Given:
The linear parent function, f(x)=x is vertically compressed by a factor of 4 and reflected over the x-axis.
To find:
The new function.
Solution:
The vertical stretch and compression is defined as
[tex]g(x)=kf(x)[/tex]
If k>1, then f(x) vertically stretched by factor k and if 0<k<1, then f(x) vertically compresses by factor [tex]\dfrac{1}{k}[/tex].
In the given problem, linear parent function, f(x)=x is vertically compressed by a factor of 4. So, [tex]k=\dfrac{1}{4}.[/tex]
[tex]g(x)=\dfrac{1}{4}f(x)[/tex]
Then, it is reflected over the x-axis.
[tex]G(x)=-g(x)[/tex]
[tex]G(x)=-\dfrac{1}{4}f(x)[/tex] [tex][\because g(x)=\dfrac{1}{4}f(x)][/tex]
[tex]G(x)=-\dfrac{1}{4}x[/tex] [tex][\because f(x)=x][/tex]
So, the new function is [tex]G(x)=-\dfrac{1}{4}x[/tex].
Therefore, the correct option is B.
Answer:g(x)=-1/4x
Step-by-step explanation:
A large bucket holds 5 gallons of water, which is about the same as 19 liters of water. A small bucket holds 2 gallons of water. About how many liters does it hold? Show all of your work.
Answer: It will hold 7.6 Litres
Step-by-step explanation:
Step 1
We know that Converting Gallons to Litres, we have that
I gallon = 3.78541
So from the question
A large bucket = 5gallons which in Litres became
5 x 3.78541=18.927 rounded up to 19litres.
-- Also IF 5 Gallons = 19 Litres
Then 1 Gallon = 19/5= 3.8 Litres
Step 2
IF large bucket of 5 gallons = 19 Litres ,
A small bucket of 2 gallons of water = 2 x 19/5= 38/5 =7.6 Litres
Find the sum
(-8z+4)+(8z-7)
Answer:
-3
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
(-8z+4)+(8z-7)
=-8z+4+8z-7 [-8z and +8z cut out]
=+4-7
=-3
Lin's job pays $8.25 an hour plus $10 of transportation allowance each week. She has to work at least 5 hours a week to keep the job, and can earn up to $175 per week (including the allowance). Represent this situation mathematically in two inequalities. Let `x` represent the number of hours Lin works in a week.
Answer:
10000
Step-by-step explanation:
what is an equetion of the line that paraell to y=3x - 8and passes through the point[4,-5]
Answer:
-2.5 I THINK
Step-by-step explanation:
solve tje equation for t. Round the answer off to two places after the decimal point.
simplify 1000^8 = 10^w
Answer: 24
i got the same question
The total weight
of 25 books is 125
pounds. How many
pounds would 70
books weigh?
70 / 25 = 2.8
125 * 2.8 = 350
therefore 70 books would be 350 pounds
Ava buys a book for $8.85 .she pays $10 bill.How much chang will see get?
Given:
Ava buys a book for $8.85 .
She pays $10 bill.
To find:
The amount of change she will get.
Solution:
We have,
Price of book = $8.85
Amount she pays = $10
Now,
Amount of change = Amount she pays - Price of nook
Amount of change = $10 - $8.85
Amount of change = $1.15
Therefore, she will get $1.15 as change.
Answer:
1.15
Step-by-step explanation:
If the selling price for laptop is $1100 and is marked down by 30% in promotional offers, then sale price after discount is
\sqrt{2x^2}\cdot \sqrt{4x}
2. What is the balance after 15 years in a savings account that earns 2% interest compounded bimonthly when the
initial deposit is $1000?
O $1300.50
N.
O $1020.11
O $1012.52
O $1348.07
Answer:
You deposit $1000 in a savings account that earns ... Balance at. End of Year. = Principal + Annual. Interest. = $1000 + $1000(0.06) ... balance in an account that earns interest compounded annually after t years. P = Principal (initial deposit) ... 15. 4.8. —. 12. 16. 268.68 ⋅72. 17. MULTIPLE CHOICE Which graph represents ...
Step-by-step explanation:
The sum of the angles of a triangle is 180°. The second angle is 35° more than the first angle the third angle is 25° more than the first angle what are the three angles
Answer:
The three angles are 40°, 75°, 65°
Step-by-step explanation:
Assume that the first angle is x
∵ The second angle is 35° more than the first angle
∴ The second angle is x + 35
∵ The third angle is 25° more than the first angle
∴ The third angle is x + 25
∵ The sum of the angles of a triangle is 180°
→ Add the three angles and equate the sum by 180°
∵ x + x + 35 + x + 25 = 180
→ Add the like terms in the left side
∴ (x + x + x) + (35 + 25) = 180
∴ 3x + 60 = 180
→ Subtract 60 from both sides
∴ 3x + 60 - 60 = 180 - 60
∴ 3x = 120
→ Divide both sides by 3 to find x
∴ x = 40
→ Find each angle by substitute x by 40
∵ First angle = x
∴ The first angle = 40°
∵ Second angle = x + 35
∴ The second angle = 40 + 35 = 75°
∵ Second angle = x + 35
∴ The third angle = 40 + 25 = 65°
∴ The three angles are 40°, 75°, 65°
Susan wanted to share her 37 seashells with her two younger brothers. If she divided her seashells between the three of them, how many would each person get?
Given :
Susan wanted to share her 37 seashells with her two younger brothers.
To Find :
If she divided her seashells between the three of them, how many would each person get.
Solution :
Let, each person will get x seashells.
So,
[tex]x = \dfrac{\text{Total number of seashells}}{\text{Number of persons}}\\\\x = \dfrac{37}{3}\\\\x = 12.333[/tex]
But as we know seashells cannot be in decimal.
Therefore, each person will get exactly 12 shells.
HELPPPPPPP PLEASEEEE PLEASEEEE PLEASEEEE PLEASEEEEE PLEASEEEEE
Answer:
1. quadrant 3
2. quadrant 2
3. L (-1,2) M (-3,1) N (-2,5)
4. L (3,0) M (1,-1) N (2,3)
Answer:
1. Quadrant III
2. Quadrant II
L=(-1,2) M=(-3,1) N=(-2,5)
3. L=(3,-4) M=(1,-3) N=(2,-7)
Step-by-step explanation:
A square rug has a side length of x. A rectangular rug has a length that is 4 yards longer than the square rug and a width that is 2 yards shorter than the square rug. If the areas of the two rugs are equal, what is the length of the rectangular rug?
Answer:
8
Step-by-step explanation:
X²=(x+4)(x-2)
x²=x²+2x+4x-8
x²=x²+2x-8
x²-x²-2x=-8
2x=8
x=4
so the square rug is 4x4 and the rectangular rug is 8x2
Find the exact length of the third side.
Answer:
x = √51
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Pythagorean Theorem: a² + b² = c²Step-by-step explanation:
Step 1: Define
Leg a = x
Leg b = 7
Hypotenuse c = 10
Step 2: Solve for x
Substitute: x² + 7² = 10²Isolate x term: x² = 10² - 7²Exponents: x² = 100 - 49Subtract: x² = 51Isolate x: x = √51help me pleaseeeee!!!
Answer:
1. distribution property
2. subtraction property
3. division property
Step-by-step explanation:
Answer:
Try division property
Two stores have movies to rent.
The first store charges a $5 per-month membership fee plus $2.50 per movie rented.
The second store has no membership fee but charges $3.50 per movie rented.
How many movies would you have to rent in order for the cost to be the same at both stores?
Answer: 5 +2.5n=3.5n You need to calculate n.
Step-by-step explanation:
A recipe calls for 3 cups of sugar and 9 cups of water. How many should be used with 2 cups of sugar?
Answer:
6 cups of water
Step-by-step explanation:
A recipe calls for 3 cups of sugar and 9 cups of water. How many should be used with 2 cups of sugar?
The question above, is solved below:
3 cups of sugar = 9 cups of water
2 cups of sugar = x
Cross Multiply
3x = 9 × 2
x = 18/3
x = 6
Hence, 2 cups of sugar = 6 cups of water
PLEASE helppppp!!!
A group of students and teachers are going on a field trip. One-ninth of the group will fit on 1/3 of a school bus. How many buses are needed to transport the entire group?
Answer:
3 buses
Step-by-step explanation:
Total number of students=1
1/9 =1/3of the school bus
1=?
(1*1/3)÷(1/9)= 3 buses
. Mrs. Nunn pours 3 juice boxes into a bowl to make punch. Each juice box holds 236 milliliters. How much juice does Mrs. Goldstein pour into the bowl? *
Answer:
708 milliliters
Step-by-step explanation:
There are 3 juice boxes and each contain 236 milliliters of juice. So 236 + 236 + 236 = 708
PLEASE HELP VERY URGENT!!!!!!!!!!!!!!!
Simplify (5 ^1/3)^3
A. 5
B. 5^9
C. 1/5
D. 5^3
Answer:
A) 5
Step-by-step explanation:
(5^(1/3))^3=5^(1/3*3)=5^(3/3)=5^1=5
Assume the average child weighs 40 pounds at age 3. Assume the
average child weighs 70 pounds at age 6. What is the average number of
pounds the child gains per year between ages 3 and 6?
Answer:
10 i think
Step-by-step explanation:
Answer: 10 pounds per year
The given unit rate is 30 pounds every 3 years.
Now, we will divide 30 pounds by 3 years.
30 pounds ÷ 3 years = 10 pounds per year
The answer is 10 pounds per year.
A LITTLE HELP HERE PEOPLE BTW IF UR RIGHT BRAINLIST IT IS........
A recycling center pays $0.10 per aluminum can and $0.05 per plastic bottle. The Cheerleading squad wants to raise $500. Let x represent aluminum cans and y represent plastic bottles. Use this description to answer all questions in this section.
Question:
(a) Write a linear equation that describes the problem
(b). If the cheerleading squad collects 6000 plastic bottles, how many cans will it need to collect to reach the goal?
Answer:
a. [tex]0.10x + 0.05y = 500[/tex]
b. 2000 cans
Step-by-step explanation:
We have the following:
[tex]Cost = \$0.10[/tex] per aluminum
[tex]Cost = \$0.05[/tex] per plastic bottle
[tex]Total = \$500[/tex]
Solving (a): The linear equation.
If 1 aluminum can costs $0.10,
x cans would cost $0.10x
If 1 plastic bottle costs $0.05,
y bottles would cost $0.05y
Total Cost:
[tex]Aluminum + Plastic = Total[/tex]
[tex]0.10x + 0.05y = 500[/tex]
b.
If y = 6000.
Solve for x
We have:
[tex]0.10x + 0.05y = 500[/tex]
Substitute 6000 for y
[tex]0.10x + 0.05* 6000 = 500[/tex]
[tex]0.10x + 300= 500[/tex]
Collect Like Terms
[tex]0.10x = 500 - 300[/tex]
[tex]0.10x = 200[/tex]
Solve for x
[tex]x = 200/0.10[/tex]
[tex]x = 2000[/tex]
WILL GIVE BRAINLIEST a card is picked from the following card find the probability that the card drawn is purple
Answer: 2/7
Step-by-step explanation: if there are 7 cards and two of them are purple, we can show this as 2/7
A government estimates the cost to design new radar technology over a period of $m$ months. The government estimates $840,000 for equipment, $15,000 for software, and $40,000 per month for wages. Use an algebraic expression to find the total cost the government estimates when the project takes 16 months to complete.
Answer:
$1,495,000
Step-by-step explanation:
From the above, we can infer that the first two costs for equipment and software are fixed cost, while wages is the cost that is influenced by the number of months (m).
The above implies that we would multiply number of months 'm' with $40,000.
= 840,000 + 15,000 + 40,000m
Where month (m) = 16
= 840,000 + 15,000 + 40,000(16)
= 840,000 + 15,000 + 640,000
= $1,495,000
Therefore, the total cost is $1,495,000
helpmepleasethankyou:)
Answer:
Step-by-step explanation:
If we take 1 cup of Original purple paint,
Ratio of blue and red paint = 2 : 3
Quantity of blue paint in 1 cup of the mixture = [tex]\frac{2\times (1)}{(2+3)}[/tex] = 0.4 cups
Similarly, ratio of blue and red paint in the New purple paint = 5 : 7
If we take 1 cup of New purple paint,
Amount of blue paint in 1 cup = [tex]\frac{5\times 1}{(5+7)}[/tex] = 0.42 cups
Therefore, shade of both the mixtures will not be same.
Since, blue color is more in quantity in New purple paint, it will be more blue than Original purple paint.
The difference btwn increasing a number by 20% and decreasing the same number by15% is 14 what is the number?
Answer:
The number is:
[tex]n = 40[/tex]Step-by-step explanation:
Let 'n' be the number
Increasing a number by 20% = (n + n×20/100)Decreasing a number by 14% = (n - n×15/100)As the difference between increasing a number by 20% and decreasing the same number by15% is 14.
Thus, the expression becomes
[tex]\left(n\:+\:\frac{n}{5}\right)\:-\:\left(n\:-\:\frac{3n}{20}\right)\:=\:14[/tex]
[tex]n+\frac{n}{5}-n+\frac{3n}{20}=14[/tex]
[tex]\frac{7n}{20}=14[/tex]
Multiply both sides by 20
[tex]\frac{7n}{20}\cdot \:20=14\cdot \:20[/tex]
[tex]7n=280[/tex]
Divide both sides by 7
[tex]\frac{7n}{7}=\frac{280}{7}[/tex]
[tex]n=40[/tex]
Thus the number is:
[tex]n = 40[/tex]Each of the letters of the word "CHANCE" is written on a slip of paper and one slip is randomly drawn. What is the probability of drawing a letter "C" ?
Answer:
6 letters in CHANCE
So, 1/6
Step-by-step explanation: