Which inequality is correctly represented by this graph
A) 3x-y>3
B) x-3y>=2
C) 3x-y<=3
D)x-3y>2
Answers
You should first solve each equation for y.
Eliminate answer choices with wrong slopes or y intercepts.
Then, because it is a dotted line, the answer will only be < or >.
And because the area is shaded to the right, it would mean that x > y.
So the answer is A) 3x - y > 3
Answer:
The correct option is A.
Step-by-step explanation:
If a line passing through two points then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
From the given graph it is clear that the related line passing through the points (0,-3) and (1,0). So, the equation of related line is
[tex]y-(-3)=\frac{0-(-3)}{1-0}(x-0)[/tex]
[tex]y+3=3x[/tex]
The (0,0) is not in the solution set. So check the equation be (0,0).
[tex]0+3=3(0)[/tex]
[tex]3=0[/tex]
This condition is false if the sign of inequality is < or ≤. Since the related line is a solid line, therefore the sign of inequality must be <.
The required inequality is
[tex]y+3<3x[/tex]
[tex]3<3x-y[/tex]
It is also written as
[tex]3x-y>3[/tex]
Therefore the correct option is A.
Related Questions
which point on the number line represents the product (5)(-2)(-1)
Answers
(-2)*(-1) gives +2 (a negative number multiplied for another negative gives a positive number).
2*5 = +10
We need to mutiply all the numbers.
5*-2 = -10
-10*-1 = 10
PLEASE HELP
Natalie borrowed $1,800 from her mother to purchase a pre-owned car. She agrees to repay this amount by paying her mother $45 per week. This situation can be modeled by the function Which inequality represents the domain for this function?
Answers
The domain of the function is x ≤ 40, representing the maximum number of weeks Natalie can take to repay the loan.
Explanation:The situation can be modeled by the function f(x) = 1800 - 45x, where x represents the number of weeks. The domain of this function represents the possible values for x. Since Natalie borrowed $1800 and agrees to repay $45 per week, the maximum number of weeks she can take to repay the loan is given by:
Therefore, the inequality that represents the domain of the function is x ≤ 40. This means that Natalie can take up to 40 weeks to repay the loan without exceeding the borrowed amount.
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A ramp leading to the freeway overpass is 200 feet long and rises 37 feet. what is the measure of the angle formed between the ramp and the freeway?
Answers
First, we find the angle made between the ramp and the rise (dashed line). Let's denote this is angle α. We make use trigonometric functions like cosine. Cosine of an angle is equal to the ratio of its adjacent side to the hypotenuse. In equation form:
cos α = 37/200, where α is the angle of inclination of the ramp
cos α = 0.185
α =cos^-1(0.185)
α = 79.34°
Next, let's denote the unknown angle as angle β. When you add the right angle and angle α, the sum would be angle β. Therefore,
β = 90° + 79.34°
β = 169.34°
A ramp leading to the freeway overpass is 200 feet long and rises 37 feet. The measure of the angle formed between the ramp and the freeway is
[tex]\mathbf{ \theta = sin^{-1} \Big ( \dfrac{37}{200} \Big)}[/tex]
From the information given:
The measure of the angle formed θ between the ramp and the freeway overpass can be determined by using the sine angle which is:
[tex]\mathbf{sin \theta = \dfrac{opposite}{hypotenuse}}[/tex]
[tex]\mathbf{sin \theta = \dfrac{37}{200}}[/tex]
[tex]\mathbf{ \theta = \dfrac{1}{sin} \Big( \dfrac{37}{200}\Big)}[/tex]
[tex]\mathbf{ \theta = sin ^{-1} \Big( \dfrac{37}{200}\Big)}[/tex]
Therefore, the measure of the angle formed between the ramp and the freeway is
[tex]\mathbf{ \theta = sin^{-1} \Big ( \dfrac{37}{200} \Big)}[/tex]
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Philip buys the pizza shown below: A circular pizza is shown. The center is labeled as point A and a point on the circumference is marked B. What does AB represent?
Answers
6x−3y=−6
solve for y
Answers
6x -3y = -6, solve for y.
Subtract -6x from both sides.
-3y = -6x - 6
Divide both sides by -3
y = 2x + 2
I hope this helps!
The solution to the equation is y = 2 + 2x.
We have,
To solve the equation 6x - 3y = -6 for y, we can isolate the term with y by performing the following steps:
Start with the equation: 6x - 3y = -6.
To isolate the term with y, subtract 6x from both sides of the equation:
6x - 3y - 6x = -6 - 6x.
This simplifies to: -3y = -6 - 6x.
Next, divide both sides of the equation by -3 to solve for y:
(-3y) / -3 = (-6 - 6x) / -3.
This simplifies to: y = 2 + 2x.
Therefore,
The solution to the equation is y = 2 + 2x.
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Given rectangle ABCD, segment AC is a diagonal, segment BE is perpendicular to segment AC at E. Segment AE = 8 inches and segment CE = 5 inches. What is the length of segment BE?
Answers
Let m(BAE)=m(ACD)=α
(BAE and ACD are congruent, since they are alternate interior angles, or Z angles)
Let m(ABE)=β.
So in triangle ABE, the measures of the angles are 90, α and β degrees.
This means that m(BCE)=β, since the 2 other angles of triangle BCE are 90 and α degrees.
thus, we have the similarity of triangles ABE and BCE,
so the following rations are equal:
[tex] \frac{AB}{BC} = \frac{BE}{CE} = \frac{AE}{BE} [/tex]
so
[tex] \frac{AB}{BC} = \frac{x}{5} = \frac{8}{x} [/tex]
so
[tex]\frac{x}{5} = \frac{8}{x}[/tex]
[tex] x^{2} =40[/tex]
[tex]x= \sqrt{40}= \sqrt{4*10}=2 \sqrt{10} [/tex] (inches)
Remark, we can also apply Euclid's theorem directly.
Part A: If (7 to the power of 2)x = 1, what is the value of x?
Part B: If (7to the power of 0)x = 1, what are the possible values of x?
Answers
49x = 1
x = 1/49
Part B
7^0 = 1
so we have
1x = 1
x = 1
Convert 350 US dollars to British pound sterling .use 1 US dollar = 0.62 British pound sterling
Answers
If Mercury's mass is 3 × 10^23 kilograms, and Saturn's mass is 6 × 10^26 kilograms, which statement is true?
Answers
Saturn has about 2,000 times more mass.
Answer:
Saturn has about 2,000 times more mass.
Alyssa is jogging near Central Park. She runs along 65th Street for about 0.19 miles, turns right and runs along Central Park West for about 0.28 miles. She then turns right again and runs along Broadway until she reaches her starting point. How long is her total run to the nearest hundredth of a mile? 0.68 miles 0.81 miles 1.15 miles 1.44 miles
Answers
The formula for this is: a^2 + b^2 = c^2
So let the first side or a be .19
and the second side be .28
and now we are looking for c which is the missing side
.19^2 + .28^2 = c^20.0361 + 0.784 = .1145
get the square root of .1145
√.1145 = it is approximately 0.34
get the total distance by adding three sides
= .34 + .19 + .28
= 0.81
The total distance covered by her is 0.81 miles.
Given thatAlyssa is jogging near Central Park.
She runs along 65th Street for about 0.19 miles, turns right, and runs along Central Park West for about 0.28 miles.
She then turns right again and runs along Broadway until she reaches her starting point.
We have to determine
How long is her total run to the nearest hundredth of a mile?
According to the question
She runs along 65th Street for about 0.19 miles, turns right, and runs along Central Park West for about 0.28 miles.
Alyssa's route can be considered a right triangle with legs of length 0.19 and 0.28 (hundredths).
The total distance run is determined by using the Pythagoras theorem.
What is the Pythagorean theorem?Pythagorean theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Therefore,
The distance run by her is,
[tex]\rm x^2 = (0.19)^2 +(0.28)^2\\\\ x^2=0.0361 + 0.784\\ \\ x^2 = .1145\\ \\ x= \sqrt{.1145} \\\\ x= 0.34[/tex]
Therefore,
The total distance covered by her is,
= .34 + .19 + .28
= 0.81 miles
Hence, the total distance covered by her is 0.81 miles.
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What does it mean for an equation to have no solution or infinitely many solutions?
PLEASE GIVE ME A DETAILED RESPONSE AS IM TAKING MODULE 7 ALGEBRA DBA TOMORROW AT 7PM
Answers
If an equation has infinitely many solutions, all equations of x will make the equation true. For example, x+1=1+x.
No-Solution implies an inconsistent equation, while infinitely many solutions indicate a condition that holds true for any value of variable.
When an equation has No-Solution, it means that there is no value of variable that satisfies equation. In other words, equation represents an inconsistent condition, and solution set is empty. For example, equation 2x + 5 = 2x + 7 has no solution because the variable x cancels out, leaving an inconsistency (5 ≠ 7),
When an equation has infinitely many solutions, it means that any value of variable will satisfy equation. The equation represents a condition that is always true, regardless of chosen value.
For example, the equation x + 5 = x + 5 has infinitely many solutions because any value of x will make the equation true (such as x = 1, x = 2, x = 3, and so on).
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What is the common difference of the following arithmetic sequence?
100, 102, 104, 106,…
Answers
The common difference in the arithmetic sequence 100, 102, 104, 106,... is 2.
Arithmetic Sequence: 100, 102, 104, 106,...
Common Difference: The common difference in an arithmetic sequence is the constant value by which each term is increased or decreased. In this sequence, the common difference is 2 because each term increases by 2.
Calculation: 102 - 100 = 2, 104 - 102 = 2, 106 - 104 = 2, so the common difference is 2.
Solve for x. A.x=7.5 B.x=16 C.x=17.5 D.x=27.5
Answers
Find the measure of an angle whose measure is 20° less than the measure of its supplement.
Answers
Measure = 20 less
Labelled as x + (x - 20) = 180
Solve.
x + (x - 20) = 180
2x = 200
/2 /2
x = 100
Angle 1: Angle 2:
x - 20 x
100 - 20 100
80
Therefore the angle is 80 degrees.
Proof: 80 + 100 = 180 (supplementary)
100 - 80 = 20 (80 is less than supplement (100)
Hope I helped :))))
The function f(x) = is reflected across the y-axis to create the function g(x). Which ordered pair is on g(x)?
Answers
Answer:
A
Step-by-step explanation:
No. Of roots in eq 8sec^x-6secx+1=0
Answers
[tex] 8\sec^2x-6\sec x+1=0\\ 8\sec^2x-2\sec x-4\sec x+1=0\\ 2\sec x(4\sec x-1)-1(4\sec x-1)=0\\ (2\sec x-1)(4\sec x-1)=0\\ 2\sec x-1=0\\ 2\sec x=1\\ \sec x=\dfrac{1}{2}\\ x\in\emptyset\\\\ 4\sec -1=0\\ 4\sec =1\\ \sec x =\dfrac{1}{4}\\ x\in\emptyset [/tex]
So, the number of solutions (real ones) is 0.
If y = f(x), and y = a f(x) is a vertical stretch or compression, a > 1 causes the graph to be stretched vertically by a factor of a.
Answers
A vertical stretch in the context of graphing functions occurs when the function is multiplied by a positive constant greater than 1, resulting in the graph being stretched vertically by that factor without affecting the y-intercept.
A vertical stretch occurs when we multiply the function by a positive constant greater than 1. For example, if we have y = a f(x) and a is greater than 1, this results in the graph being stretched vertically by a factor of a. This type of transformation doesn't affect the y-intercept since the behavior of the graph at x=0 remains unchanged. Multiplying the independent variable by a constant such as 1/2 would result in a horizontal stretching or compression, but this is different from the vertical stretching effect we are discussing here.
Additionally, suppose the vertical stretch factor is a natural number. In that case, we can think of the stretched function as being the sum of the original function added to itself repeatedly that number of times. This additive property also extends to the derivative, as the derivative of the vertically stretched function is the original derivative multiplied by the stretch factor. This is known as the vertical stretch property in the context of derivatives and calculus.
Help please.........,
Answers
y-6 = -4(x+1)
y-6 = -4x-4
add 6 to each side
y=-4x+2
A is the correct answer
I need the blue one done! please help!!
Answers
Examples: Night and Day, Black an White, Alive and Dead, Awake and Sleeping
Can i get branielst
What is the length of the hypotenuse in the triangle below ?
Answers
In 45-45-90 triangles hypotenuse = x√2 [x=leg]
If leg = 14cm, then hypotenuse = 14√2 cm.
2x – 4y = 12 3x – 6y = 21 solve
Answers
3x - 6y = 21..= x - 2y = 7
these are parallel lines with no solution
The East Bay Deli, makes 6.85 pounds of pasta salad each day. West Bay Deli makes four times that amount each day. How many combined pounds of pasta salad is made per week between the two delis? Find a fourth of their combined weekly production of pasta salad.
Answers
East Bay Deli: 6.85 lb
West Bay Deli: 4*6.85 = 27.4 lb
Total amount made per day is
6.85 + 27.4 = 34.25 lb
Total amount made per week is
34.25*7 = 239.75 lb
Answer: 239.8 lb (nearest tenth)
A fourth of the combined weekly production is
(1/4)*239.75 = 59.9375 lb
Answer: 59.9 lb (nearest tenth)
If the tire is flat, then I will have to change it. Using the statement above, first state your variables in terms of p and q and which variable represents which statement. Then write this statement in symbolic form.
Answers
Correct Answer:
p: The tire is flat. q: I will have to change it. p -> q
triangle pqr is a right triangle. If PQ = 8, what is PR?
Answers
The 30-60-90 triangle is known as a special right triangle because its angles have a unique ratio of 1:2:3. The length of the side PR in ΔPQR is 4√3 units.
What is the 30-60-90 right triangle?The 30-60-90 triangle is known as a special right triangle because its angles have a unique ratio of 1:2:3. Furthermore, the hypotenuse is twice the length of the shorter leg, and the larger leg is √3 times the length of the shorter leg.
For the given right-angled triangle, we can use the 30-60-90 rule. The 30-60-90 triangle is known as a special right triangle because its angles have a unique ratio of 1:2:3. Furthermore, the hypotenuse is twice the length of the shorter leg, and the larger leg is √3 times the length of the shorter leg.
Therefore, we can write,
PQ = 2(RQ)
8 = 2(RQ)
RQ = 4
PR = (RQ)√3
PR = 4√3
Hence, the length of the side PR in ΔPQR is 4√3 units.
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Two number cubes are rolled. If all numbers are equally likely, what is the probability that the sum is 8?
6/36 ≈ 17%
4/36 ≈ 11%
8/36 ≈ 22%
5/36 ≈ 14%
Answers
if ask you about probability of sum of two cubes from 8 to 12 ,probability is (13-n)/36
"Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one".
For the given situation,
The sample space for rolling two cubes,
s = { (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6) }
⇒[tex]n(s)=36[/tex]
The event is getting the sum 8,
[tex]e=[/tex] { [tex](2,6), (3,5), (4,4), (5,3), (6,2)[/tex] }
⇒[tex]n(e)=5[/tex]
The formula to find the probability of event, [tex]P(e)=\frac{n(e)}{n(s)}[/tex]
⇒[tex]P(e)=\frac{5}{6}[/tex]
⇒[tex]P(e)=13.8\%[/tex] ≈ [tex]14\%[/tex]
Hence we can conclude that the probability that the sum is 8 is 5/36 ≈ 14%.
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In the figure below, m ROP = 125°.
Find the measure of each arc. For each arc, write two or more complete sentences explaining which theorem or postulate you used to find your answer. Include your equations and calculations in your final answer.
Answers
Answer: Hello!
In the figure, Q and P are on opposite ends of the circle, and the same is for R and S, which means that the line that connects Q and P, or R and S, divides the circle in two equal halves. From this, we know that the angle between QoP is 180°, and the same for the angle RoS = 180°.
We also know that the angle RoP = 125°, then the angle between Q and R is the same as the angle between Q and P minus the angle between R and P.
this is : QoR = QoP - RoP = 180° - 125° = 55°
then QoR and RoP are supplementary angles, wich means that the addition adds up to 180°.
And is easy to see that the angles SoQ and PoS are reflexes of RoP and QoR respectively, then:
SoQ = 125° and PoS = 55°, where this angles also are supplementary.
Cloverville has a population of 25,000 people and is increasing at a rate of 0.2%. The population in 3 years will be
Approximately 25,500 people
Approximately 24,8500 people
Approximately 25,150 people
Answers
A=pe^rt
A ?
P 25000
E constant
R 0.002
T 3years
A=25,000×e^(0.002×3)
A=25,150 ...Answer
The Pyramid of Giza is one of the largest pyramid structures still standing in Egypt. It is a right pyramid with a square base, a base length of 230 m, and height of 150 m.
The area of the base is __________
The volume is _________
Answers
The square base has a base length of a = 230 m.
The area of the base is
A = a*a = 230*230 = 52,900 m²
The height is h = 150 m.
The volume is
V = (1/3)*A*h
= (1/3)*52900*150
= 2,645,000 m³
Answer:
The area of the base is 52,900 m²
The volume is 2,645,000 m³
Answer:
The area of the base is 52,900 m²
The volume is 2,645,000 m³
Step-by-step explanation:
N is between m and p. If MN=3x, NP=x, and MP= 6x-6, find the numerical value of MN
Answers
3x + x = 6x - 6
4x = 6x - 6
4x - 6x = -6
-2x = - 6
x = -6/-2
x = 3
MN = 3x = 3(3) = 9 <==
Answer:
3
Step-by-step explanation:
.
.
.
The ordered pair(1,0) is a solution to the inequality y true or false?