Answers
The product of the expressions are;
Step 1: (x + 2)(x + 3) and 3(x + 3)/4(x + 5)
Step 3: 4(x + 3) × 3(x + 3)/4(x + 5)
Step 4: 3/x + 5
How to determine the productIt is important to note that algebraic expressions are described as expressions that are composed of variables, terms, coefficients, constants and factors.
From the information given, we have the fraction;
4x + 8/x² + 5x + 6 × 3x + 9/4x + 20
To determine the product, let us reduce the expressions to their lowest forms, we have;
4x + 8 = 4(x + 2)
x² + 5x + 6 = (x + 2)(x + 3)
3x + 9 = 3(x +3)
4x + 20 = 4(x + 5)
Substitute the expressions
4(x + 2)/(x + 2)(x + 3) × 3(x +3)/4(x + 5)
divide the common terms
4(x + 3) × 3(x + 3)/4(x + 5)
Divide further, we have.
3/x + 5
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Related Questions
Pupils in a class were asked how they travel to school. The results were recorded in the table below
Car 13 bus 6 train 5 walk 8
If s pupil in the class was picked at random what is the probability that one of them walked to school as a percentage
Answers
Answer:
1/3
Step-by-step explanation:
Simplify to create an equivalent expression.
−
4
(
−
11
+
4
n
)
−
3
(
−
2
n
+
9
)
Answers
Answer:
Step-by-step explanation:
To simplify this expression, we will distribute the -4 and -3 to the terms inside the parentheses:
-4(-11+4n) - 3(-2n+9)
= 44 - 16n + 6n - 27
= -16n - 17
Therefore, the simplified expression is -16n - 17.
The volume of a cuboid is 630cm3.
The length is 14cm and the width is 90mm.
Whatt is the height of the cuboid in cm.
Answers
Answer:
Height = 630 / (14 x 0.9) = 47.5 cm
The entry fee to East Egg Hunt Event is $7.00. Each ride requires a ticket that cost $2.00. Cassie spent a total of $45.00. How many tickets Cassie Purchase?
Answers
Answer: 19 tickets
Step-by-step explanation: $45 - $7 = 38 38 divided by $2 = 19 tickets
if AC = 57, find the measure of AB
Answer choices:
A. 9
B. 30
C. 6
D. 27
Answers
A pyramid has a height of 5 inches and a volume of 60 cubic inches. Which of the following figures could be the base for this pyramid?
Select 3 answers that apply.
A a hexagon with an area of 36 square inches
11 a right triangle with one leg 5 inches and the hypotenuse 13 inches
ca circle with radius 4 inches
Da 4-inch by 9-inch rectangle
a 3-inch by 4-inch rectangle
a square with side length 6 inches
E
Answers
The 3 correct answers of the figures that could be the base for the pyramid that has a height of 5 inches and a volume of 60 cubic inches are:
A hexagon with an area of 36 square inches (option A)A 4-inch by 9-inch rectangle (option D)A 3-inch by 4-inch rectangle (option E)How do we calculate?The formula to find the base of a pyramid given its height and volume,
Volume of pyramid = (1/3) * Base area * Height
Substituting in the given values, we have:
60 = (1/3) * Base area * 5
Base area = 36 square inches
In conclusion, any figure with a base area of 36 square inches could be the base for this pyramid.
The following figures have a base area of 36 square inches:
A hexagon with an area of 36 square inches A 4-inch by 9-inch rectangle A 3-inch by 4-inch rectangleLearn more about pyramids at: https://brainly.com/question/218706
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Elijah works in a department store selling clothing. He makes a guaranteed salary of $500 per week, but is paid a commission on top of his base salary equal to 30% of his total sales for the week. How much would Elijah make in a week in which he made $775 in sales? How much would Elijah make in a week if he made
x dollars in sales?
Total earnings when selling $775:
Total earnings when selling $x:
Answers
Elijah's total earnings for the week if he made x dollars in sales would be: $500 + 0.3x.
What is sale?
A sale is an event or activity in which goods or services are sold at a reduced or discounted price.
What is discount?
A discount is a reduction in the price of an item or service. It is often offered as a promotion or incentive to encourage customers to buy or use a product or service.
According to given information:Total sales commission earned by Elijah for selling $775 worth of clothing:
30% of $775 = 0.3 x $775 = $232.50
Therefore, Elijah's total earnings for the week would be:
$500 (guaranteed salary) + $232.50 (commission) = $732.50
For selling x dollars worth of clothing, the commission earned by Elijah would be:
0.3x
Therefore, Elijah's total earnings for the week if he made x dollars in sales would be:
$500 (guaranteed salary) + 0.3x (commission) = $500 + 0.3x
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If I get paid $12.50 an hour and I worked a total of 15 hours and 35 minutes how much did I make?
Answers
Answer: $194.79
Step-by-step explanation:
It is easiest to approach this question in two parts.
First part is simple - multiply the wage per hour times the number of whole number you have worked. ($12.50)(15) = $187.50
Next you need to find how much you make in 35 minutes at a wage rate of 12.50 an hour. You can set up a ratio to find this out -
($12.50) | (60 min) - (x dollars) | (35 min)
then cross multiply and divide - (12.5 * 35) / 60 = 7.291
This means you make $7.29 for 35 minutes of work.
$187.50 + $7.29 = $194.79 for 15 hours 35 minutes of work.
(this is based on a per minute/hour scale)
Adrian eats 2/3's of a pack of gum each
day. How many packs of gum will he
have eaten after 7 days?
10 points given!!
Answers
What is the answer to x3 y3 z3 k?
Answers
Answer:
The equation x3+y3+z3=k is known as the sum of cubes problem.
Step-by-step explanation:
To amend a country’s constitution, 7/9 of the 84 states in that country must approve the amendment. If 66 states approve the amendment, will the constitution be amended?
Answers
Answer:
Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.
Step-by-step explanation:
To determine whether the constitution will be amended, we need to compare the number of states that have approved the amendment to the required number of states needed for approval.
The requirement is that 7/9 of the 84 states must approve the amendment. So, we need to calculate 7/9 of 84 to find out how many states need to approve the amendment:
(7/9) x 84 = 66.67
Rounding up, we see that 66.67 is equivalent to 67 states. This means that in order for the amendment to be approved, at least 67 states must approve it.
Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.
Decide if each statement is true or false and explain.
All rectangles are quadrilaterals.
Answers
Answer: True
Step-by-step explanation:
They have four sides
Answer:true.
Step-by-step explanation: All Rectangles are indeed quadrilaterals because all rectangles have 4 sides and quadrilaterals are known as a four sided shape,
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
The correct option is 1 and 4 of the given inequality –3(2x – 5) < 5(2 – x)
The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:
-6x + 15 < 10 – 5x
x < 5
Therefore, options 1 and 4 are correct. The other options do not correctly represent the inequality.
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The ratio of new car sales to used car sales at the car lot is 3:5. If the total car sales were $287,400 last month, what was the total of the used car sales?
Answers
Answer:
Therefore, the total used car sales were $179,625.
Step-by-step explanation:
Let's assume that the ratio of new car sales to used car sales is 3x:5x, where x is a constant.
The total car sales were $287,400, which means the sum of the new car sales and used car sales is $287,400:
3x + 5x = 8x
So, the total sales can be expressed as:
8x = $287,400
To find the value of x, we need to divide both sides by 8:
x = $35,925
Now, we can calculate the used car sales by multiplying 5x by the value of x:
Used car sales = 5x * x = 5 * $35,925 = $179,625
Therefore, the total used car sales were $179,625.
if you have 2 bags of candy each with 4 pieces of candy in them you will have 8 because 2x4=8
Answers
Answer:
Step-by-step explanation:
ex 2
4444
2
4444
Yes, that's correct I even tried to show you.
The 2 is the bags of candy
4 pieces of candy per bag
equals to 8 in total
PLEASE HELP ME
Given the following quadratic functions, complete the following:
1. Identify the zeros.
2. Identify the vertex.
3. Write the quadratic equation in factored form for the function that is graphed.
Answers
The zeros and vertex of each quadratic equation are:
Case 1: y = 4 · (x + 2) · (x - 2), Roots: - 2, 2, Vertex: (0, - 16)
Case 2: y = (1 / 2) · (x + 5) · (x - 3), Roots: - 5, 3, Vertex: (- 1, - 8)
Case 3: y = - 2 · (x + 4) · (x + 2), Roots: - 4, - 2, Vertex: (- 3, 2)
Case 4: y = - 2 · (x + 6) · (x + 2), Roots: - 6, - 2
Vertex: (- 4, 8)
How to analyze quadratic functions and derive their expressions
Graphically speaking, quadratic functions have the form of the parabola. The zeros are the points of parabola that are on the horizontal axis (x-axis) and the vertex is the only point of the parabola. The factor form of the parabola is:
y = C · (x - r₁) · (x - r₂)
Where:
C - Vertex constantr₁, r₂ - RootsNow we proceed to determine all the features of the quadratic function:
Case 1
Roots: r₁ = - 2, r₂ = 2
Vertex: (h, k) = (0, - 16)
C = y / [(x - r₁) · (x - r₂)]
C = - 16 / [2 · (- 2)]
C = - 16 / (- 4)
C = 4
Factor form: y = 4 · (x + 2) · (x - 2)
Case 2
Roots: r₁ = - 5, r₂ = 3
Vertex: (h, k) = (- 1, - 8)
C = y / [(x - r₁) · (x - r₂)]
C = - 8 / [(- 1 + 5) · (- 1 - 3)]
C = - 8 / [4 · (- 4)]
C = - 8 / (- 16)
C = 1 / 2
Factor form: y = (1 / 2) · (x + 5) · (x - 3)
Case 3
Roots: r₁ = - 4, r₂ = - 2
Vertex: (h, k) = (- 3, 2)
C = y / [(x - r₁) · (x - r₂)]
C = 2 / [(- 3 + 4) · (- 3 + 2)]
C = 2 / [1 · (- 1)]
C = - 2
Factor form: y = - 2 · (x + 4) · (x + 2)
Case 4
Roots: r₁ = - 6, r₂ = - 2
Vertex: (h, k) = (- 4, 8)
C = y / [(x - r₁) · (x - r₂)]
C = 8 / [(- 4 + 6) · (- 4 + 2)]
C = 8 / [2 · (- 2)]
C = 8 / (- 4)
C = - 2
Factor form: y = - 2 · (x + 6) · (x + 2)
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circumference is 1884, what is the diameter
Answers
Answer: how many places are you looking for? because it would be around 599.696332...(and more decimal numbers)
you get this from dividing 1884 by 3.14159 (pi)
need an answer NOW!! id prefer if sin cos and/or tan was used to find the side length, but its okay if you use pythagorean theorem
Answers
The length of the side of the tent is 5.8 feet calculated using the height of the equilateral triangle.
Equilateral triangle:An equilateral triangle is a type of triangle where all three sides have the same length, and all three angles are equal to 60 degrees.
The formula for the height of an equilateral triangle is given by
Height (h) = ½(√3a)Where 'a' is the equal side of the equilateral
In the given problem we use the height of the triangle to calculate the side of the triangle tenth.
Here we have
The height of the tent is 5 ft which is the height of the equilateral triangle
As we know,
Height of equilateral triangle = ½(√3a)
Let 'a' be the side of the triangle tent
=> 5 ft = ½(√3a)
Multiply by 2 on both sides
=> 5 × 2 = 2(1/2)√3a
=> √3a = 10
=> (1.732) a = 10 [ ∵ √3 1.732 ]
=> a = 5.8
Therefore,
The length of the side of the tent is 5.8 feet calculated using the height of the equilateral triangle.
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Just number 9 with work
Answers
The correct answer is (c) Left 5. The transformation is a horizontal shift to the left by 5 units.
What is equation?An equation is a statement that shows the equality between two expressions. It typically contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, division, exponentiation, or roots. An equation can be solved by finding the value(s) of the variable(s) that make the equation true. Equations are used extensively in mathematics, science, engineering, and other fields to describe relationships between different quantities and to make predictions or solve problems.
Here,
The given equation is y = 12/(x + 5), which represents a rational function. The parent function for this type of function is y = 1/x, which has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.
To transform the parent function represented by y = 1/x into y = 12/(x + 5), we need to apply the following transformations:
Vertical stretch by 12: This means that the y-values of the graph will be multiplied by a factor of 12, causing the graph to become narrower and taller. Horizontal shift left 5 units: This means that the graph will be shifted 5 units to the left, causing the vertical asymptote to move from x = 0 to x = -5.
Therefore, the correct answer is (c) Left 5, since this represents the horizontal shift of 5 units to the left. The other answer choices do not accurately describe the transformation of the parent function into the given equation.
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Circle p has a radius of 8 inches
Answers
The area of the sector that is the smaller region of the circle is evaluated to be equal to 39.1 in² to the nearest tenth.
How to evaluate for the area of the sector.The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.
the angle of the sector = 70°
the radius = 8 ft
hence the area of the sector is calculated as follows:
(70°/360°) × 22/7 × 8 in × 8 in
we simplify by division and multiplication
1/36 × 22 × 64 in²
352 in²/9
39.1111 in²
Therefore, the area of the sector that is the smaller region of the circle is evaluated to be equal to 39.1 in² to the nearest tenth.
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You are thinking about changing employment. Your goal is to work for three years and then return to university full-time, in pursuit of an advanced degree. A potential employer just offered you an annual salary of R55 000, R60 000, and R65 000 a year for the next three years, respectively. All salary payments will be made as lump sum payments at the end of each year. The offer also includes a starting bonus of R4 500, payable immediately. What is this offer worth to you today, at a discount rate of 8,25%?
Answers
Answer:
55K+60K+65K=184K
100% - 8.25%=91.75%
184000x91.75%=168820
Ans:168K
Answer:
Step-by-step explanation:
To determine the value of the offer today, we need to calculate the present value of all the cash flows using a discount rate of 8.25%.
First, let's calculate the present value of the salary payments.
PV(year 1 salary) = R55 000 / (1 + 0.0825)^1 = R50 760.87
PV(year 2 salary) = R60 000 / (1 + 0.0825)^2 = R51 423.95
PV(year 3 salary) = R65 000 / (1 + 0.0825)^3 = R52 110.69
Next, let's calculate the present value of the starting bonus.
PV(starting bonus) = R4 500 / (1 + 0.0825)^0 = R4 500
Finally, we can add up all the present values to find the total present value of the offer:
PV(total offer) = PV(year 1 salary) + PV(year 2 salary) + PV(year 3 salary) + PV(starting bonus)
PV(total offer) = R50 760.87 + R51 423.95 + R52 110.69 + R4 500
PV(total offer) = R158 795.51
Therefore, the offer is worth R158 795.51 to you today at a discount rate of 8.25%.
Helppppppppppppppppp
Answers
the worlds population hit 8 billion in 2022. suppose the population increases exponentially with doubling time of 60 years. what population can we expect in the year 2100. Answer in billions
Answers
The population in the year 2100 will be approximately 18.8 billion.
Determine exponential equation
The exponential equation to model the world population (in billions) after t years is P(t) = 8(1.011)[tex]^t[/tex], where P(t) is the population in billions and t is the number of years after 2022.
To write this equation, we need to use the information provided in the question. The initial population in 2022 is 8 billion, so this is our starting value. The growth rate is 1.1% per year, which can be written as 1.011 in decimal form.
We can use the formula for exponential growth, P(t) = P0(1 + r[tex])^t[/tex]where P0 is the initial population, r is the growth rate, and t is the number of years.
Substituting the values for [tex]P_0[/tex]and r into the equation, we get:
P(t) = 8(1.011[tex])^t[/tex]
2100-2022=78
This equation can be used to find the population after t years.
For example, to find the population after 5 years, we can substitute t = 78 into the equation and get:
P(5) = 8(1.011[tex])^78[/tex] ≈ 18.8 billion
Therefore, the population in year 2100 will be approximately 18.8 billion.
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if 62 miles is equal to 100 kilometers , what is the ratio of miles to one kilometer
Answers
Answer:
0.62 to 1
Step-by-step explanation:
62/100
Divide the numerator and denominator by 100.
62/100 = 0.62/1
The ratio is 0.62 to 1.
Answer:
Step-by-step explanation:
1 mile is equal to 1.60934 km
1km is equal to 0.621371 mile
(x^2-4x+3) + (3x^2-3x-5) ASAP PLS
Answers
Answer:
(x - 2)(4x + 1)
How many solutions and what is the solution, as an ordered pair?
Answers
Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.
what is solution ?A value or combination of values that satisfy an equation, inequality, system of equations, or system of inequalities are known as solutions in mathematics. Take the equation x2 - 3x + 2 = 0, for instance. This equation has a solution in the form of an x value that makes the equation true. The quadratic formula allows us to determine that this equation has two solutions, x = 1 and x = 2. According to this, a solution for a system of equations is a set of values that simultaneously satisfy every equation in the system. Mathematical problem-solving, which has many applications in areas like engineering, physics, economics, and more, is a crucial component of the subject.
given
We must identify the point(s) at where the two lines intersect in order to obtain the solution(s) to the system of equations depicted by the graph. The graph demonstrates that the lines cross at the location (-3, 3).
Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.
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What is m24 if m25 = (2x)° and m24 = (x +9)°?
4
X
5
m24 =
Answers
The value of angle m<4 is 66 degrees
What are supplementary angles?The angles on a straight line are supplementary, this means that the angles sum up to 180 degrees.
From the information given, we have that;
m<4 = x + 9 degreesm< 5 = 2x degreesEquate the angles to 180 degrees
We have;
m<4 + m<5 = 180
Substitute the expression for each of the angles , we have;
x + 9 + 2x = 180
collect the like terms
3x = 180 - 9
subtract the values
3x = 171
Divide by the coefficient
x = 57
But m<4 = 57 + 9 = 66 degrees
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Let f(x) = -3x - 5
What is the value of f(-5)?
Answers
Answer:
I think its 10Step-by-step explanation:
The maximum number of grams of fat that should be in a diet vary directly as a persons way a person weighing 126 pounds should have no more than 84 g of fat per day. What is the maximum daily intake for personally and 30
ponds
Answers
3) Given that f(x) = 3x – 5 g(x) = 2x – 6 and h(x) = x + 4
4 2x
Find:- i) f(-3) = ii) g[f(0)] = iii) f[h(2)] =
iv) hᴏf(x) v) h-1(1) =
Answers
The Answer for the given functions are:
i) f(-3) = -14.
ii) g[f(0)] = -16.
iii) f[h(2)] = 13.
iv) hᴏf(x) = 3x - 1.
v) h-1(1) = -3.
What is the functiοn nοtatiοn?Functiοn nοtatiοn is a way οf representing a functiοn using algebraic symbοls. It is a shοrthand way οf expressing a relatiοnship between twο quantities οr variables, where οne variable depends οn the οther.
i) Tο find f(-3), we substitute x = -3 in the expressiοn fοr f(x) and simplify:
f(-3) = 3(-3) - 5 = -9 - 5 = -14
Therefοre, f(-3) = -14.
ii) Tο find g[f(0)], we first evaluate f(0) and then substitute that value intο g(x):
f(0) = 3(0) - 5 = -5
g[f(0)] = g(-5) = 2(-5) - 6 = -10 - 6 = -16
Therefοre, g[f(0)] = -16.
iii) Tο find f[h(2)], we first evaluate h(2) and then substitute that value intο f(x):
h(2) = 2 + 4 = 6
f[h(2)] = f(6) = 3(6) - 5 = 18 - 5 = 13
Therefοre, f[h(2)] = 13.
iv) Tο find hᴏf(x), we substitute f(x) intο the expressiοn fοr h(x) and simplify:
hᴏf(x) = h[f(x)] = f(x) + 4 = (3x - 5) + 4 = 3x - 1
Therefοre, hᴏf(x) = 3x - 1.
v) Tο find h-1(1), we need tο sοlve fοr x in the equatiοn h(x) = 1:
h(x) = x + 4 = 1
Subtracting 4 frοm bοth sides, we get:
x = 1 - 4 = -3
Therefοre, h-1(1) = -3.
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