To which graph does the point (2, 4) belong?
y ≥ x + 3
y ≥ −x + 8
y ≥ 4x − 5
y ≥ −2x + 9
Answers
Answer:
Option (3) is correct.
(2,4) belongs to y ≥ 4x - 5
Step-by-step explanation:
Given : the point (2,4)
We have to find the equation of graph to which the point (2,4) belongs.
We will substitute the point in the each given equation and for which the point satisfies will contain the point.
For 1) y ≥ x + 3
Put x = 2 and y = 4
⇒ 4 ≥ 2 + 3
⇒ 4 ≥ 5 (false)
For 2) y ≥ -x + 8
Put x = 2 and y = 4
⇒ 4 ≥ -2 + 8
⇒ 4 ≥ 6 (false)
For 3) y ≥ 4x - 5
Put x = 2 and y = 4
⇒ 4 ≥ 4(2) - 5 = 8 - 5
⇒ 4 ≥ 3 (true)
For 4) y ≥ -2x + 9
Put x = 2 and y = 4
⇒ 4 ≥ -4 + 9
⇒ 4 ≥ 5 (false)
Since, the point (2,4) satisfies only inequality y ≥ 4x - 5.
Thus, (2,4) belongs to y ≥ 4x - 5
Related Questions
What type of equation would best model this data
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What is the solution set of the equation x^2 - 7x - 18 = 0
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x=9 or x=-2
Factoring this trinomial as the product of two binomials,
we have (x - 9)(x + 2) and set that equal to 0.
So we have (x - 9)(x + 2) = 0.
So either x - 9 = 0 or x + 2 = 0.
Solving for x in each equation, we find that our solution is {9, -2}.
a factor of the quadratic 6x2-11x-35
Answers
6x^2-11x-35
= (3x+5)(2x-7)
Answer: (3x+5)(2x-7)
6x^2-11x-35
x^2-11x-210
(x-21)(x+10)
(x-(21/6))(x+(10/6))
(x-(7/2))(x+(5/3))
(2x-7)(3x+5)
Final answer: (2x-7)(3x+5)
What is -4x - 5x <18 need help
Answers
Divide by both sides of the equations by [tex]-9 [/tex] like ↓
[tex] \frac{-9}{-9} \leq \frac{18}{-2} \\ \\ x \leq -2 \\ \\ Answer: x \leq -2 [/tex]
Good luck on your assignment and enjoy your day!
~MeIsKaitlyn :)
PLEASE HELP!!!!!
Which function has the following domain and range?
Domain: {−7,−3,0,4,12}
Range: {−5,1,2}
Select one:
a. {(−7,12),(−5,2)}
b. {(−7,−5),(−3,1),(0,2),(−4,5),(3,−1)}
c. {(4,1),(−3,−5),(12,2),(0,−5),(−7,1)}
d. {(−5,4),(2,12),(1,−3),(−5,−7),(1,0)}
Answers
b. {(−7,−5),(−3,1),(0,2),(−4,5),(3,−1)}
The function f(x) = –x2 + 60x – 116 models the monthly profit, in dollars, a shop makes for repairing windshields, where x is the number of windshields repaired, and f(x) is the amount of profit. Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points) Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)
Answers
Part A:
x = -b / 2 a = - 60 / ( - 2 ) = 30
Then we will charge it into the function:
f ( 30 ) = - 30² + 60 · 30 - 116 = - 900 +1,800 - 116 = 784
The vertex is ( 30, 784 ).
It means that the maximum profit is $784, when 30 windshields are repaired.
Part B:
x 1/2 = ( -60 +/- √(3600 - 464 )/ (- 2 ) = ( -60 +/- 56 ) / ( - 2 )
x 1 = 2, x 2 = 58
It means that a shop has to repair at least 2 windshields and not more than 58 windshields for making a profit.
Answer:
I believe Homer "the genius" math to be incorrect for Part A. (-30)^2+60(30)-116= 900+1800-116=2584; not 784 as he got -900 when squaring -30.
Step-by-step explanation:
help me please help me
Answers
A man wishes to construct a pultry house 12 feet long, in which to keep 20 hens. if each hen requires 4 square feet of floor space, how wide should he contruct the poultry house
Answers
Next, we use the formula for the area of a rectangle: A = LW, where L is length and W is width. Substituting all known values,
80 = 12W
W = 80/12
W = 6.67 feet
Thus, the man should construct a farm that is 6.67 feet wide.
Alive the equation 2 k+2= k+1
Answers
2k + 2 = k + 1
Subtract 1k from both sides.
k + 2 = 1
Subtract 2 from both sides.
k = -1
I hope this helps!
Justin wants to use 376 ft of fencing to fence off the greatest possible rectangular area for a garden what dimensions should he use what will be the area of the garden
Answers
the greatest rectangular area is actually a square
so 376/4 = 94 feet.
each side will be 94 feet
area of a square is 94^2
= 94 * 94 = 8836 square feet
The wildflowers at a national park have been decreasing in numbers. There were 300 wildflowers in the first year that the park started tracking them. Since then, there have been one fourth as many new flowers each year. Create the sigma notation showing the infinite growth of the wildflowers and find the sum, if possible.
I chose C, but can someone check for me? Thanks :)
Answers
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
Initial wildflowers in the first year = 1200
Every year, the number of wildflower is one fourth of the previous year.
So, it form a geometric series:
1200,300,75............
so, using sigma notation we can express the infinite growth of the wildflowers:
[tex]\sum ^{\infty}_{i=1}1200(\dfrac{1}{4})^{i-1}[/tex]
As we know that sum of infinite terms in case of geometric series is given by
[tex]S_{\infty}=\dfrac{a}{1-r}\\\\S_{\infty}=\dfrac{1200}{1-0.25}\\\\S_{\infty}=\dfrac{1200}{0.75}\\\\S_{\infty}=1600[/tex]
Therefore, there are 1600 wildflowers.
Hence, Third option is correct.
The human eye blinks about 6.25x10 to the 6th power times each year. A seal blinks about 1.01x10 to the 3rd power times per year. How many times do a human and a seal blink in one year?
Answers
A seal blinks 1,010 times a year.
The human eye blinks about [tex]\( 6.25 \times 10^6 \)[/tex] times each year, and a seal blinks about [tex]\( 1.01 \times 10^3 \)[/tex] times per year.
To find out how many times a human and a seal blink in one year, we simply take the given values for each. The question provides us with the number of times a human eye blinks in one year as [tex]\( 6.25 \times 10^6 \)[/tex]times. Similarly, it gives us the number of times a seal blinks in one year as [tex]\( 1.01 \times 10^3 \)[/tex] times.
Therefore, without the need for any additional calculations, we can state that in one year:
- A human blinks [tex]\( 6.25 \times 10^6 \)[/tex] times.
- A seal blinks [tex]\( 1.01 \times 10^3 \)[/tex] times.
These values are already given in the question and represent the total number of blinks for each species in a year. No further calculations are required to answer the question as it is asking for the number of blinks in one year, which is directly provided.
What is the right answer to this?
Answers
The distance between two buildings is 3 inches. This means we have to plug in 13 and multiply by 3.
13(3) = 39.
The distance between the two buildings is 39 miles.
Your answer is B.) 39 miles.
I hope this helps!
Please help!!! (-x/2)+(1/2x)=(-4/x)
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you can't solve that for x because when you multiply both sides by x, 0*x = 0 and [tex]0 \neq 4[/tex]
I think you made a mistake in your typing or something...unless the answer was no solution!
which equation represents the statement thirteen less then a number is forty two
Answers
x is the "variable", you're taking 13 away from that, and the answer is also given, 42.
Answer:
The equation which represents the statement thirteen less then a number is forty two is:
x-13=42
Step-by-step explanation:
Let x be any number
we are given that:
thirteen less then a number is forty two
i.e. x-13=42
Hence, the equation which represents the statement thirteen less then a number is forty two is:
x-13=42
fgh is a right triangle
Answers
Answer:
there is no picture
Step-by-step explanation:
The tangent of an angle is 3.4. what is the measure of the angle to the nearest tenth? 99.8° 73.6° 68.2° 52.9°
Answers
What is the slope of y-9=-2(x-8)
Answers
Let's write the problem: [tex]y-9=-2\left(x-8\right)[/tex]
We have to isolate for y.
[tex]y-9=-2\left(x-8\right)[/tex]
Apply the distributive property.
[tex]y-9=-2x+16[/tex]
Add 9 to both sides.
[tex]y-9+9=-2x+16+9[/tex]
[tex]y=-2x+25[/tex]
A line equation is on the form of [tex]y=mx+b[/tex]. The [tex]m[/tex] represents the slope. So, our answer would be:
[tex]m=-2[/tex]
Let me know if you have any questions regarding this problem!
Thanks!
-TetraFish
To find the slope, we must first simplify this equation, then turn it into the slope-intercept form :)
So, simplify.
y - 9 = -2x + 16
Remember : Slope-intercept form ~ y = mx+b
Where m = slope, and b = y-intercept
So, now we must add 9 to both sides.
y = -2x + 16 + 9
Simplify.
y = -2x + 25
Since (-2) is in the (m) spot, and m = slope, then -2 is our slope.
Slope = -2
~Hope I helped!~
Find the number of ways to listen to 4 different cds from a selection of 15 cds.
Answers
Thus, for this type of problem, the appropriate solution would be combination. The equation would be n!/r!(n-r)!. The factorial (!) is solved as follows: for example, 15! would be 15×14×13×12×11×10×9×8×7×6×5×4×3×2×1. Applying this process, we could now determine the answer.
15!/4!(15-4)! = 1,365 ways
Answer:
The First person who answered it was wrong! Its 32,760 I took the test lol!
Step-by-step explanation:
nPr = n!/(n-r)! <-- The equation used for this.
Quadrilateral $abcd$ is a parallelogram. if the measure of angle $a$ is 62 degrees and the measure of angle $adb$ is 75 degrees, what is the measure of angle $adc$, in degrees?
Answers
In the given parallelogram ABCD, angle $a$ is 62 degrees and angle $adb$ is 75 degrees. Angle $bd$ is calculated to be 105 degrees making angle $adc$ the supplementary to $bd$, and therefore also 75 degrees.
Explanation:In a parallelogram, opposite angles are equal and consecutive angles are supplementary (adding up to 180 degrees). In your given quadrilateral $abcd$, the measure of angle $a$ is 62 degrees and $a$ and $adb$ are consecutive angles. Therefore, knowing that angle $adb$ is 75 degrees, angle $bd$ should be the supplementary to $adb$, which is 180 - 75 = 105 degrees. Finally, since $adc$ is a straight line and $bd$ and $dc$ are parts of it, therefore angle $dc$ = 180 - angle $bd$ = 180 - 105 = 75 degrees. So, the measure of angle $adc$ is 75 degrees.
Learn more about Angles in a Parallelogram here:https://brainly.com/question/16578666
#SPJ12
Trey went to the batting cages to practice hitting. he rented a helmet for $4 and paid $0.75 for each group of 20 pitches. if he spent a total of $7 at the batting cages, how many groups of pitches did he pay for?
Answers
Write a compound inequality that represents the situation:
all real numbers at least -6 and at most 3
A) -6 < x ≤ 3
B) -6 ≤ x ≤ 3
C) -6 ≥ x ≥ 3
D) -6 < x < 3
Answers
The keywords at least and at most mean that it has to be less than or equal to/more than or equal to.
There is no value for x that can satisfy the conditions for C
-6 ≤ x ≤ 3
Letter B
Identify the y-intercept of the function, f(x) = 2x 2 + x - 4. (0,-4) (0,4) (-4,0) (4,0)
Answers
so answer is
y-intercept of the function (0,-4)
Answer:
The y-intercept of the function [tex]f(x)=2x^{2}+x-4[/tex] is [tex](0,-4)[/tex]
Step-by-step explanation:
The y-intercept of a function is the intersection between the graph of the function and the y-axis.This particular point will have a ''0'' in its x-coordinate (because all points over the y-axis have a ''0'' on its x-coordinate).Therefore, we can write the y-intercept as :
[tex]y-intercept=(0,a)[/tex]
We obtain the another coordinate ''a'' replacing ''x'' by a ''0'' in the function.
In this exercise, the function is:
[tex]f(x)=2x^{2}+x-4[/tex]
If x = 0 ⇒
[tex]f(0)=2(0)^{2}+0-4=-4=a[/tex]
We find that ''-4'' is the coordinate ''a'' that we were looking for.
We conclude that the point [tex](0,a)=(0,-4)[/tex]
And [tex](0,-4)[/tex] is the y-intercept of the function.
What is [tex] 3\sqrt{18} [/tex] + [tex] 2\sqrt{50} [/tex] simplified?
F.[tex] 19\sqrt{2} [/tex]
G.[tex] 39\sqrt{2} [/tex]
H.[tex] 77\sqrt{2} [/tex]
I. [tex] 90\sqrt{2} [/tex]
IF THERE IS WORK PLEASE SHOW THANKS:)
Answers
The table below represents the displacement of a horse from its barn as a function of time:
Time(hours) x.
0
1
2
3
4
Displacement from barn (feet) y
8
58
108
158
208
part a: what is the y-intercept of the function, and what does this tell you about the horse? part b: calculate the average rate of change of the function represented by the table between x=1 to x=3 hours, and tell what the average rate represents. part c: what would be the domain of the function of the horse continued to walk at this rate until it traveled 508 feet from the barn?
PLEASE HELP!! WILL RATE BRAINLIEST!!
Answers
A. The y-intercept (b) of a linear equation is obtained when x = 0. Therefore from the given table,
y - intercept = 8
Since at time zero the displacement is 8 ft, this means that the horse was already outside the barn initially.
B. The average rate of change of the function represents the slope of the linear equation (m). This can be calculated using the formula:
average rate of change = m = (y2 – y1) / (x2 – x1)
m = (158 – 58) / (3 – 1)
m = 50
C. Since we have determine the y-intercept and the slope, we can formulate the linear equation:
y = m x + b
y = 50 x + 8
The domain is the value of x. When y = 508, x is equivalent to
508 = 50 x + 8
x = 10 hrs
Find the function h(x) = f(x) ∘ g(x) if f(x) = x(2 - x) and g(x) = 3x.
h(x) = 0
h(x) = -32x
h(x) = 2(32x)
h(x) = 3x(2 - 3x)
Answers
Answer: h(x) = 3x(2 - 3x)
Step-by-step explanation:
Here the given functions are,
[tex]f(x) = x(2-x)[/tex]
[tex]g(x) = 3x[/tex]
[tex]h(x) = f(x) \circ g(x) = (f\circ g)(x) = f[g(x)][/tex]
[tex]= f( 3x )[/tex]
[tex]= (3x)[2-(3x)][/tex]
[tex]= 3x(2-3x)[/tex]
Hence,
[tex]h(x) = 3x(2-3x)[/tex]
⇒ Fourth option is correct.
What is the simplified form of the quantity of x plus 5, all over the quantity of 9 − the quantity of x plus 4, all over the quantity of x plus 6
Answers
(x+5)/[(9-x+4)/(x+6)]
=(x+5)/[(-x+5)/(x+6)]
=(x+5)*(x+6)/(-x+5)
=[(x+5)(x+6)]/[-x+5]
=(x^2+11x+30)/(-x+5)
the answer is:
(x^2+11x+30)/(-x+5)
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.
What is the factored form of 2x2 − 7x − 15? (2x + 3)(x − 5) (2x + 5)(x − 3) (2x − 7)(x + 8) (2x + 8)(x − 7)
Answers
(2x + 3)(x - 5) <==
is a factor of (2x+3)(x-5)
Find the polynomial f(x) that has the roots of -2, 5 of multiplicity 2. Explain how you would verify the zeros of f(x).
Answers
similarly, if 5 is a root of f, then (x-5) is a factor of f(x).
These roots have multiplicity 2 means that there are 2 of each,
so f(x) is written as (x+2)(x+2)(x-5)(x-5)
[tex]f(x)= (x+2)^{2} (x-5)^{2} [/tex]
[the most general form is f(x)= c*(x+2)^{2} (x-5)^{2}*P(x), where c is a constant and P(x) another polynomial]
To show that -2 and 5 are zeros of f, we must prove that f(-2)=0 and f(5)=0,
Using the function we wrote:
[tex]f(-2)= (-2+2)^{2} (-2-5)^{2}=0* (-7)^{2}=0[/tex]
similarly:
[tex]f(5)= (5+2)^{2} (5-5)^{2}=0 [/tex]