The factored form of y = x² - x + 12 will be (x + 3)(x - 4).
What is factor?It should be noted that a factor simply means the number than can be multiplied by another number to get the original number. The factored form is when a quadratic expression is a product of two factors, each of which is a linear expression. By expanding, or multiplying out the factors, an equation in factored form can be restated in standard form.
This will be illustrated as:
x² - x - 12
x² - 4x + 3x - 12.
x(x - 4) + 3(x - 4)
(x + 3)(x - 4)
The factored form is (x + 3)(x - 4).
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I will need help with this math problem it has three parts to it
a)The smaller break even quantity is 10
b)The quantity that must be sold to maximize the profit= 14.25
c)The maximum profit = $36.13
STEP - BY - STEP EXPLANATION
What to find?
• The smaller break even quantity is
,• The quantity that must be sold to maximize the profit
,• The maximum profit.
Given:
C(x)= 13x + 370
R(x)=70x - 2x²
a) At the break even quantity, the revenue = cost, that is no profit and no loss.
R(x) = C(x)
So that we have;
70x - 2x² = 13x + 370
Re-arrange.
-2x² + 70x - 13x - 370 =0
-2x² +57x - 370 =0
2x² - 57x + 370 = 0
We can now solve the quadratic equation above.
Using the qudaratic formula
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]a=2 b=-57 c=370
Substitute the values into the formula and evaluate.
[tex]x=\frac{-(-57)\pm\sqrt[]{(-57)^2-4(2)(370)}}{2(2)}[/tex][tex]x=\frac{57\pm17}{4}[/tex][tex]Either\text{ x=}\frac{57+17}{4}=\frac{74}{4}=\frac{37}{2}[/tex]Or
[tex]x=\frac{57-17}{4}=\frac{40}{4}=10[/tex]x = 37/2 or x=10
We take the smaller value.
Hence, x=10
Therefore, the smaller break even quantity is 10.
b)To find the quantity that will maximize the profit, find the profit function.
p(x) = R(x) - C(x)
P(x) = 70x - 2x² - (13x +370)
= 70x - 2x² - 13x - 370
P(x) =-2x² + 57x - 370
Equate to zero
-2x² + 57x - 370 = 0
2x² - 57x + 370 =0
The maximum is at x = -b/2a
b= -57 and a=2
Substitute the values
x= - (-57) /2(2)
x= 57 /4
x= 14.25
c) To find the maximum profit, simply substitute x=14.25 into the profit function and simplify.
That is;
P(x) =-2x² + 57x - 370
P(14.25) =-2(14.25)² + 57(14.25) - 370
= -406.125 + 812.25 - 370
= 36.125
≈ 36.13
Hence, the maximum profit is $36.13
The area of a trapezoid is A = 12 (b 1 + b 2)h. Which equation represents the area of a trapezoid when solved for b 1?
If the area of a trapezoid is A = [tex]\frac{1}{2} (b_{1}+ b_{2})h[/tex], then the equation represents the value of [tex]b_{1}[/tex] is [tex]b_{1}=\frac{2A}{h}-b_{2}[/tex]
The trapezoid is a quadrilateral with at least one pair of parallel sides is called trapezoid. There are four vertices and four edges in the trapezoid.
The area of the trapezoid A = [tex]\frac{1}{2} (b_{1}+ b_{2})h[/tex]
Where [tex]b_{1}[/tex] and [tex]b_{2}[/tex] are the length of the parallel sides of the trapezoid
h is the height of the trapezoid
A = [tex]\frac{1}{2} (b_{1}+ b_{2})h[/tex]
Move 1/2 to other side
[tex](b_{1}+ b_{2})h[/tex] = 2A
Move h to other side
[tex](b_{1}+ b_{2})[/tex] = [tex]\frac{2A}{h}[/tex]
Move [tex]b_{2}[/tex] to other side
[tex]b_{1}=\frac{2A}{h}-b_{2}[/tex]
Hence, if the area of a trapezoid is A = [tex]\frac{1}{2} (b_{1}+ b_{2})h[/tex], then the equation represents the value of [tex]b_{1}[/tex] is [tex]b_{1}=\frac{2A}{h}-b_{2}[/tex]
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4. What common characteristics will two parabolas in the family f(×) = a(× - 4)(× - 8) have?
• The Same roots
,• The same axis of symmetry
1) If we compare two parabolas from this family, like:
[tex]\begin{gathered} f(x)=-1(x-4)(x-8) \\ g(x)=2(x-4)(x-8) \end{gathered}[/tex]Note that the difference is in the leading coefficient "a".
2) Both parabolas will have the same roots, the same x-intercepts:
[tex]x_1=4,x_2=8[/tex]In addition to this, we can state that both will share the same axis of symmetry:
[tex]\begin{gathered} f(x)=-1(x-4)(x-8) \\ f(x)=\quad -x^2+12x-32_{} \\ h=\frac{-12}{2(-1)}=6 \end{gathered}[/tex]As well as:
[tex]\begin{gathered} g(x)=2(x-4)(x-8) \\ g(x)=2x^2-24x+64 \\ h=\frac{24}{2(2)}=6 \end{gathered}[/tex]Hence, the answer is:
0. Same roots
,1. Same axis of symmetry
An electronic store is having an 18% off sale on everything in the store to the nearest cent which of the following could represent regular prices and sale price of items in the store
during the sale choose all that apply
The following that represent the sales price and the regular prices are:
regular price: $55.43, sales price: $45.45
regular price: $29.99, sales price: $24.59
regular price: $652.30, sales price: $534.89
What are the regular prices and the sales price?Percentage is the fraction of a number out of hundred. The sign that is used to represent percentages is %.
When a discount is given on the price of an item, the price of the item would reduce by the given price or by the percent reduction.
Sales price = regular price x (1 - discount)
Sales price = regular price x (1 - 0.18)
Sales price = regular price x 0.82
Sales price when the initial price is $55.43: $55.43 x 0.82 = $45.45
Sales price when the initial price is $29.99: $29.99 x 0.82 = $24.59
Sales price when the initial price is $215.33: $215.33 x 0.82 = $176.57
Sales price when the initial price is $849.50: $849.50 x 0.82 = $696.59
Sales price when the initial price is $652.30: $652.30 x 0.82 = $534.89
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what is 42/100 of x over 35%
The value of x in the expression 42/100 of x over 35% is 0.147.
What is an expression?It should be noted that an expression is simply used to show the relationship between the variables or number given.
Therefore, the information will be expressed as:
42/100 × x/35%
= 42/100 × x/0.35
Cross multiply
100 × x = 0.35 × 42
100x = 14.7
Divide.
x = 14.7 / 100
x = 0.147
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solve each formula for the indicated letter. circle the letter next to your answer. write the letter in the box below.
(1) d = rt so, r = d/t
(2) a = F/m so, F = ma
(3) p = w/t so, t = w/p
(4) h = V/B so, B = V/h
(5) A = (abc)/(4r) so, r = (abc)/(4A)
(6) P/Q = R/S so, S = QR/P
(7) a = (v-i)/t so, v = at + i
(8) E/e = (R + r)/r so, e = Er/(R+r)
(9) 1/p + 1/q = 1/f so, f = (pq)/(p+q)
(10) 1/p + 1/q = 1/f so, p = qf/(q-f)
(11) 1/R = 1/r1 + 1/r2 so, R = (r1 r2)/(r1 + r2)
(12) 1/t = (1/a) + (1/b) so, b = (at)/(a - t)
(13) A/B = C/D so, C = AD/B
(14) A = h(a+b)/2 so, b = 2A/h - a
(15) V = Q/r1 - Q/r2 so, Q = Vr1 r2/(r2 - r1)
(16) u = F(P/T - E) so, P = (uT + EFT)/F
Joshua opened a bank account with some money he had saved. During the month, he made deposits of $25 and $40, and he made withdrawals of $15 and
$35. At the end of the month, he had $170 in his account. How much money did he have when he opened the account?
A $285
B $155
C $55
D $15
Initially, Joshua had $155 in his account.
How to find the initial amount?Deposits of $25 and $40
Withdrawals = $15, $35
At the end of the month, he had $170 in his account.
Solution:
Let x be the amount of money he had initially.
Then,
x + 25 + 40 - 15 -35 = 170
x + 65 - 50 = 170
x = 170 + 50 - 65
x = 220 - 65
x = 155
Therefore, initially, he had $155 in his account.
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A bag contains 120 marbles. Some are red and the rest are black. There are 19 red marbles for every black marble. How many red marbles are in the bag?
A bag contains 120 marbles. Some are red and the rest are black. There are 19 red marbles for every black marble. How many red marbles are in the bag?
The number of red marbles in the bag is 114 .
in the question ,
it is given that ,
total number of marbles in the bag = 120 marbles
let the number of red marbles [tex]=[/tex] r
let the number of black marbles [tex]=[/tex] b
so , According to the question
b + r = 120 ...eqn(1)
also given that for every black marble there is 19 red marbles
which is represented by , r = 19b
Substituting r = 19b in eqn (1) , we get
b + 19b = 120
simplifying further , we get
20b = 120
b = 6
and r = 19(6) = 114
Therefore , The number of red marbles in the bag is 114 .
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PLEASE HELP!!!
Explain how the cosine of an angle in the second quadrant differs from the cosine of its reference angle in the unit circle.
Answer:
the second quadrant is negative but the reference angle is exactly the same but positive
Step-by-step explanation:
looking at 150 on the unit circle in the second quadrant you will see the cosine is negative square root 3 divided by 2 but the reference angle is 30 degrees and when we look at the cosine of that which is the x value of what we see it is positive square root of 3 divided by 2
the average daily rainfall is typically 5/8 of an inch. Last year, the average daily rainfall
was only 3/8 of an inch. What percent of the typical average daily rainfall fell last year in Green Valley?
Explain how travelling to a ski resort to go skiing could influence travel time
A ski trip requires a lot of planning.You must choose your travel dates, choose the ideal location, identify the best ski resorts for your family in the area, book lodging, purchase lift tickets, schedule lessons, consider your equipment and clothing needs, and possibly book flights or a rental car.
Describe the possible effects that traveling to a ski resort might have on travel time?
Beyond making reservations, there are more actions to be taken.Making decisions, locating the best offers, and making reservations take time.While some tasks should be completed in advance, others can wait till later.Before heading to the slopes, use this helpful planning timeline to help you save some green (and your sanity). Planning is more necessary when skiing with children as it differs from skiing alone.When there was an incredible snowstorm, I remember those last-minute college ski excursions that somehow came together, allowing me to jump in an SUV with someone else and crash on their lily pad with them and 10 to 20 other pals.I have happy recollections of those ski holidays when I was a younger frog. Perhaps I have forgotten the sleepless nights spent in the company of snorers and surviving on sugar and coffee, but those things were unavoidableBut now, on our mountainous excursions, Leap, my husband, who is learning to ski, and two tadpoles are also hopping along.The majority of our preferred ski resorts involve travel by plane, which is difficult to arrange at the last minute due to our tight schedules.In addition, it appears that my standards and working hours have changed, and now I no longer consider sleeping on a couch or the floor with complete strangers to be a vacation. As a result, I must think carefully and plan ahead for my ski trips in order to accommodate a family with a toddler, a tween, and adults.You should begin planning your ski vacation up to a year in advance.Choose the ski region or areas you want to go to.For instance, focus on a specific area; perhaps you want to look into the Denver region, Lake Tahoe, or Utah.Find the finest ski resort for your family by researching ski resorts in those areas.Check out mountain statistics and trail maps to determine if there are any runs that your family will enjoy.In comparison to other resorts, you might notice that one has more terrain for beginner to intermediate skiers. When there aren't any lift tickets or lessons available, it might be difficult to compare pricing during the off-season. To illustrate, imagine that you decide to go skiing in Colorado the next winter a year in advance.To help you plan and get an idea of costs so you can budget, look at the prices of different resorts in the area during peak and off-peak seasons on their websites more than a year in advance. You can also compare the costs of different resorts in the area at both peak and off-peak times.You may discover that Keystone and Breckenridge are more affordable while still providing excellent family-friendly amenities than places like Vail and Beaver Creek.To learn more about ski resort refer
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Simplify using the laws of exponents. Leave your answer an exponential form. The box is to type in the exponent.
Use the next property:
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex][tex]\frac{x^8}{x^2}=x^{8-2}=x^6[/tex]Then, the given expression simplified is equal to x^6HELP PLEASE !!!!!!!!!!!!!!!!!!!!!!!!!!
The equation of the line perpendicular to y = - (2 / 3) · x and the point (4, - 8) is y = (3 / 2) · x - 14.
How to determine the equation of a perpendicular line
Mathematically speaking, lines are represented by equations of the form y = m · x + b, where m and b are the slope and the intercept of the line. Additionally, two lines are perpendicular to each if the product of their slopes is equal to - 1.
First, we determine the slope of the perpendicular line:
m' = - 1 / m
m' = - 1 / (- 2 / 3)
m' = 3 / 2
Second, the intercept of the perpendicular line is:
b = y - m · x
b = - 8 - (3 / 2) · 4
b = - 8 - 6
b = - 14
Then, the equation of the perpendicular line is y = (3 / 2) · x - 14.
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Carrots costs $0.99 per pound. Broccoli costs $1.50 per pound. Jack buys 3.5 pounds of carrots and 1.25 pounds of broccoli. What is Jack’s total bill?
Answer: his total bill is 7.24
Step-by-step explanation:
HELP PLSSS
(Attached to image)
The inequality is lies between the 5.26 < 5.71
The correct option is (a)
Given,
From the figure,
To see the number line and determine the which of the expression is true.
What is Inequality?
Inequality is defined as an equation that does not contain an equal sign.
Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The number line goes from 5.0 to 6.0 with 9 labeled marks in between.
Each mark increases by point one
There are five labeled points.
A point labeled 5.04 is between 5.0 and 5.1.
A point labeled 5.26 is between 5.2 and 5.3.
A point labeled 5.4 is at the mark labeled 5.4
A point labeled 5.520 is between 5.5 and 5.6.
A point labeled 5.71 is between 5.7 and 5.8.
Then the ascending order of the number line will be :
5.04 < 5.26 < 5.4 < 5.52 < 5.71
Hence, The correct option is (a)i.e., 5.26 < 5.71
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I need help with this question but no one is helping me! Can someone please help me
Answer: 36.00%
60% can be written as 0.60 and/or 6/10, which simplifies to 3/5 for easier operations. The probability of 2 students both drink coffee with breakfast can be shown as 0.60 • 0.60 = 0.36. This means there is a 36% chance of both students drinking coffee with breakfast in the morning.
Step-by-step explanation:
if g(x) = 1/2|x|-6 and h(x)=x-4 Which expression is equivalent to h(g(x))?
1/2|x| - 2
1/2|x-4| -6
1/2|x|-10
1/2|x-10|
h(g(x)) is equivalent to the expression 1/2|x|-10
What will the expression be?Given g(x) = 1/2|x|-6 and h(x) = x-4
h(g(x)) = h(1/2|x|-6)
Put the value of g(x) in the expression
Now, evaluate the expression using the definition of h(x) by replacing x in x-4 with 1/2|x|-6:
h(g(x)) = 1/2|x|-6 - 4 = 1/2|x|-10
Since h(g(x)) = 1/2|x|-10. Therefore, 1/2|x|-10 is the expression equivalent to h(g(x)) so the third option is the answer.
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David left $300 in an account that earns 5% on the money he originally deposited. When he collected his interest, he had earned $60 in interest. How long did he leave the money in the account?
The time that David left the money in the account would be = 4 years
What is an earned interest?An earned interest is the amount of money that is regularly paid to an individual who invested a specific amount of money for a stipulated period of time.
The principal amount(p)= $300
The time (T)= X
The rate of interest yield (R)= 5 %
Simple interest( SI)= $ 60
Using the formula;
SI = P×T×R/100
Make T the subject of formula;
T = SI×100/P*R
T= 60×100/300×5
T= 6000/1500
T = 4 years.
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
-0.07
Step-by-step explanation:
Find the average
Convert 39 yards into miles. Round your answer to the nearest hundredth.
The conversion from yards to miles is given by:
[tex]1\text{ mile }\to1760\text{ yards}[/tex]The conversion factor is:
[tex]\frac{1\text{ mile}}{1760\text{ yards}}[/tex]Now, if we want to know how many miles are 39 yards, we multiply 39 yards by the conversion factor:
[tex]39\text{ yards }\cdot\frac{1\text{ mile}}{1760\text{ yards}}\approx0.02\text{ miles}[/tex]One-third of a number is at least four less than the number. Which inequality represents the number?
When one-third of a number is at least four less than the number, the inequality to represent the information is C. n ≥ 6.
What is an inequality?It should be noted that an inequality is simply used to illustrate the expressions that aren't equal.
Let the number be n.
This will be illustrated as:
1/3n ≥ n - 4
Collect like terms
1/3n - n ≥ -4
-2/3n ≥ -4
Multiply through by -3/2
n ≥ -4 × -3/2
n ≥ 6
The value is n ≥ 6.
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A radioactive substance decays according to A=A0e−0.0028t, where A0 is the initial amount and t is the time in years. If A0=710 grams, find the time for the radioactive substance to decay to 366 grams. Round your answer to two decimal places, if necessary.
Solution
- The function given is:
[tex]A=A_0e^{-0.0028t}[/tex]- We have been given:
[tex]\begin{gathered} A_0=710g \\ A=366g \end{gathered}[/tex]- We are required to find the time for the radioactive substance to decay. That means we need to find the value of t in the equation.
- Thus, we have that:
[tex]\begin{gathered} 366=710e^{-0.0028t} \\ \text{ Divide both sides by 710} \\ \frac{366}{710}=e^{-0.0028t} \\ \\ \text{ Take the natural log of both sides} \\ \ln(\frac{366}{710})=\ln(e^{-0.0028t}) \\ \\ \ln(\frac{366}{710})=-0.0028t \\ \\ \text{ Divide both sides by -0.0028} \\ \\ \therefore t=\frac{1}{-0.0028}\ln(\frac{366}{710}) \\ \\ t=236.6541...\approx236.65\text{ years} \end{gathered}[/tex]Final Answer
The answer is 236.65 years
Factories often add filler when making meatballs sold by the bag. One factory obtained 90 kg of beef from overseas. They want to add 1.4 oz of filler for each
pound of beef. How many ounces of filler will the factory need in order to make meatballs out of this shipment of beef?
Use 1 Ib=0.45 kg and do not round any
computations.
One factory that obtained 90 kg of total beef from overseas. The company needs 390 oz of meat filler to make meatballs out of this shipment of beef.
What are meat fillers?In processed meat products, starches are frequently employed as fillers to bind water that would otherwise leak out of the product, increasing its texture and sensory qualities.
As cheap fillers or inferior fiber sources, items including corncobs, feathers, soy, cottonseed hulls, peanut hulls, citrus pulp, screening, weeds, straw, and cereal by-products are frequently used.
One factory that has obtained 135 kg of beef from overseas.
They want to add a total of 1.3oz of filler for each pound of beef.
Given is:
0.45 kg = 1 pound
So, 135 kg = 300 pounds
The company that wants to add a total of 1.3 oz of filler for each pound of beef.
So, for 300 pounds they will need = 390 oz of filler.
Therefore, the company needs 390 oz of filler.
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Refer to this diagram for the next five statements. Write the correct postulate, theorem, property, or definition that justifies the statement below the diagram.
Given: ∠MRS ≅ ∠MRO
m∠MRO + m∠MRS = m∠SRO
This statement is justified by the angle addition postulate.
The graph shows the linear parent function.Y5-55----Which statement best describes the function?
From the picture, we have the graph of the linear parent function f(x) = x.
We have the following statements as descriptions of the function:
A. The function is negative when x < 0.
From the graph, we see that the function takes negative values for x < 0. This statement is true.
B. The function is negative when x < 0 and also when x > 0.
The first part of this statement is true, but the second is not because that we see that the function takes positives values for x > 0. So this statement is false.
C. The function is never negative.
If we see the graph, the function is negative when x < 0. So this statement is false.
D. The function is negative when x > 0.
Again, seeing the graph we note that the function takes positive values for x > 0. So this statement is false.
So the only statement that it is true, is option A.
Question 2 of 25The coach of a college basketball team categorizes the number of pointsscored by the team in each game, with the categories being 51 - 57, 58 - 64,65 - 71, and 72 or more. If the following data represent the numbers ofpoints scored in the last 10 games, how many games were in the 51 - 57category?51, 70, 63, 59, 56, 75, 60, 55, 67, 64O A1B. 2O c. 4O D. 3
In the table, we can see that the highest number corresponds to the cats who failed. Then, if a comparative bar chart represents the data, the bar representing the number of cats that failed will be the tallest.
AnswerA. Cats who failed
(+2) The
The ratio of
women children = 11:3 and the
ratio of
men children = 5:2
Find the ratio of men:women
The ratio of both men and women 15:22
What is Ratio ?
A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
Given,
The ratio of men and children = 5:2
The ratio of women and children = 11:3
To find the ratio of men and women we have to divide both the ratio:
men/children/women/children
or,
men/children x children/women
putting the values
=5/2 x 3/11
=15/22
Hence, the ratio of men:women is 15:22
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1. 3x-4=232. 9-4x=173.6(x-7)=364. 2(x-5)-8= 34Solve equations
1. 3x - 4 = 23
add 4 to both sides
3x - 4 + 4 = 23 + 4
3x = 27
Divide both sides by 3
3x/3 = 27/3
x = 9
2. 9 -4x = 17
subtract 9 from both sides
9 -9 -4x = 17 - 9
-4x = 8
Divide both sides by -4
-4x/-4 = 8/-4
x = -2
3. 6(x-7) = 36
Divide both sides by 6
x -7 = 6
add 7 to both sides
x - 7 + 7 = 6 + 7
x = 13
4. 2(x-5) -8 = 34
Expand
2x -10 -8 = 32
2x - 18 = 32
2x = 32 + 18
2x = 50
Divide both sides by 2
x =25
whats the gcf of 96 and 40
Answer:
8
Step-by-step explanation:
Find the prime factorization of 40
40 = 2 × 2 × 2 × 5
Find the prime factorization of 96
96 = 2 × 2 × 2 × 2 × 2 × 3
To find the GCF, multiply all the prime factors common to both numbers:
Therefore, GCF = 2 × 2 × 2
GCF = 8
Answer:
8
Step-by-step explanation:
8 is the greatest number that 40 and 96 divides into
Fill in the missing parts to these two column proofs:
According to the picture:
For the first statement
[tex]AB\cong CD[/tex]The reason is: Given.
This is because it is given in the information to solve the problem.
The second statement must be:
[tex]BC\cong DA[/tex]And the reason is also: Given.
For the third statement:
[tex]AC\cong AC[/tex]The reason is the Reflexive property.
The fourth statement must be:
[tex]\Delta ABC=\Delta ADC[/tex]The reason is Side Side Side congruence postulate.
The fifth statement must be:
[tex]\measuredangle ABC=\measuredangle CDA[/tex]The reason is congruent triangles definition.