given the following sequence 3, 7, 11, 15, 19
a) find the 10th term, the 30th term, and the t^th term
b) find the sum for the first 10 terms and the first 30 terms
c) find the number needed of terms needed to have a sum of 15
d) write an algebraic representation for the sum of the first term

Answer:

[tex] \fbox{ \sf{Perimeter \: of \: a \: rectangle = 10x - 2}}[/tex]

Step-by-step explanation:

[tex] \star{ \sf{ \: \: Length \: of \: a \: rectangle ( l ) = (2x - 5) }}[/tex]

[tex] \star{ \sf{ \: Width \: of \: a \: rectangle ( w ) = (3x + 4)}}[/tex]

[tex] \star{ \sf{ \: \: Perimeter \: of \: a \: rectangle = ?}}[/tex]

[tex] \boxed{ \bold{ \sf{Perimeter \: of \: a \: rectangle = 2(l + w)}}}[/tex]

[tex] \hookrightarrow{ \sf{Perimeter \: of \: a \: rectangle = 2(2x - 5 + 3x + 4)}}[/tex]

[tex] \text{Step \: 1 : \: Collect \: like \: term}[/tex]

[tex] \text{Like \: terms \: are \: those \: which \: have \: the \: same \: base}[/tex]

[tex] \hookrightarrow{ \sf{2(2x + 3x - 5 + 4)}}[/tex]

[tex] \hookrightarrow{ \sf{2(5x - 5 + 4)}}[/tex]

[tex] \text{Step \: 2 \: : \: Subtract \: 4 \: from \: 5}[/tex]

[tex] \text{Remember !\: : the \: negative \: and \: positive \: integers \: are \: always \: subtracted \: but \: posses \: the \: sign \: of \: the \: bigger \: integer}[/tex]

[tex] \hookrightarrow{ \sf{2(5x - 1)}}[/tex]

[tex] \text{Step \: 3 \: : \: Distribute \: 2 \: through \: the \: parentheses}[/tex]

[tex] \hookrightarrow{ \sf{2 \times 5x - 2 \times 1}}[/tex]

[tex] \hookrightarrow{ \sf{10x - 2}}[/tex]

[tex] \sf{∴ \: The \: perimeter \: of \: a \: rectangle = 10x - 2}[/tex]

[tex] \text{Hope \: I \: helped !}[/tex]

[tex] \text{Best \: regards ! }[/tex]

~[tex] \text{TheAnimeGirl}[/tex]

Answer:

[tex]\huge\boxed{f^{-1}(x) = \frac{7x-5}{3}}[/tex]

Step-by-step explanation:

Given the function:

[tex]f(x) = \frac{3x+5}{7}[/tex]

Put f(x) = y

[tex]y = \frac{3x+5}{7}[/tex]

Interchange x and y

[tex]x = \frac{3y+5}{7}[/tex]

Solve for y

[tex]x = \frac{3y+5}{7}[/tex]

Multiplying both sides by 7

[tex]7x = 3y+5[/tex]

Subtracting y to both sides

[tex]7x-5 = 3y[/tex]

Dividing both sides by 3

[tex]\frac{7x-5}{3} = y[/tex]

OR

[tex]y = \frac{7x-5}{3}[/tex]

Put y = [tex]f^{-1}(x)[/tex]

So,

[tex]f^{-1}(x) = \frac{7x-5}{3}[/tex]

Hope this helped!

Answer:

Multiply by a power of 10

Step-by-step explanation:

By multiplying a power of ten, it will make the decimals whole numbers.

For example: 0.75*10=75

0.0075*10000

To eliminate the decimals, the first step we can perform is to multiply the decimal by a power of 10. If there are n numbers after the decimal point, then we will multiply the decimal by 10ⁿ.

In Algebra, a decimal is a type of number with a whole integer and a fractional part separated by a decimal point. The dot that appears between the entire number and the fractions part is the decimal point. 24.589, for example, is a decimal number. The whole number part is 24 and the fractional part is 589. The decimal point is ".".

If an equation contains decimals, then we have to check how many numbers are there in the fractions section. If there are 3 numbers like 24.589, to eliminate decimals we have to multiply 24.589 by 10³ to get a whole number [ Since 24.589×10³ = (24589/1000)× 1000 = 24589].

Therefore, to eliminate the decimals, the first step we can perform is to multiply the decimal by a power of 10. If there are n numbers after the decimal point, then we will multiply the decimal by 10ⁿ.

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Answer:

The answer is 7 video games

Step-by-step explanation:

The number of video games Austin sold will be 4.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Austin started with 26 video games and sold x video games. Caleb started with 40 video games and sold three times as many video games as Austin did.

Let x be the number of video games sold and y be the number of video games left. Then the equations will be

y = 26 - x

y = 40 - 3x

From equations 1 and 2, then we have

26 - x = 40 - 3x

3x - x = 40 - 26

2x = 14

x = 4

The number of video games Austin sold will be 4.

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Answer:

-42

Explanation:

(-6)(-7) = 42

(42)(-1) = -42

Get a calculator homie.

Answer:its negative 42

Answer:

Step-by-step explanation:

5 - (x + 5) > -2(x + 4)

Expand the terms in the bracket

That's

5 - x - 5 > - 2x - 8

- x > - 2x - 8

Add 2x to both sides

That's

- x + 2x > 2x - 2x - 8

We have the final answer as

Hope this helps you

Answer:

The answer is D

Step-by-step explanation:

There are 6 black circles and 2 red circles which could be written as 6 + -2, the positive sign from will turn into a negative bc if the -2, so then it would be 6-2=4

Answer:

  1/15

Step-by-step explanation:

.02 = [tex]\frac{2}{100}[/tex]     and   .30 = [tex]\frac{3}{10}[/tex]

cross multiply

[tex]\frac{2}{100}[/tex]  ÷  [tex]\frac{3}{10}[/tex]   = 2(10) ÷ 300

[tex]\frac{20}{300} = \frac{1}{15}[/tex]

Fraction answer: 1/15

Decimal answer: 0.066666666666667

Answer:

1

Step-by-step explanation:

Anything to the power of 0 is 1, so the answer is 1.

Answer:

18

Step-by-step explanation:

6-18=-12

\(` u`)/

Answer:

X-18

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 6-x-(-12)=0

Solve  :    -x+18 = 0

Subtract  18  from both sides of the equation : -x=-18

Multiply both sides of the equation by (-1) :  x = 18

Answer: V≈5.21 cm³

Step-by-step explanation:

To find the volume of a rectangular prism, you multiply the length, width and height.

[tex]V=wlh[/tex]

Since we were given the length, width and height, we can directly multiply them together.

[tex]V=\frac{5}{2} *\frac{5}{3} *\frac{5}{4}[/tex]             [multiply]

[tex]V=\frac{125}{24} =5.21 cm^3[/tex]

Now, we know that the volume is approximately 5.21 cm³ or 125/24 cm³.

Answer:

D(3,0) is correct answer

Answer:

A = x²+6x+8

Step-by-step explanation:

(x+4)(x+2)

x²+2x+4x+8

x²+6x+8

Answer:

y-10=1/3(x-3)

Step-by-step explanation:

I really don't want to explain, but tell me if you want an explanation and I will give it

The first term in our arithmetic sequence = 13

The common difference of our arithmetic sequence = 17 - 13 = 4

The formula for finding an equation for any arithmetic sequence is a(n) = A + B(n - 1)

A = the first term

B = the common difference.

Let's plug our numbers in.

a(n) = 13 + 4(n - 1)

Let's check to make sure we're correct.

a(1) = 13 + 4(1 - 1) = 13 + 4(0) = 13 + 0 = 13

a(2) = 13 + 4(2 - 1) = 13 + 4(1) = 13 + 4 = 17

That verifies that our formula is correct.

In conclusion,

a(n) = 13 + 4(n - 1)

Answer:

5

Step-by-step explanation:

3 squared + 4 squared = c squared

3 squared= 9   4 squared= 16

9+16=c squared

25=c squared

5= c

Answer:

x (x + 4) (x - 4)

Answer:

|4| - 2 = 2

|4| - 6 = -2

Step-by-step explanation:

Step-by-step explanation:

I=(pxRxt)/100

I=(1250×5.25×10)/100

I=656.25

amount to be paid is $1906.25 pls give me brainliest

Answer:Step-by-step explanation:

10

The value of the x is 8 if after using the property of a similar triangle.

It is defined as the law to prove that the two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

We have a triangle shown in the picture.

By using the property of a similar triangle:

2/1 = 14/(2x-9)

2x - 9 = 7

2x = 7 + 9

2x = 16

x = 8

Thus, the value of the x is 8 if after using the property of a similar triangle.

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Answer:

17/7 (2 3/7 or 2. 428571...)

Step-by-step explanation:

f(x) = 4x-2

Find f(5)

g(x) = -2x+1

Find g(-3)

Find f(5)/g(-3)

The value of f(5)/g(-3) will be 18/7.

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The value of the function are,

⇒ f (x) = 4x - 2 and

⇒ g(x) = -2x + 1

Now,

Since, The value of the function are,

⇒ f (x) = 4x - 2 and

⇒ g(x) = -2x + 1

Hence, We get;

⇒ f (5) = 4 × 5 - 2

          = 20 - 2

         = 18

And, g (- 3) = - 2 × - 3 + 1

⇒ g (-3) = 6 + 1

            = 7

Thus, The value of f(5)/g(-3) = 18/7

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Answer:

X= 4c The absolute value you can find witht the equation |4c|

Answer:

The equal number of signatures Mimi and Rita eventually collects are 70 signatures

Step-by-step explanation:

1) The initial number of signatures Mimi has = 30 Signatures

The average rate at which Mimi can collect signatures = 8 signatures per hour

The average rate at which Rita can collect signatures = 14 signatures per hour

The table of values showing the number of signatures Mimi and Rita can have at a given hour is presented as follows;

For Mimi, we have;

Hour        [tex]{}[/tex]    Number of Signatures

0         [tex]{}[/tex]           30

1         [tex]{}[/tex]            38

2         [tex]{}[/tex]           46

3         [tex]{}[/tex]           54

4         [tex]{}[/tex]           62

5         [tex]{}[/tex]           70

For Rita, we have;

Hour        [tex]{}[/tex]    Number of Signatures

0         [tex]{}[/tex]           0

1         [tex]{}[/tex]            14

2         [tex]{}[/tex]           28

3         [tex]{}[/tex]           42

4         [tex]{}[/tex]           56

5         [tex]{}[/tex]           70

2) The equation representing the number of signatures Mimi has at a given time, t, is given as follows;

The number of signatures Mimi has = 30 + 8 × t

The equation representing the number of signatures Rita has at a given time, t, is given as follows;

The number of signatures Rita has = 14 × t

3) Please find attached the required graph of the number of signatures Mimi and Rita has

4) The solution if the system of equations is given as follows;

30 + 8 × t = 14 × t

From which we have;

30 = 14 × t - 8 × t  = 6 × t

t = 30/6 = 5 Hours

By substituting t = 5 hours in the above equations, the equal number of signature of signatures Mimi and Rita can have is therefore;

30 + 8 × 5 = 70 signatures = (14 × 5) signatures

The equal number of signatures Mimi and Rita eventually collects are 70 signatures

5) The meaning of the solution is that is Mimi and Rita continue collecting signatures at their respective constant rate of 8 and 14 signatures per hour, given that Mimi already has 30 signatures, they will have the same number of 70 signatures after 5 hours

Answer:

4x² - 57x + 206

Step-by-step explanation:

To evaluate (t ￮ s)(x), substitute x = s(x) into t(x) , that is

t(x - 7)

= 4(x - 7)² - (x - 7) + 3 ← expand (x - 7)² using FOIL

= 4(x² - 14x + 49) - x + 7 + 3

= 4x² - 56x + 196 - x + 10 ← collect like terms )

= 4x² - 57x + 206

Step-by-step explanation:

400,000x600x30/32+1

400,000x600=240,000,000x30=7,200,000,000/32=

225,000,000+1=225,000,001

Really? -_-

Answer:

c has greatest ratio output with 0.6 compared to other

Step-by-step explanation: