Answer:
A
Step-by-step explanation:
Given
f(x) = - 4(x + 7)² - 6 ← expand factor using FOIL
= - 4(x² + 14x + 49) - 6 ← distribute parenthesis by - 4
= - 4x² - 56x - 196 - 6 ← collect like terms
= - 4x² - 56x - 202 → A
The equivalent function is [tex]f(x)=-4x^{2} -56x-202[/tex]
Option A is correct.
Equivalent function :The given function is,
[tex]f(x)=-4(x+7)^{2}-6[/tex]
We have to expand above function.
[tex]f(x)=-4(x+7)^{2}-6\\\\f(x)=-4(x^{2} +14x+49)-6\\\\f(x)=-4x^{2} -56x-196-6\\\\f(x)=-4x^{2} -56x-202[/tex]
Thus, the equivalent function is [tex]f(x)=-4x^{2} -56x-202[/tex]
Learn more about the quadratic function here:
https://brainly.com/question/25841119
(5x-2)+(3x+4)+90=180 find x
Answer:
92 i believe .
Step-by-step explanation:
Isabell some music playlist has 12 rock songs 15 pop songs 13 hip-hop songs and 10 oldies songs.if she sets the playlist on random shuffle what is the probability that the first song will be a pop song?
Answer:
3/10 or 30%
Step-by-step explanation:
it is the number of pop songs in the list divided by all of the songs combined.
so 15 pop songs
over
12+13+10+15=50
15/50 is you answer
simplify and get
3/10
Solve the equation and check your answer. 61 2 = 11 4 + n Which statements are correct? Check all that apply.
Answer:
its the second, third, and fifth one
Step-by-step explanation:
Because Anastasia is bored at home during the quarantine, she decides to redecorate. The dimensions of her living room are approximately 18 ft x 12 ft with a nine-foot ceiling. Instead of painting the walls like an average person would, she wants to cover them with burgundy wallpaper.
Part A: If one roll of wallpaper covers 50
2
, then determine how many rolls of wallpaper is needed to cover the living room.
Part B: If one roll of paper cost $15.90, then determine the cost of the wallpaper (before taxes).
Answer:
6 rolls of paper is needed to cover the living room
The cost of the 6 rolls is $95.40
Step-by-step explanation:
There are four walls here, two 12 ft by 9ft walls, and two 18 ft by 9ft walls
Area of a rectangle = length * height
Area of walls 1&3 = 18 * 9 = 162 [tex]ft^{2}[/tex]
Area of walls 2&4 = 12 * 9 = 108 [tex]ft^{2}[/tex]
Total area of walls = 162 + 108 = 270 [tex]ft^{2}[/tex]
One roll for every 50 [tex]ft^{2}[/tex]
270 ÷ 50 = 5.4 rolls
Since you cant buy 0.4 rolls of wallpaper, you need to buy one whole roll instead
6 rolls of paper is needed to cover the living room
One roll costs $15.90
6 rolls * 15.90 = $95.40
Danielle had planned her gift basket to be priced at $50 with a 40% gross margin. She forgot packaging costs which will be $3 per unit. If she still keeps the price at $50, how much will her gross margin percentage be after packaging costs?
a) 30%
b) 34%
c) 43%
d) 47%
The gross margin percentage after packaging costs would be a) 30%.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Danielle had planned her gift basket to be priced at $50 with a 40% gross margin.
let, The original price be 'x'.
Therefore, $50 is 140% of 'x' which is,
(140/100)×x = 50.
1.4x = 50.
x = 50/1.4.
x = 35.71.
Now, The packaging cost is $3 which makes the cost of the product 38.71.
So, (50/38.71)×100.
= 29% gross margin.
learn more about percentages here :
https://brainly.com/question/24159063
#SPJ6
What is the probability that the first marble chosen is shaded and the second marble chosen is labeled with an odd number? StartFraction 10 Over 121 EndFraction StartFraction 24 Over 121 EndFraction StartFraction 6 Over 11 EndFraction StartFraction 10 Over 11 EndFraction
Answer:
24/121, the 2nd choice on edg
Step-by-step explanation:
4/11 times 6/11 so that becomes 24/121
Answer:
24/121
Step-by-step explanation:
Which of the following is a reduction in the price of a vehicle generally offered by the manufacture?
A. Rebate
B. Cash back
C. Dealer promotion
D. Special APR financing
Answer:
Answer is A
Step-by-step explanation:
A rebate is a reduction in the price of a vehicle generally offered by the manufacturer.
Option A is the correct answer.
What is a rebate?A rebate is a type of incentive offered by a seller or manufacturer to encourage customers to purchase their products.
It is a partial refund of the purchase price that is offered to the customer after the sale has been made.
We have,
A rebate is a type of incentive that is offered by the manufacturer to the customer.
It is a refund of a portion of the purchase price of a product, in this case, a vehicle.
The rebate amount can vary based on the make and model of the vehicle, the time of year, and other factors.
Rebates are usually offered in the form of a check or a discount on the purchase price of the vehicle.
Cashback and special APR financing are also incentives that are commonly offered by car manufacturers, but they do not directly reduce the purchase price of the vehicle.
Cashback is usually a cash incentive that is given to the customer after the purchase of the vehicle, while special APR financing is a promotional interest rate offered on the car loan.
Dealer promotions are also common, but they are not typically offered by the manufacturer, and they may or may not involve a price reduction.
Thus,
A rebate is a reduction in the price of a vehicle generally offered by the manufacturer.
Learn more about rebates here:
https://brainly.com/question/14266304
#SPJ5
Find the area of the triangle below.
Answer:
73.72
Step-by-step explanation:
Using law of Sines in area:
A(triangle) = S1 * S2 * sin(theta) /2
A(triangle) = 12 * 15 * sin(55) / 2 = about 73.72 when rounded
ANSWER: 73.72
andy gets 7 out of 25wrtong in his maths test what fraction of the questions does andy answer correctly
Answer:
18/25
25/25 - 7/25 = 18/25
It is simplified
Step-by-step explanation:
Select the correct answer from each drop-down menu.
A cross section is the intersection Of a ___ and a ___
Answer:
a cross section is the intersection of a solid and a plane.
Step-by-step explanation:
Select all the correct locations on the table.
Classify each situation as exponential growth, exponential decay, or linear
Answer:
Situation 1 is exponential decay. Situation 2 is linear. Situation 3 is exponential growth.
Step-by-step explanation:
Situation 1 is exponential decay because it declined in a non linear way.
600-480=120 480-364=116
Situation 2 is linear because when it declined it has a dependent to another.
400-340=60 340-280=60
Situation 3 is exponential growth because is increases.
Jenny is making bracelets using different colored
beads. Jenny has 60 green beads and 105 blue
beads. What is the greatest number of identical
bracelets Jenny can make if she wants to use all of
the beads?
Answer:Jenny can make
18
identical necklaces, each containing 5 green and 6 blue beads.
Explanation:
Assume, each necklace contains
G
green and
B
blue beads and we have
N
such necklaces. All these variables are natural numbers.
Then we can establish the following equations in natural numbers:
N
⋅
G
=
90
N
⋅
B
=
108
Our task is to find a maximum
N
for which these two equations have a solution in natural numbers.
Obviously,
N
is a maximum common denominator of
90
and
108
.
To find the maximum common denominator of
90
and
108
, let's represent these two numbers as a product of prime numbers:
90
=
2
⋅
3
⋅
3
⋅
5
108
=
2
⋅
2
⋅
3
⋅
3
⋅
3
As we see, the maximum common denominator (a product of all prime numbers that are identical for both
90
and
108
) is
P
=
2
⋅
3
⋅
3
=
18
Therefore, assigning
N
=
18
,
G
=
5
and
B
=
6
, we obtain the solution:
Maximum number of identical necklaces is
N
=
18
with each necklace containing
G
=
5
green beads and
B
=
6
blue beads.
Answer
Step-by-step explanation:
What PERCENT of 250 is 60?
Answer:150.
Step-by-step explanation:
The equation h = –0.005x2 + x + 3 describes the path of a baseball hit into the outfield, where h is the height and x is the horizontal distance the ball travels.
a. What is the equation of the axis of symmetry?
b. What is the maximum height reached by the baseball?
c. An outfielder catches the ball three feet above the ground. How far has the ball traveled horizontally when the outfielder catches it?
Answer:
(a)x=100
(b)Maximum Height, h=53 Units
(c)x=200 Units
Step-by-step explanation:
Given the equation which describes the path of the baseball
[tex]h = -0.005x^2 + x + 3[/tex]
(a)Equation of the axis of symmetry
For a quadratic function of the form [tex]y=ax^2+bx+c[/tex], its equation of the axis of symmetry is determined by the equation:
[tex]x=-\dfrac{b}{2a}[/tex]
In the function given: a=–0.005, b=1
Therefore:
[tex]x=-\dfrac{1}{2*-0.005}=\dfrac{1}{0.01}\\\\x=100[/tex]
Equation of the axis of symmetry, x=100
(b)Maximum height reached by the baseball
The maximum height reached by the baseball occurs at the line of symmetry.
Therefore, when x=100
Maximum Height, [tex]h = -0.005(100)^2 + 100 + 3[/tex]
=53 Units
(c)When the height =3 feet, we want to determine the value of x.
[tex]h = -0.005x^2 + x + 3\\3 = -0.005x^2 + x + 3\\-0.005x^2 + x=0\\x(-0.005x + 1)=0\\-0.005x + 1=0\\-0.005x =-1\\$Divide both sides by -0.005\\x=200 Units[/tex]
Final answer:
The equation of the axis of symmetry is x = -100, the maximum height reached by the baseball is 103 feet, and to find the specific distance traveled when caught at 3 feet would require solving the quadratic equation given.
Explanation:
The equation h = –[tex]0.005x^2[/tex]+ x + 3 describes the path of a baseball hit into the outfield, where h is the height and x is the horizontal distance the ball travels.
a. What is the equation of the axis of symmetry?
The equation of the axis of symmetry for a quadratic equation in the form of [tex]ax^2 + bx + c[/tex] is given by x = –b/2a. Hence, for our equation, the axis of symmetry is x = –(1)/(2×–0.005) = –100.
b. What is the maximum height reached by the baseball?
The maximum height can be found by substituting the x-value of the axis of symmetry into the original equation. So, h = –[tex]0.005(100)^2[/tex] + 100 + 3 = 103 feet.
c. An outfielder catches the ball three feet above the ground. How far has the ball traveled horizontally when the outfielder catches it?
To find the horizontal distance when h is 3, we set the equation equal to 3: –[tex]0.005x^2 + x + 3 = 3.[/tex] Simplifying gives x values where the ball is at 3 feet off the ground. After simplification, one possible solution would be the distance before the ball reaches its peak. However, solving this particular quadratic may require a calculator for precise roots, implying the distances at which the ball is 3 feet high.
If you invest $100,000 in an account earning 8% interest compounded annually, how long will it take until the account holds $300,000?
(Round to the nearest 0.1 of a year.)
( answergoes here ) ______________________
Compound interest formulas:
A=P(1+rn)ntA=P(1+r/n)^nt and A=Pe^rt
We have been given that you invest $100,000 in an account earning 8% interest compounded annually. We are asked to find the time it will take the amount to reach $300,000.
We will use compound interest formula to solve our given problem.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex], where,
A = Final amount after t years,
P = Principal amount,
r = Annual interest rate in decimal form,
n = Number of times interest is compounded per year,
t = Time in years.
[tex]8\%=\frac{8}{100}=0.08[/tex]
[tex]300,000=100,000(1+\frac{0.08}{1})^{1\cdot t}[/tex]
[tex]300,000=100,000(1.08)^{t}[/tex]
[tex]\frac{300,000}{100,000}=\frac{100,000(1.08)^{t}}{100,000}[/tex]
[tex]3=(1.08)^{t}[/tex]
[tex](1.08)^{t}=3[/tex]
Let us take natural log on both sides of equation.
[tex]\text{ln}((1.08)^{t})=\text{ln}(3)[/tex]
Using natural log property [tex]\text{ln}(a^b)=b\cdot \text{ln}(a)[/tex], we will get:
[tex]t\cdot \text{ln}(1.08)=\text{ln}(3)[/tex]
[tex]\frac{t\cdot \text{ln}(1.08)}{\text{ln}(1.08)}=\frac{\text{ln}(3)}{\text{ln}(1.08)}[/tex]
[tex]t=\frac{1.0986122886681097}{0.0769610411361283}[/tex]
[tex]t=14.274914586[/tex]
Upon rounding to nearest tenth of year, we will get:
[tex]t\approx 14.3[/tex]
Therefore, it will take approximately 14.3 years until the account holds $300,000.
Consider the figure shown. What solid three dimensional object is
produced by rotating the rectangle about line m?
Answer:a wide cylinder
Step-by-step explanation:
Quadrilateral BCDE is inscribed in circle A, and mBED = 160".
C
А
84
160°
E
m BCD =
[Select]
degrees and mZBCD = [Select]
degrees.
what is the measure of
Answer:
20°
Step-by-step explanation:
Opposite angles of an inscribed quadrilateral are supplementary.
∠C = 180° -∠E = 180° -160°
m∠BCD = 20°
6-9x=6x-10x-24
solve for x
plzz help
Answer: 6
Step-by-step explanation:
The answer is 6 because subtract 6-9x=6x-10x-24
1. Using the floorplan below, calculate the total area of the space.
YOU MUST SHOW ALL WORK FOR CREDIT.
Breakfast)
nook
Kitchen
Formal Dining
1 unit = 5 feet
Answer:
i believe it is 185 feet
The rule at Anna's house is that if she eats all
of her vegetables and does all of her chores
each day, she earns 2 hours of internet time
which she can save. Anna started her week
with 3 hours saved. If she eats all of her
vegetables and does all of her chores each
day for 4 days straight, how many hours does
she have after the 4 days if she uses 6 hours
of her internet time?
Which of the following sets of equations
correctly represents this situation?
Sam needs to find the circumference of a circle with a diameter of 24 inches. He uses a calculator to find the circumference. Which answer is reasonable?
A. 72.013678 in
B. 75.398223 in
C. 80.332161 in
D. 85.335372 in
Answer: B
Step-by-step explanation:
Using 6 decimals for pi = 3.141592
[tex]Formula: C= \pi d\\[/tex]
[tex]C=(3.141592)(24in)\\C=75.398223in[/tex]
Please helppp meee the picture is up there to answer the question
Answer:
-6x-5
Step-by-step explanation:
Answer:
6x^2-10
Step-by-step explanation:
(5x^2+2)-(-4x^2+7)+(-3x^2-5)=
5x^2+2+4x^2-7-3x^2-5=
5x^2+4x^2-3x^2+2-7-5=
9x^2-3x^2-5-5=
6x^2-10
ASAP!!!!10 Points!!!!!
Which describes the correlation show in the scatter plot?
There is a positive linear correlation
There is a negative linear correlation,
There is no positive or negative correlation
There is a nonlinear correlation
The correlation show in the scatter plot There is no positive or negative correlation
What is Correlation?A statistical measure known as correlation expresses how closely two variables are related linearly (meaning they change together at a constant rate). It's a typical technique for describing straightforward connections without explicitly stating cause and consequence.
Given:
The positive linear correlation shows a line which is Diagonally rising.
and, The negative linear correlation shows a line which is Diagonally falling.
So, the graph we have no Correlation because it does not any falling and rising line.
Learn more about Correlation here:
https://brainly.com/question/28898177
#SPJ2
The perimeter of
the rectangular playground shown
below is 160 feet. What is the area of the
playground?
Known :
Perimeter = 160 ft
length = 50 ft
Asked :
Area = ...?
Answer :
Find the width first :
Perimeter = 2 (length + width)
160 = 2 (50 + width)
width = (160 ÷ 2) - 50
width = 80 - 50
width = 30 ft
Now, let's find the Area :
Area = length × width
= 50 × 30
= 1.500 ft²
So, the area of the playground is 1.500 ft²
Hope it helpful and useful :)
Help ASAP!! Will mark the brainliest
Answer:
a, c, b, a
Step-by-step explanation:
To reach a particular department at a warehouse, a caller must dial a 4 4 -digit extension. Suppose a caller remembers that the first and last digits of an extension are 5, 5 , but they are not sure about the other digits. How many possible extensions might they have to try? Enter your answer as a number, such as: 425
Answer:
100
Step-by-step explanation:
just took the test
The caller must consider 10 possibilities for each of the two unknown digits in the 4-digit extension. Since the first and last digits are confirmed as 5, there are 10 x 10 = 100 possible extensions they might have to try.
To calculate the number of possible extensions the caller might have to try, we can look at the structure of the 4-digit extension. Given that the first and last digits are known to be 5, the caller is unsure about the second and third digits.
Each of the unknown digits can be any number from 0 to 9. Since there are 10 possibilities for each of these two positions (the second and third digits), to find the total number of combinations, we multiply the possibilities for each digit.
The calculation is as follows:
Number of possibilities for the second digit = 10 (0-9)
Number of possibilities for the third digit = 10 (0-9)
Therefore, the total number of possible extensions is:
10 (possibilities for the second digit) imes 10 (possibilities for the third digit) = 100 possible extensions.
If a randomly selected person can ride a bike to school, what is the probability the person is a boy?
Biking to School
Can Bike Can't Bike Total
Boys
7
4
Girls
9
10
19
Total
16
14
30
the answer would be 11 out of 30 because there is 11 boys in total and the total of boys and girls is 30 so the answer is 11 out of 30
The probability that a randomly selected person who can bike to school is a boy is 7/16 or 0.4375, which means there is a 43.75% chance that the person is a boy.
Explanation:To determine the probability that a randomly selected person who can ride a bike to school is a boy, we will use the provided data.
Looking at the data table, we can see there are 7 boys who can bike to school, and the total number of students who can bike to school is 16 (this is the sum of boys and girls who can bike). In probability terms, the boys who can bike are the 'favorable outcomes' and the total students who can bike are the 'possible outcomes'.
Probability is calculated by dividing the number of favorable outcomes by the number of possible outcomes. Thus, the probability a randomly selected person can ride a bike to school is a boy is 7/16, or approximately 0.4375.
This means, if we were to randomly select a person who can bike to school, there is a 43.75% chance that the person is a boy. I hope this explanation helps explain how to determine probability using a data set.
Learn more about Probability here:https://brainly.com/question/22962752
#SPJ2
If Handel's Ice Cream is 0.4 miles away from our house, how far would it be to walk there and back?
Answer:
0.8 miles
Step-by-step explanation:
multiply 0.4 by 2
Answer: 0.8
Step-by-step explanation:
times it by 2
a 11%
b 81.7%
c 18.3%
d 22.4%
Answer: c. 18.3
Step-by-step explanation: 100 times .6 equals 60 so if you divide 11 by .6 you get 18.3
Answer:
here you go
Step-by-step explanation:
add them all together = 60
+ 40 = 100
4 boxed
40 divided by 4 = 10
add 10 onto each number
red = 21%
silver = 34%
grey = 26%
black = 19%
all of them added together = 100%
Six friends share 15 fruit bars equally how many fruit bars does each friend get
Answer:
2 1/2 bars each.
Step-by-step explanation:
That would be 15/6.