Let f(x)=25x2−2 .
The function g(x) is a vertical stretch of f(x) by a factor of 2.
What is the equation of g(x)?
Enter your answer in the box.
g(x) =
Answers
We are given function f(x) = 25x^2 -2.
g(x) is a vertical stretch of f(x) by a factor of 2.
We know, the transformation rule
y= k f(x), vertical stretch by a factor k. For k>0.
Because function f(x) is being vertical stretched by a factor of 2. So, we need to multiply f(x) function by 2.
Therefore, g(x) = 2 f(x) = 2*(25x^2-2).
Therefore, g(x) = 2*(25x^2-2) or g(x) = 50x^2-4.
Answer:
The Given function is
f(x)= 25 x² -2
Now, a function g(x) is obtained when the function f(x) is stretched by a factor of 2.
Consider point (x,y) on f(x).When function is stretched vertically by a factor of 2 ,it means, the coordinate changes from (x,y) to (x,2 y).
Since we have to stretch the function as whole, we will multiply original function by 2.
So, g(x)= 2× [25 x² - 2] =50 x² -4
g(x)=50 x²- 4
Related Questions
simplify the expression. write the answer using scientific notation 4(6.2x10^11)
Answers
[tex]4*(6.2*10^{11})[/tex]
What we must do for this case, is to rewrite the expression.
For this, we can use the associative property of multiplication.
We have then that we can rewrite the expression as:
[tex]4*(6.2*10^{11}) = (4*6.2)*10^{11}[/tex]
Finally, by rewriting we have:
[tex](24.8*10^{11})[/tex]
Answer:
the answer using scientific notation is:
[tex](24.8*10^{11})[/tex]
PLEASE HELP! WILL MARK BRAINLIEST!
Answers
5x + 20 - 5 = 3x -18 + 1
combines like terms
5x + 15 = 3x - 17
subtraction properties of equality
2x + 15 = -17
subtraction properties of equality
2x = -32
coefficients: 2 and -32
answer
first one -32 and 2
What is the solution for the system of equations?
Use the substitution method to solve.
2x+y=20−5y=−6x+12
Enter your answer in the boxes.
( , )
Answers
So, y = 6 and x = 7
Answer:
2x+y=20 and -5y=6x+12 are your equations.
You can turn 2x+y=20 into y=-2x+20
Substitute this value of y into the other equation.
-5(-2x+20)=-6x+12
10x-100=-6x+12
16x=112
x=7
Substitute this value of x into the other equation.
2(7)+y=20
y=6
Your answer is x=7 and y=6.
Experimental vs. Theoretical Probability:
John is about to roll a six-sided, fair number cube 60 times. He wants to predict how many times the cube will land on an even number. He makes a prediction of 20 times. Is it a good prediction? What would your prediction be based on theoretical probability?
Answers
To start the numbers 1 through 6 are on a number cube.
Half of them are even, 2, 4, and 6.
So it makes sense that when you roll the cube 60 times, you should have 30 even numbers. The theoretical probability is 30.
A predication of 20 is 10 less than the expected value of 30.
10 out of 30 is 33%.
The predication is off by 33%, I would argue that it is not a very good prediction.
I hope this helps, Good luck!
MrEquation
Answer:
Guy above is correct
Step-by-step explanation:
Please help(:
Two planes intersect to ____ form a line
A. Always
B. Sometimes
C. Never.
D. Inconclusive.
Which of the following is true?
A. All quadrilaterals are polygons with two pairs of parallel sides.
B. All quadrilaterals are polygons with four sides.
C. All quadrilaterals are polygons with at least one pair of parallel sides.
D. All quadrilaterals are polygons with four sides at least one pair of parallel sides.
Answers
Question 1. ALWAYS
Question 2. B. All quadrilaterals are polygons with four sides.
Explanations
Question 1:
When two planes meet they do so forming a line. This is to mean that the point of intersection is always a line.
Question 2:
It is not necessarily for a polygon to have a pair of parallel sides. A regular pentagon is polygon with no pair of parallel sides. So a quadrilateral is a polygon with four sides. The sides don’t have to parallel for it to be a quadrilateral. The correct answer is B.
Answer:
1. Two planes intersect to ALWAYS form a line. If two planes intersect, they intersect in a line. The two planes that do not intersect, they form parallel lines.
2. The true statement is :
All quadrilaterals are polygons with four sides. A quadrilateral is a geometrical shape that has four sides and four angles. These are also called polygons. There are many types of quadrilaterals like - the parallelogram, the rectangle, the square, rhombus etc.
Fan for everyone who helps, medal for whoever helps the most! :)
1. What is the sum of the polynomials?
(m + n + 3) + (m + n + 4)
2. Which expression can be used to find the difference of the polynomials?
(10m – 6) – (7m – 4)
3. Which expression can be used to find the difference of the polynomials?
(4m – 5) – (6m – 7 + 2n),
Answers
Answer:
1- The sum is: 2m + 2n + 7 = 2(m+n) + 7
2- The difference is: 3m - 2
3- The difference is: -2m - 2n + 2 = -2(m+n-1)
Explanation:
Before we begin, remember the following:
+ve * +ve = +ve
-ve * -ve = -ve
+ve * -ve = -ve
-ve * +ve = -ve
Also, remember that, we only add/subtract like terms. There are terms which have the same variable(s) raised to the same degree
Now, let's check the problems:
Problem 1:
Adding two polynomials:
(m + n + 3) + (m + n + 4)
We first start by getting rid of the brackets:
m + n + 3 + m + n + 4
Now, we add like terms:
2m + 2n + 7
As an additional step, we can take 2 as a common factor from the first two terms:
2(m+n) + 7
Problem 2:
Subtracting two polynomials:
(10m - 6) - (7m - 4)
We first start by getting rid of the brackets. Take care of the different signs while doing so:
10m - 6 - 7m + 4
Now, we add/subtract like terms:
3m - 2
Problem 3:
Subtracting two polynomials:
(4m - 5) - (6m - 7 + 2n)
We first start by getting rid of the brackets. Take care of the different signs while doing so:
4m - 5 - 6m + 7 - 2n
Now, we add/subtract like terms:
-2m - 2n + 2
As an additional step, we can take -2 as a common factor from the above expression:
-2(m+n-1)
Hope this helps :)
Which coordinate Gird shows the correct locations of P (1,2.5) Point Q which is a reflection Of point P across the Y-axis And R (2.-2.5)
Answers
"Point Q which is a reflection Of point P across the Y-axis"
Therefore, we have:
Q = (-1, 2.5)
Now we graph each ordered pair.
Note: See attached image.
The probability that it'll rain tomorrow in Ohio is 30%
The probability that it'll rain tomorrow in both Ohio and Alaska is 12%
If it rains tomorrow in Ohio what is the probability that it will rain tomorrow in Alaska?
Answers
For two independent events (let's call them A and B), the Probability of A and B both occurring is given by P(A and B) = P(B) x P(B).
For this problem, let A = rain in Ohio and B= rain in Alaska.
P(A and B) = P(A) x P(B)
[tex] \frac{12}{100} =(P(A))( \frac{3}{10} ) [/tex]
[tex]( \frac{12}{100}) ( \frac{100}{30} )=P(A)[/tex]
[tex]P(A)= \frac{12}{30}= \frac{2}{5} [/tex]
Batteries for an MP3 player usually cost $8.00, but they are on sale for 40% off. What is the discount amount? What is the sale price for these batteries?
Answers
Answer:
its b!
Step-by-step explanation:
discount is $8 = 40/100 to find that discout
is $3.20
sale price : $8.00 - $3.20 which is $4.80!
Your welcome! :D
PLEASE HELP ASAP! BRAINLIEST FOR RIGHT/BEST ANSWER!
Answers
guys i am so confused right now??
Answers
it is right
Circle Area= πr^2
Circle Area= (3.14)(7)^2
CA= (3.14)(49)
C Area = 153.94
This is a half circle so divide by 2:
153.94 ÷ 2= 76.97
Parallelogram Area= base x height
PA= 7 x 6
P Area= 42
Add the two areas together:
76.97 + 42= 118.9
ANSWER: D) 118.9 cm^2
Hope this helps! :)
Subtract 1.05 from a certain number. Multiply the difference by 0.8, add 2.84 to the product then divide the sum by 0.01 and get 700. What is the number?
Answers
The number is 6.25
Explanation:
Assume that the number we are looking for is x
First, we will set up the equations as follows:
1- Subtract 1.05 from the number (assume the result is y):
x - 1.05 = y
2- Multiply the difference by 0.8 (assume the product is z):
0.8(y) = z
3- add 2.84 to the product (assume the result is w):
z + 2.84 = w
4- divide the sum by 0.01, the quotient is 700:
w / 0.01 = 700
Now, we will work backwards as follows:
4) w / 0.01 = 700
w = 0.01 * 700
w = 7
3) z + 2.84 = w
z + 2.84 = 7
z = 7 - 2.84
z = 4.16
2) 0.8y = z
0.8y = 4.16
y = 4.16 / 0.8
y = 5.2
1) x - 1.05 = y
x - 1.05 = 5.2
x = 5.2 + 1.05
x = 6.25
Hope this helps :)
Here's the solution for this,
{(x-1.05).08}+2.84 = 700
.01
0.8x-0.84+2.84 = 700
.01
0.8x + 2 = 700
.01
0.8x + 2 =700 x 0.01
0.8x = 7 - 2
0.8x = 5
0.8 .08
The answer would be 6.25
Question 1. Evaluate 4 times a number q plus 25 when q=2
A. 27
B.31
C.33
D.42
Question 2. If p=8, evaluate 4 )2 / 9.3
A.2
B.3
C.6
D. 8
Question 3. If q=2, evaluate (24 + 18 .q) - (5q + 7)
A. 38
B. 79
C. 31
D. 21,
Answers
Two cones have the same radii but one has a height four times larger than the other. How many small cones would be needed in order to have the same volume as the larger cone?
4
8
16
64
Answers
In this case the volume of the larger cone would be 4 times as large as the smaller cone so you would need 4 small cones
Which figure shows the correct dimensions of a 14 scale drawing of the given figure?
Answers
we know that
the given figure is 20x48
the correct dimensions of a 1/4 scale drawing of the given figure is
(1/4)*20--------> 5
and
(1/4)*48--------> 12
therefore
the correct dimensions are 5x12
the answer is the option B) 5x12
hat is the volume of this prism?
Rectangular prism composed of unit cubes. Prism is 6 units by 9 units by 7 units.
-----units3
Answers
Two angles that are supplementary have a ratio of 7 to 5. what are their measurements?
Answers
12x = 180
x = 15
Therefore, the 2 angles equal (7*15) and (5*15) which equals
105 degrees and 75 degrees
Given the function f(x) = 0.5(3)x, what is the value of f−1(7)?
This question has been asked before but the answer is unclear to me.
Answers
[tex]\bf \stackrel{f(x)}{y}=0.5(3)^x\qquad \stackrel{inverse}{\boxed{x}=0.5(3)^{\boxed{y}}} \\\\\\ log(x)=log[0.5(3)^y]\implies log(x)=log(0.5)+log[(3)^y] \\\\\\ log(x)-log(0.5)=log[(3)^y]\implies log(x)-log(0.5)=y\cdot log(3) \\\\\\ \cfrac{log(x)-log(0.5)}{log(3)}=\stackrel{f^{-1}(x)}{y}\\\\ -------------------------------\\\\ f^{-1}(7)=\cfrac{log(7)-log(0.5)}{log(3)}\implies f^{-1}(7)\approx 2.402173502732879697[/tex]
A sphere has a radius of 4x + 1. Which polynomial in standard form best describes the total surface area of the sphere? Use the formula S = 4pir2 for the surface area of a sphere.
Answers
area = pi * (64x² + 32x + 4)
Using pi = 3.14:
area = 200.96 x² + 100.48 x + 12.56
Explanation:
We are given that:
area of sphere = 4 * pi * r²
radius = 4x + 1
Substitute with the radius in the given formula to get the area as follows:
area = 4 * pi * (4x+1)²
area = 4 * pi * (16x² + 8x + 1)
area = pi * (64x² + 32x + 4)
Using pi = 3.14:
area = 200.96 x² + 100.48 x + 12.56
Hope this helps :)
What is the area of a sector with a central angle of 2pi/9 radians and a diameter of 20.6mm? Use 3.14 for Ali and round your answer to the nearest hundredth.
Answers
A=πr²
A is the area of the circle.
π=3.14
r is the radius of the circle.
- To calculate the area of the sector indicated in the problem, you must apply the following formula:
As=(θ/2π)πr²
As is the area of the sector.
θ is the central angle (θ=2π/9)
π=3.14
r is the radius.
- First, you must find the radius:
r=Diameter/2
r=20.6 mm/2
r=10.3 mm
- Now, you can substitute the values into the formula As=(θ/2π)πr². Then, you have:
As=(θ/2π)πr²
As=(2π/9/2π)(π)(10.3)²
As=(π/9π)(π)(10.3)²
As=(3.14/9x3.14)(3.14)(10.3)²
- Finally, the area of the sector is:
As= 37.01 mm²
The area of the sector rounded to the nearest hundredth is [tex]$37.02 \, \text{mm}^2$[/tex].
To find the area of a sector, we use the formula:
[tex]\[ \text{Area of sector} = \frac{\text{Central angle}}{2\pi} \times \pi r^2 \][/tex]
Given that the central angle is [tex]\( \frac{2\pi}{9} \)[/tex] radians and the diameter (which is twice the radius) is [tex]$20.6 \, \text{mm}$[/tex], the radius is [tex]\( \frac{20.6 \, \text{mm}}{2} = 10.3 \, \text{mm} \)[/tex].
Now, substituting these values into the formula:
[tex]\[ \text{Area of sector} = \frac{\frac{2\pi}{9}}{2\pi} \times \pi (10.3)^2 \][/tex]
[tex]\[ = \frac{1}{9} \times \pi \times 10.3^2 \][/tex]
[tex]\[ = \frac{1}{9} \times 3.14 \times 106.09 \][/tex]
[tex]\[ = \frac{1}{9} \times 333.2086 \][/tex]
[tex]\[ \approx 37.02 \, \text{mm}^2 \][/tex]
Rounded to the nearest hundredth, the area of the sector is approximately [tex]$37.02 \, \text{mm}^2$[/tex].
Jake runs either 15 kilometers or 8,500 meters each day.He alternates short and long runs. how many meters farther will he run on his two long run days than on his two short run days?Describe how you found your answer
Answers
1. The answer must be expressed in meters, so, you have to convert 15 kilometers to meters:
1 kilometer------1,000 meters
15 kilometers---x=
x=15x1000/1
x=15,000 meters
2. Then, you have:
On his two long run days=(15,000 meters)(2)=30,000 meters
On his two short run days=(8,500 meters)(2)=17,000 meters
3. Finally, you obtain:
30,000 meters-17,000 meters=13,000 meters
How many meters farther will he run on his two long run days than on his two short run days?
The answer is: 13,000 meters
[tex](15km)( \frac{1000m}{1km} )=15000km[/tex]
We now now that the ditance he covers in his long run days is [tex]15000m[/tex], and in his short run is [tex]8.5km[/tex].
Lets find out the distance he will cover on his two long run days:
[tex]2(15000m)=30000m[/tex]
Likewise, lets find the distance he will cover in his short run days:
[tex]2(8500m)=17000m[/tex]
Now, we just need to find the difference between the tow distances:
[tex]30000m-17000m=13000m[/tex]
We can conclude that we will run 13,000 meters further in his long runs than in his short runs.
Please help
According to Cavalieri's principle,
A) the volume of the sphere is equal to the volume of the cones.
B) the volume of the sphere is equal to the volume of the cylinder.
C) the volume of the sphere is equal to two times the volume of the cones.
D) the volume of the sphere is equal to the volume of the solid between the cones and the cylinder.
Answers
Answer:
Step-by-step explanation:
The answer is d.
Answer:
d
Step-by-step explanation:
Jason draws an angle and then places the compass on the vertex and draws arc that intersects both rays. He then places the compass on each intersecting mark on each ray and draws arcs that intersect inside the angle. Which construction is he creating?
A. copying an angle
B. angle bisector
C. perpendicular bisector
D. perpendicular line through vertex of angle
Answers
How to find out how much you pay if there was a sale tax?
Answers
Consider the functions f(x) = (4/5)^x and g(x) = (4/5)^x + 6. What are the ranges of the two functions?
f(x): {y| y > _____}
g(x): {y| y > _____}
(Fill in the blank with the correct answer)
Answers
The number 0 goes in the first blank for f(x)
The number 6 goes in the second blank for g(x)
----------------------------------------------------------------------------------
Explanation:
As x gets larger and larger, the expression (4/5)^x will get smaller and smaller. What's going on is that we are repeatedly multiplying (4/5) with itself over and over if we assume x is some whole number. For example, if x = 100, then we'll have 100 copies of (4/5) multiplied out. Each time we multiply by (4/5), the result gets smaller.
The results will approach 0 but not actually get there. So this is why f(x) has the horizontal asymptote y = 0. The function values f(x) will essentially be the set of positive y values, in other words, y > 0. This covers the range for f(x). To get the range of g(x), we add 6 to the range of f(x). This is because everything on g(x) is a vertical shift upward of 6 units.
The range of f(x) = (4/5)^x is {y| y > 0}, and the range of g(x) = (4/5)^x + 6 is {y| y > 6}.
Explanation:The range of a function refers to the set of all possible output values of the function. To determine the range of f(x) = (4/5)^x, we need to consider that any positive real number raised to any power will yield a positive result. Therefore, the range of f(x) is {y | y > 0}.
For g(x) = (4/5)^x + 6, we can see that adding a constant term of 6 to the function will shift the entire graph upwards by 6 units. Consequently, the range of g(x) is {y | y > 6}.
Learn more about Range of Functions here:https://brainly.com/question/29145252
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What is the sum of the geometric series
Answers
Answer:
Hence, the sum of the geometric series is:
259
Step-by-step explanation:
We are given a geometric series as:
[tex]\sum_{i=1}^4 6^{i-1}[/tex]
i.e. we are asked to fnd the sum of first four terms of the geometric series with first term as 1
Since, the series is:
[tex]6^0+6^1+6^2+6^3[/tex]
Also, the common ratio of the series is: r=6
Since, each of the term of the series is 6 times it's preceding term.
Also we know that sum of a finite geometric series with n-terms and common ratio r is calculated by the formula:
[tex]S_n=a(\dfrac{r^n-1}{r-1})[/tex]
Here we have: a=1 and r=6 and n=4
Hence,
[tex]S_4=1(\dfrac{6^4-1}{6-1})\\\\\\S_4=\dfrac{1295}{5}\\\\\\S_4=259[/tex]
Hence, the sum of the series is:
259
On the rectangular coordinate system, what is the shortest distance between points (−4, 3) and (−2, −1)?
Answers
Shortest Distance = [tex] \sqrt{ (-2)^{2} + (4)^{2} } [/tex]
Shortest Distance = [tex] \sqrt{20} [/tex]
Shortest Distance = [tex]4.47 units[/tex]
Answer:
In other words to what the dude above me said, the answer is "a''
Step-by-step explanation:
helpppppppppppppppppppppppppppp
Answers
The last option
Explanation:
The range is defined as all the possible values of y.
For the first function:
2^x can give a value less than 2
For example:
2^-1 = 1/2 ..........> This choice is not correct
For the second choice:
2(5^x) can also give a value less than 2
For example:
2 * (5^-1) = 2/5 ...............> This choice is wrong
For the third choice:
5^(x+2) ca also give a value less than 2
For example:
5(-3+2) = 5^-1 = 1/5 ..........> This choice is wrong
For the last option:
5^x + 2
This one will always give a value greater than 2 no matter what the value of exponent is. .......> This is the correct choice
Hope this helps :)
Karen paid $43.70 for a book. The price of the book was $40. what was the sale tax rate
Answers
Answer:
9.25%
Step-by-step explanation:
We have the price book of $40 but karen pais $43.70 then the $3.70 extra that she paid it's the value of taxes. Then to know the tax rate we have to do the next procediment:
[tex]$40\longrightarrow 100\%[\text]
[tex]$3.70\longrightarrow x\%[/tex]
Where x is the tax rate, then:
[tex]x=\dfrac{\$3.70\cdot 100\%}{\$40}[/tex]
[tex]x=\dfrac{370\%}{40}=9.25\%[/tex]
Find the slope of the line that contains the points named.
X(2, -1), Y(0, 4)
5/2
2/5
-5/2
Answers
if I’m wrong I’m sorry.