There are 4 books on a shelf. books are added to the shelf at a rate of 2 books per minute. the total number of books on the shelf, y, is a function of the number of minutes, x, that the books have been added to the shelf. write an algebraic equation for the function.

Answer:

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Opposite leg / hypotenuse is the ratio for sine:

Correct choice is A.

Opposite leg / adjacent leg is the ratio for tangent:

Correct choice is C.

Adjacent leg / hypotenuse is the ratio for cosine:

Correct choice is B.

The ratio for tangent is opposite leg/adjacent leg,tan 53° is x/12.

We'll use the term sine and the symbol sin to denote the ratio of a right triangle's opposing side to hypotenuse. The cosine, denoted by the symbol cos, is the ratio between the neighboring side and hypotenuse of a right triangle.

The cosine, denoted by the symbol cos, is the ratio between the neighboring side and hypotenuse of a right triangle.

Explanation:

The first question is:

Correct answer is A: sin 40° = x/20.

The ratio for tangent is opposite leg/adjacent leg:

tan 53° = x/12

C is the proper selection.

The cosine ratio is the adjacent leg to hypotenuse:

cos 51° = 10/x

B is the proper selection.

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Each of the mortgage types should be matched with the correct description as follows:

Mortgage brokering can be defined as a strategic process which typically involves a mortgage broker acting as an intermediary between a financial institution such as a mortgage bank that is offering loans and an individual that seeks to collect (obtain) this loan.

Generally speaking, there are different types of mortgage and these include the following:

In conclusion, a government insured mortgage is a type of mortgage that requires a buyer making a 20% down payment.

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Complete Question:

Match the mortgage types with their descriptions. it requires the buyer to make a 20% down payment. a large portion of principal is paid in a single payment at the end of the loan. it has the same interest rate for the life span of the loan. it requires a lower down payment and allows buyers to have a lower credit score. it initially has a fixed rate for three to five years and then adjusts at a predetermined time. it starts with a low interest rate and then adjusts throughout the duration of the loan.

Brad takes 6 minutes to run a mile assuming he can maintain the same pace.

Given that,

One lap around the inside lane of a standard track = 400m

Time taken for Brad to jog one lap around a track = 1 minute and 30 secs

We know that one mile = 1609.34 meters = 1600 meters (approximately)

Since Brad can jog 400m in 1 minute and 30 secs

1600 meters = 400*4 meters

Assuming that he can maintain the same pace:

so, the total time taken to run 1 mile = 1 minute 30 secs * 4 = 6 minutes

Hence, Brad takes 6 minutes to run a mile assuming he can maintain the same pace.

Correct question: One lap around the inside lane of a standard track is equal to 400 meters: Brad jogs one lap around a track in one minute and 30 seconds. Assuming he can maintain this pace, how long will it take him to run a mile? Round your answer to the nearest tenth of a minute.

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The factorization of given expression is 4(2d+5e).

The factorization method uses basic factorization formula to reduce any algebraic or quadratic equation into its simpler form, where the equations are represented as the product of factors instead of expanding the brackets. The factors of any equation can be an integer, a variable, or an algebraic expression itself.

The given expression is 8d+20e.

In the given expression there are two terms and factors them are

8d= 2×2×2×d

20e= 2×2×5×e

So, the greatest common factor is 4

Now, 4(2d+5e)

Therefore, the factorization of given expression is 4(2d+5e).

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the square root 15v to the 4th power times square root of 2v to the 3rd power is 15v^2 x 2v^3, or 30v^5.

The square root of a number is a value that, when multiplied by itself, produces the original number. For example, the square root of 16 is 4 because 4 x 4 = 16. In mathematics, the square root of a number is written as a radical symbol, with the number inside the radical symbol. The square root symbol is also known as the radical symbol or radix.

To calculate this, first take the square root of 15v to the 4th power, which is 3v. Then take the square root of 2v to the 3rd power, which is 2v.

Finally, multiply 3v and 2v together to get the final answer of 30v^5.

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Complete questions as follows-
What is the square root 15v to the 4th power times square root of 2v to the 3rd power?

Answer:

1. 3/2 x m^5 x n

2. 54 x m^11 x n^9

Answer: (-4, 1) (-8, 9)

Explanation: These points are where the two functions meet

What shapes are the circles on the volleyball score  A blanket, sheet, plastic sheet, or other similar item is used by each squad. Each team starts with one ball and tosses and catches the others' balls in the blanket.

Fouls. A foul is when a player engages in play that is not permitted by the rules. A double foul occurs when two opposing players violate the rules at the same moment. A double hit occurs when a player makes several, or multiple consecutive, unlawful contacts. If a player steps above the service counter or centerline, they have made a foot error. The play court, which is 18 metres long and 9 metres wide, is surrounded by a free space that is actually 3 metres wide. The area that is at least 7 metres above the playing field and designated as the free performance space.

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Comparing the given expression with the slope-intercept form, the intercept value is calculated. And the value is -2/5.

A line's slope gives information about its steepness or indicates how much y rises as x rises. The equation is typically written as y=mx+b in slope-intercept form. The slope in this equation is represented by the letter m, and the y-intercept is represented by the letter b. The y-intercept is calculated in the subsequent step by comparing the given expression with this.

The given expression is y =- 2/5. Comparing this expression with y=mx+b, we get, m=0, x=0, and b=-2/5. Therefore, the required y-intercept is -2/5.

The complete question is -

What is the y-intercept of y =- 2/5?

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The measure of central tendency that would be the best to use as the most accurate indicator of the temperature for planning your wardrobe is the mean.

The ratio between the sum of all observations and the total number of observations in a data set is known as the mean in statistics. A data set's mean (average) is calculated by adding all of the numbers in the set, then dividing by the total number of values in the set.

When a data set is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.

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So answer is true For deductive arguments, you answer true to the question “Do the premises provide enough logical support for the conclusion

A valid argument is a deductive argument that succeeds in providing decisive logical support.

A valid argument is thus a deductive argument an argument that attempts to establish conclusive support for its conclusion  that succeeds.

An invalid argument is a deductive argument that fails in providing conclusive support.

For deductive arguments, you answer “yes” to the question “Do the premises provide enough logical support for the conclusion?” if the argument is valid, and you answer “no” if otherwise.

So answer is true For deductive arguments, you answer true to the question “Do the premises provide enough logical support for the conclusion

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Answer:

B and D

Step-by-step explanation:

-2+2=0

When a number greater than 1 is written in scientific notation, the exponent is positive.

Scientific notation is a way of expressing numbers that are very large or very small using a decimal number between 1 and 10, multiplied by a power of 10. For example, instead of writing the number 100,000,000 as 100,000,000, it can be written in scientific notation as 1 x 10^8.

The exponent of a number in scientific notation is the power of 10 that the decimal number is multiplied by, and it gives the number of places the decimal point is moved to the right or left to obtain the original number. In the example above, the exponent is 8, which indicates that the decimal point has been moved 8 places to the right to get the original number 100,000,000.

When the number is greater than 1, the exponent of scientific notation is positive and indicates that the decimal point is moved to the right.

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Answer:

-2

Step-by-step explanation:

Let's call the unknown number x.

We are given that:

1/x + 15 = 13

To find the value of x, we need to isolate x on one side of the equation.

To do this, we can subtract 15 from both sides:

1/x + 15 - 15 = 13 - 15

This gives us:

1/x = -2

To find x, we can multiply both sides by x:

x * (1/x) = x * (-2)

This gives us:

x = -2x

Therefore the number is -2

We can see here that the triangles have been attached to the corresponding angles and sides.

(a) ∠A ≅ ∠Y

    ∠B ≅ ∠Z

    ∠C ≅ ∠X

(b) Side AB ≅ Side YZ

    Side AC ≅ Side YX

    Side BC ≅ Side ZY

(c) ΔABC ≅ Δ YZX

Congruent refers to the state of two geometric figures or shapes having the same size and shape. Two figures are congruent if one can be superimposed on the other by a combination of rotation, reflection, and translation.

Congruence is often denoted by the symbol “≅”. Congruence is a fundamental concept in Euclidean geometry, and it applies to many types of geometric figures, including lines, angles, triangles, and polygons.

We can see that the various angles and sides has been shown above.

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[tex]d=\frac{|c_2-c_1|}{\sqrt{a^2+b^2}}[/tex]  is the formula used to calculate the distance between two parallel lines. This is derived from the slope-intercept equation.  

The two lines that never cross over one another are referred to as parallel lines. When the separation between these two lines is considered constant, then these two lines are parallel.

As a result, the distance between two lines can be determined by considering their perpendicular distance. The two parallel lines can be written using the slope-intercept form as y = mx + c₁ and y = mx + c₂, respectively.

Then, the formula to calculate distance is given by, [tex]d=\frac{|c_2-c_1|}{\sqrt{a^2+b^2}}[/tex]. Here, the intercepts of the two lines are c₁ and c₂, and a and b are the constants or integers.

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Therefore ,the linear function that best describes the scatterplot relating the number of books in the library is y = 10 + 8x

Two separate but related concepts are referred to as linear functions in mathematics: A polynomial function of degree 0 or 1 is referred to as a linear function in calculus and related fields if its graph is a straight line.

Here,

The points given on the scatterplot are (0,10),(4,42),(8,74) & (12,106)

By putting in the points in the given linear functions

y = 8 − 10x

y = 8 + 10x

In mathematics, the term "linear function" refers to two distinct but related ideas: In calculus and related subjects, a polynomial function of degree 0 or 1 is referred to as a linear function if its graph is a straight line.

y = 10 − 8x

y = 10 + 8x

Thus ,the  linear function which best satisfy the points given on the scatterplot is  y = 10 + 8x

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The length of YV is equivalent to 7.

Given is that UV = x + 6 and UY = x - 1. Also, WY intersects UV at Y.

We can write that -

UV = UY + YV

YV = UV - UY

YV = (x + 6) - (x - 1)

YV = x + 6 - x + 1

YV = 7

Therefore, the length of YV is equivalent to 7.

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The length of the hypotenuse of a 45 45 90 triangle with one side of length 8 is 8√2.

The length of the hypotenuse of a 45 45 90 triangle can be calculated using the Pythagorean Theorem. The Pythagorean Theorem states that the sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse. This can be expressed mathematically as a2 + b2 = c2, where a and b represent the lengths of the two sides and c represents the length of the hypotenuse.

In a 45 45 90 triangle, both sides are equal in length. This means that the mathematical equation simplifies to a2 + a2 = c2 or 2a2 = c2. To calculate the length of the hypotenuse, we can solve for c by taking the  square root of both sides, resulting in c = √2a.

In this particular example, if the length of one of the sides is 8, then the length of the hypotenuse can be calculated as c = √2(8) = 8√2. Therefore, the length of the hypotenuse of a 45 45 90 triangle with one side of length 8 is 8√2.

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Nadia made commission of $636 last week

She made $33072 commission in 2011.

In mathematics, 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,

Weekly commission of Nadia = 12%

Cost of stocks Nadia sold last week = $5300

Commission made by Nadia last week = 12% of $5300

                                                                 = (12/100) × 5300

                                                                 = 12 × 53

Commission made by Nadia last week = $636

No. of weeks in 2011 = 52 weeks

If she averages that same amount each week

Then commission made by her in 2011 = 52 × $636

                                                                 = $33072

Hence, $636 is the commission made by Nadia last week,

$33072 is the total commission made by Nadia in 2011.

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Answer:

10.4 feet

Step-by-step explanation:

26/5 = 5.2

5.2(2)=10.4

The length of the tree's shadow is 10.4 feet. Option B is correct.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

We can use similar triangles to solve this problem.

The ratio of the height of the fence post to its shadow is the same as the ratio of the height of the tree to its shadow.

(height of fence post) / (length of fence post's shadow) = (height of tree) / (length of tree's shadow)

Substituting the given values, we get:

5 / 2 = 26 / x

where x is the length of the tree's shadow.

Cross-multiplying and solving for x, we get:

x = 26 × 2 / 5

= 10.4 feet

Therefore, the length of the tree's shadow is 10.4 feet.

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The correct graph of the given systems of equations include the following: A. graph of two lines intersecting at two comma three with text on graph that reads One Solution 2, 3.

In Mathematics, a graph simply refers to a type of chart that is typically used for the graphical representation of ordered pairs (data points) on both the horizontal and vertical lines of a cartesian coordinate, which indicates the x-axis and y-axis respectively.

Next, we would use an online graphing calculator to plot the above system of equations with a point of intersection at (2, 3) as shown in the graph attached below.

By critically observing the graph of the given system of equations, we can logically deduce that it has only one solution, which is the ordered pair (2, 3);

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Answer:

[tex] \textcolor{green}{ \textbf{no}}[/tex]

[tex] x = \frac{1}{10} , y = \frac{83}{10} [/tex]

Step-by-step explanation:

y=53x+3

y=73x+1

Solve y = 53x + 3 for equ 2 | equ means equation

[tex] \sf \: 53x + 3 = 73x + 1[/tex]

Substract 73x from both sides

[tex] \sf \: 53x - 73x + 3 = 1[/tex]

Solve 53x - 73x

[tex] \sf - 20x + 3 = 1[/tex]

Substract 3 from both sides

[tex] \sf - 20x + 3 - 3 = 1 - 3[/tex]

Solve

[tex] \sf \: - 20x = - 2[/tex]

Divide both sides by -20

[tex] \sf \frac{- 20x}{ - 20}= \frac{ - 2}{ - 20} [/tex]

Solve

[tex] \sf x = \frac{1}{10} [/tex]

[tex] \sf ------------------------------------------------- [/tex]

Substitute x = 1/10 into equ 1

[tex] \sf y = 53x + 3[/tex]

Insert x = 1/10

[tex] \sf y = 53( \frac{1}{10} ) + 3[/tex]

multiply 54 by the numerator which is 1

[tex] \sf \: y = \frac{53}{10} + 3[/tex]

Turn 3 to 3/1

[tex] \sf \: y = \frac{53}{10} + \frac{3}{1} [/tex]

L.C.M = 10

[tex] \sf y = \frac{ \frac{53}{10} \times 10 \: + \: \frac{3}{1} \times 10 }{10} [/tex]

Simplify

[tex] \sf \: y = \frac{53 + 30}{10} [/tex]

Calculate 53+30

[tex] \sf \: y = \frac{83}{10} [/tex]

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The number of hours Bruce spent doing homework last week if he spent 1/5 of Darell's time is 1 hour.

Time Darell spent doing homework last week = 5 hours

Time Bruce spent doing homework last week = 1/5 of Darell's time

= 1/5 of 5

= 1/5 × 5

= (1 × 5) / (5 × 1)

= 5/5

= 1 hour

In conclusion, given the fraction of time Bruce spent doing homework last week, that means, he spent 1 hour doing homework.

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The function g is defined by the following rule. g(x) = 2x +1​ can be represented in the method given below-

How does this occur?

The function f with g is written as (fg)(x)=f(g(x)), and is understood as f of g of x. The function g will be used in place of any x in the function f, according to this statement (x)

f(x), where x is the input, is a common way to refer to a function. A function can be conceptualized as y = f in general (x).

This is how by taking various x value we can find the value of g(x) = 2x +1​

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The exponential form of 5 * 5 * 7 * 7 * 7 is [tex]5^{2}[/tex] * [tex]7^{3}[/tex] . Exponential form can be written from the prime factorization of the number.

To get the exponential form of a number we have to write the prime factorization of that number. Prime factorization of the number is that number written as a product of prime numbers or as a product of powers of prime numbers. A basic exponential function from its definition is of the form f(x) = b x, where 'b' is a constant and 'x' is a variable. generally it refers to the positive valued function of a real variable. We can find the prime factorization of a number using factor trees, which are tools used to repeatedly break a number into products until all of the factors are prime numbers.

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It is not possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm because the sum of two sides(2 cm and 3 cm) are smaller than third sides(7 cm).

In the given question, we have to check that it is possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm.

To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always grater than the third side.

To check this we firstly add the 2 and 3

2 + 3 < 7

5 > 7

Now we add 2 and 7

2 + 7 > 3

9 > 3

Now we add 3 and 7

7 + 3 > 2

10 > 2

It is not possible to construct a triangle whose sides are 2 cm 3 cm and 7 cm because the sum of two sides(2 cm and 3 cm) are smaller than third sides(7 cm).

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