Sketch the graphs of each of the following functions showing all steps on the same set of axes. Help with c)
Answers
The parent function g(x) = |x| has the following graph:
then, given the function f(x) = -3 |x-2| + 4, we have to make a stretch and a reflection, with a traslation of 2 units to the right and 4 units up, to get the following graph:
Related Questions
Alex received an 82, 89, and 91 on three tests. How many points does he need to score on his next test in order to have an average of at least a 93? Write an inequality that best represents this situation.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
test scores = 82, 89, and 91
average ≤ 93
inequality = ?
Step 02:
x = score on the next test
inequality:
(82 + 89 + 91 + x ) / 4 ≤ 93
A football is dropped from a height of 20 feet, and the ball bounces with each bounce 1/4 as high as the preceding one. What is the total height it would have traveled by the 8th bounce?
Answers
Given:
The height from whihc the ball is dropped, h=20 feet.
The height attained by the ball at each bounce can be written as a geometeric series.
Let a=20 feet be the first term of the series.
Since the ball bounces 1/4 as high as the preceding one, the common ratio of the sequence is,
[tex]r=\frac{1}{4}[/tex]The sum of n terms in a geometric sequence is,
[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]The total height traveled by the 8th bounce is given by the sum of 8 terms in a geometric series starting from a=20 ft.
The sum of the terms in a GP with a=20, r=1/4 and n=8 is,
[tex]S_8=\frac{20(1-(\frac{1}{4})^8)}{(1-\frac{1}{4})}=26.66[/tex]Now, the total height traveled by the 8th bounce is,
[tex]H=2\times S_8-a=2\times26.66-20=33.32\text{ ft}[/tex]Hence, the total height the ball would have traveled by the 8th bounce is 33.32 ft.
Yasmine is making party favors for her birthday party. She has 2/5 meter of yarn to makebracelets for 5 people. How much of a meter can Yasmine use for each bracelet?Write out the problem. Then create a model to represent the quotient.
Answers
We know that Yasmine has 2/5 meters of yarn to make bracelets for 5 people.
This means that she will have to distribute the 2/5 meters to the 5 people. This can be written as:
[tex]\frac{2}{5}\div5[/tex]And solving it, we get:
[tex]\frac{2}{5}\div5=\frac{2}{5}\cdot\frac{1}{5}=\frac{2}{25}[/tex]This means that Yasmine should use 2/25 of a meter for each bracelet.
(AWARDING BRAINLIEST!)Points P, Q, and R are collinear on PR, and PQ:PR = . P islocated at the origin, Q is located at (x, y), and R islocated at (-12,0). What are the values of x and y?
Answers
Explanation:
We can model the situation as:
Since P and R have a y-coordinate equal to 0, Q has a y-coordinate 0
Now, to calculate the x-coordinate, we can formulate the following equations:
Rx - Px = 3a
Qx - Px = 2a
Where Rx is the x-coordinate of R, Px is the x-coordinate of P and Qx is the x-coordinate of Q. So, replacing the values:
-12 - 0 = 3a
x - 0 = 2a
Now, solving for a, we get:
-12 - 0 = 3a
-12 = 3a
-12/3 = a
-4 = a
Replacing on the second equation, we get:
x - 0 = 2a
x = 2a
x = 2*(-4)
x = -8
Therefore, the coordinates of Q are (-8, 0)
Answer: (-8, 0)
Consider the function in the graph to the right. The function has a relative maximum of at x = 104 8 The function has a relative minimum of 7 6 at x = The function is increasing on the interval(s): Yo -9 8 7 6 5 4 3 2 6 8 9 10 The function is decreasing on the interval(s): 5 -6 The domain of the function is: -8 -9 10 a The range of the function is:
Answers
Given the graph of the shown function
As shown:
1) The function has a relative maximum of 1, at x = 0
2) The function has a relative minimum of -6, at x = -7
3) The function is increasing on the interval:
[tex](-7,0)[/tex]4) the function is decreasing on the intervals:
[tex](-\infty,-7),(0,\infty)[/tex]5) the domain of the function is all the possible values of x =
[tex](-\infty,\infty)[/tex]6) the range of the function is all the possible values of y =
[tex](-\infty,\infty)[/tex]Hey, I forgot how to do these. Could you helo me out?
Answers
An isosceles triangle has two congruent sides, and a right triangle has an angle measuring 90°.
If we draw a right triangle, where each leg has the same length, we have:
Since both properties can be put together, so Ryan's statement is correct, since we can draw a right isosceles triangle.
if you go mini-golfing, in which of these scenarios are you precise but not accurate? a) you hit all holes in one. b) you take six strokes at each hole. c) it always takes you a long time to get your shots in d) all of your shots are off, but they all go to the same place.
Answers
Answer: I would say (d)
Step-by-step explanation: For a lot of people their shots are always off but the chance of getting all your off shots in the same place are pretty low. Its precise but not accurate.
75PS.14 Quest Identify the solid from its net. a Choose the correct answer below O square pyramid O triangular pyramid O rectangular pyramid O rectangular prism Click to select your answer and then click Check Answer All parts showing Clear All G
Answers
We can see that the base is a rectangle. And the triangles allow us to see that the solid must be a pyramid.
So, the answer is a rectangular pyramid.
this is so confusing i do not understand what this even is
Answers
Since the triangle is dilated, the sides of the original triangle are stretched. Since J'K' is the length of one side of the triangle after the dilation, we have that:
[tex]\begin{gathered} J^{\prime}K^{\prime}=\frac{4}{3}JK,J^{\prime}K^{\prime}=13.5 \\ \Rightarrow13.5=\frac{4}{3}JK \\ \Rightarrow JK=\frac{3\cdot13.5}{4}=10.125 \end{gathered}[/tex]Then, the answer is 10.125
What is f(0)f(x)=5x – 1, if x < -2x + 3. if x > - 2
Answers
f(0)=3
Explanation
[tex]f(x)=\mleft\{\begin{aligned}5x-1\text{ if x}<-2\text{ (-}\infty,-2) \\ x+3\text{ if }>-2(-2,\infty) \\ \square\end{aligned}\mright.[/tex]Step 1
when x= 0
the function is defined
by
[tex]f(x)=x+3[/tex]Step 2
replace x= 0
[tex]\begin{gathered} f(0)=x+3 \\ f(0)=0+3 \\ f(0)=3 \end{gathered}[/tex]solve the given system3x+2y+4z=112x-y+3z=45x-3y+5z=-1
Answers
We can solve this system by elimination method. We can take
[tex]\begin{gathered} 3x+2y+4z=11 \\ 2x-y+3z=4 \end{gathered}[/tex]and multiply by 2 the second equation:
[tex]\begin{gathered} 3x+2y+4z=11 \\ 4x-2y+6z=8 \end{gathered}[/tex]and add both equations:
[tex]\begin{gathered} 7x+0+10z=19 \\ 7x+10z=19\ldots\ldots.(A) \end{gathered}[/tex]We can do something similar with 2nd and 3rd equations:
[tex]\begin{gathered} 2x-y+3z=4 \\ 5x-3y+5z=-1 \end{gathered}[/tex]but now, we can multiply by -3 the first one:
[tex]\begin{gathered} -6x+3y-9z=-12 \\ 5x-3y+5z=-1 \end{gathered}[/tex]by adding both equations, we have
[tex]\begin{gathered} -x+0-4z=-13 \\ -x-4z=-13\ldots..(B) \end{gathered}[/tex]we have removed y, then we have equation A and B with only x and z varaibles:
[tex]\begin{gathered} 7x+10z=19 \\ -x-4z=-13 \end{gathered}[/tex]by multiplying the second equation by 7 and adding to the first, we have
[tex]\begin{gathered} 10z-28z=19-7(13) \\ -18z=19-91 \\ -18z=-72 \\ z=\frac{-72}{-18} \\ z=4 \end{gathered}[/tex]Hence, we have that z=4. Now we can substitute tthis value into -x-4z=13 in order to find x:
[tex]\begin{gathered} -x-4(4)=-13 \\ -x-16=-13 \\ -x=-13+16 \\ -x=3 \\ \text{then,} \\ x=-3 \end{gathered}[/tex]Finally, we can substitute x=-3 and z=4 into the first original equation in order to find y:
[tex]\begin{gathered} 3(-3)+2y+4(4)=11 \\ -9+2y+16=11 \\ 2y+5=11 \\ 2y=11-5 \\ 2y=6 \\ y=\frac{6}{2} \\ y=3 \end{gathered}[/tex]Hence, the solution is x=-3, y=3 and z=4.
Please help quickly!! (30 POINTS) Its timed!!
Given f(x)=3x^2 −5x−2.
What is the value of f(−2/3)?
A.1
B. 8/3
C. 3
D. 10/3
Answers
Evaluating the function in x = -2/3 we will get:
f(-2/3) = 8/3
Thus the correct option is B.
What is the value of f(-2/3)?Here we know that the function is:
f(x) = 3x² - 5x - 2
Now we want to get f(-2/3), this only means that we need to replace the variable x by the number -2/3, so we will get:
f(-2/3) = 3*(-2/3)² - 5*(-2/3) - 2 = 3*(4/9) + 10/3 - 2
f(-2/3) = 4/3 + 10/3 - 2
f(-2/3) = 14/3 - 6/3 = 8/3
The correct option is B.
Learn more about evaluating functions:
https://brainly.com/question/1719822
#SPJ1
The intensity of exercise and your heart rate-positive-negative-no correlation
Answers
The intensity of excercise increases the heart rate, that is, more intensity the excersice, greater the heart rate.
It means that there is a positive correlation between int
Help find the Domain and Range please!
Answers
Answer:
Domain would be -2, range would be 1.
If A(1,2). B(5,-4) and C(-3,2) are the vertices of a triangle, which statement holds true?
Answers
Solution:
Given the vertices;
[tex]A(1,2),B(5,-4).C(-3,2)[/tex]Then;
[tex]\begin{gathered} |AB|=\sqrt{(-4-2)^2+(5-1)^2} \\ \\ |AB|=2\sqrt{13} \\ \end{gathered}[/tex]Then;
[tex]\begin{gathered} |BC|=\sqrt{(2-(-4))^2+(-3-5)^2} \\ \\ |BC|=10 \end{gathered}[/tex][tex]\begin{gathered} |AC|=\sqrt{(2-2)^2+(-3-1)^2} \\ \\ |AC|=4 \end{gathered}[/tex]Answer: Triangle ABC is scalene because all side lengths of the triangle are different.
Step-by-step explanation: does anyone know any free sites to get all Plato answers?
specifically the end of semester ones
In a dilation , if the scale factor is less than 1, the dilated image will be ??
Answers
The scale factor in the dilation determines how much bigger or smaller the image will be when compared to the original image.
If a scale factor is less than 1, the dilated image will be reduced
Allie created a garden in the shape of a right triangle. Which set of measurements could represent the lengths of the sides of her garden (G.8a) (1point) O A. lin, 5 in, and 6 in. O B. 6m., 8 m., and 10 m. O C. 9 cm, 9cm, and 9 cm O D. 3 ft 3 ft, and 4 ft
Answers
Answer
Options B, C and D represent sets of measurements that could be for the sides of Allie's triangle garden.
Explanation
If the three sides in a triangle are a, b and c with c being the longest side.
But, it should be noted that if the longest side is equal to or more than the sum of the two sides, c ≥ a + b, the triangle is not possible.
Option A
1 in, 5 in and 6 in
a = 1 in
b = 5 in
c = 6 in
a + b = 1 + 5 = 6
6 = 6
c = a + b
Hence, this set of sides is not possible.
Option B
6 m, 8 m and 10m
a = 6 m
b = 8 m
c = 10 m
a + b = 6 + 8 = 14 m
c = 10 m
10 < 14
c < a + b
This set of sides form a possible triangle
Option C
9 cm, 9 cm and 9 cm
a = 9 cm
b = 9 cm
c = 9 cm
a + b = 9 + 9 = 18 cm
c = 9 cm
9 < 18
c < a + b
This set of sides form a possible triangle
Option D
3ft, 3 ft and 4 ft
a = 3 ft
b = 3 ft
c = 4 ft
a + b = 3 + 3 = 6 ft
c = 4 ft
4 < 5
c < a + b
This set of sides form a possible triangle
Hope this Helps!!!
Hello, I need some help with Part 2 question 6! Please show work as the instructions asked! If you want me to include other completed work from the assignment for extra information, please let me know. Thank you.
Answers
Problem N 6
we have the roots
3 and (4+i)
By the conjugate complex theorem
If (4+i) is a root
then
(4-i) is a root too
so
we have at least
Zeros
x=3x=4+ix=4-iThe polynomial function is given by
(x-3)(x-(4+i))(x-(4-i))
Multiply first
(x-(4+i))(x-(4-i))
x^2+(4+i)(4-i)-x(4-i)-x(4+i)
x^2+16-i^2-4x+xi-4x-xi
x^2+16-(-1)-8x
x^2-8x+17
so
(x-3)(x-(4+i))(x-(4-i))=(x-3)(x^2-8x+17)
Apply distributive property again
x^3-8x^2+17x-3x^2+24x-51
x^3-11x^2+41x-51 ----> Polynomial functiontherefore
The code is AI need help with this practice problem solving The subject is trigonometry Make sure to read the instructions
Answers
Solution:
A complex number of the form:
[tex]z=x+iy\text{ ---- equation 1}[/tex]is expressed in polar form as
[tex]\begin{gathered} z=r(cos\theta+isin\theta)\text{ ---- equation 2} \\ where \\ r=\sqrt{x^2+y^2}\text{ ---- equation 3} \\ \theta=\tan^{-1}(\frac{y}{x})\text{ ----- equation 4} \end{gathered}[/tex]Given the complex number:
[tex]z=-3+i3\sqrt{3}[/tex]This implies that
[tex]\begin{gathered} x=-3 \\ y=3\sqrt{3} \end{gathered}[/tex]To express in polar form as shown in equation 2,
step 1: Evaluate the value of r.
From equation 3,
[tex]\begin{gathered} r=\sqrt{x^2+y^2} \\ x=-3,\text{ y=3}\sqrt{3} \\ thus, \\ r=\sqrt{(-3)^2+(3\sqrt{3})^2} \\ =\sqrt{9+27\text{ }} \\ =\sqrt{36} \\ \Rightarrow r=6 \end{gathered}[/tex]step 2: Evaluate the positive value of θ.
From equation 4,
[tex]\begin{gathered} \theta=\tan^{-1}(\frac{y}{x}) \\ =\tan^{-1}(\frac{3\sqrt{3}}{-3}) \\ \theta=-60 \\ From\text{ the second quadrant, the value of }\theta\text{ is also negative.} \\ Thus,\text{ the smallest angle will be} \\ \pi-\frac{\pi}{3}=\frac{2}{3}\pi \\ \end{gathered}[/tex]step 3: Substitute the values of r and θ into equation 2.
Thus,
[tex]z=6(cos\text{ }\frac{2\pi}{3}\text{+isin }\frac{2\pi}{3}\text{\rparen}[/tex]Thus, the polar form of the complex number is expressed as
[tex]z=6\text{ cis\lparen}\frac{2\pi}{3})[/tex]i don’t understand what it’s asking for my algebra 2
Answers
The given expression is
[tex](x+9)(x-2)-9x-6[/tex]Solve the product.
[tex]x^2-2x+9x-18-9x-6=x^2-2x-24[/tex]Then, factor the quadratic expression. Find two numbers whose product is -24 and whose difference is -2.
[tex]x^2-2x-24=(x-6)(x+4)[/tex]Therefore, the answer is (x-6)(x+4).Need help finding 2 more points on the line for question # 11
Answers
11)
The formula for calculating slope is expressed as
slope = (y2 - y1)/(x2 - x1)
From the information given,
x1 = 5, y1 = - 2
x2 = 6, y2= - 5
Slope = (- 5 - - 2)/(6 - 5) = (- 5 + 2)/1
Slope = - 3
The equation of a line in the point slope form is expressed as
y - y1 = m(x - x1)
where
m = slope = - 3
The equation of the line is
y - - 2 = - 3(x - 5)
y + 2 = - 3(x - 5)
When x = 0,
y + 2 = - 3(0 - 5) = - 3 * - 5 = 15
y = 15 - 2
y = 13
When x = 1,
y + 2 = - 3(1 - 5) = - 3 * - 4 = 12
y = 12 - 2
y = 10
Thus, two other points are
(0, 13)
(1, 10)
HELP ASAP!!!! 10 points
Answers
Each model has been labeled accordingly. See the attached image. Their respective fractions are given as follows:
A - (1/3) ÷ 3
B - (1/5) ÷ 5
C - (1/5) ÷ 3
D - (1/5) ÷ 5
E - (1/5) ÷ 3
F - (1/5) ÷ 5
What is a fraction?Fractions represent a part of a whole or, more generally, any number of equal parts. In everyday English, fractions describe how many parts of a given quantity there are, such as one-half, eight-fifths, and three-quarters.
A small part is a part of the whole. In arithmetic, numbers are represented as ratios where the numerator is divided by the denominator. In prime fraction, both are integers. Complex fractions have fractions in the numerator or denominator.
Real/False Fractions, Mixed Fractions, Equivalent Fractions, and Even/Odd Fractions are the six types of fractions in math. The numerator and denominator are the two parts of a fraction
Learn more about fractions:
https://brainly.com/question/17220365
#SPJ1
You're an amateur astronomer, and one night you seewhat appears to be a parallelogram in the constellationof Lyra. Explain how you could verify that the figure is aparallelogram.
Answers
Let:
[tex]\begin{gathered} A=(x1,y1) \\ B=(x2,y2) \\ C=(x3,y3) \\ D=(x4,y4) \end{gathered}[/tex]Points of the parallelogram
We can verify that it is a parallelogram if it satisfies the following conditions:
Two pairs of opposite sides are parallel.
Two pairs of opposite sides are equal in length.
Two pairs of opposite angles are equal in measure.
The diagonals bisect each other.
One pair of opposite sides is parallel and equal in length.
Adjacent angles are supplementary.
In order to make things a little quicker we can verify the following:
[tex]\begin{gathered} |AC|=|BD| \\ |AB|=|CD| \end{gathered}[/tex]And:
[tex]\begin{gathered} AC\parallel BD \\ AB\parallel CD \end{gathered}[/tex]The length of a new rectangular playing field is 2 yards longer than quadruple the width. If the perimeter of the rectangular playing field is 544 yards, what are its dimensions?
Answers
My first step is to draw a picture
We know the length is 4 times the width plus 2
We are told the perimeter is 544
P = 2L + 2 W
Substitute in for L
544 = 2 ( 4W + 2) + 2W
Distribute
544 = 8W + 4 + 2W
Combine like terms
544 = 10W + 4
Subtract 4 from each side
544-4 = 10W +4-4
540 = 10W
Divide each side by 10
540/10 = 10W/10
54 = W
The width is 54 yards
Now find the length
L = 4W +2 = 4(54) +2 = 218 yards
Write the slope intercept form of the equation of the line that passes through the point (4, 8) and has a slope of -2.
Answers
Answer:
[tex]y=-2x+16[/tex]
Step-by-step explanation:
Graphing another point and tracing the line back you will see a y-intercept of 16.
the function f(x) = x^1/2 is transformed to get function W.w(x)= -(3x)^1/2 - 4 what are the domain and the range of function w? domain : x is grater then or equal to ___range : w(x) is less than or equal to ___(picture listed below)
Answers
Solution:
Given:
[tex]w(x)=-(3x)^{\frac{1}{2}}-4[/tex]Rewriting the function, by applying the law of fractional exponents,
[tex]a^{\frac{1}{2}}=\sqrt{a}[/tex]Hence,
[tex]\begin{gathered} w(x)=-(3x)^{\frac{1}{2}}-4 \\ w(x)=-\sqrt{3x}-4 \end{gathered}[/tex]The domain of a function is the set of all input values that make the function defined.
The function is undefined when the value of x under the root sign is less than zero because the square root of a negative number is complex.
Hence, the domain exists when x has a value greater than or equal to 0.
Therefore, the domain is;
[tex]Domain:x\ge0[/tex]The range of a function is the set of all output values that makes the function defined.
Hence, the range exists when y is lesser than or equal to minus 4 because a value of y greater than -4, makes the function and domain undefined.
Therefore, the range is;
[tex]Range:w(x)\leq-4[/tex]What percent of $658.23 is $645.07?
Answers
The percentage of ( a% ) is to be applied on the principal amount of ( P ):
[tex]P\text{ = \$658.23}[/tex]We need to determine what percentage proportion rate ( a% ) will left us with a disposable amount of ( D ):
[tex]D\text{ = \$645.07}[/tex]The percentage formula applied at principal amount is:
[tex]D\text{ = P }\cdot\text{ }\frac{a}{100}\text{ }[/tex]We will plug in the values the respective values as follows:
[tex]\begin{gathered} a\text{ = }\frac{100\cdot D}{P} \\ a\text{ = }\frac{100\cdot645.07}{658.23}\text{ = }\frac{64507}{658.23} \\ \textcolor{#FF7968}{a}\text{\textcolor{#FF7968}{ = 98\%}} \end{gathered}[/tex]The amount of percentage reduction applied to the principal amount is ( 2% ) and $645.07 is 98% of principal $658.23.
Hence,
[tex]\textcolor{#FF7968}{98}\text{\textcolor{#FF7968}{ percent}}[/tex]Translate the following phrase into an algebraic expression. Do not simplify.6 less than the sum of y and x
Answers
6 less than "something" can be written as "something" - 6.
In this case, "something" is "the sum of y and x", which can be written as x + y
So, putting them togethre, we have:
[tex]x+y-6[/tex]helpppppppppppp meeeeeeeeeeee pleaseee!!!
Answers
We will get the compositions by evaluating the functions into the other functions, we will get:
(f o g)(x) = 16x² + 2(g o f)(x) = 4x² + 8How to find the two compositions?Remember that the composition between two functions f(x) and g(x) gives.
(f o g)(x) = f( g(x) )
So we just evaluate the first function into the second one.
Here the two are:
f(x) = x² + 2
g(x) = 4x
The first composition is:
(f o g)(x) = f( g(x) ) = g(x)² + 2
now we replace g(x) there to get:
(f o g)(x) = (4x)² + 2 = 16x² + 2
The other composition is:
(g o f)(x) = 4*f(x) = 4*(x² + 2) = 4x² + 8
Learn more about compositions:
https://brainly.com/question/10687170
#SPJ1
Explain why it works to break apart a number by place value to multiply
Answers
Step-by-step explanation:
EX. 48*7
7*40
7*8
336
It makes the problem simpler because you can see what you are multiplying individually
