Mathematics High School

100 POINTS PLEASE HELP!!!
The coordinate plane below represents a community. Points A through F are houses in the community.

graph of coordinate plane. Point A is at negative 5, 5. Point B is at negative 4, negative 2. Point C is at 2, 1. Point D is at negative 2, 4. Point E is at 2, 4. Point F is at 3, negative 4.

Part A: Using the graph above, create a system of inequalities that only contains points C and F in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (7 points)

Part B: Explain how to verify that the points C and F are solutions to the system of inequalities created in Part A. (5 points)

Part C: Erica wants to live in the area defined by y < 7x − 4. Explain how you can identify the houses in which Erica is interested in living. (2 points)

Answers

Answer 1

Answer:

[tex]\sf A) \quad \begin{cases}\sf y > -5x+5\\\sf y < -5x+12\end{cases}[/tex]

B) see below

C) points C, E and F

Step-by-step explanation:

Given points:

A = (-5, 5)B = (-4, -2)C = (2, 1)D = (-2, 4)E = (2, 4)F = (3, -4)

Part A

A system of inequalities is a set of two or more inequalities in one or more variables.

To create a system of inequalities that only contains C and F in the overlapping shaded region, create a linear equation where points C, F and E are to the right of the line and a linear equation where points C, F, A, B and D are to the left of the line.

The easiest way to do this is to find the slope of the line that passes through points C and F, then add values to move the lines either side of the points.

[tex]\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{y_F-y_C}{x_F-x_C}=\dfrac{-4-1}{3-2}=-5[/tex]

Therefore:

[tex]\sf y = -5x + 5[/tex] → points C, F and E are to the right of the line.

[tex]\sf y=-5x+12[/tex] → points C, F, A, B and D are the left of the line.

Therefore, the system of inequalities that only contains points C and F in the overlapping shaded regions is:

[tex]\begin{cases}\sf y > -5x+5\\\sf y < -5x+12\end{cases}[/tex]

To graph the system of inequalities:

Plot 2 points on each of the lines.Draw a dashed line through each pairs of points.Shade the intersected region that is above the line y > -5x + 5 and below the line y < -5x + 12.

Part B

To verify that the points C and F are solutions to the system of inequalities created in Part A, substitute the x-values of both points into the system of inequalities. If the y-values satisfy both inequalities, then the points are solutions to the system.

Point C (2, 1)

[tex]\implies \sf x=2 \implies 1 > -5(2)+5 \implies 1 > -5\quad verified[/tex]

[tex]\implies \sf x=2 \implies 1 < -5(2)+12\implies 1 < 2 \quad verified[/tex]

Point F (3, -4)

[tex]\implies \sf x=3 \implies -4 > -5(3)+5 \implies -4 > -10\quad verified[/tex]

[tex]\implies \sf x=3 \implies -4 < -5(3)+12\implies -4 < -3 \quad verified[/tex]

Part C

Method 1

Graph the line y = 7x - 4 (making the line dashed since it is y < 7x - 4).

Shade below the dashed line.

Points that are contained in the shaded region are the houses in which Erica is interested in living: points C, E and F.

Method 2

Substitute the x-value of each point into the given inequality y < 7x - 4.

Any point where the y-value satisfies the inequality is a house that Erica is interested in living.

[tex]\sf Point\: A: \quad x=-5 \implies 5 < 7(-5)-4 \implies -5 < -39 \implies no[/tex]

[tex]\sf Point\: B: \quad x=-4 \implies -2 < 7(-4)-4 \implies -2 < -32 \implies no[/tex]

[tex]\sf Point\: C: \quad x=2 \implies 1 < 7(2)-4 \implies 1 < 10 \implies yes[/tex]

[tex]\sf Point\: D: \quad x=-2 \implies 4 < 7(-2)-4 \implies 4 < -18 \implies no[/tex]

[tex]\sf Point\: E: \quad x=2 \implies 4 < 7(2)-4 \implies 4 < 10 \implies yes[/tex]

[tex]\sf Point\: F: \quad x=3 \implies -4 < 7(3)-4 \implies -4 < 17 \implies yes[/tex]

Related Questions

Once again, I’m wasting points to dazzle you all with my hand drawn cardboard cutouts of hanako and tsukasa. If you don’t know who they are then just admire the art and pretend I’m picasso. Bring up the mistakes and I’ll laugh along and criticize my art with you

Answers

Answer:

Cool art

Step-by-step explanation:

Answer:

sick bro, that's cool.

Step-by-step explanation:

do you read the manga, if you do then, broo the lastest chapter was

nice

A baseball team had 75 players show up for tryouts last year and this year had 90 players show up for tryouts. Find the percent increase in players from last year to this year.

Answers

Answer: 33.3%

Step-by-step explanation:

First find the difference between the players in try-outs over the years.

= 90 - 75

= 25

Then use this difference to find the percent increase:

= Difference / Players last years * 100%

= 25 / 75 * 100%

= 33.3%

True or False?

Is this the correct formula for using angles to see if a triangle is unique?

angle + angle <180

Answers

Answer: true

Step-by-step explanation:

No,this is not the correct formula

Which linear function represents the table
PLEASE HELP ILL GIVE BRAINLIEST

Answers

Answer:

The answer is D.

Step-by-step explanation:

Hope this helps

The answer is the most reasonable and I learned this as well.

The track team sold 40 t-shirts. Short sleeve t-shirts sold for $9.90 and long sleeve
t-shirts sold for $12.75. In all, $421.65 was taken in.
How many short sleeve t-shirts were sold?

Answers

No it’s not like him I’m not it would have Ben 3.4 shirts left

Answer:

The track team sold 31 short sleeved t-shirts.

Step-by-step explanation:

If there were 40 t-shirts sold, then you'd have to find how many short sleeved and long sleeved t-shirts were sold to get the amount of money made. Basically, all I did was start with 20:20. I multiplied the cost of each type of shirt by 20, however, the money from selling long sleeved t-shirts is a lot more than the actually amount. So then, I went to 30:10 with short sleeved and then long sleeved. The amount (when added together) was pretty close to the actual amount but it was still a tiny bit higher than the actual. So, I did 31:9 and the amount came out right.

(20 POINTS) PLZZZZZ HELPPPPPP

2. A diagonal shortcut across an empty
rectangular lot is 97 feet. The lot is 72
feet long. What is the other dimension of
the lot?
A 65 feet
C 120.8 feet
B 84.5 feet
D 169 feet

Answers

Answer:

65 ft (which is A)

Step-by-step explanation:

A² + B² = C²

72² + B² = 97²

B² = 4225

B = √4225

B = 65 ft

Aubrey's dinner cost $85 She tips the waitstaff 30%, percent for excellent service.

Answers

Answer:

She tipped $25.50 and paid a total of $110.50

Step-by-step explanation:

hope this helps you out

PLEASE HELP I CANT CONTINUE WITH MY WORK UNLESS THESE ARE COMPLETE AND CORRECT
IP Check: Solving Systems by Elimination
Teachers instructions:
Do not forget the PARENTHESIS in your answers.

Answers

Answer:

1) x=3, y=-3

Step-by-step explanation:

10x + 7y = 9 —— (1)

-4x -7y = 9 —— (2)

(1) + (2)

6x = 18

x = 18/6

x = 3

put x=3 in (1)

10(3) + 7y = 9

30 + 7y = 9

7y = 9 - 30

7y = -21

y = -21/7

y = -3

please give me brainlist if it is helpful for you

A recipe needs 1/4 tablespoons salt. the same recipe is made 5 times how much salt is used?
BTW IM IN 8TH GRADE BUT THE SCHOOL HAS NUN 4 US TO DO SO NOW THERE MAKING US LEARN THE SAME STUFF AGAIN AND I DONT REMEBER SO YA

Answers

Answer: 1 and one fourths because 1/4 times 5 is 1 1/4

Step-by-step explanation:

Answer:

1 1/4 tablespoons

Step-by-step explanation:

1/4 x 5=1 1/4 tablespoons

Ellen and Bob went to Olive Garden for dinner. Ellen’s dinner costs $24.95 and Bob’s dinner costs $21.95. If they leave an 18% tip, what is the total cost of their dinner, including tip? (Round your answer to the nearest cent, and do not include the $ sign.)

Answers

Answer: 55.34

Step-by-step explanation:

24.95 + 21.95 = 46.90

46.90 x 18%

18% = .18

46.90 x 18 = 8.442

8.44 = cost of tip

8.44 + 46.90 = 55.34

Which of the following shows the greatest percent increase?

A. 50 increased to 75
B. 500 increased to 700
C. 5,000 increased to 7,000
D. 50,000 increased to 74,000

Answers

a

i think this is right hope this helps :)

help me I keep getting it wrong

Answers

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{2}{3}[/tex] x - 6 ← is in slope- intercept form

with slope m = [tex]\frac{2}{3}[/tex]

Parallel lines have equal slopes , then

y = [tex]\frac{2}{3}[/tex] x + c ← is the partial equation

To find c substitute (9, 2) into the partial equation

2 = 6 + c ⇒ c = 2 - 6 = - 4

y = [tex]\frac{2}{3}[/tex] x - 4 ← equation of parallel line

-------------------------------------------------------------------

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{2}{3} }[/tex] = - [tex]\frac{3}{2}[/tex] , then

y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation

To find c substitute (9, 2) into the partial equation

2 = - [tex]\frac{27}{2}[/tex] + c ⇒ c = 2 + [tex]\frac{27}{2}[/tex] = [tex]\frac{31}{2}[/tex]

y = - [tex]\frac{3}{2}[/tex] x + [tex]\frac{31}{2}[/tex] ← equation of perpendicular line

PLEASE HELP WILL GIVE BRAINLIEST

15-10 dividid by 5 times 2^2 in the correct order

Answers

Answer:

12 1/2

Step-by-step explanation:

Answer:

your answer is 4x

Step-by-step explanation:

15-10 is 5

5 divided by 5 is 1

1 times 2 greater than 2 is 4

4x is your answer

Have a good day

please help anyone 15 points

Answers

Answer:

m<NOQ = 139°

Step-by-step explanation:

Since lines KM and NP are parallel, alternate exterior angles KLJ and QOP are congruent.

m<QOP = m<KLJ = 41°

Angles NOQ and QOP are a linear pair and are supplementary, so the sum of their measures is 180°.

m<NOQ + m<QOP = 180°

m<NOQ + 41° = 180°

m<NOQ = 139°

HELLPPPP PLSSSS HELPPPPPPP

Answers

The screen is black

pls help asap i will give branilest

Answers

15.010495

The caluclator can comfirm

Calculate the value of the expression 44-(5x4)

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

44 - (5 x 4) = 44 - 20

= 24

To choose the 8 songs, the director writes the name of each of the 12 songs on a slip of paper, puts them in a hat, and draws 8 slips. What is the probability that the set s/he chooses contains two of the four songs that have soprano solos?

Answers

Answer:

0.339

Step-by-step explanation:

Given that :

Total number of songs = 12

Number of songs to choose = 8

Total number of draws = 8

Selecting 2 of the 4 songs with syprano solos : 4C2

The 6 remaining songs from. The rest:

12-4C8-2 = 8C6

Total possible selections = 12C8

Hence,

probability that the set s/he chooses contains two of the four songs that have soprano solos will be :

(4C2 * 8C6) / 12C8

(6 * 28) / 495

168 / 495

= 0.339

can you please help me

Answers

Answer:

b !! (0.5, 0.5)

Step-by-step explanation:

if you used the formula to find midpoint 9i included a picture, you would get the fractions (1/2, 1/2) !! that as a decimal is 0.5 !! so the answer is b !! i really hope this helps !!

please help me on this will give you brainliest

Answers

Answer:

ST =6.9

SR =15.9

Step-by-step explanation:

a $528 video game console is on sale for 15% off. if sales tax is 6.25% what is total coast

Answers

448.80 is the price but let’s not add the sales tax 476.85

The term "off" indicates that the price of the item is reduced by the percentage off. Sales tax is however, added to the price of the item.

The total cost of the video game console is: [tex]\$476.85[/tex]

Given that:

[tex]Game = \$528[/tex]

15% off means that, the price is reduced by 15%.

So, we have:

[tex]Sales =Game - Game \times 15\%[/tex]

[tex]Sales = \$528 - \$528 \times 15\%[/tex]

[tex]Sales = \$528 -\$79.2[/tex]

[tex]Sales = \$448.8[/tex]

The total cost (when the sales tax of 6.25% is added) is:

[tex]Total = Sales + Sales \times 6.25\%[/tex]

[tex]Total = \$448.8 + \$448.8 \times 6.25\%[/tex]

[tex]Total = \$448.8 + \$28.05[/tex]

[tex]Total = \$476.85[/tex]

Hence, the total cost of the video game console is: [tex]\$476.85[/tex]

Answers

Step-by-step explanation:

The function/equation can be rewritten to fit the variables better. C=10t+2. C stands for the total cost, and t stands for the number of tickets. The total cost of tickets is the amount of tickets ($10 each) plus another $2 (probably some kind of fee).

find the missing value so that the line passing through the points has the given slope.
(10, y) and (3, 4); m= - 2/7

Answers

Answer:

y = 2

Step-by-step explanation:

use slope formula:

(4 - y) / (3 - 10) = -2/7

4-y / -7 = -2 /7

cross-multiply:

7(4 - y) = (-7)(-2)

28 - 7y = 14

-7y = -14

y = 2

Can someone help me with this
I’ll mark as brainliest.

Answers

1 = 10
2 = 12
3 = 14
4 = 16
5 = 18
6 = 20

Δweight
------------- =
Δ cost

2-1
------- =
12-10

1
—
2

Answer:

The W/C is divided by the numbers on top to the number on the bottom

may i have brainlist??

Ayako claims that there are centers of dilations through which a dilation of line n by a factor leaves n changed. Determine whether each point below represents a center of dilation that supports ayako's claim

Answers

Answer:

The answer is below

Step-by-step explanation:

The question is not complete. The points are not given, but I can explain it.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.

Dilation is the enlargement or reduction in the size of an object by a factor k. If a line AB is dilated by a factor k, with a center of dilation on the line AB, if the new line formed is A'B', then A'B' would lie on the same line AB irrespective of the dilating factor.

Dilation of a line segment is to smaller or larger a line with a specific scale factor. The line n when dilated with the center of dilation on the line, it will bring no change on the original line.

Given information

The line which is dilated is n.

Dilation

Dilation of a line segment is to smaller or larger a line with a specific scale factor. If this scale factor is more than 1 then the line segment will larger otherwise smaller.

In the given problem a line n is dilated with the a scale factor that leaves the changed of n.

If the entire line is dilated and the point of this line passes through center of dilation then the change will be nothing. If dilated from the center of dilation the scale factor does not matter.

To find center of dilation which supports Ayako's claim the point below which represents the center of dilation are not given in the problem.

Hence, The line n when dilated with the center of dilation on the line, it will bring no change on the original line.

Learn more about the center of dilation here;

https://brainly.com/question/25300368

find the value of 3 under root 54/250

Answers

Answer:

Evaluate cube root of 250- cube root of 54

3√250−3√54

Simplify each term.

53√2−33√2

Subtract 33√2 from 53√2-

2^3√2

The result can be shown in multiple forms.

Exact Form:

23√2

Decimal Form:

2.51984209....

Step-by-step explanation:

Hope it is helpful.....

The value of 3 under root 54/250 is 3 / 5.

What is a fraction?

A fraction is a numeral that represents a rational number.

Let a and b be two numbers, then their fraction can be represented as a/b.

The given fraction is,

54 / 250.

To find the value of 3 under root 54 /250,

Find cube root of 54 /250.

∛(54 / 250)

= ∛(27 / 125)

= ∛27 / ∛125

= 3 / 5

The value of cube root of 54 /250 is 3/5.

To know more about Fraction on:

https://brainly.com/question/10708469

#SPJ2

Write as an addition problem: -49 - (-3)

Answers

Answer:

-49 + 3

Step-by-step explanation:

I think this ans may help you

Equations
f) The difference of the ages of two sisters is 5 years. After 4 years, if the product of
their ages becomes 104, find their present ages.

Answers

Step-by-step explanation:

I hope this is correct.

Price-club sells a 12-ounce box of crackers for $2.59 and Shop Mart sells 1- 1 2 pound box of crackers for $4.68.

The unit price at Price-Club is $

per ounce, and the unit price at Shop Mart is $
per ounce.

Answers

Answer:

Price club: = $0.216 per ounce

Shop Mart: = $0.195 per ounce

Step-by-step explanation:

Price club: 2.59 / 12 = 0.216 per ounce

Shop Mart: 4.68 / 24 = 0.195 per ounce (1 1/2 pounds & based on 16 ounces/pound)

Answer:

0.20

Step-by-step explanation:

Find the solution of y = 3x + 3 for x = –3.

(12, –3)

(–3, –6)

(–3, 0)

(–3, –2)

Answers

Answer:

Step-by-step explanation:

Well, we know x=-3.

Substitute -3 for x in the equation, and solve. You should get -6.

(x,y)

(-3,-6)

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