By finding a common factor, we can rewrite the expression as:
54 + 72 = 18*(3 + 4)
How to rewrite the expression?The distributive property says that we can write:
C*(A + B) = C*A + C*B
In this case, we want to rewrite the expression:
54 + 72
So the first thing we need to find is a common factor between these two numbers.
We can rewrite these as:
54 = 2*3*3*3
72 = 2*2*2*3*3
The maximum common factor between these two nmbers is:
2*3*3 = 18
Then we can rewrite:
54 = 18*3
72 = 18*4
Then we can rewrite the expression as:
54 + 72 = 18*3 + 18*4 = 18*(3 + 4)
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Given U(-6, 7), V (1, -7), W (6, 4), and X (10, y). Find y such that
UV LWX.
Fine Floors can install 15 square yards of carpeting in 4 hours 30 minutes. At this rate, how long would it take to install carpeting in a room that measures 11 feet 9 inches by 13 feet 4 inches?
Answer:
Step-by-step explanation:
To figure out how long it would take Fine Floors to install carpeting in a room that measures 11 feet 9 inches by 13 feet 4 inches, we first need to determine how many square yards of carpeting are needed for the room. We can start by converting the dimensions of the room from feet and inches to yards, since that's the unit of measurement we're working with.
To convert feet to yards, we divide by 3. For example, 11 feet is equal to 11/3 = 3.67 yards. To convert inches to yards, we divide by 36 (since there are 36 inches in a yard). For example, 9 inches is equal to 9/36 = 0.25 yards.
So the length of the room in yards is 3.67 + 0.25 = 3.92 yards, and the width of the room in yards is 13/3 + 4/36 = 4.33 + 0.11 = 4.44 yards.
To determine the total area of the room in square yards, we multiply the length and width: 3.92 * 4.44 = 17.38 square yards.
Now that we know how many square yards of carpeting are needed for the room, we can use that information to calculate how long it would take Fine Floors to install the carpeting. Since we know that Fine Floors can install 15 square yards of carpeting in 4 hours 30 minutes, we can use that as the ratio for our calculation.
To calculate how long it will take to install 17.38 square yards of carpeting, we use the proportion:
(15 sq. yards) / (4 hours 30 minutes) = (17.38 sq. yards) / (x hours)
Cross multiplying and solving for x, we find: x = (4 hours 30 minutes) * (17.38 sq. yards) / (15 sq. yards)
So it would take Fine Floors approximately 5 hours and 11 minutes to install carpeting in a room that measures 11 feet 9 inches by 13 feet 4 inches.
Answer the problem in the photo below! Please answer simply:)
Answer:
32
Step-by-step explanation:
Let's start with x to the third power. x=4 So that would be 4 to the third power. that would be 4x4=16. 16x4=64. So that would be 1/2*64. That equals 32
A paint store makes lime green paint by mixing 3 parts yellow paint to 1 part blue paint. A clerk mixès 5 parts yellow paint to 2 parts blue paint. did the clerk use the correct ratio of yellow paint to blue paint? Explain.
Answer:
No
Step-by-step explanation:
The ratio used should have been 6 parts yellow paint to 2 parts blue paint
hope this helps
$29, $58, $15, $75, and $22. Find the mean absolute deviation
The mean absolute deviation of $29, $58, $15, $75, and $22 is $32.67.
How to calculate the mean deviation?The average (mean) distance between each data value and the data set mean is known as the mean absolute deviation, or MAD. The average distance between each data point and the mean is known as the mean absolute deviation of a dataset. It provides insight into a dataset's variability.
From tje information, it should be noted that the mean will be:
= (29 + 58 + 15 + 129+ 75 + 22) / 6.
= 54.67
Means absolute deviation = 1/6+25.67 + 3.33 - 39.67 + 74.33 + 20.33 + 32.67)
= 32.67
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Complete question
Find the mean absolute deviation of the fulfilled items on Sherrie's registry: $29, $58, $15, $129, $75 & $22.
A biology class examined some flowers in a local meadow. They saw 36 flowers, of which 25% were perennials. How many perennial flowers did the students see?
Answer: nine
Step-by-step explanation: 36 - 25 = 9 or 25% x 1 + 36 = 9
Answer:
9
Step-by-step explanation:
1 first split 36 by 4 because 25% is 1/4
2 once when divided you should get 9 because 9x4 is 36
what is 1+2+3+4+...+1000?
Answer:
[tex]S_{1000}=500500[/tex]
Step-by-step explanation:
[tex]\displaystyle S_n=\frac{n(a_1+a_n)}{2}=\frac{1000(1+1000)}{2}=500*1001=500500[/tex]
3x+1
1. A function f: x →
X-1
(i)
Find the images of -1 and 3.
(ii)
Find the value of x for which f(x) = 7
2. The set P = {-2,-1,0,1,2} maps onto Q by the function f(x)=x²-2, where x E P.
(i)
Find the elements of Q.
(ii)
3. Given that f(x) = 2x - 1 and g(x) = x² +1:
Find f(1 + x):
Find the range of values of x for which f(x) < -3;
Simplify f(x) - g(x).
(i)
(ii)
(iii)
,x # 1, is defined on the set (-1, 0, 2, 3, 4, 5)
Draw a diagram showing the mapping between P and Q.
(i)
4. The function f and g are defined as follows: f:x →→ 2
x-1 and g:x→ 3x + 1
Evaluate f(-) +1
(ii)
Solve f(x) = g(-2)
5. Given that f(x) = px + q, find the values od p and q, if f(2)= 4 and f(4) == 10
The function f is defined as f:x→ 3x² - 5x.
6.
(i)
Evaluate f(--3)
(ii)
7. The functions f and g are defined as: f:xx-2 and g: x2x²-1. Solve:
(i) f(x) = g(-²/-) (ii) f(x) + g(x)= 0
4
Find the values of x for which f(x) = -² 3
On solving the provide the question, we can say that - the value of the following function is f(x) = -5x - 1.
what is function?The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
[tex]x = -2, y = 9; x = -1 , y = 4; x =0, y = -1.[/tex]
x = 0 , y = -1 so c = -1.
slope of line [tex]= (4-9) / (-1-(-2)) = -5/ 1 = -5.[/tex]
function f(x) = -5x - 1.
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Answer:
Step-by-step explanation:
1. (i) f(-1) = 3(-1) + 1 = -2 and f(3) = 3(3) + 1 = 10
(ii) To find the value of x for which f(x) = 7, we can set f(x) equal to 7 and solve for x:
3x + 1 = 7
3x = 6
x = 2
2. (i) Q = {x² - 2 | x E P} = {(-2)² - 2, (-1)² - 2, (0)² - 2, (1)² - 2, (2)² - 2} = {4, 0, -2, -1, 2}
(ii) As f(x)=x²-2, and P = {-2,-1,0,1,2} mapping into Q is {-2,-1,0,1,2} to {4,0,-2,-1,2}
3. (i) f(1 + x) = 2(1 + x) - 1 = 2x + 1
(ii) To find the range of values of x for which f(x) < -3, we can set f(x) equal to -3 and solve for x:
2x - 1 < -3
2x < -2
x < -1
so x can be any value less than -1
(iii) f(x) - g(x) = (2x - 1) - (x² + 1) = 2x - x² - 2
4. (i) f(-1) + 1 = 2(-1) - 1 + 1 = -1
(ii) To solve f(x) = g(-2), we can substitute the expressions for f(x) and g(x) into the equation:
2x - 1 = 3(-2) + 1
2x - 1 = -5
2x = -6
x = -3
5. f(x) = px + q, given that f(2)= 4 and f(4) == 10
so
4 = 2p + q
10 = 4p + q
solving for p and q we get p = 3 and q = -2
6. (i) f(--3) = 3(-3)² - 5(-3) = -27
7. (i) To solve f(x) = g(-2/-4), we can substitute the expressions for f(x) and g(x) into the equation:
x-2 = (1/4)x² - 1
x-2 = x²/4 - 1
4x-8 = x²-4
x²-4x+4 = 0
x = 2, -2
(ii) To solve f(x) + g(x) = 0
x-2 + x²-1 = 0
x²-2x+1 = 0
(x-1)² = 0
x = 1
for f(x) = -² 3 the expression does not make sense, but assuming the -² is just typo then we can solve for x by substituting f(x) = -3
into the expression of f(x) = 3x² - 5x
3x² - 5x = -3
3x² - 5
A construction company is building a fence that is 1 1/3 miles long. They can building the fence 1/6 Mile every hr. How long to build the
The length of time to build the fence is 8 hours
How to determine the length of time to build the fenceFrom the question, we have the following parameters that can be used in our computation:
Length of the fence = 1 1/3 miles
Rate of building = 1/6 miles per hour
The length of time to build the fence is then calculated as
Length of time = Length of the fence/Rate of building
Substitute the known values in the above equation, so, we have the following representation
Length of time = (1 1/3 miles)/(1/6 miles per hour)
Evaluate the quotient
This gives
Length of time = 8 hours
Hence, the time taken is 8 hours
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Nancy earns Rs. 25,00,000 in 5 months. what is her annual salary
Answer:
You would first divide the amount of months by the total amount of money that she has earned in 5 months.
(You put down 25, 00, 000 so Ima just write it as 2,500,000)
25,000,000/5 = 5,000,000
She earns 5,000,000 a month, and would earn 60,000,000 per year.
Anual salary is how much money you would earn per year, so the answer is 60,000,000. (sixty million).
Step-by-step explanation:
Hope it helps! =D
A pipe has 9/16" that is threaded, but you need to trim 4/32" off of the threaded part. How long will the threaded be after the trim? a. 17/32, b. 7/8, c. 7/16, d/ 15/32
Consider the function f (x) = x.What effect does subtracting 2 from the input have on the graph of the function?
The effect of subtracting 2 from the input on the graph of the function is a translation of 2 units to the right.
What effect does subtracting 2 from the input?For any function f(x), we define a horizontal translation of N units as:
g(x) = f(x + N)
And what this does, is translate the graph N units horizontally.
if N > 0, then the translation is to the left.
if N < 0, then the translation is to the right.
Here we want to subtract 2 from the input, so we will get:
f(x - 2)
By using the definition above, we know that we will have a translation of 2 units to the right.
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Which term below refers to events that all have the same probability of occurring?
(1) same chance occurrences
(2) equal probability events
(3) evenly divided happenings
(4) equally likely outcomes
The term below that refers to events that all have the same probability of occurring is; (2) equal probability events
What is the probability of occurrence?By definition, we can say that the probability of occurrence of an event is defined as the number of trials in which a particular event happened divided by the total number of trials.
Probability = number of trials in which event happened/total number of trials.
Now, when we say that all items have the same probability of occurring, what we simply mean is they all have equal chance of occurrence or they all have equal outcomes. For example when we flip a coin, we have equal chance of getting a head or tail.
Thus, the term that best defines the above would be Option 2.
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(16,1), (17,7) find the slope of line through each pair of points
The slope of the line through each pair of points (16,1), (17,7) is 6.
A line's slope serves as a gauge for its steepness. Between any two locations on the line, it is the ratio of the vertical change to the horizontal change.
The slope of a line can be positive, negative, zero, or undefined.
In algebraic equations, the letter "m" frequently stands in for slope. In slope-intercept form, a line's equation is written as y = mx + b, where m denotes the line's slope and b its y-intercept.
To find the slope of the line that passes through two points (x1, y1) and (x2, y2), you can use the following formula
m = (y2 - y1) ÷ (x2 - x1)
where m is the slope of the line and (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, the slope of the line through the points (16,1) and (17,7) is:
m = (7 - 1) ÷ (17 - 16) = 6 ÷ 1 = 6
So the slope of the line is 6.
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Six bottles of water cost £2.10. How much does one bottle of water cost?
someone please help
A kite is flying 24 ft off the ground. Its line is pulled taut and casts a 7-ft shadow. Find the length of the line. If necessary, round your answer to the nearest tenth.
The side lengths are;
tan x = e/f
cos x = e/d
sin x = f/d
What is a right angled triangle?We know that a right angled triangle is the kind of triangle that one of the sides of the triangle would be 90 degrees.
There are some ratios that are associated with the right angled triangle and we call them the trigonometric ratios. These include the sine the cosine and the tangent. All of these ratios does depend on the lengths of the sides of the right angled triangle.
The sides of the right angled triangle are the opposite, the adjacent and the hypotenuse and these can be obtained based on the relative position of the angle.
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What is the sum of 6x+7 and 8x^2+5x-1
Answer:
8x² + 11x + 6
Step-by-step explanation:
6x + 7 + 8x² + 5x - 1 ← collect like terms
= 8x² + (6x + 5x) + (7 - 1)
= 8x² + 11x + 6
Does anunify know this ?Simplify and round the answer to the nearest hundreths place
The simplified form of the expression [tex]\sqrt[5]{1215}[/tex] is [tex]3\sqrt[5]{5}[/tex].
What are surds and indices?We know there are two types of radicals one is surds when the number has been raised by such power that it is greater than zero and less than one,
The other type of radicals are indices where a number is raised to such power that is greater than one.
Given, A radical [tex]\sqrt[5]{1215}[/tex].
Now we'll prime factor 1215.
= [tex]\sqrt[5]{5\times243}[/tex]
= [tex]\sqrt[5]{5\times3\times81}[/tex].
= [tex]\sqrt[5]{5\times3\times3\times3\times3\times3}[/tex].
= [tex]3\sqrt[5]{5}[/tex].
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Solve systems by elimination step by step
2x + y = 180
x - y = 30
The value of x=70 and y=40
The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with the multiplication or division of coefficients of the variables.
Here, 2x+y=180
x-y= 30
Here, the coefficient of y in these two equations are equal and have opposite signs. so,
2x+y= 180
x-y= 30
Now adding equation 1 and equation 2
We get,
3x= 210
x= 210/3
x= 70
Now, to find y:
Putting the value of x in equation 2
x-y= 30
70-y= 30
y= 70-30
y= 40
so, the value of x and y are 70 and 40
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Latoya's Coffee Shop makes a blend that is a mixture of coffee types A and B. In one bag of the blend, there are 6 kilograms of type A. Four bags of the blend are a total of 36 kilograms. How many kilograms of type B are there in one bag?
The Kilograms of type B that are in one bag of the Latoya's Coffee shop blend would be = 3kg
What is a mixture?A mixture is defined as the combination of two or more components which can or cannot be separated by ordinary methods.
The coffee blend of LaToya shop = Type A and B
A bag of the coffee blend = 6kg of Type A.
4 bags of coffee blend = 36kg
Therefore 4 bags of coffee blend contains = 6 see×4 = 24 kg of Type A
Type B in each bag = 36 - 24 = 12/4 = 3kg.
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Jim rented a truck for one day. There was a base fee of 16.99, and there was an additional charge of 88 cents for each mile. Jim had to pay 149.87 when he returned the truck. For how many miles did he drive the truck?
Answer:
Step-by-step explanation: Total Cost: TC = $126.07
Base fee: B = $16.95
Rate per mile: r = $0.88/mile
Distance (miles) : d -->this is what we need to find
The general formula is:
TC = B + r*d
In this problem:
$126.07 = $16.95 + ($0.88/mile)*d
126.07 - 16.95 = 0.88d (I dropped the units starting here)
d = (126.07 - 16.95)/0.88 = 124 miles (notice the parentheses. subtraction has a lower precedence than division. If you omitted them when using a graphing calculator you would get an incorrect answer)
So the answer is 124 miles.
please help asap
will give brainliest
Answer:
m<D should also be 98° due to the congruent angles theorem
Answer:
98
Step-by-step explanation:
Sides AB and DC are parallel.
Sides AD and BC are parallel.
Quadrilateral ABCD is a parallelogram.
Opposite angles of a parallelogram are congruent.
m<D = m<B = 98°
Answer: 98
List five vectors in Span (V₁ V₂). Do not make a sketch.
V₁ = (8 2 7 )
V₂ = (-6 4 0 )
List five vectors in Span (V₁ V₂).
(Use the matrix template in the math palette. Use a comma to separate vectors as needed. Type an integer or a simplified fraction for each vector element.)
Five vectors in Span (V₁ V₂) where V₁ = (8 2 7 ) and V₂ = (-6 4 0 ) is.
n(V₁ + V₂), n ∈ I, I = 1, 2, 3, 4, 5.
What is span in vector space?In mathematics, the set of all linear combinations of the vectors in S is referred to as the linear span, Denoted span(S), Either the intersection of all linear subspaces containing S, or the smallest subspace containing S, can be used to describe it. A vector space is therefore nothing more than the linear range of a set of vectors.
The vectors that are in the same span should be a multiple of the vectors
V₁ = (8 2 7 ), V₂ = (-6 4 0 )
Now, V₁ + V₂ = (2 6 7).
So, The five vectors in the span of V₁ and V₂ is,
2×(2 6 7).
= (4 12 14).
- 2×(2 6 7).
= (- 4 - 12 - 14).
3×(2 6 7).
= (6 18 21)
- 3×(2 6 7)
= (- 6 - 18 - 21).
5×(2 6 7).
= (10 30 35).
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Math Kangaroo Brazil 2020 Grade 7-8 Question. Please Solve both question 25 and 26
According to the information, Jonas realized that the four-digit sequence showing the distance traveled was the same sequence showing the time at 22h10min (question 25). Also, Lady Josephine removed 1/2 of impurities of the package of beans (question 26).
How to calculate at what time Jonas realized the sequences of distance, and time were the same (Question 25)?To calculate at what time Jonas realized the sequences of distance and time were the same we have to perform the following mathematics operation:
21h00min - 22h10min = 1h10min = 70 min1 min = 0.016h70 min = 1.16h1.16h + 21h = 22.1h = 22h10minHow to calculate what fraction of the total amount of impurities was removed from the package (question 26)?To calculate what fraction of the total amount of impurities was removed from package we have to perform the following mathematical operation:
Total impurities in package: 8%Impurities removed from the package: 4%8 / 2 = 4According to the above, we can infer that 4% of impurities equals 50% or 1/2 of the total impurities in the package.
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What is the slope of the line that passes through the points (-6, -6) and
(-9, -5)? Write your answer in simplest form.
So basically what I do is find the formula for slope.
M= y2-y1/x2-x1
So I got
-5-(-6)/-9-(-6) = 1/3
answer = 1/3
:)
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 65% salt and Solution B is 90% salt. She wants to obtain 140 ounces of a mixture that is 80% salt. How many ounces of each solution should she use?
Which value of x makes the expression equal.
5x, 7x - 6
Answer: x=3
Step-by-step explanation:
5x=7x-6
6+5x=7x
6=7x-5x
6=2x
solve for x which x=3
Answer:
x = 3
Step-by-step explanation:
Set the equations equal to each other:
5x = 7x - 6
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Division
Addition
Subtraction
~
Subtract 7x from both sides of the equation:
[tex]5x (-7x) = 7x (-7x) - 6\\5x -7x = -6\\-2x = -6[/tex]
Next, divide -2 from both sides of the equation:
[tex]\frac{-2x}{-2} = \frac{-6}{-2}\\ x = \frac{-6}{-2}[/tex]
*Remember that, when you divide two negative numbers, your answer will be positive:
[tex]x = \frac{-6}{-2} = 3[/tex]
3 is your answer for x.
x = 3.
~
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Find x, y, mzC, and mA' given m/A = y;
m/A' = 2x + 5, mc-3x-y,
mZC' = 4
The value of x = 9, y = 4, m∠C = 25 and m∠A' = 23.
What is the triangle translation?
In mathematics, a triangle translation refers to the geometric transformation in which a triangle is moved to a new position without rotating or scaling it. The triangle is simply slid along a straight line in a certain direction, and the new position of the triangle will be parallel to the original one.
Given that ΔABC translates to ΔA'B'C', we can assume that the measures of the angles are the same in both triangles. Therefore, if we know the measure of an angle in one triangle, we can assume that the measure of the corresponding angle in the translated triangle is the same.
Given:
m∠A = y
m∠A' = 2x + 5
m∠C = 3x-y
m∠C' = 4
Since opposite angles in a rectangle are congruent, m∠A=m∠C' and m∠C = m∠A'
Therefore,
y = 4
3x-y = 2x + 5
Solving this equation gives us:
x = y + 5 = 4 + 5 = 9
y=4
m∠C = 3x - y = 3(9) - 4 = 25
m∠A' = 2x + 5 = 2(9) + 5 = 23
Hence, the value of x = 9, y = 4, m∠C = 25 and m∠A' = 23.
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Please help me solve
For this problem, we know that the line's function is equal to 3 if X isn't 0. That means that for every X that isn't 0, we'll have a line at y = 3 (since we know that g(x) is just fancy for y!). We're also given that if X is equal to 0, it must be at y = 4.
Therefore, your graph should have a straight line through y = 3 EXCEPT at x = 0! At x = 0 you should just have a shaded dot at y = 4.