Answer:
t=-6
Step-by-step explanation:
Cómo resolver esta factorizacion
Therefore , the solution of the given problem of factorization comes out to be x=0 and x=1/3.
What is factorization, exactly?The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics.
Here,
Given:
thus . We do factorization of given expression and
we come on a result
=> 3x - 9x²
=> 3x (1 -3x)
x=0 and x=1/3
Therefore , the solution of the given problem of factorization comes out to be x=0 and x=1/3.
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Three times the measure of a supplement of an angle is 8 times the measure of a complement of the angle. Find the measure of the angle .
Answer:
3x of 180=8x of 90
Use this equation
What is the exponential form for 8x8x8x8 taking base as 2?
The exponential form of 8x8x8x8 is 2^(4*3) = 2^12.
HELP NOW PLS (100 POINTS)
The function f(x) = 20x + 80 represents the distance in miles a drone flew.
The function g(x) = x + 2 represents the time the drone flew in hours.
Part A: Find f(2) and g(2). Show your work. (2 points)
Part B: Find f divided by g of 2. Show your work. (2 points)
Part C: What is the domain of f divided by g of x? (2 points)
Answer:
A) f(2) = 120, g(2) = 4.
B) f'(x) = 5x + 20
C) R - {-2}.
Step-by-step explanation:
A) Just apply given value and resolve:
[tex]f(2) = 20 \times 2 + 80 = 40 + 80 = 120 \\ g(2) = 2 + 2 = 4[/tex]
B) g(2) is 4, so just divide f(x) by 4:
[tex] \frac{1}{4} f(x) = \frac{1}{4} (20x + 80) = \frac{20}{4} x + \frac{80}{4} = 5x + 20[/tex]
C)
[tex] \frac{f(x)}{g(x)} = \frac{20x + 80}{x + 2} [/tex]
Polynomials have full domain. A Quotient of polynomials is defined when denominator is not zero. In this sample, denominator is zero when x = -2, so -2 is not part of the domain. All other real numbers are part, hence R - {2}.
1. The value of F(2) = 120 and g(2) = 4.
2. The division is 5(x+4)
3. The domain is real number except -2.
What is Function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
The function f(x) = 20x + 80 represents the distance in miles a drone flew.
The function g(x) = x + 2 represents the time the drone flew in hours.
1. F(2)= 20(2)+ 80= 40+ 80= 120
and, g(2)= 2 + 2 = 4
2. The division is
= F(x) / g(2)
= (20x + 80)/ (2+2)
= 20 (x+4) / 4
= 5 (x+4)
3. The domain of F(x) / g(x) is all real number except -2.
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What is the slope of Y 10x?
Which graph represents the equation y equals one half times x plus 2? graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1 graph of a line passing through the points negative 2 comma 0 and 0 comma 1 graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2 graph of a line passing through the points negative 4 comma 0 and 0 comma 2
The correct graph is the third one: graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2.
A graph is what?News grapher using a function with inputs and outputs to depict a function. A function is a connection between two variables in which the input determines the output. In a graph, the y-axis shows the output, while the x-axis shows the input.
An unweighted, undirected graph with no graph loops or numerous edges is referred to as a simple graph (also known as a strict graph; Tutte 1998, p. 2; West 2000, p.
The line that connects the coordinates (x, y) = (-2, -3) and (y = 1/2x + 2) on this graph expresses the equation y = 1/2x + 2. (0, -2). When we enter those coordinates into the equation, we get the points on the graph, y = 1/2(-2) + 2 = -3 and y = 1/2(0) + 2 = 2.
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A company ha two manufacturing plant with daily production level of 5x 14 item and 3x - 5 item, repectively. The firt plant produce how many more item daily than the econd plant?
As per the given equation, the first plant is produce 2x+21 more items than second plant.
The term equation is known as a mathematical statement that shows that two mathematical expressions are equal.
Here we have given that the first plant produces 5x+14 items daily
And the second plant produces 3x-7 items daily
In order to find the number of items produced on first plant, then we have to calculate the differences between number of items by the two plants daily, then it can be written as by using the equations,
=> (5x+14) - (3x-7)
Now, we have to expand the equations, then we get
=> 5x+14 - 3x+7
=> 2x+21
Therefore, first plant produces 2x+21 more items daily than the second plant.
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Need help with this pls and thanks
Answer:
J
Step-by-step explanation:
Short to the point way compare it by Up to Down
4/9
Answer:
G
Step-by-step explanation:
a proportional relationship is defined by
y = ax
that means, if x = 0, then also y = 0.
let's look at the slope (the constant of change) :
y coordinate change / x coordinate change
when going from 1 point to another in the line.
we see e.g. for (4, 9) and (5, 12)
x changes by +1 (from 4 to 5).
y changes by +3 (from 9 to 12).
the slope is +3/+1 = 3.
but the slope cannot be the "constant of proportionality" ("a" above), because starting e.g. from (2, 3) to get to x = 0 would mean
x has to change by -2 (= -2×1).
and then y has to change by -6 (= -2×3) to keep the same slope "alive".
and so, for x = 0, we would get y = -3. but not 0.
the only equation with slope 3 (the factor of x, yes) is in G.
therefore, G is the right answer.
we can also check, when using x = 4, x = 5 and x = 2, we get the given y-values (9, 12, 3) from y = 3x - 3.
so, it is correct.
Mrs. Wright is planning her best friend's baby shower. She calculates that the food will cost $9 per guest, and she has already spent $43 on decorations.
Based on the questions, 13 guests are attending her best friend’s baby shower.
How did we get 13 guests as a result?Firstly, we need to write down the numbers that are already stated in the question.
The food will cost around $9 per guests. She spent $43 on decoration for the event. Then, she can afford to spend $160 for the event.43 + 9 × х = 160
Secondly, move the x to continue counting.
9x = 160 – 43
Thirdly, calculate the numbers above.
9x = 117
Then, move the X to get the answer.
X = [tex]\frac{117}{9}[/tex]
Lastly, try to finish the division.
X = 13
In conclusion, the result shows that 13 guests attend Mrs. Wright’s best friend's baby shower.
The above question is about the algebraic word problem.
A word problem is a math question written in a short story scenario. Usually, it is a simple short story that is easy to understand.
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Andrew is going to invest in an account paying an interest rate of 2.2% compounded quarterly. How much would Andrew need to invest, to the nearest hundred dollars, for the value of the account to reach $93,000 in 19 years?
Andrew would need to invest $61,300 for the account to reach $93,000.
What is Compound Interest?Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.
The equation to find final amount in compound interest is,
A = P (1 + r/n)^(n t)
Here A is the final amount, P is the initial amount, r is the rate of interest, n is the number of times compounding is done in a year, t is the time in years.
Given, A = $93,000
t = 19 years
r = 2.2% = 0.022
n = 4 (since compounding is quarterly)
93,000 = P [1 + (0.022/4)]^(4×19)
93,000 = P [1.0055]^(76)
93,000 = P (1.517)
P = 61,297.8516
To the nearest hundred dollars, P = $61,300
Hence the principal amount Andrew need to invest is $61,300.
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Which point is the reflection of (- 3 2 over the y-axis?
The reflection of (-3, 2) over the y-axis is (-3, -2).
The reflection of a point (x, y) over the y-axis is (x, -y).
Therefore, the reflection of (-3, 2) over the y-axis is (-3, -2).
To calculate the reflection of (-3, 2) over the y-axis, we first use the formula (x, -y).
In this case, x = -3 and y = 2, so the reflection of (-3, 2) over the y-axis is (-3, -2).
We can also calculate the reflection of (-3, 2) over the y-axis using the distance formula.
The distance formula is d = √(x2-x1)2 + (y2-y1)2
In this case, x1 = -3, x2 = 0, y1 = 2, and y2 = 0.
Therefore, the distance d = √(02-(-3)2 + (02-2)2 = √(9 + 4) = √13
The reflection of (-3, 2) over the y-axis is (-3, -2). This can be verified using the distance formula.
d = √(x2-x1)2 + (y2-y1)2 = √(-3-0)2 + (-2-0)2 = √(9+4) = √13
The distance d is equal to the distance between (-3, 2) and (-3, -2). Hence, the reflection of (-3, 2) over the y-axis is (-3, -2).
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I need help only have 2 hours left
Answer:
[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6} \vphantom{\dfrac12} x&-4&1&2&3&6 \\\cline{1-6} \vphantom{\dfrac12} f(x)&-20&5&10&15&30 \\\cline{1-6}\end{array}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=5x[/tex]
To complete the function table, substitute each given value of x into the given function:
[tex]x=-4 \implies f(-4)=5(-4)=-20[/tex]
[tex]x=1 \implies f(1)=5(1)=5[/tex]
[tex]x=2 \implies f(2)=5(2)=10[/tex]
[tex]x=3 \implies f(3)=5(3)=15[/tex]
[tex]x=6 \implies f(6)=5(6)=30[/tex]
Completed table:
[tex]\begin{array}{|c|c|c|c|c|c|}\cline{1-6} \vphantom{\dfrac12} x&-4&1&2&3&6 \\\cline{1-6} \vphantom{\dfrac12} f(x)&-20&5&10&15&30 \\\cline{1-6}\end{array}[/tex]
Please help thankyou:)
The total volume of the object is 40 in³
What is the volume of a solid object?The volume of a solid object encompasses the space and capacity that the object can occupy. Here, we have two shapes that make up the solid object, a cylinder, and a sphere. A cylinder is an object that resembles a tube and has two circular sides with the same radius linked by a flat round surface.
The volume of the cylinder is calculated by using the formula:
V = πr²h
where; π = 3V = 3 * 2² * 3 ..... (since radius r = d/2 = 4/2 = 2)
V = 3 * 4 * 3
V = 36 in³
The volume of the sphere = 4/3 πr³
V = 4/3 * 3 * 1³
V = 4 in³
The total volume of the object = volume of the cylinder + volume of the sphere
The total volume of the object = 36 in³ + 4 in³
The total volume of the object = 40 in³
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What transformation has changed the parent function f(x) = log2x to its new appearance shown in the graph?
A. f(x + 3)
B. f(x − 3)
C. f(x) + 3
D. f(x) − 3
The answer is Option D) f(x)-3
what is the logarithmic function?In mathematics, the logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as For x > 0, a > 0, and a ≠1, y= logₐ x if and only if x = a^y Then the function is given by f(x) = logₐ x The base of the logarithm is a. This can be read it as log base a of x.
Given here: f(x)=log2x
Now in the attached graph we clearly see that f(x)-3 is the graph that looks identical to the one given in the graph.
Hence, option D is the correct answer.
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TEST RN What is the equation of the line that passes through the point (6.0) and had a slope of -5/6? HELPP PLEASE TEST RN
An equation of the line that passes through the point (6, 0) and had a slope of -5/6 is y = -5x/6 + 5.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.Given the following parameters:
Point (x, y) = (6, 0)Slope = -5/6Substituting the given parameters into the point-slope formula, the equation of the line is given by;
y - y₁ = m(x - x₁)
y - 0 = -5/6(x - 6)
y = -5x/6 + 5
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if Mr.Kimble gets 12.6 gallons of gas for each of his 15 trips to the gas station over the summer, how much money did he spend altogether on gas?
Mr.Kimble spent an amount of $636.17 altogether on gas.
What is the idea price of Gas per gallon today?Today, the US Retail Gas Price is at a current level of 3.366, up from 3.331 last week and down from 3.381 one year ago. Hence, the amount of $3.366 will be used in our computation.
Data
He used 12.6 gallons of gas for each of his 15 trips.
The total amount of money spent altogether on gas if the price is $3.366, is computed as follows:
= ($3.366 * 12.6 gallons) * 15 trips
= $42.4116 * 15 trips
= $636.17400
= $636.17.
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Camila and her children went into a grocery tore and where they ell apple for $0. 50 each and mange for $0. 75 each. Camila ha $7. 75 to pend and mut buy no le than 11 apple and mango altogether. IfCamila decided to buy Rapple. Determine the maximum number of mango that he could buy. If there are no poible olution, hmit an empty amont
The maximum number of mangos that she could buy = 9
Let x represents the number of apples and y represents the number of mangos.
Given that:
the cost of each apple = $0.50
and the cost of each mango = $0.75
Camila has $7. 75 to spend.
This means, the total cost of apples and mangos together must be less than or equal to 7.75
So, we get an inequality,
0.50x + 0.75y ≤ 7.75
And she must buy no less than 11 apples and mangos altogether.
x + y ≥ 11
consider a system of equations.
0.50x + 0.75y = 7.75
x + y = 11
If we solve this system of equations we get x = 2 and y = 9
So, she can buy at most 9 mangos.
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How do you find the missing coordinate using the midpoint formula?
The midpoint formula is used to find the center point of a line segment, given the coordinates of the two endpoints. The formula is as follows:
Midpoint = ( (x₁+ x₂) / 2, (y₁ + y2) / 2 )
Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two endpoints of the line segment.
To find the missing coordinate using the midpoint formula, you would need to have the coordinates of one endpoint, as well as the coordinates of the midpoint. Then, you can use the formula to solve for the missing coordinate.
For example, if you have the coordinates of one endpoint as (3, 5) and the coordinates of the midpoint as (4, 6), you can use the formula to solve for the missing endpoint:
Midpoint = ( (3 + x₂) / 2, (5 + y₂) / 2 )
(4, 6) = ( (3 + x₂) / 2, (5 + y₂) / 2 )
So, by solving above equation we can get the missing coordinate
(x₂, y₂) = (5,7)
In conclusion, the midpoint formula can be used to find the missing coordinate of a line segment by using the coordinates of one endpoint and the midpoint. It is a simple and efficient way to find the missing coordinate when working with geometric shapes.
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Show two
different ways to find the answer to the problem below.
Dog and cat food are sold in 20-pound bags. There are 14 bags of dog food and 12 bags of cat food on the store shelves. How many pounds of dog and cat food are on the shelves?
Answer: There are 520 pounds of dog and cat food
Step-by-step explanation:
1. 14+12= 26
2. 26x20=520
Please help! Please! Thank you! :) 30+ points
Answer:
x=6 z=73
Step-by-step explanation:
9x+53=6x+71
3x+53=71
3x=18
x=6
9(6)+53
54+53
107
107+z=180
z=73
Peter has 18 dimes. He uses 12 dimes to buy a drink. The number of dimes he has left is one-half the number of Pennie’s he has. How many Pennie’s does Peter have? *Put this in a 5th grade understanding*
18-12=6, peter now has 6 dimes left after buying a drink. Since the number he has left is ONE HALF of the number of pennies he has. 6x2=12.
peter has 12 pennies. hoped that helped
What is an example of inequality math?
Answer: 5x − 4 > 2x + 3
Step-by-step explanation:
The expression 5x − 4 > 2x + 3 looks like an equation but with the equals sign replaced by an arrowhead. It is an example of an inequality. This denotes that the part on the left, 5x − 4, is greater than the part on the right, 2x + 3.
please help! Which equation could you use to find the original amount of ounces of rice in a box, when the current box holds 85 ounces, 25% less rice.
The equation which is use to find the original amount of ounces of rice in a box, when the current box holds 85 ounces, 25% less rice is
y = 0.25*85.
What is percentage?
A number or ratio expressed as a fraction of 100 is known as a percentage in mathematics. Though the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. An amount that is a percentage is dimensionless and has no assigned measurement.
Given:
The current box holds 85 ounces, 25% less rice.
We have to find the equation which is use to find the original amount of ounces of rice in a box, when the current box holds 85 ounces, 25% less rice.
Let, y be the original amount of ounces of rice in a box.
The current box holds 85 ounces.
The 25% less than 85 ounces are 85*0.25.
So, the equation becomes y = 0.25*85.
Hence, the equation which is use to find the original amount of ounces of rice in a box, when the current box holds 85 ounces, 25% less rice is
y = 0.25*85.
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A zip code for eagar, Arizona is 85925. Which digit is in the "hundreds" place?
What is 0 to the 0 exponent and why?
0 to the 0 exponents is undefined or indeterminate, and it's not considered as a valid mathematical operation.
The value of 0 to the 0 exponents is undefined or indeterminate. The reason for this is that the mathematical definition of exponentiation states that any number to the power of 0 is equal to 1, except for 0, which is undefined. However, when we try to apply this rule to 0 to the power of 0, it creates a paradox.
If we assume that 0 to the 0 exponents is 1, then any number raised to the power of 0 would be equal to 1, which is not true. For example, 2 to the power of 0 is not equal to 1, but 2, so this assumption doesn't hold true.
On the other hand, if we assume that 0 to the 0 exponents is 0, then any number multiplied by 0 would be 0, which is not true either. For example, 2 multiplied by 0 is not equal to 2.
Therefore, 0 to the 0 exponents is undefined or indeterminate, and it's not considered as a valid mathematical operation.
It's important to note that in some fields of mathematics such as limit, the value of 0 to the 0 exponent is defined as 1, but this is limited to the context of limit and not in general math.
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What is the mirror image of point 2 3 under origin?
The mirrors image of points (2, 3) under the origin is (-2, -3)
What is a mirror image?
A mirror image is a reflected duplicate of a seemingly identical item that is turned the other way in the plane perpendicular to the mirror surface. It manifests as an optical effect as a result of reflection off of materials like a mirror or water.
Here,
We have to find the mirror image of points (2, 3) under the origin.
We concluded that the mirror image of a point(2,3) is (-2,-3).
The coordinates of the origin are denoted by (0, 0). It means that at origin, x=0 and y=0.
Hence, the mirrors image of points (2, 3) under the origin is (-2, -3)
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Find the measurement of V.
On solving the provided question, we got to know that - they are perpendicular, they are perpendicular and they are intersecting lines
what are perpendicular lines?A straight line that intersects another straight line at a 90° angle is said to be perpendicular. A little square is placed in the middle of two vertical lines to represent a 90° angle, often known as a right angle, as illustrated. The two straight lines in this instance are perpendicular to one another since they connect at a right angle.
1) For this case, we have to define perpendicular lines:
Angle y = angle H
10x-27 - 2x + 29
x = 32
they are perpendicular
2) they are perpendicular
3) they are intersecting lines
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A piece of wood is 1212 feet long, and a nail is 33 inches long. The piece of wood is how many times as long as the nail?.
The piece of wood is as long as 48 nails. It is the quotient of the length of wood by the length of nail. In calculation, they should have the same unit length, that is inch.
How to convert feet into inches?One foot is equal to 12 inches.
Mathematically, it is expressed as
1 ft = 12 in
A piece of wood is 12 feet long. The nail has the length of 3 inches. Find the number of the nails so it equals the length of the piece of wood!
The length of piece of wood in inches would be
12 feet = 12 × 12 inches
12 feet = 144 inches
The number of nails needed so that the length would be as long as a piece of wood is
= length of wood / length of nail
= 144 inches / 3 inches
= 48 nails
Hence, a piece of wood is equal to 48 nails.
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√x = √3x
What is the solution to the equation above?
Answer:
[tex]x=0,\;x=\dfrac{1}{3}[/tex]
Step-by-step explanation:
Given equation:
[tex]\sqrt{x}=\sqrt{3}x[/tex]
Square both sides:
[tex]\implies \left(\sqrt{x}\right)^2= \left(\sqrt{3}x\right)^2[/tex]
[tex]\implies x= \left(\sqrt{3}\right)^2 \cdot \left(x\right)^2[/tex]
[tex]\implies x=3x^2[/tex]
Subtract x from both sides:
[tex]\implies x-x=3x^2-x[/tex]
[tex]\implies 0=3x^2-x[/tex]
[tex]\implies 3x^2-x=0[/tex]
Factor out the common term x:
[tex]\implies x(3x-1)=0[/tex]
Apply the zero-product property:
[tex]\implies x=0[/tex]
[tex]\implies 3x-1=0 \implies x=\dfrac{1}{3}[/tex]
Answer:
[tex] \sf \: x = \frac{1}{3} \: (or) \: x = 0[/tex]
Step-by-step explanation:
The equation given is,
→ √x = √3x
Now the value of x will be,
→ √x = √3x
→ x = (√3x)²
→ x = 3x²
→ 3x² = x
→ 3x² - x = 0
→ (3x - 1)(x) = 0
→ 3x - 1 = 0 || → x = 0
→ 3x = 0 + 1 || → [ x = 0 ]
→ 3x = 1 ||
→ [ x = 1/3 ] ||
These are the values of x.
Juan has $24 to spend at the bookstore. If books cost $6 each how many books cam he buy?
4Answer:
Step-by-step explanation:
24 divided by 4 = 6