x + 4y = -3 x + 7y = -12

Answers

Answer 1

Answer:

y = -3, x = 9

Step-by-step explanation:

ISOLATE THE X

step 1) subtract 4y from both sides.

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

step 2) simplify

x = -3 - 4y

step 3) substitute x = -3 - 4y

-3 - 4y + 7y = -12

ISOLATE THE Y

step 4)  Add similar elements: -4y + 7y = 3y

-3 - 4y + 7y = -12

step 5) Add 3 to both sides

-3 + 3y + 3 = -12 + 3

step 6) Simplify

3y = -9

step 7) Divide both sides by 3

3y/3 = -9/3

step 8) you now know y = -3

step 9) substitute y = -3 in for x = -3 - 4y

x = -3 - 4(-3)

step 10) negative times a negative equals a positive

x = -3 + 12

step 11) add -3 by 12 to get x = 9

step 12) you now have found the answer x = -3 and y = 9

Answer 2

The question involves solving a system of linear equations using the elimination method, resulting in the solution [tex]\(x = 9, y = -3\).[/tex]

The problem provided is a system of linear equations. Here's how to solve the system:

x + 4y = -3

x + 7y = -12

Subtract the first equation from the second:

[tex]\((x + 7y) - (x + 4y) = -12 - (-3)\)[/tex]

[tex]\(3y = -9\)[/tex]

Now, solve for y:

[tex]\(y = -3\)[/tex]

Substitute y back into the first equation to find x:

[tex]\(x + 4(-3) = -3\)[/tex]

[tex]\(x - 12 = -3\)[/tex]

[tex]\(x = 9\)[/tex]

So the solution is [tex]\(x = 9, y = -3\)[/tex].

The procedure used is known as the elimination method, which is a technique to solve simultaneous linear equations.


Related Questions

What scale factor did Salome use to go from Triangle R to Triangle T?

Answers

Answer:is there a picture included in this promblem

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

Eighty percent of all dentists surveyed agree: Zilch toothpaste tastes best.
Percent of Dentists Surveyed
Disagree
Do you think this information is misleading? Why or why not?
a. Yes, because it does not state how many dentists were surveyed.
b. Yes, because it does not state on the graph what percentage agrees with the statement.
C. No, because the graph shows eighty percent of the dentists agreeing with the statement.
No herause it states which toothnaste was used in the survey

Answers

Answer: the answer is gonna be A if you want to be exact

Step-by-step explanation: does not state how many dentist were interviewed.

The segment JK has coordinates at point J(1, 4) and point K(-6, -8). The segment DE has coordinates at point D(3, 3) and point E(-4, -9). Is segment JK congruent to segment DE? Explain why.

Answers

Final answer:

Segment JK is congruent to segment DE because they have the same length.

Explanation:

To determine if segment JK is congruent to segment DE, we need to compare their lengths. We can use the distance formula to find the length of each segment.

For segment JK, the coordinates are J(1, 4) and K(-6, -8). Using the distance formula, we have:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
  = sqrt((-6 - 1)^2 + (-8 - 4)^2)
  = sqrt((-7)^2 + (-12)^2)
  = sqrt(49 + 144)
  = sqrt(193)

For segment DE, the coordinates are D(3, 3) and E(-4, -9). Using the distance formula, we have:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
  = sqrt((-4 - 3)^2 + (-9 - 3)^2)
  = sqrt((-7)^2 + (-12)^2)
  = sqrt(49 + 144)
  = sqrt(193)

Since the lengths of segment JK and segment DE are both sqrt(193), they are congruent.

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1Which extegory do both shapes belong to?

Answers

They are both Parallelograms, they both are 4 sided with the opposite being parallel

The circumference of a circle is 9 m what is the area of the circle

Answers

Answer:

so maybe the answer will be 20.25m^

Using a scale of 2in: 45 miles

The distance between Troy City and Ben City is 315 miles. How far apart are they on the map? (numerical answer)

Answers

set Up a ratio:

2 inches / 45 miles = x inches / 315 miles

Solve for x

Cross multiply:

45x = 630

Divide both sides by 45

X = 630 /45

X = 14 inches apart

What is the probability that you will get a 3-digit combination correct if no digits in the combination can be repeated?
110
1504
1720
MERT QUESTION
ASK FOR HELP
TURN IT IN

Answers

Answer:

i believe its 1/6

Step-by-step explanation:

The probability of guessing a 3-digit combination correctly, with no repetition, is 1 out of 720 option C.

To calculate the probability of getting a 3-digit combination correct where no digits can be repeated, you can use the concept of permutations.

For the first digit, you have 10 options (0 through 9). For the second digit, since no digit can be repeated, you have 9 options left. For the third digit, you have 8 options left.

So the total number of possible combinations is [tex]\(10 \times 9 \times 8 = 720\).[/tex]

Therefore, the probability of getting the correct combination is:

[tex]\[\frac{1}{720}\][/tex]

So, the correct answer is option C) 1/720.

Complete Question:

What is the probability that you will get a 3-digit combination correct if no digits in the combination can be repeated?

A) 1/10

B) 1/504

C) 1/720

Multiply and simplify

Answers

Answer: The answer you clicked on in the picture is correct, (B)

Step-by-step explanation: I put the equation through a thing I know of (faMATHWAce) and got that as the answer.

What’s the square root of -16?

Answers

square root(-16) =
4 i

Answer:

It can`t be -4 because -4² = +16 and it can`t be 4² because 4² = +16

In other words, there is nothing you can square to get -16.

Step-by-step explanation:

It izz wat it izzzz!!!


The circumference of a circle is 60 kilometers. What is its radius?

Answers

Answer: 9.5493

Step-by-step explanation: circumference = 2pi*r

Answer:

9.55 simplified

Find the circumference of both circles. Use 3.14 for pi

Answers

Answer:

Larger Circle:

Radius: 12 in.

Circumference =

[tex]2\pi \: r[/tex]

= 2 x 3.14 x 12

= 75.36 in.

Smaller Circle:

Radius: (12 - 4) in. = 8 in.

Circumference = 2 x 3.14 x 8

= 50.24 in.

A company manufactures handband a wirleless

Answers

Answer:

1. 21 represents the cost of manufacturing one handband.

3. The initial start up cost is $15000.

5. The company spends $57000 to manufacture 2000 handbands.

Step-by-step explanation:

We are given the cost function for manufacturing 'h' amount of handbands and it is provided that there was initial start up costs involved.

Now, as the cost function is given by, C(h) = 21h + 15000.

We can see that the initial start up cost is $15000.

As, 'h' is the number of handbands being made. So, 21h in C(h) is the cost of manufacturing 'h' handbands.

Therefore, 21 is the cost of manufacturing one handband.

Since, C(h) = 21h + 15000.

Substituting h = 2000, we get,

C(2000) = 21×2000 + 15000.

i.e. C(2000) = 42000 + 15000.

i.e. C(2000) = 57000.

The company spends $57000 to manufacture 2000 handbands.

Since, we are provided with only cost function, we can not talk about the profit.

Hence, option 1, 3 and 5 are correct.

PLEASE MARK ME BRAINLIST!

Answer:

1. 21 represents the cost of manufacturing one handband.

3. The initial start up cost is $15000.

5. The company spends $57000 to manufacture 2000 handbands.

Step-by-step explanation:

9/(70X-10) =1/(70x-10)

Answers

uhhh I’m sorry but what is that

a box in the shape of a rectangular prism has the dimensions shown. what length of the interior diagonal of the box? round to the nearest tenth.
100 cm
80 cm
60 cm

Answers

Answer:

I keep getting 141.421... so rounded it would be 141.4

Step-by-step explanation:

The length of the interior diagonal of the box is approximately 141.4 cm.

How to find the volume and base's area of a right rectangular prism?

Suppose the base of the prism has length = l units, and width = w units.

Suppose that the height of the prism is of h units, then:

[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex]

is the volume of that prism.

The base is a rectangle with length = L units, and width = W units, so its area is:

[tex]b = l \times w\: \rm unit^2[/tex]

We are given that;

Height= 100cm

Width=80cm

Length=60cm

Now,

Using the Pythagorean theorem, we can find the length of the interior diagonal as:

diagonal = sqrt(l^2 + w^2 + h^2)

diagonal = sqrt(100^2 + 80^2 + 60^2)

diagonal = sqrt(10000 + 6400 + 3600)

diagonal = sqrt(20000)

diagonal ≈ 141.4

Therefore, the length of the diagonal of prism will be 141.4

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A geologist has 10 rocks of equal weight. If 6 rocks and a 10-ounce weight balance on a scale with 4 rocks and a 22-ounce weight , what is the weight of one of these rocks in ounces ?

Answers

Weight of each rock is 14.8 ounces.

Step-by-step explanation:

Given,

Total number of rocks = 10

6 rocks weigh 10 ounce each

4 rocks weigh 22 ounce each.

To find the the weight of each rock.

Now,

Weight of 6 rocks = 10×6 ounces = 60 ounces

Weight of 4 rocks = 22×4 ounces = 88 ounces

So,

Weight of 10 rocks = 88+60 = 148 ounces

Hence,

Weight of each rock = 148÷10 = 14.8 ounces.

Answer:  6 oz.

Step-by-step explanation:

Just did it.

Which measure of center should you use to describe two data sets that are both symmetric?

Answers

Answer:

im pretty sure its median

Step-by-step explanation:

Mean and median can be used to describe two data sets that are both symmetric.

What is Outlier?

An observation that differs abnormally from other values in a population-based random sample is referred to as an outlier. In a way, this definition defers to the analyst's (or a consensus process') judgement as to what constitutes aberrant behaviour.

Given:

Two symmetric data sets are described by the following measure of centre:

The mean and median are two numerical measures of centre that, if the distribution is symmetric, can determine the centre as the average value; otherwise, the median can be employed because it is not robust against outliers.

For example : Height of 3 students in 70, 72, 74

Mean of students= (70 +72+ 74)/ 3 = 72

and, median = 72

Hence, mean and median can be used.

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Can you simplify 7 (2x -3)

Answers

14x-21
distribute the 7 to the rest of the numbers

Answer:

simplification of the equation is:

14x-21

Use the distributive property to write an equivalent expression:
Example: 24n + 32 = 4 (6n+ 8)
(Look at the first expression. What factor goes into BOTH 24 and 32? (4 does!) So the number 4 goes on the outside of the parenthesis. 4 times what number will give me 24? (6 Does!). Then we do the same for 32...4 times what number gives me 32? (8 does!). Do you see the pattern? This means that both of these expressions are EQUIVALENT!
48x + 24

18n + 36

15 + 12k


Answers

Answer:

1. 48x + 24= 24(2x + 1)

2. 18n + 36= 18(n + 2)

3. 15 + 12k= 3(5+4k)

Step-by-step explanation:

1. What factor both goes into 24 and 48? 24 does!

so, 48x + 24= 24(2x + 1).

2. What factor both goes into 18 and 36? 18 does!

so, 18n + 36= 18(n + 2).

3. What factor both goes into 15 and 12? 3 does!

so, 15 + 12k= 3(5+4k).

Final answer:

The distributive property allows us to create equivalent expressions by factoring out a common factor from each term, resulting in expressions like 24(2x + 1), 18(n + 2), and 3(5 + 4k) for 48x + 24, 18n + 36, and 15 + 12k respectively.

Explanation:

To use the distributive property to write equivalent expressions for each of the following:

48x + 24: Both terms are divisible by 24. Therefore, the equivalent expression using the distributive property is 24(2x + 1).

18n + 36: Both terms are divisible by 18. Therefore, the equivalent expression using the distributive property is 18(n + 2).

15 + 12k: Both terms are divisible by 3. Therefore, the equivalent expression using the distributive property is 3(5 + 4k).

In each case, identifying the common factor and using it to factor out the original expression creates an equivalent expression where the terms inside the parenthesis are the results of dividing the original terms by the common factor.

The heights of a group of boys and girls at a local middle school are shown on the dot plots below.
Boys' Heights
40 41 44 46 48 50 52 54 56 58 60
Inches
Girls' Heights
40 41 44 46 48 50 52 54 56 58 60

Answers

Answer:

The girls and boys heights are equal and none are shorter or taller.

You get this answer from identifying the numbers, seeing if there is any number that is larger or shorter than 40-60.

Hope this helped!

Find the point slope equation for the line that passes through the points ( -2, -20 ) and (9, 79). Use the first point in your equation y+ =

Answers

The point-slope equation for the line passing through (-2, -20) and (9, 79), is y = 9x - 2.

To find the point-slope equation for the line that passes through the points (-2, -20) and (9, 79), we first need to calculate the slope (m). The formula for the slope is given by:

m = (Y2 - Y1) / (X2 - X1)

Using the given points, we get:

m = (79 - (-20)) / (9 - (-2)) = 99 / 11 = 9

Now, using the point-slope form of the equation y - y1 = m(x - x1), and the first point (-2, -20), we have:

y - (-20) = 9(x - (-2))

Simplifying this, we get:

y + 20 = 9(x + 2)

Or

y = 9x + 18 - 20

y = 9x - 2

This is the point-slope equation for the line that passes through the points.

Determine the coordinates of the corners of the rectangle to compute the area of the rectangle using the distance formula (round to
the nearest integer).
es )
A)
12 units
25 units?
30 units?

Answers

Answer:

25

use the formula for hypotenouse of a triangle to find the diangles as if they were the hypotenouse so 5 squared plus 10 squared is 25 plus 100 which is 125 which has the square root 11.2. so now you have the length (longer side) so for the width it's 1 squared plus 2 squared which is 1 plus 4 is 5 so the square root of 5 is about 2.2 so that's the width (shorter side) so now for the area it's 11.2 (length) times 2.2 (width) which is about 25. hope this hopes let me know if you have a question

Answer:30

Step-by-step explanation:

#5 If the diameter of a circle is 3 inches, what is the circumference to the nearest tenth? *

Answers

Answer:

9.4 inches

Step-by-step explanation:

The formula for circumference is πd

Since the diameter is 3 inches, multiply that by pi to get your answer

3π ≈ 9.4 inches

write an equation in point-slope form of the line that passes through the point (-2,4) and has a slope of 5

Answers

Answer:

y=mx+b     m= slope     b=Y-Intercept

4=5(-2)+b

Answer:

4=5(-2)+b

Step-by-step explanation:

hope this helps

On the first day it was posted online, a music video got 1750 views. The
number of views that the video got each day increased by 20% per day. How
many total views did the video get over the course of the first 5 days, to the
nearest whole number?

Answers

Final answer:

To find the total views a music video got over the first 5 days with a 20% daily increase, calculate the views for each day using a geometric sequence formula and sum them, resulting in approximately 13023 views.

Explanation:

To calculate the total views a music video got over the course of the first 5 days with a 20% daily increase starting at 1750 views, we use the geometric sequence formula V = V0 × (1 + r)n, where V0 is the initial number of views (1750), r is the daily increase rate (0.20), and n is the day number. The total views (TV) over 5 days is calculated by summing the individual daily views.

Day 1: 1750 views

Day 2: 1750 × (1 + 0.20) = 2100 views

Day 3: 1750 × (1 + 0.20)2 = 2520 views

Day 4: 1750 × (1 + 0.20)3 = 3024 views

Day 5: 1750 × (1 + 0.20)4 = 3628.8 views, rounded to 3629 views

The total views over the five days is the sum of daily views: 1750 + 2100 + 2520 + 3024 + 3629 = 13023 views.

Pls help i am so confused

Answers

Answer:

A 13

Step-by-step explanation:

8 families own 2 pets

4 families own 3 pets

1 family owns 4 pets

8+4+1 = 13

13 families owns between 2 and 4 pets

The volume of a cube is 64 inches cubed what is the measure of each side of the cube please help ASAP

Answers

Answer:

4

Step-by-step explanation:

a≈4

Name all segments parallel to GH.

Answers

All the segments that are parallel to GH in the given shape are, BC, AD and FI. Option A

How to identify all segments parallel to GH

To identify all segments parallel to GH, understand the basic structure of a cuboid and its faces.

A cuboid is a three-dimensional shape with six rectangular faces. Each face of the cuboid is parallel to the opposite face. This property allows us to identify segments that are parallel to each other within the cuboid.

To identify segments parallel to a specific segment in a cuboid, follow these steps:

Understand the orientation of the cuboid:

Visualize the cuboid and identify its three pairs of opposite faces. These faces are parallel to each other.

Identify the given segment:

Determine the specific segment in the cuboid to which you want to find parallel segments.

In this case GH

Locate the faces that contain the given segment:

Identify the faces that contain the given segment. These faces will be parallel to each other.

Based on the highlighted steps above, by visualization,

Segment BC is parallel to GH

Segment AD is parallel to GH

Segment FI is parallel to GH

Therefore, all the segments that are parallel to GH are, BC, AD and FI. Option A

Can someone please help me ASAP

Answers

Answer:

(-4,0) (0,3)

(3-0)/(0+4)= 3/4

y - 0 = 3/4(x + 4)

y = 3/4x + 3

answer is a

Step-by-step explanation:

Answer:

It¨s A

Step-by-step explanation:

you first have to find the slope by doing rise over run,I checked the table and labeled the values for the x-axis and y-axis,the found the y-intercept which is when x is always zero and y is any random number so one of the points on the table show the x is 0 and y is 3 so that means the y-intercept is 3 also written as (0,3).

What is the equation of the line through the origin and (2,5)

Answers

Answer:

y = 5/2 x

Step-by-step explanation:

First we need to find the slope

m = (y2-y1)/(x2-x1)

    = (5-0)/(2-0)

     = 5/2

We know the y intercept is 0 since it goes through the origin

y = mx+b

y = 5/2 x +0

y = 5/2 x

The area of a rectangle is 84 square inches. Its length and width are both whole numbers.
31. What is the minimum perimeter of the rectangle?!
32. What is the maximum perimeter of the rectangle?

Answers

31. the minimum perimeter of the rectangle is ( 38 ) inches.

32.the maximum perimeter is ( 170 ) inches.

To find the minimum and maximum perimeter of the rectangle, we need to consider all possible combinations of length and width that yield an area of 84 square inches.

Given that the area of the rectangle is 84 square inches, we can find all the pairs of factors of 84. These pairs will represent the possible combinations of length and width.

The pairs of factors of 84 are:

1. [tex]\( 1 \times 84 \)[/tex]

2. [tex]\( 2 \times 42 \)[/tex]

3. [tex]\( 3 \times 28 \)[/tex]

4. [tex]\( 4 \times 21 \)[/tex]

5. [tex]\( 6 \times 14 \)[/tex]

6. [tex]\( 7 \times 12 \)[/tex]

Now, we calculate the perimeter for each pair:

1. [tex]\( \text{Perimeter} = 2 \times (1 + 84) = 2 \times 85 = 170 \)[/tex]

2. [tex]\( \text{Perimeter} = 2 \times (2 + 42) = 2 \times 44 = 88 \)[/tex]

3. [tex]\( \text{Perimeter} = 2 \times (3 + 28) = 2 \times 31 = 62 \)[/tex]

4.[tex]\( \text{Perimeter} = 2 \times (4 + 21) = 2 \times 25 = 50 \)[/tex]

5.[tex]\( \text{Perimeter} = 2 \times (6 + 14) = 2 \times 20 = 40 \)[/tex]

6.[tex]\( \text{Perimeter} = 2 \times (7 + 12) = 2 \times 19 = 38 \)[/tex]

Therefore, the minimum perimeter of the rectangle is ( 38 ) inches, and the maximum perimeter is ( 170 ) inches.

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