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Answer:

m is the slope and b is the y intercept

Step-by-step explanation:

Answer:

Exponential notation is a powerful way to express repeated

multiplication of the same number. Specifically, powers of 10

express very large and very small numbers in a manner which is

convenient to read, write and compare.

• For any non-zero integer a, a–m 1

m a

=

• Laws of exponents are

(a) am × an = am+n

(b) am ÷ an = am–n

(c) (am)

n = amn

(d) am × bm = (ab)

m

(e) a° = 1, where a ≠ 0

(f)

m m

m

a a

b b

  =   

• Numbers can be expressed in expanded form by using exponents.

• Very large and very small numbers can be expressed in standard

form.

• Standard form is also called scientific notation form.

Step-by-step explanation:

Example 1 : Multiplicative inverse of 27 is

(a) 2–7 (b) 72 (c) – 27 (d) – 27

Solution : The Correct answer is (a).

Example 2 : The human body has about 100 billion cells. This number

can be written in exponential form as

(a) 10–11 (b) 1011 (c) 109 (d) 10–9

Solution : The correct answer is (b).

In examples 3 to 5, fill in the blanks to make the statements true.

Example 3 :

4

4 5 (– 4) ______ 4

  × =    

Solution : 54

Example 4 : ( ) ( ) 2 3 –3 –2 2 3 _____ × =

Solution : 6–6

Example 5 : The distance between earth and sun is 150 million

kilometres which can be written in exponential form as

_______.

Solution : 1.5 × 108 km

In examples 6 and 7, state whether the statements are true (T) or false (F):

Example 6 : Very small numbers can be expressed in standard form

using positive exponents.

Solution : False.

Example 7 : (–10) × (–10) × (–10) × (–10) = 10–4

Solution : False.

Step-by-step explanation:

Answer:

8 & 14

Step-by-step explanation:

Let

Cost of senior tickets be x and students be y

In day 1

4x + 5y = 102

In day 2

7x + 5y = 126

Subtract both

7x + 5y - (4x + 5y) = 126 - 102

7x + 5y - 4x - 5y = 24

7x - 4x = 24

3x = 24

x = 24/3

x = 8

From 1

4(8) + 5y = 102

32 + 5y = 102

5y = 102 - 32

5y = 70

y = 70/5

y = 14

The amount of total current liabilities reported on the balance sheet equals to; $178,000.

Current liabilities entails set of amount or responsibility owed within an accounting period.

Particulars                                       Amount

Accounts payable                          $32,000

Notes payable (current portion)    $41,000

Salaries and wage payable           $34,000

Rent                                                 $12,000

Accounts receivable                     $59,000

Total current liabilities                  $178,000

Therefore, the amount of total current liabilities reported on the balance sheet equals to ; $178,000.

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Answer:

-8 and -6.

Step-by-step explanation:

Let the first even integer be a.

Since the second is a consecutive even integer, it is given by (a + 2).

Half of the smaller (i.e. a) is equal to two more than the larger (i.e. a + 2). In other words:

[tex]\displaystyle \frac{a}{2} = (a + 2) + 2[/tex]

Solve for a:

[tex]\displaystyle \begin{aligned}\displaystyle \frac{a}{2} &= (a + 2) + 2\\ \\ \frac{a}{2} &= a + 4\\ \\ a &= 2a + 8 \\ \\ a &= -8 \end{aligned}[/tex]

In conclusion, the two even, consecutive integers are -8 and -6.

The equation for the length of the rectangle is L = 30 - W.

The given parameters:

perimeter of Andy's rectangular patio = 60 feet

The formula for perimeter of a rectangle is calculated as follows;

[tex]P = 2(L+W)[/tex]

Where;

P is the perimeter

L is the length of the rectangle

W is the width of the rectangle

To find the equation for the length of the rectangle, make L the subject of the formula;

[tex]P = 2(L+W)\\\\60 = 2(L+W)\\\\divide \ both \ sides \ by \ 2\\\\\frac{60}{2} = \frac{2(L+W)}{2} \\\\30 = L+ W\\\\L = 30 - W[/tex]

Thus, the equation for the length of the rectangle is L = 30 - W.

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Answer:

Coordinates are numbers which determine the position of a point or a shape in a particular space (a map or a graph).

In primary school children are taught Cartesian coordinates, which they are introduced to in Year 4. Points are marked by how far along they are on the x axis (the horizontal axis) and how far up they are on the y axis (the vertical axis).

Step-by-step explanation:

Answer:

4 cm

Step-by-step explanation:

A ratio shows us the number of times a number contains another number. The distance between Conor's house and Oscar's house on the map will be 4 cm.

A ratio shows us the number of times a number contains another number.

Given that 1 cm on the map represents 750 m in real. Therefore, we can write the ratio as,

Ratio = Length on the map / Length in real = 1cm / 750m

Now, it is also mentioned that Conor's house is 3000 m from Oscar's house. Therefore, the ratio can be written as,

Ratio = Length between the house in map / Length between the house in real = 1 cm /750 m

Length between the house in map = (1 cm × Length between the house in real) / 750 m

Length between the house in map = (1 cm × 3000m) / 750 m

Length between the house in the map = 4 cm

Hence, the distance between Conor's house and Oscar's house on the map will be 4 cm.

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Answer: Its B and C

Which equations shows the variable terms isolated on one side and the constant terms isolated on the other side for the equation 3 x minus 5 = negative 2 x + 10? Select two options.

x = 5

–15 = –5x

5x = 15

–15 = 5x

x = -5

Answer:

x²+8x+16

Step-by-step explanation:

f(x) = (x+4)²

= (x+4)(x+4)

= x² + 4x + 4x + 16

= x² + 8x + 16

Answer:

C.

y=2 · 3xy equals 2 times 3 superscript x baseline

Step-by-step explanation:

y=2 ·  3 xy equals 2 tim

Answer:

[tex]2(x + y + 1)[/tex]

Step-by-step explanation:

[tex]x + 2y + x + 2[/tex]

[tex]x + x = 1x + 1x[/tex]

[tex](1 + 1)x = 2x[/tex]

[tex]2x + 2y + 2[/tex]

[tex] = 2(x + y + 1)[/tex]

Answer:

A. the slope value is 1/4

B. 0

C. y = 1/4x

Step-by-step explanation:

A: the slope can be calculated with the formula

[tex]m = \frac{rise}{run} = \frac{y2 - y1}{x2 - x1} [/tex]

m is the slope

(x1, y1) is your first coordinate point (any point will work)

(x2, y2) is your second coordinate point (any point will work)

Plug in your values, in this case I chose (0,0) and (4,1) as the two coordinates:

[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{1 - 0}{4 - 0} = \frac{1}{4} [/tex]

B: the y-intercept is the y-coordinate of where the graph touches the y-axis and in this case the coordinate is (0,0) where the y coordinate is 0.

C:

the equation of the graph is y = mx + b.

m is the slope = 1/4

b is the y-intercept = 0

Therefore the equation is y = 1/4x

Answer:

m= 1/10

Step-by-step explanation:

1. Move the terms so that will be 3m - 2m=-1/2 + 3/5

2. Subtract the m values so that will be 3m - 2m= 1 or m

3. Calculate the sum.

4. So the answer will be m= 1/10. M because we subtracted 2 from 3 which make us 1 so we say it m and 1/10 by doing 1/2 + 3/5.

Answer:

Step-by-step explanation:

3m - 3/5 = 2m - 1/2

3m - 2m = 3/5 - 1/2

m = 0.1

32/7 to a mixed number is 4 and 4/7

Answer:

Jennifer - 1st

Susan - 2nd

Emily - 3rd

Janice - 4th

Maria - 5th

Step-by-step explanation:

Susan is 2nd.

Places 1, 3, 4, and 5 are left.

Janice and Jennifer both start with J. None of the other swimmers start with the same first letter. One is 1st and one is 4th.

Since Maria finished immediately after Janice, and Janice must be 1st or 4th, Janice can't be first since 2nd place is already taken. This means that Janice is 4th and Maria is 5th.

Places 1 and 3 are left.

We know Jennifer is 1st or 4th and since 4th is taken, Jennifer is first.

Place 3 is left.

Emily must be 3rd since that is the only spot left.

Answer:

(1)

Step-by-step explanation:

x - 2 = - 5             Add 1 to each side

x = - 5 + 2

x = - 3

Now go to the next part

(x - 2)^2

(-3 - 2)^2

(- 5)^2

Now it's a good idea at this point to separate the squared. It means that two numbers that are the same are to be multiplied together.

(-5)(-5)  Two minuses are going to give you a plus.

5 * 5 = 25

(-5) * (-5) also give you 25

The answer is (1)

Answer:

b 30% is the right answer

Answer:

Variable data is defined as information and figures used to build control charts. Variable data can be used to create average (X-bar) charts, range charts, and sample standard deviation charts or "S-charts."

Answer:

Step-by-step explanation:

A restaurant can hold no more than 160 people, it means it can hold 160 people or less.

This is shown as:

Correct choice is D

Answer:

2 1/10 miles.

Step-by-step explanation:

8 - (2 1/2 + 3 2/5)

= 8 -  (5/2  + 17/5)

= 8 - (25/10 + 34/10)

= 8 - 59/10

= 80/10 - 59/10

= 21/10

= 2 1/10 miles.

Answer:

[tex] \frac{2}{3} x = 5 \\ 2x = 5 \times 3 \\ 2x = 15 \\ x = \frac{15}{2} = 7.5 \\ thank \: you[/tex]

Answer:

two out of 30

30 x 6 = 180

2 x 6 = 12

if 2 out of 30 are defective, and there are 180 total, 12 should be expected to be defective

Step-by-step explanation:

Answer:

55-9

Step-by-step explanation:

you subtract

Answer:

after 6 years

Step-by-step explanation:

thats when the lines intersect, (6,300)

There will be equal enrollment in Spanish and French classes after 6 years from now.

The red line shows the number of students enrolled in French class each year from now and blue line shows the number of students enrolled in Spanish class each year from now.

The point of intersection of the lines is the point which lies in both the line.

So, it represents the point or time when there are same number of students enrolled in both French and Spanish classes.

From the graph, we can see that the two lines at a point [tex](6,300)[/tex]. The value on the [tex]x[/tex]-coordinate shows the years from now. So, we can say that there will be equal number of students enrolled in two classes after 6 years.

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Answer:

a) language

b) 2/15

Step-by-step explanation:

For the first part, you can start by making the denominators same

you take the LCM of 3 and 5 which is 15

Language books are now 10/15 since you multiply the nominator and denominator by 5

While science books are 3/15

10/15 : 3/15 making it obvious that language books are more

if the remaining are math books then

total books - (language + science books) = math books

10/15 + 3/15 = 13/15 (non math books)

15/15 - 13/15 are math books making 2/15 of them math books

Answer:

no

Step-by-step explanation:

it depend on the question

Step-by-step explanation: