Write an equation for (k) and (t)

Based on the table and equation given:Gymnastics is less expensive when the classes is 1.Ice-skating is less expensive when the classes is 3 or 4.

For 1 class, substitute x = 1 into y = 18x + 20:

y = 18(1) + 20

y = $38

For 2 class, substitute x = 2 into y = 18x + 20:

y = 18(2) + 20

y = $56

For 3 class, substitute x = 3 into y = 18x + 20:

y = 18(3) + 20

y = $74

For 4 class, substitute x = 4 into the equation y = 18x + 20:

y = 18(4) + 20

y = $92

From the above, we can conclude that, Gymnastics is less expensive when the classes is 1.

Ice-skating is less expensive when the classes is 3 or 4.

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Answer:

Step-by-step explanation:

Due to the cast of the shadow regardless of that the line will still be 11 feet due to the lines length

The difference between a formal and informal proof in arithmetics is that a formal proof uses equations, whereas an informal proof only uses text. That is option D.

A formal proof is defined as the concept used in arithmetics to show that the final answer to an expression obeys a particular rule of an equation or formula.

An informal proof is defined as the concept that shows the answer to a mathematical expression without the use of formula or derived equation.

Therefore, the difference between the formal and informal proof is that a formal proof uses equations, whereas an informal proof only uses text.

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The value of the given logarithmic expression is -142.20.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Given the logarithmic values as,

log₃ (t) = 5.44

log₃ (y) = 11.03

log₃ (z) = 7.74

Now, the value of the expression can be written as,

12 log₃ (z⁷ / y⁵t²)

= 12 { log₃ (z⁷) - [ log₃ (y⁵) + log₃ (t²) ] }

= 12 { 7log₃ (z) - [ 5log₃ (y) + 2log₃ (t) ] }

= 12 [7×7.74 - (5×11.03 + 2×5.44)]

= 12 [ 54.18 - (55.15 + 10.88)]

= 12(54.18-66.03)

= 12 × (-11.85)

= -142.20

Hence, the value of the given expression is -142.20.

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Answer: m=8/7

Step-by-step explanation:

use this formula m=y2-y1/x2-x1

The solution of the logarithmic expression is 2x² - x - 6 = 0.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

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 expression is log(x) + log3(2x - 1) = log3 (6). The expression will be solved as below,

log(x) + log3(2x - 1) = log3 (6)

log ( 3x (2x-1) = log18

3x ( 2x - 1 ) = 18

x ( 2x - 1 ) = 6

2x² - x = 6

2x² - x - 6 = 0

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Answer:

Step-by-step explanation:

The graph of y = 8 is a horizontal line through 8, on the y-axis

Answer: -2

Step-by-step explanation:

Slope is rise/ run or y2 - y1 / x2 - x1

We see that y goes down by 6, and x go over by 3

So slope is -6/3 = -2

Clare's mistake is at the second step and the solution to the equation is -65/11.

In Mathematics, the distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a particular numerical value, the same result and output would be obtained as when each addend is multiplied respectively by the same numerical value, and the products are added together.

Based on the information provided above, we can logically deduce that Clare's mistake is at the second step because the product of 12 and 5 is equal to 60, rather than 72. Additionally, Clare did not distribute the negative sign to all the terms of the equation.

By applying the distributive property of multiplication to the given mathematical expression, we have the following:

12(5 + 2y) = 4y - (5 - 9y)

60 + 24y = 4y - 5 + 9y

60 + 24y = 13y - 5

24y - 13y = -5 - 60

11y = -65

y = -65/11

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To find the answer to this problem, you will need to use the Pythagorean Theorem.

What is the Pythagorean Theorem?

The Pythagorean Theorem is an equation that represents the summation of the sides of a right triangle.

a² + b² = c², where a is the shortest leg of the triangle, b is the longest leg and c is the hypothenuse.

You have been given a (12) and b (16)

First, plug your given information into the equation: 12² + 16² = c²

Next, simplify your equation by squaring both terms:

12² = 144

16² = 256

Then, add these two answers together: 144+ 256= 400

This leaves you with the equation: 400 = c²

To isolate the c as an individual term, take the square root of both sides:

          [tex]\sqrt{400} = \sqrt{c^{2} }[/tex]

The above equation leaves you with the answer 20 = c, which is the hypothenuse

The gradient of this straight line through the points is 0.16.

The gradient of this lines simply means that it would require one (1) unit to use £0.16 worth of electricity.

Mathematically, the gradient of a straight line can be calculated by using this formula;

Gradient, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Gradient, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided through this graph, we have the following data points:

Points on x-axis = (30, 100).

Points on y-axis = (4, 15).

Substituting the given points into the formula, we have the following;

Gradient, m = (15 - 4)/(100 - 30)

Gradient, m = 11/70

Gradient, m = 0.16

This ultimately implies that, £0.16 worth of electricity would require one (1) units to be used by David.

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Answer: second and third from the top right

Step-by-step explanation: 1:2 and 1 to 2 are the same thing, and are ratios. The rest of the answers have nothing to do with ratios.

Answer:

1. 29 2. 35

Step-by-step explanation:

check the attached file

Mrs. smith told her students that anyone who scores over 90% on the test will get an extra 30 minutes of recess: Among the group contingency this is an independent group,

A particular kind of contingency known as a group contingency (GC) takes use of peer influence by using group reinforcement.

The instructor may use a group contingency to praise an entire class or a smaller subset of pupils for finishing assignments, exhibiting good classroom behavior, or engaging in other desired behavior. Multiple kids' problematic behaviors can be addressed at once using group contingencies.

Dependent, independent, and interdependent group contingencies are the three different types.

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The complete question is as follows:

Mrs. Smith implemented a procedure where she exclaimed that if any student scored over 90% on the test, they would get an extra 30 minutes of recess. Which group contingency is this?

a. Token economy

b. Dependent group contingency

c. Interdependent group contingency

d. Independent group

Answer:

[tex]\frac{3m^{2}n-2-40nm }{6m}[/tex]

Step-by-step explanation:

∠2 is congruent to ∠6 based on corresponding angle theorem.

So here ,

Since in this question they are corresponding angles of parallel lines cut by a transversal, they are ∠2 ≅ ∠6 according to the Vertical Angles Theorem.

The complete question is : "Lines c and d are parallel lines cut by transversal p. Horizontal and parallel lines c and d are cut by transversal p. On line c where it intersects with line p, 4 angles are formed. Clockwise, from uppercase left, the angles are: 1, 2, 3, 4. On line d where it intersects with line p, 4 angles are formed. Clockwise, from uppercase left, the angles are: 5, 6, 7, 8. Which must be true by the corresponding angles theorem?"

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Answer:

$80

Step-by-step explanation:

His buying cost for 1 pair of shoes: $49

His selling price for 1 pair of shoes: $65

His profit on selling 1 pair of shoes: $65 - $49 = $16

His profit on selling 5 pairs of shoes: 5 × $16 = $80

Answer: 2(x-5)(x+3)

Step-by-step explanation:

(x+3)(2x-10)

2(x-5)(x+3)

Answer:

The sequences below is geometric sequences. 8,16,32

Step-by-step explanation:

It is geometric as far as it goes.

Notice that the ratio between each successive pair of terms is constant:

4/2=2

8/4=2

16/8=2

That these ratios are all the same is sufficient for the given terms to form a geometric sequence with general term:

an=[tex]2^{n}[/tex]

The sequence then continues:

2

,

4

,

8

,

16

,

32

,

64

,

128

,

256

,

512

,

1024

,

2048

,

...

The question is in the "...". Any finite number of terms does not determine an infinite sequence.

For example we can match the sequence  

2

,

4

,

8

,

16

 with a cubic polynomial:

[tex]a_{n}[/tex]=1/3([tex]n^{3}[/tex] -3[tex]n^{2}[/tex] +8n)

Then we would find that the next terms would be  

30

,

52

,

84

,

.

the second 4 11 ,17 is wrong

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The ratio of heads to tails in the probability test is 2:1 or (D) 2/1.

A ratio is a relationship or comparison between two numbers belonging to the same unit in order to determine how much larger one number is than the other.

For instance, if a test result is 7 out of 10, the ratio of the number of points earned to the total number of points is 7:10.

So, we know that the coin is flipped 36 times in the probability test:

Head = 24

Tails = 36 - 24 = 12

The ratio of heads to Tails:

Heads:Tails
24:12

24/12

2/1

2:1

Therefore, the ratio of heads to tails in the probability test is 2:1 or (D) 2/1.

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Complete question:
In a probability, experiment Eric flip a coin 36 times. The coin landed on the head 24 times. What is the ratio of heads to tails in this experiment?

A.3/2

B.1/2

C.2/3

D.2/1

The value of a and b for the given polynomial function f(x)=(x-a)(x-b) are a= -1, 2 and b=2, -1.

A function is said to as polynomial when a variable in an equation, such as a quadratic equation or cubic equation, etc., has only positive integer exponents or non-negative integer powers. For instance, the polynomial 2x+5 has an exponent of 1. The zero polynomial function, linear polynomial function, quadratic polynomial function, and cubic polynomial function are the four most common types of polynomials in precalculus and algebra.

Given,

f(x)=(x-a)(x-b)

From the above graph, f(x) passes through points (2, 0), (-1, 0), (0, -2)

Let us take (2, 0)

(2-a)(2-b)=0

4-2b-2a+ab=0

(-1, 0)⇒(-1-a)(-1-b)=0

1+b+a+ab=0

(0, -2)⇒-2=(-a)(-b)

ab= -2

a= -2/b

4-2b-2a-2=0

-2a-2b+2=0

a+b-1=0

b²-2b+b-2=0

b(b-2)+1(b-2)=0

b= 2 or b= -1

a+2-1=0

a= -1

a-1-1=0

a=2

The value of a and b for the given polynomial function f(x)=(x-a)(x-b) are a= -1, 2 and b=2, -1.

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Answer:

m∠1 = (180 - 110)° = 70°

m∠2 = (180 - 115)° = 65°

m∠3 = 115°

m∠4 = m∠2 = 65°

m∠5 = (180 - (65 + m∠1))° = 45°

m∠6 = m∠5 = 45°

m∠7 = m∠6 = 45°

The least number of point the team could have scored is the LCM of the factors given = 60.

Factor 1 = 3

Factor 2 = 4

Factor 3 = 5

therefore, LCM  

= 4 * 5 * 3   [because they don't have any factors in common]

= 60

The positive integers that can divide a number evenly are referred to as factors. Let's say we multiply two numbers to produce a result. The product's factors are the number that is multiplied.

Each number has a self-referential element. There are several examples of factors in everyday life, such putting candies in a box, arranging numbers in a certain pattern, giving chocolates to kids, etc. We must apply the multiplication or division method in order to determine a number's factors.

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On solving the provided question, we got that - The maximized value of the objective function is 38

Relationships between a group of inputs and one output per input are referred to as functions. A function is, to put it simply, a connection between inputs that are all connected to the same output. There is a domain and a codomain, or scope, for every function.

Given is the objective function:

Max P = 5x + 3y

The following are the constraints:

3x + 6y ≤ 48

2x + 8y ≤ 56 \sx ≥ 0 y ≥ 0

We employ the graphical method to achieve this.

The graph of the constraints is included as an attachment.

The graph leads us to the following doable point:

[tex](x,y) = (4,6)[/tex]

[tex]Substitute 4 for x and 6 for y in the objective function.\\Max P=5x+3y[/tex]

so,

[tex]P = 5x4+x6\\P = 38[/tex]

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After dividing 451 by 51, we get a quotient of 008 and a remainder of 43.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.

The other operations are multiplication, addition, and subtraction.

On a fundamental level, counting the instances in which one number is included within another is one interpretation of the division of two natural numbers.

It's not necessary for this number to be an integer.

For instance, if 20 apples are distributed equally among 4 persons, each person will get 5 of them.

So, we have 451/51.

Now calculate as follows:

451/51

Quotient = 008

Remainder = 43

(Refer to the image attached below)

Therefore, after dividing 451 by 51, we get a quotient of 008 and a remainder of 43.

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The Domain and range tends to (-∞,∞) and for more clarity see the graph mentioned below.

Define Domain and Range

Given expression is,

f(x) = -1/4x³ + 4x - 3

In this x ∈ R, so

Domain = (-∞,∞) , { x|x  ∈ R }

Range =   (-∞,∞) ,{ y|y ∈ R }

Hence, the Domain and range tends to (-∞,∞) and for more clarity see the graph mentioned below.

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Answer:

The equation of the line that passes through the point (-6, -7) and has a slope of 1/3 is:

x - 3y + 15 = 0

Step-by-step explanation:

The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

To find the equation of the line that passes through the point (-6, -7) and has a slope of 1/3, we can use the point-slope form of a line:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line and m is the slope of the line.

Plugging in the given values, we have:

y - (-7) = (1/3)(x - (-6))

Which simplifies to:

y + 7 = (1/3)x + 2

Multiplying both sides by 3, we have:

3y + 21 = x + 6

Subtracting 21 and 6 from both sides, we have:

3y - x - 15 = 0

Therefore, the equation of the line that passes through the point (-6, -7) and has a slope of 1/3 is:

x - 3y + 15 = 0

Answer:

For this question, you would have to subtract

1.679-1.439 = 0.24   Melvin pays 0.24 cents less. (not that much honestly lol!!)

To minimize the amount of paper used to create a rectangular poster with a given amount of printing and specific margins, you can use the formula for the area of a rectangle to determine the dimensions that will minimize the area of the poster.

In this case, the area of the poster must be at least 48 square inches to contain the printing, and the margins at the top and bottom must be 3 inches each, for a total of 6 inches. The margins at the sides must be 1 inch each, for a total of 2 inches. Therefore, the minimum area of the poster is 48 + 6 + 2 = 56 square inches.

To minimize the amount of paper used, we want to find the dimensions of the poster that will have the smallest possible area while still satisfying the constraints on the margins and the amount of printing. We can do this by using the formula for the area of a rectangle:

A = lw

where A is the area of the rectangle, l is the length, and w is the width.

In this case, we want to find the length and width that will minimize the area of the rectangle while still satisfying the constraints on the margins and the amount of printing. We can do this by setting the area of the rectangle equal to the minimum area we calculated above (56 square inches) and then solving for the length and width:

A = lw = 56

lw = 56

We can then use the constraints

The equivalent equation is when n is equal to 4.

        axc = bxc.

Here given equation,

7n = 28

Multiply both sides of equation by 1/7

7n x 1/7 = 28 x 1/7

7n / 7 = 28 / 7

n = 28 / 7

n = 4

So the equation equivalent to 7n = 28 is n = 4.

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