Ryan wants to use the distributive property to rewrite the addition problem shown so that the numbers left in the parentheses have no common factor except 1. Write an equivalent expression that has numbers in parentheses whose only common factor is 1. (54 + 72)

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.

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.

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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The simplified form of the expression [tex]\sqrt[5]{1215}[/tex] is [tex]3\sqrt[5]{5}[/tex].

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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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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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.

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  

The effect of subtracting 2 from the input on the graph of the function is a translation of 2 units to the right.

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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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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The side lengths are;

tan x = e/f

cos x = e/d

sin x = f/d

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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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.

The term below that refers to events that all have the same probability of occurring is; (2) equal probability events

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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On solving the provide the question, we can say that - the value of the following function is f(x) = -5x - 1.

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

Answer:

No

Step-by-step explanation:

The ratio used should have been 6 parts yellow paint to 2 parts blue paint

hope this helps

The mean absolute deviation of $29, $58, $15, $75, and $22 is $32.67.

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.

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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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).

To calculate at what time Jonas realized the sequences of distance and time were the same we have to perform the following mathematics operation:

To calculate what fraction of the total amount of impurities was removed from package we have to perform the following mathematical operation:

According 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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The length of time to build the fence is 8 hours

From 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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Answer:

8x² + 11x + 6

Step-by-step explanation:

6x + 7 + 8x² + 5x - 1 ← collect like terms

= 8x² + (6x + 5x) + (7 - 1)

= 8x² + 11x + 6

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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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

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

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

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

:)

The Kilograms of type B that are in one bag of the Latoya's Coffee shop blend would be = 3kg

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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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]