Answer:
[tex]f^\prime(x)=-2|x-1|-3[/tex]
Step-by-step explanation:
Write the equation for f(x)=IxI but vertically stretch it by a factor of 2, flip it over the x axis, shift it down 3 units, shift it 1 unit to the right
We have the (parent absolute value) function:
[tex]f(x)=|x|[/tex]
And we want to write a new function which represents the previous function: 1) Vertically stretched by a factor of 2, 2) flipped over the x-axis, 3) shifted down 3 units, and 4) shifted 1 unit to the right.
1)
To vertically stretch/compress a function, we multiply the function by a constant a.
If a is greater than 1, it is a vertical stretch. If a is less than 1 (and greater than 0), it is a vertical compression.We want to vertically stretch our function by 2. So, we will multiply our function by 2. Therefore:
[tex]f^\prime(x)=2|x|[/tex]
2)
We want to flip the function over the x-axis.
To flip a function over either axis:
Multiply by negative 1 to flip the function over the x-axis.Substitute x for -x to flip the function over the y-axis.Since we want to flip our function over the x-axis, we will multiply it by -1. So:
[tex]f^\prime(x)=-2|x|[/tex]
3)
We want to shift our function down by 3 units.
To shift a function vertically, we simply add the vertical shift to our function.
Since we are shifting downwards by 3 units, we will add -3 to our function. So:
[tex]f^\prime(x)=-2|x|-3[/tex]
4)
Finally, we want to shift our function 1 unit to the right.
To shift a function horizontally, we replace the x with (x-n), where n is the horizontal shift.
Since we are shifting our function to the right, n=1. Therefore, we will replace x with (x-1). So, our function becomes:
[tex]f^\prime(x)=-2|x-1|-3[/tex]
And we have our final function.
Note: In general, try doing the vertical/horizontal stretches first, x/y-axis reflections second, and then vertical/horizontal shifts last to avoid mistakes.
can you answer my questions quick
Answer:
6 servings
Step-by-step explanation:
Let's say there are x 2/3 cup servings in a 4 cup container.
We multiply 2/3 by x to get the amount of cups that will produce and set that equal to 4 (because we want 4 cups):
(2/3) * x = 4
Divide both sides by 2/3, or multiply both sides by the reciprocal 3/2:
x = 4 * (3/2) = 12/2 = 6
The answer is 6 servings.
Please answer these series of questions! I will give high points and brainliest!
A. Reduce 3/51 to its simplest terms
B. Solve 7 divided by 3 (in fractions!)
C. 19 divided by 3 (fractions)
D. Reduce 50/80 to simplest terms
E. Reduce 9/14 to simplest terms
F. Reduce 36/54 to simplest terms
G. Solve 55 divided by 12 (fractions)
H. Reduce 9/153 to simplest terms
That’s all! ( please answer correct my life is depending on it, my mom will literally beat me up )
Answer:
A: 1/17 or decimal form: 0.058
B: 7/3 or mixed #: 2 1/3
C: 19/3 or mixed #: 6 1/3
D: 5/8
E: 9/14
F:2/3
G: 55/12 or mixed #: 4 7/12
H: 1/17
Step-by-step explanation:
Item 21
The temperature of dry ice is −109.3°F. This is 184.9°F less than the outside temperature. Write and solve an equation to find the outside temperature t (in degrees Fahrenheit).
An equation is −109.3=
.
The outside temperature is
∘F.
Answer:
Step-by-step explanation:-109.3=t-184.9
T=75.6
please solve this problem for me
Answer:
11/4800
Step-by-step explanation:
Two lines, A and B, are represented by the equations given below!
Line A: y = x - 4
Line B: y = 3x + 4
Which of the following shows the solution to the system of equations and explains why?
A. (-3,-5), because the point satisfies ONE of the equations
B. (-3,-5), because the point lies between the two axes
C. (-4,-8), because the point satisfies BOTH equations
D. (-4,-8), because the point does not lie on any axis
Answer:
The solutions to the system of equations are:
[tex]y=-8,\:x=-4[/tex]
Thus, option C is true because the point satisfies BOTH equations.
Step-by-step explanation:
Given the system of the equations
[tex]\begin{bmatrix}y=x-4\\ y=3x+4\end{bmatrix}[/tex]
Arrange equation variables for elimination
[tex]\begin{bmatrix}y-x=-4\\ y-3x=4\end{bmatrix}[/tex]
[tex]y-3x=4[/tex]
[tex]-[/tex]
[tex]\underline{y-x=-4}[/tex]
[tex]-2x=8[/tex]
[tex]\begin{bmatrix}y-x=-4\\ -2x=8\end{bmatrix}[/tex]
solve for x
[tex]-2x=8[/tex]
Divide both sides by -2
[tex]\frac{-2x}{-2}=\frac{8}{-2}[/tex]
[tex]x=-4[/tex]
[tex]\mathrm{For\:}y-x=-4\mathrm{\:plug\:in\:}x=-4[/tex]
[tex]y-\left(-4\right)=-4[/tex]
[tex]y+4=-4[/tex]
[tex]y=-8[/tex]
The solutions to the system of equations are:
[tex]y=-8,\:x=-4[/tex]
Thus, option C is true because the point satisfies BOTH equations.
I need the answer to this question please 4(3 - 2x) = 15
The correct answer would be -3/8 or in decimal form -0.375 :)
Which expression has a value of 8?
1. 720 divided by 9
2. 720 divided by 90
3. 7200 divided by 9
4. 7200 divided by 90
Answer:
720 divided by 90
Step-by-step explanation:
72 divided by 9 is 8. 720 divided by 9 is 80 because you're keeping the 0, but when dividing, take away the zeros if both numbers have a zero to make it easier
Lucia invests $5000 at a rate of 4.5% per year compound interest. Calculate the value of her investment at the end of 7 years.
The value of her investment at the end of 7 years is $11804
How to determine the value?The given parameters are
Principal, P = $5000
Rate, r = 4.5%
Time, t = 7 years
The value is then calculated as:
Value = P * P(1 + r)^t
So, we have:
Value = 5000 + 5000 * (1 + 4.5%)^7
Evaluate the expression
Value = 11804
Hence, the value of her investment at the end of 7 years is $11804
Read more about compound interest at:
https://brainly.com/question/24924853
#SPJ1
pls help me with this lol
Answer:
a) 95 miles
b) Chester
c) 194 miles
Step-by-step explanation:
Chart Reading
From the chart, we can know the relative distances from each place as follows:
a) From Hereford to Chester there are 95 miles
b) Kendal is 99 miles from Chester
c) If Ellen drives from Kendal to Hereford, passing by Chester, she will drive 99+95=194 miles
Note this last result is different from the direct distance from Kendal to Chester since the 201 miles are not specified if they are through Chester or not.
Middle School
Mathematics
Find x.
A. 8
B. 12
Answer:
17²=15²+x²
289=225+x²
288-225=x²
64=x²
x=6
Answer:
8
Step-by-step explanation:
By Pythagoras theorem,
(hypotenuse)² = (altitude)² + (base)²
(17)² = x² + (15)²
(17)² - (15)² = x²
289 - 225 = x²
x² = 64
x = √64
x = 8
hope this helps you!
Find the sum of of a series, I’ll give brainliest if you got the correct answers :)
How do I do 3 x 10^5
Answer: 3(10^5)
=3*10^5
=3*(10*10*10*10*10)
=300000
This is how you should do It, just when it is squared you should times the number like up here you times 10 times 10 5 times so if you see it you don't times it by 5 you do 10 times 10 times 10 times 10 times 10 like this
You should get it now
Have a good day
Yours,
Nathaniel
Step-by-step explanation:
Y=6x+21
-x+3y=12
Find x and y please
27 : 18 = 13 : x find x
Answer: 27:18 and 13:x can also be written as 27/18 and 13/x
therefore, 27:18 = 13:x
27/18 = 13/x
27/18 *13= x
x = 19.5
Hope it helped u,
pls mark as the brainliest
and put thanks
^_^
Write the equation of the line, in slope-intercept form, with the
following information:
slope: -2
point: (5,-4)
Answer:
Step-by-step explanation:
y + 4 = -2(x - 5)
y + 4 = -2x + 10
y = -2x + 6
Brett picks tomatoes from his garden and bags them up to give to his neighbors. He starts with 36 bags of tomatoes and gives out 12 bags every hour until there are none left.
Use the Segment tool to plot a graph representing the number of bags of tomatoes Brett has left to give away from the time he starts giving them away until he has no bags left.
Answer:
I would start the graph at (0,36) and go down 12, right 1 until you reach the end of the graph
Step-by-step explanation:
Hope it helps
In 2003, the average attendance per game for a football team was about (1 × 104) + (9 × 103) + (9 × 102). What is this number in standard form?
show work
Answer:
1.99 * 10^4
Step-by-step explanation:
Here, we want to write the addition in standard form
= (1 * 10^4) + (9 * 10^3) + (9 * 10^2)
= 10,000 + 9000 + 900
= 19,900
so the number in standard form is;
1.99 * 10^4
12 to the fifth power divided by six to the third power
Answer:
1152
Step-by-step explanation:
This is it simplified.
Answer:
1152
Step-by-step explanation: 248832 over
63
=
248832
216
=1152
for f(x) = -8x +8, find f(-3)
Answer:
f(x)=-8x+8
f(-3)
ANSWER: 11/8
You bought a magazine for $6 and 4 candy bars. If you spent a total of $14, how much did each candy bar cost?
Answer:
2$
Step-by-step explanation:
first you need to subtract the cost of the magazine from the total. now you have 8$ left, divide this by the number of candy bars, 4, and you get 2$.
don't forget to add the dollar sign, it might save you points
HELP !!!!!40 POINTS AVAILABLE
2. d+g/h. When d=29, g = 16. and h=9
(1 point)
A.8
B.2.375
C.5.375
D.5
Answer:
5
Step-by-step explanation:
29 plus 16 is 45 and 45 divided into 9 is 5
Pls help show work please
HELP ME PLEASEEEEEEEEEEEEEEEEE YOU CAN GET BRAINEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
its red okay? i hop help
Answer:3:1. Yellow
Step-by-step explanation:
Solve for x.
*2 =
= 1
A)
-10
22
B)
C)
D
4.
Answer:
1+x=b;b+x=c;c+x=d;d+x=89
Step-by-step explanation:
Translation of, “Six less than twice the value of x,”.
Answer:
2x-6
Step-by-step explanation:
2 × x × x × 3 × y × y × y
how do i do this?
Answer: [tex]6x^2y^3[/tex]
Explanation:
The numbers 2 and 3 multiply to 6, so that's why the final coefficient is 6.
The x terms multiply to [tex]x*x = x^2[/tex]
The y terms multiply to [tex]y*y*y = y^3[/tex]
The exponent tells us how many copies of the base to multiply.
So overall, [tex]2*x*x*3*y*y*y = 6x^2y^3[/tex]
Write as a product:
a2+b2–2ab –25
Answer: -a2 - 2ab - b2 + 25 =
-1 • (a2 + 2ab + b2 - 25)
Final result :
-a2 - 2ab - b2 + 25
Step-by-step explanation:
Y'all I need HELPPPPPP
Answer:
x = 13
arc RQ = 160°
Step-by-step explanation:
The length of smaller arc RQ is twice of the inscribed angle it sees
(5x + 15) × 2 = 10x + 30
9x + 17 + 6x - 12 + 10x + 30 = 360° add like terms
25x + 35 = 360
25x = 360 - 35
25x = 325 divide both sides by 25
x = 13 now the measure of arc RQ
10x + 30 ➡ 10 × 13 + 30 = 160°
The measures of the angles of a triangle solve for X
Answer:
x = 7
Step-by-step explanation:
Because this is a right triangle, one angle is a right angle (90°). All triangles have all three angle measures adding up to 180°, so the other two angles' measures add up to 90° (90 + 90 = 180).
Combine like terms of the angle measures.
6x + 9x = 15x
-3 + (-12) = -15
15x - 15
Because the sum of the measures of the two angles have to equal 90,
15x - 15 = 90
Add 15 from both sides.
15x = 105
Divide both sides by 15.
x = 7
To check, substitute 7 in both expressions.
6(7) - 3 = 39
9(7) - 12 = 51
39 + 51 + 90 (the measure of the right angle) = 180, so the value of x is 7.
I hope this helped :)
the functions f(x), g(x), and h(x), find the average rate of change over the interval -3≤x≤5