[tex]~~~(x^2 -4)(x^2 +6x +9)\\\\=(x^2 -2^2)(x^2 +2 \cdot 3x +3^2)\\\\=(x+2)(x-2)(x+3)^2[/tex]
(Need help answering these questions… please don’t give me links in the comments, because it doesn’t help me. Answer it in comments please. )
A bucket holds 5 gallons of water and a barrel holds 8.4 buckets of water.
a. What is the conversion factor to change gallons to buckets?
b. What is the conversion factor to change buckets to barrels?
c. A gallon (gal) of water is equivalent to 128 fluid ounces (fl oz). How many fl oz of water are in 1 barrel?
Answer:
a) 1/5 bucket = 1 gallon
b) 8.4 buckets = 1 barrel
c) 5376 fl oz per barrel
Step-by-step explanation:
a) From the given information, 1 bucket = 5 gallons. This means 1/5 of a bucket is 1 gallon.
b) From the given information, 8.4 buckets = 1 barrel. This seems to be in the form that the question is asking for. If the question was asking how many barrels were in a bucket the answer would be 1/8.4 barrels = 1 bucket.
c) From the previously determined conversion factors, we can take ounces to barrels by converting barrels down to gallons.
1/8.4 barrels = 1 bucket; 1/5 bucket = 1 gallon; 1 gallon = 128 fluid ounces
We need to set up a series of fractions that use these factors:
[tex]\frac{128 fl oz}{1 gallon}*\frac{1 gallon}{1/5 buckets}*\frac{1 bucket}{1/8.4 barrels}[/tex]
These fractions can be simplified to [tex]\frac{128 fl oz}{1 gallon}*\frac{5 gallon}{1 bucket}*\frac{8.4 buckets}{1 barrel}[/tex]
Multiply the fractions: 5376 fl oz per barrel
(Note that the units cancel out in the fractions so that only fluid ounces per barrel are left.)
Select the value of each expression.
33.6
[4 x (4 + 3)]- 3
[(7-5)+ =] × 2
2
x
(5.4 + 3) x (62)
[9 ÷ 3 + 6] x 3
25
0
27
[
[
[
Answer:
the answer is [9÷3+6]×
Step-by-step explanation:
the Answer is [9÷3+6]×3 =25
What is true of the function g(x) = -2x² + 5?
O g(x) is the multiplication of g and x.
O-212 +5 is the input of the function.
The variable x represents the independent variable.
The variable g represents the input of the function.
Answer:
C.) The variable x represents the independent variable
Step-by-step explanation:
The variable "x" is the independent variable because that is the value that we can manipulate. We cannot manipulate the dependent variable because it is determined by the independent variable. In that case, "y" would be the dependent variable because its value is dependent on what "x" is.
A.) is incorrect because g(x) symbolizes the input of the variable "x" into the g function.
B.) is incorrect because "x" is the input.
D.) is incorrect because "x" is the input.
Write the equation in standard form for the circle with center (9,0) and radius 3
15.
In the following graph we observe line segment AB being mapped by translation to line segment A'B'.
A. In two or more sentences, explain what test you could perform to check the validity of this translation.
B. Prove mathematically that the translation is valid using the test you mentioned above.
The translation of line AB to line A'B' is valid and the translation rule is (x,y) ⇒ (x - 7, y - 3)
How to validate the translation?The graph that completes the question is added as an attachment
From the graph, we have:
A = (3,9) and B = (5,6)
A' = (-4,6) and B' = (-2,3)
Subtract the x and y coordinates of A' from A and B' from B.
So, we have:
AA' = (3 + 4, 9 - 6)
AA' = (7, 3)
BB' = (5 + 2, 6 - 3)
BB' = (7, 3)
See that:
AA' = BB' = (7, 3)
This means that the line AB is translated 7 units left and 3 units down
How to prove the translation mathematicallyThe translation above means:
(x,y) ⇒ (x - 7, y - 3)
Recall that:
A = (3,9) and B = (5,6)
So, we have:
A' = (3 - 7, 9 - 3)
A' = (-4, 6)
Also, we have:
B' = (5 - 7, 6 - 3)
B' = (-2, 3)
Hence, the translation is valid
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Credit card A has an APR of 22% and an annual fee. All else being equal, at about what balance will the cards offer the same deal over the course of a year? (Assume all interest is compounded monthly)
All else being equal, at a $1,333.33 balance, the two credit cards will offer the same deal (finance charge) over a year.
What is a credit card finance charge?A credit card finance charge is the fee associated with using credit.
Credit card issuers use the finance charges to minimize non-payment risks and earn some profits for extending credit to cardholders.
Data and Calculations:Card A Credit B
APR 22% 25%
Annual fee $40 $0
To calculate the balance required, the required equation is
= 22%x + $40 = 25%x
Where x = required balance
Thus,
= 0.22x + $40 = 0.25x
= $40 = 0.03x (0.25x - 0.22x)
= 0.03x = $40
x = $40/0.03
x = $1,333.33
Question Completion:Credit card A has an APR of 22% and an annual fee of $40, while credit card B has an APR of 25% and no annual fee.
Thus, all else being equal, at a $1,333.33 balance, the two credit cards will offer the same deal over the course of a year.
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Find the area of each triangle.
Answer:
a) 30 square units
b) 36 square units
c) 18 square units
Step-by-step explanation:
Area of a triangle = 1/2 × base × height
Part (a)Base = 10
Height = 6
⇒ Area = 1/2 × base × height
= 1/2 × 10 × 6
= 30 units²
Part (b)Base = 12Height = 6⇒ Area = 1/2 × base × height
= 1/2 × 12 × 6
= 36 units²
Part (c)Base = 6Height = 6⇒ Area = 1/2 × base × height
= 1/2 × 6 × 6
= 18 units²
Yolanda saves all the money from a regular baby-sitting job. The money in her savings account is increasing according to the equation y = 6x + 50, where x = number of hours worked and y = savings in dollars. Which table of values matches this equation?
Answer:
Table D
Step-by-step explanation:
I have all of the tables listed below and the correct one circled! I used to tutor my cousin about this topic!
I hope this helps and please feel free to comment, ask questions, give feedback, and correct me if I am wrong!
Have a great day!
:)
The 4th table in the option is the correct one.
What is an equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Yolanda saves all the money from a regular baby-sitting job. The money in her savings account is increasing according to the equation y = 6x + 50, where x = number of hours worked and y = savings in dollars.
The given equation is y = 6x + 50
Put x = 0
y = 50
Put x = 5
y = 80
Put x = 10
y = 110
Put x = 15
y = 140
Creating the table,
x y
0 50
5 80
10 110
15 140
Hence, we get the table.
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A roller coaster’s height is given by the equation h = –.086t^2 + 6t + 50, where t represents the time in seconds. How long will it take riders to pass over the hill and reach ground level? hint: Set h = 0.
34.88 seconds
50.00 seconds
50.17 seconds
77.29 seconds
The time it will take the ride to reach the floor is 77.29 seconds
Quadratic equationsThese are equations that has a leading degree of 2.
Given the function that represents the height of the roller coaster
h(t) = –0.086t^2 + 6t + 50,
At the ground level, h = 0
Substitute
h(t) = –0.086t^2 + 6t + 50,
–0.086t^2 + 6t + 50 = 0
0.086t^2 - 6t - 50 = 0
Factorize
On factorizing, the time it will take the ride to reach the floor is 77.29 seconds
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Answer:
D) t = 77.29 seconds
Step-by-step explanation:
The height of the rollercoaster at ground level is zero.
Therefore, to find how long it will take riders to pass over the hill and reach ground level, set h = 0 and solve for t.
Set the equation equal to zero:
[tex]-0.086t^2 + 6t + 50=0[/tex]
Solve the equation using the quadratic formula.
What is the quadratic formula?The quadratic formula is a formula that can be used to find the solutions of any quadratic equation, which is an equation of the form ax²+bx+c=0, where a, b, and c are constants and x is the variable.
[tex]\boxed{x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}}[/tex]
In this case:
a = -0.086b = 6c = 50Substitute these values into the quadratic formula and solve for t:
[tex]t=\dfrac{-6 \pm \sqrt{6^2-4(-0.086)(50)}}{2(-0.086)}[/tex]
[tex]t=\dfrac{-6 \pm \sqrt{36+17.2}}{-0.172}[/tex]
[tex]t=\dfrac{6 \pm \sqrt{53.2}}{0.172}[/tex]
[tex]t=-7.52228495..., \;\; 77.2897268...[/tex]
As time is positive only, t = 77.29 seconds (2 decimal places).
Select the correct answer.
Over which interval of the domain is function h decreasing?
25?
Answer:
the function is only increasing.
Step-by-step explanation:
PLEASE HELP! i need done ASAP.
Answer:
m<A = 120
m<BCD = 120
m<DEC = 30
m<BFE = 90
Step-by-step explanation:
m<A is 120 cause all internal angles equal 720 added together in hexagons. 720 ÷ 6 = 120
m<BCD is 120 cause regular hexagons have eqaul angles
m<DEC is 0 cause total of the angle of triangle of triangle EDC is 180 where m<D = 120 which leaves m<E + m<C = 60 since they are equal we can combine them to m<E • 2 = 60. Divide and we get 30
m<BFE = 90 cause m<AFB = 30 and m<AFE = 120 subtract 120 and 30 to get 90
Emily completed reading 24/3 books in 32/4 days. Find the number of books she would have completed in one day.
The number of books she would have completed in one day will be 2 books.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given that:-
Emily completed reading 24/3 books in 32/4 days
Emily completed 8 books in 4 days. The number of the books will be calculated by using the expression below:-
4 days = 8 books
1 day = 8 / 4 = 2 books
Therefore the number of books she would have completed in one day will be 2 books.
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Dylan bought seven candy bars for $10.50. How much did he pay for each candy bar?
Answer: 1.5 or 1 1/2
Step-by-step explanation:
He payed $1.50 for each candy bar
Question 5 ? Question What does the x-intercept of this relationship represent? O the initial amount of plant food the length of time it takes for Ryan to use all the plant food O the amount of plant food used each day O the length of time it takes for the height of the plant to reach 72 centimeters
Answer:
O the amount of plant food used each day
Step-by-step explanation:
O the initial amount of plant food the length of time it takes for Ryan to use all the plant food is the y-intercept therefore wrong.
O the length of time it takes for the height of the plant to reach 72 centimeters
Hailey created her own cleaning service and uses the equation t = 20n + 15 to represent her total earnings, t, for each job. If she earned a total of $80, how many hours, n, did she work?
Step-by-step explanation:
t = 20n + 15
t = 80
80 = 20n + 15
65 = 20n
n = 65/20 = 13/4 = 3.25 hours
find the prime factorization of 420
Answer:
2,3,7,2,5
Step-by-step explanation:
When you factorize a number you divide them until the outcome numbers are prime. 420 is equal to 42 and 10.
42 is equal to 6 and 7 and 6 is 2 times 3
2,3,7 is prime
10 is 2 times 5
2 and 5 is prime
Answer:
420 = 2² × 3 × 5 × 7
Step-by-step explanation:
The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, ...
To find which prime numbers multiply together to make 420, start by dividing 420 by the first prime number, 2:
⇒ 420 ÷ 2 = 210
As 210 is not a prime number, we need to divide again. Let's try dividing by 2 again:
⇒ 210 ÷ 2 = 105
As 105 is not a prime number, we need to divide again. 105 is not divisible by 2, so let's try dividing it by the next prime number, 3:
⇒ 105 ÷ 3 = 35
As 35 is not a prime number, we need to divide again. 35 is not divisible by 2 or 3, so let's try dividing it by the next prime number, 5:
⇒ 35 ÷ 5 = 7
As 7 is a prime number, we can stop.
Therefore, 420 is the product of all the prime numbers we found together with the final one:
⇒ 420 = 2 × 2 × 3 × 5 × 7
As 2 appears twice, we can write this using exponents:
⇒ 420 = 2² × 3 × 5 × 7
Ted needs 2500 metres for job. What length is this in kilometres
Answer:
2.5 kilometers
Step-by-step explanation:
One kilometer is 1000 meters
To convert from metres to kilometers, we divide by 1000
2500 ÷ 1000 = 2.5km
For each of the number lines, write an absolute value equation in the form |x - c |=d,
where c and d are some numbers, to satisfy the given solution set.
The absolute value equation that satisfy the solution set of -4 and -8 is |2 - x| = -6
How to determine the absolute value equation?The solution sets on the number line are given as:
x = {-8, -4}
Calculate the average of the solutions
Mean = (-8 - 4)/2
Mean = -6
Calculate the difference of the solutions divided by 2
Difference = (-4 + 8)/2
Difference = 2
The absolute value equation is the represented as:
|Difference - x | = Mean
Substitute known values
|2 - x| = -6
Hence, the absolute value equation is |2 - x| = -6
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Answer:
|b+6|=2
Step-by-step explanation:
How many whole numbers are there between 32 and 96?
Answer:
there are 20 while numbers between 32 and 96
Step-by-step explanation:
hope it helps and give me a brainliest
The number of whole numbers that come between 32 and 96 will be 64.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The number of whole numbers that come between 32 and 96 is given as,
⇒ 96 - 32
⇒ 64
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Which polygon is a convex heptagon?
A polygon has 7 sides. No angles go inside of the shape.
A polygon has 8 sides. No angles go inside of the shape.
A polygon has 8 sides. One angle goes inside of the shape.
A polygon has 7 sides. One angle goes inside of the shape.
Option (A) "A polygon has 7 sides. No angles go inside of the shape" is correct.
What is a regular polygon?A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.
As we know, a convex heptagon is a polygon with seven sides, seven internal angles, and seven vertices, which means that a convex heptagon has seven sides.
A convex heptagon is a polygon that has 7 sides. No angles go inside of the shape.
Thus, option (A) "A polygon has 7 sides. No angles go inside of the shape" is correct.
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Answer: the first option
Step-by-step explanation:
what is the type of rule in which you can find any number of term in sequence without knowing the first or previous term
The type of rule that can be used to find any number of terms in sequence without knowing the previous term is called the Explicit rule formula.
What is the Explicit rule formula?The formula that determines the sequence's nth term is the explicit rule of an arithmetic sequence.
Using explicit formulae, one can compute any term in a series without first determining the value of the terms that came before it.
Therefore, we can conclude that the type of rule that can be used to find any number of terms in sequence without knowing the previous term is called the Explicit rule formula.
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Solve for x to the nearest tenth of centimetre
Answer:
Step-by-step explanation:
Mark purchased a 12-pack of soda for
$5.86. What is the unit rate per soda?
(Round to the nearest cent!)
Answer:
$0.49 per soda
Step-by-step explanation:
The cost per soda is found by dividing the cost by the number of sodas.
__
$5.86/(12 sodas) = $0.48833.../soda ≈ $0.49/soda
The unit rate is $0.49 per soda.
The revenue, in dollars, of a company that makes toy cars can be modeled by the polynomial 3x2+4x-60. The cost, in dollars, of producing the toy cars can be modeled by 3X2-x+ 200. The number of toy cars sold is represented by X
The equation that represents the profit function is P(x) = 5x - 260
How to determine the profit function?The given parameters are:
C(x) = 3x^2 - x + 200 --- cost function
R(x) = 3x^2 + 4x - 60 --- revenue function
The profit function is calculated as:
P(x) =R(x) - C(x)
This gives
P(x) = 3x^2 + 4x - 60 - 3x^2 + x - 200
Evaluate the like terms
P(x) = 5x - 260
Hence, the equation that represents the profit function is P(x) = 5x - 260
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Find the volume of the prism.
8in. 5in. 5in
Find the area A and circumference C of a circle of diameter 12 cm. Use 3.14 for . Round the result to the nearest tenth.
Answer:
Area: 113cm²
Circumference: 37.7cm
Step-by-step explanation:
to find area use the formula πr², π being Pi (3.14) and r being radius
radius = 6cm (half the diameter)
3.14 × 6² = 113.04cm²
to find the circumference use the formula πd
diameter = 12cm
3.14 × 12 = 37.68
ADEF is translated 5 units straight up so that point F lands on the x-axis. where does point D land?
Point D would be translated to the point (0, 5).
What is translation?Translation is an aspect of geometry that moves plane shapes from one point to another along the cartesian coordinates without changing the form in which the shape exists.
Analysis:
Point D is at (0,0) if it is translated up from 0,0 the point D moves 5 units along the y-axis while x axis remain same. So that the new point of D becomes (0,5)
In conclusion, the point D will land at point (0,5)
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4^2/5 / 4^x/5 = 4^0
Can you help me please
sally has 10 pounds she wants to buy 28 cans of soda which cost 26p each. how much money does she spend and does she have enough
Answer:
she will need 728 pounds to buy 28 cans but she only has 10 pounds so she doesn't even have enough for 1 can of soda
PLEASE HELP!!! I WiLL GIVE BRAINLIEST!!!!!
Identify the coefficients of x, y and z
5z - 2 + 6x + 3y
Answer:
x=5 y=3 z=5
Step-by-step explanation:
The coefficient is the number in front of the variable
Answer:
coefficient of x: 6coefficient of y: 3coefficient of z: 5Step-by-step explanation:
The coefficient in an expression is the multiplier of a designated part of a term of the expression.
__
coefficients hereThe given expression is
5z -2 +6x +3y
It consists of four (4) terms, added together. One term is a constant, -2. The others each have a single variable that is multiplied by a constant. When we ask for the coefficient of the variable, we are asking for the value of that constant multiplier.
The term containing x is 6x. The multiplier of x in that term is 6, so we say ...
the coefficient of x is 6.
The term containing y is 3y. The multiplier of y in that term is 3, so we say ...
the coefficient of y is 3.
The term containing z is 5z. The multiplier of z in that term is 5, so we say ...
the coefficient of z is 5.
__
other coefficientsIn an expression such as πr²h, different parts of the expression will have different coefficients. If we ask for the coefficient of the expression, we are generally asking for the constant: π. (The Greek letter pi is the symbol used to represent the irrational constant ratio between the circumference and diameter of a circle. Is is about 3.1415926535....)
If we ask for the coefficient of h, we are asking for the product (πr²) that multiplies h in this expression. Similarly, the coefficient of r² is (πh). Note that we have specified a "designated part" of the expression for which we want the coefficient. This is important when we are solving equations.
__
The commutative property of multiplication means that parts of a product can be written in any order. That is, 5·z is the same product as z·5. When the constant and variable parts of the expression can be unambiguously identified, the order does not matter. In some cases, a constant coefficient may come in several parts: 3z·5·2 has a z-coefficient of 30, for example.
See below for a case where there may be some ambiguity.
__
exponentsIn the expression r², the constant 2 that comes after the variable, written as a superscript, is called an "exponent," not a coefficient. Often on Brainly, and sometimes in curriculum materials, you will see this written as r2, because superscripts do not get properly rendered. If you're writing this in plain text, the form r^2 is preferred.