What is the domain and range of this picture?

Answer:

45

Step-by-step explanation:

180 - 45 - 90 = 45

The Arithmetic sequences are-

The common difference must be same for the sequence to be arithmetic;

d₁ = a₂- a₁

d₂ = a₃ - a₂

Thus, d₁ = d₂

Check the common differences for given sequences are-

A. -5, 5, -5, 5, - 5, 5....

d₁ = 5 - (-5) = 10

d₂ = -5 - 5 = -10

d₁ ≠ d₂, not a Arithmetic sequences

B. 96, 48, 24, 12, 6...

d₁ = 48 - 96 = -48

d₂ = 24 - 48 = -24

d₁ ≠ d₂, not a Arithmetic sequences

C. 18, 5.5, -7, -19.5, -32...

d₁ = 5.5 - 18 = -12.5

d₂ = -7 - 5.5 =  - 12.5

d₁ = d₂,  Arithmetic sequences

D. -1, -3, -9, -27, -81....

d₁ = -3 -(-1) = -2

d₂ = -9 - (-3) = -6

d₁ ≠ d₂, not a Arithmetic sequences

E. 16, 32, 48, 64.....

d₁ = 32 - 16 = 16

d₂ = 48 - 32 = 16

d₁ = d₂,  Arithmetic sequences

Thus, the common difference must be equal for Arithmetic sequences.

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Answer:

9y^2 + 9x - 18 or 9(y^2 + x - 2)

Step-by-step explanation:

9(y^2+x)=18

9y^2 + 9x=18

9y^2 + 9x - 18 = 0

9(y^2 + x - 2) = 0

Answer: (3x^3)^3 = 3^3 (x^3)^3 = 27 (x^3)^3 = 27^3x3 = 27^9

27^9

Answer:

27x^9

Step-by-step explanation:

Distribute.

3^3 (x^3)^3

27 (x^3)^3

Power of a power.

27x^3 times 3

Multiply.

27x^9

Answer:

208

Step-by-step explanation:

4*30 = 120

(15-4) * 8 = 88

88 + 120 = 208

Answer:

208 cm

Step-by-step explanation:

Solving right side first. 8*15=120

Take out 8cm from 30. 30 - 8 = 22

22*4= 88

88 + 120 = 208

Check work I found the total area and the white rectangle.

15*30=450 which in total area

15-4=11 11 is the left/right side of the white rectangle

30-8=22 22 is the top/bottom side of the white rectangle.

22*11= 242

208+242=450

Answer:The missing number is 7

Step-by-step explanation:

if 4+5+16 is 25 then you will need 7 more to make it 32 so you can divide by 4 and get 8

Using translation concepts, we have that:

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, the parent function is:

g(x) = |x|.

The translated function is:

f(x) = 3|x + 1| - 6.

The multiplication by 3 means that the function was stretched vertically by a factor of 3, hence:

The 3 will make the parent function vertically stretch by a factor of 3.

At x -> x + 1, we have that the function was shifted one unit left, hence:

The x + 1 will make the parent function shift horizontally left 1 unit.

For the subtraction by 6, the function was shifted down 6 units, hence:

The -6 will make the parent function shift vertically down 1 unit.

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The only set of elements that satisfied the equation 2x-1= -13 is {-6}.

A set is a combination of specific quantities in which the meaning of each variable must be the same.

For example {1,2,3,4,5,6...} is a set of natural numbers in which each variable is representing a natural number so the overall meaning is the same among all.

Another example could be a set of whole numbers like that.

Given the equation,

2x-1= -13

By taking -1 right-hand side

2x = -13 + 1 = -12

By dividing 2

x = -6

Hence "The only set of elements that satisfied the equation 2x-1= -13 is {-6}".

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The number of hours Becky took to finish typing the essay is 3 hours.

A division is a process of splitting a specific amount into equal parts.

We have,

Number of words in the essay = 4,100

Becky can type 20 words per minute.

Becky has already typed 500 words.

So the remaining words are:

= 4,100 - 500

= 3,600

Now,

The number of hours to complete 3,600 words:

= 3,600 minutes / 20

= 180 minutes

We know that,

1 hour = 60 minutes

3 hours = 180 minutes

= 3 hours

Thus the number of hours Becky took to finish typing the essay is 3 hours.

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Answer: Answer is 0.52

Step-by-step explanation:

So we have the fraction 13 Out of 25.

step 1: here we divide numerator(which is 13) by denominator(which is 25).

step 2: first we make denominator 100 by multiplying by 25 with 4 and also 13 with 4.

ie. [tex]\frac{13 * 4}{25 * 4}[/tex]

step 3: we get [tex]\frac{52}{100}[/tex]

step 4: now we can easily write the decimal fraction. ie. 0.52

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The principle can makes 4 groups with 7 girls and 8 boys.

The biggest number that divides each of the two or more numbers is known as the HCF, or highest common factor. The Greatest Common Measure (GCM) and Greatest Common Divisor are further names for HCF (GCD). The least common multiple, or LCM, is used to determine the smallest common multiple of any two or more numbers. LCM and HCM are two separate approaches.

According to the given statement ;

We are given that 28 girls and 32 boys volunteer to plant at a school.

The principle divided the girls and boys into identical groups that have girls and boys in each group.

We have to find that how much the principle can make greatest number of groups.

We will find HCF of 28 and 32

28= 2X2X7

32= 2X2X2X2X2

Highest common factor of 28 and 32 =2X2=4

Therefore, the principle can makes 4 groups with 7 girls and 8 boys.

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Height is h = 8 and base  = 19 inch in triangle .

What Does a Triangle's Area Mean?

Area of a triangle whose base is b and height is h is =1/2 * b * h

Let the height of given triangle be h inch and as base of a triangle is 3 inch greater than the height, base is ( 2h + 3)

b = 2h + 3

Hence, its area is 1/2 × h ×  (2h + 3 ) = 76 inch²

So,   1/2 × h × (2h + 3)  = 76

       2h² + 3h  = 76 × 2

       2h² + 3h - 152 = 0

       2h² + 19h - 16h - 152 = 0

       h( 2h + 19 ) -8 (2h + 19) = 0

        (h-8) ( 2h - 19)

 now   h = 8    and  h = -19/2  but height of triangle cannot be negative.

Hence height is h = 8 and base = 2 * 8 + 3 = 19 inch

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[tex](-1)x\times(-1)^{12}\implies -x\times(-1)^{2+2+2+2+2+2} \\\\\\ -x\times(-1)^2 (-1)^2 (-1)^2 (-1)^2 (-1)^2 (-1)^2 \implies -x\times 1\cdot 1\cdot 1\cdot 1\cdot 1\cdot 1\implies -x[/tex]

bear in mind that any value raised to an even power, will always positivize.

The value of expression |-4 + 3| · 8 is 8.

What is Modulus function?

A modulus function is a function which gives the absolute value of numbers or variable.

The expression is given as;

| -4 + 3 | * 8

Now, Solve the expression as;

⇒ | -4 + 3 | * 8

⇒ | - 1 | * 8

⇒ 1 * 8

⇒ 8

Since, Modulus of a negative number gives the positive of that number.

Hence, The value of expression |-4 + 3| · 8 is 8.

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Answer:

Step-by-step explanation:

sub equation 1 into 2

2-5x=x²-2x-8

0=x²-2x+5x-8-2

0=x²+3x-10

0=(x-2)(x+5)

x=2 or x=-5

sub x into equation 1

y=2-5(2)                            or        y=2-5(-5)

y=-8                                              y=27

The interest owed is $40

Interest is the amount of money paid when a loan is collected

The amount is $500

The interest rate is 8%

Therefore the interest owed can be calculated as follows

= 8/100 × 500

= 0.08 × 500

= 40

Hence the interest owed is $40

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Answer:

rHrhstdu.guf.ugdtuy.

Step-by-step explanation:

1. -16 -4 = -20

4. -13 -2 = -15

7. -12-7= -19

10.-23-6= -29

13. 4 + 9 = 13

16. 5 + 3 = 8

19. 4+ 10 = 14

22. -4 + 1 = 3

2.-19-28 = -47

5. 9-3 = 6

8. -21-1= -22

11. 1-3 = -2

14. -8 + 8 =0

17. -5 + 9 =4

20. 6+-3 = 3

23. -2 -2 = -4

3. 3 .10 =30[ there is no sign so these numbers are multiplied ]

6. 1-5= -4

9. 20-8= 12

12. -9 -0 = -9

15. 4 + 6 = 10

18. 2 + 2 = 4

21. -6 -5 = -11

24. 4 + 1 = 5

The value of complex number 6 + 7i / 6-7i is -13 / 85 + 84i/85

Complex numbers are those that are represented as a+ib, where a and b are actual numbers and I is a fictitious number termed a "iota." I has the value (-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im).

Given the complex number is -

6 + 7i / 6-7i

⇒ 6 + 7i / 6 - 7i × 6 + 7i / 6 + 7i

⇒ (6+7i)² / 6² - 7²(i²)

Using (a+b)² = a² + b² + 2ab    

⇒ 6² + (7i)² +2(6)(7i) / 36 - 49(-1)

⇒ 36 - 49 + 84i / 36 + 49

⇒ -13 + 84i / 85

⇒ -13 / 85 + 84i/85

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The values for the net change and average change is given as-

7. Net change = 2 , Average change = 2/3.

8. Net change = -2, Average change = -1/2.

9. Net change = -4, Average change = 4/5.

10. Net change = 4, Average change = 2/3.

Given two points on the graph of f(x), (a,f(a)) and (b,f(b)), the net change would be the contrast between the different f(x) values.

Part 7:

The points on x axis are;

a = 1 and b = 4

f(b) = f(4) = 5

f(a) = f(1) = 3

Thus, net change is; f(b)−f(a)

= f(4) - f(1)

= 5 - 3

net change = 2

The average change;

=  [f(b)−f(a)]/(b - a)

= [f(4) - f(1)]/(4 - 1)

net change = 2/3.

Part 8:

The points on x axis are;

a = 1 and b = 5

f(b) = f(5) = 2

f(a) = f(1) = 4

Thus, net change is; f(b)−f(a)

= f(5) - f(1)

= 2 - 4

net change = -2

The average change;

=  [f(b)−f(a)]/(b - a)

= [f(5) - f(1)]/(5 - 1)

net change = -2/4 = -1/2

Part 9:

The points on x axis are;

a = 0 and b = 5

f(b) = f(5) = 2

f(a) = f(0) = 6

Thus, net change is; f(b)−f(a)

= f(5) - f(0)

= 2 - 6

net change = -4

The average change;

=  [f(b)−f(a)]/(b - a)

= [f(5) - f(0)]/(0 - 5)

net change = -4/-5 = 4/5

Part 10:

The points on x axis are;

a = -1 and b = 5

f(b) = f(5) = 4

f(a) = f(-1) = 0

Thus, net change is; f(b)−f(a)

= f(5) - f(-1)

= 4 - 0

net change = 4

The average change;

=  [f(b)−f(a)]/(b - a)

= [f(5) - f(-1)]/(5 + 1)

net change = 4/6 = 2/3

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Value of both the integers as three times the largest consecutive integer is 15 less than 2/3 the smallest one is -7, -9.

As given,

Let x, x +2 be two consecutive odd integers

Three times largest integer=3( x+2)

15 less than 2/3 smallest integer=(2/3)x -15

Equation :

3(x+2)=(2/ 3)x -15

⇒ 3x +6=(2x -45)/3

⇒ 9x-2x= -18 -45

⇒ 7x=-63

⇒ x =-9

and x+2 =-7

Therefore, value of both the integers as three times the largest consecutive integer is 15 less than the 2/3 the smallest one is -7, -9.

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In each game, the probability that player A wins the game is 13/20 and player B wins the game is 7/20.

To find the probability:

Therefore, in each game, the probability that player A wins the game is 13/20 and player B wins the game is 7/20.

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Answer:

B

Step-by-step explanation:

An expression is a set of terms combined using the operations +, -, x or ÷, for example 4 x − 3 or 5 x 2 − 3 x y + 17 . An equation is a statement with an equals sign, which states that two expressions are equal in value, for example 4 b − 2 = 6

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

50

6m-n

Let m = 9 and n = 4

when m = 5 and n = 38

N-6m6*9-4

Multiply first

54-4

Then subtract

50

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Answer: 19

Step-by-step explanation:

2+1+1+12+3=19

1125  money will she have at the end of 10 years in the account  after Simple Interest.

What is a basic example and interest?

Mary plans to invest = 2500

t = 10 yr

r = 4.5 %

simple intrest = prt/100

                       = 2500 * 10 * 4.5 /100

                        = 1125

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The solution is:

[tex]-7\leq x\leq -4[/tex] or [tex]-2\leq x\leq 1[/tex]

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of TU

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{-8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-8}-\stackrel{y1}{5}}}{\underset{run} {\underset{x_2}{-2}-\underset{x_1}{1}}} \implies \cfrac{-13}{-3}\implies \cfrac{13}{3}[/tex]

hmmmm, well, if that's so, then the slope of VW will be the negative reciprocal of that only if both are really perpendicular, so

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{13}{3}} ~\hfill \stackrel{reciprocal}{\cfrac{3}{13}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{13}}}[/tex]

since now we know the slope if VW, let's use it

[tex](\stackrel{x_1}{7}~,~\stackrel{y_1}{-9})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{y}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{y}-\stackrel{y1}{(-9)}}}{\underset{run} {\underset{x_2}{-6}-\underset{x_1}{7}}} \implies \cfrac{y +9}{-13}~~ = ~~\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{3}{13}}\implies y+9=\cfrac{3(-13)}{-13} \\\\\\ y+9=3\implies {\LARGE \begin{array}{llll} y = -6 \end{array}}[/tex]

Answer:

20

Step-by-step explanation:

the line equals 180 degrees total.

so subtract the angle we already know from the total...

180- 100=80

then, make an equation with the last two variables since we know both of them added together should equal 80

80=x +3x

Combine like terms

80=4x

Divide by 4

20=x