The nth term of a sequence is 10n – 8 .Find the 20th term and 50th term.

Answer:

Width   W = 7 m

Length  L =  9 m

Step-by-step explanation:

Area of a rectangle = L * W

Area = 63 m²

L = 3W - 12

Area = L * W

66 = (3W - 12) * W

63 = 3W² - 12W

3W² - 12W - 63 = 0     ( solve W by using quadratic equation)

       -(-12) ± √ -12² - 4 * 3 * (-63)

W = -------------------------------------------

                      2 * 3

W = 7 ;  W = - 3  

therefore use W = 7 m

solve for L:

L = 3W - 12

L = 3(7) - 12

L =  9 m

check:

Area = L * W

63 =  9 * 7

63 = 63  ----- OK

Hi

perimeter of rectangle is  : 2 length+2 width .

to progress in math, you must practice.

So , I let you  do the first one which is the esaiest.

48 ) V147+ V147 + V108+V108 =    2V147 +2V108  = 2 ( V147+V108)

Answer:

8 and 5.

Step-by-step explanation:

8 x 5 = 40

8 + 5 = 13

Answer:

3953

Step-by-step explanation:

67x59 = 3953

Answer:

Los Amigos deberían comprar pizzas vendidas por la primera pizzería que cuestan S / 0.032 por cm² para obtener más ganancias.

Step-by-step explanation:

Los parámetros dados son;

El diámetro de las pizzas vendidas por la primera pizzería = 40 cm

El precio de las pizzas vendidas por la primera pizzería = S / 40

El diámetro de las pizzas vendidas por la segunda pizzería = 25 cm

El precio de las pizzas vendidas por la segunda pizzería = S / 25

El área de las pizzas vendidas por la pizzería = π × D² / 4

El área de las pizzas vendidas por la primera pizzería = π × 40² / 4≈1256.64 cm²

El costo por unidad de superficie de las pizzas vendidas por la primera pizzería = S / 40 / (1256.64 cm²) ≈ S /0.032/cm²

El área de las pizzas vendidas por la segunda pizzería = π × 25² / 4≈490.87 cm²

El costo por unidad de superficie de las pizzas vendidas por la primera pizzería = S / 25 / (490.87 cm²) ≈ S /0.051/cm²

Las pizzas vendidas por la primera pizzería que cuestan S /0.032/cm² s más baratas y producirán mejores ganancias que las pizzas vendidas por la segunda pizzería que cuestan S /0.051/cm²

Por lo tanto, los amigos deben comprar pizzas vendidas por la primera pizzería que cuestan S /0.032 / cm² para obtener más ganancias.

Answer:

5 + 2[tex]\sqrt{6}[/tex]

Step-by-step explanation:

Given

[tex]\frac{\sqrt{3}+\sqrt{2} }{\sqrt{3}-\sqrt{2} }[/tex]

Multiply numerator/ denominator by the conjugate of the denominator

The conjugate of [tex]\sqrt{3}[/tex] - [tex]\sqrt{2}[/tex] is [tex]\sqrt{3}[/tex] + [tex]\sqrt{2}[/tex]

= [tex]\frac{(\sqrt{3}+\sqrt{2})(\sqrt{3}+\sqrt{2}) }{(\sqrt{3}-\sqrt{2})(\sqrt{3}+\sqrt{2}) }[/tex] ← expand numerator/ denominator using FOIL

= [tex]\frac{3+\sqrt{6} +\sqrt{6}+2 }{3-2}[/tex]

= [tex]\frac{5+2\sqrt{6} }{1}[/tex]

= 5 + 2[tex]\sqrt{6}[/tex] → with a = 5 and b = 2

Answer:

itś between 30 and 45 but my best guest is 30

Step-by-step explanation:

Answer:

55

Step-by-step explanation:

because i said so

Step-by-step explanation:

x+y=9

x=9-y ----------(i)

Now in second eqn put the value of x

2x -3y=8

2(9-y) - 3y=8

18 - 2y - 3y=8

18-8=5y

10=5y

y=2

Then put the value of y in eqn (i)

x=9-y

x=9-2

x=7

I hope this will be helpful for you.

Answer:

Step-by-step explanation:

Given,

x + y = 9

2x - 3y = 8

Using substitution method:

In this method , a variable is expressed in terms of another variable from one equation and it is substituted in the remaining equation.

[tex] \mathsf{x + y = 9}[/tex]

Move y to right hand side and change it's sign

⇒[tex] \mathsf{x = 9 - y}[/tex]⇔equation ( i )

Now, put the value of X from equation ( i )

⇒[tex] \mathsf{ 2 (9 - y) - 3y = 8}[/tex]

Distribute 2 through the parentheses

⇒[tex] \mathsf{18 - 2y - 3y = 8}[/tex]

Collect like terms

⇒[tex] \mathsf{18 - 5y = 8}[/tex]

Move constant to right hand side and change it's sign

⇒[tex] \mathsf{ - 5y = 8 - 18}[/tex]

Calculate

⇒[tex] \mathsf{ - 5y = - 10}[/tex]

Divide both sides of the equation by -5

⇒[tex] \mathsf{ \frac{ - 5y}{ - 5} = \frac{ - 10}{ - 5} }[/tex]

Calculate

⇒[tex] \mathsf{y = 2}[/tex]

Now, Put the value of y in the equation ( i )

⇒[tex]x = 9 - 2[/tex]

Calculate the difference

⇒[tex] \mathsf{x = 7}[/tex]

Hence, x = 7 and y = 2

The possible solution of the system is the ordered pair ( x , y )

[tex] \mathsf{(x \: , y \: ) = (7 , \: 2)}[/tex]

---------------------------------------------------------

Check if the given ordered pair is the solution of the system of equation

⇒[tex] \mathsf{7 + 2 = 9}[/tex]

⇒[tex] \sf{2 \times 7 - 3 \times 2 = 8}[/tex]

Simplify the equalities

⇒[tex] \sf{9 = 9}[/tex]

⇒[tex] \mathsf{8 = 8}[/tex]

Since all of the equalities are true , the ordered pair is the solution of the system.

[tex] \mathsf{ \underline{ \bold{(x \:, y \: ) = (7 \:, 2)}}}[/tex]

Hope I helped!

Best regards!!

Answer:

No!

Step-by-step explanation:

This question is essentially asking if [tex]\frac{5}{6}[/tex] = [tex]\frac{3}{4}[/tex]

Well we can easily tell that it doesn't, but if we want to check, we can do cross multiplication.

So we are trying to find out if 5(4) = 3(6).

5(4) = 20 and 3(6) = 18.

[tex]20 \neq 18[/tex] so [tex]5:6 \neq 3:4[/tex]

They are not equal!

Answer:

No, because the numbers in the given ratio must be multiplied by the same number.

Step-by-step explanation:

Right on E 2020

Answer:

100. 120

101. 28

102. 1

103. 24

Step-by-step explanation:

Number of Permutation (P) can be obtained as follow:

nPr = n! / (n– r)!

Number of Combination (C) can be obtained as follow:

nCr = n! / (n– r)! r!

With the above ideas in mind, let us determine the answers to the questions given above.

100. Evaluation of ₅P₄

nPr = n! / (n– r)!

₅P₄ = 5! /(5 – 4)!

₅P₄ = 5! / 1!

₅P₄ = 5 × 4 × 3 × 2 × 1 / 1

₅P₄ = 120

101. Evaluation of ₈C₂

nCr = n! / (n– r)! r!

₈C₂ = 8! / (8 – 2)!2!

₈C₂ = 8! / 6!2!

₈C₂ = 8 × 7 × 6!/ 6! × 2 × 1

₈C₂ = 8 × 7 / 2 × 1

₈C₂ = 56/2

₈C₂ = 28

102. Evaluation of ₇C₀

nCr = n! / (n– r)! r!

₇C₀ = 7! / (7 – 0)!0!

₇C₀ = 7! / 7!0!

Note: 0! = 1

₇C₀ = 7! / 7!

₇C₀ = 1

103. Evaluation 4!

4! = 4 × 3 × 2 × 1

4! = 24

Answer:

0-2 x-intercepts and 0-1 y-intercepts

Step-by-step explanation:

A quadratic function can have anywhere from 0 to 2 x-intercepts. This is possible because a function can have 0, 1, or 2 solutions.

A parabola can also have either 0 or 1 y intercepts. It is possible for the function to not intercept the y axis at all, and it is also possible for it to intercept it exactly one time.

Answer :

y=7x-47

Step-by-step explanation:

[tex] (8, 9) = (x_1,y_1) \\ m = 7 \\ y - y_1 = m(x - x _1) \\ y - 9 = 7(x - 8)[/tex]

[tex]y - 9 = 7x - 56 \\ y = 7x - 56 + 9 \\ y = 7x - 47[/tex]

I hope it helps

Answer:

4.

Step-by-step explanation:

f^-1(x) is the inverse of f(x). That means that f(x) = 2x - 6 becomes...

x = 2y - 6

2y - 6 = x

2y = x + 6

y = 1/2x + 3.

When x = 2...

y = 1/2(2) + 3

= 1 + 3

= 4.

Hope this helps!

Answer:

(6,26)

Step-by-step explanation:

You will take the points and graph them since these are both positive equations they will go up and to the right.

both intersect at (6,26)

also if you forgot how to graph it, I got you

1. find the rate of change (as I will call it) THIS IS YOUR NUMBER NEXT TO THE X!!! this means that the line will go up 4 and over 1 then your whole number, in this example would be 2 is your y-intersect (the place on the y-axis where the line passes) after that you should be able to draw your lines and find the poi!

Please comment if I got something wrong! I don't want to be giving bad advice

Answer:

k=3 z=-6

Step-by-step explanation:

12k=36

k=36/12

k=3

-6z=36

z=36/-6

z=-6

12(3)-6(-6)=36

Answer:

how you convert feet to square feet

length X width = square feet

if the board is 3ft long and 1 foot wide

3ft X 1ft = 3square feet

so the length is 3 feet

Answer:

Step-by-step explanation:

the answer is 9

Answer:

20 questions

Step-by-step explanation:

Given

[tex]Correct \Marks= +5[/tex]

[tex]Incorrect\ Marks= -2[/tex]

[tex]Score\ Obtained = 30[/tex]

[tex]Number\ of\ correct\ answers = 10[/tex]

Required

Number of questions answered

First, we need to get the total correct marks obtained by Roy

This is calculated by multiplying the correct marks by number of correct answers

[tex]Total = +5 * 10[/tex]

[tex]Total = +50\ marks[/tex]

Subtract this from the total scores obtained; This gives the total incorrect answer obtained by Roy

[tex]Incorrect = Scores\ Obtained - Total[/tex]

[tex]Incorrect = 30 - (+50)[/tex]

Open bracket

[tex]Incorrect = 30 - 50[/tex]

[tex]Incorrect = -20[/tex]

Divide this by -2 to get the number of incorrect answers

[tex]Incorrect\ Answers = \frac{-20}{-2}[/tex]

[tex]Incorrect\ Answers = 10[/tex]

Add this to the number of correct answers to give the total number of question answered

[tex]Total = Correct\ Answers + Incorrect\ Answers[/tex]

[tex]Total = 10 + 10[/tex]

[tex]Total = 20[/tex]

Hence, Roy answered a total of 20 questions

Answer:

5.1 gallons

Step-by-step explanation:

Using the information provided, we know that there is of course 40.8 gallons of paint to be divided into 8 containers. This means we must use a division problem to figure out our answer.

We are splitting the 40.8 gallons into the 8 containers so that means our dividend is 40.8 and our divisor is 8. With this information, we can go ahead and put this into an expression of:

40.8/8

If you have a calculator, you can plug that equation in to get 5.1, but if you don't then a bit of easy long division will get you the same answer of 5.1 gallons.

Answer: 51 gallons

Step-by-step explanation:

Answer:

The domain is x cannot equal 1 and range cannot equal 0. The first option you have is correct

Step-by-step explanation:

Answer:

-1/8

Step-by-step explanation:

lim x approaches -6     (sqrt( 10-x) -4) / (x+6)

Rationalize

   (sqrt( 10-x) -4)      (sqrt( 10-x) +4)

    ------------------- * -------------------

       (x+6)                 (sqrt( 10-x) +4)

We know ( a-b) (a+b) = a^2 -b^2

a= ( sqrt(10-x)   b = 4    

(10-x) -16

-------------------

(x+6) (sqrt( 10-x) +4)    

-6-x

-------------------

(x+6) (sqrt( 10-x) +4)

Factor out -1 from the numerator

-1( x+6)

-------------------

(x+6) (sqrt( 10-x) +4)

Cancel x+6 from the numerator and denominator

-1

-------------------

(sqrt( 10-x) +4)

Now take the limit

lim x approaches -6    -1/ (sqrt( 10-x) +4)

                                      -1/ (sqrt( 10- -6) +4)

                                      -1/ (sqrt(16) +4)

                                      -1 /( 4+4)

                                        -1/8

Answer:

[tex]\displaystyle \lim_{x \to -6}\frac{\sqrt{10-x}-4}{x+6} =-\frac{1}{8}[/tex]

Step-by-step explanation:

We want to evaluate the limit:

[tex]\displaystyle \lim_{x \to -6}\frac{\sqrt{10-x}-4}{x+6} \\[/tex]

When attempting to evaluate a limit, we should always try direct substitution. This yields:

[tex]\displaystyle \begin{aligned} &\Rightarrow \frac{\sqrt{10-(-6)}-4}{(-6)+6} \\ \\ &=\frac{\sqrt{16}-4}{-6+6}\\ \\ &=\frac{4-4}{-6+6}\\ \\ &=\underbrace{\frac{0}{0}}_{\text{Indeterminate}} \end{aligned}[/tex]

Since the result is an indeterminate form, we can try simplifying the limit.

Let's cancel the square root in the numerator. We can use the difference of two squares. Recall that:

[tex](a-b)(a+b)=a^2-b^2[/tex]

The expression in the numerator is:

[tex]\sqrt{10-x}-4[/tex]

Therefore, to cancel it out, we will multiply it by:

[tex]\sqrt{10-x}+4[/tex]

Multiply. This yields:

[tex]=\displaystyle \lim_{x \to -6}\frac{\sqrt{10-x}-4}{x+6}\cdot\frac{\sqrt{10-x}+4}{\sqrt{10-x}+4} \\[/tex]

Simplify:

[tex]\displaystyle \begin{aligned} &= \lim_{x \to -6}\frac{(\sqrt{10-x})^2-(4)^2}{(x+6)(\sqrt{10-x}+4)}\\ \\ &=\lim_{x\to-6}\frac{(10-x)-(16)}{(x+6)(\sqrt{10-x}+4)}\\ \\ &=\lim_{x \to \ -6}\frac{-x-6}{x+6(\sqrt{10-x}+4)}\end{aligned}[/tex]

Factor:

[tex]\displaystyle \lim_{x \to \ -6}\frac{-(x+6)}{(x+6)(\sqrt{10-x}+4)}[/tex]

Cancel:

[tex]\displaystyle \lim_{x \to \ -6}-\frac{1}{\sqrt{10-x}+4}[/tex]

Now, we can attempt direct substitution again. Thus:

[tex]\displaystyle \begin{aligned} &\Rightarrow -\frac{1}{(\sqrt{10-(-6)}+4)}\\ \\ &=-\frac{1}{\sqrt{16+4}}\\ \\ &=-\frac{1}{(4+4)} \\ \\ &=-\frac{1}{8}\end{aligned}[/tex]

Therefore:

[tex]\displaystyle \lim_{x \to -6}\frac{\sqrt{10-x}-4}{x+6} =-\frac{1}{8}[/tex]

Answer:

The total population = 9514.2857143 people.

Step-by-step explanation:

Let the total population be represented by X

In the question, we are told that,1332 people are under the age of 20 and this value = 14% of the total population.

Therefore, the total population is calculated as

14% of X = 1332

14/100 × X = 1332

14X/100 = 1332

Cross Multiply

14X = 1332 × 100

X = 1332 × 100/14

X = 9514.2857143

Therefore, the total population = 9514.2857143 people.

Answer:

12x+16-4y

Step-by-step explanation:

Answer:

lets start with x = 5x+7x=12x

now y = 2y-6y= -4y

now reg numbers = 8+8=16

now add all of them not litteraly add by add as in make them into a expression

so

12x-4y+16

Answer:

2π² or 19.74

Step-by-step explanation:

Given r = π

Then:

or

Explanation:

The idea is to isolate y getting it by itself. We can do this a number of ways, but possibly the quickest way is to add y to both sides

x/2 - y + 6 = 0

x/2 + 6 = 0+y

x/2 + 6 = y

y = x/2 + 6

This is now in slope intercept form, more or less. We could rewrite the x/2 as (1/2)x to get

y = (1/2)x + 6

Then compare this to y = mx+b and note the slope is m = 1/2 and the y intercept is b = 6.

Side note: the quality of the snapshot is fairly good. I've seen much worse.

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▹ Answer

152 - 20 + 80

▹ Step-by-Step Explanation

'Withdrawing' means taking out money which would be represented with a minus sign.

'Deposit' means you are adding money which would be represented with a plus sign.

Therefore, the answer is:

152 - 20 + 80

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

10

Step-by-step explanation:

pi is 3.14...

pi - 1 is 2.14...

question becomes 1<2.14x and 2.14x < 10

1/2.14 < x, 0.46... < x

x < 10/2.14, x < 4.67...

combining

0.46< x < 4.67

x can be 1, 2, 3, 4

Answer:

Step-by-step explanation:

pi - 1 = 3.14 - 1 = 2.14

x has to be an integer, and the result must be greater than 1.

1 works.

1 < 2.14*1 < 10  2.14 is between 1 and 10.

2 works

1 < (2.14)*2 < 10

1 < 4.28 < 10

3 works

1 < 2.14 * 3 < 10

1 < 6.42 < 10

4 might work

1 < 2.14*4 < 10

1 < 8.56 < 10

and it does work.

5 can't work

1 < 5 * 2.14 < 10

1 < 10.7 < 10 is not true.

Answer: 1,2,3,4

Answer:

The difference between the 4th term of both series is 7

Step-by-step explanation:

The formula for the nth term of an APS is a + (n - 1)×d

The first term of one of the series = -1

The first term of the other of the series = -8

The fourth term of both series is thus;

4th term first series = -1 + (4 - 1)× d = -1 + 3·d

4th term second series =  -8 + (4 - 1)× d = -8 + 3·d

The difference between the 4th term of both series = -1 + 3·d - (-8 + 3·d)

-1 + 3·d - (-8 + 3·d) = -1 + 3·d  + 8 - 3·d = 8 - 1 = 7

The difference between the 4th term of both series = 7.

Answer:

A: (x-3, y+4)

Step-by-step explanation:

A coordinate plane is basically just a number line with two axes.

If we move a numbet right 3, to return it back we’d need to bring it left 3.

If we move a number down 4, we need to bring it up 4 to bring it back to it’s original position.

So to get it back, we need to add the opposite.

(x + 3), 3’s opposite is -3

(y - 4), -4’s opposite is 4.

Hope this helped!

Answer:

0.123 GSD are expected to be received by each JPY.

Step-by-step explanation:

The exchange rate is the ratio of GSD per each JPY, that is:

[tex]x = \frac{12.33\,GSD}{100\,JPY}[/tex]

[tex]x = 0.123\,\frac{GSD}{JPY}[/tex]

Which means that 0.123 GSD are expected to be received by each JPY.