Consider each of the following word problems.
Write a word sentence to represent what you are going to do with the numerical values.
Include the proper brackets, exponents and operation signs.
Substitute the words with an appropriate variable.
Solve each problem in good form.

1. The school library had a used book sale. Paperbacks were 25 cents each and hardcover books
were $1.25 each. There were 54 paperbacks and 163 hardcover books sold. How much money did
the library raise?
2. Tamara has to go on a business trip. Including taxes, her round trip airfare is $398.60 and her
room costs $115.70 per night. The cab fare from the airport to the hotel is $40.00. If Tamara
stays for two nights, how much does the trip cost, excluding the cost of food?
3. Paula repairs swimming pools and earns $14.50/h for the first 35 h she works in a week. For
hours over 35 h, she earns 1.5 times as much. If she works 48 hours in a week, how much does she
earn?
4. Will and Liam collect baseball cards. Will has 26 cards and Liam has 19. They decided to combine
their cards. Because they shared, their father decided that he would triple the number of cards
that they had. After that, their friend Nestor thought that he would add his cards to their bunch.
Nestor didn’t know how many cards he had but he knew that he could lay them out in rows and that
they would make a square with one side of his square having 8 cards. How many cards did the boys
have altogether?

Answer:

70 members

Step-by-step explanation:

Let's call the number of total members x. We know that 30% or  [tex]\frac{3}{10}[/tex] of the members forgot, so our equation looks like this:

[tex]\frac{3}{10}x = 21[/tex]

Then, we will multiply both sides by 10 to get rid of the fraction:

3x = 210

Finally, we will divide both sides by 3 to find out our variable, x:

x = 70

So, there are 70 members in total.

Hope this helped!

Answer:

Step-by-step explanation:

Let angle A = w - 15 degree , angle B = -w + 1 degree and angle X = w + 34 degrees then:

We know that the exterior angle of a triangle is equal to the sum of two interior opposite angles.

therefore, w + 34 = w - 15 + (-w +1)

w + 34 = w - 15 - w + 1

w = -15 - 34 = - 49 degrees

since angle cannot be negative

therefore w = 49 degrees

To rewrite the inequalities in slope-intercept form, the student would first need to solve for y.

2x + 3y > 6 can be rewritten as 3y > -2x + 6 and then solving for y by dividing both sides by 3, the student can have y > (-2/3)x + 2

x-4y > 8 can be rewritten as -4y > -x + 8, and then solving for y by dividing both sides by -4 , the student can have y < (1/4)x - 2

To graph the inequalities, the student would plot the y-intercepts of the equations, which are (0,2) and (0,-2) and then use the slope to find a second point to plot, and then graph the line. Then, based on the inequality symbol the student should shade the appropriate side of the line. If the inequality is greater than > or less than < then they shade one side, otherwise if the inequality is less than or equal to >= or greater than or equal to <= they shade both sides.

It's also important to remember that the slope intercept form is y=mx+b where m is the slope, and b is the y-intercept, if the student already has the equation in this form, they only need to plot the y-intercept point and use the slope to get a second point.

The builder needs building sand weighing 6.3 * 10⁶ g and contains 9 * 10¹⁰ grains

An equation is used to show the relationship between numbers and variables.

A brick layer needs 6300 kg of building sand

The conversion from kg to g is:

1 kg = 1000 g

a) 6300 kg in grams is:

6300 kg = 6300 kg * 1000 g per 1 kg = 6,300,000 g = 6.3 * 10⁶ g

b) 1 grain = 7 * 10⁻⁵ g

6.3 * 10⁶ g = 6.3 * 10⁶ g * 1 grain / (7 * 10⁻⁵ g) = 9 * 10¹⁰ grain

The builder needs 6.3 * 10⁶ g of building sand

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The drama "The Importance of Being Earnest" contains many inconsistencies. Algernon's criticism of the lower class for not providing a better moral example for the upper class is paradoxical because the higher class must set the standard because it is the ruling class.

A remark that logically contradicts itself or runs counter to one's expectations is referred to as a paradox.

It is a claim that, despite appearing to be supported by genuine premises and sound reasoning, leads to a logically untenable or self-contradictory conclusion.

One of the most straightforward yet well-known paradoxes is the liar paradox, sometimes known as the liar's paradox statement.

A paradox exists when someone says, "This statement is a lie" or "This statement is false," because if it were true, the statement would be speaking the truth.

In "The Importance of Being Earnest", the play has multiple contradictions.

Because the upper class is required to lead because it is the governing class, Algernon's dissatisfaction with the lower class for not setting a better moral example for the upper class is paradoxical.

Therefore, the drama "The Importance of Being Earnest" contains many inconsistencies. Algernon's criticism of the lower class for not providing a better moral example for the upper class is paradoxical because the higher class must set the standard because it is the ruling class.

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Answer:

56a+40b

Step-by-step explanation:

43a plus 13a is 56a, -12b + 52b is 40b, together it's 56a+40b

The domain and scope of the identity function are the same. Equation for the identity function is  f(x) = x, or y = x.

An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable). A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.

identity function are the same.

Equation for the identity function is

f(x) = x, or y = x.

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On solving the provided question, we can say that by unitary method Irene spend on gas =  $ 33.82

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

by unitary method

Irene must pay back the money she used for gas.

Irene filled up her tank with gas for $33.82.

One gallon of gasoline costs $3.80.

There are 6.1 gallons of the petrol Irene purchased in the tank.

amount required = 15 -6.1 = 8.9 gallons

1 gallon = 3.8 dollars

8.9 gallons = $ 33.82

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No solution is a fraction that cannot be represented as a fraction of integers.

A fraction is a division of two numbers, and no solution occurs when the divisor is 0, because division by 0 is undefined.

For example, consider the fraction 2/0. This is a fraction with no solution because division by 0 is undefined. To explain this further, let's look at the formula for division: a/b = c. In this formula, a is the dividend, b is the divisor, and c is the quotient. In the fraction 2/0, the dividend is 2 and the divisor is 0, so when we try to calculate the quotient, we get c = 2/0. Since division by 0 is undefined, the result is no solution.

To summarize, no solution occurs when a fraction's divisor is 0 because division by 0 is undefined. This means that no fraction can be represented as a fraction of integers when the divisor is 0 because there is no solution.

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Answer:

g (x) = −7 x 2 + 26 x + 8

Step-by-step explanation:

Answer:

  Manuel can make 5 batches of muffins using Recipe 1

Step-by-step explanation:

You want to know the value of b in the equation 2b = 10, where b is the number of batches of muffins Manuel can make using recipe 1.

Divide both sides of the given equation by 2 so solve for the value of b.

  (2b)/2 = (10)/2

  b = 5

Manuel can make 5 batches of muffins using Recipe 1.

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The 3 parts of a quadratic equation are standard form, factored form and vertex form.

A quadratic equation is a polynomial equation of degree two in one variable of type f(x) = ax² + bx + c where a, b, c, ∈ R and a ≠ 0.

There are three forms of quadratic equations

Standard form of quadratic equation y = ax² + bx + c

factored form of quadratic equation y = a(x − r₁)(x − r₂​)

Vertex form of quadratic equation y = a(x − h)² + k

Each of the above quadratic forms looks unique, allowing the different problems to be more easily solved in one form than another.

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$1862  is Devi red from his biweekly paycheck for medical insurance

percentage, a relative value indicating hundredth parts of any quantity.

The annual cost of Randall coverage is 4900.

The college pays 62% of the cost.

We need to find How much is Devi red from his biweekly paycheck for medical insurance

Let us convert 62% to decimal value by dividing with 100

62/100=0.62

Now multiply 0.62 with 4900

0.62×4900

3038

Now subtract 3038 from 4900

4900-3038

1862

Hence, $1862  is Devi red from his biweekly paycheck for medical insurance

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The amount of the proposed increase is, Rs 1071.4

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The annual gym subscription for a single member is Rs.1000,

And, An annual family membership is Rs.1500.

Here, A single membership increased cost 5/7 of a family membership.

Hence, The increased cost = 5/7 of 1500

                                          = 1071.4 Rupees

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A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question.

In a right triangle, the hypotenuse is the longest side, the "opposite" side is the one that faces a particular angle, and the "adjacent" side is the one that faces that angle.

Step 1: Simplify both sides of the equation.

[tex]$$4 g-6=8$$\\Step 2: Add 6 to both sides.$$\begin{aligned}& 4 g-6+6=8+6 \\& 4 g=14\end{aligned}$\\$Step 3: Divide both sides by 4 .$$\begin{aligned}& \frac{4 g}{4}=\frac{14}{4} \\& g=\frac{7}{2}\end{aligned}$$[/tex]

[tex]$g=3 \frac{1}{2}$[/tex]

Therefore, the correct answer is option a)[tex]$g=\frac{7}{2}$[/tex].

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Leo's balance after 8 months is $1725.

A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.

Example:

2, 4, 8, 16 is a geometric sequence.

We have,

1500, 1530, and 1560 is a geometric sequence.

First term.

a = 1500

Common ratio.

r = 1.02

The nth term of a geometric sequence is a[tex]r^{n-1}[/tex].

Now,

For n = 8,

8th term.

= 1500 x [tex]1.02^7[/tex]

= 1500 x 1.15

= 1725

Thus,

The balance after 8 months is $1725.

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-6,7 is in 2nd Quadrant of a coordinate plane because the coordinate of x is negative integer and the coordinate of y is positive integers.

It is possible to find any point in a 2D plane or 3D space using coordinates, which are ordered pairs of points. We may have observed the use of grids in mathematics. We can plot any point using these grids and its coordinates.

Cartesian coordinates, also known as the coordinates of a point in a 2D plane, are two integers, or occasionally a letter and a number, that identify a specific point's precise location on a grid. This grid is referred to as a coordinate plane.

The X-axis is the horizontal axis and the Y-axis is the vertical axis of a coordinate plane, which has four quadrants.

To plot -6, 7 point on coordinate first we find the point -6 on the left side of plane on x axis. the we go upward and find point y=7 parallel to y axis.

this point is -6,7.

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We find the sine and cosine of an acute angle by taking the ratio of the length of the side opposite to the angle with respect to the length of the side adjacent to the acute angle.

What is the tangent of the angle?

The ratio of the right-angle triangle's base or perpendicular is known as the tangent of the angle.

The ratio of two of the right-angled triangle's three sides is used to define the sine, cosine, and tangent of an acute angle.

Here,

We have to find out how is a right triangle used to find the sine and cosine of an acute angle is there a unique right triangle that must be used.

We concluded that a right triangle can be used to determine the tangent of any acute angle, by taking the ratio of the length of the side opposite to the angle with respect to the length of the side adjacent to the acute angle.

Hence, we find the sine and cosine of an acute angle by taking the ratio of the length of the side opposite to the angle with respect to the length of the side adjacent to the acute angle.

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The values of p that satisfy the inequality for all[tex]$q > 0$[/tex] are

[tex]$p > \frac{3+\sqrt{21}}{2}$[/tex]and [tex]$p < -\frac{3+\sqrt{21}}{2}$[/tex]

Given:[tex]$$\frac{3(pq^2 p^2q 3q^2 3pq)}{p q} > 2p^2q^2$$[/tex]

Step 1: Multiply both sides by [tex]$\frac{pq}{3}$[/tex] to get: [tex]$$pq^3 p^2q 3q^2 3pq > 2p^2q^3$$[/tex]

Step 2: Simplify the left side to get: [tex]$$3p^2q^3+3pq^3+3q^2 > 2p^2q^3$$[/tex]

Step 3: Divide both sides by [tex]$q^2$[/tex] to get: [tex]$$3p^2q+3pq+3 > 2p^2$$[/tex]

Step 4: This is a quadratic inequality in[tex]$p$[/tex]with solution[tex]$p > \frac{3+\sqrt{21}}{2}$[/tex] and [tex]$p < -\frac{3+\sqrt{21}}{2}$[/tex]. Therefore, the values of p that satisfy the inequality for all  [tex]$p > \frac{3+\sqrt{21}}{2}$[/tex] and [tex]$p < -\frac{3+\sqrt{21}}{2}$[/tex]

the given inequality can be simplified to a quadratic inequality in p by multiplying both sides by[tex]$\frac{pq}{3}$[/tex], simplifying the left side, and dividing both sides by[tex]$q^2$[/tex] The solution of the quadratic inequality is

[tex]$p > \frac{3+\sqrt{21}}{2}$[/tex] and

[tex]$p < -\frac{3+\sqrt{21}}{2}$[/tex]. Therefore, the values of p that satisfy the inequality for all [tex]$q > 0$[/tex] are

[tex]$p > \frac{3+\sqrt{21}}{2}$[/tex]and

[tex]$p < -\frac{3+\sqrt{21}}{2}$[/tex], which means that any value of p that is greater than[tex]$\frac{3+\sqrt{21}}{2}$[/tex] or less than

[tex]$-\frac{3+\sqrt{21}}{2}$[/tex]will satisfy the inequality for all [tex]$q > 0$[/tex]

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The graph of the function g(x) is added as an attachment

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

f(x) equals log2 x

Express the equation properly

So, we have

f(x) = log₂(x)

Also, we have

g(x) = -log₂(x - 3)

The transformation from f(x) to g(x) is that:

This means that

g(x) = -f(x - 3)

So, we apply the above transformations on the graph of f(x) to form g(x)

See attachment for graph of g(x)

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Relief refers to the highest and lowest point elevation in an area.

Relief

Relief is the term used for the differences in height from place to place on the land’s surface and it is greatly affected by the underlying geology. Relief relies on the hardness, permeability and structure of a rock.

elevation

The elevation of a geographic location is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface.

geology

Geology describes the structure of the Earth on and beneath its surface, and the processes that have shaped that structure. It also provides tools to determine the relative and absolute ages of rocks found in a given location, and also to describe the histories of those rocks.

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Answer: Relief

Step-by-step explanation:

Relief refers to the highest and lowest point elevation in an area.

Slope is the measure of steepness

Topography refers to the arrangement of the land in an area

Elevation on the other hand is the distance above sea level

Answer:

x^2-9

Step-by-step explanation:

-3 + 3 = 0 so the x terms cancel out.  This leaves you with only x^2-9

Step-by-step explanation:

Let A be the sum from 100 to 300

so the sum of 97 to 298 =

A - (299+300) + 97 +98

= A - 403

One final test that lasts three hours is given in addition to four-hour exams that are given by the teacher. The student's last grade is an 83.29.

The final exam result was an 80, which counts as 31 hour examinations if the exam scores range from 60 to 81, which totals to 97,87. In order to accomplish this, we must multiply three eighty by 62, 81, 97, and 87, which equals a 31-hour exam.

The whole time for the final exam, which is 31 hours, will be added up and divided by 7, giving us an average final grade for the student of 81.To reduce the number's number of significant digits in order to approximate it. Rounding down from 15.4 to 15.5, from 15.51 to 15.5 or 16, from 0.499 to 0, and from 970,000 to 1 million.

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Answer:

[tex] \sf \: 7.31[/tex]

Step-by-step explanation:

Now we have to,

→ round a number to 2 decimal places.

The number is,

→ 7.3084

Let's solve the problem,

→ 7.3084

→ ≈ 7.308

→ [tex] \boxed{ \sf ≈ 7.31} [/tex]

→ ≈ 7.3

Hence, the answer is 7.31.

Answer: 88

Step-by-step explanation:

Answer: 88

Step-by-step explanation: 5x5=25 + 9x7=63 ----> 25+63= 88

:)

ggggggggggggrssdfffffffffffffffffffffffffffffffffrsssssssssshggh

Answer:

5 × x + 8

Would be the equation you are looking for.

Answer:

X of M is 6, Y of M is 4, Pair is (6,4)

Step-by-step explanation:

M = 6

M = 4

M (6,4)

Answer:

34 + 23 = 57

57 - 5 = 52

Therefore, she has 52 toy horses.

The number of ducks on the farm is 12 legs / 2 legs/duck = 6 ducks.

To determine this:

Each cow has 4 legs, so the cows have 3 cows * 4 legs/cow = 12 legs.

Each chicken has 2 legs, so the chickens have 8 chickens * 2 legs/chicken = 16 legs.

We know the total number of farm animal legs is 40 legs.

So the number of duck legs can be calculated by subtracting the number of cow legs and chicken legs from the total number of farm animal legs: 40 legs - 12 legs - 16 legs = 12 legs.

Since each duck has 2 legs, the number of ducks on the farm is 12 legs / 2 legs/duck = 6 ducks.

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