when there are fractions in an equation, how do you determine what number to multiply by in order to rewrite the equation into a simpler form?

From the given table it is visible that the value of s(5)=4.2

When the variables and constants in a mathematical expression are given values, the outcome of the computation it describes is the expression's value. The amount that the function assumes for these argument values is the value of a function, given the value(s) assigned to its argument(s).

functions with return values and arguments. Functions with arguments and no return values.... This function takes arguments and returns a value.

functions with return values and no arguments.

without return values and without arguments

Function value can mean: The result of applying a function to an argument in mathematics. a closure in computer science.

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The errors in the equation is shown below.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 8 is an equation.

We have,

4a² x 3[tex]a^5[/tex]

= 4 x 3 x [tex]a^{2 + 5}[/tex]

= 12 [tex]a^7[/tex]

[tex]x^6[/tex] x (x) x x³

= [tex]x^{6 + 1 + 3}[/tex]

= [tex]x^{10}[/tex]

[tex]3^4[/tex] x 2³

= 3 x 3 x 3 x 3 x 2 x 2 x 2

= 81 x 8

= 648

Thus,

The equation is solved correctly above.

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Answer:

8.5

Step-by-step explanation:

this is a right triangle so we could use the formula, which is Pythagorean theorem

so it is [tex]13.5^{2} -10.5^{2} =72\\\sqrt{72} =8.5[/tex]

Answer: 1 1/6

Step-by-step explanation:

The solution is given below.

In maths a bar model is a pictorial representation of a problem or concept where bars or boxes are used to represent the known and unknown quantities. Bar models are most often used to solve number problems with the four operations – addition and subtraction, multiplication and division.

here, we have,

"5y=95"

"6b=12"

"168/c=8"

" v / 7=5"

so, the bar model ,

y = 95/5

  =19

b= 12/6

 = 2

c = 168/8

 = 21

v = 5* 7

  = 35

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Answer:

[tex]5x - 6 = 44 \\ \longrightarrow \: 5x = 44 + 6 \\ \longrightarrow \: 5x = 50 \\ dividing \: both \: sides \: by \: 5 \: \\ \\ \longrightarrow \: \cancel\frac{5x}{5} = \cancel\frac{50}{5} \\ \\ \longrightarrow \:\boxed{ x = 10}[/tex]

hope helpful! :)

Answer:

Step-by-step explanation:

5x - 6 = 44

5x = 50

x = 10

---------------------

check

5 x 10 - 6 = 44     (remember pemdas)

44 = 44

the answer is good

The value of b for which ∫b0cos(ex)dx is minimum is π/2e..

To find the value of b for which the definite integral ∫b0cos(ex)dx is a minimum, we can find the critical points (i.e. local extrema) of the integrand cos(ex) in the interval [0, 2].

Since cos(ex) is a periodic function with period 2π/e, it suffices to consider the interval [0, 2π/e]. In this interval, cos(ex) has its maximum value of 1 at x = 0, and its minimum value of -1 at x = π/2e and x = 3π/2e.

Since e is positive, the function cos(ex) is increasing on the interval [0, π/2e) and decreasing on the interval (π/2e, π/e].

Therefore, if b is in the interval [0, π/2e), the integral is minimized when b = 0. If b is in the interval [π/2e, π/e], the integral is minimized when b = π/2e.

Since the maximum value of b is 2, and 2 < π/e, it follows that the integral ∫b0cos(ex)dx is minimized when b = π/2e.

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Coin tossing has a simple event of heads or tails, a joint event of multiple coin combinations, the complement of heads is tails, and sample space is {heads, tails}.

a. A simple event in coin tossing is getting either heads or tails on a single coin flip.

b. A joint event in coin tossing is getting heads on one coin and tails on another coin, for example.

c. The complement of getting heads on a coin flip is getting tails. The complement of getting tails is getting heads.

d. The sample space in coin tossing consists of all the possible outcomes of a single coin flip. This can be represented as a set, such as {heads, tails}. The sample space is the set of all possible outcomes of the experiment.

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Answer:

y = 6x

Step-by-step explanation:

Each value of x is multiplied by 6 to get the corresponding y value

The graph goes through (5.44,2) and (8.16,3) is false.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

Given that price for gasoline is represented by the equation y = 2.72x,

where y r represents the total price for x gallons of gasoline

We have to check whether the line passes through (5.44,2) and (8.16,3)

From the equation the slope is 2.72.

Now let us check whether the two points gives the same slope.

m=3-2/8.16-5.44

=1/2.72

=0.36

Hence,  the graph goes through (5.44,2) and (8.16,3) is false.

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The player who has better batting average is Jenna

They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

Calculating the ratio of both players we get:

Jenna ratio = 7/10

Jenna ratio = 0.7

Taha ratio = 10/16

Tasha ratio = 0.63

0.7 > 0.63

7/10 > 10/16

Jenna > Tasha

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Correctly written question:

In baseball each time a player get to hit the ball it is recorded.  The ratio of hit compared to the total attempt is their batting average. Each player on the team wants to have the highest batting average to help their team the most. So far Jenna has hit the ball 7 times out a 10 and Tasha has hit the ball 10 out of 16 time. Which player has a ratio that mean they have a better batting average?

Area of square B is 729.

Now, According to the question:

A square is a two-dimensional figure with four sides. It is also known as a quadrilateral. The area of a square is defined as the total number of unit squares in the shape of a square. In other words, it is defined as the space occupied by the square.

"Information available from the question"

We have been given that the ratio of the side length of square a to the side length of square b is 4:9. The side length of square a is 12 yards.

First of all, we will find the side length of square b using proportions as:

[tex]\frac{a}{b} = \frac{4}{9}[/tex]

[tex]\frac{12}{b}=\frac{4}{9}[/tex]

Cross multiplying the equation:

4b = 108

b = 108/4

b = 27

We know that area of a square is [tex]side^2[/tex]

=> b = 27

Area of square = [tex]27^2[/tex]

Area of square = 729

Hence, Area of square B is 729.

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After the second month, the charge will remain the same. 14 + 28 (2) = $70 would be the final price.

The first club offers a lower membership cost but a higher monthly fee in this instance, while the second club offers the polar opposite.

The computation would then be as follows to determine how long it would take for the total cost of each health club to equalize:

Example:

1 club fee equals 2 clubs fees

14+ 28x= 24+ 23x

28x-23x= 24-14

5x= 10 \sx=2

After the second month, the charge will remain the same. 14 + 28 (2) = $70 would be the final price.

The Complete Question.

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Answer: 35/4

Step-by-step explanation:

8x4=32

32+3=35

The polynomial function is f(x) = (x - 3)((x - 2)² + 9)

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

Zeros: x=3, 2 +-3i

The polynomial can be repesented as

f(x) = product of (x - zeros)

using the above as a guide, we have the following:

f(x) = (x - 3)(x - (2 - 3i))(x - (2 + 3i))

This can be expressed as

f(x) = (x - 3)((x - 2)² + 9)

hence, the polynomial is f(x) = (x - 3)((x - 2)² + 9)

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Answer:

You provided plenty of background information, but please provide a question to be answered.

The conclusions with regards to the similar right triangles, Yvonne needs to prove the Pythagorean Theorem are;

PQ/PR = PS/PQ and QR/PR = RS/QR

Pythagorean Theorem outlines the relationship between the length of the hypotenuse side and the lengths of the legs of a right triangle. The theorem states that the sum of the squares of the lengths of the legs of a right triangle, is equivalent to the square of the length of the hypotenuse side.

The specified similar triangles are;

ΔPQR ~ ΔQSR ~ ΔPSQ

PQ/PS = PR/PQ...(1)

(PQ)² = PS·PR

QR/RS = PR/QR...(2)

(QR)² = RS·PR

(PQ)² + (QR)² = PS·PR + PR/RS = PR·(PS + RS) = PR×PR = (PR)²

(PQ)² + (QR)² = (PR)²

Equations (1) and (2), can be expressed as follows;

PQ/PS = PR/PQ...(1)

Multiply both sides by PS/PR

PQ/PS × (PS/PR) = PR/PQ × (PS/PR)

PQ/PS × (PS/PR) = PQ/PR

PR/PQ × (PS/PR) = PS/PQ

Therefore;

QR/RS = PR/QR...(2)

Multiplying both sides by (SR/PR). we get;

QR/SR × (RS/PR) = QR/PR

PR/QR × (RS/PR) = RS/QR

Therefore, the conclusions about the triangles, Yvonne can use in her proof of the Pythagorean Theorem are;

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one is above sea level the other below sea level, so their distance is just their sum from sea level, so hmmm let's convert the mixed fractions to improper fractions and then sum them up.

[tex]\stackrel{mixed}{16\frac{1}{4}}\implies \cfrac{16\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{65}{4}} ~\hfill \stackrel{mixed}{7\frac{3}{8}} \implies \cfrac{7\cdot 8+3}{8} \implies \stackrel{improper}{\cfrac{59}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{65}{4}+\cfrac{59}{8}\implies \cfrac{(2)65~~ + ~~(1)59}{\underset{\textit{using this LCD}}{8}}\implies \cfrac{130+59}{8}\implies \cfrac{189}{8}\implies 23\frac{5}{8}[/tex]

Yes -20 degrees and 340 degrees are co-terminal angles

are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. For example, the angles 30°, –330°.

The coterminal angles can be positive or negative. To find the coterminal angles, simply add or subtract 360 degrees as many times as needed from the reference angle. All of these angles are coterminal angles.

co-terminal angles are found by adding or subtracting 360° to the angles.

for example the co-terminal angles of -10° = -10° + 360 = 350°

Similarly The co-terminal angles of -20 = -20+360 = 340°

therefore the -20 and 340 are co-terminal angles

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If distinct vertices of an octagon are chosen at random , then the probability that they are adjacent is 2/7 .

An Octagon has 8 vertices, so there are 8 possible vertices to choose from. To find the probability that two chosen vertices are adjacent, we need to determine the number of ways in which two adjacent vertices can be chosen,

Since there are 8 vertices and each vertex has 2 adjacent vertices,

The total number of pairs of vertices in octagon is = ⁸C₂  =  28;

the possible Adjacent pairs are : {(1,8),(1,2),(2,3),(3,4),(4,5),(5,6),(6,7),(7,8)} ;

So , probability of vertices being adjacent is = 8/28 ;

Simplifying further , we get ;

Probability ⇒ 2/7 .

Therefore , the probability that vertices are adjacent is 2/7 .

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The volume of the box will be 3136 cu. inches and the largest volume the box can be made of is also the same.

The amount of space occupied by a three-dimensional object as measured in cubic units.

The given square after getting folded turns into a box of 28*28*4 inches. The volume of the box can be determined by using the formula of volume of the cuboid.

Volume of the cuboid = 28*28*4

Volume of the cuboid  =3136 cu. inches

The largest volume that the box can have is 3136 cu. inches as when increasing the height, the length or the width will decrease and so does the volume.

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The sum-of-minterms form of the function f(a,b,c) = a'b + ac is (a'b + ac).

To convert a function with three variables to sum-of-minterms form, we first need to determine the truth table of the function, which lists all possible combinations of inputs and the corresponding outputs. Then, we identify the minterms (i.e., combinations of inputs that result in a 1 output) and represent each minterm as a binary number. The sum-of-minterms form of the function is then the sum of all the binary numbers representing the minterms.

For example, consider the function f(a,b,c) = a'b + ac. (The truth table for this function is attached below)

From the truth table, we can see that the minterms are (0,1,1) and (1,0,1), which can be represented as binary numbers 011 and 101, respectively. The sum-of-minterms form of the function is then:

f(a,b,c) = 011 + 101 = (a'b + ac)

So, the sum-of-minterms form of the function f(a,b,c) = a'b + ac is (a'b + ac).

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The model that is most likely rule out on the basis of this simulation is 40%

Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.

First set of trials:  ththththht ( where T = Tails ; H = Heads)

Number of heads = 5

Number of outcomes = 10

Second set of trials: ttthtthtth

Number of heads = 3

Number of outcomes = 10

Total number of heads = 5 + 3 = 8

Total number of outcomes = 10 + 10 = 20

Probably of heads = 8/20 * 100%

Probably of heads = 0.4*100%

Probably of heads = 40%

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Answer:

2x - 5y = 10

Step-by-step explanation:

the equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

given

y = [tex]\frac{2}{5}[/tex] x - 2 ( multiply through by 5 to clear the fraction )

5y = 2x - 10 ( subtract 2x from both sides )

- 2x + 5y = - 10 ( multiply through by - 1 )

2x - 5y = 10 ← in standard form

For the orthogonal matrices, the product of two invertible matrices is also invertible.

Orthogonal matrices are matrices that have a special property: the dot product of each of their rows or columns is equal to 0.

The dot product of two vectors is equal to 0 when the vectors are orthogonal to each other, meaning they are perpendicular.

Since U and V are orthogonal matrices, each is invertible by the definition of orthogonal matrices.

The inverse of an orthogonal matrix is its transpose.

This is because the dot product of each row (or column) with itself is equal to 1, so the transpose of an orthogonal matrix is its inverse.

The product of two invertible matrices is also invertible, so UV is invertible.

Answer C is correct.

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Answer:  Town B

Step-by-step explanation:

Town A -

2400 - 2000 = 400

percentage increase = 400/2000x100

                                   = 20 %

Town B -

2300 - 1800 = 500

percentage increase = 500/1800x100

                                   = 27. 78 %

The perimeter of the actual triangle is 74 and option D is the correct answer.

The scale factor is the difference in size between the original item's scale and that of the new object, which is a representation of it (bigger or smaller).

Given that the scaled dimension of the triangular face has the following dimensions:

PQ = 12

QR = PQ(1 + 25/100) = 12(125/100) = 15

PR = 2/3 (QR) = 2/3 (15) = 10

The scaling factor is 1/2 hence the actual dimensions of the triangle would be:

Original segments (1/2) = Scaled segment

Scaled (2) = Original

Using the above we have:

PQ = (12)(2) = 24

QR = (15)(2) = 30

PR =(10) (2) = 20

The perimeter of the triangle is the sum of all it sides:

P = 24 + 30 + 20

P = 74

The perimeter of the actual triangle is 74 and option D is the correct answer.

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Answer:

10%

Step-by-step explanation:

11.6/11.1 = 0,1045045

Answer:

0 [tex]\neq[/tex] 16

two equations have no solution and if you graphed them their lines would not intersect, they would be parallel

Step-by-step explanation:

we can substitute the value of 'y' which is '2x' into the second equation as follows:

-6x + 3(2x) = 16

-6x + 6x = 16

0 [tex]\neq[/tex] 16

therefore, these two equations have no solution and if you graphed them their lines would not intersect, they would be parallel