Function g is a transformation of function f.
Graph shows 2 exponential functions. First curve f enters quadrant 3 at (minus 6, minus 2) rises through (0, minus 1) and (1, 0) and (2, 2) in quadrant 1. Second curve g enters quadrant 2 at (minus 6, 6) falls through (0, 3) and (1, 0) in quadrant 1.
What is the equation of function g?
g(x) = f(x)
Answers
The equation of function g(x) in terms of f(x) is g(x) = -3[f(x)].
What is an equation?
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given:
genera form of an exponential function is y=aeᵇˣ
Now, equation for f(x) is
f(x) = [tex]e^{(log \;2)x} -2[/tex]
Similarly, graph for g(x) is
g(x) = [tex]-3e^{(log \;2)x} +6[/tex]
Comparing the two function a relation can be establish
g(x) = -3[f(x)]
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Answer:
shifted to the left two units
g(x)=-f(x+2)
Step-by-step explanation:
Related Questions
Tricia recorded the number of pets owned by each of her classmates. these data points represent the results of her survey. 0, 3, 2, 4, 1, 0, 0, 3, 2, 1, 2, 1, 1, 3, 4, 2, 0, 0, 1, 1, 1, 0, 3 create a dot plot that represents the data.
Answers
The dot plot of the data recorded by Tricia about number of pets owned by each of her classmates looks like scattered and some points are in one line.
Given number of pets owned by each of her classmates are: 0, 3, 2, 4, 1, 0, 0, 3, 2, 1, 2, 1, 1, 3, 4, 2, 0, 0, 1, 1, 1, 0, 3.
We have to create dot plot of the data given in the question.
Firstly we have to give a code to each value which represents friend of Tricia.
A dot plot is a statistical chart which have points but they are presented in dot form. Each dot shows a value .There are two common, yet different versions of the dot chart.
After giving codes the table will look like:
Friend Number of pets
1 0
2 3
3 2
4 4
5 1
6 0
7 0
8 3
9 2
10 1
11 2
12 1
13 1
14 3
15 4
16 2
17 0
18 0
19 1
20 1
21 1
22 0
23 3
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5.7x10^6 as an ordinary number
Answers
Answer:
5700000
Step-by-step explanation:
after this i will only have 4 questions please and ty!
Answers
Answer:D
Step-by-step explanation:
this expression gives the original price reduce by 15%. The second term adds the tax to the price after the sale has been applied
Chloe bought an equal number of forks and spoons for a party. The forks were sold at 3 for 2$ and the spoons were sold at 4 for 3$. She spent 5$ more on spoons than on forks. How much did she spend altogether?
Answers
60 forks 60÷3=$20
60 spoons 60÷4=$15
$20+$15=$35 total spent for forks and spoons
which of the following must be true?
Answers
Answer:
C
Step-by-step explanation:
Answer C is correct. The absolute value of 10 is 10 and that of -10 is 10. Same result.
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6
4
2
10 8 64-2
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4
6
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Ta OnciC
A circle centered at the origin contains the point
(0, -9). Does (8, √17) also lie on the circle? Explain.
O No, the distance from the center to the point
(8, √17) is not the same as the radius.
O No, the radius of 10 units is different from the
distance from the center to the point
(8, √17).
O Yes, the distance from the origin to the point
(8, √17) is 9 units.
O Yes, the distance from the point (0, -9) to the point
(8, √17) is 9 units.
Answers
Approximate value of √17
~4+So the point is (8,4)
As we can see in graph the point is contained by the circle
Hence the distance
√(0-8)²+(9-4)²√8²+5²√89Approximately 9 units
Option D
Answer:
Yes, the distance from the origin to the point (8, √17) is 9 units
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where:
(a, b) is the centerr is the radiusGiven:
center = (0, 0)r = 9Substitute the given values into the formula to create the equation of the circle:
[tex]\implies (x-0)^2+(y-0)^2=9^2[/tex]
[tex]\implies x^2+y^2=81[/tex]
To find if point [tex]\sf (8, \sqrt{17})[/tex] lies on the circle, substitute x = 8 into the found equation and solve for y:
[tex]\implies 8^2+y^2=81[/tex]
[tex]\implies 64+y^2=81[/tex]
[tex]\implies y^2=81-64[/tex]
[tex]\implies y^2=17[/tex]
[tex]\implies y=\sqrt{17}[/tex]
As y = √17 when x = 8, this proves that point (8, √17) lies on the circle.
The distance from the origin to any point on the circle is the radius.
Therefore, as the radius is 9 units, the distance from the origin to the point (8, √17) is 9 units.
Dude this should be so easy but this is going in one ear and out the other how do I do this send help
Answers
Answer:
0.5 hours
Explanation:
Given:
speed: 17 miles/hourdistance: 8 milesFormula:
time taken = distance ÷ speedSolve:
time taken = 8 ÷ 17 = 0.4706 ≈ 0.5 hours (rounded to nearest tenth)The image of ΔABC after a reflection across Line E G is ΔA'B'C'.
2 triangles are shown. Line E G is the line of reflection. Line segment D D prime has a midpoint at point F. Line segment C C prime has a midpoint at point G. Points B and B prime share a point. Angle C G F is a right angle.
Which triangle must be a right triangle and why?
ΔA'B'C' is right because it is the image of ΔABC.
ΔADC is right because AA' intersects AC at A.
ΔBCC' is right because B lies of the line of reflection.
ΔBGC is right because Line E G is perpendicular-to CC'.
Answers
Δ DGC is right angled triangle because Line E G is perpendicular-to CC', Option D is the correct answer.
What is Triangle ?Triangle is a polygon with three sides , angles and vertices.
It is given that the there are two Triangles , ABC and A'B'C' as an image of the ABC
* Line segment AA' has a midpoint at point F
*D is the mid point of the line joining BB' .*
The figure is attached with the answer.
the line of reflection of the object is always perpendicular to the object and the image.
it is also given that CGF is a right angle.
Therefore triangle DGC is right angled triangle , (the option given in the question is incorrect ) , Line E G is perpendicular-to CC'.
Option D is the correct answer.
Please Refer to the image for correct coordinates.
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Pam’s eye-level height is 324 ft above sea level, and adam’s eye-level height is 400 ft above sea level. how much farther can adam see to the horizon? use the formula d = startroot startfraction 3 h over 2 endfraction endroot, with d being the distance they can see in miles and h being their eye-level height in feet.
Answers
Adam can see the horizon at a distance of [tex]\sqrt{6}mi.[/tex]
Given that the height of Pam's eye level above sea level is [tex]324ft[/tex] and the height of adam's eye level above sea level is [tex]400ft[/tex].
The formula used to find the distance they see in miles is [tex]d=\sqrt{\frac{3h}{2}}[/tex].
Let the height of Pam's is [tex]h[/tex] and the height of adam's is [tex]h'[/tex].
The distance of Pam from the horizon can be given as [tex]d=\sqrt{\frac{3h}{2}}[/tex].
Substitute these values,
[tex]\begin{aligned}d&=\sqrt{3\times \frac{324}{2}}\\ d&=\sqrt{486}\\ d&=\sqrt{81\times 6}\\ d&=9\sqrt{6}\end[/tex]
And the distance of adam from the horizon can be given as [tex]d=\sqrt{\frac{3h'}{2}}[/tex].
Substitute these values,
[tex]d'=\sqrt{3\times \frac{400}{2}}\\ d'=\sqrt{600}\\ d'=\sqrt{100\times 6}\\ d'&=10\sqrt{6}[/tex]
The net distance of adam from the horizon is
[tex]\begin{aligned}d_{\text{net distance}}&=d'-d\\ &=10\sqrt{6}-9\sqrt{6}\\&=\sqrt{6}\end[/tex]
Hence, the adam can see the horizon at a distance of [tex]\sqrt{6}mi[/tex].
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Answer:
B
Step-by-step explanation:
it said sooo
3x[tex]3x^{2} +8x-10[/tex]
Answers
The solution to the quadratic equation 3x² + 8x - 10 by using the quadratic formula is x = 0.927 or -3.594
Solving quadratic equations.Quadratic equations are algebraic expressions that are represented in the power of the second degree. They usually take the form ax² + bx + c
From the given information, we are to solve the quadratic equation:
3x² + 8x - 10Using the quadratic formula:
[tex]\mathbf{=\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]
where:
a = 3b = + 8c = - 10[tex]\mathbf{= \dfrac{-(8)) \pm \sqrt{(8)^2 - 4(3 \times (-10))}}{2(3)}}[/tex]
[tex]\mathbf{= \dfrac{-(8)) \pm \sqrt{64 -4 (-30)}}{6}}[/tex]
[tex]\mathbf{= \dfrac{-(8)) \pm \sqrt{64+120}}{6}}[/tex]
x = 0.927 or -3.594
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Maria is on a hike. if she hikes to the scenic lookout on the following map first, she will have to hike farther than if she went straight to the end of the hike. 3 connected points on a coordinate plane. the point labeled, "maria," is at 4, -4. the point labeled, "end," is at -5, 5. a solid line connect the points "maria" and "end." the point labeled, "scenic lookout," is at 2, 3. dashed lines connect "maria" to "scenic lookout" and connect "scenic lookout" to "end." coordinate values on the map are in kilometers. how much shorter is the path straight to the end of the hike than past the scenic lookout? round your final answer only to the nearest kilometer. \text{km}kmstart text, k, m, end text
Answers
The path straight to the end of the hike is 6 km farther than past the scenic lookout.
How to determine the difference in the parts?The map is not given, but the question can still be answered
From the question, the positions are given as::
Maria = (4, -4)
Scenic = (2, 3)
End = (-5, 5)
The distance between Maria and the end point is calculated using:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]
So, we have:
[tex]Route\ 1 = \sqrt{(4 + 5)^2 + (-4 -5)^2}[/tex]
[tex]Route\ 1 = 13[/tex]
The distance between Maria and the scenic lookout is calculated using:
[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2[/tex]
So, we have:
[tex]Route\ 2 = \sqrt{(4 - 2)^2 + (-4 -3)^2}[/tex]
[tex]Route\ 2 = 7[/tex]
The distance between both routes is:
Distance = 13 - 7
Evaluate
Distance = 6
Hence, the path straight to the end of the hike is 6 km farther than past the scenic lookout.
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A shoe making company makes 256 pairs of boots in a day how many pairs of boots do they make in 260 days
Answers
Answer:
66560 pairs
Step-by-step explanation:
let the number of pairs of boots the company makes in 260 days = X
1day -----------------256pairs
260days-------------X
cross multiplying
1×X = 260×256
X= 66560
therefore, in 260days, he makes 66560 pairs
question below
What matrix is the result of m*H?
Enter your answer by filling in the boxes. Enter any fractions as simplified fractions.
Answers
Answer:
[tex]m \times H=\left[\begin{array}{c c c}\boxed{-9} & \boxed{36} & \boxed{-\dfrac{9}{2}}\end{array}\right][/tex]
Step-by-step explanation:
Calculate the value of m
Given:
[tex]3\left[\begin{array}{c c}-1 & 2 \\4 & 8\end{array}\right]=\dfrac{2}{3}m \times \left[\begin{array}{c c}-1 & 2 \\4 & 8\end{array}\right][/tex]
Therefore:
[tex]\implies 3=\dfrac{2}{3}m[/tex]
[tex]\implies m=3 \times \dfrac{3}{2}[/tex]
[tex]\implies m=\dfrac{9}{2}[/tex]
Calculate the value of H
Given:
[tex]\left(H+ \left[\begin{array}{c c c}1 & 4 & -2\end{array}\right]\right)+\left[\begin{array}{c c c}3 & 2 & -6\end{array}\right]=\left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right]+\left(\left[\begin{array}{c c c}1 & 4 & -2\end{array}\right]+\left[\begin{array}{c c c}3 & 2 & -6\end{array}\right]\right)[/tex]
Therefore:
[tex]\implies H= \left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right][/tex]
Calculating m × H
[tex]\implies m \times H=\dfrac{9}{2} \times \left[\begin{array}{c c c}-2 & 8 & -1\end{array}\right][/tex]
[tex]\implies m \times H=\left[\begin{array}{c c c}\dfrac{9}{2}(-2) & \dfrac{9}{2}(8) & \dfrac{9}{2}(-1)\end{array}\right][/tex]
[tex]\implies m \times H=\left[\begin{array}{c c c}-9 & 36 & -\dfrac{9}{2}\end{array}\right][/tex]
write a function rule for the table
hours worked 2,4,6,8 and pay 15,30,45,60
Answers
Answer:
f(x) = 7.5x
Step-by-step explanation:
you can find the slope by using the slope formula (y2-y1)/(x2-x1). you can use any of the values but for this example I'll be using (2, 15) and (4, 30).
(30-15)/(4-2) = 15/2 = 7.5.
now we can use one of the coordinates to find the y-intercept by plugging the known values in the equation y=mx+b where m is the slope and b is the y-intercept.
for this example I'll be using (2, 15) but you could use any of the values you gave.
15 = 7.5(2) + b
15 = 15 + b
0 = b
so now we have the function rule
f(x) = 7.5x + 0 or just f(x) = 7.5x
pls help!! determine the period! thx
Answers
Answer:
T=5
Step-by-step explanation:
Select the correct answer.
What is the solution for x in the equation?
9-10x=2x+1-8x
OA.
O B.
O C.
O D.
x = 2
x = -2
X =
x
= -1
||
12
112
Answers
[tex]9-10x=2x+1-8x\\\\9-10x=-6x+1\\\\9=4x+1\\\\8=4x\\ \\ x=\boxed{2}[/tex]
The value of the x in the equation 9 - 10x = 2x + 1 - 8x is 2. The correct answer is A) x = 2.
An equation is a combination of numbers, variables, functions, and often symbols arranged in a peculiar order. The equation comprises two or more expressions distinguished by the equality sign(=). The equations are solved to estimate the values of variables.
The given equation is
9 - 10x = 2x + 1 - 8x
-10x - 2x + 8x = 1 - 9
-4x = -8
4x = 8
x = [tex]\frac{8}{4}[/tex]
x = 2.
Thus, the correct option is A) x = 2.
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-19+[27-(14+(5-2)×4÷2))]
simplify
Answers
Answer:
-12
Step-by-step explanation:
What is the best name for the part of the figure
identified by the arrow?
O line of reflection
O line of symmetry
O plane of reflection
O axis of symmetry
Answers
The best name for the part of the figure identified by the arrow is the plane of reflection option third is correct.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
We have given a three-dimensional figure.
As we can see the arrow is pointing at the plane.
A triangular prism is reflected over the given plane and creates a mirror image of a triangular prism.
A plane is a plane of symmetry.
Thus, the best name for the part of the figure identified by the arrow is the plane of reflection option third is correct.
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If F= {(1,5), (4, 1), (2, 7)}and g= {(3, 1), (5 4) (-6,2)} represent fog in mapping of agram and to find fog in ordered pair form
Answers
From the given mappings, we have
[tex]f(1) = 5, f(4) = 1, f(2) = 7[/tex]
and
[tex]g(3) = 1, g(5) = 4, g(-6) = 2[/tex]
Then the composition of [tex]f[/tex] with [tex]g[/tex], or [tex]f\circ g[/tex], is
[tex]\boxed{f\circ g = \{(3,5), (5,1), (-6, 7)\}}[/tex]
since
[tex]g(3) = 1 \implies (f\circ g)(3) = f(g(3)) = f(1) = 5[/tex]
[tex]g(5) = 4 \implies (f\circ g)(5) = f(4) = 1[/tex]
[tex]g(-6) = 2 \implies (f\circ g)(-6) = f(2) = 7[/tex]
Please please help what is equivalent to this??
Answers
The correct option is Option A: [tex]16^{3x/4}[/tex] is equivalent to the expression [tex](\sqrt[4]{16})^{3x[/tex].
The rules of the exponent are
(a) [tex]a^m*a^n=a^{m+n[/tex]
(b)[tex]a^m/a^n=a^{m-n[/tex]
(c)[tex](a^b)^c=a^{bc}[/tex]
(d) [tex]\sqrt[n]{a}=a^{1/n[/tex]
here the given expression is [tex]16^{3x/4}[/tex]
we can rewrite the expression as
[tex]16^{3x/4}[/tex]
as we know by the rule of the exponent that [tex](a^b)^c=a^{bc}[/tex]
=[tex](16^{1/4})^{3x[/tex]
as we know by the rule of the exponent [tex]\sqrt[n]{a}=a^{1/n[/tex]
=[tex](\sqrt[4]{16})^{3x[/tex]
Therefore the correct option is Option A: [tex](\sqrt[4]{16})^{3x[/tex]
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if three hard drives are using 132 5/8 watts, what is the number of watts used per hard drive?
1. 44 7/24 watts
2. 42 5/24 watts
3. 42 7/24 watts
4. 44 5/24 watts
whoever answers correctly i will give brainliest.
Answers
132/3 = 44
5/8 / 3 = 5/8 x 1/3 =5/24
answer: 4. 44 5/24 watts
Answer:
[tex]\sf 4. \quad 44\frac{5}{24}\:\:watts[/tex]
Step-by-step explanation:
Given information:
3 hard drives are using 132 5/8 wattsTo find the number of watts used per hard drive, divide the total amount of watts by 3.
Convert the mixed number into an improper fraction:
[tex]=\sf 132 \frac{5}{8}[/tex]
[tex]\sf =\dfrac{132 \times 8+5}{8}[/tex]
[tex]\sf =\dfrac{1061}{8}[/tex]
Divide by 3:
[tex]=\sf \dfrac{1061}{8} \div 3[/tex]
[tex]\sf =\dfrac{1061}{8} \times \dfrac{1}{3}[/tex]
[tex]\sf =\dfrac{1061 \times 1}{8 \times 3}[/tex]
[tex]\sf =\dfrac{1061}{24}[/tex]
Convert back into a mixed number:
[tex]\sf =\dfrac{1061}{24}[/tex]
[tex]\sf =\dfrac{1056+5}{24}[/tex]
[tex]\sf =\dfrac{1056}{24}+\dfrac{5}{24}[/tex]
[tex]= \sf 44\frac{5}{24}[/tex]
Therefore, the number of watts used per hard drive is [tex]\sf 44\frac{5}{24}[/tex] watts.
Which set of equations has 3, 1 as its solution
Answers
Answer:
D.) A and D
Step-by-step explanation:
To find which set of equations has the solution (3,1), you need to identify where on the graph this point lies. Remember, in a point, the first number listed (3) is the "x" value and the second number (1) is the "y" value.
First, look for x = 3. This is the number located on the x-axis (horizontal line).
From this spot, since y = 1, move up 1 unit.
At this point, two lines intersect. These lines are lines A and D.
What is the polynomial? Quick I need answer
Answers
Answer:
An algebraic expression containing two or more terms is called a polynomial
Answer:
Its C
Step-by-step explanation:
it worked finally
36 students for 3 teachers =
1.0
5
12 students for 1 teacher.
Answers
Answer:
12
Step-by-step explanation:
36 divided by 3 =12 for 1 teacher
The nth term of a sequence is -2n - 4. Work out the 50th term of the sequence.
Answers
Answer:
-104
Step-by-step explanation:
1) Substitute 50 into n.
-2(50) - 4
-100 - 4
-104
You just looked at the graph of this system of equations. Why will the lines never intersect? y = –x + 5 y = –x – 3
Answers
Answer: same slope, y int are different
Step-by-step explanation:
Both these lines never intersect because they have the same slope.
they both go down 1 over 1, and also their y interecepts are different
The probabilities that Sani, Kolo and Tato will hit a target are 3/4, 2/3 and 7/3 respectively If all three men shot once what is the probability that target will be hit only once
Answers
Step-by-step explanation:
get the lcm of the numerals and the denominators then simplify
hope it is correct
Solve x/3 = x+2/2. X=
Answers
Answer:
I will assume that the term "x+2/2" is meant to be "(x + 2)/2)." Otherwise the equation would read (x/3) = x + 1
Step-by-step explanation:
(x/3) = (x + 2)/2
x = 3*(x+2)/2 [Multiply both sides by 3]
x = (3x + 6)/2
x = (3/2)x + 6/2
x - (3/2)x = 3
-0.5x = 3
x = -6
====================
Check:
Does (x/3) = (x + 2)/2 for x = -6?
(-6/3) = (-6 + 2)/2
-2 = -4/2
-2 = -2 YES
Which expression is equivalent to (3^2) ^-2
Answers
[tex](3^{2} )[/tex]^-2=(9)^-2=1/9^2=1/81
hope it helps!
Today’s weather map shows the jet stream flowing west to east toward Washington, D.C., at a speed of 70 knots. If the ground speed needs to be 450 knots to make it from Washington to Kansas City on time, what does the plane’s speed need to be?
Answers
Considering the direction of the wind, it is found that the plane's speed needs to be of 520 knots.
What is the ground speed?The ground speed, considering that the wind is flowing from Kansas City to Washington, and the trip is Washington to Kansas City, is given by:
G = Plane speed - Wind speed.
Hence:
450 knows = Plane speed - 70 knots.
Plane speed = 520 knots.
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