five more than the quotient of nine and three
Answer:
n / 9 + 5 = 3
Step-by-step explanation:
1) Is it possible to end up with two different prime factorizations for a number, or will you always end up with the same list of prime factors?
2) What was true about all of the numbers in the final lists of factors? Why?
3) Can two different numbers have the same prime factorization? Why or why not?
4) Explain how writing a number as a product of prime numbers is a way of representing that number.
How does knowing that the prime factorization of 40 is 2 × 2 × 2 × 5 help you know every possible factor of 40?
5) How is what you did in the Action Task related to the colour code in the Minds On Activity?
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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Find the area, in square units, of AABC plotted below.
C(-6,-2)
D(-7,-5) d
A(-4,-6)
B(2,-8)
Check the picture below.
so the base of that triangle is AB whilst the height of it is CD, so let's get them
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-6})\qquad B(\stackrel{x_2}{2}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(~~2 - (-4)~~)^2 + (~~-8 - (-6)~~)^2} \implies AB=\sqrt{(2 +4)^2 + (-8 +6)^2} \\\\\\ AB=\sqrt{( 6 )^2 + ( -2 )^2} \implies AB=\sqrt{ 36 + 4 } \implies AB=\sqrt{ 40 }\implies \stackrel{base}{AB=2\sqrt{10}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ C(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\qquad D(\stackrel{x_2}{-7}~,~\stackrel{y_2}{-5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ CD=\sqrt{(~~-7 - (-6)~~)^2 + (~~-5 - (-2)~~)^2} \\\\\\ CD=\sqrt{(-7 +6)^2 + (-5 +2)^2} \\\\\\ CD=\sqrt{( -1 )^2 + ( -3 )^2} \implies CD=\sqrt{ 1 + 9 } \implies \stackrel{height}{CD=\sqrt{ 10 }} \\\\[-0.35em] ~\dotfill[/tex]
[tex]A=\cfrac{1}{2}(\stackrel{b}{2\sqrt{10}})(\stackrel{h}{\sqrt{10}})\implies A=\sqrt{10}\cdot \sqrt{10}\implies A=\sqrt{10^2}\implies {\Large \begin{array}{llll} A=10 \end{array}}[/tex]
What is the slope of a line perpendicular to the line whose equation is 3x-6y=144
Answer: 1/2
Step-by-step explanation:
If we have an equaton in a standard form, that is y = mx + b, our slope is m (the coefficient of x). So, let's transform 3x - 6y = 144 into the standard form.
3x - 6y = 144
-6y = - 3x + 144
y = -3/(-6)x - 144/6
y = (1/2)x - 24
As I mentioned above, the slope is the coefficient of x. Here our slope is 1/2.
In an office building, 88 offices are currently being rented. This represents 80% of the total units. How many offices are there in the building?
There are offices in the building.
Answer:4
Step-by-step explanation:
The carnival is in town and has a game where players try to throw darts at a rectangular target. The length of the target is 2 centimeters shorter than twice the width. If the perimeter of the target is 20 centimeters, find the dimensions of the target.
The length of the target is 4cm and the width of the target is 6cm.
What are the dimensions of the target?A rectangle is an object that has four sides and four right angles. The sum of angles in a rectangle is 360 degrees. The perimeter of a rectangle is the distance round the rectangle.
Perimeter = 2( length + width)
Length = w - 2 Width = w20 = 2(w - 2 + w)
20 = 2(2w - 2)
20 / 2 = 2w - 2
10 = 2w - 2
10 + 2 = 2w
12 = 2w
w = 12/2
w = 6
Length = 6 - 2 = 4
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Which Macabacus add-in feature automatically calculates the column totals in the data table and inserts them into the column chart as displayed on the right?
Answer:
Yes
Step-by-step explanation:
Answer: Charts -> Stacked Totals -> Stacked Bar Totals
Step-by-step explanation:
after filling in in Macabacus the only add in feature that puts totals is stacked bar
4 1/3 — 2 7/9
Please help quick
Answer: 1 2/3 or 5/3
Step-by-step explanation: if you change 4 1/3 to a different denominator of 9, you will get 4 3/9. Then, you will do 4 3/9-2 7/9 which equals 1 2/3.
What is the reciprocal of 3 7/8
The reciprocal of 3 7/8 is 8/31.
To find the reciprocal of a number, we invert the fraction by swapping the numerator and denominator.
Let's calculate the reciprocal of 3 7/8.
First, we need to convert the mixed number into an improper fraction. To do this, we multiply the whole number (3) by the denominator (8) and add the numerator (7). This gives us:
3 7/8 = (3 x 8 + 7) / 8 = 31/8
Now, to find the reciprocal, we invert the fraction:
Reciprocal of 31/8 = 8/31
Therefore, the reciprocal of 3 7/8 is 8/31.
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PLEASE HELP ME WITH THIS
The simplified form of the given expression is x + a - 4
Simplifying an ExpressionFrom the question, we are to simplify the given expression
From the given information, we have that
g(x) = x² - 4x,
Now,
We are to simplify
[tex]\frac{g(x)-g(a)}{x -a}[/tex]
First, we will determine g(a)
From the given function,
g(x) = x² - 4x
∴ g(a) = a² - 4a
Thus,
[tex]\frac{g(x)-g(a)}{x -a}[/tex] becomes
[tex]\frac{x^{2} -4x-(a^{2}-4a)}{x -a}[/tex]
[tex]\frac{x^{2} -4x-a^{2}+4a}{x -a}[/tex]
[tex]\frac{x^{2} -a^{2} -4x+4a }{x -a}[/tex]
Factoring
[tex]\frac{(x+a)(x-a)-4(x-a) }{x -a}[/tex]
Further factorization
[tex]\frac{(x-a)((x+a)-4) }{x -a}[/tex]
Dividing
((x +a) -4)
x + a - 4
Hence,
The simplification gives x + a - 4
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Please help
The second angle of a triangle is 104 more than the first angle. The third angle is two times the first. Find
the three angles.
First angle:
Second angle:
Third angle:
estimate. i need help
Answer:
350'000
Step-by-step explanation:
The real # is 369,852, so 350,000 is closest to all the other options.
Can someone help me on these three questions? can someone solve and show me how you did it so i can understand
The graph of the function gives the type of function, (continuous or discrete function) the domain and the range as follows;
(A, 2A)
First graph;
Discrete function
Domain; {x| x = -8, -2, 3, 6}
Range; {y| y = 5, 4, -2, 7, }
Second graph
Continuous function
Domain; -4 < x < ∞
Range; 1 ≤ y < 9
(A3.A) 1. The slope of the graph is -1.5
2. The slope of the graph is 1.5
What is a function?A function is an equation defining the relationship between input and output variables
(A, 2A)
A continuous function is one in which a continuous variation in the input values produces a continuous variation in the output. Therefore, a continuous function does not have discontinuity and it has a defined output within the interval in which it is contagious
A discrete function is one that have input values and output only at specified points, such that the function does not have inputs, and therefore, outputs at certain points.
The points in the scatter plot of the first graph are separate and not linked, such that the function is not contagious between any two x–values, which gives;
The function is a discrete function
The domain, which is the set of possible x–values is; {x| x = -8, -2, 3, 6}
The range is {y|y = 5, 4, -2, 7, }
The line joining the points on the second graph, indicates that the graph has values for all input or x–values
Therefore, the function of the graph is a continuous function
The domain is; -4 < x < ∞The range is 1 ≤ y < 9(A3. A) 1. Points on the graph are:
(0, 2), (2, -1)
The slope is given by the equation;
Slope = ∆y ÷ ∆x
Which gives;
Slope = (-1 - 2)/(2 - 0) = -3/2 = -1.52. The given function is; -3•x + 2•y = -6
To find the slope, the function is expressed in the slope and intercept form, y = m•x + c, as follows;
-3•x + 2•y = -6
2•y = 3•x - 6
Therefore;
2•y = 3•x - 6
y = (3•x - 6) = 1.5•x - 3
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grade 12 mathematics
The value is =[tex]\frac{-73}{22}[/tex]
What is limit ?The values that a function approaches for the specified input values are known as limits in mathematics. Limits are essential to calculus and mathematical analysis because they help define concepts like integrals, derivatives, and continuity. It's employed in the analysis process and always has to do with how the function behaves at a specific moment. In the idea of the limit of a topological net, the limit of a sequence is further generalized and connected to the limit and direct limit in the theory category.
Given That : [tex]\lim_{x \to \33} \frac{(Fx)^{3}-3x }{2x^{2} -f(x)}[/tex] and f(x)= -4
[tex]\lim_{x \to \33} \frac{(Fx)^{3}-3x }{2x^{2} -f(x)}[/tex]
F(x)= -4
=[tex]\frac{-64-9}{18+4}[/tex]
=[tex]\frac{-73}{22}[/tex]
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Two similar solids are given, find the missing information. Please
step 1
Find out the scale factor
Remember that
If two figures are similar, then the ratio of their volumes is equal to the scale factor elevated to the cubic
so
Let
s ----> scale factor
s^3=11,000/8,019
s=1.11
step 2
Remember that
If two figures are similar, then the ratio of their surface areas is equal to the scale factor squared
so
s^2=SA/1,134
s=1.11
1.11^2=SA/1,134
SA=(1.11)^2*(1,134)
SA=1,400 yd2
The answer is 1,400 square yardsIf “d = rt” then “t = [?] / [?].” Substitute the correct variable for the question mark in the numerator and denominator.Select one:a. r/db. d/rc. t/dd. .t/r
To solve the equation;
[tex]d=rt[/tex]To solve for t, we shall take the following steps;
[tex]\begin{gathered} d=rt \\ \text{Divide both sides by r;} \\ \frac{d}{r}=\frac{rt}{r} \\ r\text{ cancels out r on the right side of the equation;} \\ \frac{d}{r}=t \\ \text{Therefore;} \\ t=\frac{d}{r} \end{gathered}[/tex]ANSWER:
The correct answer is option (b)
[tex]\frac{d}{r}[/tex]Help with this problem pls
nswer:
[tex](f\circ g)(x)\text{ = 4x}^2+26x+29[/tex]Explanation:
ere, we want to solve the given composuite function
What we have to do is to replace the x in f(x) with the entirety of g(x)
We have that as:
[tex]\begin{gathered} (f\circ\text{ g\rparen\lparen x\rparen = f\lparen g\lparen x\rparen\rparen} \\ =\text{ f\lparen2x+9\rparen} \end{gathered}[/tex]Now, we replace x in f(x) with 2x+9 as stated
We have that as:
[tex]\begin{gathered} f(2x+9)\text{ = \lparen2x+9\rparen}^2-5(2x+9)\text{ - 7} \\ f(2x+9)\text{ = 4x}^2+36x+81-10x-45-7 \\ f(2x+9)\text{ = 4x}^2+36x-10x+81-45-7 \\ f(2x+9)\text{ = 4x}^2+26x+29 \end{gathered}[/tex]2+ I5rI = 12 Solve each equation
The solution of the equation for the values of r is -2 and 2.
What is referred as the modulus function?A modulus function returns the magnitude of such a number regardless of its sign. It's also known as the absolute value function.The modulus function, signified by |x| in mathematics, gives the modulus of a real number x. It returns a non-negative value for x. The modulus but rather absolute value of the a number is also known as the number's distance from its origin or zero.For the expression
2+ I5rI = 12
Subtract both side by 2
2 + I5rI -2 = 12 - 2
I5rI = 10
Open the modulus function as;
-5r = 10+5r = 10Solve for each term
-5r = 10
Divide both side by -5,
r = 2
Now,
5r = 10
Divide both side by 5,
r = 2
Therefore, the solution of the equation is for r = -2 and 2.
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Laura is paid only on commission. She is paid weekly and receives 1.6% of her gross sales. Last week, she had sales of $57000, $23000, $41000, $49000, and $37000. What is Laura's weekly commission?
Answer:
$3,312.00
Step-by-step explanation:
If we add up her sales we get 207,000
We multiply that by .016 to get $3,312.00
What is an equation of the line that passes through the points (5, 0) and
-2, -3)?
Answer:
Equation of line is given as y = mx + c, where m is the gradient and c is the y-intercept.
Find gradient of the line first.
Formula of gradient is given as y2-y1 ÷ x2-x1 or y1-y2 ÷ x1-x2, where x and y are the coordinates of the points.
Gradient = (-3-0) ÷ (-2-5) = 3/7
Eqn is y = 3/7x + c
Substitute either one of the coordinates into the equation to find c.
0 = 3/7(5) + c
c = -15/7
Hence, the equation of the line is y = 3/7x - 15/7
Joanne and her friends went on a hiking vacation to the national park. They
covered 2 miles on the first day. They went on a 4-mile hike and 8-mile hike on
day 2 and day 3, and the hiking distance continued to increase in a geometric
sequence. How many miles did Joanne and her friends hike on the 4th day?
Answer: 16 miles
Step-by-step explanation:.
A cell phone company charges $55 a month for unlimited text and $0.50 per minute for phone calls. The bill last month was $66. Write an equation to find out how many minutes for phone calls were charged on the bill. (use notes in the Schoology "Notes" folder)
we can write an equation
[tex]T=55+0.50m[/tex]where T is the total price, 55 the fixed charge, 0.5 the cost per minute and m the minutes used
if the total is 66 we must to replace T=66 and solve m
so
[tex]\begin{gathered} 66=55+0.50m \\ 0.50m=66-55 \\ m=\frac{11}{0.50} \\ \\ m=22 \end{gathered}[/tex]were charged 22 minutes on the bill
Can anyone explain this?
Answer:
Using a class size of 6.
Range = Highest value - Lowest value = 100 - 1 = 99
No. Of class = range/class size = 99/6 = 16.5 ~ 17/classes.
Upper-class limit of class (1) = Lower class limit of class (1) + class size - D
=> 1 + 6 - 1 = 7 - 1 = 6
.: UCL1 = 6
The table is shown below:
please help me with this problem
answer:
[tex]\frac{-c-d}{d+2c}[/tex]the third one
The length of a rectangle is 21 yards. The width of the rectangle is 5 yards. What isthe area of the rectangle?
To find the area of a rectangle, we can use the following formula
[tex]Aread\text{ of a reactangle = \lparen length\rparen}\times\text{ }(width)[/tex]Therefore, to find the total area we have to multiply his length by his width.
Using the data given in the question, we know that the length is 21 yards and the width is 5 yards. Therefore we find that:
[tex]Area\text{ of the rectangle =}(21\text{ yards\rparen}\times\text{ \lparen5 yards\rparen}=105\text{ yards}^2[/tex]we conclude that the area of the rectangle is 105 yards^2.
Note that the units of the area are square units
Shantel told her hired hand Warren to gather eggs from the henhouse. Warren collected 30 eggs and brought them to Shantel. Shantel inspected
them and complained that 40% of them were broken. How many of them were still good eggs?
eggs were still good.
Answer:
18 eggs are still good.
Step-by-step explanation:
If 40% was broken then 60% are still good.
30(.6) = 18
Answer: 18 eggs were not broken and considered good.
Step-by-step explanation: 30 x 40% is the amount of eggs that were broken.
30 x 60% would be the amount of eggs that were still good.
This is becuase the total percentage must add up to be 100% between good eggs and broken eggs.
30 x .60 = 18 So 18 eggs were good
30 x .40 = 12, so that was the number of eggs that were broken
You could have done this problem two ways. Either calculate the broken eggs and subtract from the total. 30-12 = 18, or you could have just calculated the correct amount from figuring the percentage of eggs that were good from the beginning.
Graph H(x) =|x+5| and t(x)=|2x+5|
The graph of the function H(x) = "x+5" and the graph of the function t(x) = "2x+5" are displayed in the picture that is attached below.
This is further explained below.
What is Graph?Generally, The set of ordered pairings that satisfy the condition [tex]"\displaystyle f(x)=y"[/tex] is the graph of the function f.
These pairings, which are Cartesian coordinates of points in two-dimensional space and hence constitute a subset of this plane, are found under the usual scenario in which both x and f(x) are real values.
In conclusion, The Graph of the function H(x) =|x+5| and t(x)=|2x+5| is given in the image attached below.
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A plant biologist studies the height of sunflowers. He measures a large sample of sunflowers and creates a probability distribution. The distribution is normal in shape with mean 112 cm and standard deviation 16 cm.
What is the probability (approximately) that a sunflower will be less than 136 cm tall?
Enter a number in decimal form, e.g. 0.68, not 68 or 68%.
The probability that sunflower will be less than 136 cm tall is 0.9332.
How to calculate the probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
From the information, the biologist measures a large sample of sunflowers and creates a probability distribution and the distribution is normal in shape with a mean 112 cm and a standard deviation 16 cm.
It should be noted that the following can be deduced:
Mean = 112
Standard deviation = 16
Sunflower should be less than 136. This will be x < 136.
Therefore, the probability will be;
P(X < 136)
= P(Z < [(number - mean) / standard deviation)]
= P(Z < [136 - 112)/16]
= P(Z < 1.50)
= 0.9332
It should be noted that the probability is gotten by looking at the value of x in the z table.
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Given a piece of metal with a mass of 124 grams and a volume of 21 cubic centimeters (cm^3) what is its density? Use the correct formula to obtain your answer. You may work on a separate piece of paper.
13.6 g/cm^3
88 g/cm^3
5.9 g/cm^3
0.21 g/cm^3
We need to know about density to solve this problem. The density of the piece of metal is 5.9 g/[tex]cm^{3}[/tex], so option (c) is the correct answer.
Density is a substance's mass per unit volume. The symbol commonly used for density is ρ. Density can be calculated by dividing the mass by volume. In this question we know that mass of the metal piece is 124 grams and the volume is given to be 21 cubic centimeters. The density can be calculated by dividing the mass by volume of the metal piece.
density =mass/ volume= 124/21=5.90 g/[tex]cm^{3}[/tex]
Therefore the density of the piece of metal is 5.9 g/[tex]cm^{3}[/tex] , so option (c) is the correct answer.
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Please help I’ll mark you as brainliest if correct!!!
Answer:
1710
Step-by-step explanation:
simplify | 1×10^3 + 7×10^2 + 4×10 = 1710