MATHEMATICS HIGH SCHOOL

I need help solving. The answer is (2,-6)Which ordered pair is the solution to the system of equations?

{x=1/2y+5
2x+3y=−14




(8, 9)

(−1, −12)

(18, 14)

(2, −6)

Answers

Answer 1
Answer:

Since we are given x in terms of y, the most efficient way to solve it would be to substitute in the (1)/(2)y+5 for x in the second equation. So, we then have:

2((y)/(2)+5)+3y=-14 \implies \ny+10+3y=-14 \implies \n4y+10=-14 \implies\n4y=-24 \implies \ny=-6

So, now that we have our y, we can find x. We can actually use either equation, top or bottom, to find x, but to be efficient we should use the top one since we have x in terms of y, so:

x=(-6)/(2)+5 \implies \nx=-3+5 \implies \nx=2

So, our ordered pair is (2,-6).

Related Questions

Linear equation 4.5 + 1.5y=24x-y=4
A student wrotw a variable expression n-5 for the word phrase n less than 5. explain the students error
What are the first five terms in the arithmetic sequence An=6n, starting with n=1?
A bag contains 135 marbles some white and some transparent. The ratio of white marbles to transparent ones is 3 : 6. How many white marbles are there?
Graham and Hunter are circus performers. A cable lifts Graham into the air at a constant speed of 1.5 ft/s. When Graham’s arms are 18 ft above the ground, Hunter, who is standing directly underneath Graham, throws Graham a ball as the cable continues to lift him higher. Hunter throws the ball from a position 5 ft above the ground with an initial velocity of 24 ft/s. Which system of equations can be used to model this situation?A) h=18+1.5th=5+24t-16t^2B) h=18+1.5th=5+24t+16t^2C) h=18+1.5th=5+24tD) h=18t+1.5t-16t^2h=5+24t-16t^2

Four less than the sum of a number and 7 is eight more than twice that number. find the number.

Answers

Answer:

-5

Step-by-step explanation:

To find the number, let's break down the problem step by step.

First, let's assign a variable to represent the unknown number. Let's call it "x."

According to the problem, "four less than the sum of a number and 7" can be written as "(x + 7) - 4."

Next, the problem states that this expression is "eight more than twice that number." So, we can write this as "2x + 8."

Now, we can set up an equation based on the information given:

(x + 7) - 4 = 2x + 8

Let's solve this equation to find the value of x.

First, let's simplify the left side of the equation:

x + 7 - 4 = 2x + 8

x + 3 = 2x + 8

Next, let's isolate the variable by subtracting x from both sides:

x - x + 3 = 2x - x + 8

3 = x + 8

To isolate x, we need to get rid of the 8 by subtracting it from both sides:

3 - 8 = x + 8 - 8

-5 = x

Therefore, the number is -5.

To check our answer, let's substitute -5 into the original equation and see if it holds true:

( -5 + 7) - 4 = 2(-5) + 8

2 - 4 = -10 + 8

-2 = -2

The equation holds true, which confirms that the number is indeed -5.

Using the example above, the new high way will be a total of 54 miles long. Will the highway be finished in 8 months

Answers

The above problem is incomplete. I have read the whole problem.

Given:
54 miles long highway
5 3/5 miles constructed per month.

Will the highway be finished in 8 months?

5 3/5 ⇒ ((5*5)+3)/5 = 28/5

28/5 * 8/1 = 28*8 / 5*1 = 224/5 = 44.8 miles or 44 4/5 miles

No. The highway can not be finished in 8 months. Only 44.8 miles or 44 4/5 miles will be constructed by that time.

54 ÷ 28/5 = 54 * 5/28 = 54*5 / 28 = 270 / 28 = 9.64 months or 9 18/28 or 9 9/14 months must be spend to complete the highway.

Juanita is 15 years old and her brother is 5. what is the ratio of juanitas age to her brother age.

Answers

It is a 3 to 1 (3:1) ratio

A merry-go-round has a radius of 10 ft. To the nearest tenth of a foot, what distance does the merry-go-round cover when it rotates through an angle of 72°?For my first try, I got 62.9 as my answer, and it was marked wrong. I did this a second time, and got 12.6. I would like to check with anyone else to see if I got the answer right.

The answers for this question were:

62.9, 12.6, 25.1, or 125.7

Answers

Answer:

12.6

Step-by-step explanation:

The distance covered by the merry-go-round if makes a complete circle (360°) is its circumference:

circumference = 2*π*radius = 2*π*10 = 62.8 ft

This distance corresponds to 360°, for 72°:

62.8 ft / x ft = 360° / 72°

x = (72/360)*62.8

x =  12.6 ft
Yes, the correct answer is 12.6 ft.

Using the formula of arc length, that is
s = rθ
where s = arc length, r = radius, θ = angle (unit must be in radian)
With r = 10 ft and θ = 72 deg ( π/180 deg) = 1.26 rad,
s = (10)(1.26) = 12.6 ft

Deanna collected data on the favorite sports of the students of two grades. The table shows the relative frequencies of rows for the data collected: Favorite Sport Swimming Running Volleyball Row totals Grade 8 0. 14 0. 18 0. 22 0. 54 Grade 9 0. 17 0. 24 0. 05 0. 46 Column totals 0. 31 0. 42 0. 27 1 Based on the data, which statement is most likely correct? In Grade 8, 14 students liked swimming. In Grade 9, 31% of students liked swimming. In Grade 8, 22% of students liked volleyball. In Grade 9, 5 students liked volleyball.

Answers

Answer:

In Grade 8, 22% of students liked volleyball.

Step-by-step explanation:

Given:

The table representing the relative frequencies of different sports in different grades among the students.

                          Swimming      Running    Volleyball                   Row totals

Grade 8                        0.14           0.18         0.22                          0.54

Grade 9                        0.17           0.24        0.05                          0.46

Column totals              0.31           0.42        0.27                             1

Relative frequency gives the ratio of the number of quantities of a particular kind and the total number of quantities.

From the above table, we can conclude the following points:

Grade 8:

14% liked swimming, 18% liked running and 22% liked volleyball. So, a total of 54% students liked playing sports.

Grade 9:

17% liked swimming, 24% liked running and 5% liked volleyball. So, a total of 46% students liked playing sports.

Combining students of grade 8 and 9:

31% liked swimming, 42% liked running and 27% liked volleyball.

From all the options available, we observe that, third option is only correct.

In Grade 8, 22% of students liked volleyball.

shannon walked 1 and 2/3 miles on Wednesday and 2 and 3/5mileson Thursday. What was the total distance, shannon walked during those 3 days? Could you also change it to kilometers

Answers

Total miles walked = 1 + 2/3 + 2 + 3/5
LCM: 15
(15+10+30+9)/15
64/15 miles
Shannon walked 64/15 miles. (4.266...miles)
 Conversion into kilometres = 6.865..... (343/50 kilometres)
Other Questions
Which property of addition is shown below? a + bi + c + di = a + c + bi + di
Eva played her favorite video game for 14 hours last week. Today, Eva's parents restricted her to 4 additional hours each week for the next 7 weeks. Create the function, f(x), that models Eva's total video game time, and explain what each number in the situation represents graphically, using complete sentences.
Find x (4x - 3) – ( x + 5) = 3(10 - x)please.....
The inequality 3(x + 2) > 4(x – 3) is equivalent to which of the following inequalities?F. x < –6 G. x < 5 H. x < 9 J. x < 14 K. x < 18 Can anyone explain me how to make this one step by step?