Answer:
The polynomial is irreducible.
Step-by-step explanation:
The polynomial 3p²-15pq+20q² can be factored as (p-2q)(3p-10q).
What is the Factorization?Factorization, also known as factoring, is the breakdown of one element into a product of other objects, or factors, which when multiplied together generate the original. For example, the number 21 factors into primes as 3 × 7, and the polynomial x² − 9 factors as (x+3)(x-3).
The polynomial is given as follows:
3p²-15pq+20q²
It is required to find the factorization of the given polynomial.
The greatest common factor (GCF) of the coefficients (3, -15, 20), is 3.
Rewrite the polynomial using the GCF of 3. We get:
3(p²-5pq+6q²)
We need to find two numbers that multiply to 6q² and add to -5pq.
The numbers are -2q and -3p.
Combine the factored quadratic expression with the GCF of 3.
3(p-2q)(p-3q)
Therefore, the correct factorization of the polynomial 3p²-15pq+20q² is 3(p-2q)(p-3q).
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A and B are two events. P(A) = 0.54; P(B) =0.42; p(A or B) = 0.85. Find the probability of A and B.
Answer:
0.98
Step-by-step explanation:
Work Shown:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.13 + 0.85 - 0
P(A or B) = 0.98
Note that P(A and B) is 0. This is because we are told A and B are mutually exclusive events. This means both events cannot happen simultaneously. An example would be flipping a coin to have it land on heads and tails at the same time.
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.
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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
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.
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.
One employee pours 6 ounces of coffee in the large frappuccino.
Does this follow the instructions above? Why or why not?
Answer:
The employee's action is not following the instructions.
Step-by-step explanation:
The drinks table has some recommendations to make some drinks exclusive to the establishment such as the Large Frapuccino or the Small Chai Tea, which in its first line corresponding to the Large Frapuccino specifies that at least 8 ounces of coffee should be used, which it wants to say is the minimum amount of coffee that can be added to it is 8 ounces, and the value could be higher than that, but never lower, which is why by adding only 6 ounces to the Frapuccino you are totally ignoring the instructions.
will givebrainliest if answered correct
Answer:
60
Step-by-step explanation:30+30
Answer:
I think this is 120.
What is the x-value of point A?
Answer: 5
Step by Step Explanation:
$99 for 2 video games plus 8% tax.
Can you answer with steps please
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:
An item is priced at $13.29. If the sales tax is 4%, what does the item cost including sales tax?
So first, we have to find 4% of 13.29.
13.29*0.04=0.5316, or rounding is 0.53.
Now add 0.53 and 13.29=13.82
I hope this helps.
Help ASAP!! Will mark the brainliest
Answer:
a, c, b, a
Step-by-step explanation:
Haley has 3 more than 2 times as many math problems for homework than
Shelly. Together they have 33 problems for homework. How many
problems did Haley have for homework? *
Answer:
99
Step-by-step explanation:
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:
For 14 points please help
Answer:
4 cups, 3 ounces
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
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:
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
Consider the diagram below where measure of angle CDE=127 degrees.
Select all of the statements that are true.
A. measure of angle EDF=53 degrees
B. measure of arch EGD=127 degrees
C. measure of arch ED=106 degrees
D. measure of angle GAE=53 degrees
E. measure of arch EGD=254 degrees
The statements A and D are true.
Based on the diagram, here are the true statements:
A. measure of angle EDF=53 degrees:
This is true because angle EDF and angle CDE are supplementary angles, meaning they add up to 180 degrees.
Since we're given that measure of angle CDE=127 degrees, we can find measure of angle EDF by subtracting 127 from 180:
measure of angle EDF = 180 degrees - 127 degrees = 53 degrees.
D. measure of angle GAE=53 degrees:
This is true because angle EDF and angle GAE are corresponding angles.
Corresponding angles are pairs of angles that are on opposite sides of a transversal and that share a common endpoint with the transversal.
They are equal in measure.
Since we've already determined that measure of angle EDF=53 degrees, we can conclude that measure of angle GAE=53 degrees as well.
Therefore, the statements A and D are true.
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
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:
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.
Which of the quadratic functions has the narrowest graph?
y = −10x2
y = −0.9x2
y = 9x2
Explanation:
The equation y = ax^2+bx+c has the value of 'a' determine how wide or narrow the graph is. The closer 'a' is to zero, then the wider it gets; while the further 'a' is from 0, the narrower it gets.
What we need to do is look for equations in which the 'a' value is furthest from 0. In this case, it's with y = -10x^2 since a = -10 is furthest from zero compared to a = -0.9 and a = 9. Set up a number line to help see this. You can also use absolute values to get the job as well.
Therefore, y = -10x^2 has the most narrowest graph.
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.
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:
solve the following system x=2 5x+4y=-22
Answer:
x = 2
y = -8
Step-by-step explanation:
Since it already gives you x, all you need to do is plug it into the equation:
5x + 4y = -22
5(2) + 4y = -22
10 + 4y = -22
Then, subtract 10 from both sides:
10 + 4y = -22
- 10 - 10
__________
4y = -32
Finally, divide both sides by 4:
4y = -32
y = -8
So now you have, x = 2 and y = -8
Answer:
X=2
5x +4y= -22
5(2)+4y = -22
10+4y= -22
4y= -22-10
4y= -32
Y= -8
The answers are :
X = 2
Y = -8
Step-by-step explanation:
Albert's hourly pay is $8.10. He has an hourly pay of $12.15 when he
vorks more than 40 hours. He worked 45 hours last week. What is Albert's
gross pay for this pay period?
270.12
184.25
384.75
0
225.85
Answer: Albert's gross pay for this pay period is $384.75
Step-by-step explanation:
Given : Albert's hourly pay is $8.10
His hourly pay is $12.15 when he work more than 40 hours
Last week working hours = 45 hours
Therefore
For first 40 hours he got $8.10 hourly and for more 5 hours he got $12.15 hourly
So
Pay of first 40 hours = [tex]40 \times 8.10[/tex] = $324
Pay for next 5 hours= [tex]5 \times 12.15[/tex] = $ 60.75
Total Gross pay = $324+$ 60.75 =$384.75
Hence , Albert's gross pay for this pay period is $384.75
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
Larry accumulated $3,000 in credit card debt. If the interest rate is 10% per year and he does not make any payments for 2 years, how much will he owe on this debt in 2 years for monthly compounding?
Answer:
3,655.21
Step-by-step explanation:
The amount that Larry owes on his debt after 2 years is $20,514.
What is compound interest?The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.
Given information is for monthly compounding as below,
The accumulated money in credit card is, P = $3000.
The rate of interest is 10% per year.
Then, the rate of interest per month is, r = 10/12 = 5/6%.
The time for compounding in years is 2 years.
Then in months, n = 2 × 12 = 24 months.
The formula for amount in compound interest is given as,
A = P(1 + r/100)ⁿ
Substitute the corresponding values to get,
A = 3000(1 + (5/6)/100)²⁴
= 3000 × 6.838
= 20514
Hence, the amount owed by Larry on the debt after 2 years is $20,514.
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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.
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