Given f(x)=x^2, write the equation of the transformed function if g(x)=f(x-1)
Answers
Answer:
1. g(x) = (x - 1)²; translation of 1 unit to the right.
2. g(x) = 3^(x + 1) - 2; translation to the left of 1 unit and translation of 2 units down.
Step-by-step explanation:
1.
f(x) = x²
g(x) = f(x - 1)
g(x) = (x - 1)²
Since x was replaced by x - 1, g(x) is similar to f(x) with a translation of 1 unit to the right.
2.
f(x) = 3^x
g(x) = f(x + 1) - 2
g(x) = 3^(x + 1) - 2
Since x was replaced by x + 1, which is the same as x - (-1), there is a translation to the left of 1 unit. In addition, the -2 causes a translation of 2 units down.
Related Questions
The table shows the ratio of people who ate a certain type of lunch to the total number of people who ate lunch. A total of 840 people ate lunch. What statement is true?
Answers
The sum of the individual lunch ate by people is equal to the total number of people who ate lunch.
What is an equation?An equationi is an expression that shows the relationship between two or more variables and number.
Given that the total number of people who ate lunch is 840, hence:
The sum of the individual lunch ate by people is equal to the total number of people who ate lunch.
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Can't figure out the other ones. There are two inages for this. Use the square to answer the following questions. DC=8.5 and DW=6
Answers
Answer:
6; 12; 8.5; 90°; 90°; 45°; 45°
Step-by-step explanation:
A square has all sides the same length, and diagonals the same length. The diagonals bisect the right angles in the corners, and they cross at right angles.
__
As you have already observed, ...
BW = DW = 6
AC = BD = 2(DW) = 2(6) = 12
Further, ...
DA = DC = 8.5 . . . . sides of a square are the same length
∠DWA = 90° . . . . . diagonals cross at right angles
∠ABC = 90° . . . . . corner angles are right angles
∠ABD = 45° . . . . . the diagonal cuts the corner angle in half
∠DCA = 45° . . . . . all of the acute angles are congruent
_____
Additional comment
A square is a rhombus that is also a rectangle. The relevant characteristics are ...
all sides of a rhombus are congruentthe diagonals of a rhombus cross at right angles. Each bisects the vertex angles at either end, which are congruent.the corner (vertex) angles of a rectangle are right anglesDylan has a total of 25 marbles. He gives ! marbles to his sister, Jane. What fraction
of marbles did Jane receive?
Answers
The Dylan sister Jane received 1/5 marbles, which is a part of 25 if the Dylan has a total of 25 marbles.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The total number of marbles Dylan has = 25
The total number of marbles Dylan gave to his sister = 5
If we choose one marble out of 25 = 1/25
If we choose 5 marbles = 5(1/25) = 1/5
Thus, the Dylan sister Jane received 1/5 marbles, which is a part of 25 if the Dylan has a total of 25 marbles.
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If y varies directly with x and y = 87 when x = 3, find y when x = 5. Write and solve a direct variation equation to find the answer
Answers
Answer:
145
Step-by-step explanation:
y=kx
87=3k
k= 87/3
k= 29
y=29×5
y= 145
Nancy has 8 meters of rope. How many pieces of rope of length 1/2 meter can she cut from it
Answers
Answer:
16
Step-by-step explanation:
8 divided by 1/2 is
8 times 2
which is
16
Whats the area of this shape?
Answers
The area of the shape shown in the image which is in the shape of kite figure is 168 squared centimeters.
What is the area of the kite figure?The area of the kite figure is half of the product of its diagonals. Area of kite figure can be find out using the following formula.
[tex]A=\dfrac{pq}{2}[/tex]
Here, p and q are the diagonals of the kite.
The length of the first diagonal of the kite figure is,
p=6+15
p=21 cm
The length of the second diagonal of the kite figure is,
q=8+8
q=16 cm
Thus, the area of kite figure is:
[tex]A=\dfrac{21\times16}{2}\\A=\dfrac{21\times16}{2}\\A=168\rm\; cm^2[/tex]
Thus, the area of the shape shown in the image which is in the shape of kite figure is 168 squared centimeters.
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Volleyball players are randomly placed on teams by spinning a spinner with four congruent, colored sections. They are assigned positions on the team by rolling a six-sided die. The team colors are red, black, green, and purple.
What is the conditional probability of rolling a 5 given that the spinner landed on black?
A. 1/6
B. 1/24
C. 2/5
D. 1/4
Answers
split 54 between 4 people
Answers
Answer:
your answer is 13.2
Step-by-step explanation:
Which function best models the data in the graph? y = 10.1x 101 y = x2 101 y = 101(2x) y = 1.01x2 101
Answers
Based on the calculations, the function which best models the data in the graph is y = 10.1x + 101.
How to determine the function?Mathematically, the equation of a line in standard form is given by this formula:
y - y₁ = m(x - x₁)
Where:
m is the slope.y is the point on the horizontal axis.x is the point on the vertical axis.In order to determine the function which best models the data in the graph shown in the image attached below, we would calculate the slope of the data by using this formula:
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}\\\\Slope = \frac{202\;-\;101}{10\;-\;0}\\\\Slope = \frac{101}{10}[/tex]
Slope = 10.1.
For the function, we have:
y - y₁ = m(x - x₁)
y = 10.1(x - 0) + 101
y = 10.1x + 101.
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The next part is D then C
Step-by-step explanation:
Determine the sum of the terms in the series 25 + 30 + 35 + ⋯ + 245. Show your work.
Answers
Answer:
6075
Step-by-step explanation:
Given series is: 25 + 30 + 35 + ⋯ + 245.Here, first term (a) = 25Common difference (d) = 5Last term [tex](a_n) = 245[/tex]First we find the number of terms that this series has by the following formula:[tex]a_n = a+(n-1)d[/tex]Plugging the values of a, d and [tex]a_n[/tex], we find.[tex]245 = 25+(n-1)5[/tex][tex]\implies 245 - 25=(n-1)5[/tex][tex]\implies 220=(n-1)5[/tex][tex]\implies \frac{220}{5}=n-1[/tex][tex]\implies 44=n-1[/tex][tex]\implies 44+1=n[/tex][tex]\implies\red{\bold{ n=45}}[/tex]Thus, the given series contains 45 terms.Next, we find the sum of the given series using the formula given below.[tex]S_n = \frac{n}{2}(a+a_n)[/tex][tex]\implies S_{45}= \frac{45}{2}(25+245)[/tex][tex]\implies S_{45}= \frac{45}{2}(270)[/tex][tex]\implies S_{45}=45*135[/tex][tex]\implies\orange{\boxed{\boxed{\boxed{\bold{ S_{45}=6075}}}}}[/tex]Find the slope of the tangent line to the curve y = 3x2
- 2x at the point (1,2)
Studying for final pls help
Answers
Answer:
slope is 4
Step-by-step explanation:
since your trying to find the slope of the tangent line, you have to find the first derivative, once you do plug in your x to give your slope at the designated spot,
1/3 + 1/4 + ? = 1
? = the answer
Answers
Answer:
5/12 (corrected)
Convert with lowest common denominator, 12(find by multiplying)
1/3 = 4/12
1/4 = 3/12
Add the fraction's numerators
4 + 3 = 7
Subtract by 1 whole
7/12 - 12/12 = 5/12
Thus, your answer is 5/12
Answer:
5/12
Step-by-step explanation:
to give the fractions the same denominator, find their gcm
3 * 4 = 12
therefore multiply 1/3 by 4/4 to get 4/12
multiply 1/4 by 3/3 to get 3/12
3/12 + 4/12 = 7/12
to find the remainder subtract
12/12 - 7/12 = 5/12
your answer is 5/12
hope this helps:)
Please help i will give brainliest
Answers
Answer:
See below
Step-by-step explanation:
The flat line portions of the graph are where Tim is not moving....the first flat area is where he had the puncture to fix....the second is tea-time
A/ 16:00 - 16:20 20 minutes
B/ 2000 meters in 10 minutes would be 12 000 m /hr = 12 km/hr
C/ No, he was slower ....on the way there it took him 20 minutes total cycling time
15:30 to 15:40 plus 15:50 to 16:00
if v1 = (3,7) and v2 = (2,4), then v1 v2 is equal to which of the following
Answers
Answer:
If it is dot product, then 32.
Step-by-step explanation:
3*2+7*4
6+28
32
Probability & Sampling:Question 8
Mr. Evans wanted to compare the math grades of his 6th
grade students and 7th grade students. He displayed the
data on dot plots.
Answers
The conclusion that Mr. Evans can make is that On average, students in 6th Grade have lower grades than students in 7th Grade.
What is a dot plot?This is also known to be a dot chart. It is said to be a statistical chart that is made up of data points which are known to be plotted on a little and simple scale.
Note that based on the dotted plot of the student's grade, the conclusion that can be drawn or the one that Mr. Evans can make is that On average, students in 6th Grade have lower grades than students in 7th Grade.
See full question below
What conclusion can Mr. Evans make? Hint: Find the mean
answer choices
On average, students in 6th Grade have lower grades than students in 7th Grade.
On average, students in 6th Grade have higher grades than students in 7th Grade.
Students will always have a lower math grade in 6th Grade than 7th Grade.
On average, students in 6th Grade and 7th Grade have about the same grade
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What line is perpendicular to y−7=4/5(x+3)?
A. y= −5/4x+1
B. y= 5/4x+1
C. y= 4/5x+1
D. y= −4/5x+1
Answers
Answer: The correct answer would be C. y= 4/5x+1
Step-by-step explanation:
[tex]y-intercept=\frac{47}{5}[/tex]
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
y-7-(4/5*(x+3))=0
STEP
1
:
4
Simplify —
5
Equation at the end of step
1
:
4
(y - 7) - (— • (x + 3)) = 0
5
STEP
2
:
Equation at the end of step 2
4 • (x + 3)
(y - 7) - ——————————— = 0
5
STEP
3
:
Rewriting the whole as an Equivalent Fraction
3.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 5 as the denominator :
y - 7 (y - 7) • 5
y - 7 = ————— = ———————————
1 5
Equivalent fraction: The fraction thus generated looks different but has the same value as the whole
Common denominator: The equivalent fraction and the other fraction involved in the calculation share the same denominator
3.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
(y-7) • 5 - (4 • (x+3)) 5y - 4x - 47
——————————————————————— = ————————————
5 5
Equation at the end of step
3
:
5y - 4x - 47
———————————— = 0
5
STEP
4
:
When a fraction equals zero :
4.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now, to get rid of the denominator, I multiply both sides of the equation by the denominator.
Here's how:
5y-4x-47
———————— • 5 = 0 • 5
5
Now, on the left hand side, the 5 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
5y-4x-47 = 0
Equation of a Straight Line
4.2 Solve 5y-4x-47 = 0
CalderonJ recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx + b" is the formula of a straight line drawn on a Cartesian coordinate system in which "y" is the vertical axis and "x" is the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 5y-4x-47 = 0 and calculate its properties
Notice that when x = 0 the value of y is 47/5 so this line "cuts" the y axis at y= 9.40000
y-intercept = 47/5 = 9.40000
Calculate the X-Intercept :
When y = 0 the value of x is 47/-4 Our line therefore "cuts" the x axis at x=-11.75000
x-intercept = 47/-4 = -11.75000
Calculate the Slope :
The slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 9.400 and for x=2.000, the value of y is 11.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 11.000 - 9.400 = 1.600 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 1.600/2.000 = 0.800
A wheel on Aldo's bicycle is 0.3m in diameter. Aldo rides the bicycle in a race, and the wheel turns 45 times during the course of the race. How long is the race?
Use the value 3.14 for pi. Round your answer to the nearest tenth. Do not round any intermediate steps.
Answers
Answer:
42.39m Please round it to nearest tenth.I haven't rounded it
If dave decides to go scuba diving for the first time. If he descends at -2 1/3 feet every second, at what depth will he be at after 3 1/2 seconds.
Answers
Answer:
-8.66666667 feet because:
Step-by-step explanation:
-2 1/3 x 3 = 7
-2 1/3 ÷ 2 = 1.66666666667
7 + 1.6666666667 = 8.66666667
Which is the equation of a hyperbola with directrices at x = ±2 and foci at (6, 0) and (−6, 0)?
Answers
Answer:
[tex]\displaystyle \frac{x^2}{12}-\frac{y^2}{24}=1[/tex]
Step-by-step explanation:
Since the directrices are vertical lines:
Use the hyperbola equation [tex]\displaystyle \frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex] Foci are [tex](\pm c,0)[/tex][tex]a^2+b^2=c^2[/tex][tex]a[/tex] and [tex]b[/tex] are half the lengths of the tranverse and conjugate axes respectivelyDirectrices are located at the lines [tex]\displaystyle x=\pm\frac{a^2}{c}[/tex]We assume the center to be [tex](h,k)\rightarrow(0,0)[/tex]Since we already know our directrices are at the lines [tex]x=\pm2[/tex] and we know that [tex]c=\pm6[/tex] from our foci, we can solve for the value of [tex]a^2[/tex]:
[tex]x=\frac{a^2}{c}\\\\2=\frac{a^2}{6}\\\\12=a^2[/tex]
This allows us to solve for the value of [tex]b^2[/tex]:
[tex]a^2+b^2=c^2\\\\12+b^2=6^2\\\\12+b^2=36\\\\b^2=24[/tex]
Thus, our equation for the hyperbola is [tex]\displaystyle \frac{x^2}{12}-\frac{y^2}{24}=1[/tex].
billy has 2.4m of ribbon for crafts. he wants to share it evenly with 12 friends. how many centimeters of ribbon would 7 friends get
Answers
You would have to do 2.4 divided by 12 to get 0.2. Then multiply 0.2 by 7 to get 1.4.
Answer:
140cm
Step-by-step explanation:
We first have to change 2.4 meters into centimeters. And the formula for that is (x)m = (x)cm x 100.
So 2.4 x 100 = (x)m. We can solve this by moving the "." two times to the right and we will get 2.4m = 240cm.
The next step is to divide it by twelve because Billy wants to share it with 12 friends. 240cm/12 = 20cm per person.
Then we have to multiply 20 with 7 to see how many centimeters 7 friends would get.
20*7 = 140. So the answer is 140cm.
Simplify: 39x+21x-4. Round to the nearest ten
Answers
Answer:
60x-4
Step-by-step explanation:
39x+21x=60x
Therefore, you are left with 60x-4, which is in its simplest form.
So confused! Anyone good at this?
Answers
Answer:
x = 90 degrees.
Step-by-step explanation:
These are all regular octagons and the value of x = 2 * external angle of an octagon.
The sum of external angles of a polygon sum to 360 degrees and in the case of an octagon each external angle = 360/8 = 45 dgrees,
So angle x = 2*45 = 90 degrees.
Please help fghgbvnghgbvhgghg
Answers
Answer:
x=326
Step-by-step explanation:
0.3x - 34 + 0.2x -39 = 90.
Simplify this equation.
0.5x = 163
x = 326
Which statement is true about the circumference of a circle?
A: The circumference is the measurement around the circle.
B: The circumference is the measurement of the radius.
C: The circumference is the measurement of the diameter.
D: The circumference is double the radius.
Answers
Answer:
[tex]\large\boxed{\textsf{A: The circumference is the measurement around the circle.}}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked what's true about the Circumference.}[/tex]
[tex]\large\underline{\textsf{What is the Circumference?}}[/tex]
[tex]\textsf{The Circumference is the sum of all the arcs of a circle.}[/tex]
[tex]\textsf{Arcs are the curved edges of a circle that make up the \underline{Perimeter}.}[/tex]
[tex]\textsf{Because the Circumference makes up all of the Arcs in a circle, which is the perimeter;}[/tex]
[tex]\textsf{Option A is the most reasonable choice, as the circumference is the perimeter of}[/tex]
[tex]\textsf{a circle.}[/tex]
F is directly proportional to A. If F=36 when A=9 find, F when A=4
Answers
Answer:
16
Step-by-step explanation:
f=ka
36=9k
k=4
f=4×4
f=16
I need help asap please
Answers
Answer:
52 seconds5833 feetStep-by-step explanation:
Each plane has a starting altitude and a fixed rate of climb. Its altitude at some time t will be the sum of the starting altitude and t times the rate of climb.
__
plane Aaltitude = starting altitude + t × rate of climb
a(t) = 4000 +35.25t
plane Bb(t) = 2427 +65.5t
same altitudeThe planes will be at the same altitude at the same time when ...
a(t) = b(t)
4000 +35.25t = 2427 +65.5t
1573 = 30.25t . . . . . . . . . . subtract 2427+35.25t
52 = t . . . . . . . . . . . . . divide by 30.25
That altitude is ...
a(52) = 4000 +35.25×52 = 4000 +1833 = 5833
summary52 seconds will pass before the planes are at the same altitude.
Their altitude then will be 5833 feet.
Part of the population of 7,500 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 3 of them are infected. How many elk are likely to be infected?
Answers
When the sample is given, the number of elk are likely to be infected is to be considered as the 450.
Calculation of the number of elk:Since the population is 7,500.
The random sample is 50.
So here be like
[tex]7500[/tex] ÷ [tex]50[/tex] × [tex]3[/tex]
= 450
hence, When the sample is given, the number of elk are likely to be infected is to be considered as the 450.
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What does X= and what is the angle
A. Corresponding
B.same side interior
C. Alternate interior
D.Alternate exterior
Answers
There are 20 boys and 18 girls in a class find the percentage of {1} boys {2} girls, in the class
Answers
Answer:
1. 52.63% 2. 47.36%
Step-by-step explanation:
20 + 18 = 38 total people
20 divided by 38 = 0.5263 to 52.63%
18 divided by 38 = 0.4736 to 47.36%
Hope this helps!
The sum of the digits of a two - digit number is 15. if the the digits were reversed , the number increases by 9 . Find the number .
Stay away if u don't know the ans.
Well explained ans needed :)
Answers
Answer:
78
Step-by-step explanation:
Let the two-digit number have the digits a and b.
It mentions that they add up to 15.
Then the possible numbers are :
69 (6 + 9 = 15)78 (7 + 8 = 15)=============================================================
Let's reverse the numbers :
69
69 ⇔ 9696 - 69 = 27Not the right number ×78
78 ⇔ 8787 - 78 = 9This is correct √=============================================================
Solution :
Hence, the number needed is 78
Step-by-step explanation:
no. 10y+x
no. formed by reversing the digits = 10x+ y
ATQ
EQ(1)= x+y=15
EQ (2)=10x+y+9=10y +x ( Digits are reversed)
9x-9y=-9
x-y=-1
x+y=15 ( given)
2x=14,x=7
and y=15–7=8
thus the number=78
