Mathematics Middle School

PLEASE HELP. WILL OFFER 50 POINTS AND BRAINLIEST FOR CORRECT ANSWER!

Graph the two lines
2x + 3y = 18
3x -4y > 16.
Give the Domain and Range, Slope, and Y-intercept for each line. Graph each equation above on the graph below and show all work. Give the Domain and Range, Slope, and Y-intercept for each line. Explain in detail how you got each answer.

2x + 3y = 18 3x -4y > 16
Slope-Intercept Form: Slope-Intercept Form:
Domain: Domain:
Range: Range:
Slope: Slope:
Y-intercept: Y-intercept:

Answers

Answer 1

Answer:

For Equation 1:

Domain: [tex]\mathbb{R}[/tex]Range: [tex]\mathbb{R}[/tex]Slope: [tex]\displaystyleP-\frac{2}{3}}[/tex]Y-intercept: 6

For Equation 2:

Domain: [tex]\mathbb{R}[/tex]Range: [tex]\mathbb{R}[/tex]Slope: [tex]\frac{3}{4}[/tex]Y-intercept: -4

Step-by-step explanation:

We are given two lines - one is an equation and one is an inequality.

Neither are in slope-intercept form (y = mx + b), so we need to make these adjustments.

Slope-intercept form has two key parts to the equation: m, which is the slope of the line and b, which is the y-intercept of the line.

Equation 1

[tex]\displaystyle2x+3y=18\\\\3y = -2x + 18\\\\y = -\frac{2}{3}x+6[/tex]

With this, we can now determine the domain, range, slope, and y-intercepts for this line.

For Equation 1, because our equation is in slope-intercept form, we can find the slope and the y-intercept.

Our equation is [tex]y=-\frac{2}{3}x+6[/tex]. Therefore, our m is [tex]-\frac{2}{3}[/tex] and our b is 6.

Because the equation is linear, there is no instance in which the line will not meet an x- or y-value. Therefore, our domain and range is all real numbers, or [tex]\mathbb{R}[/tex].

Domain: [tex]\mathbb{R}[/tex]Range: [tex]\mathbb{R}[/tex]Slope: [tex]\displaystyleP-\frac{2}{3}}[/tex]Y-intercept: 6

Equation 2

[tex]\displaystyle3x-4y>16\\\\-4y>-3x+16\\\\y < \frac{3}{4}x-4[/tex]

Now that we have solved the inequality, we can determine our slope, the domain, and the range of the function.

We can use the same tactic as before - m is our slope and b is our y-intercept. Therefore, [tex]\frac{3}{4}[/tex] is our slope and -4 is our y-intercept.

Because the inequality represents a line, our domain is all real numbers, or [tex]\mathbb{R}[/tex]. If we were to plug in any number for x, y would be true for that value. Therefore, our range is also all real numbers, or [tex]\mathbb{R}[/tex].

Domain: [tex]\mathbb{R}[/tex]Range: [tex]\mathbb{R}[/tex]Slope: [tex]\frac{3}{4}[/tex]Y-intercept: -4

Related Questions

Leslie drank 4/5 pint of juice and Hank drank 7/10 pint of juice. Who drank more

Answers

Leslie did. If you multiply 4/5 by two, you get 8/10. 8/10 is greater than 7/10.

Leslie, since 4/5 is equal to 8/5 (multiply the top and bottom by two, to have the same denominator as 7/10) which is greater than, 7/10

please help im confused

Answers

25) It is a right triangle

3²+4²=5²
9+16=25
25=25

26) It is a right triangle

6²+8²=10²
36+64=100
100=100

27) Not a right triangle

5²+5²=10²
25+25=100
50=100

28) It is a right triangle

5²+12²=13²
25+144=169
169=169

Hope this helps :)

Anna plants peas in 3/8 of her garden and herbs in 1/8 of it. she divides the rest of the garden into 6 sections. what fraction of the original garden is in each section?

Answers

To find this answer you will first subtract the two fractions from the original size of one whole garden. After that take the remaining amount and break it into six sections. This answer would represent the fraction of the original garden that is in each section. Here are the steps:
1. Add the two fractions together to get 4/8 or 1/2. This means that half of it is left.

2. Take the 1/2 that remains and divide it by 6 (1/2 divided by 6 = 1/2 x 1/6). The answer is 1/12.

3. 1/12 of the original garden is in each section.

what is the answer to 50% of 4=

Answers

50% of 4 = 2 . . . . . .

What is the slope-intercept equation of the line through the points (-7,2) (-2,1)

Answers

The answer is -1/5. If you use slope intercept formula of (-7,2) and (-2,1) you get -1/5

Emma buys a game for $26.84. She pays for the game with a $20 bill and two $5 bills.
How much change should she receive? - $3.16
List the change in coins and bills. - ??

Answers

3 one dollar bills
One dime
6 pennies

Evaluate sin[2 arccos( -8/17 )].

Answers

Recall that [tex]\sin2x=2\sin x\cos x[/tex], so that

[tex]\sin\left(2\arccos\left(-\dfrac8{17}\right)\right)=2\sin\left(\arccos\left(-\dfrac8{17}\right)\right)\cos\left(\arccos\left(-\dfrac8{17}\right)\right)[/tex]

Dealing with the cosine terms is simple, since [tex]\cos(\arccos x)=x[/tex] (so long as [tex]0\le \arccos x\le\pi[/tex], which is true here). So

[tex]\cos\left(\arccos\left(-\dfrac8{17}\right)\right)=-\dfrac8{17}[/tex]

To find the sine, we can make a substitution of [tex]\theta=\arccos\left(-\dfrac8{17}\right)[/tex]. In other words, we suppose that [tex]\theta[/tex] is some angle that satisfies [tex]\cos\theta=-\dfrac8{17}[/tex].

If this is the case, then we have

[tex]\sin^2\theta=1-\cos^2\theta=\dfrac{225}{289}\implies\sin\theta=\pm\sqrt{\dfrac{225}{289}}=\pm\dfrac{15}{17}[/tex]

But which value do we choose? We know that [tex]\cos\theta[/tex] is negative, which means [tex]\theta[/tex] must be between [tex]\dfrac\pi2[/tex] and [tex]\pi[/tex]. The sine of any angle [tex]\theta[/tex] in this interval will always be positive, so in fact

[tex]\sin\theta=\sin\left(\arccos\left(-\dfrac8{17}\right)\right)=\dfrac{15}{17}[/tex]

Putting everything together, we get

[tex]\sin\left(2\arccos\left(-\dfrac8{17}\right)\right)=2\left(\dfrac{15}{17}\right)\left(-\dfrac8{17}\right)=-\dfrac{240}{289}[/tex]

Find the measure of <7

Answers

Hey there! :D

Vertical angles are congruent, they have the same measure.

So, <7 and <5 are vertical angles. They share the same vertex, and if you were to draw a straight line between them, it would connect and bisect them both equally.

<5= 45, so <7= 45.

I hope this helps!
~kaikers

1/4-(2006 + .20)+2x2-4

Answers

-2005.95. I googled it. May want to double-check though, and if you get something differentx let me know.

You are buying salsa at the grocery store. You have a manufacturer’s coupon for $0.50 off and the store is offering 50% off if you buy 2 containers. One container of salsa costs $3.25. What is your final cost?

Answers

3.25*2 = 6.5*0.5 = 3.25-0.50 = $2.75

Answer: Final cost will be $2.75.

Step-by-step explanation:

Since we have given that

Cost of salsa container = $3.25

Off on coupon = $0.50

Final cost of one salsa container is given by

[tex]3.25-0.50\\\\=\$2.75[/tex]

Hence, the final cost will be $2.75.

if he bought two containers

Cost of two containers is given by

[tex]3.25\times 2\\\\=\$6.50[/tex]

Coupon 50% off is given by

[tex]6.50\times 0.5\\\\=3.25[/tex]

So, Final cost is given by

[tex]6.25-3.25-0.5\\\\=\$2.75[/tex]

Hence, Final cost will be $2.75.

marco deposited $500 in a savings account earning 4% simple intrest over 5 years what was the total amount of intrest earned at the end of 5 years a. 40, b. 50, c. 100, d.200

Answers

The formula in computing the simple interest of a savings account is:

I = Prt

Where I = interest earned

P = principal amount deposited

r = rate

t = time in years

You are asked to find the total amount of interest earned at the end of 5 years. Substituting the amounts to the formula:

I = $500 (4%) (5)

I = $100

Therefore, the total amount of interest earned at the end of 5 years is $100.

Simplify the expression so there is only one positive power for each base
(3^-2•7^-5)^-4

Answers

= 3^(-2*-4)*7*(-5*-4)= 3^8*7^20

D is the answer

Answer:The and is D

Step-by-step explanation:

Guys help me please:(

Answers

x = -2
y = -5
For this case, you must realize that the solution to the system of equations is the ordered pair:
(x, y) = (- 2, -5)
Graphically, they are two lines that intersect in the third quadrant.
Answer:
See attached image.

EXPLAIN HOW A NUMBER LINE CAN BE USED TO FIND THE DIFFERENCE
FOR 34-28

Answers

You can count the marks on the line + the lower number to have the answer of 14

A number line can help you solve this equation because it can specifically tell the exact spots between the numbers and you can easily get the answer without checking your answer!

Which equation best describes the line of best fit?

A) y=6x +10

B) y=x−10

C) y=10x +70

D) y=2/3x

Answers

The y-value changes from 10 to 70 as the x-value changes from 0 to 10. That makes the slope (70 -10)/(10 -0) = 6, and the y-intercept = 10.

Selection A is the appropriate equation.

Hello! I need a bit of help with this one! Thanks

of the calculators sold this week, 3/8 of them were blue and of those, 2/9 were broken. What fraction of the calculators were blue and broken?

Answers

so 2/9 of the 3/8 calculators were broken.

2/9 x 3/8 = 1/12 of the calculators were broken.

What are the operations used to
solve this equation5/6x-2=-2/3x+1

Answers

addition
multiplication

Need help! Stuck in this question.

Answers

this is the answer i got on this calculator

There are 18 muffins on a plate. If they are split equally among 9 people, how many muffins will each person get? Write three equations to solve it.

Answers

Each person would get 2 muffins

1. 18/9=2
2. m = muffins & p = people m/p=t
3.18 muffins divide 9 people equal 2 muffins for everyone

How do u solve this system with substitution?

Answers

4x - (2x - 5) = 7

4x - 2x + 5 = 7

2x + 5 = 7

2x = 2

x = 1

y = 2(1) - 5

y = 2 - 5 = -3

Find the value of X in the triangle.

Please explain. Thanks.

Answers

29°

triangles can only have 180°

This is a right triangle, so one angle is 90°, leaving us with 90° left

90°-61°= 29°

X=29
You have a right angle, they're always 90 degrees, plus 61 degrees = 151, next you subtract 151 from 180 = 29 degrees.

Which model is most appropriate for the data shown in the graph below

Answers

it's an exponential graph.

it is an Exponential graph

Sarah build a dollhouse the floor the dollhouses Square Sara covers the floor with 144 square inches of tile how long in inches is one side of the dollhouse floor?
A. 12
B. 38
C. 72
D. 144

Answers

All you have to do is find the square root of the area because the area is the side length squared.

square root of 144 = 12

So a side length is 12

A. 12x12 is 144 and the tile has to be a 12 by 12 to have 144 tiles.

Answer this correctly plz

Answers

The area of the triangle is
  A = (1/2)bh
  = (1/2)(3 ft)(6 ft)
  = 9 ft^2

That triangular area is not carpeted, so the carpet area is
  72 ft^2 -9 ft^2 = 63 ft^2.

A line containing the points (2, 16) and (-8, -4) intersects the y-axis at what point?

Answers

We first need to find the slope of this line: (-4-16)/(-8-2) = -20/-10 = 2.
We write this as slope-intercept: y = 2x + b(b is the y-intercept). Now we plug in on of the above points: 16 = 2(2) + b, and b is equal to 12.
---
Hope this helps!

Final answer:

To find the y-intercept of a line, we can use the equation y = mx + b. By substituting the coordinates of one of the given points into the equation, we can solve for b and find the y-intercept. The y-intercept is the point where the line intersects the y-axis.

Explanation:

The line containing the points (2, 16) and (-8, -4) can be represented by the equation y = mx + b, where m is the slope and b is the y-intercept. To find the y-intercept, we need to substitute the values of one of the given points into the equation and solve for b.

Using the point (2, 16), we have 16 = m(2) + b. Substituting the values of the other point gives us -4 = m(-8) + b. We can solve this system of equations to find the values of m and b.

16 = 2m + b-4 = -8m + b

By subtracting equation 2 from equation 1, we can eliminate b and solve for m. After finding the value of m, we can substitute it back into either equation to find the value of b. This will give us the y-intercept.

Once we have the values of m and b, we can write the equation of the line in the form y = mx + b. The y-intercept will be the point at which the line intersects the y-axis.

Learn more about Finding the y-intercept of a line here:

https://brainly.com/question/35319761

#SPJ11

Kenji's dog ate 3/12 of e treats in a box of dog treats on Monday. His dog ate 2/12 of the treats on Tuesday. What fraction more of the box of the treats did his dog eat on Monday than on Tuesday?

Answers

1/12 of the box of dog treats

3/12-2/12= 1/12

40% of college students scored more than 70% on a math test 120 students scored below that how many total students took the math test

Answers

there were 200 students in total

How does the height of the triangle compare to the height of the rectangle

Answers

The triangle's height must be 3 times that of the rectangle for the areas to be the same.

For a triangle, A = (1/3)bh
For a rectangle, A = bh

If we let h represent the height of the rectangle and H represent the height of the triangle, we have
.. (1/3)bH = A = bh
.. H = 3h . . . . . . multiply the above equation by 3/b

Can someone pls tell me how to solve this

Answers

Since we find the cube root of 216, we get 6, which is the answer

Take the cube root of both sides. Or, if you cant see that, just plug in each awnser and see which one ends up being correct. 6^3=216

if the length of FH is 18 units, what is the value if x

Answers

Answer:

The value of x is 3

Step-by-step explanation:

Given that the length of FH is 18 units

we have to find the value of x.

Point G lies between F and H in which measurements are

[tex]\text{FG=4x and GH=2x}[/tex]

[tex]FH=4x+2x=6x\thinspace units[/tex]

[tex]6x=18[/tex]

Divide by 6 throughout the equation.

[tex]x=\frac{18}{6}=3[/tex]

The value of x is 3 cm.

Option 1 is correct.

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