Answer:
4ab2(7a2b2 5a - 4b)
Step-by-step explanation:
28a3b4 20a2b2 − 16ab3
The GCF of 28, 20 and 16 is 4.
GCF of the variables is ab2
So the answer is
4ab2(7a2b2 5a - 4b)
Answer:
4ab2(7a2b2 5a - 4b)
Step-by-step explanation:
Why are all the multiples of 8 even?
All the multiples of 8 represents they are even numbers because of the following property:
Odd × even = Even
As given in the question,
Given number is equal to 8,
Multiples are those numbers which we get after multiplying the given number to any of the integer.
Multiples of 8 are equal to:
8, 16, 24, 32, 40, 48, 56, ..... so on.
Even numbers are those numbers which get divided by 2 without leaving the remainder.
Odd × odd = Odd
Even × even = even
Odd × even = Even
When we multiply any number by an even number result is always an even number.
Example:
2 (even) × 2(even) = 4(even)
2 (even) × 3 (odd ) = 6 (even)
Here
8 is an even number multiplying any integer to 8 is always an even number.
Therefore, all the multiples of given number 8 are always an even number as Odd × even = Even.
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What is the value of 9^−6/9^−4?
Answer:
[tex]\frac{1}{81}[/tex]
Step-by-step explanation:
using the property of exponents
• [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]\frac{1}{a^{(n-m)} }[/tex] , then
[tex]\frac{9^{-6} }{9^{-4} }[/tex]
= [tex]\frac{1}{9^{(-4-(-6))} }[/tex]
= [tex]\frac{1}{9^{(-4+6)} }[/tex]
= [tex]\frac{1}{9^2}[/tex]
= [tex]\frac{1}{81}[/tex]
Answer:
1/81
Steps:
move 9^-6 to the denominator using the negative exponent rule
b^-n=1/b^n
1/9^-4 x 9^6
Multiply 9^-4 by 9^6 by adding the exponents
1/9^2
Raise 9 to the power of 2
1/81
How would you classify angle 1 and angle 5?
Answer: Alternate Exterior Angles
Step-by-step explanation:
Simply, both angles are outside the paralell lines.
You earn $28.50 per hour. Worked 34 hours last week. What was your gross pay?
Your answer
Answer:$969
Step-by-step explanation:
what is three fourths plus one third
Answer:
3/4 + 1/3 = 13/12 = 1 1/2
Step-by-step explanation:
Add the expreion (-4/5t 5/3) and (-3 2t)
a)-19/5t 11/3
b)13/15t - 1
c)-4/3t 1
d)6/5t - 4/3
The addition of the algebraic expression is = [tex]\frac{6}{5} t - \frac{4}{3}[/tex], so option (d) is correct.
Given that,
The expression (-4/5t + 5/3) and (-3 + 2t)
The addition of algebraic expressions requires categorizing the terms in an algebraic expression into two types - like and unlike terms.
An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). ...
These expressions are represented with the help of unknown variables, constants and coefficients.
Then, take up the like terms and add them.
The addition of algebraic expression is;
= [tex]-\frac{4}{5} t + \frac{5}{3} -3+2t[/tex]
= [tex]-\frac{4}{5} t+2t+\frac{5}{3} -3[/tex]
= -0.8t + 2t + 1.66 - 3
= 1.2t - 1.34
= [tex]\frac{6}{5} t - \frac{4}{3}[/tex]
Therefore,
The addition of the algebraic expression is = [tex]\frac{6}{5} t - \frac{4}{3}[/tex], so option (d) is correct.
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what is 7/10+1/2+38 and type the anserw for me betterly
Answer: 39 1/5
Step-by-step explanation:
7/10 + 1/2 + 38
= 7/10 + 5/10 + 38
= 12/10 + 38
= 38 12/10
= 39 2/10
= 39 1/5
If the 38 was supposed to be 3/8, heres the answer :
7/10 + 1/2 + 3/8
= 28/40 + 20/40 + 15/40
= 63/40
= 1 23/40
I just need to know what kind of polynomial expression and the amount of terms
For the given bi-quadratic polynomial with 4 terms, the constant is -1/6, the leading term is -9x⁴ and the leading coefficient is -9.
What is a polynomial?When two or more algebraic terms are added, subtracted, or multiplied (no division), the result is a mathematical expression known as a polynomial. Constants, positive exponents, and at least one variable are all commonly present in polynomial expressions.
Consider the given polynomial,
The highest power of the variable is 4. Therefore this type of polynomial is called a bi-quadratic polynomial.
The portions of the equation that are often separated by "+" or "-" signs are known as polynomial terms. The number of terms in the above equation is 4.
The term which does not contain any variables are called constant. For the given polynomial the constant is -1/6.
The term with the largest power of the variable is the leading term. The leading term's coefficient is the leading coefficient.
For the above polynomial, the leading term is -9x⁴ and the leading coefficient is -9.
Therefore the above for the given bi-quadratic polynomial with 4 terms, the constant is -1/6, the leading term is -9x⁴ and the leading coefficient is -9.
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The function g is given in three equivalent forms. Which form most quickly reveals the vertex?
Choose 1 answer:
(Choice A) A g(x)=3(x+3)(x-1),
(Choice B) B g(x)=3x^2+6x-9
(Choice C) C g(x)=3(x+1)^2-12
What is the vertex?
Since the function g is given in three equivalent forms, a form which most quickly reveals the vertex is: C. g(x) = 3(x + 1)² - 12.
The vertex is equal to (-1, -12).
What is the vertex form of a quadratic equation?In this exercise, you are required to determine and select the vertex form of a function g that is written in three equivalent forms. Mathematically, the vertex form of a quadratic equation is given by this formula:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided, we can reasonably infer and logically deduce that a mathematical expression which quickly reveals the vertex of the quadratic equation is given by g(x) = 3(x + 1)² - 12.
Since the directrix is horizontal, the axis of symmetry would be vertical. Additionally, the distance (a) from directrix to vertex on the axis of symmetry is equal to 3.
In conclusion, the vertex of this quadratic equation is given by the ordered pair (-1, -12).
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3 Look at the equation below.
y = 2x - 2
Which situation is best described by the
equation?
The temperature at 2:00 A.M. is 2°C and
rises 2° each hour for x hours.
The temperature at 2:00 A.M. is -2°C and
rises 2° each hour for x hours.
The temperature at 2:00 A.M. is 2°C and
drops 2° each hour for x hours.
The temperature at 2:00 A.M. is -2°C and
drops 2° each hour for x hours.??
Answer:the temperature at 2:00 am is 2C and drops 2 each hour for X hours
Step-by-step explanation:
What if these particles is able to leave the atom?
1.Electrons
2.Protons
3.Neutrons
A chemical element's atom is a particular type of particle of substance. A positively charged electron or many negatively charged electrons encircle the central nucleus of an atom.
What if these particles is able to leave the atom?Electrons: If an electron leaves an atom, it is said to be ionized. Ionization can occur through various processes, such as collision with another particle or exposure to electromagnetic radiation.
Protons: Protons are found in the nucleus of an atom, and are held in place by the strong nuclear force. If a proton were to leave the nucleus, it would no longer be a stable atom and it would become an ion.
Neutrons: Neutrons are also found in the nucleus of an atom and are held in place by the strong nuclear force. If a neutron were to leave the nucleus, it would no longer be a stable atom, and it would become a different element.
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Please help it’s argent
Answer:
40%
Step-by-step explanation:
no of children = 16
no of adult = 24
total = 40
percentage of people who are children =
[tex] \frac{16 \\ }{40} \times 100\%[/tex]
[tex] = \frac{1600 \\ }{40} \%[/tex]
[tex]40\% \\ [/tex]
i hope this helped
The length of a rectangle is 7 les than twice the length of the width if the area of the rectangle is 15 square meters, find the dimensions of the rectangle define your variables and write an equation PLEASE HURRY SHOW STEPS
For the given area 15 m², The length of rectangle is 3 and breadth is 5.
The equation for calculating a rectangle's area. Rectangle's surface area. A = l × b. Once the length and breadth of a rectangle are known, its area may be computed. The area of the rectangle can be calculated as a square unit by multiplying the length and width.
Given,
Let length of rectangle = L
Breadth of rectangle = B
According to the question,
L = 2B - 7
Area = 15 m²
Area of rectangle = Length × Breadth
⇒ 15 = (2B - 7)(B)
⇒ 15 = 2B² - 7B
⇒ 2B² - 7B - 15 = 0
⇒ 2B² - 10B + 3B - 15 = 0
⇒ 2B(B - 5) + 3(B - 5) = 0
⇒ (2B + 3)(B-5) = 0
⇒ B = 5 or B = -3/2
The value of Breadth cannot be negative
L = 2(5) - 7
L = 3
The length of rectangle is 3 and breadth is 5.
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Could the points A(-2,1), B(4,7), and C(1,4) be three vertices of rectangle ABCD?
O No, since AB and BC are not perpendicular.
OYes, since a fourth point can always be determined to form a rectangle.
OYes, since AB and BC form a right angle.
O No, since AB and BC are not parallel.
Since, AB and BC are not perpendicular,
No, Points A(-2,1), B(4,7), and C(1,4) cannot be three vertices of rectangle ABCD.
The correct option is A.
What is rectangle?A rectangle is a quadrilateral in which all the angles are equal and the opposite sides are equal and parallel.
A rectangle is a closed two-dimensional figure with four sides, all the angles of a rectangle are equal to 90°.
Given points
A(-2,1),
B(4,7), and
C(1,4)
For being vertices of rectangle
Angle between line segment AB and BC should be 90°.
Slope of line AB
m = (y - y')/(x-x')
m = (7 - 1)/(4 - -2)
m = 6/6
m = 1
Slope of line BC
m' = (y - y")/(x - x")
m' = (7 - 4)/(4-1)
m' = 3/3 = 1
Since slope of the two lines is same that is both are parallel, which is only possible when A, B, C are in a straight line.
Hence, points A(-2,1), B(4,7), and C(1,4) cannot be three vertices of rectangle ABCD.
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Isabella spends $4.87 on paintbrushes and paint. How many of each item does she buy? $0.99 each for a jar of paint. $0.95 each for a paintbrush
Answer:
Isabella can buy together 5 paintbrushes ( p ) and jars of paint ( p ) : j + p = 5, She can`t buy 4 items ( because 4 * $0.99 = $3.96 < $4.87 ) and she also can`t buy 6 items ( 6 * $0.95 = $5.70 > $4.87 ). So: p = 5 - j. Another equation is: 0.95 * ( 5 - j ) + 0.99 j = 4.87, 4.75 - 0.95 j + 0.99 j = 4.87; 0.04 j = 0.12; j = 0.12 : 0.04; j = 3, p = 5 - 3 = 2. We can prove it: 0.95 * 2 + 0.99 * 3 = 1.90 + 2.97 = 4.87. Answer: Isabella buys 2 paintbrushes and 3 jars of paint.
Ryan deliver flower to two cotumer. He drive 12 minute at an average peed of 40 mile per hour to reach the firt cotumer. He drive for 15 minute at an average peed of 50 mile per hour to reach hi econd cutomer. During the 27 of driving time how many mile doe Ryan drive?
The total distance Ryan drives during the 27 minutes of driving time is 20.5 miles.
Ryan delivers flowers to two customers and drives 12 minutes at an average speed of 40 miles per hour to reach the first customer and 15 minutes at an average speed of 50 miles per hour to reach the second customer.
To find the total distance that Ryan drives during the 27 minutes of driving time, we can use the formula: distance = speed x time
We know that Ryan drives 12 minutes at 40 miles per hour and 15 minutes at 50 miles per hour. So we can use the formula to find the distance for each part of the trip and then add them together:
distance = 40 miles/hour x (12 minutes / 60 minutes/hour) = 8 miles
distance = 50 miles/hour x (15 minutes / 60 minutes/hour) = 12.5 miles
The total distance Ryan drives during the 27 minutes of driving time is 8 miles + 12.5 miles = 20.5 miles
Therefore, The total distance Ryan drives during the 27 minutes of driving time is 20.5 miles.
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How do you find the length of a segment with the midpoint and endpoint?
To find the length of a line segment given the coordinates of the midpoint and one endpoint, you can use the distance formula. The distance formula is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) and (x2, y2) are the coordinates of two points, and d is the distance between the points.
Given the midpoint (mx, my) and one endpoint (ex, ey) you can use the following steps to find the length of the segment:
Calculate the difference in the x-coordinates and square it: (ex - mx)^2Calculate the difference in the y-coordinates and square it: (ey - my)^2Add the two values from steps 1 and 2Take the square root of the result from step 3. This is the length of the line segment.For example, if the midpoint of a segment is (5,7) and one endpoint is (7,10), the length of the segment is:
d = √((7-5)^2 + (10-7)^2)
d = √((2)^2 + (3)^2)
d = √(4+9)
d = √13
the length of the segment is √13 units.
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Place the numbers in order from least to greatest.
In a certain city, each block is about 275
meters long. If the post office is 13 blocks
away from the library, approximately how
many miles is it from the post office to the
library? Round your answer to the nearest
tenth.
Using linear equations, it is 3570metre from the post office to the
library
What is a linear equation ?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form
Ax + B = 0
e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.
The standard form of a linear equation in two variables is of the form
Ax + By = C
e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
Length of each block=275 meter
let's Create a linear equation from this i.e. 275x where x=number of blocks.
No. of blocks from post office to the library = 13 (x=13)
so, distance of post office to the library= 275*13
=3575meter
≈3570 meter (round to nearest 10th)
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What is y 3x 10 in function notation?
The equation y = 3x + 10 can be written in function notation as f(x) = 3x + 10.
In this notation, x is the input variable, and f(x) is the output or dependent variable.
Function notation is used to express the relationship between two variables, where one variable is a function of the other. In this case, the equation y = 3x + 10 tells us that y is a function of x, with a slope of 3 and a y-intercept of 10.
So, in function notation, this equation can be written as:
f(x)=3x+10
In conclusion, the equation y = 3x + 10 can be written in function notation as f(x) = 3x + 10. This notation expresses the relationship between the two variables x and y, where y is a function of x, represented by f(x) with a slope of 3 and a y-intercept of 10.
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The complete question is:
What is y = 3x + 10 in function notation?
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Urgent help needed urgent urgent
The polynomial for x2 -4 in function notation is (x+2)(x-2) since a function produces an output from an input.
what is function ?Mathematics deals with numbers and their variants, equations and related structures, shapes and their locations, and locations where they might be found. The term "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is an association between inputs and outputs where each input results in a single, unique output. A domain and a codomain, or scope, are assigned to each function.The input is an x. On functions, one-to-one functions, many-to-one functions, within functions, and on functions are the four main categories of functions that are available.
given
A function creates an output from an input.
The name of the function, f (x) f(x) f(x)f, left parenthesis, x, right parenthesis, and the output, f (x) f(x) f(x)f, left parenthesis, x, right parenthesis, are all enclosed in parentheses.
x2 -4
(x2 - 2*2)
= (x+2)(x-2)
The polynomial for x2 -4 in function notation is (x+2)(x-2) since a function produces an output from an input.
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Alex has 2/4 quarts of chocolate milk left in a jug. In another jug he had 2 1/2 pints of chocolate milk . Can Alex pour the milk from both jugs into a third jug that has a capacity of 2 gallons.
Answer:
Yes, he can
Step-by-step explanation:
We have to find the total of Chocolate milk Alex has by taking
2 1/2 = 5/2
2/4 + 5/2 = 2/4 + 10/4 = 12/4 = 3 quarts of chocolate milk
1 gallon = 4 quart
And here, Alex only has 3 quarts of chocolate milk, so he can pour the milk from both jugs into a third jug.
A virus is spreading around Brookfield. At the moment, 685 people are infected. If the virus is
spreading at a rate of 13% each day, how many people in all will have caught the virus in 3
days?
If necessary, round your answer to the nearest whole number.
A virus spreading around Brookfield will infect 988 people in the next 3 days.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
Number of people infected by the virus = 685
The rate at which the virus is infecting = 13%
The virus is spreading at 13% rate each day.
To deduce the number of people who will get infected in next 3 days.
The final equation will be -
= 685 × ( 1 + 13%)³
= 685 × (113/100)³
= 685 × (1.13)³
= 685 × 1.442
= 987.77 ≈ 988
Therefore, the number of people who will get infected is 988.
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What is the formula for a 45 degree triangle?
Using the formula of Pythagorean Theorem we can find a 45 degree triangle.
The degrees of the triangle's three inner angles give rise to its name, 45, 45, and 90. The triangle formed by the angles 45, 45, and 90 is said to be isosceles since two of the angles are less than the third.
Due to the fact that this triangle has one angle that is precisely 90 degrees, it is also regarded as a right triangle.
The following guidelines apply to the 45-45-90 triangle's characteristics:
1. There must always be a right angle in one angle.
2. The second pair of angles must always be 45-degree angles.
3. A triangle has two equal-length sides, but the third side is always longer.
Using the Pythagorean Theorem - Since a 45-45-90 triangle has a right angle, the length of its sides may be calculated using the Pythagorean Theorem.
Recall the formula for the Pythagorean Theorem:
a^2 + b^2 = c^2.
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-8r-3(-6-5r)=8-5(4-2r) show work pleaseeeee
Answer:
[tex]r=-2[/tex]
Step-by-step explanation:
First, apply the distributive property: A(B + C) = AB + AC
[tex]-8r-3(-6-5r)=8-5(4-2r)[/tex]
[tex]-8r+18+15r=8-20+10r[/tex]
Then, get all of the r's on one side.
[tex]-8r+18+15r=8-20+10r[/tex]
↓ subtract 18 from both sides
[tex]-8r+15r=8-2+10r[/tex]
↓ subtract 10r from both sides
[tex]-8r+5r=8-2[/tex]
Finally, solve for r by combining like terms, then dividing by -3.
[tex]-3r = \ 6\\\overline{\, -3 \: } \ \ \ \ \overline{-3}[/tex]
[tex]r = -2[/tex]
The number of fish in a lake decreased by 53% between last year and this year last year there where 245 fish in the lake what is the population this year?
The number of fish remaining in the lake this year will be 115.
What does a population mean?A population mean any group that shares at least one characteristic. Populations are more than just individuals. People, animals, businesses, buildings, motor vehicles, farms, objects, or events are examples of populations.
Data
The decrement in number of fish = 53%.
Number of fish previous year = 245
Remaining number of fish will be 47%.
The population of fish this year will be:
= 47% * 245 fish
= 115 fish.
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What is equality for Class 7?
In mathematics, equality refers to the relationship between two expressions or values, indicating that they are equivalent or have the same value.
For example, the equation "2 + 3 = 5" states that the left side of the equation (2 + 3) is equal to the right side of the equation (5). Equality can be represented using the symbol "=", which is called the equality sign or equal sign.
Equality can also be used in other mathematical concepts such as congruence, similarity, and equivalence. For example, two triangles are congruent if they have the same shape and size, two figures are similar if they have the same shape but different sizes, and two equations are equivalent if they have the same solutions.
Equality in mathematics is transitive, meaning that if a = b and b = c, then a = c, and reflexive, meaning that a = a for any value of a.
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Mario and Russell plot a triangle on a coordinate grid and then perform a
rotation and a translation. Russell thinks the original triangle and final triangle
are congruent but Mario disagrees. Which student is correct and why?
Russell is correct. Since neither rotations no translations preserve distance, the
triangles are congruent.
O Mario is correct. Since neither rotations not translations preserve distance, the
triangles are not congruent.
Mario is correct. Since both rotations and translations preserve distance, the triangles
are congruent.
►
Russell is correct. Since both rotations and translations preserve distance, the
triangles are congruent.
Since two triangle are considered to be congruency if each of their 3 sides, and Mario is correct, the correct response is SSS.
How may a triangle's congruence be demonstrated?If a triangle's size and shape are a perfect match, it is said to be congruent. The symbol is contained in the word "congruent". The three sides and three angles of two triangle are said to be congruent when their three sides and three angles coincide.
Here,
As illustrated below, start by writing the names of the triangles' vertices, starting with triangles DAB and BCD.
AB = CD
DA = BC
Side BD is the same in both triangles, therefore
BD = BD
The fact that the triangle DAB & BCD have the same number of angles on each side indicates that they are congruent and utilise the SSS property of a congruence triangle.
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Find an expression to present the perimeter of the triangle below
i am sorry i don't know the answer
What is the area of the triangle?
2 m
4 m
3 m
square meters
first
Semi perimeter (S)=(2+4+3)/2
=9/2=4.5
now
area=
[tex] \sqrt{4.5(4.5 \times 2)(4.5 \times 4)(4.5 \times 3)} [/tex]
[tex] \sqrt{s( s- a)( s-b )( s- c)} [/tex]
which is equal to
99.20