1. A tool rental company charges $25 for the first hour of a tractor rental. Each additional hour costs $20 per hour. Which statement describes the relationship between total cost and hours?
A It is proportional; each ratio for related pairs is equivalent.
B It is proportional; each x-term is a multiple of the previous term.
C It is not proportional; each ratio y/x for related pairs is not equivalent.
D It is not proportional; each x-term is not a multiple of the previous term.​

Linear Decay  is the equation .

What is Linear Decay?

Is linear decay exponential?

Scientists are studying the growth of a particular virus in a large community.

The case count, C, in the community after d days can be modeled with the equation: C = 181(1.07)d

This equation is showing Linear Decay .

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Answer:

C

Step-by-step explanation:

20+80 = 100

a triangle equals 180* so

1080-100=80 or just use a calculator OR with your brain

The length of the sides of the triangle is 11 inches.

Triangle:

Triangle is defined as the three-sided polygon that consists of three edges and three vertices

Given,

If the perimeter of the triangle is 33 inches, then we have to find the sides of the triangle.

Let x be the sides of the triangle, we know that the triangle has 3 sides.

And lest us consider this one as equilateral triangle.

So, the formula for perimeter is,

Perimeter = 3 x sides

Here we know the value of perimeter then the value of the sides are,

33 = 3 x sides

sides = 11

So, the value of the sides is 11.

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Given : Regular price of MP3 player was $200. It was marked down by $60.

Required: Percent discount

Explanation:

Marked Price = $200

Discount given = $60

So, percent discount =

Final answer : Percentage discount is 30%

The equivalent expression of 2⁻³ / 2⁻⁵ will be 2².

Option A is true.

What is a mathematical expression?

Expression in math is defined as the collection of the numbers, variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The mathematical expression is,

⇒ 2⁻³ / 2⁻⁵

Now, The rule of exponent is;

[tex]\frac{a^{x} }{a^{y} } \\a^{x} * a^{-y} \\a^{x+ (-y)} \\a^{x-y}[/tex]

Hence, Solve the expression by rule of exponent as;

The mathematical expression is,

⇒ 2⁻³ / 2⁻⁵

⇒ 2⁻³ / 2⁻⁵

⇒ 2⁻³ × 2⁵

⇒ 2⁻³⁺⁵

⇒ 2²

So, 2⁻³ / 2⁻⁵ = 2²

Thus, The equivalent mathematical expression of 2⁻³ / 2⁻⁵ will be 2².

Option A is true.

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Answer:

35.224137931

Step-by-step explanation:

2010: 1266.66

1970: 35.96

1266.66/35.96=35.224137931

Without the actual data for the average prices of gold in 2010 and 1970, I cannot provide the exact quotient. However, if we assume that we have the data, we can calculate the quotient by dividing the average price of gold in 2010 by the average price of gold in 1970. The resulting quotient would indicate how many times more expensive gold was in 2010 compared to 1970.

For example, if the average price of gold in 2010 was $1,500 per ounce and the average price in 1970 was $35 per ounce, then the quotient would be:

$1,500 / $35 = 42.86

This means that the average price of gold in 2010 was 42.86 times more expensive than the average price in 1970.

It is important to note that the actual quotient will depend on the actual data for the average prices of gold in 2010 and 1970.

The equation of line is given by y-12=4(x-5).

What is equation of line with slope intercept form?

The equation of a line in point-slope form can be written as

y-y_1=m(x-x_1) where (x_1,y_1) is the points line passes through.

(y-12)=4(x-5)

Where m=4 and x_1=5,y_1=12

Hence, the equation of line is

y=4x-5+12

y=4x+7

The equation of line with the form of slope intercept form is y-12=4(x-5).

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nswer : D) 1I, II and III

The value of m such that x +4 is a factor of 5x³ + 18x² + mx + 16 is; -4.

It follows from the task content that the value of m for which x +4 is a factor of 5x³ + 18x² + mx + 16 is to be determined.

Hence, if x + 4 is a factor, it follows that x = -4 is a zero of the expression.

Therefore; 5(-4)³ + 18(-4)² + m(-4) + 16 = 0.

-320 + 288 - 4m + 16 = 0.

-16 - 4m = 0

4m = -16

m = -16/4

m = -4.

Ultimately, the value of m for which x+4 is a factor of 5x³ + 18x² + mx + 16 is; -4.

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The solution for the quadratic equation is -5/2, 2/3

Given,

The equation: 18a² - 30 = -33a

We have to solve this equation

We can convert this equation into a quadratic equation:

18a² + 33a - 30 = 0

Now lets solve this quadratic equation with quadratic formula:

Quadratic formula = [tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]

Here,

a = 18, b = 33 and c = -30

Now we can solve:

[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]

= [tex]\frac{-33(+-)\sqrt{33^{2} -4(18)(-30)} }{2(18)}[/tex]

=  [tex]\frac{-33(+-)\sqrt{1089-(-2160)} }{36}[/tex]

= [tex]\frac{-33(+-)\sqrt{1089+2160} }{36}[/tex]

= (- 33 ± √3249) / 36

= (- 33 ± 57) / 36

Solve for:

(- 33 + 57) / 36 = 24/36 = 2/3

Solve for:

(- 33 - 57) / 36 = - 90/36 = - 30/12 = -10/4 = -5/2

That is, the solution for the quadratic equation is -5/2, 2/3

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The value of x based on the given expression - 2/5x + 3 = 2/3x + 1/3 is 2 1/2

- 2/5x + 3 = 2/3x + 1/3

- 2/5x - 2/3x = 1/3 - 3

(-6 - 10)x / 15 = (1-9) / 3

-16/15x = -8/3

x = - 8/3 ÷ -16 / 15

x = - 8/3 × -15/16

= (-8 × -15) / (3 × 16)

= 120 / 48

= 2 1/2

In conclusion, the solution to the expression - 2/5x + 3 = 2/3x + 1/3 is 2 1/2

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The correct approaches that can be used to solve the increase in area are

The area of the circle has an estimated increment of 527.52 square mm

The area of a shape is the amount of space on the shape

For all regular quadrilaterals, you multiply the side lengths to determine the area

From the question, the given parameters are:

Previous radius = 42

New radius = 44

Calculate the change in the radius

dr = New radius - Previous radius

Substitute the known values in the above equation

So, we have

dr = 44 - 42

Evaluate

dr = 2

The above method leads to a differentiation problem where dr = 2

So, the correct approaches to the problem include

The area of a circle is

A = πr²

Differentiate

d(A) = 2πr * dr

Where

r = 42

dr = 2

So, we have

d(A) = 2 * 3.14 * 42 * 2

Evaluate

d(A) = 527.52

Hence, the estimated increase in the area is 527.52 square mm

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The expression is equivalent to the 360[tex]k^2[/tex] - 48k

Given the Expression :
8k5∙9k−2(6k2)2

It means

(8k × 5) × 9k - 2(6k × 2) × 2

Now, Multiply the monomials

360[tex]k^2[/tex] - 2(6k × 2) × 2

Again, Multiply the monomials,

= 360[tex]k^2[/tex] - 48k

Hence, The expression is equivalent to the 360[tex]k^2[/tex] - 48k

What is Monomial ?

A monomial is a polynomial, which has only one term. A monomial is an algebraic expression with an single term but can have multiple variable and a higher degree too.

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The thing that has occurred if an increase in temperature accompanies a reaction is A. Energy was released.

There are many other types of reactions in chemistry, but the exothermic reaction and the endothermic reaction are the two most common forms.

Respiratory reaction is an example of an exothermic reaction, which is one in which energy is released in the form of heat. Exothermic reactions transfer energy from the system to the environment, raising the ambient temperature.

An endothermic reaction is one in which energy is removed from the system during the process. An example of an endothermic reaction is photosynthesis, in which plants use solar energy to produce food.

Therefore, a chemical reaction is said to be exothermic when it releases energy and causes a change in the environment's temperature.

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The degree of our simplified answer is =  4

what is polynomials ?

Polynomials are sums of the terms of form k· x^ n, where k is any number  and n is positive integers. polynomials are algebraic expression that consist of variable and coefficient. variables are also sometimes called Indeterminates

an example of polynomial with one variable is x^2+x-12.

so,

after expanding the identity (4t^2-5u)^2, it becomes:

 16t^4+25u^2-40ut^2

as we know in case of polynomial highest degree from the polynomial is consider as the degree of that polynomial.

hence,

           The degree of this equation is 4.

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The interest that will be earned when the city is issuing bonds to raise money for a building project is $670.

It should be noted that the formula for the calculation is the interest is given as:

Interest = Principal × Rate × Time / 100

where P = $6700

R = 2%

Time = 5 years

Interest = Principal × Rate × Time / 100

Interest = (6700 × 2 × 5) / 100

= 670

The interest is $670.

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The required expressions about the geometry figure can be proven as follows;

1. The measure of ∠2 and ∠3 are congruent by the substitution property of equality

2. ∠2 and ∠3 are congruent, (∠2≅∠3) by the property of equality

The property of equality are properties that enable the solution of algebraic equations to be found and they include, addition, subtraction, multiplication, division, reflexive, substitution, transitive and symmetric properties.

1. The required paragraph to prove that ∠2 ≅ ∠3 is as follows:

Given that ∠1 and ∠2  form a linear pair, then their sum is 180°. Given that the sum of the measure of ∠1 and ∠3 is also 180°, then the sum of ∠1 and ∠2 is equal to the sum of ∠1 and ∠3. Therefore, by the addition property of equality, ∠2 ≅ ∠3.

2. The two column proof is as follows:

Statement               [tex]{}[/tex]                       Reasons

1. ∠ABC = ∠1 + ∠2 is ⊥                  1. Given

2. ∠ABC = 90°                               2. Definition of a perpendicular line

3. ∠1 + ∠2 = 90°                             3. Substitution property of equality

4. ∠1 and ∠3 are complementary  4. Given

5. ∠1 +∠3 = 90°                                5. Definition of complementary

6. ∠1 + ∠2 = ∠1 +∠3                         6. Substitution property of equality

7. ∠2 ≅ ∠3                                       7. Addition property of equality

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Consider the first equation,

This equation passes through (0,-2) and (2,1).

second

This equation passes through (0,2) and (4,0).

Now we can plot the points and join them to get the corresponding lines on the graph as,

It is observed that the two lines intersect at point (2,1).

So the solution to the given equations must be x=2 and y=1.

The quotient of 550six and 50six​ is obtained by the calculation to be   11 six

We know that the result that we obtain after we have carried out a division operation is called a quotient. In this case, we have been required to carry out the operation of division in base six.

We could start by converting the both values to base 10 as follows;

(5 * 6^2) + (5 * 6^1) + (0 * 6^0) = 180 + 30 + 0 = 210 ten

(5 * 6^1) + (0 * 6^0) = 30 + 0 = 30 ten

Then we carry out the division in base ten; 210 ten/30 ten = 7 ten

We convert back to base six to obtain 11 six

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The number of ways that the line up can be possible when eleven bands have volunteered to perform but there is only enough time for five of the bands to play is 462 ways.

Eleven bands have volunteered to participate in the charity concert, but there is only enough time for five of them to do so. This involves combinations and permutations, it should be highlighted.

Therefore, the number of ways that the line up can be possible will be:

n! / (n − r)!

where n is the number of things to choose from and we choose r of them

= 11! / (11 - 5)!5!

= 11! / 6!5!

= 462

There are 462 ways.

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When we reflect a point along the x-axis, the x coordinate stays the same BUT the y coordinate is negated.

A point (x,y) becomes (x, -y)

et us apply this rule to the points J, A, and R. SThis is shown below:

The graph of the triangle will look like >>>

the second one

Step-by-step explanation:

if 75 is the minum speed then you need to go more than 75 and less than 80 which is what the second one is showing

A number is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. The fraction of the counters that Lesley gets is 5/9.

A number is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

A fraction exists a quantity that exists not a whole number. In Math's, a fraction usually contains a numerator and a denominator.

The fraction of the counters that Lesley gets

= number of counters she gets / total number of counters

= 10/18 = 5/9

Therefore, the fraction of the counters that Lesley gets 5/9.

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The true statement is Statement A which is dogs of breed B typically weigh more than dogs of breed A using histogram in probability concept.

The likelihood of each possible occurrence is displayed on the y-axis of a probability histogram. A histogram is a statistical data display that makes use of rectangles to illustrate the frequency of data items in successive numerical intervals of equal size. The dependent variable is plotted along the vertical axis in the most typical type of histogram, while the independent variable is plotted along the horizontal axis. The distribution of data is depicted graphically in a histogram. A collection of neighboring rectangles, each with a bar that represents a certain type of data, is used to illustrate a histogram. Fill L1 with the values of the random variable (remember to use the class midpoints for continuous random variables). The associated percentages should be entered into L2 with a decimal format.

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[tex] = - 6x - 8x - 5 + 8 \\ = - 14x + 3[/tex]

The third option is the answer!!!

The graph is attached below.

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The whole numbers are defined as numbers that include naturals and zero. Not a fraction, decimal or negative numbers.

So in this case, the whole numbers are: 5 ; 0; 10.

Answer:

3 f

Step-by-step explanation:

(-1)+(4)

-+(4)

-+4

-f+4

-f+4

3

3