What system of linear inequalities is shown in the graph?
Enter your answers in the boxes.
Answers
Answer:
y ≤ (-2)x+2
y < (1/3)x + 2
Step-by-step explanation:
First, we'll want to figure out the lines that are intersecting.
To find the equation of a line given two points (of form y=mx+b), we can first find the slope (m). This is equal to (y₂-y₁)/(x₂-x₁) for points (x₁,y₁) and (x₂,y₂). Then, we can plug a point in and solve for b.
For the line that has points at (1,0) and (2, -2), our slope is
(y₂-y₁)/(x₂-x₁) = (-2-0)/(2-1)
= (-2)/1
= -2
Our equation is therefore y= (-3/2)x+b. Plugging a point like (2,-2) in, we get
-2 = (-2)(2) + b
-2 = -4 + b
add 4 to both sides to isolate b
b =2
Our equation is thus y = (-2)x+2
For the other line, with points at (-3,1) and (0,2), our slope is (2-1)/(0-(-3)) = 1/3
Then, our equation is y=(1/3)x+b
plug (-3,1) in
1 = (1/3)(-3) + b
1 = -1 + b
add 1 to both sides to isolate the b
b =2
Our equation is thus y=(1/3)x + 2
Our equations are y=(1/3)x + 2 and y = (-2)x+2. In the graph shown, the shaded area is under both the lines (it is also to the left of them, not to the right or on top). Therefore, we can say that the shaded area is less than the line.
For y = (-2)x+2, the line is not dotted, so the line is included in the region. This means that our inequality is y ≤ (-2)x+2 (note the ≤ rather than simply the < sign)
For y=(1/3)x + 2, the line is dotted, so it is not included in the region. This means that our inequality is y < (1/3)x + 2
Related Questions
A=E
BCE=90
BF=AC
AC=EC
Answers
==========================================================
Explanation:
HL stands for Hypotenuse Leg. This rule works only for right triangles.
So we must have two hypotenuses that are congruent, and we must have two legs that are congruent
The diagram shows that AB = DE are the congruent hypotenuses. So we have "H" taken care of. We just need the "L" portion.
We can see that only choice D works, which is AC = EC. If we knew that AC and EC were the congruent legs, then we have enough info to use HL.
is the perpendicular bisector of . Point T is the midpoint of . Point U lies on . If the length of is 7 units, the length of is how many units?
Answers
Complete question is;
RS is the perpendicular bisector of PQ . Point T is the midpoint of PQ. Point U lies on RS. If the length of UP is 7 units, the length of UQ is ______ units.
Triangle is attached
Answer:
UQ = 7 Units
Step-by-step explanation:
From the image attached, we can see that;
T is the midpoint of PQ
Thus;
PT = TQ
Since RS is perpendicular to PQ, then we can say that;
∠PTU = ∠QTU
Now, from SAS congruence theorem, we can say that;
△PTU = △QTU
Thus, from corresponding sides of both triangles, we can say that;
UP = UQ
Thus,
UQ = 7 Units
Answer:
7 units
Step-by-step explanation:
Use properties to evaluate
(2)-27
3)
QUESTION
3
-3
O O O O
27
-27
Answers
Which table shows a function that is increasing only over the interval (–2, 1), and nowhere else?
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 6, negative 3, negative 1, 1, 3, 6.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 2, negative 4, negative 1, 1, 4, 3.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 3, negative 5, negative 7, negative 6, 1, negative 1.
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries 5, 7, 1, 0, negative 4, negative 2.
Answers
Answer:
the answer is c
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
How do I solve this problem?
Answers
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Short answer: to solve this problem, follow directions.
a. Write the inequalitiesLet c and p represent numbers of cakes and pies produced daily. Then the constraints are ...
2c +3p ≤ 108 . . . . . . . . available hours of preparation time
1c +0.5p ≤ 20 . . . . . . . available hours of decoration time
p ≥ 0, c ≥ 0 . . . . . . . . . negative numbers of cakes or pies cannot be produced
__
b. Sketch the feasible regionIt works well to let a graphing calculator do this.
The feasible region is the doubly-shaded area with vertices ...
(0, 0), (0, 36), (3, 34), (20, 0)
__
c. Write the profit functionProfit is $25 per cake and $12 per pie, so is ...
p = 25c +12p
__
d. Determine maximum profitThe attached table shows the profit for the various mixes of cakes and pies in the feasible region. The most profit is had by production of cakes only.
The maximum profit is $500 per day for production of 20 cakes.
_____
Additional comment
We have used x for cakes and y for pies in the attachment, because those are variables that the Desmos calculator prefers.
As is sometimes the case, the production point giving maximum profit leaves one of the resources (preparation time) only partially utilized.
Use Pythagoras to find the height and hence, the area of the triangle
below. Give height to 1 decimal place and area to the nearest whole. Write
answer in format: h= A= *
20 mm
Val
Answers
Answer:
h=17.3 A=173
Step-by-step explanation:
Calculator
Answer:
height = 17.3 mm
area = 173 mm²
Step-by-step explanation:
all three sides are of the same length (20 mm).
so, the height actually splits the baseline in half
(2 × 10 mm) while hitting it at a 90 degree angle.
so, we use Pythagoras, where the full side opposite of this 90 degree angle is c (Hypotenuse), the height of the main triangle is one side, and half of the baseline is the other side.
c² = a² + b²
20² = 10² + height²
400 = 100 + height²
300 = height²
height = 17.3 mm
the area of the main triangle is baseline (20) times height divided by 2.
so,
At = 20×17.3/2 = 10×17.3 = 173 mm²
giving the funtions f(x)=2x-5 and g(x)=3x2=2 perform the indicated operation
Answers
Answer:3165
Step-by-step explanation:
Please help solve x and round all answers to the nearest tenth
Answers
First one is cos 32 = x/14
Also if ur really tired and just want the answers just download an app called Socratic and it will give u all the answers for the worksheet
Solve the mean for the data set. (4,11,25,1,17,34,11,30)
A. 12
B. 14.5
C. 16.6
D. 18.9
Answers
Answer:
The mean is C. 16.6
Step-by-step explanation:
the mean is the average, to find the average add all the numbers together and divide by the amount of numbers
4+11+25+1+17+34+11+30=133
133/8 = 16.6
if the radius of a sphere is7 cm find its volume
Answers
Answer:
1437.33 cm square
Step-by-step explanation:
Now we will use the frmula to et the volume of a sphere
volume of sphere is
4÷3pi r cube
where r is the radius of the sphere
a local community college has 860 students. Of these 860 students, 220 ride bicycles. Write the number of bike riders as a fraction of the number of students at the college in simplest form
Answers
Answer:
11/43
Step-by-step explanation:
A local community college has 860 students
Out of this 860 students, 220students ride bikes
Therefore the fraction of bike riders to the number of students can be calculated as follows
= 220/860
= 11/43
Hay 31 estudiantes en una clase. Ocho (8) estudiantes miden más de 6 pies de altura. Diecisiete (17) estudiantes miden 5-6 "a 6'-0" de altura. Seis (6) estudiantes miden menos de 5-2". ¿Cuál es la razón entre el número de estudiantes de menos de 5'-2" y el número de estudiantes de más de 6 'de altura?
Answers
Answer:
4/3
Step-by-step explanation:
If we are given the value of α. How can we find the value of β?
Answers
Answer:
β = 140 - α
we know that the "missing" angle is 40° since 40 + 140 = 180
we also know that the total sum of angles in a triangle is 180
so β = 180 - 40 - α
or β = 140 - α
Step-by-step explanation:
What is the monetary amount of 31 quarters, 13 dimes, 5 nickels and 3 pennies?
Answers
Answer:
$9.33
Step-by-step explanation:
quarter = 25 cents
dime = 10 cents
nickel = 5 cents
penny = 1 cent
31 (0.25) = 7.75
13 (0.10) = `1.30
5 (0.05) = 0.25
3(0.01) = 0.03
7.75 + 1.30 + 0.25 + 0.03 = 9.33
Answer:
$9.33 or 933 cents
Step-by-step explanation:
Concepts:
Coins are a form of currency. They're tiny, flat, and made of metal. There are various types of coins worldwide, but the main ones in the USA are quarters, dimes, nickels, and pennies. To write the value of a coin, you can use the format $0.00 or use cents/¢ at the end of it. One quarter is worth 25 cents, one dime is worth 10 cents, one nickel is worth 5 cents, and one penny is worth one cent.Expressions are mathematical sentences that have at least two terms with numbers/variables and at least one operationSolving:
Since we know the value of each coin, let's set up an expression:
q = 25, d = 10, n = 5, p = 1
(31 · q) + (13 · d) + (5 · n) + (3 · p)
Now, let's solve our expression!
1. Plug in the values of q, d, n, and p
(31 · 25) + (13 · 10) + (5 · 5) + (3 · 1)2. Simplify the terms in the parentheses
(31 · 25) + (13 · 10) + (5 · 5) + (3 · 1)(775) + (130) + (25) + (3)775 + 130 + 25 + 33. Add all the terms together
775 + 130 + 25 + 3905 + 25 + 3930 + 3933Now, we know the the monetary amount of 31 quarters, 13 dimes, 5 nickels and 3 pennies is 933 cents. However, we can also write it in decimal form by moving the decimal point to the left 2 times from the last digit of 933, 3: 933.0 -> 93.30 -> 9.330, and 9.330 = 9.33. Therefore, the answer is 933 cents or $9.33.
One of the legs of a right triangle measures 9 cm and the other leg measures 2 cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answers
Answer:
Approximately 9.2
Step-by-step explanation:
For right triangle, if you know 2 sides, you can find the third using pythagorean theorem, a^2 + b^2 = c^2. 'a' and 'b' are the lengths of the legs, while 'c' is the hypotenuse. You can plug in what you know into this formula:
9^2 + 2^2 = c^2
81+4 = c^2
c = √85, or approximately 9.2
Point B is the image of point A when point A is rotated about the origin. What is known about point A and B?
5
A
B
-5
o
5 x
का
O Point B is the result of a 180° rotation.
O Point A and B have the same x-coordinate.
Answers
Answer:
the fourth option (A and B are the same distance from the origin)
Step-by-step explanation:
since B is the result of a rotation of A around the origin, they are both on the same circle (center point is the origin). so, they have both the same distance (the radius of the circle) from the center of the circle, which is the origin.
the third option is tempting, as the rotation was 90 degrees, but it was clockwise !
What is 2f+4f + 2-3 evaluated at f= 3?
|
Answers
Answer:
17
Step-by-step explanation:
2f + 4f + 2 - 3 when f = 3
1) first we multiply 3 wherever f is
2 x 3 + 4 x 3 + 2 - 3 (solve)
6 + 12 + 2 - 3
18 + 2 - 3
20 - 3
17
Answer:
6+12+2-3=17
Step-by-step explanation:
evaluate expression: evaluate each expression when a = "-2" b=4 and c=-10
2a+b
ac-b
a+b/a
8a+5b
-4a-b
3c/-5
Answers
Answer:
2a+b=0
ac-b=16
a+b/a=-4
8a+5b=-4
-4a-b =4
3c/-5=6
8.
The table shows the estimated number of deer living in a forest over a five-year period. Are the data best represented by a linear, exponential, or quadratic model? Write an equation to model the data.
A. quadratic; y = 0.79x2 + 98
B. linear; y = 0.79x + 98
C. quadratic; y = 98x2 + 0.79
D. exponential; y = 98 • 0.79x
Answers
Answer:
D. exponential; y = 98 • 0.79x
Step-by-step explanation:
Answer:
Option D is correct.
Exponential model are the data best represented.
Equation:
Step-by-step explanation:
An exponential function is in the form of .....[1] where a is the initial value and b≠0 , b > 1.
Consider any two points from the table;
(0, 98) and ( 1, 77)
Then substitute these in [1];
For (0, 98)
x = 0 and y = 98 substitute in [1] we get;
98 = a
Similarly, For (1, 77)
we have;
77 = ab
Substitute the value of a =98 we get;
Divide both sides by 98 we get;
⇒ b = 0.79
We get an equation;
Therefore, the data represent here is, Exponential function.
also, an equation to model the data is;
...............................................................................................................................................
All the functions grow with x except B that decreases when x grows. That i your function. Also check that when you divide the population of two consecutive years, the ratio remains 0.79 approx
The solution is D
...............................................................................................................................................
Exponential would be the correct answer I believe...
...............................................................................................................................................
For a better understanding of the explanation provided here please find the attachment.
The solution will employ the use of the trial and error method and basic math.
As can be see from the given data, the deer population keeps on falling from the year zero. Thus, we can safely conclude that the quadratic and the linear models will not represent the situation at all.
We are left with the exponential model and since we have in it we can see that the deer population will fall as the years pass.
We have checked it in the table that has been provided and we have concluded that the data is best represented by the exponential model because when the exponential formula is applied it is almost equal to the actual number of deers.
Please check the attached table for a better understanding.
Help me! thank you so much
Answers
Answer:
Step-by-step explanation:
[tex]\frac{sinxcos^3x-cos xsin^3x}{cos^42x-sin^42x} \\=\frac{sin x cos x(cos^2x-sin ^2 x)}{(cis^2 2x+sin^2 2x)(cos^2 2x-sin ^22x)} \\=\frac{2sin x cos x cos 2x}{2(1)(cos 4x)} \\=\frac{sin 2x cos 2x}{2 cos 4x} \\=\frac{2 sin 2x cos 2x}{4 cos 4x} \\=\frac{sin 4x}{4 cos 4x} \\=\frac{1}{4} tan 4x[/tex]
helppppppppppppppppppppppppppppppp
Answers
find x you know
|8-x|=x^2+x
Answers
Write an expression for the area of the square below.
4x + 2
A. 8x2 + 16x + 4
B. 16x2 + 16x + 4
C. 8x + 4
D. 16x2 + 6x + 4
Help
Answers
Area = Side^2
Area =( 4x + 2 )^2
Area = (4x)^2 + 2(4x)(2) + (2)^2
Area = 16x^2 + 16x + 4
Thus the correct answer is option B .
Chukwu, Abdul and kunle are to share $142, such that Abdul gets $11.00 less than Chukwu and $7.00 more than Kunle. How much is Chukwu's share?
Answers
Answer:
Chukwu's share is of $57.
Step-by-step explanation:
This question is solved by a system of equations.
I am going to say that:
Chukwu's share is x.
Abdul's share is y.
Kunle's share is z.
Chukwu, Abdul and kunle are to share $142
This means that [tex]x + y + z = 142[/tex]
Abdul gets $11.00 less than Chukwu
This means that:
[tex]y = x - 11[/tex]
$7.00 more than Kunle.
This means that:
[tex]y = z + 7[/tex]
So
[tex]z = y - 7[/tex]
[tex]z = x - 11 - 7[/tex]
[tex]z = x - 18[/tex]
How much is Chukwu's share?
We want to find x, so:
[tex]x + y + z = 142[/tex]
[tex]x + x - 11 + x - 18 = 142[/tex]
[tex]3x - 29 = 142[/tex]
[tex]3x = 171[/tex]
[tex]x = \frac{171}{3}[/tex]
[tex]x = 57[/tex]
Chukwu's share is of $57.
What is the distance from the plane
Answers
Answer:
here's the answer to your question about
please help! i have no idea
Answers
Answer:
θ = 51.7
SOH-CAH-TOA
CAH: COS = ADJ/HYP cos(θ) = 19.4/29.3
θ = 48.5
93.2 + 48.5 + x = 180
x = 38.3
90 + 38.3 + θ = 180
θ = 51.7
Step-by-step explanation:
Guys please help me solve this its so stressful
Answers
Answer:
Given:- [tex]y=-5x^3+10x+20[/tex]
A parabola attain maximum height at the vertex: formula to find x-coordinate of vertex is, [tex]x=-\frac{b}{2a}[/tex]
plug in a=-5 and b=10
so, [tex]x=-\frac{10}{2(-5)} =-\frac{10}{-10} =1[/tex]
Now plug in x=1 to get maximum height,
[tex]y=-5(-1)^2+10(1)+20[/tex]
[tex]=-5+10+20[/tex]
[tex]=+25[/tex]
so, maximum heigh reached by the rocket was 25 yards
Rocket will hit the ground when y=0
[tex]0=-5x^2+10x+20[/tex]
[tex]0=-5(x^2-2x-4)[/tex]
[tex]\frac{0}{-5} =\frac{-5}{-5} (x^2-2x-4)[/tex]
So, [tex]x^2-2x-4=0[/tex]
quadratic formula is,
[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
plug in a=1, b=-2,and c=-4
[tex]x=-\frac{(-2)=-\sqrt{(-2)^2-4(1)(-4)} }{2(1)}[/tex]
[tex]=\frac{2=-\sqrt{4+16} }{2}[/tex]
[tex]=\frac{2+-\sqrt{20} }{2}[/tex]
[tex]=\frac{2+-2\sqrt{5} }{2}[/tex]
[tex]=1+-\sqrt{5}[/tex]
[tex]=1-\sqrt{5} ,1+\sqrt{5}[/tex]
[tex]=1-5.236,1+2.236[/tex]
[tex]=-1.236,3.236[/tex]
So, it takes 3.2 seconds to hit the ground.
OAmalOHopeO
10000-10000+100000-100000
Answers
Answer:
0
Step-by-step explanation:
A group has more than $120 to spend. The inequality 5x + 20 > 120 represents the cost to rent a hall for a conference, where x represents the number of hours the group can rent the hall. Which of the following is the solution for this situation?
Answers
Answer:
x>20
Step-by-step explanation:
You want to try and get the x alone so
5x + 20 > 120
-20 -20 Subtract 20 from each side
5x > 100
5x/5 > 100/5 Divide 5 from each side
x > 20
f(x) = 3+3x-1+3x^4 , g(x) = -x^3+x^2-x+2-x^4. tính f(x)+g(x) và f(x) -g(x)
Answers
Step-by-step explanation:
= 3+3x-1+3x^4 , g(x) = -x^3+x^2-x+2-x^4. tính f(x)+g(x) và f(x) -g(x)
