Prime numbers are those numbers that are divisible only by the number itself and by 1. Such numbers are 2, 3, 5, and 7 etc.
Factorization is when we write a given mathematical term in product of its various factors. Suppose we are provided with a mathematical expression of:
x^2 + 3x + 2
We will undergo its Factorization and write the expression in its possible factors:
( x + 1 ) ( x + 2)
By multiplying these factors, we will get the actual expression x^2 + 3x + 2.
Prime Factorization is a method of identifying which prime numbers multiply together to give the original value/expression.
Suppose we have a number 60, then the prime factors of it will be:
60
6 x 10
2 x 3 2 x 5
In the problem statement above, we are provided with some popular dog breeds, and we are expected to find the prime factors of each of the given weights of the breed.
The weights that have a prime factorization of exactly three number are as follows:
Prime factors of 20 (Cocker Spaniel)
= 2 x 2 x 5
Prime factors of 50 (Siberian Husky)
= 2 x 5 x 5
Prime factors of 70 (Golden Retriever)
= 2 x 5 x 7
Weights that have the same number in their prime factorization are:
Prime factors of 81 (German Shepherd)
= 3 x 3 x 3 x 3
Prime factors of 25 (Beagle)
= 5 x 5
So, the prime factorization of the weights of the dog breeds are being found. While Labrador Retriever 67 is a prime number itself.
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A trapezoid has sides of length 19.5 centimeters, 16.9 centimeters, 19.5 centimeters, and 18
centimeters. What is the perimeter?
centimeters
the answer is correct because you gave text evidence
A car tire has a radius of 1.5 feet. if the tire is rotating at 800 rpm, what is the speed of the car in miles per hour (1 mile = 5,280 feet)? round the answer to the nearest tenth. the car is traveling approximately miles per hour.
Answer:85.7 miles per hour
Step-by-step explanation:
Need help ez question
Answer:
x = 0.25
Step-by-step explanation:
[tex]9\sqrt{x} =5-2x[/tex]
[tex]81x = 25 - 20x + 4x^{2}[/tex]
[tex]0=4x^{2} -101x+25[/tex]
[tex]0 = 4x^{2} -1x-100x+25[/tex]
[tex]0=x(4x-1)-25(4x-1)\\0=(x-25)(4x-1)[/tex]
[tex]x=25,\frac{1}{4}[/tex]
[tex]2*25+9\sqrt{25} =5\\50+9*5=5\\50+45=5\\95=5[/tex]
[tex]2*\frac{1}{4}+9\sqrt{\frac{1}{4} } =5 \\0.5+9*\frac{1}{2} =5\\0.5+4.5=5\\5=5[/tex]
Answer:
[tex]x=\dfrac{1}{4}[/tex]
Step-by-step explanation:
Given equation:
[tex]2x+9\sqrt{x}=5[/tex]
Subtract 2x from both sides to isolate the square root:
[tex]\implies 2x+9\sqrt{x}-2x=5-2x[/tex]
[tex]\implies 9\sqrt{x}=5-2x[/tex]
Square both sides to eliminate the square root:
[tex]\implies (9\sqrt{x})^2=(5-2x)^2[/tex]
[tex]\implies 81x=(5-2x)(5-2x)[/tex]
[tex]\implies 81x=25-20x+4x^2[/tex]
Subtract 81x from both sides:
[tex]\implies 81x-81x=25-20x+4x^2-81x[/tex]
[tex]\implies 0=25-101x+4x^2[/tex]
[tex]\implies4x^2-101x+25=0[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:
[tex]\implies ac=4 \cdot 25=100[/tex]
[tex]\implies b=-101[/tex]
Therefore, the two numbers are -1 and -100 as:
[tex]\implies -1 \cdot -100=100=a[/tex]
[tex]\implies -1+(-100)=-101 =b[/tex]
Rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies4x^2-x-100x+25=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(4x-1)-25(4x-1)=0[/tex]
Factor out the common term (4x - 1):
[tex]\implies (x-25)(4x-1)=0[/tex]
Apply the zero-product property:
[tex](x-25)=0 \implies x=25[/tex]
[tex](4x-1)=0 \implies x=\dfrac{1}{4}[/tex]
Input each solution into the original equation to check its validity:
[tex]\begin{aligned}x=25 \implies 2(25)+9\sqrt{25}&=5\\50+9(5)&=5\\50+45&=5\\95 & \neq 5\end{aligned}[/tex]
Therefore, x = 25 is not a valid solution.
[tex]\begin{aligned}x=\dfrac{1}{4}\implies 2\left(\dfrac{1}{4}\right)+9\sqrt{\dfrac{1}{4}}&=5\\\dfrac{1}{2}+9(\dfrac{1}{2})&=5\\\dfrac{1}{2}+\dfrac{9}{2}&=5\\\dfrac{10}{2}&=5\\5 & = 5\end{aligned}[/tex]
Therefore x = ¹/₄ is a valid solution.
Therefore, the only valid solution to the equation is x = ¹/₄.
In Problem 17, verify that the functions fand g are inverses of
each other by showing that (f o g) (x) = x and (g o f) (x) = x.
Problem 17:
f(x) = 1/x g(x) = 1/x
Answer:
you are very very very correct
In advertising, the decay factor describes how an advertisement loses its effectiveness over time. In math, would you expect a decay factor to increase or decrease the value of y as x increases?
When the value of x will increase then decay factor will decrease the value of y.
Given that the decay factor describes how an advertisement loses its effectiveness over time.
Exponential decay will tell us the process of reducing an amount by a consistent percentage of rate over a particular period of time. Exponential decay is the reciprocal of exponential growth when a quantity decreases by the same factor in equal intervals of time, the constant coefficient of the exponential decay function is less than 1. This can be expressed as (1 - r) and is called the decay factor.
According to the definition of the decay factor, its say that when the value of x increases then the decay factor of the value of y will decrease.
Hence, the value of x will increase then decay factor will decrease the value of y.
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The number line shows the distance in meters of two birds, A and B, from a worm located at point X:
Part A: Expression for the distance in meters between given two birds using subtraction = 2.5 - (-2.5)
Part B: The distance between two birds using additive inverse 2.5- (-2.5) =5 meters
What is an expression and additive inverse?An expression is an combination of numbers and mathematical operations such as addition, subtraction, division and multiplication with equating any two terms.
Additive inverse : Additive inverse of an number a is the number that when adds to a gives zero .
Let b be additive inverse of a, then a + b =0
Then, b = -a
Given two birds A and B are at points x= -2.5 and y = 2.5 respectively
Therefore, the expression for the distance in between given two birds
= y - x = 2.5- (-2.5)
We an clearly see that -2.5 is additive inverse of 2.5
Distance between the two birds = 2.5 -(-2.5) =2.5 +2.5 = 5 meters
Therefore, the expression for distance between the two birds A and B is 2.5-(-2.5) and the distance is 5 meters.
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What is the factored form of 2 x³+5 x²-12 x ?
(F) x(2 x-3)(x+4) (H) x(2 x+4)(x-3) (G) (2 x²-3)(x+4) (I) (2 x-4)(x+3)
After solving, the factors of equation 2x³+5x²-12x are:
(F) x(2x-3)(x+4)What basically is an equation?An equation is a mathematical statement composed of two representations joined by an equal sign.An example of an equation is 3x - 5 = 16. After attempting to solve this equation, we get the value for the variable x as x = 7.So,
Given the equation: 2x³+5x²-12x
Then,
2x³+5x²-12xx[2x²+5x-12]x[2x²+x( - )-12]x[2x²+x(8-3)-12]x[2x²+8x-3x-12]x[2x(x+4)-3(x+4)]Factors are: x(2x-3)(x+4)
Therefore, after solving, the factors of equation 2x³+5x²-12x are:
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What is the equation of a line that passes through the point (2,−2) and is perpendicular to y=x4−3 ?
The equation of a line perpendicular to y = 4x - 3 that passes through the point (2,-2) is y = -1/3x - 3/2
How to find the equation of the perpendicular line?The equation of the line is given as
y = 4x - 3
Rewrite the equation as
y = 4x - 3
A linear equation is represented as
y = mx + c
Where
Slope = m
So, we have
m = 4
The slopes of perpendicular lines are opposite reciprocals
This means that
m2 = -1/m1
So, we have
m = -1/4
Evaluate
m = -1/4
The equation of the perpendicular line is then calculated as
y = m(x - x1) + y1
Where
(x1, y1) = (2, -2)
This gives
y = -1/4(x - 2) - 2
Evaluate
y = -1/3x + 1/2 - 2
Evaluate the sum and the difference
y = -1/3x - 3/2
So, the equation of a line perpendicular to y = 4x - 3 that passes through the point (2,-2) is y = -1/3x - 3/2
Hence, the required equation of a line perpendicular to y = 4x - 3 that passes through the point (2,-2) is y = -1/3x - 3/2
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Find the solution(s) to the system of equations. Select all that apply. y=x²-5 y=x-3
Answer:
x = 2, y = -1
x = -1, y = -4
Step-by-step explanation:
Both equations are equal to y, so just set x - 3 = x^2 - 5 and solve.
The scale of a map is 2.6 ft = 89
miles
Map: 5.6 ft
Actual:
miles
Actual miles is [tex]\frac{2492}{13}[/tex]
According to the question,
Given that,
Map is 5.6 ft
scale of Map is 2.6 ft which is equal to 89 miles
Actual miles = [tex]\frac{5.6 * 89}{2.6}[/tex]
= [tex]\frac{498.4}{2.6}[/tex]
multiply both the numerator and denominator with the same integer
= [tex]\frac{4984}{26}[/tex]
= [tex]\frac{2492}{13}[/tex]
Actual miles is [tex]191\frac{9}{13}[/tex] ≈ 1.916923 ×[tex]10^{2}[/tex]
Definition of miles per hour unit: ≡ 1 mi / 3600 s = 1609.344 m / 3600 s. In American public life, this is the most commonly used speed unit. Cars speeds are measured in mpg. Interpretation: The speed at which the body moves 1 mile (or 1609.344 metres) in 1 hour.
Definition of feet per second unit: ≡ 1 ft / 1 s = 30.48 cm / 1 s. Abbreviation is fps. In America, perhaps this is the second most commonly used speed unit in public life (after miles per hour). Definition: The speed at which the body moves 1 foot (or 30.48 centimetres) in 1 second.
Convert Miles to Feet
Multiply your speed in miles per hour by 5,280. This is the number of feet in a mile. The result is your speed in feet per hour. For example, 60 miles per hour times 5,280 feet per mile is 316,800 feet per hour.
Convert to Feet per Minute
Divide your speed in feet per hour by 60. This is the number of minutes in an hour. Therefore, the result is your speed in feet per minute. For example, 316,800 feet per hour divided by 60 minutes per hour is 5,280 feet per minute.
Convert to Feet per Second
Divide your speed in feet per minute by 60. This is the number of seconds in a minute. Therefore, the result is your speed in feet per second. For example, 5,280 feet per minute divided by 60 seconds in a minute equals 88 feet per second.
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Evaluate the expression A=3, b=1/2.and c=4
8ab/2bc
Answer: 3
Step-by-step explanation:
First substitute values in :
8(3)(1/2)/ 2(1/2)(4)
Then simplify :
12/ 4
3
This diagram is a straightedge and compass construction. A is the center of one circle, and B is the center of the other. A rhombus is a quadrilateral with 4 congruent sides
Answer:
Step-by-step explanation:
Answer:
This diagram is a straight edge and compass construction . A is the centerof one circle , and B is the centre of the other . A rhombus is a quadrilateral with 4 congruent sides
Step-by-step explanation:
There are 100 people on the swim team.today, they are going to a big swim meet on the other side of town. if each minivan can take 15 people how much minivans will they need.
Using the mathematical operation such as division, the swim team, which has 100 people on it, needs 7 minivans to take them on the other side of town.
If there are 100 people on the swim team that will be divided into minivans that can only occupied by 15 people, divide 100 by 15 to know how many vans they will need.
100 people ÷ 15 people/minivan
100 ÷ 15 = 6 r 10
This means that the swim team will need 6 minivans and still, 10 people don't belong to any minivan yet. So, 1 additional minivan will be needed for the remainder of 10 people.
Hence, the swim team will be needing 7 minivans to cater 100 people on their team.
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Elena’s father put $460 into a savings account for her. The account pays 2.5% simple interest each year. If he neither adds nor withdraws money from the account, how much interest will the account earn after 4 years? Round to the nearest cent.
Answer:
$46
Step-by-step explanation:
So, the principal amount, P = $460
Yearly simple interest, R = 2.5% which equals 0.025
Time(T) which is 4 years.
The interest(I) for the amount, P at the rate of R yearly, after T years,
Elena's account will earn $46.
To rationalize the denominator of 4√4/25, by what number would you multiply the numerator and denominator of the fraction?
Rationalization is multiplying a surd by another similar surd to obtain a rational number. In mathematics, a surd is an expression involving a square, cube, or another kind of root symbol. The surd used for multiplication is called the rationalization factor (RF). Rationalize the denominator to make it easier to perform calculations with rational numbers. Rationalizing a denominator with a fraction removes all root terms, such as square roots and cube roots, from the denominator.
[tex]\frac{4}{\sqrt{\frac{4}{25}}}[/tex]
[tex]\begin{aligned}&\frac{4}{\frac{\sqrt{4}}{\sqrt{25}}}\\&\frac{\frac{4}{\sqrt{2^2}}}{\sqrt{5^2}}\end{aligned}[/tex]
[tex]\frac{4}{\frac{\sqrt{2^2}}{\sqrt{5^2}}}[/tex]
[tex]\frac{4}{\frac{2}{5}}[/tex]
[tex]\begin{aligned}&4 \div \frac{2}{5} \\&4\left(\frac{5}{2}\right) \\&\frac{4 \cdot 5}{2} \\&2 \cdot 5\end{aligned}[/tex]
[tex]10[/tex]
And if the question is like this,
[tex]$\frac{4 \cdot \sqrt{4}}{25}$$\frac{4 \cdot \sqrt{2^2}}{25}$$\frac{8}{25}$[/tex]
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y varies directly with x .
If x=2 when y=4 , find y when x=5 .
After direct variation y =10 when x = 5.
What specifically do we mean by "direct variation"?Direct variation equations use the same phrase to give the reader a hint.The phrase is either "directly proportional" or "directly varies."The area of a square, for instance, is proportional to the square of its side.If y varies directly as x and y = 6 when x = 2, the variational constant is k = 3.As a result, the direct variation equation is y = 3x.So,
The initial statement is y = kx
Then to find y when x = 5.
K constant will be y/x ⇒ 4/2That is y = kx ⇒ y = 4/2 × xWhen x = 5:
y = 4/2 × 5 ⇒ y = 10Therefore, after direct variation y =10 when x = 5.
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34. Marianne figured out that her father's age
is her age plus five to the power of four, less
365, minus 22, all divided by six. If her father
is 42, how old is Marianne?
ats true
Marianne's age is 14 years old if her father's age is her age plus five to the power of four, less 365, minus 22, all divided by six.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Marianne figured out that her father's age is her age plus five to the power of four, less 365, minus 22, all divided by six. If her father is 42.
Let x be the Marianne age
(x + 5⁴ - 365 - 22) (1/6) = 42
x + 238 = 252
x = 14 years
Thus, Marianne's age is 14 years old if her father's age is her age plus five to the power of four, less 365, minus 22, all divided by six.
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Factor each expression.
9 x²-25
After factorization of the expression 9x²-25, the answer comes to:
(3x - 5)²What do we mean by an expression?An expression or mathematical expression is a finite mixture of symbols that is well-formed according to context-dependent rules. To help determine the order of operations and other aspects of logical syntax, mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.Many authors differentiate between an expression and a formula, with the former referring to a mathematical object and the latter referring to a statement about mathematical objects.So,
The given expression is: 9x²-25
Then,
9x²-253²x²-5²(3x)²-(5)²(3x - 5)²Therefore, after factorization of the expression 9x²-25, the answer comes to:
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I really need help I will give you 5 stars and alike.
Answer:
the area is 935 square inches, and the perimeter is 39 inches
Step-by-step explanation:
Hey there!
In order to find the perimeter and area of the board, we must first list out the information we already know
----------------------------------------------------------------------------------------------------------
- The original board has a length of 44 - The original board has an area of 1496- The original board has a perimeter of 156- The new board has a length of 11----------------------------------------------------------------------------------------------------------
There is a tiny pattern in here:
The original board has a length of 44 while the new one has the length of 11
This means that, the original board had dimensions 4 times the length of the new board
In order to find the area or perimeter, we need to know the width of the new board
To do this, we divide 1496 by 44
That gets us 34
This means that the width of the old board is 34
Now we divide 34 by 4 which gets us 8.5
This means, 8.5 is the width of the new board
Now that we know this, we can easily find the area and the perimeter of the new board
8.5 + 8.5 + 11 + 11 = 39
This means, the perimeter is 39
8.5 x 11 = 935
This means, the area is 935
This brings us to the conclusion that the area is 935 square inches, and the perimeter is 39 inches!
I need help. 2(x + 6) = 2x + 12
HELP!! The slope of the line below is 3. Write the equation of the line in point-slope form, using the coordinates of the labeled point. Do not use parenthesis on the y-side. (-1,1)
The equation of the line in point-slope form is y-1 = 3 ( x + 1)
Equation of a line:
The equation of a line, in point-slope form, is designated using:
y-y0= m( x - x0)
In which the point is given by(x0,y0) and m is the slope.
Slope of the line below is 3 (given in the question).
This means that m = 3
(-1,1)
This means x= -1 and y =1
equation of the line
y - y0 = m( x- x0)
y-1 =m(x-(-1))
y-1=m(x + 1)
substituting the value of m is 3
y-1= 3 ( x + 1)
Therefore, The equation of the line in point-slope form is y-1= 3 (x + 1)
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Evaluate the expression 2x² - 4 when x = -3.
Answer: 32
Step-by-step explanation: 2(-3)2. -4
If lindley requests an extension to file her individual tax return in a timely manner, the latest she could pay her tax due without penalty is::_________
If Lindley requests an extension to file her individual tax return, the latest she could pay her tax due without penalty is April 15th.
What is an individual tax return?A person or married couple must submit an official form known as an individual tax return to a federal, state, or local taxing authority in order to record any taxable income they received within a certain time period, typically the previous year.
This document is used to determine how much tax was paid in excess of what was required during that time period.
In this case, if Lindley requests an extension to file her individual tax return, the latest she could pay her tax due without penalty is April 15th.
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If Lindley requests an extension to file her individual tax return, the latest she could pay her tax due without penalty is:
April 15th.
October 15th.
August 15th.
November 15th.
None of the choices are correct.
please help!! 10 points+ brainlist!!
Answer:
Mean - 67 inches
Median - 67 inches
Mode - 68 inches
Step-by-step explanation:
Definitions of the words:
Mean - The average number of the data set.
Median - The middle number in the data set when ordered from least to greatest.
Mode - The value that appears most frequently.
Mean:
We can add them up and divide by the number of values in the set, 7.
469 / 7 = 67
Median:
We can order them from least to greatest and see which one is the 4th one.
60, 62, 66, 67, 68, 68, 78.
67 is in the middle, so that is our median.
Mode:
Only 68 is repeated twice in the set, so 68 is the mode.
Hope this helped! Have a great day!
Select the locations on the number line to plot the points −2 , −11 , and −17 .
Number Line :
In math, a number line can be defined as a straight line with numbers placed at equal intervals or segments along its length. A number line can be extended infinitely in any direction and is usually represented horizontally.
or
A number line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, for example, plotting a point.
On a number line, a number on the left is always less than a number on the right. Similarly, a number on the right is always greater than a number on the left.
The Number Line app helps students visualize number sequences and illustrate strategies for counting, comparing, adding, subtracting, multiplying, and dividing. Choose number lines labeled with whole numbers, fractions, decimals, or negative numbers. Or use a custom number line, with or without tick marks, and set your own interval.
Show intervals between points on the line using forward or backward jumps above and below the line. Jumps can also be labeled with their values or left blank. Add custom tick marks to the number line to show equivalence or compare number values.
Basic Number Line Skills:
1. Find the dot marked on a number (and name the dot)
2. Place a dot at the desired location
3. Find the desired number below the number line’s tick mark*
-17 -11 -2 0
-----|-----------------|----------|----------------|-----------------------------------------------Number line
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Put the correct number in each box
1/7=4/? = ?/56
Find the coordinates of the point where y - 4x = 1 crosses the y-axis
Step-by-step explanation:
to cross the y-axis x must be 0.
so,
y - 4×0 = 1
y = 1.
so, the point is
(0, 1)
Expand each logarithm.
log₈8 √3a⁵
The expansion of the expression log₈8 √3a⁵ is
1+ log 3/2log 8 +5 log a/ log 8.
Given that the expression is log₈8 √3a⁵.
We are required to expand the expression.
The change of base formula is used to write a logarithm operation again as a fraction of logarithms with a new base.
The expression is log₈8 √3a⁵.
log₈8 √3a⁵= (log 8 +log [tex]\sqrt{3}[/tex] +log [tex]a^{5}[/tex])/log 8
=1+ log 3/2log 8 +5 log a/ log 8 (We know that log [tex]m^{n}[/tex]=n log m)
Hence the expansion of the expression log₈8 √3a⁵ is
1+ log 3/2log 8 +5 log a/ log 8.
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Rate my art HONESTLY
It’s Queen Elizabeth II pointillism
Any tips on how to fix her neck are appreciated
I would say avoid adding any more detail to the eyes and facial features. normally pointillism uses alot more dots and makes them most concentrated in darker areas. i would recommend trying to add shadows to most of it or adding more detail to the hat. Ii think her neck looks ok but there isn't really a way to get rid of the diagonal that you made.
Answer:
I think its great! I think add more hair to the side of head there. other than that it resembles her quite nicely!
Step-by-step explanation:
Vertical 1.
3+ 12, an incomplete mathematical sentence.
Addition 3+ 12, an incomplete mathematical sentence. 1.3+ 12=13.3
Addition is a mathematical procedure that is used to add numbers. The sum of the given numbers is the result of adding the given numbers. For instance, if we add 2 and 3, (2 + 3), the result is 5. We used the addition function on two numbers, 2 and 3, to produce the sum, 5
Symbol for Addition
Different symbols are used in mathematics. One of the most used arithmetic symbols is the addition symbol. We read about adding two numbers, 2 and 3, in the definition of addition above. If we look at the addition pattern (2 + 3 = 5), the symbol (+) joins and completes the two integers.
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