8 Here are the descriptions of two numbers.
The smallest multiple of 5 greater than 1000
The largest multiple of 9 with three digits
Work out the difference between these two numbers.

The slope of the line that contains the the given points is 1/5 .

The slope of the line containing the two points (x₁ , y₁) and (x₂ , y₂) is calculated using the formula

slope = (y₂ - y₁)/(x₂ - x₁)

In the question ,

it is given that the

line contains the points x [tex]=[/tex] -4 , y [tex]=[/tex] -3

and x = 1 , y = -2 .

we need two points to find the slope of the line

Substituting the values in the formula for slope ,

we get

slope = (-2 -(-3))/(1-(-4))

= (-2+3)/(1+4)

= 1/5

Therefore , The slope of the line that contains the the given points is 1/5 .

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Answer:

83.978 the thousandth digit is 3, 78.934 the thousandth digit is 8,84.765 the thousandth digit is 4

Answer:

Step-by-step explanation:

Ok:

1. Identify the thousandths digit

The numbers to the left of the decimal point are the ones and hundreds digits

The first number to the right of the point is the tenths digits

The second to the right of point i s the Hundreths

The third number to the right of point is the thounsandths which is what we are looking for!

2. Apply to problem!

1. 83.978 : Thousandths digit is 8

2. 78.934 : Thousandths digit is 4

3. 84.765 : Thousandths digit it 5

Extra tips and tricks writing as fractions!Ps: Some are not simplified!

1. 83.978= 83 978/1000 as fraction

2. 78.932= 78 932/1000 as fraction

3. 84.765= 84 765/1000 as fraction

The fault with Jerome's approach as required in the task content is; he tries to add 3 and 5 by switching 5 and 6, but, he forgets to switch the signs too.

Commutative property of addition is a property of addition which posits that Changing the order of addends does not change the sum.

On this note, the use of the commutative property of addition on the given expression; 3 - 6 + 5 would yield the expression; 3 + 5 - 6.

Consequently, the fault with Jerome's approach is that; he tries to add 3 and 5 by switching 5 and 6, but, he forgets to switch the signs too.

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Answer:

p=17

Step-by-step explanation:

P = 3n+2r+t -1

when n=3, r=2, and t=5?

we will just substitute for the values

p=3(3)+2(2)+5-1

p=9+4+4

p=9+8

p=17

;- The value for p is 17

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Cost will be $180 and so will be the revenue.

 Linear equations are equations of the first order. The linear equations are defined for lines in the coordinate system. When the equation has a homogeneous variable of degree 1 (i.e. only one variable), then it is known as a linear equation in one variable. A linear equation can have more than one variable. If the linear equation has two variables, then it is called linear equations in two variables and so on. Some of the examples of linear equations are 2x – 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x – y + z = 3.

Cost: C=72+6s, where s is the number of shirts sold

Revenue: R=10s

Break-even is where they are equal

72 + 6s = 10s

72/4 = s

s = 18 shirt s

Cost will be $180 and so will be the revenue.

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The number of full turns per minute is 235.

Given that, a cycle Wheel does 1645 full turns in 7 minutes.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Here,

The number of full turns per minute = Number of full turns/Number of minutes

= 1645/7

= 235 full turns per minute

Therefore, the number of full turns per minute is 235.

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4(a + 8)

multiply out:

= 4a + 32

The domain and range of the functions represented by the graph is equal to [-2, 2]. Also, the range of the functions represented by the graph is equal to [-2, 2].

The horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

Similarly, the vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

Note: Each interval on this graph represent -1 unit.

By critically observing the graph of this function shown, we can reasonably infer and logically deduce the following:

Domain = [-2, 2].

Range = (-2, 2).

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Each part of Nick's and Autumn's expressions mean can be explained as follows;

Nick;

Autumn:

ler

Nick expression:

[tex] {20( \frac{1}{2} })^{w} [/tex]

Where,

the amount of substance he begins with = 20

the amount of substance left after each week = 1/2

If w = 2

[tex] {20( \frac{1}{2} })^{w} [/tex]

[tex]{20( \frac{1}{2} })^{2} [/tex]

= 20(0.25)

= 5 milligrams

Autumn's expression:

[tex] {(1 - 0.5)}^{w} [/tex]

The one outside of parentheses = the initial amount of the substance.

The one inside of parentheses = 100% of the original amount of the substance.

0.5 represents the 50% of the substance that is lost each time period

[tex] {(1 - 0.5)}^{w} [/tex]

[tex] {(1 - 0.5)}^{2} [/tex]

= (0.5)²

= 0.25 milligrams

Complete question:

Nick starts with 20 milligrams of a radioactive substance. The amount of the substance decreases by 1/2 each week for a number of weeks, w. He writes the expression 20(12)w to find the amount of radioactive substance remaining after w weeks. Autumn starts with 1 milligrams of a radioactive substance. The amount of the substance decreases by 50% each week for a number of weeks, w. She writes the expression (1-0.5)w to find the amount of radioactive substance remaining after w weeks. Use the drop-down menus to explain what each part of Nick's and Autumn's expressions mean.

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Answer:

A

Step-by-step explanation:

∠ A and ∠ B are vertically opposite angles and are congruent. that is

∠ A and ∠ B are vertical angles

Answer:

Step-by-step explanation:

it help by showinbng thta

The final velocity of a vehicle with a mass of 800kg is 20000 m/s.

So, calculate the final velocity as:

Now, we know that:

Insert values in the formula and calculate as follows:

Rounding off: v =  20000 m/s

Therefore, the final velocity of a vehicle with a mass of 800kg is 20000 m/s.

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The original function of y = -1/3|x| was translated 2 units to the right and 5 units up.

In Mathematics, there are four (4) main types of transformation and these include the following:

In Mathematics, the translation of a geometric figure (shape) to the right simply means adding a digit to the numerical value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure (shape) that is translated up simply means adding a digit to the numerical value on the y-coordinate (y-axis) of the pre-image.

In this scenario, the original function was shifted 2 units to the right and then shifted 5 units up to produce the new function as follows:

Original function (x, y)    →     New function (x + 2, y + 5)

y = -1/3|x|                         →        y = -1/3|x + 2| + 5

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Answer:

1,198 cm

Step-by-step explanation:

To find the diameter, use the formula d = 2r.

d = 2(599)

d = 1,198

Answer:

Step-by-step explanation:

Take the amount, $4.75, multiplied by x will give you the total amount of money raised and just put that into the equation format:

$4.75 (x) = total amount of money raised

Answer:

[tex]y = |x - 3|+ 5[/tex]

y = |x| is the equation that forms the triangular shape. -3 and 5 reflect the shape to that position.

Answer:

The answer is –3 < 1

Step-by-step explanation:

-3 is below zero. 1 is above zero. therefore, -3 less than 1

Answer:

D, 3216

Step-by-step explanation:

Calculators are great. I love calculators.

Answer:20 dollars per hour

Step-by-step explanation:60/3 = 20

20 dollars per hour

7 x 20 = 140

Considering the dimensions of the rectangular prism and it's volume, it is found that:

The volume of a rectangular prism is given by the multiplication of the dimensions of the prism, which are the width symbolized by w, the height symbolized by h and the length symbolized by l, that is:

V = l x w x h.

In the context of this problem, from the image, the dimensions are given as follows:

Then the polynomial expression regarding the volume of the prism is obtained as follows:

V(x) = 2x(x - 3)(2x - 5)

V(x)= 2x(2x² - 11x + 15)

V(x) = 4x³ - 22x² + 30x.

The features of the polynomial expression V(x) = 4x³ - 22x² + 30x is obtained as follows:

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Answer:

(- 25, 5 )

Step-by-step explanation:

- 3x - 6y = 45 → (1)

- 5y = x → (2)

substitute x = - 5y into (1)

- 3(- 5y) - 6y = 45

15y - 6y = 45

9y = 45 ( divide both sides by 9 )

y = 5

substitute y = 5 into (2)

- 5(5) = x , then

x = - 25

solution is (- 25, 5 )

Answer:

182 minutes

Step-by-step explanation:

0.09x+5=21.38

         -5.   -5

0.09x=16.38

/0.09.   /0.09

  X=182

182 minutes

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The number of way in which bride can rank the three Djs out of 6 is 120.

There are several different ways we might rank the three DJs.

Therefore, we must identify the permutation P. (6,3).

ⁿPₓ = n!/(n - x)!

⁶P₃ = 6!(6-3)!

⁶P₃ = 6×5×4

⁶P₃ = 120

Thus, the number of way in which bride can select the three Djs out of 6 is 120.

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The value of 1/10 of 0.5 lies between 0.1 and 0.2

A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.

Given:

Point on the number line to show the value that is 1/10 of 0.5

So, 1/10 of 0.5

= 1/10 x 0.5

= 0.05

Hence, the value of 1/10 of 0.5 lies between 0.1 and 0.2

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a) The derivative of the composite function is F'(x) = [2 · [(1 / 3) · x³ + 7] + 6] · x².

b) The standard form of the polynomial is F'(x) = (2 / 3) · x⁵ + 7 · x².

Chain rule is a differentiation rule use to find the derivative of a composite function of the form f(u(x)), whose operation is defined below:

df / dx = (df / du) · (du / dx)

a) Let be f(x) = x² + 6 · x - 40 and g(x) = (1 / 3) · x³ + 7, such that F(x) = f(g(x)). Then, the resulting expression for the derivative of the function is obtained below:

F'(x) = [2 · g(x) + 6] · g'(x)

F'(x) = [2 · [(1 / 3) · x³ + 7] + 6] · x²

b) Now we proceed to expand the polynomial in its standard form:

F'(x) = [(2 / 3) · x³ + 7] · x²

F'(x) = (2 / 3) · x⁵ + 7 · x²

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1. Therefore, the sequence is geometric.

2. Therefore, the sequence is arithmetic.

3. Therefore, the sequence is neither arithmetic nor geometric.

4. Therefore, the sequence is geometric.

5. Therefore, the sequence is neither arithmetic nor geometric.

For the arithmetic, geometric, and harmonic sequences, a collection of sequences and series formulas is provided below. The sequence and series formulas presented here contain formulas for determining the sum of the n terms in a series as well as the nth term of the sequence.

A common difference exists between two succeeding terms in an arithmetic series. There is a typical ratio between succeeding terms in a geometric series.

1. Given sequence is 27, 9, 3, ...

As the difference between the number is large.

So, we will check for geometric sequence.

[tex]r = \frac{27}{9} = \frac{3}{3} = \frac{1}{3}[/tex]

Therefore, the sequence is geometric.

2. Given sequence is 4, 8, 12, ...

As we can see there is uniform difference of 4

Therefore, the sequence is arithmetic.

3. Given sequence is 50, 56, 60, ...

As the difference between the number is not uniform.

So, we will check for geometric sequence.

[tex]r = \frac{50}{56} \neq \frac{56}{60}[/tex]

There, the sequence is neither arithmetic nor geometric.

4. Given sequence is 36, 12, 4, ...

As the difference between the number is large.

So, we will check for geometric sequence.

[tex]r = \frac{36}{12} = \frac{12}{4} = 3[/tex]

Therefore, the sequence is geometric.

5. Given sequence is 4, 24, ...

The number of terms is very less and hence we can't decide.

There, the sequence is neither arithmetic nor geometric.

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