Answer:
A horizontal translation of 5 units to the left.
Step-by-step explanation:
Given the parent linear function:
[tex]\displaystyle f(x)=x[/tex]
To shift vertically n units, we can simply add n to our function. Hence:
[tex]f(x)=x+n[/tex]
So, a vertical shift of 5 units up implies that n=5. So:
[tex]f(x)=x+5[/tex]
As given.
However, to shift a linear function horizontally, we substitute our x for (x-n), where n is the horizontal shift. So:
[tex]f(x-n)=(x-n)[/tex]
Where n is the horizontal shift.
For example, if we shift our parent linear function 1 unit to the right, this means that n=1. Therefore, our new function will be:
[tex]f(x-1)=(x-1)[/tex]
Or:
[tex]f(x)=x-1[/tex]
We notice that this is also a vertical shift of 1 unit downwards.
Therefore, we want a number n such that -n=5.
So, n=-5.
Therefore, it we shift our function 5 units to the left, then n=-5.
Then, our function will be:
[tex]f(x-(-5))=(x+5)\text{ or } f(x)=x+5[/tex]
Hence, we can achieve f(x)=x+5 from f(x)=x using a horizontal translation by translating our function 5 units to the left.
Which of the following describes a way to graph the function g(x) = -1/2 |x|?
Solve it in algebraically
y= 4x – 11
y=-8x + 13
Answer:
y=4x−11
Step 1: Flip the equation.
4x−11=y
Step 2: Add 11 to both sides.
4x−11+11=y+11
4x=y+11
Step 3: Divide both sides by 4.
[tex]\frac{4x}{4}[/tex] = [tex]\frac{y+11}{4}[/tex]
x= [tex]\frac{1}{4} y[/tex] + [tex]\frac{11}{4}[/tex]
y=-8x + 13
Step 1: Flip the equation.
−8x+13=y
Step 2: Add -13 to both sides.
−8x+13+−13=y+−13
−8x=y−13
Step 3: Divide both sides by -8.
[tex]\frac{-8x}{8}[/tex] = [tex]\frac{y- 13}{-8}[/tex]
x= [tex]\frac{-1}{8}y[/tex] + [tex]\frac{13}{8}[/tex]
18 cajas de manzanas y peras fueron llevadas a la escuela. Las peras trajeron 210 kg en 6 cajas. ¿Cuántos kilos de manzanas fueron llevadas a la escuela si cada caja de manzanas pesa 7 kg más que una caja de peras 18 cajas de manzanas y peras fueron llevadas a la escuela. Las peras trajeron 210 kg en 6 cajas. ¿Cuántos kilos de manzanas fueron llevadas a la escuela si cada caja de manzanas pesa 7 kg más que una caja de peras?
Answer:
504 kilos de manzanas fueron llevados a la escuela.
Step-by-step explanation:
Sean [tex]x[/tex], [tex]y[/tex] la cantidad de cajas de manzanas y peras, respectivamente. De acuerdo con el enunciado, tenemos el siguiente sistema de ecuaciones:
Total de cajas
[tex]x+y = 18[/tex] (1)
Masa de cada caja de peras
[tex]y\cdot m_{P} = 210[/tex] (2)
[tex]y = 6[/tex] (3)
Masa de caja de manzanas
[tex]m_{M} = m_{P}+7[/tex] (4)
De (2) en (3), tenemos que la masa de cada caja de peras es:
[tex]m_{P} = 35\,kg[/tex]
Por (4), encontramos que la masa de cada caja de manzanas es:
[tex]m_{M} = 35\,kg+7\,kg[/tex]
[tex]m_{M} = 42\,kg[/tex]
Finalmente, de (1) tenemos la cantidad de cajas de manzana:
[tex]x = 18-y[/tex]
[tex]x = 12[/tex]
La cantidad de kilos de manzanas llevada a la escuela se obtiene al multiplicar la cantidad de cajas de manzana por la masa de cada caja:
[tex]M = (12)\cdot (42\,kg)[/tex]
[tex]M = 504\,kg[/tex]
504 kilos de manzanas fueron llevados a la escuela.
Is the answer a, b, c, or d
Answer:
Step-by-step explanation:
B
Answer:
d 11x + 24
Step-by-step explanation:
Perimeter = 5x + 3 + 2x + 6 + 4x + 15
= (5x + 2x + 4x) + (3 + 6 + 15)
= 11x + 24
Reese is selling lemonade at the parade. He gets to keep 50% of the money he collects. A large lemonade is $6.00 and a small lemonade is $2.00. The expression represents 50% of the money he collects. 0.50(6l + 2s) Use the Distributive Property to expand the expression. The simplified expression is
Answer:
3l + 1s
Step-by-step explanation:
Given that:
The expression to represent 50% of the money collected : 0.50(6l + 2s)
Expanding the expression :
0.50(6l + 2s)
(0.50 * 6l) + (0.50 * 2s)
3l + 1s
Hence, the simplified expression is 3l + 1s
plsss I need help..i will remark ur answer as a brilliant answer
Answer:
9.3. your ans. nabsbss
Does octane matter? Some people believe that higher octane fuels result in better gas mileage for their cars. To test this claim, a researcher randomly selected 11 individuals (and their cars) to participate in the study. Each individual was given 10 gallons of 87-octane fuel and 10 gallons of 92-octane fuel. The number of miles each driver was able to drive until they ran out of gas with each type of fuel is recorded below.
Complete Question
The government believes that higher-octane fuels result in better gas mileage for their car. To test this claim, a researcher randomly selected 11 individuals to participate in the study. Each participant received 10 gallons of gas (87-octane and 92-octane) and drove his car on a closed course. The number of miles driven until the car ran out of gas was recorded. A coin flip was used to determine whether the car was filled up with 87-octane first or92-octane first, and the driver did not know which fuel was in the tank.
We conducted a paired t-test to see if higher-octane fuels result in better gas mileage, and the test statistic was found to 1.74.
Calculate the p-value.
Answer:
The p-value is [tex]p-value = 0.0562[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 11
The test statistics is [tex]t = 1.74[/tex]
The null hypothesis is [tex]H_o : \mu _1 = \mu_2[/tex]
The alternative hypothesis is [tex]H_a : \mu _1 > \mu_2[/tex]
Here [tex]\mu_1[/tex] is the gas millage for 87-octane fuel while
Here [tex]\mu_2[/tex] is the gas millage for 92-octane fuel
Generally the degree of freedom is mathematically represented as
[tex]df = n- 1[/tex]
[tex]df =10[/tex]
Generally from the student t -distribution table the probability of t = 1.74 at a degree of freedom of [tex]df =10[/tex] is
[tex]p-value = P( t > 1.74) = 0.0562[/tex]
This bottle contains 200 mL of liquid plant food. What is the best estimate of how much the bottle can hold when it is filled to the FULL mark?
Answer: 1,000 ml
Step-by-step explanation:
From the looks of it, the 200ml mark is about a fifth of the volume needed to get to the FULL mark.
If 200 is ¹/₅, the full mark will be;
= 200/ ¹/₅
= 1,000 ml
Answer:
1000 ml
Step-by-step explanation:
What is the place the 8 is in in the number 38,341,097.54
9.) At the electronics store where you
sells for $459.20, what was the original
price of the tv
Answer:
558.7805
Step-by-step explanation:
help me please and thank you
Answer:
4 dollars per pint. You can 0.25 pint per dollar. For 20 dollars
u can get 5 pints. 8 pints will be 32 dollars.
Answer:
Per pint is $4
You get a .25 pint for 1 dollar
You get 5 pints for $20
It cost $32 for 8 pints of raspberries
Step-by-step explanation:
Once you find the unit rate you can multiply and divide depending on the question.
Can someone help me ASAP !
Hope this helps! Have a nice day!
Help will give crown
Answer:
x y
2 9
3 7
4 5
5 3
Step-by-step explanation:
Answer:
9
7
5
3
The order is from up to down
What is the simplified form of 15 x to the eighth power over 24 y to the fifth power divided by 4 x to the fourth power over 8 squared ? (6 points)
4 y cubed over 5 x to the fourth power
4 y to the fourth power over 5 x cubed
5 x to the fourth power over 4 y cubed
5 x cubed over 4 y to the fourth power
Answer:
5 x to the fourth power over 4 y cubed
The ratio of income Mr. John to his expenditure is 8 : 7. If his expenditure of one year is ₹ 1,26,000, what is his monthly income?
Answer:
₹ 12000 .
Step-by-step explanation:
It is given that,
The ratio of income Mr. John to his expenditure is 8 : 7
Expenditure = ₹ 1,26,000
Let the income is 8x and expenditure is 7x.
ATQ,
7x = 1,26,000
x = ₹ 18000
Yearly income = 8x
= 8(18000 )
= ₹ 144000
Monthly income,
[tex]M=\dfrac{144000}{12}\\\\=12000[/tex]
Hence, his monthly income is ₹ 12000 .
Nico rolled two number cubes 250 times. use the complement to find the experimantal propability of not rolling a 3 on the blue number cube, NC2.
Answer:
the probability is 0%
Step-by-step explanation:
is there options like
A
B
C
options
what is the lowest term of 27/45
Answer:
3/5
Step-by-step explanation:
[tex] \frac{27}{45} = \frac{27 \div 9}{45 \div 9} = \frac{3}{5} \\ [/tex]
Which expression shows how 8⋅54 can be rewritten using the distributive property?
8⋅50+8⋅4
8⋅50+8⋅54
4⋅50+4⋅4
50⋅8+50⋅4
Answer:8 * 54 = 8 * 50 + 8 * 4 = 8(50 + 4)
Step-by-step explanation:
A circle has a radius of 12. Find the area of the sector whose central angle is 120°.
Is 5x + 2 a numerical expression?
Answer:
Yes
Step-by-step explanation:
Yes, this is a numerical expression because x represents a number. This number is unknown, so x = 1 --- 5x (1) + 2 is equivalent to 5x + 2. 5x (1) +2 is a numerical expression, SO that means that 5x + 2 is a numerical expression.
there are between 25 and 43 students in a class
the ratio of boys to girls is 5 : 7
how many students are in the class?
Answer:
36
Step-by-step explanation:
Since the sum of the ratios is 5+7=12 the total number of students must be divisible by 12
The only number within the given range is 36
The number of students should be in the class should be considered as the 36.
Calculation of the number of students:Since
there are between 25 and 43 students in a class
the ratio of boys to girls is 5 : 7
So here the total ratio should be like
= 5 + 7
= 12
So here the number of students should be divisible by 12
So, it should be 36
Learn more about ratio here: https://brainly.com/question/13111469
What is the solution to the equation x/2 - 4 = 6?
x = 5
x = 20
x = 1
x = 10
Answer:
x=5
hope it helps.....
Answer:
I got the answer from the Tutor.
what is 53829-(-538)7902(6)=?
Answer:
25561485
Step-by-step explanation:
if f(x)=5x^4+3, then what is the remainder when f(x) is divided by x-1?
Answer:
8
This is actually fairly simple. If you take the x-1 and set it equal to 0 you get 1. And if you plug that value into the x you get 8, which is the remainder. This is called the remainder value theorem.
Step-by-step explanation:
If the slope of y=2x+5 is changed to -2, how does the graph change?
The positive graph of y = 2x + 5 changes to the negative graph which moves downward from left to right when the slope is changed to -2.
What is Slope?Slope of a line is defined as the difference in the y coordinates divided by the difference in the x coordinates of two points.
Slope of a line is usually denoted by the letter m.
First let us take the graph of y = 2x + 5.
Take x intercept and y intercept of this graph.
x intercept is the point where line touches X axis and y intercept is the point where line touches Y axis.
From the equation of the line, y intercept = 5
So we get a point (0, 5)
Now to find x intercept, let y = 0 in the equation, then x = -2.5
So we get another point (-2.5, 0)
So the line y = 2x + 5 passes through the points (0, 5) and (-2.5, 0).
Now if the slope changed to -2, equation becomes y = -2x + 5.
y intercept is same.
So one point of the line will be (0, 5)
To find x intercept, let y = 0 in the second equation, then x = 2.5
So the second line passes through the points (0, 5) and (2.5, 0)
That is, the graph which goes upward from left to right changed to the graph downward from left to right.
Hence, when the slope changed to -2, the graph goes downward from left to right.
To learn more about Slope, click:
https://brainly.com/question/3605446
#SPJ2
Pls solve... will give brainliest... linear inequality
the length of a rectangle is 4cm more than double its width. the perimeter of the rectangle is 116cm. Find the length and the width of the rectangle
Answer:
l = 31 cm
w = 27 cm
Step-by-step explanation:
l = w + 4
p = 2l + 2w
p = 2(w+4) + 2w
116 = 2(w+4) + 2w
116 = 2w + 8 + 2w
116 = 4w + 8
108 = 4w
27 = w
l = w + 4
l = 27 + 4
l = 31
hope this helps, pls mark brainliest :D
Answer:
w=18 L=40
Step-by-step explanation:
w
---------
| |
| | 2w+4
| |
---------
2(2w+4)+ 2(w)=116
6w+8=116
6w=108
w=18
2(18)+4
36+4
40
Which geometric series converges?
A. 1/5 + 2/5 + 4/5 + 8/5 +...
B. 1/5 + 6/5 + 36/5 + 216/5 +...
C. 1/5 + 2 + 20 + 200 +...
D. 1/5 + 1/20 + 1/80 + 1/320 +...
Answer:
D. 1/5 + 1/20 + 1/80 + 1/320
Step-by-step explanation: i got you bro
Answer:
answer is D
Step-by-step explanation:
Help I can’t fail plz help
Last year ten examiners spent 6 hours marking all the exam papers.
This year the same process took only three hours.
How many examiners were there this time if they marked the same set of papers at the same rate?
Answer: 20 examiners.
Step-by-step explanation:
We know that 10 examiners need 6 hours to mark all the papers.
Then if R is the rate at which one examiner can mark all the papers, we have the equation:
(10*R)*6h = marking all the papers = 1
(i will use the 1 to represent the complete task)
then we have:
(10*R)*6h = 1
60h*R = 1
R = 1/60h
This means that only one examiner would need 60 hours to mark all the papers.
This time, we have N examiners, and they marked the same amount of papers in 3 hours, then we have thee equation:
(N*R)*3h = 1
(N*1/60h)*3h = 1
N*(3h/60h) = 1
N*(1/20) = 1
N = 1/(1/20) = 20
N = 20
This time, there are 20 examiners.