Find the coordinates of the vertices of the figure formed by each system of inequalities. x + y < 9 x - 2y < 12 y < 2x + 3 a. (0, 0), (0, 1), (2, 0) c. (9, 1), (2, 3), (5, 6) b. (10, -1), (-6, -9), (2, 7) d. (0, -1), (2, -1), (3, 6)
Answers
Answer:
b. (10, -1), (-6, -9), (2, 7)
Step-by-step explanation:
One way to solve this problem is by graphing (see attachment). In fact, that actually is the easiest way to do this.
First, graph x + y < 9 (red part on the attachment). To do this, isolate the y so that it's like a regular linear equation: y < -x + 9. Graph the line y = -x + 9 first, and then choose a point either on the left or right of the line to plug in for x and y.
Let's just choose (0, 0), which is on the left of the line: 0 < -0 + 9 ⇒ 0 < 9. Since this is a true statement, we know that we should shade the left side of the equation, and not the right side.
Now, graph x - 2y < 12 (blue part on the attachment). It's the same process here as the first inequality. For this one, we find that we also shade to the "left" of the line (it's more "up" than "left", but you get the idea).
Finally, graph y < 2x + 3 (green part on the attachment). Again, it's the same process. For this, we shade to the right.
Now look at the three points that they intersect at: they are (2, 7), (-6, -9), and (10, -1). The answer is thus B.
Step-by-step explanation:
Step 1: Graph each of the inequalities
x + y < 9
x - 2y < 12
y < 2x + 3
It comes out that the vertices are (2, 7), (10, -1), and (-6, -9)
Answer: Option B
Related Questions
4. Francisco says, "36 is 75% of 48." Is Francisco correct or incorrect?
Show your reasoning using a Tape Diagram."
Answers
Answer:
see below
Step-by-step explanation:
Is means equal and of means multiply
36 = 75% * 48
36 = .75* 48
36 = 3/4* 48
36 =36
Using the tape diagram
Divide 48 into 4 pieces
12 12 12 12
Then circle 3 of them
12 +12 + 12
36
Answer:
Correct
Step-by-step explanation:
75% of 48
75/100 × 48
3/4 × 48
36
Divide the tape of length 48 units into 4 parts, 3 parts add up to 36
Please help. The correct and best answer gets brainiest! 29 points!!
(please make sure you are correct and show your work, no guessing)
Answers
Answer:(15, 100)
Step-by-step explanation:
first find the coordinates of the point above (3, 20)
you just look at the x axis and where the point is in this case x would be 6 and then you find y which would be 40
so the coordinate would be (6, 40)
now subtract (6, 40) by (3, 20)
6-3= 3
40- 20= 20
you get the first coordnites which is what you add (12,80) to
12 +3= 15
80+ 20= 100
you get the coordinates (15, 100)
Find the 23rd term of this sequence -25,-15,-5,5....
Answers
Answer:
195
Step-by-step explanation:
To find the 23rd term of this sequence, we can use the arithmetic sequence formula [tex]a_{n} =a_{1} +(n-1)d[/tex] where,
[tex]a_{n}[/tex] = [tex]n^{th}[/tex] term
[tex]a_{1}[/tex] = first term
[tex]n[/tex] = term position
[tex]d[/tex] = common difference
[tex]a_{23}=-25+(23-1)10[/tex]
[tex]a_{23} =195[/tex]
(01.01)
Evaluate 9 − 3 ⋅ 2 + 4. (1 point)
Group of answer choices
Answers
Answer: 7
Step-by-step explanation: 9-3•2+4
9-6+4
=7
Write the equation of a circle with a center at (-2,-10) and a radius of 1.2.
A) (x + 2)2 + (y + 10)2 =1.2
B) (x - 2)2 + (y - 10)2 = 1.2
C) (x + 2)2 + (y + 10)2 = 1.44
D) (x + 2)2 + (y + 10)2 = 14.4
Answers
Answer:
The correct option is the letter "C", [tex](x + 2)^2 + (y + 10)^2 = 1.44[/tex].
Step-by-step explanation:
The standard form for a circle's equation has the following structure:
[tex](x - x_c)^2 + (y - y_c)^2 = r^2[/tex]
Where [tex](x_c,y_c)[/tex] are the coordinates of the center of the circle and [tex]r[/tex] is the radius. Applying the data from the problem we have:
[tex](x - x_c)^2 + (y - y_c)^2 = r^2\\\[[x - (-2)]^2+ [y - (-10)]^2 = (1.2)^2\\(x + 2)^2 + (y + 10)^2 = 1.44[/tex]
Therefore the correct answer is the letter "C", [tex](x + 2)^2 + (y + 10)^2 = 1.44[/tex].
A cone with a radius of 7ft and a height of 12ft is filled with wet sand. you took that sand and built a pyramid with a base of 4ft by 5ft how tall would the resulting pyramid be?
Answers
Answer:
95.36 ft
Step-by-step explanation:
Volume of a Cone[tex]=\frac{1}{3}\pi r^2 h[/tex]
Radius=7 ft, Height=12 ft
Therefore the volume of sand in the cone
[tex]=\frac{1}{3}\pi *7^2*12\\=615.7522$ ft^2[/tex]
If the sand was used to build as pyramid with a base of 4ft by 5ft.
Volume of a Pyramid[tex]=\frac{1}{3}*$Base Area* Height[/tex]
[tex]615.7522=\frac{1}{3}*(4*5)* Height\\615.7522=\dfrac{20}{3}* Height\\$Multiply both sides by \dfrac{3}{20}\\$Height =615.7522*\dfrac{3}{20}\\\\$Height of the pyramid=95.36 ft[/tex]
2. Why was Susan Weiss' work not
considered important?
Answers
Answer:
she was a woman.
Plz, answer this question I need help. I'll mark you as brainliest and give you 5 stars.
Answers
Answer:
pretty sure its D but idk
Step-by-step explanation:
PLEASE HELP ME ILL GIVE BRANLIEST!!! (and 50 points!)
A company mixes two kinds of cleansers to get a blend they sell for 59 cents a liter. One of the cleansers costs 50 cents per liter, and the other 80 cents per liter. How much of each kind should be mixed to get 2,000 liters of the blend?
Answers
Answer:
x = the 50c cleanser
y= the 80c cleanser
x= 1400 liters
y=600 liters
I'm pretty sure this is right
Compared to its 'parent' function f(x)=x^2, describe the changes if f(x)=-x^2-3
Answers
Answer:
It is inverted and shifted down 3 units.
Red is f(x) = x^2
Purple is f(x) = -x^2 -3
Step-by-step explanation:
is the relation a function?
please help.
Answers
Answer:
Yes
Step-by-step explanation:
A function has one input (x-value) per output (y-value).
In other words, a relation that does not repeat any x values is a function.
{(3,4) , (5,0) , (2,4) , (-5,-5)}
The domain of the relation is:
{-5,2,3,5}
Since none of the numbers repeat in the domain, the relation is a function.
Help asap . thank youu
Answers
Answerr:turturtyuturtyurtyurtujj
Step-by-step explanation:
hmhmhgmfgjrtyhetyhtrhtrthrtngjthgfrtyu
Answer:
No
Step-by-step explanation:
If you graph the line, you will get an exponential function
Can someone help with the following question. Explain why it's the answer
Thank you.
Answers
Because B and D are equations and C has a less than sign.
What is the equation of the line that has a slope of –4 and passes through the point (2, 3)?
Answers
Answer:
y=-4x+11
Step-by-step explanation:
We can use the point-slope form of a line to solve this, which is
y - y₁ = m (x - x₁), where (x₁ , y₁) is a point and m is the slope.
We have:
y - 3 = -4(x - 2)
y - 3 = -4x + 8
y = -4x + 11
Hope this helps!
ok so I must be stupid but pls help
Answers
It is A and D
They both have a volume of 80
What is the length of Line segment A J if Line segment A B is parallel to lines segment J K?
8 in.
8.75 in.
10.25 in.
14 in.
Answers
Answer:
8.75 in.
Step-by-step explanation:
See attachment for the figure.
As you can see, ∆ HBA & ∆HKJ are similar,
HB/HA = HK/HJ
3/5.25 = 8/HJ
3HJ/5.25 = 8
3HJ = 42
HJ = 14 in.
AJ = 14 - 5.25
AJ = 8.75 in.
Therefore, the length of Line segment AJ is 8.75 in.
Answer:
(B) 8.75
Step-by-step explanation:
How many times were you able to transfer any contents of the cone into the cylinder? What comparison can you make between the volume of the cone and the volume of the cylinder?
Answers
Allison currently has a balance of $2,300 in her checking account. She deposits a $345
paycheck, a $30 rebate check and a personal check for $600 into her checking account. She
withdrawals $350 in cash. How much will she have in her account after the transaction?
Answers
Answer:
2925
Step-by-step explanation:
2300 starting
Deposit means add
2300+ 345+30+600 =3275
Withdrawal means subtract
3275-350 =2925
She has 2925 in the account
Which is the graph of g(x) = [x+3]
Answers
Answer:
Option D
Step-by-step explanation:
The graph of g(x) = ⌈x + 3⌉ is the graph of the parent function h(x) = ⌈x⌉ that has been shifted to the left 3 units.
The correct choice is D
I just need a bit more clarification (just checking if my answer is right)
I put: C
But I just want more clarification.
Answers
Answer:
I think it's right. you should be fine
The area of a rectangle is equal to its length times its width. If the area of a rectangle
is 14x + 42 square feet, which option(s) could be the length and width of that rectangle?
Answers
Answer:
Either x+15 or x-17.
Step-by-step explanation:
Maria has 7 gal of water Mike has 23 qt of water. How many more pints of water does Maria have then Mike
Answers
Answer:
i think 10
Step-by-step explanation:
there is 8 pints in 1 gallon and 2 pints in 1 quart so that means in 23 quarts theres 46 pints and in 7 gallons there is 56 so 56-46 is 10 if that is what the question is asking lmk if the question is wrong
The side length of a square is 5.25 inches. What is its area? What is its perimeter? Be sure to show your work for credit and don't forget to label units!
Answers
Answer:
Step-by-step explanation:
area of a square is just L^2 or one of the sides squared
and the perimeter is 4L
that means
Area = 5.25^2
= 27.5625 in^2
Perimeter = 4 * 5.25
= 21 in
A second-grade student is 4 feet tall. Her teacher is 5 2/3 feet tall.
How many times as tall as the student is the teacher?
What fraction of the teacher’s height is the student’s height?
Can anyone help with this please?
Answers
Answer:
1. 17/12
2. 12/17
Step-by-step explanation:
The teacher is 1.42 times as tall as the student and the required fraction is given by 17/12
What is a ratio?The quantitative relation between two amounts shows the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"
Given here; Height of the student = 4 ft. and height of teacher =5²/₃
Ratio of the height of the teacher and student is
= 5+2/3 / 4 ( 5²/₃=5+2/3 , property of mixed fractions)
= 17/3 × 1/4
=17/12
=1.4166
Thus we can say that the height of teacher is 1.42 times as tall as the student.
Also as given above the teacher's height is 17/12 the students height.
Hence, The teacher is 1.42 times as tall as the student and the required fraction is given by 17/12
Learn more about ratios here:
https://brainly.com/question/13419413
#SPJ5
3 is what percentage of 5
Answers
Answer:
60%
Step-by-step explanation:
is means equals and of means multiply
3 = P * 5
divide each side by
3/5 = P
.6 = P
Change to a percentage by multiplying by 100
60%
Answer: 60%
Step-by-step explanation:
3/5 * 100
3 * 20
What is the slope of the line that passes through the points (6, 4) and (3,8)?
Answers
Answer:
-5/3
Step-by-step explanation:
you have to do slope formula
a fully inflated car tire loses 2% of its air every day. if the tire atarted with 4460 cubic feet of air, write an equation to show how much air it had after d days.
Answers
Answer:
Step-by-step explanation:
4460=d*2
Please answer correctly !!! Will mark brainliest !!!!!!
Answers
Answer:
5(x-4)-6
Step-by-step explanation:
If we subtract 6 from both sides, using the additive property of equality, we get that y, or f(x), equals 5(x-4)-6
Combine the like terms to create an equivalent expression:
−3x-6+(-1)
Answers
Answer:
-3x-7
Step-by-step explanation:
The like terms here are -6 and -1. When we add the two, we get -7. Therefore, the answer is -3x-7. Hope this helps!
For which values of x is the function
Y=x+4/(x+5)(x+11)
not defined? Select all that apply.
-4
5
-5
11
Answers
Answer:
x = - 5, x = - 11
Step-by-step explanation:
Given
y = [tex]\frac{x+4}{(x+5)(x+11)}[/tex]
The denominator cannot be zero as this would make y undefined.
Equating the denominator to zero and solving gives the values that x cannot be, that is
(x + 5)(x + 11) = 0
Equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
x + 11 = 0 ⇒ x = - 11
Thus
x = - 11 and x = - 5 are excluded values.