Answer:
The vertex of the graph moves to a point twice as far from the y-axis.
Step-by-step explanation:
How does the graph of y = a(x – h)2 + k change if the value of h is doubled?
The vertex of the graph moves to a point twice as far from the x-axis.
The vertex of the graph moves to a point twice as far from the y-axis.because the role of h is to indicate the distance of the vertex from the y-axis.
The vertex of the graph moves to a point half as far from the x-axis.
The vertex of the graph moves to a point half as far from the y-axis.
Transformation involves changing the position of a function.
When h is doubled in [tex]\mathbf{y = a(x - h)^2 + k}[/tex], the vertex of the graph moves to a point twice as far from the y-axis.
The function is given as:
[tex]\mathbf{y = a(x - h)^2 + k}[/tex]
When the value of h is doubled, the new function becomes:
[tex]\mathbf{y' = a(x - 2h)^2 + k}[/tex]
Rewrite as:
[tex]\mathbf{y' = a(x - h- h)^2 + k}[/tex]
The above equation means that:
Function y will be translated to the right by h units
Assume the vertex is:
[tex]\mathbf{Vertex = (2,5)}[/tex]
The new vertex will be:
[tex]\mathbf{Vertex = (4,5)}[/tex]
Comparing the vertices, it means that:
The new function will have its vertex twice as far from the y-axis
Hence, option (b) is correct.
Read more about transformation at:
https://brainly.com/question/13801312
The graph of h(x) is a translation of f (x) = RootIndex 3 StartRoot x EndRoot. On a coordinate plane, a cube root function goes through (negative 3, negative 1), has an inflection point at (negative 2, 0), and goes through (negative 1, 1). Which equation represents h(x)?
Answer:
The correct option is;
[tex]h(x) = \sqrt[3]{x + 2}[/tex]
Step-by-step explanation:
Given that h(x) is a translation of f(x) = ∛x
From the points on the graph, given that the function goes through (-1, 1) and (-3, -1) we have;
When x = -1, h(x) = 1
When x = -3, h(x) = -1
h''(x) = (-2, 0)
Which gives
d²(∛(x + a))/dx²= [tex]-\left ( \dfrac{2}{9} \cdot \left (x + a \right )^{\dfrac{-5}{3}}\right )[/tex], have coordinates (-2, 0)
When h(x) = 0, x = -2 which gives;
[tex]-\left ( \dfrac{2}{9} \cdot \left (-2 + a \right )^{\dfrac{-5}{3}}\right ) = 0[/tex]
Therefore, a = (0/(-2/9))^(-3/5) + 2
a = 2
The translation is h(x) = [tex]\sqrt[3]{x + 2}[/tex]
We check, that when, x = -1, y = 1 which gives;
h(x) = [tex]\sqrt[3]{-1 + 2} = \sqrt[3]{1} = 1[/tex] which satisfies the condition that h(x) passes through the point (-1, 1)
For the point (-3, -1), we have;
h(x) = [tex]\sqrt[3]{-3 + 2} = \sqrt[3]{-1} = -1[/tex]
Therefore, the equation, h(x) = [tex]\sqrt[3]{x + 2}[/tex] passes through the points (-1, 1) and (-3, -1) and has an inflection point at (-2, 0).
Answer: B
Step-by-step explanation:
If $6a^2 + 5a + 4 = 3,$ then what is the smallest possible value of $2a + 1$?
Answer: 0
Step-by-step explanation:
The given equation: [tex]6a^2+5a+4=3[/tex]
Subtract 3 from both the sides, we get
[tex]6a^2+5a+1=0[/tex]
Now , we can split 5a as 2a+3a and [tex]2a\times 3a = 6a^2[/tex]
So, [tex]6a^2+5a+1=0\Rightarrow\ 6a^2+2a+3a+1=0[/tex]
[tex]\Rightarrow\ 2a(3a+1)+(3a+1)=0\\\\\Rightarrow\ (3a+1)(2a+1)=0\\\\\Rightarrow\ (3a+1)=0\text{ or }(2a+1)=0\\\\\Rightarrow\ a=-\dfrac{1}{3}\text{ or }a=-\dfrac{1}{2}[/tex]
At [tex]a=-\dfrac{1}{3}[/tex]
[tex]2a+1=2(-\dfrac{1}{3})+1=-\dfrac{2}{3}+1=\dfrac{-2+3}{3}=\dfrac{1}3{}[/tex]
At [tex]a=-\dfrac{1}{2}[/tex]
[tex]2a+1=2(-\dfrac{1}{2})+1=-1+1=0[/tex]
Since, [tex]0< \dfrac{1}{3}[/tex]
Hence, the possible value of 2a+1 is 0.
first answer gets best marks
Answer:
A, B, E
Step-by-step explanation:
I attached everything that I thought it would help you.
Hope this helps ;) ❤❤❤
What is the sum of 3x to the second power +2x-1
Answer:
[tex]3x^2+2x+1[/tex]
Step-by-step explanation:
Sum means to add and second power means that the exponent is "2". So, the expression is:
=> [tex]3x^2+2x+1[/tex]
It cannot be simplified further.
!!!!PLEASE HELP!!!!!
Answer:
inverse = ( log(x+4) + log(4) ) / (2log(4)), or
c. y = ( log_4(x+4) + 1 ) / 2
Step-by-step explanation:
Find inverse of
y = 4^(-6x+5) / 4^(-8x+6) - 4
Exchange x and y and solve for y.
1. exchange x, y
x = 4^(-6y+5) / 4^(-8y+6) - 4
2. solve for y
x = 4^(-6y+5) / 4^(-8y+6) - 4
transpose
x+4 = 4^(-6y+5) / 4^(-8y+6)
using the law of exponents
x+4 = 4^( (-6y+5) - (-8y+6) )
simplify
x+4 = 4^( 2y - 1 )
take log on both sides
log(x+4) = log(4^( 2y - 1 ))
apply power property of logarithm
log(x+4) = (2y-1) log(4)
Transpose
2y - 1 = log(x+4) / log(4)
transpose
2y = log(x+4) / log(4) + 1 = ( log(x+4) + log(4) ) / log(4)
y = ( log(x+4) + log(4) ) / (2log(4))
Note: if we take log to the base 4, then log_4(4) =1, which simplifies the answer to
y = ( log_4(x+4) + 1 ) / 2
which corresponds to the third answer.
write a compound inequality that the graph could represent
Answer:
second option
Step-by-step explanation:
A middle school took all of its 6th grade students on a field trip to see a play at a theatre that has 2000 seats. The students filled 65% of the seats in the theatre. How many 6th graders went on the trip?
Answer: 1,300 students went on the trip
Step-by-step explanation: So we know that 65% filled the seats so let's turn that into a fraction. [tex]\frac{65}{100}[/tex] . Now we know that there are 2,000 seats in total so let's put that into a fraction. [tex]\frac{x}{2,000}[/tex] The x represents the students that went on the trip.
[tex]\frac{65}{100} = \frac{x}{2,000}[/tex] we have to cross multiply
65(2,000) = 100 (x)
130,000 = 100 (x)
130,000 ÷ 100
1,300 = x So now we know that 1,300 went to the trip students
Right triangle ABC is located in A(-1,-2), B(-1,1) and C(3,1) on a coordinate plane. what is the equation of a circle with radius AC?
A) (x+1)*2+(y+2)*2=9
B) (x+1)*2+(y+2)*2=25
C) (x-3)*2+(y-1)*2= 16
D) (x-3)*2+(y-1)*2=25
Answer:
Hey there!
First, we want to find the radius of the circle, which equals the length of line segment AC.
Length of line segment AC, which we can find with the distance formula: [tex]\sqrt{25\\[/tex], which is equal to 5.
The equation for a circle, is: [tex](x-h)^2+(y-k)^2=r^2[/tex], where (h, k) is the center of the circle, and r is the radius.
Although I don't know the center of the circle, I can tell you that it is either choice B or D, because the radius, 5, squared, is 25.
Hope this helps :) (And let me know if you edit the question)
Answer: The equation of the circle is (x+1)²+(y+1)² = 25
Step-by-step explanation: Use the Pythagorean Theorem to calculate the length of the radius from the coordinates given for the triangle location: A(-1,-2), B(-1,1) and C(3,1) The sides of the triangle are AB=3, BC=4, AC=5.
Use the equation for a circle: ( x - h )² + ( y - k )² = r², where ( h, k ) is the center and r is the radius.
As the directions specify, the radius is AC, so it makes sense to use the coordinates of A (-1,-2) as the center. h is -1, k is -2 The radius 5, squared becomes 25.
Substituting those values, we have (x -[-1])² + (y -[-2])² = 25 .
When substituted for h, the -(-1) becomes +1 and the -(-2) for k becomes +2.
We end up with the equation for the circle as specified:
(x+1)²+(y+1)² = 25
A graph of the circle is attached. I still need to learn how to define line segments; the radius is only the segment of the line between the center (-1,-2) and (1,3)
A total of $10,000 is invested in two mutual funds. The first account yields 5% and the second account yields 6%. How much was invested in each account if the total interest earned in a year is $575?
Answer:
$2,500 was invested in the first account while $7,500 was invested in the second account
Step-by-step explanation:
Here in this question, we want to find the amount which was invested in each of the accounts, given their individual interest rates and the total amount that was accorded as interest from the two investments
Now, since we do not know the amount invested , we shall be representing them with variables.
Let the amount invested in the first account be $x and the amount invested in the second account be $y
Since the total amount invested is $10,000, this means that the summation of both gives $10,000
Mathematically;
x + y = 10,000 ••••••(i)
now for the $x, we have an interest rate of 5%
This mathematically translates to an interest value of 5/100 * x = 5x/100
For the $y, we have an interest rate of 6% and this mathematically translates to a value of 6/100 * y= 6y/100
The addition of both interests, gives 575
Thus mathematically;
5x/100 + 6y/100 = 575
Multiplying through by 100, we have
5x + 6y = 57500 •••••••••(ii)
From 1, we can have x = 10,000-y
let’s substitute this into equation ii
5(10,000-y) + 6y = 57500
50,000-5y + 6y = 57500
50,000 + y = 57500
y = 57500-50,000
y = 7,500
Recall;
x = 10,000-y
so we have;
x = 10,000-7500 = 2,500
Consider the function represented by the table.
What is f(0)?
04
O 5
06
O 7
Answer:
6
Step-by-step explanation:
From the table given defining a function, the values of "x" on the table represents the input of the function, which gives us an output, f(x), which can be labelled as "y" in some instances.
Thus, the value of f(0), is simply the output value we would get, given an input value of "0".
So therefore, f(0) = 6. That is, at x = 0, f(x) = 6.
Answer: 6
Step-by-step explanation:
Solve the equation and show the solution set on a number line: |x+5|=x+5
Answer: x ≥ -5
Step-by-step explanation:
First, let's see how the function f(x) = IxI works:
if x ≥ 0, IxI = x
if x ≤ 0, IxI = -x
Notice that for 0, I0I = 0.
Ok, we want that:
|x+5| = x+5
Notice that this is equivalent to:
IxI = x
This means that |x+5| = x+5 is only true when:
(x + 5) ≥ 0
from this we can find the possible values of x:
we can subtract 5 to both sides and get:
(x + 5) -5 ≥ 0 - 5
x ≥ -5
So the graph in the number line will be a black dot in x = -5, and all the right region shaded.
something like:
-7__-6__-5__-4__-3__-2__-1__0__1__2__3__4__ ...
Determine the inequality represented by the following diagram
Steve paid $3.29 for a pizza. He now has $35.86. With how much money did he start?
Answer:
$39.15
Step-by-step explanation:
We can find that Steve started with $39.15, by adding the price he has now and the price he paid for the pizza.
35.86+3.29=$39.15
Answer:
$39.15
Step-by-step explanation:
$35.86 + $3.29 = $39.15
hOpEfUlLy ThIs HeLpEd!! :33
Question 4. In the graph, lines f and g intersect at P(6,6). What is the area, in square units, of the shaded region? * E. 15 F. 21 G. 27 H. 30
Answer:
E
Step-by-step explanation:
i guess the dotted lines outline a square
so get the area of the square which is 6×6=36
then don't focus on the shaded part but unshaded you'll see two right angled triangles
[tex]a = 1 \div2b \times h[/tex]
you will get a total for both as 21
then get the area of the square 36-21=15
so the area becomes 15
WILL MARK BRAINLIEST!!! PLZ HELP!!!
Answer:
x = -5.
Step-by-step explanation:
The solutions of the equation is when the two functions intersect. That is at (-5, 5.5), so where x = -5.
Hope this helps!
Answer:
x = -5
Step-by-step explanation:
f(x) = g(x) has more than one solution, because they intersect at two points.
The question asks for one solution of f(x) = g(x).
One point where they intersect is at (-5, 5.5), as shown in the graph.
(x , y)
x = -5, y = 5.5
find x value A. 8.96 B. 10.83 C. 5.10 D. 6.09
Answer:
6.09
Step-by-step explanation:
in ADB
[tex]a ^{2} + b^{2} = c ^{2} [/tex]
to get hypotenuse=8.96
this is height of ABC so use tan
[tex] tan(55.8)= 8.96 \x[/tex]
x=6.09
Answer:
D
Step-by-step explanation:
To find x, we first to to find the line between A&B.
Use the pythagoram theorem to do this A^2+B^2=C^2
4.9^2+7.5^2=C^2
80.26=C^2
square root each side
Side AtoB=8.958
We now know the side length of the opposite and adjacent for the angle C. So according to SohCahToa we need to use Tangent.
So Tan(55.8)=(8.958/x)
We you solve for x, the answer is 6.088
Draw a diagram of this statement,
Fifteen thousand dollars was raised by the booster club. This was two thirds of
the goal.
Use your diagram to determine the percent by which the booster club fell short of their goal
Answer:
The percentage by which the booster club fell short is 33% as shown on the chart
Step-by-step explanation:
To represent the given data pictorially, a pie chart is suitable
The circumference of the pie chart will represent the amount to be raised by the booster club and a sector of the circle which is two-thirds of the circumference represents the amount raised
Given that the amount raised = 2/3×Goal = $15,000, we have;
We represent the amount raised as a sector of the circle as follows;
Sector angle = 2/3×360° = 240°
Total sector of goal amount = Entire circle = 360°
Amount club fell short = 360° - 240° = 120°
The goal amount = 3/2 × $15,000
Percentage by which the club fell short = 120/360×100 = 1/3×100 = 33.33%
Plzzzzzzzzzzzz helpppppppppp
Answer:
B. The horizontal cross-sections of the prisms at the same height have the same area.
Step-by-step explanation:
Notice that the cone and the pyramid have the same volume. This is important.
This follows the Cavalieri's principle that, for the case of 3 dimensions, as the present case, it states, roughly, that if we have two bodies like the cone and the pyramid, and if we have parallel planes crossing each section, and we always have the same area, these two bodies have the same volume.
In this case, both, cone and pyramid have the same volume, then (reciprocally):
B. The horizontal cross-sections of the prisms at the same height have the same area.
Answer:
B. The horizontal cross-sections of the prisms at the same height have the same area.
Step-by-step explanation:
ap333x
Help plz down below with the question
Answer:
The SAS Postulate
Step-by-step explanation:
SAS means Side-Angle-Side; that is, two sides are equal and an angle between those sides are equal. We're given two sides: TK and TL, and we're given that 1 is congruent to 2. Knowing the latter, we can conclude that the angle between them (let's call it 1.5 for our purposes) will be congruent to itself. Since 1.5 is the angle right in the middle of two congruent sides, our answer is SAS.
If you have 2345 and you multiple it by 2 divide it by 6 and add on 22299 what will the answer be?
Answer:
69242/3 or 23080.666667
Step-by-step explanation:
2345 is multiplied by 2. Then the result is divided by 6. Then 22299 is added to the final result.
2345 × 2
= 4690
4690/6
= 2345/3
2345/3 + 22299
= 69242/3
What does the denominator of the fraction \dfrac23 3 2 start fraction, 2, divided by, 3, end fraction mean?
Answer: It represents that 2 will be divided into 3 equal parts.
Step-by-step explanation:
Numerator is the top number in a fraction. It represents the total item it has to divide.Denominator is the bottom number in a fraction. it represents the number of equal parts the item is divided into.The given fraction : [tex]\dfrac{2}{3}[/tex]
here, Numerator = 2
Denominator = 3
It represents that 2 will be divided into 3 equal parts.
(pic inside) What is the approximate value of the function at x = 1?
Answer: -2
Step-by-step explanation:
When x = 1, y = -2.
Hope it helps <3
The mean one-way commute to work in Chowchilla is 7 minutes. The standard deviation is 2.4 minutes, and the population is normally distributed. What is the probability of randomly selecting one commute time and finding that: a). P (x < 2 mins) _____________________________ b). P (2 < x < 11 mins) _____________________________ c). P (x < 11 mins) ________________________________ d). P (2 < x < 5 mins) _______________________________ e). P (x > 5 mins)
Answer:
The answer is below
Step-by-step explanation:
Given that:
The mean (μ) one-way commute to work in Chowchilla is 7 minutes. The standard deviation (σ) is 2.4 minutes.
The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
a) For x < 2:
[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]
From normal distribution table, P(x < 2) = P(z < -2.08) = 0.0188 = 1.88%
b) For x = 2:
[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]
For x = 11:
[tex]z=\frac{x-\mu}{\sigma}=\frac{11-7}{2.4} =1.67[/tex]
From normal distribution table, P(2 < x < 11) = P(-2.08 < z < 1.67 ) = P(z < 1.67) - P(z < -2.08) = 0.9525 - 0.0188 = 0.9337
c) For x = 11:
[tex]z=\frac{x-\mu}{\sigma}=\frac{11-7}{2.4} =1.67[/tex]
From normal distribution table, P(x < 11) = P(z < 1.67) = 0.9525
d) For x = 2:
[tex]z=\frac{x-\mu}{\sigma}=\frac{2-7}{2.4} =-2.08[/tex]
For x = 5:
[tex]z=\frac{x-\mu}{\sigma}=\frac{5-7}{2.4} =-0.83[/tex]
From normal distribution table, P(2 < x < 5) = P(-2.08 < z < -0.83 ) = P(z < -0.83) - P(z < -2.08) = 0.2033- 0.0188 = 0.1845
e) For x = 5:
[tex]z=\frac{x-\mu}{\sigma}=\frac{5-7}{2.4} =-0.83[/tex]
From normal distribution table, P(x < 5) = P(z < -0.83) = 0.2033
im stuck on this question helm me out I will mark you as brainliest
Answer: it is =4176000000000000
Step-by-step explanation:
(2.9)(100000)(7.2)(10^2)
5(10^−8)
=
(290000)(7.2)(10^2)
5(10^−8)
=
2088000(10^2)
5(10^−8)
=
(2088000)(100)
5(10^−8)
=
208800000
5(10^−8)
=
208800000
5(1/100000000)=
208800000/1
20000000
=4176000000000000
hope i helped
-lvr
Suppose a firm in a competitive market earned $1,000 in total revenue and had a marginal revenue of $10 for the last unit produced and sold. What is the average revenue per unit, and how many units were sold?
Answer:
$5 and 50 units
Step-by-step explanation:
Grace starts with 100 milligrams of a radioactive substance. The amount of the substance decreases by 14 each week for a number of weeks, w. She writes the expression 100(14)w to find the amount of radioactive substance remaining after w weeks. Ryan starts with 1 milligram of a radioactive substance. The amount of the substance decreases by 40% each week for a number of weeks, w. He writes the expression (1 – 0.4)w to find the amount of radioactive substance remaining after w weeks. Use the drop-down menus to explain what each part of Grace’s and Ryan’s expressions mean.
Answer:
100= Initial Amount
1/4= decay factor for each week
w= number of weeks
1/4w= decay factor after w weeks
1 - 0.4= decay factor for each week
w= number of weeks
0.4= percent decrease
Step-by-step explanation:
Please help me it will mean a lot
Answer:
A) a=25
B) b=14
Step-by-step explanation:
A) a/5+3=8
First you need to subtract 3 from both sides.
(a/5+3)-3=(8)-3
Then simplify
a/5=5
Multiply both sides by 5
(a/5)*5=(5)*5
Then simplify
a= 25
B )3b/7-1=5
First you need to add 1 to both sides
(3b/7-1)+1=(5)+1
Simplify
3b/7=6
Multiply both sides by 7
(3b/7)*7=(6)*7
Simplify
3b=42
Divide both sides by 3
(3b)/3=(42/3)/3
Simplify
b= 14
(Brainliest???) :P
If a cone is 5 meters tall and has a radius of 3 meters, What is its volume? 15π m3 60π m3 45π m3 30π m3
Answer:
V = 15 pi m^3
Step-by-step explanation:
The volume of a cone is
V = 1/3 pi r^2 h
The radius is 3 and the height is 5
V = 1/3 pi ( 3)^2 *5
V = 15 pi m^3
Answer:
15 pi m3
Step-by-step explanation:
PLEASE HELP ASAPPPP!!!
Solve the right triangle given that mA =30°, mC = 90° and a = 15. Then round your result to ONE decimal place
Answer:
m∠B = 60°
b = 26 units
c = 30 units
Step-by-step explanation:
In a right triangle ACB,
By applying Sine rule,
[tex]\frac{\text{SinA}}{a}=\frac{\text{SinB}}{b}=\frac{SinC}{c}[/tex]
m∠A = 30°, m∠C = 90°
m∠A + m∠B + m∠C = 180°
30° + m∠B + 90° = 180°
m∠B = 180° - 120°
m∠B = 60°
Therefore, [tex]\frac{\text{Sin30}}{15}=\frac{\text{Sin90}}{c}=\frac{\text{Sin60}}{b}[/tex]
[tex]\frac{1}{30}=\frac{\text{Sin90}}{c}=\frac{\text{Sin60}}{b}[/tex]
[tex]\frac{1}{30} =\frac{1}{c}=\frac{\frac{\sqrt{3}}{2}}{b}[/tex]
[tex]\frac{1}{30}=\frac{1}{c}=\frac{\sqrt{3}}{2b}[/tex]
[tex]\frac{1}{30} =\frac{1}{c}[/tex] ⇒ c = 30 units
[tex]\frac{1}{30}=\frac{\sqrt{3}}{2b}[/tex]
b = 15√3
b = 25.98
b ≈ 26 units
values of r and h, what do you notice about the proportions of the cylinders?
Answer:
Below
Step-by-step explanation:
r us the radius of the base and h is the heigth of the cylinder.
The volume of a cylinder is given by the formula:
V = Pi*r^2*h
V/Pi*r^2 = h
We can write a function that relates h and r
Answer:
One of the cylinders is short and wide, while the other is tall and thin.
Step-by-step explanation:
sample answer given on edmentum