After the vertical stretch by factor 3 the function becomes g(x)=3x².
The given function is f(x)=x² is vertically stretched by the factor 3.
When we stretch a function vertically, we multiply the base function by its scale factor. Hence, we have g(x) = 3·f(x). Let’s make sure to distribute 3 to each of the term in f(x).
Here, g(x)=3×x²
g(x)=3x²
Therefore, after the vertical stretch by factor 3 the function becomes g(x)=3x².
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What is the volume of a box that is 16 by 14?
Answer:
I need the length, width, and height
Step-by-step explanation:
hich linear function has the steepest slope?
y = negative 8 x + 5
y minus 9 = negative 2 (x + 1)
y = 7 x minus 3
y + 2 = 6 (x + 10)
The function with the steepest slope is \(y = 7x - 3\).
The correct answer is C.
The linear function with the steepest slope is the one with the highest absolute value for the coefficient of x.
Let's compare the coefficients of x in each of the given functions:
\(y = -8x + 5\)
Slope: -8
\(y - 9 = -2(x + 1)\)
Simplifying, we get \(y - 9 = -2x - 2\)
Rearranging, we have \(y = -2x + 7\)
Slope: -2
\(y = 7x - 3\)
Slope: 7
\(y + 2 = 6(x + 10)\)
Simplifying, we get \(y + 2 = 6x + 60\)
Rearranging, we have \(y = 6x + 58\)
Slope: 6
Therefore, the steepest slope is the \(y = 7x - 3\).
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guys im du.mb help me plz
Answer:
..
...the second one .......
15 points! please help pleasee!
Step-by-step explanation:
the perimeter is the sum of the lengths of all outside sides.
at the top is a triangle.
at the bottom is a rectangle.
the triangle looks like an isoceles triangle (both legs are equal), but the given measurement tells us otherwise.
if it were isoceles, the height would split the baseline into 2 equal halves (20/2 = 10ft).
per Pythagoras the 12 ft Hypotenuse would be
Hypotenuse² = 10² + 10² = 100 + 100 = 200
Hypotenuse = sqrt(200) = 14.14213562... and NOT 12 ft.
so, we need to calculate the actual part of the 20ft baseline (again Pythagoras) :
12² = 10² + part²
144 = 100 + part²
44 = part²
part = sqrt(44) = 6.633249581... ft
that means the 2nd part of the baseline is
20 - 6.633249581... = 13.36675042... ft
and we get the second leg of the large triangle again via Pythagoras :
leg² = 10² + 13.36675042...² = 100 + 178.6700168...
leg² = 278.6700168...
leg = sqrt(278.6700168...) = 16.69341238... ft
we need to sum up both legs of the triangle, 2 widths and one length of the rectangle, as the triangle base line and the second length of the rectangle cover each other up, and are not visible to the outside of the combined object.
P = 12 + 16.69341238... + 8 + 8 + 20 = 64.69341238... ft ≈
≈ 64.69 ft
risms
gure.
The rectangular prism has
✓ lateral faces.
The rectangular prism has a surface area of
square inches.
Answer:
4 lateral faces
254 square inches
Answer:
The one above is right just did it on edge.
Step-by-step explanation:
what is the value of 5 in the number 124.519 write your answer as a fraction
Answer:
5/10 or 1/2
Step-by-step explanation:
1=hundreds
2=tens
4=units
.
5=tenths
1=hundredths
9=units
The value of 5 in the given decimal number is \(\frac{5}{10}\)
Given :
A decimal number 124.519
In the given number 5 is in tenth place
Lets expand the number and check
\(124.519\\1 \cdot 100+2\cdot 10+4+5\cdot \frac{1}{10} +9\cdot \frac{1}{100}\)
now we look at the value of 5 in the given decimal number
\(5\cdot \frac{1}{10} \\\\ \frac{5}{10} \\ \frac{1}{2}\)
The value of 5 in the given decimal number is 5/10
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2. Kurt designs a square flower garden that has the same area as a rectangular one. The length of the rectangular
garden is 10 feet longer than the side of the square garden. The width of the rectangular garden is 5 feet shorter
than the side of the square. Find the side length of the rectangular garden.
low
The side length of the the rectangular garden are 20 feet by 5 feet.
Calculating the size of a Rectangular GardenLet
s = side length of the square garden
l = length of the rectangular garden
w = width of the rectangular garden
From the problem statement,
area of the square garden = area of the rectangular garden
Since the area of a square is just the side length squared, we can write:
s² = l * w
We also know that the length of the rectangular garden is 10 feet longer than the side of the square garden, and that the width of the rectangular garden is 5 feet shorter than the side of the square garden. We can express them as:
l = s + 10
w = s - 5
Now we can substitute these expressions for l and w into our first equation:
s² = (s + 10) * (s - 5)
Expanding the right-hand side, we get:
s² = s² + 5s - 50
0 = 5s - 50
5s = 50
Dividing both sides by 5, we get:
s = 10
Since the side length of the square garden is 10 feet.
We can use this to find the dimensions of the rectangular garden:
l = s + 10 = 10 + 10 = 20
w = s - 5 = 10 - 5 = 5
So the dimensions of the rectangular garden are 20 feet by 5 feet.
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4 to the 3 power, x 4 to the 4th power, divide by 4 to the 9th power
Answer:
We can simplify the expression as follows:
4^3 * 4^4 / 4^9
First, we can simplify the terms in the numerator by adding the exponents of 4:
4^3 * 4^4 = 4^(3+4) = 4^7
Now, we can substitute this value in the expression:
4^7 / 4^9
To divide powers with the same base, we can subtract their exponents:
4^(7-9) = 4^(-2)
Therefore, the simplified expression is:
4^3 * 4^4 / 4^9 = 4^(-2)
So, the final answer is 1/16 or 0.0625.
6x = 52 − 2y 5x + 7y = 70 Question 1 What is the first step when solving the given system by the elimination method?
The solution of the equations 6x = 52 − 2y and 5x + 7y = 70 by elimination method will be (7, 5).
What is the solution to the equation?In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.
The equations are given below.
6x = 52 - 2y
6x + 2y = 52
3x + y = 26 ...1
5x + 7y = 70
(5/7)x + y = 10 ...2
Subtraction equation 2 from equation 1, then we have
3x - (5/7)x = 26 - 10
(16/7)x = 16
x = 7
Then the value of 'y' is given as,
3(7) + y = 26
21 + y = 26
y = 5
The solution of the equations 6x = 52 − 2y and 5x + 7y = 70 by elimination method will be (7, 5).
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Pls help I will give out points and make u the Brainly
Answer:
x=4
Step-by-step explanation:
thats the answer ^^
Answer:
its the second one
Evaluate the expression
[3(15+4)2 +2(20+5)2]0
0
5
1
2
0, 5, 5, 1, 2
is evaluate
Please tell me how much it would be for 1
Answer: tall is 12 dollars
Step-by-step explanation:
Solve 3^5x=10
HELP PLS
Answer:
x = 10/243
Step-by-step explanation:
3^5x = 10
243x = 10
Divide 243 on both sides
10/243
I don't need help but I am giving the answer to everyone :) hope it helps
The number of cannonballs in illustration is 506.
What is illustration?Math Illustrations enables you to produce more useful geometry figures for your students in less time by fusing the constraint-based design of Geometry Expressions with simple-to-use sketching and graphing features.
The number of cannonballs in the first layer = 1² = 1
Number of cannonballs in the second layer = 2² = 4
Number of cannonballs in the third layer = 3² = 9
So, the generalized formula to count the balls is given as
= n(n + 1) (2n + 1)/ 6
Here, n= the total number of layers
Put n =11
11(11 + 1)(2(11) + 1) / 6
= 11(12)(23)/6
= 3036/6
= 506
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Choose the two rectangles that have an area of 24 square centimeters.
slope of line (-3,-2) and (-1,-5)
Answer:
−3/2
Step-by-step explanation:
Hope this helps
:D
A survey found that 31% of all teens buy soda (pop) at least once each week. Seven teens are randomly selected. The random variable represents the number of teens who buy soda (pop) at least once each week. What is the value of n
Answer:
The value of n is 7.
Step-by-step explanation:
For each teen, there are only two possible outcomes. Either they buy soda at least once each week, or they do not. Since they were selected randomly, the teens are independent of each other, which means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
And p is the probability of X happening.
In the binomial distribution, we have that n is the size of the sample. In this question, seven teens are randomly selected, which means that the value of n is 7.
The vertices of a rectangle are W(1, 2) X(4, 2) Y(4, 23) and Z(1, 23) Find the perimeter of the rectangle. Use words, numbers, or models to justify your answer.
The vertices of a rectangle are W(1, 2) X(4, 2) Y(4, 23) and Z(1, 23) Find the perimeter of the rectangle is 16.
Step-by-step explanation:We could use the distance formula to find the distance between the points in this problem, but when we look we see that the sides of the rectangle are parallel to the x and y-axis for each pair of sides. The first two points have a distance of 3 because 4-1=3. Since it is a rectangle, the opposite side will have the same length. For the sides perpendicular, we look at the points with the same x coordinate. Using (4,2) and (4,-3), we can calculate the length of the side by finding the distance by adding the absolute values of the y coordinate. 2+3=5. This means that the triangle has two sides with a length of 5 and two sides with a length of 3. Adding these together, 5+5+3+3 = 16.
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I REALLY NEED HELP , “ a company is designing a new cylindrical water bottle. the volume of the bottle will be 207 cm *to the 3rd power* the height of the water bottle is 8.4 cm. what is the radius of the water bottle?”
Answer:
Radius, r = 2.80 cm
Step-by-step explanation:
Given the following data;
Volume of cylinder = 207 cm³
Height = 8.4 cm
Pie, π = 3.14
To find the radius of the water bottle;
Mathematically, the volume of a cylinder is given by the formula;
V = πr²h
Where;
V is the volume of a cylinder.
r represents the radius of the cylinder.
h represents the height of the cylinder.
Substituting into the formula, we have;
207 = 3.14 * r² * 8.4
207 = 26.376r²
r² = 207/26.376
r² = 7.85
r = √7.85
Radius, r = 2.80 cm
Write sixty-five and three hundredths
a. as a decimal number
as a mixed number
Step-by-step explanation:
answer in decimal form 65.03
answer in mixed number form 65 3/100
HELP PLEASE SHOW STEPS I HAVE NO IDEA WHAT TO DO. I HAVE BEEN TRYING TO FIGURE IT OUT BUT I CAN’T.
Answer: \(x^{2} +23x+49\)
Step-by-step explanation:
To find the area of the shaded region, you must find the area of the larger rectangle [(x+10)×(2x+5)] and subtract the area of the smaller rectangle [(x+1)×(x+1)] from it.
First, you simplify the larger rectangle's area:
(x+10)×(2x+5) = \(2x^{2} +25x+50\)
Then, simplify the smaller rectangle's area:
(x+1)×(x+1) = \(x^{2} +2x+1\)
Finally, subtract the smaller rectangle's area from the larger rectangle's area:
\((2x^{2} +25x+50) - (x^{2} +2x+1) = x^{2} +23x+49\)
Therefore, the final answer is \(x^{2} +23x+49\).
I hope this helps!
\(\text{Area of rectangle}=\text{lengh}\times\text{width}\\\text{Area of square}=\text{side}^2\)
You just need to find differens between rectangle and square
\(\text{lengh}\times\text{width}-\text{side}^2\\\\(x+10)(2x+5)-(x+1)^2=2x^2+5x+20x+50-x^2-2x-1=x^2+23x+49\)
\(x^2+23x+49\:\text{is our answer}\)
A factory that manufactures bolts is performing a quality control experiment. Each object should have a length of no more than
12
centimeters. The factory believes that the length of the bolts exceeds this value and measures the length of
76
bolts. The sample mean bolt length was
12.07
centimeters. The population standard deviation is known to be
σ
=
0.28
centimeters.
What is the test statistic
z
?
What is the
p
-value?
Does sufficient evidence exist that the length of bolts is actually greater than the mean value at a significance level of
α
=
0.1
?
Answer:i dont know
Step-by-step explanation:
PQ and QR are 2 sides of a regular 12-sided polygon
Answer:
Step-by-step explanation:
How do you write the fraction of 6/6 as a sum of fractions in three different ways
Answer:
3/6 + 3/6 | 4/12 + 8/12 | 2.5/6 +3.5/6
Step-by-step explanation:
Anyone’s knows how do this and the answer?
Answer:
12 -16. 19
4. 8. 22
3. -9. -4
Step-by-step explanation:
13-1 = 12
-10-6= -16
12 - -7 = 12+7=19
6-2 = 4
Keep subtracting
Suppose it is certain that an earthquake will occur someday. What is the probability (to the nearest percent) that it will occur while you are at work? Assume you are at work 8 hours per day, 240 days per year.
Answer:
22%
Step-by-step explanation:
Given that:
Number of hours at work daily = 8 hours
Number of days at work per year = 240
Total number of hours at work per year = Number of hours at work daily \(\times\) Number of days at work per year
Total number of hours at work per year = 8 \(\times\) 240 = 1920 hours
Total number of days in an year = 365
Total number of hours per day = 24
Total number of hours in an year = 24 \(\times\) 365 = 8760
Here, to find the probability that the earthquake will occur while the person is at work, we actually have to find the fraction of number of hours at work to the total number of hours in an year.
Therefore, the required probability is:
\(\dfrac{1920}{8760} \approx \bold{0.2191}\)
Therefore the probability to the nearest percent is: 22%
packaging idaho produce company ships potatoes to its distributors in bags whose weights are normally distributed witb. nean weight of 50 pounds and a standard deviation of .5 pounds. if a bag of potatoes is selected at random from a shipment, what is the probability that it weighs more than 51 pounds
The probability that it weighs more than 51 pounds exactly 53 pounds.
Given that, mean weight of 50 pounds and a standard deviation of 0.5 pounds.
We need to find the probability that it weighs more than 51 pounds,
P(X = 53) = 0
z = (51 - 50) / 0.5 = 2.00
P(X > 51) = P(z > 2.00) = 0.0228
z1 = (49 - 50) / 0.5 = -2.00
z2 = (51 - 50) / 0.5 = 2.00
P(49 < X < 51) = P(-2.00 < z < 2.00) = P(z < 2.00) - P(z < -2.00) = 0.9772 - 0.0228 = 0.9544
Hence, the probability that it weighs more than 51 pounds exactly 53 pounds.
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A certain substance in an experiment was being stored at −2.4°F. It was then placed on a table where the temperature was raised by 5.3°F.
What was the new temperature of the substance?
7.7°F
2.9°F
−2.9°F
−7.7°F
Answer:
2.9°F
Step-by-step explanation:
Make Sure you are not putting in -2.9°F
The new temperature of the substance is 2.9°F.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now it is given that,
Temperature of a substance in an experiment = −2.4°F
Raise in temperature when it was placed on a table = 5.3°F
So, the new temperature = Temperature of a substance in an experiment + Raise in temperature when it was placed on a table
⇒ the new temperature = −2.4°F + 5.3°F
⇒ the new temperature = 2.9°F
this is the required new temperature.
Thus, the new temperature of the substance is 2.9°F.
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am I right for part A. And please help me with B
a) The radius of the sphere is given as follows: 27.13 ft.
b) The surface area can be checked as follows: S = 4 x 3.14 x 27.13² = 9244.
How to obtain the surface area?The surface area for a sphere of radius r is given by the equation presented as follows:
S = 4πr².
The surface area for this problem is given as follows:
9244 ft².
Hence the radius is given as follows:
\(r = \sqrt{\frac{9244}{4 \times 3.14}}\)
r = 27.13 ft.
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Asked has saved $27 in bills to buy a bicycle helmet. Which set of bills represent the $27 Aksel has saved?
Answer:
A $20
A $5
And 2 ones.
add them up it =27
Step-by-step explanation: