to translate an expression from words into a mathematical expression, _______________

If a lever was used with an effort arm of 12 meters and a load arm of 6 meters, the work that would have been done would've been (A) 50 J.

Using a lever makes work simpler and quicker since it only takes a bit of effort to move a heavy load.

The efficiency of the machine goes up when the output force is bigger than the input force - the formula for this is Output Force divided by Input Force.

Eff = ( output force/input force ) x 100 %

The amount of force you get is determined by this equation.

F ( out ) = load x distance moved by the load

The force you put in is calculated using this equation.

F ( input ) = effort x distance moved by the effort

If we had used a lever with an effort arm of 12 meters and a load arm of 6 meters, the work that would have been done could be calculated.

work = ( 600   x 6  ) / ( 12  x 6  )

work = 50 J

Therefore, if a lever was used with an effort arm of 12 meters and a load arm of 6 meters, the work that would have been done would've been (A) 50 J.

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Complete question:

600 joules of work are used to lift a box from the ground to a height of six meters. how much work would have been done if a lever would have been used with an effort arm of 12 meters and a load arm of 6 meters?

a.  50 J

b. 100 J

c. 600 J

d. 72 J

On solving the provided question, we can say that equality of given trapezium we find, y=13/10 and x=21

A convex quadrilateral with exactly one pair of opposite sides that are parallel to one another is called a trapezium. When drawn on a piece of paper, the trapezium is a two-dimensional shape that resembles a table. A quadrilateral is a polygon in Euclidean geometry that has four sides and four vertices.

Since ABCD~PQRS

then, on comparing

5y-3/4 = 7/8

y=13/10

On comparing angle,

3x+24=87°

3x=63°

x=21

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Answer: Your answer would be 152 cm

Step-by-step explanation:

Outer part of the shape:

Length  =  18 cm  

width  =  12 cm

Area of large rectangle  =  (18 ⋅ 12)

=  216 cm2------(1)

Inner part of shape:

Length  =  6 cm

width  =  3 cm

Area of small rectangle  =  (8 ⋅ 8)

=  64 cm2------(2)

(1) – (2)

=  (216 – 164) cm2

=   154 cm2

I hope this helps!

The expression that should be subtracted is 4x² - 3y² - xy.

An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.

We will be using the concept of addition and subtraction of algebraic expressions to solve the given question.

Let us assume the missing part is X.

Therefore according to the question,

(3x² - 4y² + 5xy + 20) - (X) =  - x² - y² + 6xy + 20

Let us shift the terms to find the value of X

X = 3x² - 4y² + 5xy + 20 - (- x² - y² + 6xy + 20)

X = 3x² - 4y² + 5xy + 20 + x² + y²- 6xy - 20

X = 4x² - 3y² - xy

Thus, the expression that should be subtracted is 4x² - 3y² - xy.

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Answer: 3:2

Step-by-step explanation:

If 3/5 of the marbles are blue, then the last 2/5 will be yellow.

Answer:

Hey there! So as you know, 3 out of 5 marbles are blue, which can be written as 3/5. To find the ratio of blue to yellow marbles, we need to find the number of yellow marbles.

We know that 5 marbles are blue and yellow combined, and 3 of them are blue, so that leaves 5-3 = 2 yellow marbles.

So the ratio of blue marbles to yellow marbles is 3:2, or 3/2. It means that for every 3 blue marbles, there are 2 yellow marbles.

After subtraction (3x+4) - (x+7), the resultant answer is 2x-3.

One of the four operations used in mathematics, along with addition, multiplication, and division, is subtraction.

Removal of items from a collection is represented by the operation of subtraction.

For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches.

So, we have:

(x+7) and (3x+4)

We have to subtract as:

(3x+4) - (x+7)

Now, subtract as follows:

(3x+4) - (x+7)

3x+4 - x-7

2x-3

Therefore, after subtraction (3x+4) - (x+7), the resultant answer is 2x-3.

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The cost of Lisa food is 32 dollars.

Lisa ordered food from a delivery service. She tipped the driver $4.80. This was 15% of the total cost of her food. The cost of her food can be calculated as follows:

Therefore,

let

x = cost of her food

Hence,

15% of x = 4.80

15 / 100 × x = 4.80

0.15x = 4.80

divide both sides by 0.15

Hence,

x = 4.80 / 0.15

x = 32 dollars

Therefore,

cost of food = 32 dollars.

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To find the number of relations from a set A to a set B, you need to consider the number of possible mappings or functions between the elements of set A and set B.

For example, if set A has 3 elements and set B has 4 elements, then the number of relations from A to B is [tex]3^4[/tex] = 81.

Note that not all possible mappings are necessarily valid relations, for example, a function is a type of relationship that has a unique output for each input, so it's a one-to-one relation, whereas a relation can be one-to-one or one-to-many, and also it's a subset of all possible mappings from A to B.

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Using division we know that each job site will receive 458 sand bags.

Multiplication is the opposite of division.

If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.

Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.

So, we know that:

Number of bags: 10992

Bags to be distributed are 24 jobs.

Now, to know the number of bags each job site will receive:

10992/24

458

Therefore, using division we know that each job site will receive 458 sand bags.

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Unknown numbers are 68, 31.50, 20, 600, 150, 50, 400%, 25%, 50, and 500 as percentages or rates.

A number or ratio that is expressed as a fraction of 100 is known as a percentage in mathematics. There are also sporadic uses of the acronyms "pct.," "pct," and "pc." However, the percent sign "%" is widely used to signify it. There are no dimensions to the percentage amount. Percentages are essentially fractions because they have a numerator of 100. Put the percent sign (%) next to a number to indicate that it is a percentage. For instance, you would score a 75% if you answered 75 out of 100 questions on a test correctly (75/100). Divide the money by the total to get percentages, then multiply the result by 100. The formula (value/total) x 100% is used to determine the percentage.

given

1. percentage

p = base x rate

= 80 x 85%

= 68

2. percentage

= 70 x 45%

= 31.50

3. base

b = percentage ÷ rate

= 7 ÷ 35%

= 20

4. base

= 660 ÷ 110%

= 600

5. base

= 120 ÷ 80%

= 150

6. base

= 125 ÷ 250%

= 50

7. rate

= 64 ÷ 16 x 100

= 400%

8. rate

= 85 ÷ 340 x 100

= 25%

9. base

= 13 ÷ 26%

= 50

10. base

= 2.5 ÷ 0.5%

= 500

Unknown numbers are 68, 31.50, 20, 600, 150, 50, 400%, 25%, 50, and 500 as percentages or rates.

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The percentage of piece of cake not served is 8.33%

Now, According to the question:

Let's know:

What is percentage ?

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Given ,

Total number of equal pieces of cake = 24 piece

Number of pieces served at the party =?

So, Number of pieces of cake not served = 20 - 18

Fraction of cake not served =

Number of pieces not served/ Total no. of pieces of cake

Fraction of cake not served = 2/24

Fraction of cake not served =  1/12

Now, In percentage = [tex]\frac{1}{12}[/tex]× 100 = 8.33%

Hence, The percentage of piece of cake not served is 8.33%

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The perimeter of the parallelogram is 16x - 8

The properties of a parallelogram are;

The formula for perimeter of a parallelogram is;

Perimeter = 2(a + b)

substitute the values

Perimeter = 2(6x - 4 + 2x)

collect like terms

Perimeter = 2(8x - 4)

expand the bracket

Perimeter = 16x - 8

Hence, the value is  16x - 8

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Answer:

[tex]\frac{9}{8}[/tex]

Step-by-step explanation:

4.5 yr : 4 yr can be expressed in fractional form as

[tex]\frac{4.5}{4}[/tex] ( multiply numerator / denominator by 2 for whole numbers )

= [tex]\frac{9}{8}[/tex] ← in simplest form

Answer:

y=x-4

Step-by-step explanation:

y=mx+b

Answer: y=x-4

Step-by-step explanation:

The first step is to see what point runs through the y-axis, so you can get your y-intercept. The line runs through (0, -4), so -4 will be your y-intercept.

To calculate the slope, we can use the formula, y2-y1/x2-x1 to find the slope. We have to take two definite points to solve this. an example of two definite points is (1, -3), and (0,-4). So the change in y would be              -4-(-3), which is -1, and for the change in x, 0-1 is -1 (Think of (1,-3) as point one, and (0,-4) as point 2). SO -1/-1 is 1, making the slope 1, making the equation y=x-4

The meaning of 2n in mathematics is just a simple series that gives us different values when we put the integral values of n.

Oftentimes we come across a special series in the mathematical problems.

This mathematical series can be simplified into a quite simpler and a shorter form.

The given form 2n is also nothing but just yet another example of the mathematical series.

When we put the values of end to be 1,2,3,4,5,6,7,8...

We get the values of the expression to be 2,4,6,8,10...

This mathematical series makes problem easier for us understand and solve.

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Answer: The expression (p^20)(p^-4)^2 is equivalent to p^n, where n is the power of p in the simplified expression.

To simplify the expression, we need to use the rule of exponents which states that when multiplying two powers of the same base, we can add their exponents.

So, (p^20)(p^-4)^2 = p^20 * (p^(-4))^2 = p^20 * p^(-8) = p^(20+(-8)) = p^12

So the value of n is 12.

Step-by-step explanation:

Answer: 12

Step-by-step explanation: 22+26=48

60-48=12. SO she 12 minutes left

The inequality can be simplified into a compound inequality:

x > 2.43

x < -16.7

Here we want to solve the following inequality:

|0.7*x + 5| > 6.7

To solve it, we need to isolate the variable x. The first thing we need to do is "break" the absolute value part, then we will get a compound inequality.

0.7*x + 5 > 6.7

0.7*x + 5 < -6.7

Now we can isolate x in both of these inequalities:

0.7*x > 6.7 - 5

0.7*x < -6.7 - 5

0.7*x > 1.7

0.7*x < -11.7

x > 1.7/0.7

x < -11.7/0.7

x > 2.43

x < -16.7

That is the solution of the inequality.

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The slope is m and the y-intercept is b in an equation in slope-intercept form (y=mx+b). It is also possible to rewrite some equations so that they take the shape of a slope-intercept diagram.

The slope is m and the y-intercept is b in the slope-intercept version of the equation (y=mx+b). We can also change some equations to be written in slope-intercept form.

We concentrate on the two constants (numbers) m and b when applying the slope intercept formula. The y-intercept, or the place where the graph crosses the y-axis, is represented by b, whereas m denotes the slope, or steepness, of the line.

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation.

The slope intercept form is:

y = mx + b

where b is the y-intercept and m is the slope.

You only need to enter those into the formula with the information already provided:

y= 4+ 9

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We checked the equation of lines are not parallel to each other.

The two lines when located at the same plane and equidistance from each other are called parallel lines. The properties of parallel lines as shown in equation is that both have same slope but different y intercept.

Two parallel lines never intersect.

equation of line passes through the point (- 3, -3) and (3, 9)

is given by the formula [ y - y₁] = [(y₂- y₁) / (x₂- x₁)] [x - x₁}

                                      [ y- (-3)] = [9 - (-3) / 3- (-3)] [x - (-3)]

                                 (y +3) = [(9+3)/ (3+3)] (x+3)

                                  y+ 3 = 12/ 6 (x+3)

                                  y+3 = 2 (x+3)

                                   y+3 = 2x+6

                                   y = 2x+3 this is the first line.

equation of line passes through (-5, 12) and (1, 0)

                          [y - 12] = [(0 - 12) / 1 - (-5)] [x - (-5)]

                       y -12 = -12/ 6 (x+5)

                         y - 12 = -2 x - 10

                        y = - 2x + 2

the above is the equation of second line.

the above two equation have same slope but different sign. Hence, the lines are not parallel to each other.

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By dividing any number 3 to simplify the expression.

What is simplifying an expression?

To simplify an expression, create a similar expression devoid of any similar terms. Therefore, we will rewrite the expression using the fewest number of terms possible.

When you simplify an expression, your goal is essentially to make it as simple as you can. There shouldn't be any additional multiplying, dividing, adding, or subtracting to be done at the conclusion.

One third is one part of three equal parts. When you split an object or number into thirds, you divide it by three.

Thirds are calculated by dividing by 3.

For example: One third of 24 =1/3 of 24 = 24/3 = 8.

Hence, by dividing any number 3 to simplify the expression.

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The value of a base refers to the number that is used as the foundation or foundation number in a mathematical system or system of numbers. A base is typically represented by a number that is used to indicate the power or exponent to which it is raised in order to produce a certain value.

The number of base is the number of different digits or symbols that are used in a particular mathematical system or system of numbers. For example, in the decimal (base 10) system, there are 10 different digits (0–9) that are used to represent different values. In the binary (base 2) system, there are only two different digits (0 and 1) that are used to represent different values. The number of the base can also be referred to as the radix of a number system.

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Answer:

[C] 3 3/4 Miles

Step-by-step explanation:

Given:

Zoe jogs 3/4 of a mile every 1/5 of an hour.

How many miles does Zoe jog per hour?

[A] 3/20 Miles

[B] 4/15 Miles

[C] 3 3/4 Miles

[D] 6 2/3 Miles

Solve:

Since, Zoe jogs 3/4 of a mile every 1/5 hour. And 5/5 = 1 hour.(Also known as 60 minutes) Which means 1/5 is 12 minutes. In order to find how much Zoe jogs per hour, we have to multiply.

Knowing that;

1/5 = 12 minutes

2/5 = 24 minutes

3/5 = 36 minutes

4/5 = 48 minutes

5/5 = 60 minutes (1 Hour)

Hence, 3/4 Multiply by 5.

3/4 × 5 = 3.75 = 15/4 = 3 3/4

As a result, Zoe jogs 3 3/4 miles per hour.

RevyBreeze

The expression that is equivalent is  b Over a. Option D

Index form of a number can simply be defined as that number written as an exponential expression.

It could also be written as a single number that is raised to another number.

Other names for index forms are scientific notation and standard forms.

From the information given, we have that;

This can be represented as;

b^-2/ab^-3

Take the inverse of the denominator

b^-2 × a^-1 b^3

Now, add the exponents of the like variables

b^-2+3 . a^-1

Add the exponents

b^1.a^-1

Hence, the expression is b/a

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Answer: 10

Step-by-step explanation:

5x2 = 10

Answer:

10 lol.....................

Answer:

  6 units

Step-by-step explanation:

You want the length of the hypotenuse of a right triangle with legs 5 and √11.

The Pythagorean theorem tells you the relation between the legs a, b, and the hypotenuse c of a right triangle is ...

  c² = a² +b²

  c² = 5² +(√11)²

  c² = 25 +11 = 36

  c = √36 = 6

The length of the third side is 6 units.

Answer:

B

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer: 11

Step-by-step explanation:

Let the number be N.

Let's set up the equation.

2N + 15 = 37

Let's subtract 15 from both sides.

2N = 22

Divide both sides by 2, and you get

N = 11

Final Answer : 11

Answer:

The answer would be 3x/8.

Step-by-step explanation:

Both fractions would need to have a common denominator, so you could multiply x/2 by 4 on both the top and bottom to get 4x/8.

You could then subtract both the numerators from each other.

4x-x=x

The denominator will stay the same.

X/8.