find the common difference

Answer:

slope = - [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (3, 1)

m = [tex]\frac{1-2}{3-0}[/tex] = - [tex]\frac{1}{3}[/tex]

Answer:

-6

Step-by-step explanation:

The average rate of change of a function, f(x), on interval [a,b] is (f(b)-f(a))/(b-a).

So the avereage rate of change of a function, f(x)=x^2+5x+1, on [-9,-2] is

(f(-2)-f(-9))/(-2--9)

(f(-2)-f(-9))/(7)

Stop!

To find f(-2), you replace x in f(x) = x^2 + 5x + 1, with (-2) giving you f(-2)=(-2)^2+5(-2)+1=4-10+1=-6+1=-5.

To find f(-9), you replace x in f(x) = x^2 + 5x + 1, with (-9) giving you f(-2)=(-9)^2+5(-9)+1=81-45+1=36+1=37.

Continue!

(f(-2)-f(-9))/(7)

=(-5-37)/7

=(-42)/7

=-42/7

=-6

Answer:34/45

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

The there smallest consecutive odd numbers are 1,3 and 5

Therefore the smallest possible perimeter of such triangle = 8

Answer:

Step-by-step explanation:

[tex]5\frac{1}{6}=\frac{(5*6)+1}{6}=\frac{31}{6}[/tex]

Answer:

31/6 (improper fraction).

Step-by-step explanation:

5 1/6 = (6 × 5) + 1/6 = 31/6

31/6 is the improper fraction.

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Answer:

A

Step-by-step explanation:

A linear function is a straight line

b,c,d all have curves so they are not linear functions

Answer:

The rate charged by first mechanic per hour= x =$85

The rat charged by second mechanic per hour =y = $70

Step-by-step explanation:

Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of $1900. What was the rate charged per hour by each mechanic if the sum of the two rates was $155 per hour?

Solution

Let

x= hourly rate of the first mechanic

y= hourly rate of the second mechanic

Derive two equations to solve for the two unknowns

10x + 15y = 1900 (1)

x + y = 155 (2)

From (2)

x + y = 155

x=155-y

Substitute x=155-y into (1)

10x + 15y = 1900

10(155-y) + 15y =1900

1550 -10y + 15y =1900

5y =1900-1550

5y=350

Divide both sides by 5

y= 70

Substitute y=70 into (2)

x + y = 155

x + (70) =155

x=155 - 70

= 85

x= 85

The rate charged by first mechanic per hour= x =$85

The rat charged by second mechanic per hour =y = $70

Answer:

60 ounces.

Step-by-step explanation:

Given:

A mixture contains 5 parts of white paint for every 4 parts of blue paint.

i.e. Ratio of white paint : blue paint = 5 : 4

Quantity of White paint = 75 ounces

To find:

How many ounces of blue paint = ?

Solution:

Here, we are given the ratio of white and blue paint in the mixture.

Also, we are given the quantity of white paint in the paint can.

And we have to find the quantity of other paint in the can.

Let us use all the given statements to find the unknown quantity of blue paint.

Ratio of white paint : blue paint= Ratio of quantity of white paint: blue paint

[tex]\dfrac{5}{4} = \dfrac{75}{\text{Quantity of blue paint}}\\\Rightarrow \text{Quantity of blue paint} = 15 \times 4\\\Rightarrow \text{Quantity of blue paint} = 60\ ounces[/tex]

So, the quantity of blue paint in the can is 60 ounces.

Answer:

y = -2x/3 + 531

Step-by-step explanation:

Answer: C. 5

Step-by-step explanation:

[tex]6 \cdot3\div \sqrt{9}-1[/tex]

[tex]6 \cdot 3=18[/tex]

[tex]\sqrt{9}=3[/tex]

[tex]18\div \:3-1[/tex]

[tex]18\div \:3=6[/tex]

[tex]6-1[/tex]

[tex]=5\\[/tex]

The value is 16.

The square root of a number is that factor of a number which when multiplied by itself gives the original number. Squares and square roots are special exponents. Consider the number 9. When 3 is multiplied by itself, it gives 9 as the product. This can be written as 3 × 3 or 3^2. Here, the exponent is 2, and we call it a square.

We can use four methods to find the square root of numbers and those methods are as follows:

Given:

6 · 3 ÷ √9 - 1

6*3 = 18

√9 - 1 = 3-1 = 2

So,

6 · 3 ÷ √9 - 1

=18- 2

=16

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Answer:

A. 260

Step-by-step explanation:

Answer:

square root 260

Step-by-step explanation:

On mine it is D. but the answer is the square root of 260

Answer:

-13a

Step-by-step explanation:

Since -8 and -5 have like variables, you can subtract them. -8-5 is -13, so the answer is -13a.

Answer:

-13a

Step-by-step explanation:

These two numbers are already like terms, so you can subtract it easily.  

First, don't look at the a.

-8-5= -13 because if something is negative and gets subtracted, that means it'll still be negative.

Now that we now it equals -13, we can add the variable a back onto the answer.  We get -13a.  

Answer:

It will take 0.75B hours for the return leg

Step-by-step explanation:

Here, given that the first leg of the trip was for B hours at 3 miles per hour , we want to calculate the number of hours the return leg will take at 4 miles per hour given that it is the same distance.

Mathematically, we know that ;

Distance = speed * time

So the distance taken on the first leg of the trip would be;

Distance = 3 miles per hour * B hours = 3B miles

Now, this distance was traveled on the return leg also.

This means that the time taken here will be;

Time on return leg = distance/speed = 3B/4 = 0.75B hours

Answer:

The correct option is C.

Step-by-step explanation:

The two patterns are defined as follows:

Form the two patterns as follows:

Pattern A : 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 0

Pattern B : 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0

The first several terms of Patterns A and B are shown by:

Pattern A: 20, 18, 16, 14, 12, 10

Pattern B: 20, 19, 18, 17, 16, 15

Thus, the correct option is C.

Answer:

The correct option is;

b. Stem and leaf plot

Step-by-step explanation:

A stem-and-leaf plot shows the data shape and the densities of the different classes in a graphical form such that the information in the data such as the data characteristics are self displayed by the data numbers arranged in the stem-and-leaf plot. The stem-and-leaf plot keeps the raw numerical data, in the form they were obtained and by their arrangement, outliers are easily spotted.

Answer:  b. stem-and-leaf plot

Step-by-step explanation:

hope this helps

Answer:

In short, 0 is the only number such that for any number x, x + 0 = x. ... So, the reason that any number to the zero power is one is because any number to the zero power is just the product of no numbers at all, which is the multiplicative identity, 1

Answer:The zero exponent rule states that any term with an exponent of zero is equal to one. This lesson will go into the rule in more detail, explaining how it works and giving some examples. There will also be a quiz to test your knowledge.

The zero exponent rule is one of the rules that will help you simplify exponents. Let's first define some terms as they relate to exponents. When you have a number or variable raised to a power, the number (or variable) is called the base, while the superscript number is called the exponent, or power.

Usually, you'll see this written with the base being a normal-size number (or letter, if you're working with a variable). The exponent will be in a slightly smaller font, raised a little up above and to the right of the base. However, in some formats, like this one, you'll see the base, a mark called a caret that looks like an inverted V, and then the exponent. So if you have a base of 2 and an exponent of 3, we'll write that out here as 2^3 = 8.

Now that you know the terms, let's go back to the zero exponent rule. The zero exponent rule basically says that any base with an exponent of zero is equal to one. For example:

x^0 = 1

Answer:

I think 1/2 is the ans

Step-by-step explanation:

quadratic function equation

would help

Step-by-step explanation:

Answer in attached picture...

hope it helps

Answer:

Step-by-step explanation:

Use the property of 30°-60°-90° right triangle.

The ratio of sides:

Compare with the given:

Apply the property of 30-90-60 angle

So

Answer:

B.

[tex] \frac{275\pi}{6} {m}^{2} [/tex]

Step-by-step explanation:

[tex]area \: of \: sector \: is \\ \frac{the \: angle}{360} \times \pi {r}^{2} \\ hence \: we \: have \\ \frac{165}{360} \times {(10m)}^{2} = \frac{275\pi}{6} {m}^{2} [/tex]

Answer:

16 slices

Step-by-step explanation:

4 apples times 4 slices (as there is 4 slices per apple)

So, 4×4=16

Hope this helps :)

Answer:

2040 miles

Step-by-step explanation

Gas costs 1.35 per gallon and Jose had 81 dollars for gasoline

with this info we can find out how many gallons of gas Jose can buy.

81 divided by 1.35 is 60 gallons of gas

we also know that he can travel 34 miles for each gallon of gas

with this we can find out how far jose can travel

34 multiplied by 60 is 2040 miles

so, with $81, Jose can travel 2040 miles if gas prices are $1.35

Answer:

None of the answers seem to be correct.

Step-by-step explanation:

The given equation is of the form y = mx + b where m is the slope and b is the y-intercept.

Here, m = -14

Two parallel lines have the same slope. So, the slope of the new line will be -14.

To calculate the y-intercept substitute x=4 and y=4 in the equation.

4 = (-14)(4) + b

Solving for b, we get b = 60.

So, the new equation will be y = -14x + 60

The equation of the line parallel to the given line is y =-14x+60, none of the given options is correct.

The equation of the straight line is given by y = mx +c , Where m is the slope of the line and c is the y-intercept.

The equation of the line is y = -14x -3

The slope of the line parallel to this will be the same as the given line.

m = -14 for both the lines

The line equation parallel to the given line is

y = -14x +c

The line passes through the points (4,4)

4 = -14 * 4 + c

c = 60

y = -14x +60

Therefore, the equation of the line parallel to the given line is y =-14x+60.

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Answer:

2. A

3. C

4. B

Step-by-step explanation:

2. To answer # 2, just add all the sides together...

(5x-7) + (3x-4) + (2x-6)

=  10x - 17

3. To answer # 3, divide/mulitply both the numerators and denominators by the same number and check to see if that answer matches the displayed answer...

a) 28 divided by 7 is 4,  so divide the whole fraction by 7 to see if the fraction is proportional...  

  28/7 = 4

  49/7 = 7

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

b) 4 goes into 16  4 times so multiply [tex]\frac{4}{7}[/tex] by 4...

   4 x 4 = 16

   7 x 4 = 28

   [tex]\frac{16}{28}[/tex] =  [tex]\frac{16}{28}[/tex]

c) 4 goes into 16 4 times so multiply the whole fraction by 4...

   4 x 4 = 16

   7 x 4 = 28

   [tex]\frac{16}{28}[/tex] ≠ [tex]\frac{16}{35}[/tex]

d) 4 goes into 20 5 times to multiply the whole fraction by 5...

   4 x 5 = 20

   7 x 5 = 35

   [tex]\frac{20}{35} = \frac{20}{35}[/tex]

C is the answer because the fractions are not proportional.

4) 25% is a quarter of 100%. A third of 100% is 75%.

   $120 - 0.25($120) = $90

   Another expression for the for sale price is...

   B) 0.75($120) = $90

Answer:

x = -6

Step-by-step explanation:

x^2 +12x +36=0

What 2 numbers multiply to 36 and add to 12

6*6 = 36

6+6 = 12

(x+6) (x+6) = 0

Using the zero product property

x+6 = 0  x+6 =0

x=-6   x=-6

Since they are the same we only list the solution once

Answer:

[tex]-6[/tex]

Step-by-step explanation;

[tex]x^{2} +12x+36=0[/tex]

Comparing with ax² +bx² + c=0

where a =1 , b=12, and c= 36

[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

substituting the values of a, b, and c to find the value of x

[tex]x=\frac{-12\pm \sqrt{12^2-4\cdot \:1\cdot \:36}}{2\cdot \:1}[/tex]

[tex]x=\frac{-12+,-\sqrt{144-144} }{2}[/tex]

[tex]x=\frac{-12+,-0}{2} =-6[/tex]

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Answer:

m∠C = 102°

Step-by-step explanation:

This diagram is a Quadrilateral inscribed in a circle

The first step is to determine what m∠B

is

The sum of opposite angles in an inscribed quadrilateral is equal to 180°

m∠D + m∠B = 180°

m∠B = 180° - m∠D

m∠B = 180° - 80°

m∠B = 100°

Second step is we proceed to determine the exterior angles of the circle

m∠ADC = 2 × m∠B

m∠ADC = 2 × 100°

m∠ADC = 200°

m∠ADC = m∠CD + m∠AD

m∠AD = m∠ADC - m∠CD

m∠AD = 200° - 116°

m∠AD = 84°

The third step is to determine m∠BAD

m∠BAD = m∠AD + m∠AB

m∠BAD = 84° + 120°

m∠BAD = 204°

The final step Is to determine what m∠C is

It is important to note that:

m∠BAD is Opposite m∠C

Hence

m∠C = 1/2 × m∠BAD

m∠C = 1/2 × 204

m∠C = 102°