MATHEMATICS HIGH SCHOOL

The graph of the following system of equations is (4 points)-2x + y = 3
4x + 2y = 2

a. overlapping lines
b. parallel lines
c. intersecting lines

Answers

Answer 1
Answer: \left\{\begin{array}{ccc}-2x+y=3\n4x+2y=2&|divide\ both\ sides\ by\ 2\end{array}\right\n\left\{\begin{array}{ccc}-2x+y=3&|add\ (-2x)\ to\ both\ sides\n2x+y=1&|subtract\ 2x\ from\ both\ sides\end{array}\right\n\left\{\begin{array}{ccc}y=2x+3\ny=-2x+1\end{array}\right\Rightarrow\ the\ slope \left\{\begin{array}{ccc}m=2\nm=-2\end{array}\right\ |different\n\nConclusion:\ \boxed{\boxed{C}\ intersecting\ lines}
Answer 2
Answer: -2x + 1y = 3 ⇒ 4x - 2y = -6
 4x + 2y = 2 ⇒ 4x + 2y = 2
                               -4y = -8
                                -4     -4
                                  y = 2
                      4x + 2(2) = 2
                          4x + 4 = 2
                                 -4  -4
                                4x = -2
                                 4      4
                                 x = -1/2
                             (x, y) = (-1/2, 2)
The answer to the problem is C. intersecting lines.

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Factor 35v–7w +42x. Write your answer as a product with a whole number greater than 1.
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Equation4(5x–9)=−2(x+7) # x = 1 Explanation Write the equation. Add 2x to each side. 30 :: Multiply on each side. :: 22x = 22 :: 22x-36= -14 Add 36 to each side. Reason Given Distributive Property Addition Property of Equality Addition Property of Equality Division Property of Equality :: 20x - 36 = -2x - 14 :: Divide each side by 22.

Which of the following equations is y = x2 – 5x – 14 in factored form?Oy= (2-7)(2+2)
Oy= (x + 7) (x - 2)
Oy= (x - 5)(x – 14).
Oy= (x + 5) (x + 14)
Need help ASAP PLS

Answers

Answer:

Y = (x - 7) (x + 2)

Step-by-step explanation:

Two sides of a triangle have lengths 10 and 15. What must be true about the length of the third side? less than 25 / less than or equal to 25 /equal to 25/ more than 25

Answers

The length of the third side of a triangle is always less than the sum of the other two legs. Therefore if we add the two legs we obtain,

leg 1 + leg 2

10 + 15 = 25

Since the sum of the legs is 25, thus, the third leg should be less than 25. 

Answer:

A. Less than 25.

Step-by-step explanation:

Let x represent 3rd side of triangle.

We have been given hat two sides of a triangle have lengths 10 and 15.

We will use triangle inequality theorem to find the 3rd side of the triangle. Triangle inequality theorem states that 3rd side of a triangle must be less than the sum of other two sides of triangle.

Using triangle inequality theorem, we can set following inequalities:

x+10>15

x+10-10>15-10

x>5

Therefore, the length of third side should be greater than 5.

10+15>x

25>x

x<25

Therefore, the length of third side should be less than 25 and option A is the correct choice.

The number of hours slept at night is related to the number of minutes spent exercising that day. A collection of data on the number of minutes spent exercising, x, and the number of hours slept, y, is shown in the table.x 30 37 40 45 52 55 61 65 71 76
y 6.25 6 6.5 7 6.5 7.25 7.5 8 8.65 8.5
Which linear equation best models the relationship between x and y?

Answers

Answer:

the answer is A

Step-by-step explanation:

took the test

Final answer:

The linear equation that best models the relationship between the number of minutes spent exercising and the number of hours slept is y = 0.04643x + 4.607.

Explanation:

The relationship between the number of minutes spent exercising, x, and the number of hours slept, y, can be modeled by a linear equation. To find the equation, we can use the formula for a line, y = mx + b, where m is the slope and b is the y-intercept.

To find the slope, we need to calculate the difference in y-values divided by the difference in x-values for any two points on the line. Let's take the first and last points: (30, 6.25) and (76, 8.5).

Slope (m) = (8.5 - 6.25) / (76 - 30) = 0.04643

Next, to find the y-intercept, we can substitute one point and the slope into the equation and solve for b. Let's use point (30, 6.25):

6.25 = 0.04643 * 30 + b

b = 4.607

Therefore, the linear equation that best models the relationship between x and y is y = 0.04643x + 4.607.

Learn more about Linear equation here:

brainly.com/question/32634451

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A family is having a pool built in their backyard. If their yard is rectangular and measures 7x by 6x and the pool is circular with a radius of 2x how much of the yard will be left over after the pool is built?a. 38x2
b. 42x2 – 4x2
c. 42x2 – 2x2
d. 38x2

Answers

Area of a rectangular yard:
A 1 = L x W = 7 x * 6 x = 42 x²
Area of a pool:
A 2 = r² π = ( 2 x )² π = 4 x² π
A = A 1 - A 2
A = 42 x² - 4 x² π
Answer: B ) 42 x² - 4 x² π

Iola has $75. She buys a pair of shoes on sale for one-half off and a pair of socks for $6. She has $32 left. Which equation can be used to find x, the regular price of the shoes?

Answers

Answer:

To solve for the problem above, let x be the regular price of the shoe.

1/2x is the one-half price of the shoe then we add 6 for the pair of socks,

1/2x + 6, then lola has 32 left so we add that too, 1/2x + 6 + 32 = 75. The total amount of lola spent is 75 - 32, which is 1/2x + 6.

Step-by-step explanation:

Can someone help me please!!!Let N be the least postive integer whose digits sum to 2018. Compute the sum of the digits of N+1.

Answers

Answer: 3

Explanation:

Since we want the least number of integers, divide by the largest integer (9).

2018 ÷ 9 = 224 remainder 2

So, N = 2999...999 (there are 224 of the 9's)

Thus, N + 1 = 2999...999 + 1 (there are 224 of the 9's)

                  = 3000...000     (there are 224 of the 0's)

The sum of the digits is: 3 + 0 + ... + 0  (there are 224 of the 0's)

                                      = 3
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