1) A prime factorization of a particular number will always give the same prime factors.
2) All the factors in the list when multiplied will give the original number.
3) No, two different numbers cannot have the same prime factorization.
4) The prime factors of 40 are 2 and 5.
1) We anticipate finding factors in prime factorization that can add to themselves to get the original number. The original number can be obtained by multiplying the remaining components together as long as the first factor can divide the quantity without leaving a remnant.
Prime factorization of the number, 15 goes thus;
15/3=5
5/5=1
3*5=15
So, all the factors multiply to give the original number.
2) Numbers that split an original number evenly or precisely are known as its factors. A factor is a whole number that can divide a larger number in two equal halves.
3) The collection of prime numbers that can be multiplied together to produce a given number is known as the prime factorization of that number. Because the same set of numbers must provide the same result when multiplied together, two separate numbers cannot have the same prime factorization.
4) Any number can be represented as a sum of prime numbers using prime factorization. A number with exactly two elements, 1 and the number itself, is said to be a prime number. As an illustration, the prime factorization of 18 is 2 3 3. Here, the two main elements or prime factors of 18 are 2 and 3.
The prime factorization of 40 is :
40 = 2 × 2 × 2 × 5
Hence, the prime factors of 40 are 4 and 5.
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HURRY Consider the equation 3x3 + 14x2 – 14x + 60 = 0. The real solution is –6. What are the nonreal solutions?
Negative 2 i StartRoot 26 EndRoot, 2 i StartRoot 26 EndRoot.
4 minus 2 i StartRoot 26 EndRoot, 4 + 2 i StartRoot 26 EndRoot.
StartFraction negative 2 + i StartRoot 26 EndRoot Over 3 EndFraction, StartFraction negative 2 minus i StartRoot 26 EndRoot Over 3 EndFraction.
StartFraction 2 + i StartRoot 26 EndRoot Over 3 EndFraction, StartFraction 2 minus i StartRoot 26 EndRoot Over 3 EndFraction.
The non-real solutions are (2 + i√26)/3 and (2 - i√26)/3
How to determine the non-real solutions?The equation of the polynomial expression is given as:
3x^3 + 14x^2 - 14x + 60 = 0
From the question, we have
x = -6
This gives
So, we have
x + 6 = 0
The next step is to divide the polynomial equation 3x^3 + 14x^2 - 14x + 60 = 0 by x + 6 = 0
This is represented as
3x^3 + 14x^2 - 14x + 60/x + 6
Using a graphing calculator, we have
3x^3 + 14x^2 - 14x + 60/x + 6 = 3x^2 - 4x + 10
Next, we determine the solution of the quadratic expression 3x^2 - 4x + 10 using a quadratic formula
So, we have
x = (-b ± √(b² - 4ac))/2a
This gives
x = (4 ± √((-4)² - 4 * 3 * 10))/2 * 3
So, we have
x = (4 ± √-104)/6
This gives
x = (4 ± 2√-26)/6
Divide
x = (2 ± √-26)/3
Rewrite as
x = (2 ± i√26)/3
Split
x = (2 + i√26)/3 and x = (2 - i√26)/3
Hence, the non-real solutions of the polynomial expression are x = (2 + i√26)/3 and x = (2 - i√26)/3
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i am needing help with this
Side BC is opposite to angle BAC, in the picture.
Answer: Angle BAC - first option
a department store buys 300 shirts at a cost of 3600 and sells them at a selling price of $20 each find the percent markup
We have the following:
To find the percent markup, we must calculate the profits, knowing that there are 300 shirts and they sell them for a total of $ 20
[tex]300\cdot20=6000[/tex]Now we subtract from what was initially spent and then divide by that same amount and multiplying by 100 we will know the percent markup
[tex]\frac{6000-3600}{3600}\cdot100=66.67\cong67[/tex]Which means that the percent markup is 67%
Hihuvhhhhhvhhhuuibvjj
Given expression is (a+b)^8 and we need to find the 5th term of this series.
Explanation -
The general binomial expression is given as
[tex](x+y)^n=^nC_0x^ny^0+^nC_1x^{n-1}y^1+^nC_2x^{n-2}y^2+............upto\text{ x}^0[/tex]So the given expression can be written as
[tex](a+b)^8=^8C_0a^8b^0+^8C_1a^7y^1+^8C_2a^6b^2+^8C_3a^5b^3+^8C_4a^4b^4+...[/tex]So the 5th term will be
[tex]\begin{gathered} 5th\text{ term = }^8C_4a^4b^4 \\ The\text{ general comb}\imaginaryI\text{nat}\imaginaryI\text{on formula }\imaginaryI\text{s = }^nC_r=\frac{n!}{(n-r)!r!} \end{gathered}[/tex]Then we have
[tex]\begin{gathered} 5th\text{ term = }\frac{8!}{(8-4)!4!}a^4b^4 \\ 5th\text{ term = }\frac{8\times7\times6\times5}{4!}a^4b^4 \\ 5th\text{ term = }\frac{8\times7\times6\times5}{4\times3\times2\times1}a^4b^4=2\times7\times5\times a^4b^4=70a^4b^4=70(ab)^4 \end{gathered}[/tex]So the final answer is 70(ab)^4Find the surface area and volume of the solid. Round each measure to the nearest tenth, if necessary.
The surface area and volume of the solid are 104 in² and 60 in³
How to determine the volumeIt is important to note that the figure takes the shape of a cuboid.
The formula for determining the surface area of a cuboid is expressed as;
SA = 2lw + 2lh + 2hw
Where;
SA is the surface areal is the length of the cuboidw is the width of the cuboidh is the height of the cuboidNow, let's substitute the values into the formula, we have;
Surface area = 2(5× 2) + 2(5 ×6) + 2(6 × 2)
expand the bracket
Surface area = 2(10) + 2(30) +2 (12)
Surface area = 104 in²
The formula for volume is given as;
Volume = l × w × h
Volume = 5 × 2 × 6
Volume = 60 in³
Thus, the values are 104 in² and 60 in³
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write an expression that can be used to find the value of x in the diagram below
since the angles are opposite by the vertex, we have that the expression to find the value of x is:
[tex]4x-1=55[/tex]and if we solve it, we obtain:
[tex]4x=54[/tex][tex]x=13.5[/tex]John and Savanah are saving money to go on a trip to Mexico. They need at least $2,545 in order to go. John tutors English and Savanah works as a babysitter to raise money. John charges $15 per hour and Savanah charges $20 per hour. The number of hours that Savanah has scheduled is no more than five times the number of hours John has scheduled. Savanah will babysit at least 40 hours.. Write a set of constraints to model the problem, with x representing the number of hours John tutors and y representing the number of hours Savanah babysits
The group of restrictions used to simulate the issue includes
y<5x andy [tex]\geq[/tex] 40hours How to construct a set of restrictions to represent the issue:The issue includes the following information.
They require $2,545 split by John's and Savanah's hours. Savanah's hours are no more than five times John's. Savanah will babysit the kids for 40 hours.The limitations for modeling the problem are as follows: The gap between the number of hours Savanah has reserved and those that John has is no more than five times.
Savanah will provide child care for a minimum of 40 hours, but no longer than that, indicating that it is less than; as a result.
,y<5x
Meaning "at least 40 hours" is "at least 40 hours." 40 hours or more may be expressed as
y ≥ 40 hours
The two necessary restrictions are represented as y< 5x and y=> 40 hours in an inequality model.
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A person from Switzerland consumes about 9.1 kilograms of chocolate per
year. A person from the United States consumes about 4.7 kilograms of
chocolate per year. How many times as much chocolate will a Swiss
person consume in one year than someone from the United States? Round
your final answer to the nearest tenths
Answer:
switzerland was the leading country in chocolate consumption per capita in 2017, with citizens eating nearly nine kilos of the sweet stuff in that year. World renowned for the chocolate they produce, it seems the Swiss themselves can’t get enough of the candy. Germany, the country’s neighbor, is equally addicted, importing the largest share of Swiss chocolate of all countries in the world.
Step-by-step explanation:
Answer: a swede would consume 1.9 times as much chocolate as an American.
Step-by-step explanation: 9.1 / 4.7 = 1.93617021. round to the nearest tenth = 1.9.
1.93617021 times 4.7 equals 9.1
Which is greater? -7/10 or -0.66?
Answer:
-7/10
Step-by-step explanation:
First, we obviously need to convert 0.66 into a fraction. Since -7/10 cannot be changed, we need to change AND simplify -0.66.
-0.66 is equal to -66/100, but we can still simplify this. We can divide the numerator and denominator by 2.
66 divided by 2 is 33.
100 divided by 2 is 50.
-33/50 CANNOT be simplified anymore.
So -7/10 _ -33/50. Which is greater?
-7/10 is closer to 0 on the number line. -33/50 isnt.
So -7/10 is the answer.
-7/10 > -0.66
If you mix 3 oz of blue paint with 2 oz of yellow paint, and then decide to create 20 oz of the same mixture, how many ounces of yellow paint do you need?
tata:
• Blue paint (,: B,) 3
,• ellow poaint (
,• Mixture obtained ( ),O
,• Total mixture (), T
,• Total yellow paint (): , TY
Proportion f Y:
[tex]Y=\frac{2}{5}=0.4[/tex]TY:
[tex]TY=Y\cdot T=0.4\cdot20=8oz[/tex]nswer: 8oz
ummary:
0. We got the proportion of yellow paint in the mixture
,1. We multiply the proportion by the total mixture to know how many ounces of yellow paint is needed.
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
74.44
Step-by-step explanation:
[tex]P(10)=0.018(10)^3-0.294(10)^2+3.065(10)+55.190 \\ \\ =74.44[/tex]
A crane has a cable with a breaking strain of 6400 kg
measured to 2 significant figures.
It is used to lift crates which weigh 90 kg measured to the nearest 10 kg.
What is the
greatest number of crates that can safely be lifted
at one time without breaking the cable?
Some working must be shown.
The greatest number of crates that can safely be lifted at one time without breaking the cable is 71.
What is GCF?
The biggest positive integer m that divides both x and y is the GCF of two or more non-zero integers, x, and y. The GCF stands for greatest common factor. In this case, greatest can be changed to highest, and factor to divisor. The highest common factor is often referred to as the biggest common factor, highest common factor, or highest common divisor (GCD). GCF is usually always utilised with fractions, which are frequently employed in daily life. You can obtain the necessary reduced form by determining the GCF of the denominator and numerator of a fraction or ratio.
A crane has a cable with a breaking strain of 6400 kg measured to 2 significant figures. It is used to lift crates which weigh 90 kg measured to the nearest 10 kg.
We need to calculate the greatest number of crates that can safely be lifted at one time without breaking the cable.
According to the question,
It is given that, the breaking strain of the crane is 6,400 kilograms and each crate is 90 kilograms.
Thus, to know the number of crates (n) that can safely lift is equal to the weight of the crane is 6,400 kilograms divided by is 90 kilograms.
thus,
[tex]n=\frac{weight of the crane}{weight of each crate}\\ \\n=\frac{6400}{90}[/tex]
so, n= 71.111≈71
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help meeeeee plssss with steps
Answer:
p = 18, q = 0
Step-by-step explanation:
The expression on the left side of the equation is
[tex]\large \text {$ \dfrac{\sqrt{5}+\:2}{\sqrt{5}-2}+\dfrac{\sqrt{5}-\:2}{\sqrt{5}+2} $}[/tex]
Multiply the denominators to get a common denominator:
[tex]\text{$\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)$}[/tex]
= [tex]\left(\sqrt{5}\right)^2-2^2[/tex] ∵ (a + b)(a - b) = a² - b²
[tex]=5-4\\\\= 1[/tex]
[tex]\large \text {$ \dfrac{\sqrt{5}+\:2}{\sqrt{5}-2}+\dfrac{\sqrt{5}-\:2}{\sqrt{5}+2} $}\\\\[/tex]
[tex]=\dfrac{\left(\sqrt{5}+2\right)\left(\sqrt{5}+2\right)}{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)} + \dfrac{\left(\sqrt{5} - 2\right)\left(\sqrt{5} - 2\right)}{\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)}[/tex]
Since denominator
[tex]\text{$\left(\sqrt{5}-2\right)\left(\sqrt{5}+2\right)$} = 1,[/tex]
the expression becomes
[tex]=\left(\sqrt{5}+2\right)^2 + \left(\sqrt{5}-2\right)^2\\\\= 5 + 4\sqrt{5} + 4 + 5 - 4\sqrt{5} + 4\\\\[/tex]
[tex]= 10 + 8 = 18[/tex]
Therefore
[tex]\large \text {$ \dfrac{\sqrt{5}+\:2}{\sqrt{5}-2}+\dfrac{\sqrt{5}-\:2}{\sqrt{5}+2} = p + q\sqrt{5}$}\\\\\\= > \large \text{$ 18 = p + q\sqrt{5}$}[/tex]
Now [tex]\sqrt{5}[/tex] is an irrational number and p = rational so since there is no [tex]\sqrt{5}[/tex] term on the left side, q = 0 and p = 18
A local car dealership is trying to sell all of the cars that are on the lot. Currently, there are 725 cars on the lot, and thegeneral manager estimates that they will consistently sell 50 cars per week.1. Write and solve an inequality that can be used to find the number of full weeks, w, it will take for the number ofcars to be fewer than 125. Since w is the number of full or complete weeks, w = 1 means at the end of week 1.
Number of cars in the lot = 725 cars
W is the number of full or complete weeks
Also, 50 cars per week = 50w;
For every week, the cars will be reducing by 50;
(A) Hence , the inequality is given as;
[tex]725-50w<125[/tex][tex]\begin{gathered} 725-125<50w \\ 600<50w \\ \frac{600}{50}12 \end{gathered}[/tex]Moving waves can be described either as a function of time or as a function of
a. amplitude.
b. frequency.
c. speed.
d. position.
Moving waves can be described either as a function of time or as a function of position
What is a wave?A wave is a dynamic disturbance of one or more quantities that propagates in physics, mathematics, and related sciences. When waves oscillate frequently around an equilibrium value at a certain frequency, they are said to be periodic.
In a medium, a wave is a disturbance or variation that gradually transfers energy from one point to another. It can be an elastic deformation or a change in pressure, electric or magnetic strength, electric potential, or temperature.
It should be noted that it can be a function of the position as well as the time.
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A Sony LCD TV has a selling price of $925 and a 62% markup on selling price. What is the dollar markup and what is the cost?
Answer
Selling price = $ 925
Mark percentage = 62%
[tex]\begin{gathered} \text{Let's x represent Cost price i.e C. P=x} \\ \text{Selling price =C P +profit} \\ Profit\text{ =}\frac{\text{62x}}{100} \\ \\ S\text{. P =x+}\frac{\text{62x}}{100} \\ S\text{. P=x+0.62x} \\ S\mathrm{}P=1.62x \\ \therefore1.62x=925 \\ \end{gathered}[/tex][tex]\begin{gathered} \therefore1.62x=925 \\ \text{Divide both sides by 1.62} \\ \therefore\frac{1.62x}{1.62}=\frac{925}{1.62} \\ \\ x=570.99 \end{gathered}[/tex]The cost price is 570.
Jonah studied z hours for a big test. Francesca studied a fourth as long. Write an algebraic expression for long Francesca studied.
The expression for study hours of Francesca will be ( Z + 4 ) hours.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Jonah studied z hours for a big test. Francesca studied a fourth as long as Jonah studied.
The expression will be written as Francesca studied 4 hours more than Jonah.
Francesca's study time = ( Z + 4 ) hours
Therefore, the expression for study hours of Francesca will be ( Z + 4 ) hours.
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Pls help need asap!thx
Answer:
(0,7]
Step-by-step explanation:
It is an open circle at 0 and a closed circle at 7.
The midpoint of AB is M(6, 3) . If the coordinates of A are (7, 4) , what are the coordinates of B?
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +7}{2}~~~ ,~~~ \cfrac{ y +4}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE M}}{(6~~,~~3)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +7}{2}=6\implies x+7=12\implies \boxed{x=5} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +4}{2}=3\implies y+4=6\implies \boxed{y=2}[/tex]
Which graph represents the solution set of the system of inequalities?
The correct graph that represents the solution set of the system of inequalities is in Option(b).
What is Inequality in mathematics?Inequality is a statement of an order relationship (greater than, greater than, or equal to, less than, or less than or equal to) between two integers or algebraic expressions in mathematics.
The given system of inequalities are,
y < -3x - 2
y ≤ x - 2
We have to select the graph that represents the solution set of the system of inequalities.
y < -3x - 2
Let, y = -3x - 2
Now, plot the graph of the line y = -3x - 2 with a Dotted line ( as < is a strict inequality).
y ≤ x - 2
Let, y = x - 2
Now, plot the graph of the line y = x - 2 on the graph.
The area between the two lines of inequalities on the graph represent the solution set.
Upon comparison with the graphs in the options, the correct graph is present in Option(b).
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After a 70% reduction, you purchase a new clothes dryer on sale for $204. What was the original price of the
clothes dryer?
Answer:$346.8
Step-by-step explanation:
1. X - 70% = 204
Want to get the value of X
2. X + 70% = 204 + 70%
= X = 204 x 1.7
= X = $346.8
Answer:
Original Price = $680
Step-by-step explanation:
Think about what a 70% reduction in price means.
If the original price of an item is $100 then a 70% reduction would mean that it costs 70% less from the original price. This means you would be paying only 30% of the original price
Let the original price be $P
Then the price you pay after 70% reduction is 30% of P
= P x 30/100
= P x 0.3 (30% = 30/100 = 0.3)
= 0.3P
We are given that this sale price = $204
--> 0.3P = 204
Dividing both sides by 0.3 gives us the value for P
0.3P/0/3 = 204/0.3
P = 204/0.3 = 680
So
Original Price = $680
We can double check our computations as follows
If original price = 680, then a reduction of 70% would be a discount of
0.7 x 680 = 476
Price after discount = Original Price - Discount
= 680 - 476 = 204
So our results are consistent
building a is 881 ft tall and contains 66 stories. building b contains 103 stories. if the two buildings have the same number of feet per floor approximately the height of building b. what is the approximate height of building b?
Answer:
approximately 1,375 feet
Step-by-step explanation:
Set up and solve this proportion:
[tex] \frac{881}{66} = \frac{h}{103} [/tex]
[tex]66h = 90743[/tex]
[tex]h = 1375[/tex]
So the height of building b is about 1,375 feet.
can u pls help me with this question
Answer:
Explanation:
eight of the bush when it was first planted int he garden = 12cm
After 2 weeks, its height = 120% of Height when it was planted.
[tex]=120\%\text{ of 12cm}[/tex]We solve for the result.
[tex]\begin{gathered} =\frac{120}{100}\times12 \\ =1.2\times12 \\ =14.4\operatorname{cm} \end{gathered}[/tex]The bush was 14.4cm tall after two weeks.
Translate the sentence into an equation
Nine times the sum of a number and 7 is equal to 5
Use the variable y for the unknown number
what is the measure of a
Answer:
Measure of Angle A is 100°
Step-by-step explanation:
The sum of interior angles of a polygon is given by the formula :
(n-2)×180 (where n is the number of sides)
n = 6
(6-2)×180 =
4 × 180 = 720
So :
A + B + C + D + E + F = 720
Substitute values given in diagram (angle d is 90 as the little square indicates a right angle) (Calling angle a as x) :
x + 135 + 115 + 90 + 110 + 170 = 720
Simplify :
x + 620 = 720
Subtract 620 from both sides :
x = 720 - 620
x = 100
Measure of Angle A is 100°
Hope this helped and have a good day
HELP INTERSECTIONS AND UNIONS!!
Given: A= {0,3,5,7,9,11,12}
B={-3,5,8,9,11,14}
C={-2,1,5,7}
1.) (A ∩ B) U C
2.) (B U C) ∩ A
The most appropriate choice for sets, union and intesrsection of set will be given by
1) (A ∩ B) U C = {-2, 1, 5, 7, 9, 11}
2) (B U C) ∩ A = {5, 7, 9, 11}
What is set and union and intersection of set?
Set is a well defined collection of distinct objects. Set can be empty as well as non empty.
Writing all the elements of two or more sets together in one set is known as union of sets.
Writing the common elements of two or more sets in one set is known as intersection of sets.
Given,
A= {0,3,5,7,9,11,12}
B={-3,5,8,9,11,14}
C={-2,1,5,7}
For 1)
(A ∩ B) = {5, 9, 11}
(A ∩ B) U C = {-2, 1, 5, 7, 9, 11}
For 2)
(B U C) = {-3, -2, 1, 5, 7, 8, 9, 11, 14}
(B U C) ∩ A = {5, 7, 9, 11}
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In how many ways can the digits in the number 9666111 be arranged?
========================================================
Explanation:
The unique digits are: 9, 6, 1
9 shows up once6 shows up three times1 shoes up three timesThere are 1+3+3 = 7 digits with the repeats mentioned. If we could somehow tell the 6's apart and the 1's apart, then we'd have 7! = 7*6*5*4*3*2*1 = 5040 different permutations.
But because we can't tell the 6's apart, nor the 1's apart, this means we have to divide by (3!*3!). Each 3! represents the number of times the 6's show up and same goes for the 1's.
So (5040)/(3!*3!) = 5040/(6*6) = 5040/36 = 140 is the number of ways to rearrange the digits
Help me with this question within 1-5 minutes please
Answer:
[tex]-12w + x[/tex]
Step-by-step explanation:
question:
[tex]-3w - 3x - 7w + 4x - 2w[/tex]
first you add all the 'w' together.
(-3)+(-7)+(-2) = -10+(-2)=-12
so, [tex]-12w - 3x + 4x[/tex]
second you add all the 'x' together
(-3)+(4) = 1
so, [tex]-12w+1x[/tex]
then simplify:
[tex]-12w + x[/tex] <--answer
hope this helps!
Shandra owns a goldfish that currently weighs 0.50 ounces. With each inch that the goldfish grows, the goldfish weighs an additional0.15 ounces.PARTACreate an equation that Shandra can use to find the number of inches, r, it will take for the goldfish to weigh 1.1 ounces.PART BHow many more inches does the goldfish need to grow to weigh 1.1 ounces?inches
A.
The initial weight of the goldfish is 0.5 ounces.
Then, for each inch it grows, its weight increases by 0.15 ounces.
So, using the variable r to represent the number of inches it grew, we can write the following equation to determine the value of x for a weight of 1.1 ounces:
[tex]0.5+0.15r=1.1[/tex]B.
Solving the equation for r, we have:
[tex]\begin{gathered} 0.15r=1.1-0.5 \\ 0.15r=0.6 \\ r=\frac{0.6}{0.15} \\ r=4 \end{gathered}[/tex]It needs to grow 4 more inches.
QUESTION 3After surgery a patient was put on a restricted diet. In the first 2 days after surgery the patient was only allowed to consume•800 Cal/day. In the following 3 days the patient was allowed to consume 1100 Cal/day. In the final 4 days at the hospital thepatient was allowed to consume 1500 Cal/day.a) What was the average energy per day consumed? Round answer to the one if necessary.b) What is the unit symbol for the answer?
Given the patient consumption rate on his diet:
[tex]\begin{gathered} 1-2\text{days}=\text{ 800 Cal/day} \\ 2-3\text{days}=1100\text{ Cal/day} \\ 3\text{ -4days=1500 Cal/day} \end{gathered}[/tex](a) Average energy per day consumed will be since the number of days = 4
[tex]\begin{gathered} =\frac{800+1100+1500}{4} \\ =\frac{3400}{4} \\ =850\text{ Cal} \end{gathered}[/tex]The average energy per day consumed = 850 Cal(b) The unit symbol for the answer = calorie