Which point is a solution to the linear inequality y<
-1/2x+2
O (2, 3)
O (2,1)
O (3,-2)
O (-1,3)
Answers
Answer: Choice C. (3,-2)
A diagram is shown below.
===============================================
Explanation:
There are two approaches we can take. Since we're given a list of choices, we can plug each of the coordinates one at a time into the inequality. If we get a true statement, then it is a solution.
For choice A, we have x = 2 and y = 3 paired up together. Plugging them into the given inequality leads to...
y < (-1/2)*x + 2
3 < (-1/2)*2 + 2
3 < -1 + 2
3 < 1
This is false because 3 is not smaller than 1. So (2,3) is not a solution. You should find that choice B leads to a similar situation because
y < (-1/2)*x + 2
1 < (-1/2)*2 + 2
1 < -1+2
1 < 1
and 1 cannot be smaller than itself. So (2,1) isn't a solution either.
However, choice C is the answer since,
y < (-1/2)*x + 2
-2 < (-1/2)*3 + 2
-2 < -1.5 + 2
-2 < 0.5
This is true because -2 is to the left of 0.5 on the number line. So that's why (3,-2) is a solution.
For choice D, you should find that (-1,3) doesn't make the inequality true.
-----------------------------------------------------------
An alternative approach:
As a visual way to solve this problem, we can graph the given inequality by following these steps
Draw a dashed line through the points (0,2) and (4,0). This forms the graph of y = (-1/2)x + 2Shade below the dashed lineWe make the boundary line dashed because points on the boundary do not count as solution points. This is due to the lack of "or equal to" in the inequality sign. We shade below the boundary line because of the "less than".
As the diagram below indicates, the blue region consists of every (x,y) solution point that makes y < (-1/2)*x + 2 true.
The diagram also shows that only point C is in that blue region, making it a solution point. Point B on the boundary does not count as a solution. You can think of the dashed line as an electric fence you can only get closer to, but can't touch, in terms of determining a solution point.
So effectively, this is a quick and easy way to find solutions if you have a graphing calculator or online graphing tools (such as Desmos or GeoGebra).
Related Questions
find the labeled points
Answers
Answer:
A= (6,76.5)
B =(32,18)
C=(80,0)
Step-by-step explanation:
The inequalities given are ;
3x + 8y ≥ 240
9x + 4y ≥ 360
x≥6
y≥0
The graph for the inequalities is as follows;
From the graph,
A= (6,76.5)
B =(32,18)
C=(80,0)
I need this pls and thank you.
Answers
LET ME KNOW IF THIS HELPED
James can finish a job in 1.5 hours. Jane can finish the same job in one hour. How long will it take them to finish this job if they work together?
Answers
Answer:
36 minutes
Step-by-step explanation:
thank me later
Graph DEF and its image when you translate DEF using vector
Answers
Answer:
The image coordinates are D'(8, 5), E'(12, 3) and F'(10,0)
Step-by-step explanation:
Given the vertices of △ DEF are D (2, 5), E (6, 3), and F (4, 0). We have to translate the triangle using the vector (6, 0)
Now, translation by vector (6, 0)
D (2, 5)=D'(2+6, 5+0)=D'(8, 5)
E (6, 3)=E'(6+6, 3+0)=E'(12, 3)
F (4, 0)=F'(4+6, 0+0)=F'(10,0)
Now, we have to label the coordinate of the triangle or to get image of triangle after translation.
Hence, The image coordinates are D'(8, 5), E'(12, 3) and F'(10,0)
Step-by-step explanation:
Mr. Falco baked blueberry muffins several times in May using the recipe shown. He used 3 3/4 cups of milk in all. How many times did he bake muffins? Use the equation 1/4t = 3 3/4.
Answers
Answer:
use fraction caculator
Step-by-step explanation:
srry for wrong answer just need points for this question ineed only one more answer for so again i am so srry pls dont get amd or just dont pay any attention to this
Answer:15
Step-by-step explain
3 3/4 divided by 1/4
3 3/4=15/4
15/4 divided by 1/4=15
for 25 points can someone please do 5-12 for me on a piece of paper, PLEASE. I really need help asap its due at midnight and I've done some but Im totally stuck, so can someone please do it?
Answers
I posted the photo of all the step and answers for each question
Hope this helped
Mr. Fowler's science class grew two different varieties of
plants as part of an experiment. When the plant samples
were fully grown, they compared their heights.
Pls help
Answers
Option D is the correct option.
What is Mean Absolute Deviation?'The mean absolute deviation (MAD) is the mean (average) distance between each data value and the mean of the data set.'
According to the given problem,
The mean height Variety A = 19 [ from the table ]
The mean height of variety B = 13 [ from the table ]
The spread is given by the mean absolute deviation, which 1.2 for Variety A and 2.4 for Variety B. So we can see that, the spread in Variety A is lesser than the spread in Variety B, which shows that the average height of Variety A varies less than the average height of Variety B.
We can see from the table that the average height of a variety A is indeed greater than that of Variety B. Also we can see that the Mean Absolute deviation of Variety A is 1.2 which is lesser than the Mean Absolute deviation of Variety B.
Hence, option D is correct since the average height of Variety A is greater than Variety B, and also the mean varies lesser in Variety A than in Variety B.
Learn more about mean absolute deviation here: https://brainly.com/question/10528201
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Marbelle has 10 shoes. Hailey has 4 shoes. Mabye has 400 shoes. How many shoes do they have all togherter?
Answers
Answer:
414
Step-by-step explanation:
10+4+400=414
Answer:
414
Step-by-step explanation:
Find the slope of the line that goes through the following points.
A. –1
B. 1
C. –4
D. –7
Answers
Answer: B) Slope is 1
Step-by-step explanation:
Y² - Y¹ divide by X² - X¹
Plug in: -3 - (-4) divide by 1 - 0
= 1 divide by 1
= Slope is 1
yes its me the one iwth 55 zeroes
i have another random question for u
50389203029138213/932810392748392748329473
Answers
Answer:
thanks
Step-by-step explanation:
50389203029138213/932810392748392748329473
What are the solutions of this quadratic equation
Answers
Answer:
It's A.
Step-by-step explanation:
What is the area of the shaded region?
Answers
Answer:
58x i think. i hope thiss helps
Answer:
31x
Step-by-step explanation:
x * 5 = 5x
3x * 12 = 36x
36x - 5x = 31x
first you have to find the area of the big rectangle and the little rectangle too and then subtract the area of the big rectangle to the little rectangle to find the area of the Shaded region
There are 9 female performers in a dance recital. The ratio of men to women is 2:3. How many men are in the dance recital?
Answers
Answer:
6 men
Step-by-step explanation:
For each percentage, find a matching statement to describe it.
10% of a number
25% of a number
50% of a number
75% of a number
80% of a number
100% of a number
Equal to that number
12 of that number
14 of that number
110 of that number
34 of that number
45 of that number
Answers
Answer:
mk,m
Step-by-step explanation:
mlmkm km
Is 6x and 4x+2 equivalent
Answers
Answer:
Is 6x and 4x+2 equivalent
? No!
Step-by-step explanation:
6x doesn't equal 4x+2
In order for them to be the same you would have to add the same terms example:
4x+2x would equal 6x
Extra explaining:
The only way for those term to be added would be if they had the same variable since only 4x has a variable the 2 cant be added. In math you CANNOT move your variables off of a number and add them back on after.
PLEASE HELP! how do you find Angle B, Angle C and length of A?
Answers
The following information is known about a loan.
Time = 7 years
Interest rate = 6%
Interest = $840.00
What was the principal on the loan?
$200.00
$352.8ghing
$1.862.50
O $2.000.00
Answers
Answer:
B. $352.80
Step-by-step explanation:
edge 2021
The principal on the loan with interest rate of 6% is $2000.
Given that a loan is given in the interest rate of 6%, interest received is $840 and the duration of the loan is 7 years,
We need to find the principal on the loan,
To find the principal on the loan, we can use the formula for simple interest:
Interest = Principal × Rate × Time
In this case, we know the interest is $840.00, the rate is 6%, and the time is 7 years.
Let's solve for the principal:
Principal = Interest / (Rate × Time)
Principal = $840.00 / (0.06 × 7)
Principal ≈ $840.00 / 0.42
Principal ≈ $2000.00
Therefore, the principal on the loan is $2000.00.
Learn more about simple interest click;
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Solve the following proportions p/18= 8/72 pls help
Answers
Answer:
p = 2
Step-by-step explanation:
[tex]\frac{p}{18}[/tex] = [tex]\frac{8}{72}[/tex]
to work with smaller numbers you can look to reduce
for example, 8/72 can be reduced to 1/9
[tex]\frac{p}{18}[/tex] = [tex]\frac{1}{9}[/tex]
now you can cross-multiply:
9p = 18
p = 18/9 which is 2
Please help, due tomorrow. will give brainlist if correct
Given f(x)=3x^2-2x+k, and the remainder when f(x) is divided by x-3 is 35, then what is the value of k?
Answers
Answer:
14
Step-by-step explanation:
compare the divisor x-3 with x-a which will get you 3 and then use remainder theorem
Help me for cookie pls
Answers
Answer:
x = 83°
Step-by-step explanation:
ZW is a straight angle which means it is equal to 180°
So 97° + x° = 180°
180° - 97° = 83°
please help asap everything is in the ss
Answers
A tool set on price for $424.15 dollars and the original sales price was 499.00 what percent of the original price is the sale price at now ?
Answers
Answer:
15% = percent of the discount
85% = percent of the original price that you pay now
ZA and ZB are supplementary angles. If mZA = (x + 6) and m
ZB = (7x +30)°, then find the measure of ZA.
Answers
Answer:
za=24
Step-by-step explanation:
supplementary angles add up to equal 180
180=7x+x+30+6
step 1 combine like terms
180=8x+36
step 2 subtract 36 from each side
144=8x
step 3 divide each side by 8
x=18
now we just plug in 18 to x in x+6
18+6=24
Answer:
24°
Step-by-step explanation:
The sum of supplementary angles is 180°.
Thus, we can set up our equation as:
(x + 6) + (7x + 30) = 180
Combine like terms.
8x + 36 = 180
Isolate the variable by subtracting 36 from both sides.
8x = 144
Divide both sides by 8.
x = 18
Now, let's revisit the equation for m∠ZA, and plug in our x.
((18) + 6)°
24°
f(x)=sin x-3 cos x is a sinusoid true or false
Answers
Answer:
true
Step-by-step explanation:
Can u help me?? please
Answers
Answer:
you checked the right box. Its b
Step-by-step explanation:
22/5 divided by 2/5 is 11
b
help ive been stuck on this for a while now
Answers
Answer:
a. 18
b.10
c.64
Step-by-step explanation:
a. 27/3=9
9x3=27
9x2=18
b. 36/9=4
9x4=36
40/4=10
c. 48/3=16
3x16=48
4x16=64
Suppose your friend's parents invest $15,000 in an account paying 7% compounded annually. What will the balance be after 10 years?
Answers
Answer:
$25,500
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 7%/100 = 0.07 per year,
then, solving our equation
I = 15000 × 0.07 × 10 = 10500
I = $ 10,500.00
The simple interest accumulated
on a principal of $ 15,000.00
at a rate of 7% per year
for 10 years is $ 10,500.00.
1.
Omar is making Shortbread for 16 people.
He has found this recipe on a website.
EH
Shortbread
Serves 8
Butter
Caster Sugar
Plain Flour
Cornflour
150g
759
1759
50g
How much of each ingredient will he need for 16 people?
Answers
Answer:
300g butter, 1518g caster sugar, 3518g plain flour, 100g cornflour
Step-by-step explanation:
servings show are for 8, times everything by 2 to get 16 servings :)
1) x < -14
please help i don’t know how to do this
Answers
Answer: See the diagram below.
This diagram shows a closed filled in circle at -14 on the number line. Also, the shaded region is to the left of the closed circle. This visually represents values that are smaller than -14, or equal to -14.
The filled in circle is used to indicate "include this endpoint". In contrast, an open hole indicates "do not include this endpoint" which is only used if the inequality was [tex]x < -14[/tex] instead of [tex]x \le -14[/tex]. The "or equal to" portion is why we include the endpoint.
Which names this amount ? Select all that apply .