Use the Distributive Property to simplify
1/7 x (56 - 1/4)
Leave your answer in simplest form in the form of a/b − c/d

If one of your numbers is a whole number, put a 1 in that denominator

15 represents the angle ONB.

Answer:

The point-slope form of the equation of the line with slope 3 passing through the point (1, 2)

Step-by-step explanation:

point-slope formula, which states that given a point (x1, y1) and a slope m, the equation of the line can be written as y - y1 = m(x - x1)

y - 2 = 3(x - 1

Answer:

22,-89

Step-by-step explanation:

let the numbers be x and y .

x+y=-45

x-y=-89

add

2x=--134

x=-67

-67+y=-45

y=-45+67=22

a) The algebraic fraction \(\frac{{x + 2}}{{(x - 1)^2}}\) is proper. b) The algebraic fraction \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\) can be expressed as \(-\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

Let's solve each part step by step and determine whether the fraction is proper or improper, and then express it accordingly.

a) \(\frac{{x + 2}}{{(x - 1)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 1 (linear term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is less than the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

\(\frac{{x + 2}}{{(x - 1)^2}} = \frac{A}{{x - 1}} + \frac{B}{{(x - 1)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 1)^2)\) to eliminate the denominators:

  (x + 2) = A(x - 1) + B.

Expand the equation and collect like terms:

  x + 2 = Ax - A + B.

Equate the coefficients of like terms:

  Coefficient of x: 1 = A.

  Constant term: 2 = -A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = 1.

Substituting A = 1 into the constant term equation: 2 = -1 + B, we find B = 3.

Therefore, the partial fraction decomposition is:

  \(\frac{{x + 2}}{{(x - 1)^2}} = \frac{1}{{x - 1}} + \frac{3}{{(x - 1)^2}}\).

b) \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}}\):

Step 1: Determine the degree of the numerator and the denominator:

  - Degree of the numerator = 2 (quadratic term)

  - Degree of the denominator = 2 (quadratic term)

Since the degree of the numerator is equal to the degree of the denominator, the fraction is proper.

Step 2: Express the proper fraction in partial fractions:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = \frac{A}{{x - 4}} + \frac{B}{{(x - 4)^2}}\).

Step 3: Find the values of A and B:

Multiply both sides of the equation by \(((x - 4)^2)\) to eliminate the denominators:

  (4x^2 - 31x + 59) = A(x - 4) + B.

Expand the equation and collect like terms:

  4x^2 - 31x + 59 = Ax - 4A + B.

Equate the coefficients of like terms:

Coefficient of \(x^2\): 4 = 0 (No \(x^2\) term on the right side).

Coefficient of x: -31 = A.

Constant term: 59 = -4A + B.

Solve the system of equations to find the values of A and B:

From the coefficient of x, A = -31.

Substituting A = -31 into the constant term equation: 59 = 4(31) + B, we find B = -25.

Therefore, the partial fraction decomposition is:

  \(\frac{{4x^2 - 31x + 59}}{{(x - 4)^2}} = -\frac{{31}}{{x - 4}} - \frac{{25}}{{(x - 4)^2}}\).

The above steps provide the solution for each part, including determining if the fraction is proper or improper and expressing it in partial fractions.

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The effectiveness depends on your score of working.

How effective is it to go to your manager to request others take on some activities?

Certainty implies, indeed, that favorable things will happen and uncertainty  implies favorable things won't happen.

If we go to our manager, requesting that others should take some activities. It certainly depends upon the our score in the office. if we are hard working than in situations manager could approve our request and if our score is low or we are not a hard worker than result may no be in our favor.

Thus, the effectiveness depends on your score of working.

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Answer:

It is proportional to the amount of minutes being used

Step-by-step explanation:

The reason is when I divided 80 by 12 it gave me 6.66666667

When I divided 60 by 9 it gave me the exact same answer

Answer:

C. 124°

Step-by-step explanation:

The angles that have measurements given must add up to 180 because together they create a straight line, which is 180°.

To solve, set up an equation like this:  \(\frac{2}{3}\)x + x + 40 = 180. Combine the  \(\frac{2}{3}\)x and x to get 1 \(\frac{2}{3}\)x. Then, subtract 40 from both sides and you'll end up with the equation 1 \(\frac{2}{3}\)x = 140.

Divide by sides by 1 \(\frac{2}{3}\) and the answer is x = 84.

Now you know the measure of x. Since angle ACD and angle BCE and vertical angles, they must have the same measure.

To solve, just find the measure of ACD by inputting 84 into the equation x+40. The answer is 124, meaning that the measure of angle BCE is also 124°.

I hope this makes sense and helps! Feel free to ask for clarification! ☺

Answer:

x = 47

Step-by-step explanation:

x + 121 = 4x - 20

-3x + 121 = - 20

-3x = -141

x = 47

So, the answer is x = 47

Answer:

ok

Step-by-step explanation:

ok fjFjxggkgclclcchlclcullcucuclcvuullulj

Using the concept of ratio and proportions, Shanice will need 7 gallon for 14 lawns.

Proportion is a mathematical concept that describes the relationship between two or more related quantities. It is usually expressed as a ratio or a fraction, which indicates how much of one quantity there is compared to the other. Proportions are used in many areas of mathematics and science, including statistics, geometry, and physics.

In this problem, we have to find the ratio or proportion to which she uses fuel per lawn.

2 gallons = 4 lawns

1 gallon = x lawn

x = (4 * 1) / 2

x = 4 / 2

x = 2 lawn

So, she uses 1 gallon on 2 lawns

We can set an equation of proportionality for this or go straight ahead and equate to find the number of gallons required for 14 lawns.

1 gallon = 2 lawn

x gallon = 14 lawn

x = (14 * 1) / 2

x = 7 gallon

She will need 7 gallons to work on 14 lawns.

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Answer:

Step-by-step explanation:

The inequality 5x+12y ≤ 30 represents a shaded region in the xy-plane that includes all the points that satisfy the inequality. To graph this inequality, we can first graph the equation 5x+12y = 30, which is the boundary line of the shaded region.

To graph the boundary line, we can find its x- and y-intercepts:

x-intercept: Set y = 0 and solve for x: 5x + 12(0) = 30, which gives x = 6.

y-intercept: Set x = 0 and solve for y: 5(0) + 12y = 30, which gives y = 2.5.

So the boundary line passes through the points (6, 0) and (0, 2.5).

Next, we can determine which side of the boundary line to shade. One way to do this is to pick a test point that is not on the line and plug it into the inequality. For example, the point (0,0) is a convenient test point. Plugging in x=0 and y=0 into the inequality, we get:

5(0) + 12(0) ≤ 30

which simplifies to 0 ≤ 30. Since this is true, we know that the region containing the point (0,0) is part of the shaded region, and therefore the shaded region is the one that contains the origin.

Putting it all together, we can graph the inequality by drawing the line 5x+12y = 30 and shading the region below the line, as shown in the figure below:

    |

 3  |       x

    |      /

 2  |     /

    |    /

 1  |   /  

    |  /  

 0  | /    

    ------------

      0  6

The shaded region includes all the points below the line 5x+12y=30, including the points on the line.

Answer:

B

Step-by-step explanation:

the sum of the 3 angles in a triangle is 180° , so

∠ c + 56° + 38° = 180°

∠ c + 94° = 180° ( subtract 94° from both sides )

∠ c = 86°

Answer:

2646

Step-by-step explanation:

is the correct answer for This question

The required equivalent expression is (216 x 16).

The correct is D.

In mathematics, an expression is a phrase that has at least two numbers or variables and at least one maths operation. Addition, subtraction, multiplication, or division are all examples of maths operations. An expression's structure is as follows:

(Number/variable, Math Operator, Number/variable) is an expression.

We have the Expression as,

6³ x 4²

Now, expand the exponents as

6³

= 6 x 6 x 6

= 216

and, 4² = 4 x 4 = 16

Thus, the required equivalent expression is (216 x 16).

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Answer:

b

Step-by-step explanation:

Answer:

its b

Step-by-step explanation:

the zeros are

x=-1.5 -----> multiplicity 1

x=0

x=2 ----> multiplicity 2

possible function

y=-x(x+1.5)(x+2)^2 -----> leading coefficient must be negative

Factor of polynomial m are 0,   6n⁴.

What is polynomial in maths?

A polynomial is an expression in mathematics made up of variables (also known as indeterminates) and coefficients, and it only uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of the variables. The polynomial x2 4x + 7 is an illustration of one with a single indeterminate x.

= 30m³n⁴ - 5m⁴

= 5m³(6n⁴ - m )

let 5m³(6n⁴ - m ) = 0

       5m³ = 0

         m = 0

 6n⁴ - m = 0

      m =   6n⁴

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A man who weighs 185 lb on Earth weighs 30.8 lb on the Moon

Two variables are said to be directly proportional if as one variable increases/decreases, the other variables does the same by the same amount.

Let y represent the weight of object on earth and x represent the weight of object on the moon.

y ∝ x

y = kx

When y = 66, x = 10.92, hence:

66 = 10.92k

k = 6

When y = 185 lb:

185 = 6x

x = 30.8 lb

A man who weighs 185 lb on Earth weighs 30.8 lb on the Moon

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Answer:

30.8lb

Step-by-step explanation:

The total cost for the family of four is $944

Cost denotes the amount of money that a company or a person spends on the creation or production or acquiring of goods or services.

Here the family needs the service if transportation.

The cost of adult is $280. Out of four members , two are under 3years. This means the total cost for adult is 2 × 280 = $560

The cost of under 3 is ⅔ of the cost of adult.

= ⅔ × 280= $192

The cost of the two under 3 = 2 × $192 = $384

therefore the total cost for the family is $560 +$384 = $944

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Kala spun the spinner 1000 times and got the following results:

- Yellow: 400 times

- Red: 300 times

- Blue: 300 times

1. Calculate the amount of sales tax:

  - The item costs $350 before tax.

  - The sales tax rate is 14%.

  - To find the sales tax amount, multiply the cost of the item by the tax rate:

    Sales tax = $350 * 0.14 = $49.

2. Determine the total cost of the item including tax:

  - Add the sales tax amount to the original cost of the item:

    Total cost = $350 + $49 = $399.

3. Analyze the spinner results:

  - The spinner has 10 equal-sized slices.

  - There are 4 yellow slices, 3 red slices, and 3 blue slices.

  - Kala spun the dial 1000 times.

4. Calculate the frequency of each color:

  - Yellow: Kala got 400 yellow results out of 1000 spins.

  - Red: Kala got 300 red results out of 1000 spins.

  - Blue: Kala got 300 blue results out of 1000 spins.

5. Calculate the probability of landing on each color:

  - Yellow: Probability = Frequency of yellow / Total spins = 400 / 1000 = 0.4.

  - Red: Probability = Frequency of red / Total spins = 300 / 1000 = 0.3.

  - Blue: Probability = Frequency of blue / Total spins = 300 / 1000 = 0.3.

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Answer:

54

Step-by-step explanation:

12*9/2=108/2=54mm^2

Answer: c

Step-by-step explanation:

Answer: B.792

Step-by-step explanation:

Answer:

hii im looking at the same thing  you just have to do the multiplication on that

Step-by-step explanation:

after four passes through the filtration system, 99.19% of the original contaminants will have been removed from the water sample

How to solve the question?

Each time the water passes through the filtration system, 70% of the contaminants are removed, which means that 30% of the contaminants remain in the water. After the first pass, 30% of the original contaminants are left in the water. After the second pass, 30% of the remaining 30% is left, which is equivalent to 9% of the original contaminants. After the third pass, 30% of the remaining 9% is left, which is equivalent to 2.7% of the original contaminants. Finally, after the fourth pass, 30% of the remaining 2.7% is left, which is equivalent to 0.81% of the original contaminants.

Therefore, after four passes through the filtration system, 99.19% of the original contaminants will have been removed from the water sample. This calculation can be obtained by subtracting the final percentage of contaminants left (0.81%) from 100%.

It's important to note that while passing the water through the filtration system multiple times increases the overall percentage of contaminants removed, it's not a substitute for regular maintenance and replacement of the filtration system's components. Over time, the filtration system's effectiveness can diminish, and it's crucial to follow the manufacturer's instructions for proper maintenance and replacement to ensure that the system continues to function optimally.

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we are given the following expression:

The commutative property states that the order of the terms can be changed and the result is the same. therefore, applying the commutative property we get:

Answer:

A)360

B)180

Step-by-step explanation:

Part-A:

For this question, we don't have to care about what integer they are, we just need to care about the number of integers we are given. considering the question, we understand that we are dealing with permutation .we're given 6 numbers so we want to figure out the permutation of 4 out of 6. the formula which is used for permutation is given by,

\( \displaystyle P(n,r) = \frac{n!}{(n - r)!} \)

where:

we've already sorted out that

substitute:

\( \displaystyle P(6,4) = \frac{6!}{(6 - 4)!} \)

simplify parentheses:

\(\displaystyle P(6,4) = \frac{6!}{2!} \)

simplify division:

\( \rm\displaystyle P(6,4) = \frac{6!}{2!} = \frac{6 \times 5\times 4 \times 3 \times2! }{2!} = \boxed{360}\)

hence,

360 plates of vehicles consisting of 4 different digits can be made out of the integer 4,5,6,7,8,9

Part-B:

to solve this question, we need to know about the divisibility rule of 2 which is A number is divisible by 2 if the last digit is an even number

notice that half the values of the set are even, thus half of our total permutations will be even and thus divisible by 2, since we have already figured out the permutations of 4 digits plate out of 6 i.e 360 therefore 180 of these number will be divisible by 2

Alternate:

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so it is a four digit plate. After we choose the last digit, we only need 3 digits, choosing from 5 values left. The answer can be therefore be found by multiplying of possible values for the last digit (3) by the number of ways re-arrange 3 distinct values (3!) by the number of ways to choose 3 values from 5, giving the same answer of 3 x 3! x C(5,3) = 180.

Answer:

Step-by-step explanation:

_ _ _  4  => 5*4*3=60

_ _ _  8  => 5*4*3=60

_ _ _  6  => 5*4*3=60