f(x) ⇒ a*f(x)
This results in a vertical stretch, or compression.
When a > 1, we refer to this as a vertical stretch by a factor of a.When 0 < a < 1, we typically refer to this as a vertical compression by a factor of [tex]\dfrac{1}{a}[/tex].**There are multiple correct answers when asked about a, or vertical stretches/compressions.
Let's say we're given [tex]\dfrac{1}{2}f(x)[/tex]. In this case, 0 < a < 1.We could say the following:
f(x) underwent a vertical stretch by a factor of [tex]\dfrac{1}{2}[/tex].f(x) underwent a vertical compression by a factor of 2.Both of the above responses are correct.
Solving the QuestionWe're given:
We multiply the parent function by [tex]\dfrac{3}{4}[/tex].In this case, 0 < a < 1.
This results in a vertical stretch by a factor of [tex]\dfrac{3}{4}[/tex].This results in a vertical compression by a factor of [tex]\dfrac{4}{3}[/tex].AnswerTrue and false. Yes, we did modify the vertical stretch factor of the function to induce a type of vertical stretch. No, it is not a vertical stretch per se, but it is rather a vertical compression.
Beth and Brianne had a yard sale to raise money. They donated 2 of their profits to their 10 school sports teams, 3 to the animal shelter, and 1 to the hospital. Which model can be 10 10 used to find the total fraction of their profits that they donated? Explain your thinking.
Answer:
Model 1
Step-by-step explanation:
Model 1 correctly displays the amount of money Beth and Brianne donated and raised at the yard sale. 2/10 + 3/10 + 1/10 = 6/10 (this would be the total amount donated.If 6/10 was donate, 4/10 of the total profit still remains. Model 2 does not represent the total profit that the girls have remaining.Which expression is equivalent to the following complex fraction?
Consider the fraction first ;
[tex]{:\implies \quad \sf \dfrac{\dfrac{3}{(x-1)}-4}{2-\dfrac{2}{(x-1)}}}[/tex]
[tex]{:\implies \quad \sf \dfrac{\dfrac{3-4(x-1)}{\cancel{(x-1)}}}{\dfrac{2(x-1)-2}{\cancel{(x-1)}}}}[/tex]
[tex]{:\implies \quad \sf \dfrac{3-4x+7}{2(x-1-1)}}[/tex]
[tex]{:\implies \quad \boxed{\bf{\dfrac{-4x+7}{2(x-2)}}}}[/tex]
Hence, Option B) is required answer
Find the sum of a finite arithmetic sequence from n=1 to n=5 using the expression -3(4)^n-1
Answer:
Step-by-step explanation:
Arithmetic sequaence:
[tex]\sf a_n = -3(4)^n - 1\\\\a_1=-3*4^1 -1\\\\ = -3*4 - 1\\\\ = -12 - 1\\\\a_1=-13[/tex]
[tex]a_2 = -3*4^2-1\\[/tex]
= -3*16 -1
= -48 - 1
= -49
difference = second term - first term
= -49 -(-13)
= -49 + 13
d = -36
[tex]\boxed{S_n=\dfrac{n}{2}[2a + (n-1)d]}[/tex]
[tex]\sf S_5=\dfrac{5}{2}*[2*(-13} + 4*(-36)]\\\\ =\dfrac{5}{2}[-26-144]\\\\=\dfrac{5}{2}*(-270)[/tex]
= 5*(-135)
= -675
A straight line has gradient - 1/2 and y-intercept 3.
Write the equation of the line in the form of ax + by + c
Answer:
[tex] - \frac{1}{2} x - y + 3 = 0[/tex]
Step-by-step explanation:
as shown in drawing
Convert the unit of weight. Use 1 lb = 16 oz. Express your answer in exact simplest form. 3 lb = _____ oz
3lb= ⋅ = _____oz ?
Answer:
48
Step-by-step explanation:
one pound equals 16 ounces so multiply each side by three and you get that 3 lb equals 48 ounces
Answer:
48 oz
Step-by-step explanation:
We know 1 lb = 16 oz. That means that to find how many oz are in 3 lbs, you have to multiply 16 by 3. That equals 48.
NEED HELP ASAP The salaries of Nathan and Trisha are in the ratio of 5:9. Trisha's salary is £16800 more than Nathan's. Find Nathan's salary.
Answer:
From the ratio
The difference is 9 - 5 = 4
Hence Trisha has 4 units more than Nathan and this resulted to 16800
Therefore 1 unit will be
16800 / 4 = 4200
Nathan’s salary is 5 units
5 * 4200 = 21000
Box size | number of mufffons
Small. 4
Medium. 6
Large. 8
Extra large 12
How many muffins are needed to fill all the boxes? Show your work
A car travels 80 miles on 3 gallons of gas. At the same rate (in miles per gallon) l, how many miles will the car be expected to travel on 5 gallons of gas?
A. 48
B. 130
C. 133 1/5
D. 160
Answer:
C
Step-by-step explanation:
If abc is an equilateral triangle bc must be 2cm true or false?
Answer:
I would say False
if xy=2√3 the value of x^4+y^4=?
Step-by-step explanation:
wrong question or incomplete question
Point q is located on the coordinate grid at (-9.73,-3.32) in which quadrant is point q called
Answer:
III
Step-by-step explanation:
The signs of both x and y are negative in the 3rd quadrant.
__
x-values are negative in the left half-plane.
y-values are negative in the bottom half-plane.
Both coordinates are negative in the lower-left quadrant, number III.
Geometry: Trig Pile Up Activity
The measure of the unknown angle is 53 degrees.
The length of the unknown side of the blue triangle is 4.43 cm
Right angle triangleRight angle triangle have one of its angles as 90 degrees.
The sum of angle in a triangle is 180 degrees.
Therefore, the measure of the unknown angle can be calculated as follows:
let
x = unknown angle
x = 180 - 90 - 37 = 53°
Therefore, let's find the unknow length of the blue triangle.
tan 53 = opposite / adjacent
tan 53 = 6.9 / a
a = 6.9 / 1.327
a = 5.1996985682
a = 5.2
The green triangle hypotenuse = 5.2 + (5.2 - 2.6) = 7.8 cm
Therefore,
sin 59 = opposite / 7.8
opposite = 7.8 × 0.8571673007
opposite = 6.68590494548
opposite side = 6.69 cm
The hypotenuse of the blue triangle = 6.69 - 2 = 4.69 cm
Therefore,
sin 71 = x / 4.69
x = 4.69 × 0.94551857559
x = 4.43448211956
x = 4.43 cm
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Does anyone know the answers? Need help!!
Answer:
nice handwriting
Step-by-step explanation:
help help help help math math
Answer:
2
Step-by-step explanation:
the line is straight and is set on 2 so y<2
Write the rate in lowest terms.
During a bad storm there was 2 in of rain in 4 hr.
The rate in lowest terms is_____?
Answer:
1/2 in/hr
Step-by-step explanation:
2 in / 4h = 1/2 inch per hour
Please help i wan't a good grade but I can't figure this out.
Answer:
angle DCE
Angle DEC
Angle ABF
Step-by-step explanation:
you had the wrong order
A 22° B 54° С What is the measure of AD? O 108° 0 27° 126 54°
Answer:
A. 108
sorry if im wrong but if u am I'm so sorry
A store sells a workout outfit that consists of a jacket, a t-shirt, and a pair of shorts. The store purchases the jacket for $34, the t-shirt for $9, and the shorts for $12. The percent of markup is 28%. Find the selling price of the outfit.
PS: include show work please I have to submit this in like 3 hours thankyou
Answer:
The Outfit costs $70.4.
Step-by-step explanation:
Add the selling price together
34 + 9 + 12 = 55
Multiply by the markup (Profit)
100% = 1
28% = 0.28
55 x 1.28 = 70.4
Find the simple interest on the loan of $2500 for 2 years at 5%.
$
(Simplify your answer. Round to the nearest cent as needed.)
Answer:
Step-by-step explanation:
simple interest=prt
p=principle amount
r=rate
t=time
here p=$2500
r=5 %=0.05
t=2 years
simple interest=2500×2×0.05=$250
The simple interest on the loan of $2500 for 2 years at 5% is $250
How to determine the value?The formula for calculating simple interest is expressed as;
I = PRT/100
Such that the parameters of the formula are;
P is the principal amountI is the simple interestR is the interest rateT is the timeNow, substitute the values, we get;
Simple interest = 2500 × 5 × 2/100
Multiply the values
Simple interest =25, 000/100
Simple interest =$250
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#SPJ2
-0.5(14a - 22) = ? this for my work, please help me.
Answer:
-7a+11
Step-by-step explanation:
A data set is normally distributed with a mean of 8.1 and a standard deviation of 3.8.
What percentage of the data is above 8.6?
Enter your answer as a number to the nearest whole percentage, like this: 42%
Answer:
45%
Step-by-step explanation:
Your graphing calculator, statistics app, or spreadsheet can tell you that 45% of the normally-distributed data is above 8.6 when the mean is 8.1 and the standard deviation is 3.8.
CAN SOMEONE HELP PLS?? I rlly dont get this.
The little square on the angle means that the entire angle is 90 degrees
The larger angle is made up of two angles of measure 'x - 18' and 'x'
Let's put that into an equation form:
(x - 18) + (x) = 90
2x - 18 = 90
2x = 108
x = 54
So x = 54
Hope that helps!
help me please mark U as BRAINLIEST
Hope this helps. Good luck
How do you solve this?
2sinXcosX=sinX
The equation representa Function A and the graph represents Function B
Answer:
D) Slope of Funcation B = - Slope of Function A
Step-by-step explanation:
The equation for the line is:
y=mx+b
Where m is the slope and b is the y-intercept
In this question, we are only interested in the slope.
For function A, we can see that the equation is f(x) = -2x + 1
Going back to the equation, we can see that -2 is the slope
Now for function B, we need to find the slope by looking at the graph.
To do this, you need to remember that the slope is y/x, or rise over run. (This is saying that every time the y happens, the x also happens. For example, if the slope is 1/2, every time the line goes up 1 unit, it goes to the right 2 units)
So for the function, we can see that when you move to the right 1 unit (run), you also move up 2 units (rise), so the slope would be
2
Comparing the slope of both the functions
Function A is -2
and
Function B is 2
So the answer is D
Kaya rented a limousinefor prom. There was a one-time charge of $100 plus an hourly rate of $50 per hour. Her
total cost for the night was $300. How many hours did she rent the limo?
Answer using 2 step equations and X as variable
What is the range of this data set?
36.6, 39.8, 33.3, 34.8, 35.8, 39.6, 36.7, 36.9, 37.5, 32.2, 33.1, 33.3
Answer:
Step-by-step explanation:
39.8 - 32.2 = 7.6
Range is subtracting the highest and lowest numbers by each other .
Based on the calculations, the range for this data set is equal to 7.6.
What is a range?In Mathematics, a range can be defined as the difference between the highest number and the lowest number contained in a data set.
Mathematically, range is calculated by using this formula;
Range = Highest number - Lowest number
From the given data set, we have:
Highest number = 39.8.Lowest number = 32.2.Substituting the given parameters into the formula, we have;
Range = 39.8 - 32.2
Range = 7.6.
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What angles are acute GFE mlk dbc dba
Answer:
d and a
Step-by-step explanation:
an acute is an angle less than 90 degrees. a 90 degree angle is a right angle (klm) the only 2 angles smaller than (klm) are (gfe) and (dba)
A very slow man walks
20 cm.in 0.5 left, what his
velocity in meter per second?
135.99 rounded to two significant figures
Answer:
1.3×10^1
Step-by-step explanation:
For this, you need to use scientific notation
First, let's round up the decimal points
135.99 = ~ 136
1.3 ×.10^1