3x² + 6x - 24
Simplify 3.
3(x² + 6x - 8)
Think of x² +2x−8. Factor the expression by grouping. First, we need to rewrite the expression as x² + ax + bx - 8. To find a and b, set up a system to be solved.
a + b = 2ab = 1( −8 ) = −8Since ab is negative, a and b have opposite signs. Since a+b is positive, the positive number has a greater absolute value than the negative. Show all pairs of integers whose product is −8.
−1,8−2,4Calculate the sum of each pair.
−1 + 8 = 7−2 + 4 = 2The solution is the pair that gives sum 2
a=−2b=4Rewrite x² + 2x − 8 as (x² − 2x ) + (4x − 8).
(x² − 2x ) + (4x − 8)Simplify x in the first group and 4 in the second.
x ( x − 2) + 4( x − 2 )Simplify the common term x−2 with the distributive property.
( x − 2 )( x + 4 )The entire factored expression is rewritten.
3 ( x − 2 )( x + 4 ) ===> Answer
We conclude that the correct option is "B".
{ Pisces04 }A 10-year annuity pays $1,850 per month, and payments are made at the end of each month. If the APR is 12 percent compounded monthly for the first five years, and APR of 8 percent compounded monthly thereafter, what is the value of the annuity today?
Based on the amount the annuity pays per month and the APR, the value of the annuity today is $133,349.85.
What is the present value of the annuity?First, find the present value of the annuity at 5 years:
= 1,850 x present value interest factor of annuity, 60 months, 8/12%
= 1,850 x 49.32
= $91,242
Then find the present value of the annuity from 5 years till date:
= (1,850 x present value interest factor of annuity, 60 months, 12/12%) + ( 91,242) / (1 + 1%)⁶⁰)
= (1,850 x 44.955) + ( 91,242) / (1 + 1%)⁶⁰)
= $133,349.85
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draw a basic market graph. Title it the market for the product in your news article. Label axes, curves, eqilibruim price and equilibrium quantity
The basic market graph is attached below.
What do you mean by market equilibrium?A market is said to have reached equilibrium price when the supply of goods matches demand.
The equilibrium price is the only price where the plans of consumers and the plans of producers agree, where the amount consumers want to buy of the product, quantity demanded, is equal to the amount producers want to sell, quantity supplied. This common quantity is called the equilibrium quantity.
Quantity of gasoline:
Explanation of graph: The demand curve, D, and the supply curve, S, intersect at the equilibrium point E, with an equilibrium price of 1.4 dollars and an equilibrium quantity of 600.
The equilibrium is the only price where quantity demanded is equal to quantity supplied. At a price above equilibrium, like 1.8 dollars, quantity supplied exceeds the quantity demanded, so there is excess supply.
At a price below equilibrium, such as 1.2 dollars, quantity demanded exceeds quantity supplied, so there is excess demand.
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El alto de una caja "y" mientras que su ancho es "g" pies.
¿Cuál es el perímetro de la caja en pulgadas?
O [(g+y)x 2]
O10[(g+y)x 6]
12[(g+y)x 4]
O 12[(g+y)x 2]
Por definición de perímetro y considerando el cambio de unidades, el perímetro de la caja en pulgadas es 12[(g+y)×2].
Definición de perímetroEl perímetro de un figura geométrica plana se denomina a la longitud de su contorno. El perímetro es, por tanto, una medida de longitud.
En otras palabras, el perímetro de una figura de dos dimensiones es la distancia alrededor de la figura y es el resultado de la suma de los lados de una figura geométrica plana. Por lo que para el cálculo del perímetro es necesario conocer el número de lados de la figura y la longitud de cada uno de esos lados.
Perímetro de una cajaUna caja se puede considerar como una figura que tiene cuatro lados con dos medidas diferentes (alto y ancho).
El alto de la caja es "y" mientras que su ancho es "g" pies, por lo que su perímetro P es calculado como:
P= 2g + 2y= 2×(g+y) pies
Luego, se puede aplicar la siguiente regla de tres para realizar el cambio de unidades a pulgadas: si 1 pies equivale a 12 pulgadas, 2×(g+y) pies equivales a cuantas pulgadas?
[tex]P=\frac{2x(g+y) piesx12 pulgadas }{1 pie}[/tex]
Resolviendo
P= 12[(g+y)×2] pulgadas
Finalmente, el perímetro de la caja en pulgadas es 12[(g+y)×2].
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Which list shows all the factors of 24?
A. 1, 2, 3, 4, 6, 8, 12, 24
B. 1, 2, 3, 4, 6, 12, 24
C. 1, 2, 4, 5, 6, 12, 24
D. 1, 2, 4, 6, 12, 24
Answer!!
it would be a
Step-by-step explanation:
Geometry
Exact volume
Answer:
Exact volume: [tex]\frac{30184\pi}{3}[/tex]Approximate volume: 31608.6Step-by-step explanation:
The volume of the cylinder is [tex](\pi)(14^{2})(42)=8232\pi[/tex].
The volume of the hemisphere is [tex]\frac{2}{3}(\pi)(14^{3})=\frac{5488}{3}\pi[/tex].
Adding these together gives the exact volume to be [tex]\frac{30184\pi}{3}[/tex].
To the nearest tenth, this is 31608.6 square feet.
provide two more examples of relationship patterns found in mathematics and describe the pattern in each case
The examples of relationship patterns found in mathematics are arithmetic sequence and geometric sequence.
How to depict the sequence?It should be noted that an arithmetic sequence has a common difference. An example is given as: 2, 4, 6, 8. There's a common difference of 2.
For the geometric progression, there's a common ratio. A example is 2, 4, 8, 16, 32. Here, there's a cookie ratio of 2 when the numbers are divided.
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Simplify.
(2 + 8i) + (3 + 8i)
Answer:
Step-by-step explanation:
5+16i
Answer:
5 + 16i
Step-by-step explanation:
(2 + 8i) + (3 + 8i)
• Collect the like terms:
2 + 3 + 8i + 8i
⇒ 5 + 16i
If 2 sticks of butter make 36 cookies, how many sticks are you going to need to buy to make 3,000?
15) Complete.
Purchase Price: $450
Finance Charge: $82,50
Down Payment: $150
Number of Payments: 18
Monthly Payment:
O a.) $22.15
Ob.) $20.45
Oc.) $21.25
Od.) $22.25
The monthly payment for this purchase with a price of $450, a finance charge of $82.50, a down payment of $150, and 18 monthly payments is c.) $21.25.
What is the monthly payment?The monthly payment is the periodic payment made to settle a mortgage loan.
When the total mortgage payment is determined, the monthly payment can be calculated as the dividend of the total mortgage payment and the number of monthly payments.
Data and Calculaitons:Purchase Price: $450
Finance Charge: $82,50
Down Payment: $150
Number of Payments: 18
Total mortgage payment = $382.50 ($450 + 82.50 - 150)
Monthly payment = $21.25 ($382.50/18)
Thus, the monthly payment for this purchase with a price of $450, a finance charge of $82.50, a down payment of $150, and 18 monthly payments is c.) $21.25.
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I NEED ANSWERS QUICK PLS
The total surface area of the cuboid is 143.52 cubic cm
Surface area of a cuboidThe formula for calculating the surface area of a cuboid is expressed as:
SA = 2(lw + wh + lh)
where
l is the length = 7.2cm
w is the width = 3.1cm
h is the height = 4.8cm
Substitute
SA = 2(7.2*3.1 + 7.2*4.8 + 3.1*4.8)
SA = 2(22.32 + 34.56 + 14.88)
SA= 143.52 square cm
Hence the total surface area of the cuboid is 143.52 cubic cm
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The graph provided show the volume (in cubic inches) of air in a balloon as it chang
over time.
What is the volume of the balloon in cubic inches after 20 seconds?
The volume of the balloon is 500 cubic inches after 20 seconds
How to determine the volume?From the given graph, we have:
Time on the x-axisVolume on the y-axisAlso from the graph, we have:
V(20) = 500
This means that:
The volume of the balloon is 500 cubic inches after 20 seconds
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simplify (7^5)^3
A. 7^15
B. 35^3
C. 7^8
D. (1/7)^3
Answer:
7^15
Step-by-step explanation:
7^5^3 = 7^(5*3) = 7^15
Find the equation of a line whose slope is 1/2 and intersects negative y-axis at a distance of 7 units from the origin.
Answer:
Step-by-step explanation:
[tex]y=\frac{1}{2} x-7[/tex]
Answer:
y = 1/2x - 7
Step-by-step explanation:
The slope equation is: y = mx + b
m being the slope
b being the y-intercept
The problem says that the slope is 1/2, and says that it intersects negative y-axis, therefore the y-intercept is negative, so -7
What is the range of the function graphed below?
Answer:
[tex]\boxed{-\infty < y\leq 2}[/tex]
Step-by-step explanation:
See the appendix.
The set of values is the interval [tex]y\in (-\infty , 2 >[/tex] .
[tex]y\in (-\infty , 2 > ~~\Leftrightarrow ~~\boxed{-\infty < y\leq 2}[/tex]
A website reports that 14% of the world's population is Hindi and 33% are Christian. If there are approximately 6,840,507,000 people in the world, how many are Hindi and how many are Christian according to the website?
According to statistics, a person will devote 34 years to sleeping and watching TV. The number of years sleeping will exceed the number of years watching TV by 22. Over the lifetime, how many years will the person spend on each of these activities?
Considering the definition of an equation and the way to solve it, a person will devote 28 years watching TV and 6 years sleeping.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.
The members of an equation are each of the expressions that appear on both sides of the equal sign while the terms of an equation are the addends that form the members of an equation.
The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.
To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.This caseBeing "x" the number of years watching TV, and knowing that:
The number of years sleeping will exceed the number of years watching TV by 22.A person will devote 34 years to sleeping and watching TV.the equation in this case is:
x + (x+22) =34
Solving:
x + x =34 -22
2x= 12
x= 12 ÷ 2
x=6
As the number of years sleeping will exceed the number of years watching TV by 22, then x +22= 6 +22= 28 years.
Finally, a person will devote 28 years watching TV and 6 years sleeping.
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The two-way table represents data from a survey asking students whether they plan to attend college, travel, or both after high school.
A 4-column table with 3 rows. The first column has no label with entries travel, not travel, total. The second column is labeled college with entries 43, 24, 67. The third column is labeled not college with entries 10, 5, 15. The fourth column is labeled total with entries 53, 29, 82.
Which is the marginal relative frequency for students who plan to attend college? Round the answer to the nearest percent.
18%
22%
35%
82%
Using it's concept, it is found that the marginal relative frequency for students who plan to attend college is of 82%.
What is a relative frequency?A relative frequency is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there are a total of 82 students, 67 of which plan to attend college, hence the relative frequency is:
f = 67/82 = 0.82 = 82%.
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Answer:
82%
Step-by-step explanation:
The answer above is correct.
The square of the product of 6 and a number.
The statement, square of the product of 6 and a number can be written as 6x²
Mathematical expressionProduct = multiplication (×)let
x = unknown number
product of 6 and a number= 6 × x
= 6x
square of the product of 6 and a number= 6x²
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the function f(x)= x1/3 is transformed to get function h. h(x)= (2x)1/3+5 which statements are true about function h
The transformation of a function may involve any change. The function f(x) is vertically stretched and shifted 5 units upwards to form h(x).
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units, y=f(x+c) (same output, but c units earlier)Right shift by c units, y=f(x-c)(same output, but c units late)Vertical shift
Up by d units: y = f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: y = k \times f(x)Horizontal stretch by a factor k: y = f(\dfrac{x}{k})The function f(x)=x^(1/3) is transformed to form the function of h(x)=(2x)^(1/3)+5. Therefore, the transformation made to the function is,
Vertically stretched by a factor of 2^(1/3) ⇒ 2^(1/3) × x^(1/3) = (2x)^(1/3)
Up by 5 units ⇒ (2x)^(1/3) + 5
Hence, the function f(x) is vertically stretched and shifted 5 units upwards to form h(x).
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complete the flow chart to prove
someone pls help me pls pls asap
Vertical angles theorem (top one): [tex]\angle 1 \cong \angle 3[/tex]
Given: [tex]\angle 1 \cong \angle 2[/tex]
Transitive property of congruence: [tex]\angle 3 \cong \angle 4[/tex]
Vertical angles theorem (bottom one): [tex]\angle 2 \cong \angle 4[/tex]
Four students in an art class mixed red and blue paint to make purple. The amounts they used are shown in the table. Which student made a different shade of purple than the other students.
Based on the mixtures of the four students in the art class, the student with a different shade of purple would be Aiden.
Why would Aiden's mixture be different?In order to solve this question, look at the ratio of red paint to blue paint for all the students:
Alec:
1¹/₃ : ²/₃
2 : 1
Rosa:
2¹/₂ : 1 ¹/ ₄
2 : 1
Aidan:
4¹/₂ : 2
2.25 : 2
Zoe:
5 : 2¹/₂
2 : 1
Notice that Aidan's mixture is the only one that is different and so will have a different shade of purple as a result.
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Answer:
its aidan
Step-by-step explanation:
f(x) = 7x + 1 - 8
g(x) = -2
Find (f - g)(x).
A. (f-g)(x) = |7x - 5|
B. (f-g)(x) = 7x - 7+2
C. (f-g)(x) = |7x| - 5
D. (f-g)(x) = |7x+1-6
Answer: 7x-5
Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)=(7x+1-8)-(-2)=\boxed{7x-5}[/tex]
Answer:
D. (f-g)(x) = |7x+1|-6
Step-by-step explanation:
f(x) = |7x + 1| - 8
g(x) = -2
(f - g)(x) = f(x) - g(x) = |7x + 1| - 8 - (-2)
(f-g)(x) = |7x + 1| - 6
Data are collected about the amount of time, in minutes, each band member spends practicing. How does a single outlier change the lower and upper quartiles of the collected data?
A single outlier does not affect the values of the quartiles.
A single outlier causes the values of the quartiles to move slightly away from the outlier.
A single outlier doubles the values of the quartiles.
A single outlier causes the values of the quartiles to move slightly toward the outlier.
A single outlier does not affect the values of the quartiles.
What is the effect of the outlier on the value of the quartiles?
An outlier is a number that is way smaller or way larger than that of other numbers in a data set. An outlier does not affect the values of the upper and lower quartiles. This is an advantage of the upper and lower quartiles over range.
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edward nolan has room for 28 bedding 1.99
The minimum that Nolan would have to spend is $33.84 while the maximum he has to spend is $35.94
How to solve for the minimum amount10 * 0.84 = 8.4
8 * 1.29 = 10.32
8 * 1.89 = 15.12
The minimum is = 8.4 + 10.32 + 15.12
= 33.84 dollars.
How to solve for the maximum10 * 1.89 = 18.9
8 * 1.29 = 10.32
8 * 0.84 = 6.72
The sum of the maximum is given as 18.9 + 10.32 + 6.72
= $35.94
Complete questionEdward Nolan has room for 26 bedding plants in his garden. He can get pansies for $1.89 each, marigolds for $1.29 each, and zinnias for $0.84 each. He plans to buy 10 of one type and 8 each of the other two types of plants. (a) What is the minimum (in $) Edward will have to spend? $ Incorrect: Your answer is incorrect. (b) What is the maximum (in $) Edward could spend? $ Incorrect: Your answer is incorrect.
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solve for the value of Y.
90=7y+8+8y+7
Answer:
y = 5
Step-by-step explanation:
1) Simplify 7y+8+8y+7 to 15y + 15.
90 = 15y + 15
2) Subtract 15 from both sides.
90 - 15 = 15y
3) Simplify 90 - 15 to 75.
75 = 15y
4) Divide both sides by 15.
75/15 = y
5) Simplify 75/15 to 5.
5 = y
6) Switch sides.
y = 5
(2x-1)²+8√2xy=4
4y-√8xy-1=1
(x² + 2√xy) = 5/4
2y - √2xy = 0
How to factorize the expressionFrom the first equation
(2x-1)²+8√2xy=4
Expand the bracket
(2x-1) (2x+ 1) + 8√2xy = 4
4x² + 2x -2x - 1 + 8√2xy = 4
4x² - 1 + 8√2xy = 4
Collect like terms
4x² + 8√2xy = 4 + 1
4x² + 8√2xy = 5
Find the common factor
4(x² + 2√xy) = 5
(x² + 2√xy) = [tex]\frac{5}{4}[/tex]
For equation 2, we have
4y-√8xy-1=1
4y - [tex]\sqrt{4 *2 xy }[/tex] = 1 -1
4y - [tex]2\sqrt{2xy}[/tex] = 0
Find the common factor
[tex]2(2y - 2\sqrt{2xy} ) = 0[/tex]
[tex]2y - 2\sqrt{2xy} = 0[/tex] × 2
[tex]2y - \sqrt{2xy} = 0[/tex]
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1O less than the quotient of a number c and 13
Answer:
c/13 - 10
Step-by-step explanation:
Classify the following triangle as acute, obtuse, or right.
Answer:
cool
Step-by-step explanation:
pooop
HELP!! EASY 50 POINTS!!
Select the correct answer. With which set of information can you construct a unique triangle? A. the measurements of all the angles B. the lengths of two sides C. the measurements of two angles D. the lengths of all the sides E. the measurement of one angle
In a plane, if line ℓ is perpendicular to line m and _____, then ℓ ⊥ n.
Answer:
n
Step-by-step explanation: