$\dfrac{(n-1)S^2}{\chi^2_{\frac{\alpha}{2}}} < \sigma^2 < \dfrac{(n-1)S^2}{\chi^2_{1-\frac{\alpha}{2}}}$

Putting values, we get,

$=\dfrac{(67-1)3.85}{81.085} < \sigma^2 < \dfrac{(67-1)3.85}{51.770}\\\\=3.13$

Thus, (3.13,4.91) is the required 80% confidence interval for the population variance of the weights.

8 0

3 years ago

Select the equation that most accurately depicts the word problem.

stiv31 [10]

One half of a certain number is 95 is depicted by <span>1/2 · n = 95</span>

3 0

3 years ago

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