Word Problems
1) Sandy has 22 books in her library. She bought several books at a yard
over the weekend. She now has 61 books in her library. How many be
did she buy at the yard sale?
) How many ink cartridges can you buy with 143 dollars if
one cartridge costs 11 dollars ?
) Melanie is baking a cake. The recipe calls for 6 cups of flour. She alre
4 cups. How many more cups does she need to add ?

5 * root(x ^ 2, 3) is the equivalent expression.

Simply multiplying the radicands and placing the result behind the radical sign is all that is required to multiply two square roots. The square root of the product of the radicands, in other words, is equal to the product of two square roots.

Only if the numbers under the radical sign are equal can you add or subtract square roots themselves. The original number will still be in the radical sign after adding or subtracting the coefficients (numbers in front of the radical sign). Implement the suggested action.

5 * root(x ^ 2, 3) is the equivalent expression.

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Answer:

Trim A

Inches = 36

Feet = 3

Yards = 1

Trim B

Inches = 216

Feet = 18

Yards = 6

The value of 8(x + 7) is 8x + 56.

The value of 6(11 + x) is 66 + 6x.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The distributive property of  multiplication over addition states that,

a x (b + c) = a x b + a x c

Now,

8 x (x + 7)

= 8 x (x) + 8 x 7

= 8x + 56

6 (11 + x)

= 6 x 11 + 6 x (x)

= 66 + 6x

Thus,

The value is 8x + 56 and 66 + 6x.

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The radius of the sphere is 9 centimeters.

The area of the outer surface of a sphere is the surface area of a sphere.

And its formula:

The surface area of the sphere is 4πr².

Where r is the radius of the sphere.

Given:

The surface area of the sphere is 4πr².

Where r is the radius of the sphere.

So,

surface area of the sphere = 4πr²

324π cm² = 4πr²

Simplifying,

r² = 324π/4π

r² = 324/4

r² = 81

r = 9

Therefore, the radius is 9 centimeters.

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the speed of the car

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Reason:

The term "gradient" is the same as "slope".

Recall that slope = rise/run = (change in y)/(change in x).

The change in y represents how far you travel, as the distance is along the vertical axis. The change in x is the time duration.

Then,

speed = distance/time

which helps show the slope of this distance-time graph is the speed of the car. The steeper the slope, the faster the car.

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An example:

The equation y = 50x has slope 50. The x is the time and y is the distance traveled.

At time x = 0 hours, you have traveled y = 0 miles.

At time x = 1 hour, you have traveled y = 50 miles.

The two points (0,0) and (1,50) are on this line. Use the slope formula to get a slope of 50, which represents the speed of the car in miles per hour (mph). Or note that y = 50x is in the form y = mx+b

m = slope = 50

b = y intercept = 0

Answer:

times it by

Step-by-step explanation:

3×3=9, 9×3=27, 27×3=81, 81×3=243

sorry if this isn't the answer your looking for.

4x2 - 3y2 - xy should be taken away from 3x² 4y² 5xy 20 obtain X² y²+ 6xy 20

A fraction is a percentage of a whole. This entire sentence could be referring to a single location or a collection of locations. The English word "fraction" originates from the Latin word "fraction," which means "to break." As the first society to comprehend fractions, the Egyptians used fractions to solve a number of mathematical problems, including the distribution of food and resources and the absence of a metal currency.

Assume X is the component that is absent.

As a result, the answer to the question is

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

To determine the value of X, let's change the words.

X is equal to (-x2 - y2 + 6xy + 20) = 3x2 - 4y2 + 5xy + 20.

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

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

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Answer:

meter per second(m/s)

Answer:

Hey there! The metric system has a unit called meters per second for measuring speed. It's abbreviated as m/s and it's used to measure how far something travels in a certain amount of time. For example, if something goes 50 meters in 10 seconds, its speed would be 50 m/s / 10 s = 5 m/s. There are other units for measuring speed too, like kilometers per hour (km/h) and centimeters per second (cm/s). It just depends on what you're measuring and how precise you need to be.

________________________________________________________

Well, speed is all about how far something goes in a certain amount of time. So if you increase the distance traveled or decrease the time it takes to travel that distance, the speed will increase. On the other hand, if you decrease the distance traveled or increase the time it takes to travel that distance, the speed will decrease.

There are all sorts of situations where knowing the speed of something is important. For example, if you're driving a car, it's important to know how fast you're going so you can stay safe and follow the speed limits. In sports, measuring speed can help coaches and players improve their performance. And in science, measuring the speed of light or other phenomena can help us better understand the world around us. So as you can see, speed is a pretty important concept!

Answer:

The zeros are -2.5 and 2.

Step-by-step explanation:

2x^2 +x-10 = 0

2x^2 - 4x + 5x - 10 = 0

2x(x - 2) + 5(x - 2) = 0

(2x + 5)(x - 2) = 0

2x + 5 = 0 gives x = -2.5.

x - 2 = 0 gives x = 2.

Note that It is not a good idea to guess what a value on a graph might be if it is beyond the points that are already plotted. The reason for this is that the guess might not be accurate. Generally, it is better to stay within the defined data limits.

In mathematics, a graph is defined as a graphical representation or diagram that organizes facts or values. The graph's points frequently reflect the relationship between two or more objects.

Because they display information quickly and readily, graphs and charts are powerful visual aids. It's no surprise that graphs are widely utilized in print and electronic media. Data can often be easier understood when displayed as a graph rather than a table since the graph might illustrate a pattern or comparison.

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The area is measurement of the surface of a shape. To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle or a square. Area, A, is x times y.

Two triangles' area: 18×24÷6x3 = 432cm^2

The widest rectangle's area: 30×7 = 210cm^2

The rectangle facing the left's area: 18×7= 126cm^2

The rectangle facing the ground's area: 24×7= 168cm^2

Total Surface Area: 432+210+126+168 = 936cm^2

=936cm^2

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To estimate the true proportion of home owners who have vegetable gardens to within 6 percentage points with confidence, a sample size of 384 would be needed.

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The logarithmic function y log x is defined as

[tex]$\log_b \text x = \text y \leftrightarrow \text b^y= \text x[/tex].

An exponent that is expressed in a unique way is called a logarithm. As an illustration, we are confident that the exponential formula 32 = 9 is correct. In this instance, the base is 3, and the exponent is 2. The formula will be written as log3 9 = 2 in the logarithmic form.

This is expressed as "9 divided by base 3 is 2" in words. The exponent has been effectively lowered to the mainline in this case. However, despite the fact that this was done to make division and multiplication easier, logarithms are still very useful in mathematics.

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When we construct the confidence interval their sample must have some conditions which are as follows,

Therefore , these are the conditions which the administrator should use to construct a one-sample z interval for a proportion.

When two ratios are equivalent to each other , they are said to be in a state called proportion. The proportion formula is used to see whether  the given ratios or fractions are equal or not . The proportion formula can be given as, The product of means is equal to the the product of extremes. This can be written as ad = bc.

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The interpretation of the slope is that the cost per minute is $2

From the question, we have the following parameters that can be used in our computation:

C(m) = 2m + 15

Where

m = number of minutes

C(m) = cost function

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = 2

This means that the slope is 2

And it means that the cost per minute is $2

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The percentage of adults from this country who viewed a college education as essential for success x years after the first year can be represented by the function P(x) = 31 + 2.6x.

What is the percentage function?

To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100. Percentage formula = (Value/Total value) × 100. Example: 2/5 × 100 = 0.4 × 100 = 40 per cent.

The percentage of adults from this country who viewed a college education as essential for success x years after the first year can be represented by the function:

P(x) = 31 + 2.6x

Where P(x) is the percentage of adults who viewed college education as essential for success x years after the first year, and x is the number of years after the first year.

The function shows that the percentage increase by 2.6 every year for x years after the first year, and the initial percentage is 31%.

This function is representing a linear trend since the coefficient of x is constant.

Hence, The percentage of adults from this country who viewed a college education as essential for success x years after the first year can be represented by the function P(x) = 31 + 2.6x.

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The distance traveled from the starting point to the ending point is 30.35 km.

What is a bearing?

A bearing tracks the rotation of an angle around the north line in a clockwise fashion. The line connecting the compass's centre to a location and measuring its bearing in degrees as it moves clockwise from north is known as the bearing.

The ship travels 50 km on a bearing of 27°, and then travels on a bearing of 117° for 140 km.

The x-coordinate of the final point is -

50 cos (27°) + 140 cos (117°) = -19

The y-coordinate of the final point is -

50 sin (27°) + 140 sin (117°) = 23.67

The distance from (0,0) to the final point is as follows -

d = √(-19)^2+(23.6)^2)

= √(921.27)

= 30.35 km

Therefore, the distance traveled is 30.35 km.

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Answer: 1. The first graph has the x and y axis values as minutes and frequency, but the title is bicycling.

2. it's a dotted graph, which doesn't give enough information since that graph does not have to be linear, but when you have a graph like that you want a line graph.

Answer:

the other dude answered it better than i did

Step-by-step explanation:

Answer:

Step-by-step explanation:

-2y-10=x-10x

-2(-14) - 10= x - 10x

28 - 10 = x - 10x

18= x-10x

18= -9x

/-9    /-9

-2=x

Each side when you plug in (-2) for x and (-14) for y you get 18.

If, when you plug in the number, you get different numbers for each side, then that means there's a mistake and the answer is wrong.

Hope this helps!

(A) (x+4)(x-1)=0 is the proper factors form of the given equation x²+3x-4=0.

A factor is a number that completely divides another number.

To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

So, we have the equation:

x²+ 3x - 4 = 0

By dividing the center term, this quadratic equation can be reduced to its simplest form.

The result of dividing the middle word is:

x² + 4x - x - 4 = 0

One way to spell it is as:

x (x + 4) - 1 (x + 4) = 0

Now, we obtain:

(x + 4) (x - 1) = 0

Therefore, (A) (x+4)(x-1)=0 is the proper factors form of the given equation x²+3x-4=0.

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Correct question:

Which of the following is the correct factored form of the given equation x2+ 3x - 4 = 0?

(A) (x +4) (x - 1) = 0

(B) (x - 4) (x - 1) = 0

(C) (x - 4) (x +1)= 0

Multiply each digit by its corresponding place value and add the results: 11 + 0.011

11.011 = 11 + 0.011 = 11.011

Once the bits of the binary number have been multiplied by the corresponding positional weights, the binary number can then be converted into its corresponding decimal number by adding the resulting products.

To convert a number in base 2 (binary), base 8 (octal) or base 16 (hexadecimal) to a base 10 (decimal) number, you can use the following method:

Write the number in base 2, 8, or 16 and the corresponding base 10 place values.

Multiply each digit by its corresponding place value and add the results.

For example, to convert the base 10 number 11.011 to a base 10 number:

Write the number and the corresponding base 10 place values: 11.011

Multiply each digit by its corresponding place value and add the results: 11 + 0.011

11.011 = 11 + 0.011 = 11.011

As the number is already in base 10, it does not need to be converted. The value is 11.011

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The function Formula is, f(t) = 6t + 8.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation.  The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The collection of values that could result in a function's outputs is known as the co-domain.

Given:

Carolina charges an initial fee plus $6 for each hour of work

Her total fee for a 4-hour job = $32

So, if she work for 't' hours then linear equation will be of the form

f(t) = mt + b

Here m is the constant rate = 6

Now we plug in the values and find out b, m=6

f(t) = mt + b

32 = 6(4) + b

32= 24 + b

8 = b

So, the function is f(t) = 6 t+8.

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The given set of ordered pairs does not satisfy a linear function.

A linear function is one that, when plotted, forms a straight line. Therefore, non-linear functions are all non-linear functions. We can discern if a function is linear or non-linear from its input/output table or equation, but graphing may be the quickest way to do it.

Given:

The given set of ordered pairs is:

{(3, 2), (4, 3), (5, 4), (6, 5)}

To find:

Whether the given set of ordered pairs satisfies a linear function or not.

Explanation:

The slope of a linear function is:

m = (y₂ - y₁)/ (x₂ -x₁)

The slope of the linear function passes through the points  and  is:

m₁ = (3-1)/(3-1)

m₁ = 2/2

m₁ = 1

The slope of the linear function passes through the points  and  is:

m₂ = (9-3)/(5-3)

m₂ = 6/2

m₂ = 3

Therefore m₁ ≠ m₂ therefore the given set of ordered pairs does not satisfy a linear function.

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The fraction which is equivalent to 4/6 is 8/12 as asked in the question.

2 x 4 = 8 and

3 x 4 = 12

Therefore, they satisfies the condition of an equivalent numbers.

Equivalent numbers are those which on reducing to it's lowest terms gives the same number.

Other example , 2/4 is equivalent number to 8/16 .

Equivalent fractions are those fractions which has different numerators and denominators but the same value when reduced to their lowest terms. For, example 2/4 and 3/6 are comparable fractions because they both equal 12.

A fraction is a portion of a number written in terms of numerator and denominator. Equivalent fractions represent the same percentage of the whole.

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Definition of Ray:

'A part of a line that has one endpoint and extends indefinitely in one direction'.

The correct statement is A.

A ray is a part of the line having one fixed point and the other point does not have an end. It means that a ray has one terminating end and the other end is extending infinitely.

Given definitions of ray:

A. a part of a line that has one endpoint and extends indefinitely in one direction.

B. the set of all points in a plane that are a given distance away from a given point.

C. lines that lie in the same plane and do not intersect.

D. a part of a line that has two endpoints.

Only statement A satisfies the definition of ray.

Hence, the definition of ray is described by statement A.

A part of a line that has one endpoint and extends indefinitely in one direction.

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Answer:

Step-by-step explanation:

                                                             !:}

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0     1/9            2/9                   3/9     4/9        5/9   6/9   7/9   8/9  9/9

Center : Mean  Before the introduction of the new course, center = average(121,134,106,93,149,130,119,128) = 122.5  After the introduction of the new course, center =  average(121,134,106,93,149,130,119,128,45) = 113.9  The center has moved to the left (if plotted in a graph) because of the low intake for the new course.  Spread before introduction of the new course :  Arrange the numbers in ascending order:  (93, 106,119, 121), (128, 130,134, 149) Q1=median(93,106,119,121) = 112.5 Q3=median(128,130,134,149) = 132  Spread = Interquartile range = Q3-Q1 = 19.5  After addition of the new course,

(45,93, 106,119,) 121, (128, 130,134, 149)

Q1=median(45,93,106,119)=99.5

Q3=median (128, 130,134, 149)= 132

Spread = Interquartile range = 132-99.5 =32.5

We see that the spread has increased after the addition of the new course.

On solving the provided question, we can say that So, the total surface area of cuboid is larger by (610 — 600 = IO) cm2

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

(Lateral surface area of cube = 4edge2

lateral surface area of cuboid =2h (l + b)

[tex]2 x 8(12.5+ 10)\\= 16 x 22.5\\= 360\\[/tex]

lateral surface area of the cube is larger by (400

- 360

= 40)cm2

Total surface area of cube = 6edge2

= 600

lateral surface area of cuboid

[tex]=2 (lb + bh + hl)\\2(12.5 x 10+ x 8+8 x 12.5)\\= 2 (125 + 80 + 100)\\= 610[/tex]

So, the total surface area of cuboid is larger by (610 — 600 = IO) cm2

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The statement given here is true as 5x and 5 are like terms.

This is because like terms have the variables of same degree . Therefore, 5x and x are like terms as both of them have x to the power 1 , which means both are of degree 1.

Like terms differs from the unlike terms only in case of numerical component.  By summing the coefficients of  like terms , similar phrases can be regrouped. Like terms in a polynomial equation are those terms  that have the same variables and these variables have the same powers, but with different coefficients.

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