The graph of f(x) is stretched vertically by scale factor 3 and translated 2 units to the right to give the graph of 3f(x - 2)²
Step-by-step explanation:
Let us revise the vertical stretch and the horizontal translation
A vertical stretching is the stretching of the graph away from the x-axis If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched by multiplying each of its y-coordinates by k.If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h) If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)∵ f(x) = x²
∵ f(x) is multiplied by 3
- 3 is greater than 1, then the graph of f(x) is stretched vertically
by scale factor 3
∴ The graph of f(x) is stretched vertically by scale factor 3
∵ x² is changed to (x - 2)²
- That means the graph of f(x) translated 2 units to the right
∴ The graph of f(x) is translated 2 units to the right
The graph of f(x) is stretched vertically by scale factor 3 and translated 2 units to the right to give the graph of 3f(x - 2)²
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Jill babysits and earns y dollars at a rate of $8 per
hour plus a $5 transportation fee. Samantha
babysits and earns 2y dollars at $16 per hour plus
a $10 transportation fee. Write a system of equations
and graph to determine the number of hours each needs
to babysit to earn the same amount of money.
There are 3 dollars per hour per babysitting job for they will get the same amount.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Jill babysits and makes x dollars per hour plus a $5 transportation charge. Samantha babysits and makes two thousand dollars per hour extra transportation cost of $10
As per the given question, the required system of equations would be as:
Jill: y = 8 - 5
8- 5 = 3
y = 3 dollars per hr per babysitting job
Samantha: 2y = 16 -10
2y = 6
2/2 = 6/2
3 dollars per hr per babysitting job
They will get the same amount regardless of how many hours they babysit
Thus, there are 3 dollars per hour per babysitting job for they will get the same amount.
Learn more about the equation here:
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A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 30 books and each large box can hold 40 books. There were twice as many large boxes sent as small boxes, which altogether can hold 330 books. Determine the number of small boxes sent and the number of large boxes sent.
Answer:
Step-by-step explanation:
x = small box and y = large box
30x + 40y = 330
y = 2x
30x + 40(2x) = 330
30x + 80x = 330
110x = 330
x = 330/110
x = 3 <===== 3 small boxes
y = 2x
y = 2(3)
y = 6 <=== 6 large boxes
check...
30x + 40y = 330
30(3) + 40(6) = 330
90 + 240 = 330
330 = 330 (correct)
Skippy has a total of $10,000 to split between two investments. One account offers 4% simple interest, and the other account offers 8% simple interest. For tax reasons, he can only earn $500 in interest the entire year. How much money should Skippy invest in each account to earn $500 in interest for the year
Skippy should invest $ 7500 in account offering 4 % interest and $ 2500 in account offering 8 % simple interest
Solution:
Given that Skippy has a total of $10,000 to split between two investments
One account offers 4% simple interest, and the other account offers 8% simple interest
Total interest earned = 500
Number of years = 1
Let the principal with rate of interest 4 % is x
So the principal for rate of interest 8 % is 10000 - x
Total interest earned = simple interest for 4 % interest + simple interest for 8 % interest
Simple interest is given as:
[tex]S.I = \frac{pnr}{100}[/tex]
Where "p" is the principal and "r" is the rate of interest and "n" is the number of years
Therefore,
[tex]\text{ Total interest earned } = \frac{x \times 1 \times 4}{100} + \frac{10000-x \times 1 \times 8}{100}[/tex]
[tex]500 = 0.04x + (10000 - x)0.08\\\\500 = 0.04x + 800 - 0.08x\\\\-300 = -0.04x\\\\x = 7500[/tex]
Therefore skippy should invest $ 7500 in account offering 4 % interest
And skippy should invest (10000 - x) = (10000 - 7500) = $ 2500 in account offering 8 % interest
There are twice as many boys as girls in Mr.Brown's first period Algebra class. the class is 24 students total. How many more boys than girls are in the class?
explanation needed.
HERE'S YOUR ANSWER:
Let number of girls be- x
and number of boys be- 2x(boys are 2 times NO. of girls)
therefore
x + 2x = 24
3x = 24
x = 24/3
x = 8
hence number of girls = 8
boys are 2 times more than girls = 16
HOPE IT HELPS...
HI. Can you help???
The table shows the total distance a spider traveled after a light was turned on.
Between which two consecutive times was the average rate of change the greatest?
Question 3 options:
A. between Second 11 and Second 15
B.between Second 19 and Second 28
C. between Second 5 and Second 11
D.between Second 15 and Second 19
Answer:
The maximum rate of change is between second 15 and second 19.
Step-by-step explanation:
See the attached table.
The table shows the total distance a spider traveled after a light was turned on.
Now, the average rate of change between two consecutive times in the table is given by
= [tex]\frac{\textrm {Total change in Distance in feet}}{\textrm {Total change in Time in seconds }}[/tex]
Therefore, between second 5 and second 11, the average rate of change = [tex]\frac{7 - 4}{11 - 5} = 0.5[/tex]
Between second 11 and second 15, the average rate of change = [tex]\frac{13 - 7}{15 - 11} = 1.5[/tex]
Between second 15 and second 19, the average rate of change = [tex]\frac{20 - 13}{19 - 15} = 1.75[/tex]
Between second 19 and second 28, the average rate of change = [tex]\frac{24 - 20}{28 - 19} = 0.44[/tex]
Therefore, the maximum rate of change is between second 15 and second 19. (Answer)
- What is the percent of increase from 5,000 to 8.000?
Answer:
increase is 37.5%
Step-by-step explanation:
3000/8000 *100= 37.5%
What is measure of angle D?
pls provide explanation
The sum of 3 consecutive even numbers is 408. What is the largest of the numbers
Answer: 138
Step-by-step explanation:
Let the first number be x , the second number be x + 2 and the third number be x + 4 since they are consecutive even numbers.
Their sum implies:
x + x + 2 + x + 4 = 408
3x + 6 = 408
subtract 6 from both sides
3x + 6 - 6 = 408 - 6
3x = 402
divide through by 3
3x/3 = 402/3
Therefore x = 134.
The numbers are :
134 , 136 and 138 , this means that the largest number is 138
Selecto two ratios that are equivalent to 3:12
Answer:
1 : 4 and 6 : 24
Step-by-step explanation:
We can generate equivalent ratios by dividing or multiplying each part of the ratio by the same value
Divide both parts by 3 , then
3 : 12 = 1 : 4 ← in simplest form
Multiply both parts by 2
3 : 12 = 6 : 24
dolphin is 30 feet below the surface of the water. She rises 23 feet, sinks 17 feet, and finally rises another 27 feet. If there are no other changes, the dolphin is
Answer:
Dolphin is 3 feet above the surface of the water.
Step-by-step explanation:
Dolphin is 30 feet below the surface of the water, then its position on the vertical number line is -30.
She rises 23 feet - add 23, sinks 17 feet - subtract 17, and finally rises another 27 feet - add 27.Thus,
[tex]-30+23-17+27\\ \\=(-30-17)+(23+27)\\ \\=-47+50\\ \\=3[/tex]
Dolphin is 3 feet above the surface of the water.
Final answer:
After a series of movements, the calculated final position of the dolphin is 3 feet above the surface of the water, which is a reasonable result for a dolphin.
Explanation:
The question involves calculating the final position of a dolphin relative to the water surface after a series of vertical movements (rising and sinking). Initially, the dolphin is 30 feet below the surface. Then, the following movements occur:
The dolphin rises 23 feet.
The dolphin sinks 17 feet.
The dolphin rises another 27 feet.
To find out where the dolphin is relative to the surface after these movements, we can sum the changes in position:
Initial position: -30 feet (below the surface is considered negative)
+ Rise 23 feet: -30 + 23 = -7 feet
+ Sink 17 feet: -7 - 17 = -24 feet
+ Rise 27 feet: -24 + 27 = +3 feet
After calculating these movements, the dolphin is 3 feet above the surface of the water. Dolphins are known to be able to jump several times their length out of the water, and considering they measure about 2 meters long, this result of the dolphin being 3 feet above the water is reasonable.
Simplify the expression with distributive property: 8 ( x + 3 )
Answer:
8x+24
Step-by-step explanation:
8(x+3)=8x+24
The graph represents the function f(x) = x2 + 3x + 2. If g(x) is the reflection of f(x) across the x-axis, g(x) = . (Write the function in standard form. Use ^ to indicate an exponent.) Reset Next
Answer:
g(x) = - (x² + 3x + 2) = - x² - 3x - 2
Step-by-step explanation:
The graph represents the function f(x) = x² + 3x + 2.
Now, g(x) is the function which is obtained by reflecting f(x) across the x-axis.
While a graph of a function reflects across x-axis then its y-values will change sign for a fixed value of x.
Therefore, the function g(x) will be given by
g(x) = - (x² + 3x + 2) = - x² - 3x - 2 (Answer)
Can someone please help. It’s fine if the answer not correct at least you tried. But could anyone help because I can’t figure out the answer
WAR is given as 57 degrees.
If you draw a line from W to R, the angle WRA would also be 57 degrees.
57 + 57 = 114
The measure of AR = 180 -114 = 66 degrees.
Answer:
66.
Step-by-step explanation:
If You See W.And R., They Are The Same Angle's, So If They Are Little And Big At The Same Time, You Can Notice It Will Be 66* :)
Tell Me If You Have Any Problomes With These!!!!
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Aiko types at a rate of 70 words per minute.
After typing at the same rate for 3 minutes, he had typed a total of 210 words.
This situation can be represented with a linear equation written in point-slope form, where x represents the number of minutes and y represents the number of words.
Use this information to complete each statement about the linear equation.
The slope of the linear equation is ____
One point on the graph of a linear equation will be ___
This linear equation can be written as ____
In this question, we're trying to make an equation for the given scenario and answer a couple of leading questions.
We know that Aiko types at a rate of 70 words per minute
We would represent this as 70x
x = minutes
We are also given more information that he types 210 words in 3 minutes, that still follows our "70x" scenario.
So our equation would be:
y = 70x
The slope of the linear equation would be 70 or 70/1
The slope would be 70 because this is the change that's happening each minute.
A point on a graph would be at (1 , 70)
You would put this equation into a graph, and you would grab a point that's on the linear line. I'll insert a picture of the graph
The linear equation would be written as: y = 70x
The beginning point would be at 0, since Aiko doesn't type anything for 0 minutes.
Answer:
1 The slope of the linear equation is 70
2 One point on the graph of a linear equation will be 3, 210
3,This linear equation can be written as y-210=70(x-3)
Step-by-step explanation:
The adjoining figure is the figure of two pillars
mounted a squared pyramid on the top. Find the
total cost of tiling the pillars at the rate of
Rs 52 per square feet.
Answer:
[tex]Rs\ 4,296[/tex]
Step-by-step explanation:
step 1
Find out the lateral area of the pillars
we know that
The lateral area of a rectangular prism is equal to
[tex]LA=PH[/tex]
where
P is the perimeter of the base
H is the height of the prism
Determine the perimeter of the base
[tex]P=4(1)=4\ ft[/tex] ----> is a square base
[tex]H=6\ ft[/tex]
The lateral area is equal to
[tex]LA=4(6)=24\ ft^2[/tex]
Remember that the number of pillars is 2
so
[tex]LA=2(24)=48\ ft^2[/tex]
step 2
Find the cost of tiling the pillars at the rate of Rs 52 per square feet
Multiply the lateral area of the two pillars by the rate
so
[tex]48(52)=Rs\ 4,296[/tex]
A geometry student says; "I got lost in that lesson - I wrote down that AD/AB = AC/AB but I have no idea
where it comes from."
Which of the following should have been the proportion that the student wrote?
answer choices:
a) AD/AB=AB/AC
b) AD/AC=AB/AB
c) AB/AD=AB/AC
d) AB/AC=AB/AD
Answer:
Therefore the choice is
a) AD/AB=AB/AC
Step-by-step explanation:
In Δ ADB and Δ ABC
∠A ≅ ∠A …………..{Reflexive Property}
∠ ADB ≅ ∠ ABC ..............{ measure of each angle is 90° given }
Δ ADB ~ Δ ABC ….{Angle-Angle Similarity test}
If two triangles are similar then their sides are in proportion.
[tex]\frac{AD}{AB} =\frac{AB}{AC}\ \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]
Therefore the choice is
a) AD/AB=AB/AC
Answer:
Therefore the choice is
a) AD/AB=AB/AC
Step-by-step explanation:
In Δ ADB and Δ ABC
∠A ≅ ∠A …………..{Reflexive Property}
∠ ADB ≅ ∠ ABC ..............{ measure of each angle is 90° given }
Δ ADB ~ Δ ABC ….{Angle-Angle Similarity test}
If two triangles are similar then their sides are in proportion.
Therefore the choice is
a) AD/AB=AB/AC
In December one artificial Christmas tree cost $159. In January the same tree cost $62. Find the percent of decrease to the nearest whole percent.
Answer:
[tex]61\%[/tex]
Step-by-step explanation:
Cost in December[tex]=\$159[/tex]
Cost in January[tex]=\$62[/tex]
Total decrease in the cost[tex]=159-62=\$97[/tex]
[tex]Percentage\ decrease=\frac{97}{159}\times100\\\\=61.006\approx 61\%[/tex]
I bought 6 and 1/2 pounds of potatoes from the local supermarket for a total price of $5.20 write an equation that would give the total cost of any amount of potatoes in pounds
Answer:
x - 0.8y
Step-by-step explanation:
5.20/6.5 = $0.80 per pound
x = total cost of potatoes
y = number of potatoes
x = 0.8y
a company makes concrete bricks shaped like rectangular prisms. Each brick is 10 inches long, 6 inches wide, and 4inches tall. If they used 13,200 cubic inches of concrete, how many bricks did they make?
Answer:
55
Step-by-step explanation:
Volume of a rectangular prism is width time length times height.
V = WLH
The volume of each brick is:
V = (6 in) (10 in) (4 in)
V = 240 in³
The total volume is 13,200 in³, so the number of bricks is:
13,200 in³ / 240 in³ = 55
3. Which polynomial is equal to
(-3x2 + 2x - 3) subtracted from
(x3 - x² + 3x)?
A 2x² + 2x² + x -
B-2x² + 2x² + x + 3
C x² + 2x² +
x3
Dx² + 2? + x + 3
X
Which polynomial is equal to (-3x^2 + 2x - 3) subtracted from (x^3 - x^2 + 3x)?
Answer:The polynomial equal to (-3x^2 + 2x - 3) subtracted from (x^3 - x^2 + 3x) is [tex]x^3 + 2x^2 + x + 3[/tex]
Solution:Given that two polynomials are: [tex](-3x^2 + 2x - 3)[/tex] and [tex](x^3 - x^2 + 3x)[/tex]
We have to find the result when [tex](-3x^2 + 2x - 3)[/tex] is subtracted from [tex](x^3 - x^2 + 3x)[/tex]
In basic arithmetic operations,
when "a" is subtracted from "b" , the result is b - a
Similarly,
When [tex](-3x^2 + 2x - 3)[/tex] is subtracted from [tex](x^3 - x^2 + 3x)[/tex] , the result is:
[tex]\rightarrow (x^3 - x^2 + 3x) - (-3x^2 + 2x - 3)[/tex]
Let us solve the above expression
There are two simple rules to remember:
When you multiply a negative number by a positive number then the product is always negative. When you multiply two negative numbers or two positive numbers then the product is always positive.So the above expression becomes:
[tex]\rightarrow (x^3 - x^2 + 3x) + 3x^2 -2x + 3[/tex]
Removing the brackets we get,
[tex]\rightarrow x^3 - x^2 + 3x + 3x^2 -2x + 3[/tex]
Combining the like terms,
[tex]\rightarrow x^3 -x^2 + 3x^2 + 3x - 2x + 3[/tex]
[tex]\rightarrow x^3 + 2x^2 + x + 3[/tex]
Thus the resulting polynomial is found
Using the pencil, plot the point (2, -4).
Answer:
Please see pic
Step-by-step explanation:
Go two places to the right (on x axis), then four places down (on y axis)
Sorry it would not let me attach a pic
Which number belongs in the whole numbers area of the diagram?
A) −15
B) 1.5
C) 12
D) 7/8
Answer:
the answer is C) 12
Step-by-step explanation:
rawr
How do you solve -3x+28=10
Answer: x = 6
Step-by-step explanation: To solve for x, we must first isolate the term containing x which in this problem is -3x.
Since 28 is being added to -3x, we subtract 28 from both sides of the equation to isolate the -3x. On the left, the +28 and -28 cancel out and on the right 10 - 28 is -18 so we have -3x = -18.
Now we can finish things off by just dividing both sides of the equation by -3. On the left the -3's cancel and we have x. On the right, -18 divided by -3 is 6 so we have x = 6 which is the solution to our equation.
You divide two numbers and the quotient is 2.5. What might the two numbers be? Show at least 5 solutions.
Answer:
5/2
Step-by-step explanation:
Hi again, This is the last time I annoy you guys with this, but I really need help with my last question.
It would have a greater slope and perhaps start higher on the y axis.
Step-by-step explanation:
I assume you can choose your own numbers as long as they are higher than the current. This means the numbers on your y axis will change but not the numbers on your x axis because that determines the time. So let's change the y axis numbers from going by 20 and make them go by 25. You could technically keep the dots in the same place as long as you change the y axis numbers because you are still earning more money.
a chef cooks 9 lbs of chicken for 36 people and 17 lbs of chicken for 68 people
Answer:
[tex]\frac{1}{4} lbs/person[/tex]
Step-by-step explanation:
Here is the complete question: Find the rate of change for the situation:
A chef cooks 9 lbs of chicken for 36 people and 17 lbs of chicken for 68 people.
Given: 1st situation, A chef cook 9 lbs chicken for 36 people.
2nd situation, chef cook 17 lbs chicken for 68 people.
∴ 1st situation, weight of chicken per person= [tex]\frac{9\ lbs}{36\ person} = \frac{9}{36}[/tex]
Weight of chicken per person= [tex]\frac{1}{4} lbs/ person[/tex]
2nd situation, weight of chicken per person= [tex]\frac{17\ lbs}{68\ person} = \frac{17}{68}[/tex]
Weight of chicken per person= [tex]\frac{1}{4} lbs/ person[/tex]
In both the situation chef cook same amount of chicken per person, which is [tex]\frac{1}{4} lbs/ person[/tex]
∴ Rate of change is [tex]\frac{1}{4} lbs/ person[/tex]
Answer:
i guess 1/4
Step-by-step explanation:
Anwser themm!!!!!! HELP ASAP MATH
Answer:
Please see the detailed answers below:
Step-by-step explanation:
Solution 1:
Sandwich = $9.25
Salad = $4.35
Tax = 7.5%
=> ($9.25 + $4.35) x 7.5 / 100 = 13.6 x 0.075 = $1.02
The amount of Tax on Veena's meal is $1.02
Solution 2:
Book read by Christian = (1/4) / (2/3) = (1/4) x (3/2) = 3/8
Christian will read 3/8 books per week.
Solution 3:
Sale Price = (100 - Discount Rate) x Cost Price
Let Y = Sale Price
By Putting the values in above equation:
Y = (100 - 45) x $650
Y = 0.55 x $650
Y = $357.5
Hence the Sale Price of the bicycle will be $357.5
Solution 4:
Percent error = [(Experimental Value - Accepted Value) / Accepted Value] x 100
Percent error = [(15.5 - 14.5) / 14.5] x 100
Percent error = [1 / 14.5] x 100
Percent error = 2.2%
Hence the percent error in Mark's estimate is 2.2%
consider this scatter plot. you which line best fits the data
Answer:
line c
Step-by-step explanation:
What is the value of log 43? Use the calculator. Round your answer to the nearest tenth.
Answer:
The value of log 43is 1.633
Step-by-step explanation:
Explanation:
Suppose you know that:
[tex]\begin{array}{l}{\log 2 \approx 0.30103} \\{\log 3 \approx 0.47712}\end{array}[/tex]
Then note that:
[tex]43=\frac{129}{3} \approx \frac{128}{3}=\frac{2^{7}}{3}[/tex]
So
[tex]\log 43 \approx \log \left(\frac{2^{7}}{3}\right)=7 \log 2-\log 3 \approx 7 \cdot 0.30103-0.47712=1.63009[/tex]
We know that the error is approximately:
[tex]\log \left(\frac{129}{128}\right)=\log 1.0078125=\frac{\ln 1.0078125}{\ln 10} \approx 0.00782 .3=0.0034[/tex]
So we can confidently give the approximation:
[tex]\log 43 \approx 1.633[/tex]
Answer:
1.6
Step-by-step explanation:
It's 1.633, when you round to the nearest tenth, it's B) 1.6
If x2 = 20, what is the value of x?
Answer:
[tex]x=-2\sqrt5\ and\ x=2\sqrt5[/tex]
Step-by-step explanation:
Given:
The given equation to solve is:
[tex]x^2=20[/tex]
In order to solve the above equation, we take square root on both the sides.
While taking square root on both sides, we must consider both positive and negative values. So, this gives:
[tex]\sqrt{x^2}=\pm\sqrt{20}[/tex]
From the definition of square root function, we have
[tex]\sqrt{a^2}=a[/tex]
Therefore,
[tex]x=\pm\sqrt{20}[/tex]
Now, writing 20 into the product of its prime factors, we have
[tex]20=2^2\times 5[/tex]
Therefore, [tex]x=\pm\sqrt{2^2\times 5}[/tex]
We also know, [tex]\sqrt{a\times b}=\sqrt{a}\times\sqrt{b}[/tex]
So, [tex]\sqrt{2^2\times 5}=\sqrt{2^2}\times \sqrt{5}=2\sqrt5[/tex]
Therefore, [tex]x=\pm2\sqrt5[/tex]
So, there are two values of 'x'. They are:
[tex]x=-2\sqrt5\ and\ x=2\sqrt5[/tex]