Let f(x)represent a function.

Answer:

a₂₅ = 157

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 13 and d = 6 , then

a₂₅ = 13 + (24 × 6) = 13 + 144 = 157

The equivalent expression of each expression given, using the distributive property, are:

a. 6x + 10

b. 49a + 42

c. 20a² + 40ab

d. 8xy - 6y²

e. 27z - 30z²

f. 18x + 24 + 12y

g. 22c² + 77ac

h. 40b + 16bs + 24b³

i. 7a³ - 21a² + 42a

j. 36p² + 27p - 45

If we have an expression given as a(b + c), according to the distributive property, we can write an equivalent expression by using the term "a" to multiply each of the terms within the bracket, which will give us: a(b + c) = ab + ac.

a. 2(3x + 5), applying the distributive property, multiply each of the terms within the parentheses by 2:

2(3x) + 2(5)

6x + 10

Therefore, the equivalent expression of 2(3x + 5) is 6x + 10.

b. 7(7a+6)

7(7a) + 7(6)

= 49a + 42

c. 5a(4a+8b)

= 5a(4a) + 5a(8b)

= 20a² + 40ab

d. 2y(4x-3y)

= 8xy - 6y²

e. 3z(9 - 10z)

= 27z - 30z²

f. 6(3x + 4 + 2y)

18x + 24 + 12y

g. 11c(2c + 7a)

22c² + 77ac

h. 8b(5 + 2s + 3b²)

40b + 16bs + 24b³

i. 7a(a² - 3a + 6)

7a³ - 21a² + 42a

j. 9(4p² + 3p - 5)

36p² + 27p - 45

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The number of songs that he transferred per minute is 1 5/7 songs per minute (option B).

In order to determine the number of songs he can transfer in one minute, divide the number of songs transferred in 1 2/3 by the number of minutes.

Division is the process of determining the quotient of two or more numbers. It entails grouping a number into equal groups using another number. The sign that is used to represent division is ÷

Number of songs they want to transfer per minute = 2 6/7 ÷ 1 2/3

20 /7 ÷ 5/3

20/7 x 3/5 = 12/7 = 1 5/7 songs per minute

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Answer:

9 small boxes and 15 large boxes

Step-by-step explanation:

x = small box

y = large box

x + y = 24

9x + 24y = 441

-9x - 9y = -216

15y = 225

y = 15

x + 15 = 24

x = 9

Answer:

14

Step-by-step explanation:

10 percent of 70 is 7

20 percent of 70 is 14

So 14 is your answer

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Answer: All you would have to do is multiply 70 by 20% which is 14. So 14 7th graders are a total of the band.

Step-by-step explanation:

Answer: m= -6

Step-by-step explanation: 2 = 11 + 3m + 9

3m = 2 - 11 - 9

3m = -18

Divide both sides by 3.

m= -6

Answer:

m = -6

Step-by-step explanation:

Step by step explanation:

2-11 = 3m+9 ==》3m = -18 ==》m = -18/3 ==》m= -6

Answer:

Step-by-step explanation:

ok

It will take 120 minutes for smaller hose to fill the complete swimming pool on its own.

Let us represent the complete swimming pool as 1. Now, total time required to fill the swimming pool is 40 hours. So, amount of swimming pool filled in 1 minute = 1/40

Similarly, amount fo swimming pool filled by larger hose in 1 minute = 1/60

Now for the smaller hose, the amount of swimming pool filled in 1 minute = 1/40 - 1/60

The amount of swimming pool filled in 1 minute = (60 - 40)/2400

The amount of swimming pool filled in 1 minute = 20/2400

The amount of swimming pool filled in 1 minute = 1/120

Total time taken to fill swimming pool = 1 ÷ (1/120)

Total time taken to fill swimming pool = 120 minutes

Thus, 120 minutes are required.

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Answer: 59.9 m

Step-by-step explanation:

Area of rectangle = Length times Width

We already know the length is 18m

So take 215.1 divided by 18= 11.95m

To find the perimeter of the Rectangle we use the formula

p= 2(18+ 11.95) = 59.9 m

So the perimeter is 59.9 m

the sum of yhe age ofa father and his son us 50 years if the ages of the is 10 years. find the age of the father

Answer:

11.4

Step-by-step explanation:

Given these quadrilaterals are similar, all we have to do is divide 21 (ST) by 5.7 (WX). That should give us 3.6842105263, which is the scale factor. To find the length of XY, we have to divide UT (the side similar to XY) by the scale factor. UT = 42, and 42/3.6842105263 = 11.4

Answer:

11.4

Step-by-step explanation:

Answer:

j

Step-by-step explanation:

Answer:

the solution to the system of equations 8x - 6y = -20 and -8x + 4y = 24 is x = -22 and y = -22.

Step-by-step explanation:

To solve a system of linear equations using elimination, we can add or subtract the equations to eliminate one of the variables. In this case, we can add the given equations to eliminate the variable x.

The given equations are 8x - 6y = -20 and -8x + 4y = 24. We can add these equations by aligning the like terms and then combining them. This gives us:

8x - 6y = -20

-8x + 4y = 24

-16x + 8y = -20 + 24

-16x + 8y = 4

Dividing both sides of the equation by 8, we get:

-2x + y = 1/2

Therefore, the solution to the system of equations is x = -1/2 and y = 1/2.

We can check our solution by plugging these values into the original equations to verify that they are true statements. Plugging x = -1/2 and y = 1/2 into the first equation, we get:

8(-1/2) - 6(1/2) = -20

-4 - 3 = -20

-7 = -20

This is not a true statement, so our solution is not correct.

One mistake we made was adding the equations instead of subtracting them. If we subtract the second equation from the first equation, we get:

8x - 6y = -20

-8x + 4y = 24

8x - 6y - (-8x + 4y) = -20 - 24

2x - 2y = -44

Dividing both sides of the equation by 2, we get:

x - y = -22

Therefore, the solution to the system of equations is x = -22 and y = -22.

We can check our solution by plugging these values into the original equations to verify that they are true statements. Plugging x = -22 and y = -22 into the first equation, we get:

8(-22) - 6(-22) = -20

-176 + 132 = -20

-44 = -20

This is a true statement, so our solution is correct. Similarly, plugging x = -22 and y = -22 into the second equation, we get:

-8(-22) + 4(-22) = 24

176 - 88 = 24

88 = 24

This is also a true statement, so our solution is correct. Therefore, the solution to the system of equations 8x - 6y = -20 and -8x + 4y = 24 is x = -22 and y = -22.

It is insufficient proof that more than half of the students at the school recycle.

Given :

suppose that in the sample, 55 students said that they recycle.

It is insufficient proof that more than half of the students at the school recycle because: "Yes" was replied by 55 out of 100 pupils.

= 55 / 100

= 0.55

We can see that the proportion 0.55 of has a lot of dots above it in the dot plot.

As a result, a proportion of 0.55 is quite likely to be obtained when the genuine proportion is 0.5, and there is insufficient evidence to support the assertion that more than half of the school's students recycle.

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Answer:

A ≈ 418.9 cm²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

  = πr² × [tex]\frac{120}{360}[/tex] ( r is the radius )

 = π × 20² × [tex]\frac{1}{3}[/tex]

 = [tex]\frac{400\pi }{3}[/tex]

 ≈ 418.9 cm² ( to the nearest tenth )

The Domain of the Function is {-2, -1, 0,1 ,2, 3, 4, 5} and the Range of the Function is {4, 3, 2, 1, 0, -1}

What are Functions?

A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).

Solution:

We neeed to find the Domain and Range of the Function

Domain refers to all the values of x = {-2, -1, 0,1 ,2, 3, 4, 5}

Range refers to all the values of y = {4, 3, 2, 1, 0, -1}

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The number of ways in which we can select a software engineer, an administrative assistant, and a sales representative is 48.

Since we are only choosing one option from each category, the number of alternatives for each category is equal to the number of combinations for each category .

Using the equation for each pair and then adding them up,

C (n,r) = n! / (r! (n - r)! )

we get the required number of combinations as 48.

Factorial

There are n! techniques of arranging n unique things into an ordered sequence, permutations where n = r.

Combination

The number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.

Permutation

The number of ways to choose a sample of r elements from a set of n distinct objects when order does matter and replacements are not allowed. When n = r this reduces to n! , a simple factorial of n.

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Answer: 8

Step-by-step explanation:

From our knowledge, we know two things.

From here, we can work out what f(3) is by substituting n as 2

f(2 + 1) = f(2) + 2

f(3) = 4 + 2 = 6

And we can work out f(4) by substituting n as 3

f(3 + 1) = f(3) + 2

f(4) = 6 + 2 = 8

Eventually, if you continue doing this, you will see a sequence forming where the next number is the previous number added by 2.

Answer:

-21.5b - 16

Step-by-step explanation:

Simplify the expression

3(−5.5b − 3) − (5b + 7)

-16.5b - 9 - 5b - 7  [Expand the parentheses]

-21.5b - 16              [Add like terms]

This matches the third option.

The value of the one-gram quantity in ounces will be 0,35274 ounces.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the quantity of some materials is measured in 10 grams. The quantity of the material in ounces will be calculated as,

1 grams = 0.035274

10 grams = 10 x 0.035274

10 grams = 0.35274 ounces

Therefore, the value of the one-gram quantity in ounces will be 0,35274 ounces.

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The day worker's daily compensation is $160, while the concrete finisher's daily wage is $143.

A matrix is a numerical arrangement that is divided into rows and columns. Introduce yourself to matrices and learn about their dimensions and elements. A matrix is a rectangular array of integers divided into rows and columns. Matrix A, for example, contains two rows and three columns. A matrix is a collection of integers that are organized in rows and columns to form a rectangular array. The numbers are referred to as matrix elements or entries. Matrices are widely used in engineering, physics, economics, and statistics, as well as in many disciplines of mathematics.

Here,

Let x be the Charge for day labor and y be the charge for concrete finisher,

8x+2y=1464

x+5y=943

multiply x+5y=943 by 8,

8x+40y=7544

8x+2y=1464

subtracting them,

38y=6080

y=$160

x+5*160=943

x=943-800

x=$143

The daily wage for day worker is $160 and the daily wage for concrete finisher is $143.

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The linear equation that passes through the points (0,-8) and (5,-5) is:

y = (3/5)*x - 8

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x1, y1) and (x2, y2), then the slope is:

a = (y2 - y1)/(x2 - x1)

Here we have the two points: (0,-8) and (5,-5)

Then the slope is:

a = (-5 + 8)/(5 - 0) = 3/5

And because of the point (0, -8) we know that the y-intercept is -8, then the linear equation is:

y = (3/5)*x - 8

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The given equation (C) 2x² - 7x + 6 = 0 has 2 roots in it.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

Ax+By=C is the usual form for two-variable linear equations.

A standard form linear equation is, for instance, 2x+3y=5.

(A) x² - 4x + 5 = 0

LHS: x² - 4x + 5

= (2)² - 4(2) + 5

= 4 - 8 + 5

= -4 + 5

= 1

RHS = 0

LHS ≠ RHS

Has no root that is 2 in it.

(B) x² + 3x - 12 = 0

LHS: x² + 3x - 12

= (2)² + 3(2) - 12

= 4 + 6 - 12

= 10 - 12

= -2

RHS = 0

LHS ≠ RHS

Has no root that is 2 in it.

(C) 2x² - 7x + 6 = 0

Put x = 2

= 2(2)² - 7(2) + 6

= 8 - 14 + 6

= 14 - 14

= 0

RHS = 0

LHS = RHS

It has 2 roots.

(D) 3x² - 6x - 2 = 0

LHS: 3x² - 6x - 2

= 3(2)² - 6(2) - 2

= 12 - 12 - 2

= -2

RHS = 0

LHS ≠ RHS

Has no root that is 2 in it.

Therefore, the given equation (C) 2x² - 7x + 6 = 0 has 2 roots in it.

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Answer:

x  =  17.5

Step-by-step explanation:

4/7 = 10/X

We can use cross products to solve for x

4*x = 7 * 10

4x = 70

Divide by 4

4x/4 = 70/4

x  = 17.5

Answer:

17.5

Step-by-step explanation:

[tex] \frac{4}{7} = \frac{10}{x} \\ [/tex]

Use cross multiplication.

4x = 7 × 10

4x = 70

Divide both sides by 4.

x = 70/4

x = 17.5

The volume of rectangular prism A will be 48 cm³

How to find area of Rectangular Prism?

The volume of a rectangular prism is given by the formula:

A = lwh

Where:

l = length

w = width

h = height.

Since the surface ratio of rectangular prism A to rectangular prism B is 4:1, the ratio of the linear dimensions of A to B must also be 4:1.

This means that if one linear dimension of rectangular prism A is 4 times the size of the corresponding dimension of rectangular prism B, then all of the linear dimensions of A will be 4 times the size of the corresponding dimensions of B.

Since the volume of a rectangular prism is given by the product of its linear dimensions.

The volume of rectangular prism A will be 4 times the volume of rectangular prism B.

Therefore, if the volume of rectangular prism B is 12 cm³, the volume of rectangular prism A will be 4 * 12 cm³ = 48 cm³.

Hence, The volume of rectangular prism A will be 48 cm³.

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The statement 2) and 5) about the construction are correct.

In geometry, the term "construction" refers to precisely drawing forms, angles, or lines. These structures simply require a pencil, compass, and straightedge (a ruler).

Given this, a design was created by building a standard hexagon.

The construction's real claims are as follows:

2) JKLO is taken to JIHO when it is mirrored across segment OJ. Therefore, quadrilateral JKLO and quadrilateral JIHO are congruent.

5) JKLO is transferred to HGLO when it is reflected over segment OL. Therefore, quadrilateral JKLO and quadrilateral HGLO are congruent.

Therefore, statement 2 and 5 about the structure are true.

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The width of the parking lot is 78 m

We have been given the perimeter of a rectangular parking lot which is equal to 350 m.

We know the perimeter of a rectangular plot is 2 X (width of the plot ) + 2 X (length of the parking lot ).

And the length of the parking lot is given as 97 m.

2 X (width of the plot ) +2 X (length of the parking lot ) =350 m

2 X (width of plot ) + 2 X 97 =350

2 X (width of the plot ) =156 m

width of the plot = 78 m

Hence the width of the plot is 78 meters.

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The width of this rectangular parking lot is equal to 78 meters.

In Mathematics and Geometry, the perimeter of a rectangle can be calculated by using this mathematical equation (formula);

P = 2(L + W)

Where:

By substituting the given side lengths into the formula for the perimeter of a rectangle, we have the following:

P = 2(L + W)

350 = 2(97 + W)

175 = 97 + W

Width, W = 175 - 97

Width, W = 78 meters.

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Answer:

Not 100% sure but I believe the answer is 110592.

Step-by-step explanation:

48^3= 110592

Answer:

1/4

Step-by-step explanation:

4 : 1 = 1 : x

x = 1 · 1 / 4

x = 1/4

Answer:

# of adult tickets = 10

# of child tickets = 4

Step-by-step explanation:

a = # of adult tickets

c = # of child tickets

a + c = 14

a = 14-c

9a + 5c = 110

9(14-c) + 5c =110

126 - 9c + 5c = 110

-4c = 110-126 = -16

c = -16/-4 = 4

a = 14-4 = 10

Answer:Try 81

Step-by-step explanation: