The expression 14x⁴y³ - 42x³y⁴ is rewritten to 14x³y³(x - y)
What is an algebraic expression?
An algebraic expression can be described as a mathematical expression that is made up of terms, coefficients, variables, factors and constants.
They are also made up of some arithmetic operations, such as;
SubtractionMultiplicationDivisionBracketParenthesesAddition, etcFrom the information given, we have the algebraic expression;
14x⁴y³ - 42x³y⁴
Now, factor the common numbers, we have;
14(x⁴y³ - 3x³y⁴)
Factor the common variables, we get;
14x³y³(x - y)
Hence, the expression is 14x³y³(x - y)
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Tobias is constructing barriers to prevent cars from driving on a bike path. He can make conical pylons using the dimensions shown. If he used the
same amount concrete to construct a spherical barrier, how tall would it be? Express your answer in terms of π?
Is it:
A)1 2/3 π
B)3 2/3 π
C)4 1/3 π
D)5 π
The volume of the cone is (2/3)π cubic feet. And the radius of the spherical barrier would be 0.8 ft. and the height would be 2r = 2(0.8) = 1.6 ft. The correct option is A.
What is volume?Space occupied by an object in three-dimensional space is called as volume of an object. In simple words, space is taken by object.
Given:
Tobias is constructing barriers to prevent cars from driving on a bike path. He can make conical pylons using the dimensions shown.
He used the same amount of concrete to construct a spherical barrier.
According to the information given in the exercise, the height and the radius of the pylons are the following:
Height h = 2 ft
Radius r = 1 ft
So, the volume of the cone,
= (1/3)πr²h
= (1/3)π(1)²(2)
= (2/3)π cubic feet.
And the volume of the sphere is twice the volume of the cone.
So, the volume of the sphere,
4πr³/3 = 2π/3
2r³ = 1
r³ = 1/2 = 0.5
r = ∛0.5 = 0.8 ft.
Therefore, the radius of the spherical barrier would be 0.8 ft. and the height would be 2r = 2(0.8) = 1.6 ft.
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How do you find the parent function of a line?
The parent function of a line (usually of the form y = ax + b) is y = x.
The most basic form of a function is a parent function. Its essential shape is not changed in any manner. In mathematics, some graphs are frequently seen. Because of this, the graphs of quadratic functions, square roots, absolute values, cubics, and cube roots are among the original, widespread functions that are referred to as parent graphs.
For instance, you should still be able to identify the parabola that has undergone various transformations when you view a u-shaped graph that has been inverted and stretched vertically.
Linear FunctionLinear functions have x as the term with the highest degree and a general form of y = a + bx. All linear functions have a straight line as a graph. The parent function of linear functions is y = x, and it passes through the origin. The domain and range of all linear functions are all real numbers.
These functions represent relationships between two objects that are linearly proportional to each other.
Therefore, the parent function of a line (usually of the form y = ax + b) is y = x.
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Which is not a polynomial a 4x2 2x 1 by 3 YC x3 1 D y2 5y 1?
2) y+ 3÷y is the equation that is not a polynomial. Using addition, subtraction, multiplication, and division of numbers .
what is polynomial ?Using just the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables, a polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients. Using addition, subtraction, multiplication, and division of numbers, a polynomial is an equation that combines variables, constants, and exponents (No division operation by a variable).
given
An algebraic mathematical equation known as a polynomial might have two components. coefficients and parameters
You can combine the solutions to these algebraic equations to achieve the result.
It follows the general formula as follows:
a + a1 + a+ …
2)y+ 3y is the equation that deviates from the formula above.
So, 2)y+ 3y is the equation that is not a polynomial.
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How do you find the value of x in a two step equation?
Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One results from multiplying a number by its reciprocal, or inverse.
Inverse operations, such as addition and subtraction, multiplication and division, are pairs of mathematical operations where one operation reverses the effect of the other. The term "inverse" refers to the reciprocal of a number, i.e., x - 1 = 1 / x. One results from multiplying a number by its reciprocal, or inverse.
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Salma's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Salma $5.60 per pound, and type B coffee costs $4.40 per pound. This month's blend used three times as many pounds of type B coffee as type A, for a total cost of $451.20. How many pounds of type A coffee were used?
Answer: hi
11,28 pound / usd
Step-by-step explanation:
A baker places 4 muffins in each box. Which is the total number of muffins in 8 boxes?
Answer: 32
Step-by-step explanation: 4 x 8 = 32 . I am concerned how simple this is ;-;
Answer:
32
Step-by-step explanation:
each boxes have 4 muffins
so,in 8 boxes
by question
8×4=32
A dumpster is shaped like a rectangular prism. It has a width of 8 feet, a height of 5 feet, and a volume of 880 cubic feet. What is the length of the dumpster
Help please radicals
Answer:
5√2
Step-by-step explanation:
Hello!
To simplify the radical, we can identify perfect square factors in the radicand or the number inside the square root.
We know that 50 is 25 times 2, so we can expand the radical like this...
[tex]\sqrt{50[/tex][tex]\sqrt{25*2}[/tex][tex]\sqrt{25} * \sqrt2[/tex]Now we can simplify each radical:
[tex]\sqrt{25} * \sqrt2[/tex][tex]5\sqrt2[/tex]The simplified form is 5√2.
i need hlep with this q
The slope of the line is 40 if the points are joined.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
given:
Take two points from the graph as (2, 80) and (4, 160)
Then, the slope of line is
slope, m = ( 160- 80) / ( 4- 2)
slope, m = 80 /2
slope , m = 40
Hence, the slope is 40.
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h=?ft
what is the correct answer
Answer:
h = 4 ft
Step-by-step explanation:
the area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height )
here b = 8 and h = 3 , then
A = 8 × 3 = 24 ft²
Now consider the other base b = 6 with perpendicular height h , then
6h = 24 ( divide both sides by 6 )
h = 4
How do you plot the point 3?
Here the point 3 can be taken as (3,0) or (0, 3) ; For first, move right 3 units along the x-axis. No vertical component is there , as the y-coordinate is 0 here; For second, move 3 units along the y-axis. Since the x-coordinate is 0, there is no horizontal component.
A point is marked in a coordinate plane using its coordinates when it is plotted in a coordinate system.
The intersection of the x-axis, a horizontal number line, and the y-axis, a vertical number line, creates a 2D coordinate plane.
At the coordinate plane's origin, where the two axes (plural for axis) intersect, four right angles are formed. On a coordinate plane, a grid is frequently drawn to make it simpler to plot points.
In a 2D coordinate plane, a point's location is represented by an ordered pair of numbers (x, y). An ordered pair of numbers is used to represent the location of a point in a 2D coordinate plane (x, y). The first number in the pair represents the point's location along the x-axis, and the second number represents its location vertically (y-axis).
Count x squares from the origin along the x-axis, then count y squares in the direction of the y-axis to plot the point (x, y) in the coordinate plane.
Here the point 3 can be taken as (3,0) or (0, 3) ; For first, move right 3 units along the x-axis. No vertical component is there , as the y-coordinate is 0 here; For second, move 3 units along the y-axis. Since the x-coordinate is 0, there is no horizontal component.
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Find the radius of a circle that has a sector area of 165.6 cm2 and an angle measure of 129*. Round your answer to the nearest tenth.
To find the radius of a circle given the area of a sector and the measure of the central angle of the sector, we can use the formula:
radius = sector area / (central angle measure / 360)
In this case, the sector area is 165.6 cm2 and the central angle measure is 129*. Plugging these values into the formula gives us:
radius = 165.6 / (129 / 360)
= 165.6 / (129 / 360)
= 165.6 / (0.3583)
= 462.9 cm
Rounding this value to the nearest tenth gives us a radius of approximately 463 cm.
Graph the image of square KLMN after a translation 6 units left and 4 units up.
The coordinates of the image of the square KLMN are:
K = (0, -1)
L = (2, -1)
M = (2, 1)
N = (0, 1)
The graph of the image is given below.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
The coordinates of the square KLMN are:
K = (6, -5)
L = (8, -5)
M = (8, -3)
N = (6, -3)
Now,
Translation of 6 units left and 4 units up.
This means,
K = (6 - 6, -5 + 4) = (0, -1)
L = (8 - 6, -5 + 4) = (2, -1)
M = (8 - 6, -3 + 4) = (2, 1)
N = (6 - 6, -3 + 4) = (0, 1)
Thus,
The image of the square KLMN will be on the following coordinates.
K = (0, -1)
L = (2, -1)
M = (2, 1)
N = (0, 1)
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Pls help question 9,10 and 11. And can u explain or show how u make the equation ?
A car that travels 20 miles in 1/2 hour at consent speed travels at the same rate as a car that travels 30 miles in 3/4 hour at a constant speed.
Explain how the Distributive Property can be used to solve the equation 3(x+4)=36. Multiply the first term in the parentheses by 3, then add 3 to the second term in the parentheses. Then solve the equation using inverse operations.
Aisha bought 15 apples and oranges for $9.00. each orange costs $0.50, and each apple costs $0.65. let x represent the number of oranges and y represent the number of apples. which system can be used to find the number of apples and oranges aisha bought? x y = 15. 0.5 x 0.65 y = 9.00 x = y. 0.5 x 0.65 y = 9.00 x y = 9. 0.5 x 0.65 y = 15.00 x = y. 0.5 x 0.65 y = 15.00
Both (x + y = 15) and (0.5x + 0.65y = 9.00) make up the equation system.
What is an equation ?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
The statement is not an equation if there is no "equal to" sign in it
According to our question-
x is the quantity of oranges.
y is the quantity of apples.
Oranges plus apples equal 15, or x plus y equals 15, so Aisha purchased 15 pieces of fruit.
Apples cost $0.65 and oranges cost $0.50. The fruit cost Aisha $9.00.
0.5x (the total cost of the oranges) + 0.65y (the total cost of the apples) equals 9.00 (the total cost of the fruit).
x + y = 15
0.5x + 0.65y = 9.00
As a result, the system of equations is (0.5x + 0.65y = 9.00) and (x + y = 15).
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The question is in the picture I would appreciate if you could explain how to get the answer thank you.
Answer: the cost for Internet increase by 5/4 per minute
Step-by-step explanation:
The newest streaming service costs $9.24 per month with
tax. If tax is 5%, how much is the streaming service before
tax and how much does a year of the service cost?
Señor Ochoa is planting a garden in the corner of his yard. Before he does any planting, however, he wants to make a
scale drawing showing where he wants each vegetable and fruit to go. So far, he has drawn the perimeter of his garden.
The actual length of the vertical and horizontal legs of his triangular garden is 3 meters.
6 cm
6 cm
8. 5 cm
After making his drawing, he decides that his scale is way too small. Instead, he wants the vertical and horizontal legs of
the triangle on his drawing to be 18 centimeters. Make a new scale drawing with the new dimensions of the scale
drawing. Make sure to label all three sides of the garden and include the new scale.
Señor Ochoa draws the perimeter of the garden with actual length of the vertical and horizontal legs of his triangular garden 3 meters as 6cm in his initial drawing with 18.5cm third side. Then new drawing with the vertical and horizontal legs of 18 cm
A scale drawing is a representation of an object or space that is reduced or enlarged in proportion to the actual size. To make a new scale drawing of Señor Ochoa's garden with the new dimensions of 18 centimeters for the vertical and horizontal legs of the triangle, you would need to apply a scale factor of 18/6 = 3 to the original drawing.
So, you would multiply each original dimension by 3 to get the new dimensions for the scale drawing.
The new scale drawing would be:
6cm × 3 = 18cm
6cm × 3 = 18cm
8.5cm × 3 = 25.5cm
The new scale is
= scale dimension/ original dimension
= 18cm/ 3m
= 18cm/ 300cm
= 3/ 50
It is also worth noting that as you are changing the scale, the measurement of the hypotenuse of the triangle would be affected, which is the square root of 3 meters, that would be approximately 25.5cm, which is the same as the original measurement on the original drawing.
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Show the correct relationship between altitude and boiling point.
Altitude
Boiling Point Temp.
The relationship between altitude and boiling point is given below.
What is altitude?
Altitude is the height above sea level. It is usually measured with a barometer or GPS satellite. Altitude can be used to describe the height of an airplane, a mountain, or even the position of a satellite in space. Altitude can also be used to measure how high a person is standing on Earth. Altitude can also be used to compare the relative heights of two different points on Earth. Altitude is an important factor when flying, as it can determine air pressure, air temperature, and wind speed.
Sea Level 212°F
1,000 ft. 211°F
2,000 ft. 210°F
3,000 ft. 209°F
4,000 ft. 208°F
5,000 ft. 207°F
6,000 ft. 206°F
7,000 ft. 205°F
8,000 ft. 204°F
9,000 ft. 203°F
10,000 ft. 202°F
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Here is a piece of cake each piece of cake has the same number of candles how old is rongopai
Rongopai's age is equal to the total number of candles on the cake, thus I need to determine what that is.
How to estimate Rongopai's age?What I need to figure out because I am aware that Rongopai's age is equal to the total number of candles on the cake.
The number of pieces the cake was sliced into must first be determined. A quarter has a specific appearance to me. This is how it would seem (the teacher traces a quarter shape on the circle). There must have been more than four pieces since this one seems a little smaller.
Each cut's location may be identified using my finger. Given that all the pieces must be the same size, I'm predicting the locations of each line using the first piece as a reference.
Here would be the approximate location of the first line, followed by here and here (the teacher draws a line with her finger) (tracing two more lines). the third line. In my mind, the lines and parts are somewhat "visible." Four "invisible" pieces plus the one drawn in are present when I count backward.
The complete question is:
A teacher wants a student to see how visualising the size of a share (in this case, a piece of cake) can be used to work out how many shares are needed to make a whole:
“Here is a piece of Rongopai’s birthday cake. Each piece of cake has the same number of candles. How old is Rongopai?”
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Age of Rongopai is 20 years.
What means one fifth of a circle?One fifth of a circle means if a circle can be divided into five equal parts, then one fifth is one of them.
How old is Rongopai?
As per the figure given, there is shown a 1 fifth of a circular birthday cake.
As all the piece of cake is equal in size so the total number of cake piece is five.
the number of candles in each piece is four.
the total number of candles present in the whole cake is = 5 × 4
the total number of candles = 20
Therefore, Rongopai is 20 years old.
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maddox has $12.25 to spend on sports drinks. Each drink costs $1.75. Use the guess, check, and revise strategy to solve the equation 1.75d=12.25 to find d, the number of drinks Maddox can buy.
What is the solution to the system of equations 3x 2y 7 and Y 3x 11?
The solution of the given system of equations is x = -7/3 and y = 7.
The given system of equations is given as,
3x + 2y = 7
y = 3x + 11
To solve this system of equations, we need to eliminate one of the variables. We can eliminate y by subtracting the second equation from the first.
3x + 2y = 7
y = 3x + 11
⇒ 3x + 2y - y = 7 - 11
⇒ 3x + 2y - 3x - 11 = -4
⇒ 2y - 11 = -4
⇒ 2y = -4 + 11
⇒ 2y = 7
Now, substitute the value of y in the first equation to find the value of x.
3x + 2(7) = 7
⇒ 3x + 14 = 7
⇒ 3x = 7 - 14
⇒ 3x = -7
⇒ x = -7/3
Therefore, the solution of the given system of equations is x = -7/3 and y = 7.
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Hi! I need Help With The Bottom Answers Someone Already Answered The Top So Just The Bottom Questions!
F:4+4=8
A:23+8+4=35
H:53+3+28=84
I:11+17+93=121
I:24+8+3=35
I think that is all correct
!PLEASE HELP ASAP!
These two figures are similar. Find the length of side x.
the length of side x = 12.5.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Here, we have,
From the given figure, we get.
These two figures are similar.
so, we have,
8/x=y/5 ............(1)
10/15=4/z ......(2)
8/15=y/z .....(3)
Solving we get,
x=12.5
Hence, the length of side x = 12.5.
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Find the approximate number of grams of milk fat in a 200-gram serving of whole milk.
The answer is :6.5g
CANN SOEMOEN PLS HELP ME PLS. I DONT KNOW WHAT TO DO AND THIS IS ALREADY A WEEK LATE.
Answer:
y = 72 and x = 36
Step-by-step explanation:
So firstly, the outside angle is 108, right? And the total of all angles in a triangle is 180 degrees. So:
180 - 108 = 72
Then the other angle, angle x, is also 72 degrees. That's because they are supplementary angles.
Now that we know x = 72 degrees. To find the y angle, you add 72 and 72 together. Which is 144.
Then you do 180 - 144. Which is 36. So, x = 72 and y = 36
I hope it helped you!
Drag each label to the correct location on the net. Each label can be used more than once, but not all labels will be used.
Identify the dimensions of the net that will give a surface area of 48 sq cm. The area of each part of the net is shown in the figure.
As a result, the response to the query that the area provided With interiors of 32 and 44 square feet, respectively, the future complex will consist of a 60.1-foot circular.
Describe the Area.Finding out how big a rectangle or rectangle is is the simplest (and most used) method. Divide the width by the altitude to find the area of a rectangle. Since all sides of a square are equal in length, determining the area of unit only requires knowledge of the size of one of its sides.
Here,
Here is the formula for area:
The area formula is length times width.
=> 8 × 4
= >32ft²
Following space will be on the trapezoid:
=>(14 + 18)/2 × 4
=> 44ft²
By multiplying the measurement by two, the perimeter will indeed be determined. Knowing this,
= 2(8 + 4) + (14 + 8 + 4 + 5.6 + 4.5)
= 24 + 36.1
= 60.1 ft
In light of this, the answer to the area-related question is
For the specified polygon, 60.1 square feet.
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A school administrator asks each student if they participate in a sport and if they participate in a club. The results are shown below.
Participates in a Sport
Yes No Total
Participates in a Club Yes 620 450 1070
No 325 535 860
Total 945 985 1930
What percentage of students do not participate in a sport?
27.7%
44.6%
51.0%
62.2%.
answer is 51.1
The percentage of students who do not participate in a sport is C. 51.0%.
How to calculate the percentage?To find the percentage of students who do not participate in a sport, we can use the following formula:
(Number of students who do not participate in a sport) / (Total number of students) * 100%
From the table, we can see that the number of students who do not participate in a sport is 985, and the total number of students is 1930. So, plugging these values into the formula gives us:
= 985 / 1930 * 100%
= 51.03%
So, about 51.03% of students do not participate in a sport.
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Point lies on the diagonal of square with . Let and be the circumcenters of triangles and respectively. Given that and , then , where and are positive integers. Find .
Point P lies on the diagonal AC of square ABCD with AP > CP. Let [tex]$O_1$[/tex] and [tex]$O_2$[/tex] be the circumcenters of [tex]$\triangle \mathrm{ABP}$[/tex] and [tex]$\triangle \mathrm{CDP}$[/tex] respectively. Given that AB = 12 and [tex]$\angle \mathrm{O}_1 \mathrm{PO}_2=120^{\circ}$[/tex], then [tex]$\mathrm{AP}=\sqrt{\mathrm{a}}+\sqrt{\mathrm{b}}$[/tex],
where a and b are positive integers.
The value of a + b is 96.
Let mid-point of DC be E and mid-point of AB be F.
Since [tex]$\mathrm{O}_1$[/tex] and [tex]$\mathrm{O}_2$[/tex] are circumcenters, therefore both lie on the perpendicular bisectors of DC and AB passing through E and F.
Now, [tex]$\mathrm{O}_1 \mathrm{P}=\mathrm{O}_1 \mathrm{~B}$[/tex] and [tex]$\mathrm{O}_2 \mathrm{P}=\mathrm{O}_2 \mathrm{D}$[/tex]
Also [tex]$\angle \mathrm{CAB}=\angle \mathrm{ACD}=45^{\circ}$[/tex]
Therefore [tex]\angle \mathrm{BO}_1 \mathrm{P}=2 \times 45^{\circ}=90^{\circ}=\angle \mathrm{DO}_2 \mathrm{P}$[/tex]
Angle subtended by an arc of a circle at its center = 2 × the angle subtended at its circumference
Therefore [tex]\angle \mathrm{O}_1 \mathrm{~PB}$[/tex] and [tex]$\angle \mathrm{O}_2 \mathrm{PD}$[/tex] are isosceles right triangles.
Using the above information and symmetry,
[tex]$\angle \mathrm{DPB}=120^{\circ}$[/tex]
Also, [tex]$\triangle[/tex]ABP is congruent to [tex]$\triangle[/tex]ADP (SAS)
and [tex]$\triangle[/tex]CPB is congruent to [tex]$\triangle[/tex]CPD (SAS)
Therefore [tex]\angle \mathrm{APB}=\angle \mathrm{APD}=60^{\circ}[/tex]
And [tex]\angle \mathrm{CPB}=\angle \mathrm{CPD}=120^{\circ}[/tex]
Now, [tex]$\angle \mathrm{ABP}=(180-60-45)^{\circ}=75^{\circ}$[/tex]
[tex]\Rightarrow \angle \mathrm{O}_1 \mathrm{BF}=30^{\circ}[/tex]
And [tex]$\angle \mathrm{PDC}=(180-120-45)^{\circ}=15^{\circ}$[/tex]
[tex]\Rightarrow \angle \mathrm{O}_2 \mathrm{DE}=30^{\circ}[/tex]
Therefore [tex]\triangle \mathrm{O}_1 \mathrm{BF}$[/tex] and [tex]$\triangle \mathrm{O}_2 \mathrm{DE}$[/tex] are right angled triangles.
BF = DE = [tex]\frac{12}{2}[/tex] = 6
[tex]\Rightarrow O_1 B=O_2 D=4 \sqrt{3}[/tex]
And PB = PD = [tex]\frac{4 \sqrt{3}}{\cos 45^{\circ}}=4 \sqrt{6}[/tex]
Now, Let x = AP
Using law of cosine on [tex]$\triangle[/tex]ABP, we have
[tex]& 96=x^2+144-24 x \times \frac{1}{\sqrt{2}} \\[/tex]
[tex]& \Rightarrow x^2-12 \sqrt{2} x+48=0 \\[/tex]
[tex]& \Rightarrow x=\sqrt{72} \pm \sqrt{24}[/tex]
Taking the positive root, AP = [tex]\sqrt{72}+\sqrt{24}$[/tex]
Therefore a + b = 72 + 24 = 96
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Point P lies on the diagonal AC of square ABCD with AP > CP. Let [tex]$O_1$[/tex] and [tex]$O_2$[/tex] be the circumcenters of [tex]$\triangle \mathrm{ABP}$[/tex] and [tex]$\triangle \mathrm{CDP}$[/tex] respectively. Given that AB = 12 and [tex]$\angle \mathrm{O}_1 \mathrm{PO}_2=120^{\circ}$[/tex], then [tex]$\mathrm{AP}=\sqrt{\mathrm{a}}+\sqrt{\mathrm{b}}$[/tex], where a and b are positive integers. Find a + b. (correct answer +5, wrong answer 0 )