Describe the graph of the function.y = |x – 4| – 7
Answers
(x-4)=0 ===> x=4,
so that now you have to plot 2 functions!
For x<= 4: what's inside the absolute value (x-4) is negative, right?, then let's make it +, by multiplying by -1:
|x-4| = -(x-4)=4-x
Then:
for x<=4, y = -x+4-7 = -x-3
for x=>4, (x-4) is positive, so no changes:
y= x-4-7 = x-11,
Now plot both lines. Pick up some x that are 4 or less, for y = -x-3, and some points that are 4 or greater, for y=x-11
In fact, only two points are necessary to draw a line, right? So if you want to go full speed, choose:
x=4 and x= 3 for y=-x-3
And just x=5 for y=x-11
The reason is that the absolute value is continuous, so x=4 works for both:
x=4===> y=-4-3 = -7
x==4 ====> y = 4-11=-7!
abs() usually have a cusp int he point where it is =0
Hope it helps, despite being this long!
We are given a function as:
[tex]y=|x-4|-7[/tex]
We know that this function is a transformation of the parent function y=|x| i.e. the modulus function.
The rule that holds in this transformation is:
It is a translation of the parent function 4 units to the right and 7 units down.
Also, the graph of the function is attached to the answer.
Related Questions
Help^^^^^^^^^^^^^^^^^
Answers
----------------------------------------------
Work Shown:
I'm assuming the problem is -4*(1-x) <= -12+2x where the first term is -4 and not 4
-4*(1-x) <= -12+2x
-4*(1-x) <= -12+2x
-4+4x <= -12+2x
-4+4x-2x <= -12+2x-2x
-4+2x <= -12
-4+2x+4 <= -12+4
2x <= -8
2x/2 <= -8/2
x <= -4
To graph x <= -4, you plot a closed circle at -4. Then you shade to the left of the closed circle. This matches with choice D
Determine the growth factor corresponding to 25% increase.
a.
1.75
c.
25
b.
1.25
d.
0.25
Answers
growth factor is 1 + 0.25 = 1.25
Answer:
Step-by-step explanation:
Alright, lets get started.
The given increase is 25 %.
Which means in terms : [tex]25*\frac{1}{100}[/tex]
That will be equal to : [tex]0.25[/tex]
So, the growth of 0.25 means the complete term will be :
[tex]1+0.25=1.25[/tex]
Hence the growth factor of 25 % will be equal to 1.25 : Answer
Hope it will help :)
How do you solve
8(x-1)-2x=-(x+50)
Answers
8x-2x-x= 50+8
5x=58
x=58/5
= 11.6
The solution to the equation 8(x-1) - 2x = -(x + 50) is x = -6.
To solve the equation 8(x-1) - 2x = -(x + 50).
First, distribute the 8 to the terms inside the parentheses:
8x - 8 - 2x = -(x + 50)
Simplify the left side of the equation:
6x - 8 = -(x + 50)
Distribute the negative sign to the terms inside the parentheses:
6x - 8 = -x - 50
Isolate the x terms on one side and the constant terms on the other side:
6x + x = -50 + 8
Combine like terms:
7x = -42
Divide both sides of the equation by 7:
7x / 7 = -42 / 7
x = -6
Therefore, the solution to the equation 8(x-1) - 2x = -(x + 50) is x = -6.
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A dress is priced at $21.42. The store is having a 30%-off sale. What was the original price of the dress?
Answers
.7x = $21.42
Divide both sides by .7
x = $30.60
A pet store has k tanks of fish. Each tank has 30 fish. Using k, write an expression for the total number of fish in the store.
Answers
Total number of fish=[number of tanks]*[number of fish in each tank]
f(k)=k*30
f(k)=30k
the answer is f(k)=30k
find the area of a regular nonagon with a side length of 7 and an apothem of 5
Answers
If side length = 7 then apothem = 9.6162
You make $30,000.00 and your spouse makes $35,000.00. using the 20% range, calculate the least and greatest amount you spend on housing
Answers
30,000 x 0.20 = $6,000 least amount
30,000 +35,000 = 65,000
65000 x 0.20 = $13,000 greatest amount
If sam walks 650 meters in x minutes then write an algebraic expression which represents the number of minutes it will take sam to walk 1500 meters at the same average rate.
Answers
Find the radius of a circle with an x-intercept of -2 if the circle’s center is (2,3) on a coordinate plane.
5
25
16
9
Answers
let : A(2;3) and : P(-2; 0)
the radius of a circle is : AP = √((2+2)² +(3-0)²)=√25 = 5
Radius of the circle is option (1) 5 units
What is radius?A radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length.
What is circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center
Center of the circle is (2,3) on a coordinate plane,
Radius of the circle with an x intercept of -2
There for the point is (-2,0)
Distance between the (2,3) and (-2,0) = Radius of the circle
Distance between (2,3) and (-2,0)
D= [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
Substitute the values
[tex]D=\sqrt{(-2-2)^{2}+(0-3)^{2} }\\D=\sqrt{16+9} \\D=\sqrt{25}\\ D=5[/tex]
Hence, the radius of the circle is option (1) 5 units
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A line has no width and extends infinitely far in _____ directions.
Answers
What are the rigid transformations that will map
△ABC to △DEF?
Translate vertex A to vertex D, and then reflect
△ABC across the line containing AC.
Translate vertex B to vertex D, and then rotate
△ABC around point B to align the sides and angles.
Translate vertex B to vertex D, and then reflect
△ABC across the line containing AC.
Translate vertex A to vertex D, and then rotate
△ABC around point A to align the sides and angles.
Answers
Answer:
The answer above is correct! The answer is option D.
Step-by-step explanation:
Hope this helped clarify :D
Translating vertex A to vertex D, and then rotate △ABC around
point A to align the sides and angles will bring about a rigid
transformation.
What is Rigid transformation?This is the transformation which preserves the Euclidean
distance between every pair of points. This could be as a result
of the following:
RotationReflectionTranslation etc.Option D when done will preserve the distance between the
points when vertex A is translated to vertex D as they contain
the same angle with other sides and angles being made to
align.
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Please Help ASAP!
Will award brainliest!
Answers
ratio of AB to DE = 30/6 = 5
do 24/6 = 4
x = 4
The Cool Company determines that the supply function for its basic air conditioning unit is S(p) = 40 + 0.008p^3 and that its demand function is D(p) = 200 - 0.16p^2, where p is the price. Determine the price for which the supply equals the demand.
Answers
S(p) = D(p)
40 + 0.008p³ = 200 - 0.16p²
We transpose all the terms to left side of the equation.
0.008p³ + 0.16p² - 160 = 0
Then, we factor out the given function. This can either be done through long division or synthetic division. Divide the equation by 0.008.
p³ + 20p² - 20000 = 0
One of the roots of the equation is 21.86. This is the only real root of the equation and the rest are imaginary.
Hence, the price should be approximately $21.86 before the demand and supply is breakeven.
ssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssssss. (I needed to fill up this space somehow).
Answers
#3 In the figure below, the measure of Arc AC is 65 degree and if angle abc is equal to 78 degree.
True or false
Answers
False, The measure of Arc AC is not 65 degree if angle ABC is equal to 78 degree.
What is Circle?
The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The statement is,
The measure of Arc AC is 65 degree if angle ABC is equal to 78 degree.
Now,
Since, Sum of Measure of arc AC and angle ABC is equal to 360 degree.
So, In angle ABC is 78 degree.
Then, Measure of arc AC = 360 - 78
= 282 degree.
Thus, The measure of Arc AC is not 65 degree if angle ABC is equal to 78 degree.
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How much would $120 invested at 86% interest compounded monthly to be worth after 21 years round to the nearest cent
Answers
A=p (1+r/k)^kt
A future value?
P present value 120
R interest rate 0.86
K compounded monthly 12
T time 21 year
A=120×(1+0.86÷12)^(12×21)
A=4,510,568,953.1372
which of the following functions are graphed below
Answers
Answer:
The equation of given graph is f(x)=[x]-6
C is correct
Step-by-step explanation:
We are given a graph and to find the equation of graph.
It is a graph of greatest integer function or floor function.
Parent function of greatest integer function:
[tex]f(x)=[x][/tex]
For x = 0 to x= 1 , f(x)=0
For x =1 to x=2 , f(x)=1
We are given a function,
For x = 0 to x= 1 , f(x)=-6
For x = 1 to x= 2, f(x) = -5
If we shift 6 unit down the parent function. We will get original function.
[tex]f(x)=[x]-6[/tex]
Hence, The equation of given graph is f(x)=[x]-6
(02.02 LC)
Figure ABCD is rotated by 180 degrees about the origin in the counterclockwise direction to obtain figure A′B′C′D′:
Which statement best compares the lengths of the sides of the two figures?
Length of AB = Length of C′D′
Length of CD = Length of A′B
′ Length of CD = Length of B′C′
Length of AB = Length of A′B′
Answers
Length AB=Length A'B'
The graph shows the distance, y, that a car traveled in x hours:
A graph is shown with x axis title as Time in hours. The title on the y axis is Distance Traveled in miles. The values on the x axis are from 0 to 5 in increments of 1 for each grid line. The values on the y axis are from 0 to175 in increments of 35 for each grid line. A line is shown connecting ordered pairs 1, 35 and 2, 70 and 3, 105 and 4, 140. The title of the graph is Rate of Travel.
What is the rate of change for the relationship represented in the graph?
fraction 1 over 35
fraction 1 over 34
34
35
Answers
Answer: 35
Step-by-step explanation:
The rate of change of a graph is given by :-
[tex]k=\dfrac{\text{Change in y avlues}}{\text{Change in x values}}[/tex]
For points : (1, 35) and (2, 70)
The rate of change for the relationship in the graph is given by :-
[tex]k=\dfrac{70-35}{2-1}=35[/tex]
Hence, the rate of change for the relationship represented in the graph = 35.
The rate of change of the relationship shown in the graph is 35 miles per hour.
Linear equationLinear equation is in the form:
y = mx + b
where y, x are variables, m is the rate of change and b is the y intercept.
Let y represent the elevator height after x seconds.
From the graph using points (0, 0) and (4, 140):
m = (140 - 0)/(4 - 0) = 35
The rate of change of the relationship shown in the graph is 35 miles per hour.
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The area of a triangle is 92 cm2. the base of the triangle is 8 cm. what is the height of the triangle?
a. 11.5 cm
b. 23 cm
c. 4 cm
d. 46 cm
Answers
Answer: b. 23 cm
Step-by-step explanation:
We know that area of a triangle is given by :-
[tex]\text{Area}=\dfrac{1}{2}bh[/tex], where b is the base of triangle and h is the height of the triangle.
Given : The area of a triangle is [tex]92\ cm^2[/tex]
The base of the triangle = 8 cm
Let h be the height of the triangle , then we have
[tex]92=\dfrac{1}{2}(8)h\\\\\Rightarrow\ h=\dfrac{92}{4}\\\\\Rightarrow\ h = 23[/tex]
Hence, the height of the triangle = 23 cm
If f(x)=4^x , which statements are true of g(x)? Check all that apply
Answers
Check the 4th box; the graph is translated down 1 unit because the y goes down by 1.
The true statements about functions f(x) and g(x) are:
b. g(x) = 4^x - 1d.The function f(x) is translated 1 units down to get the function g(x) How to determine the true statements?The function f(x) is given as:
f(x) = 4^x
From the table of values, we can see that the function g(x) is 1 less than the function f(x).
This means that:
g(x) = f(x) - 1
This can be rewritten as:
g(x) = 4^x - 1
In transformation, it means that the function f(x) is translated 1 units down to get the function g(x)
Hence, the true statements are: b and d
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Find the midpoint of A and D. Simplify completely.
option 5 is none of these.
Answers
A = (1,3)
D= (5,0)
midpoint = (x1+x2)/2 , (y1+y2)/2
5+1=6/2 =3
3+0=3/2 = 3/2
(3,3/2)
The following table shows information collected from a survey of students regarding their grade level and transportation they use to arrive at school. What is the probability that a randomly selected eighth grader takes the bus?
Answers
---------------------------------------------------------------------
---------------------------------------------------------------------
Work Shown:
A = student selected is an eighth grader
B = chosen student takes bus
P(A) = probability of selecting eighth grader
P(A and B) = probability of selecting eighth grader AND student who takes bus
P(A and B) = probability of selecting eighth grader who takes the bus
P(B|A) = probability of selecting someone who takes the bus given they are an eighth grader
P(B|A) = [P(A and B)]/[P(A)]
P(B|A) = 0.11/0.44
P(B|A) = 0.25
Hiram raises earthworms. In a square of compost 4 ft by 4 ft, he can have 1000 earthworms. How many earthworms can he have if his square of compost has a side length that is 8 times longer?
A. 8000
B. 64,000
C. 256,000
D. 32,000
Answers
area=length times widtha
rea=4 times 4=16 square feet
so every 16 square feet is 1000 earthworms
so ratio of worms to area is 1000:16
if each side length is 8 then
8 times 8=64 area
but how many worms?
1000:16=?:64
1000/16=?/64
times both sides by 64
64000/16=?
4000=?
wat, not listed? why
if we assume it's a cube then
voluem is 4^3 or 64
1000:64 is the ratio
if 8ft then 8^3=512
so
1000:64=?:512
1000/64=?/512
512000/64=?
8000=?
I guess it was a cube then
A would be the answer
Solve the equation by extracting the square roots. when a solution is irrational, list both the exact solution and its approximation rounded to two decimal places.
Answers
In this case,
x^2 - 196 = 0
x^2 = 196
we take the square root of both sides in order to extract x
square root x^2 = square root 196
x = +- 14
there are two roots in this function which are positive and negative numbers.
square of a positive number leads to a positive number while the square of a negative number also yields to a positive number.
Find the x- and y-components of the vector d⃗ = (9.0 km , 35 ∘ left of +y-axis).
Answers
Final answer:
The x- and y-components of the given vector are calculated using trigonometric functions, resulting in -5.16 km along the x-axis and 7.37 km along the y-axis, considering the direction of the vector relative to the axes.
Explanation:
The question asks to find the x- and y-components of the vector d⟷ = (9.0 km, 35° left of +y-axis). To solve this, we use trigonometric functions, specifically sine and cosine, because the vector makes an angle with the axis.
Given the vector makes a 35° angle to the left of the +y-axis, this effectively means it is 35° above the -x-axis (or equivalently, 55° from the +x-axis in the second quadrant). We can calculate the components as follows:
y-component: Dy = D*cos(35°) = 9.0 km * cos(35°) = 9.0 km * 0.8191 = 7.37 kmx-component: Dx = -D*sin(35°) = -9.0 km * sin(35°) = -9.0 km * 0.5736 = -5.16 km (negative because it's in the direction of the -x axis)The negative sign in the x-component indicates that the direction is towards the negative x-axis. Therefore, the x- and y-components of the vector are -5.16 km and 7.37 km, respectively.
1. [tex]\(\mathf{d}\): \(d_x = -3.8 \text{ km}, d_y = 8.2 \text{ km}\)[/tex]
2. [tex]\(\mathf{v}\): \(v_x = -4.0 \text{ cm/s}, v_y = 0\)[/tex]
3. [tex]\(\mathf{a}\): \(a_x = 10.3 \text{ m/s}^2, a_y = -14.7 \text{ m/s}^2\)[/tex]
To find the [tex]\( x \)[/tex]- and [tex]\( y \)[/tex]-components of vectors given in terms of magnitude and direction, we need to decompose the vectors using trigonometric functions. Let's go through each problem step by step.
1. Find the [tex]\( x \)[/tex]- and [tex]\( y \)[/tex]-components of the vector [tex]\( \mathf{d} = (9.0 \text{ km}, 25^\circ \text{ left of } +\mathbf{y}\text{-axis}) \)[/tex].
First, understand that "25° left of +[tex]\( y \)[/tex]-axis" means the vector is rotated 25° counterclockwise from the [tex]\( y \)[/tex]-axis.
Decomposition:
- Magnitude, [tex]\( d = 9.0 \text{ km} \)[/tex]
- Angle from the [tex]\( y \)-axis, \( \theta = 25^\circ \)[/tex]
To find the components:
- [tex]\( d_x = d \sin(\theta) \)[/tex]
- [tex]\( d_y = d \cos(\theta) \)[/tex]
However, since the angle is counterclockwise from the [tex]\( y \)-axis[/tex] and to the left, the [tex]\( x \)[/tex]-component is negative.
Therefore:
- [tex]\( d_x = -9.0 \sin(25^\circ) \)[/tex]
- [tex]\( d_y = 9.0 \cos(25^\circ) \)[/tex]
Calculating these:
- [tex]\( d_x \approx -9.0 \times 0.4226 \approx -3.8 \text{ km} \)[/tex]
- [tex]\( d_y \approx 9.0 \times 0.9063 \approx 8.2 \text{ km} \)[/tex]
So, the components are:
- [tex]\( d_x \approx -3.8 \text{ km} \)[/tex]
- [tex]\( d_y \approx 8.2 \text{ km} \)[/tex]
2. Find the [tex]\( x \)[/tex]- and [tex]\( y \)[/tex]-components of the vector [tex]\( \mathf{v} = (4.0 \text{ cm/s}, -x \text{-direction}) \).[/tex]
Since the vector is given in the [tex]\(-x\)[/tex]-direction, it means the entire magnitude is in the [tex]\( x \)[/tex]-direction and negative.
Decomposition:
- Magnitude, [tex]\( v = 4.0 \text{ cm/s} \)[/tex]
- Direction: [tex]\(-x\)[/tex]
Therefore:
- [tex]\( v_x = -4.0 \text{ cm/s} \)[/tex]
- [tex]\( v_y = 0 \text{ cm/s} \)[/tex]
So, the components are:
- [tex]\( v_x = -4.0 \text{ cm/s} \)[/tex]
- [tex]\( v_y = 0 \text{ cm/s} \)[/tex]
3. Find the [tex]\( x \)[/tex]- and [tex]\( y \)[/tex]-components of the vector [tex]\( \mathbf{a} = (18 \text{ m/s}^2, 35^\circ \text{ left of } -y \text{-axis}) \)[/tex].
"35° left of -[tex]\( y \)[/tex]-axis" means the vector is rotated 35° counterclockwise from the negative [tex]\( y \)[/tex]-axis.
Decomposition:
- Magnitude, [tex]\( a = 18 \text{ m/s}^2 \)[/tex]
- Angle from the [tex]\(-y \)[/tex]-axis, [tex]\( \theta = 35^\circ \)[/tex]
To find the components:
- [tex]\( a_x = a \sin(\theta) \)[/tex]
- [tex]\( a_y = -a \cos(\theta) \)[/tex]
However, since the angle is counterclockwise from the [tex]\(-y \)[/tex]-axis and to the left, the [tex]\( x \)[/tex]-component is positive.
Therefore:
- [tex]\( a_x = 18 \sin(35^\circ) \)[/tex]
- [tex]\( a_y = -18 \cos(35^\circ) \)[/tex]
Calculating these:
- [tex]\( a_x \approx 18 \times 0.5736 \approx 10.3 \text{ m/s}^2 \)[/tex]
- [tex]\( a_y \approx -18 \times 0.8192 \approx -14.7 \text{ m/s}^2 \)[/tex]
So, the components are:
- [tex]\( a_x \approx 10.3 \text{ m/s}^2 \)[/tex]
- [tex]\( a_y \approx -14.7 \text{ m/s}^2 \)[/tex]
The correct question is:
1. Find the [tex]$x$[/tex] - and [tex]$y$[/tex]-components of the vector [tex]$d \boxtimes=(9.0 \mathrm{~km}, 25 \boxtimes$[/tex] left of [tex]$+\mathrm{y}$[/tex]-axis).
2. Find the [tex]$\mathrm{x}$[/tex] - and [tex]$\mathrm{y}$[/tex]-components of the vector [tex]$\mathrm{v} \boxtimes=(4.0 \mathrm{~cm} / \mathrm{s},-\mathrm{x}$[/tex]-direction [tex]$)$[/tex].
3. Find the [tex]$x$[/tex] - and [tex]$y$[/tex]-components of the vector [tex]$a \boxtimes=(18 \mathrm{~m} / \mathrm{s} 2,35 \boxtimes$[/tex] left of [tex]$-y$[/tex]-axis [tex]$)$[/tex].
The table below shows 10 data values:
88
92
94
80
85
90
72
83
93
91
What is the five-number summary for these data?
Minimum = 72, Q1 = 83, median = 89, Q3 = 92, maximum = 94
Minimum = 80, Q1 = 85, median = 89, Q3 = 91, maximum = 93
Minimum = 80, Q1 = 83, median = 90, Q3 = 92, maximum = 93
Minimum = 72, Q1 = 85, median = 90, Q3 = 91, maximum = 94
Answers
72 80 83 85 88 90 91 92 93 94
From the arrangement, we can see that the minimum is 72 and the maximum is 94. Next, the median is the middle number of the data. Since there are 10 data points, we take the average of the middle 2 numbers. The median is (88+90)/2 = 89.
When you talk about the quartiles, you draw divisions in your set. Q₁ is the middle data between the smallest and the median; Q₂ is the median; and Q₃ is the middle data between the largest and the median.
72 80 83 85 88 | 89 | 90 91 92 93 94
Q₁ is 83
Q₂ is 89
Q₃ is 92
Therefore, in summary, the answer is: Minimum = 72, Q1 = 83, median = 89, Q3 = 92, maximum = 94
D is (8,4) it just got cut off
Answers
-2x-6y=-26 (this is the second equation multiplied by -1)
2x=14 (added the equations together, 6y is cancelled out by -6y)
x=7
Now plug this value in to one of the equations to get y value
4(7)+6y=40
28+6y=40
6y=12
y=2
The answer is B
A computer training institute has 625 students that are paying a course fee of $400. Their research shows that for every $20 reduction in the fee, they will attract another 50 students. What fee should the school charge to maximize their revenue?
$275
$380
$320
$325
Answers
If no changes are made, the school has a revenue of :
625*400$/student=250,000$
2.
Assume that the school decides to reduce n*20$.
This means that there will be an increase of 50n students.
Thus there are 625 + 50n students, each paying 400-20n dollars.
The revenue is:
(625 + 50n)*(400-20n)=12.5(50+n)*20(20-n)=250(n+50)(20-n)
3.
check the options that we have,
a fee of $380 means that n=1, thus
250(n+50)(20-n)=250(1+50)(20-1)=242,250 ($)
a fee of $320 means that n=4, thus
250(n+50)(20-n)=250(4+50)(20-4)=216,000 ($)
the other options cannot be considered since neither 400-275, nor 400-325 are multiples of 20.
Conclusion, neither of the possible choices should be applied, since they will reduce the revenue.
Answer: it’s D $325
Step-by-step explanation:
the fee the school should charge to maximize their revenue is $325
Jonathan sets a camera on a tripod to film birds in a nest. The camera is 1.8 m off the ground and 16.4 m away from the tree. The angle of elevation from the camera to the bird’s nest is 29°. How far above the ground is the bird’s nest? Round your answer to the nearest tenth of a meter. 7.3 m 9.1 m 10.9 m 14.3 m
Answers
n=16.4tan29°+1.8
n≈10.9 meters (to nearest tenth of a meter)
we need to find the area of the other leg
alright
we have one leg is 16.4
the other one is ?
tan(29°)=?/16.4
16.4tan(29°)=?
and the height of the nest is ?+height of camera=?+1.8
so
16.4tan(29°)+1.8≈10.8907
so about 10.9m