Solve for x...........................................................

The given equation is equivalent to Option D .

The mission option is

A. x+10= x+10

B. x+9 =x² + 20x + 100

C. x² +81 = x² + 100

D. x² + 81 = x² +20x + 100

An equation is a mathematical statement formed when two algebraic expression is equated by an equal sign .

An equation is given in the question

[tex]\rm \sqrt{x^2 + 81} = x +10[/tex]

[tex]\rm {x^2 + 9^2} = (x +10)^2[/tex]

[tex]\rm {x^2 + 81} = x^2 +20x + 100[/tex]

Therefore the given equation is equivalent to Option D .

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Answer:

3 * (x + 3) = x * 5 - 3

Answer:

Step-by-step explanation:

1/2 chance for 1

1/4 for 2

1/8 for 3

1/16 for 4

1/32 for 5

1/64 for 6

1/128 for 7

1/256 for 8

1/512 for 9

1/1024 for 10

As AB and ED are parallel, they have the same slope. This means that since lines that are colllinear with parallel segments are parallel, lines l and m are parallel.

Answer:

To find the mean of a given data set, add up all the values then divide by how many numbers ...

Step-by-step explanation:

#a

V={Vowels of English alphabets}

#b

C={cube numbers between 0 to 50}

#c

M={y:y is a multiple of 3 less than 20}

71% subtracted from 100% is 29%

Add or subtract the given percent from 100%.

71%

The percentage (p) is given as:

p = 71%

When subtracted from 100%, we have:

100% - p

Substitute p = 71%

100% - 71%

71 subtracted from 100 is 29.

So, we have:

100% - 71% = 29%

Hence, 71% subtracted from 100% is 29%

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If [tex]\frac{3+\sqrt{8} }{3-\sqrt{8} } +\frac{3-\sqrt{8} }{3+\sqrt{8} }=a+b\sqrt{2}[/tex], the value of a and b is given as a = 34 and b = 0

An equation is an expression that shows the relationship between two or more variables or numbers.

[tex]\frac{3+\sqrt{8} }{3-\sqrt{8} } +\frac{3-\sqrt{8} }{3+\sqrt{8} }\\ \\\frac{9+6\sqrt{8}+8+9-6\sqrt{8}+8 }{(3-\sqrt{8} )(3+\sqrt{8} )} \\\\\frac{34}{9-8} =34+0\sqrt{2}[/tex]

If [tex]\frac{3+\sqrt{8} }{3-\sqrt{8} } +\frac{3-\sqrt{8} }{3+\sqrt{8} }=a+b\sqrt{2}[/tex], the value of a and b is given as a = 34 and b = 0

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Step-by-step explanation:

the volume of a cylinder is as for any other regular 3D object :

ground area ×height

the ground area of a cylinder is a circle, so it is

pi×radius² × height

the radius is always half of the diameter (of the diameter is airways twice the radius).

radius = 6/2 = 3 ft.

the volume is then

pi × 3² × 9 = pi × 9 × 9 = pi × 81 ft³

so, the answer is 81pi ft³.

Answer: 60( 1 - 72)

Step-by-step explanation: i think it might be right so heres a proof

Answer: 123.84

Step-by-step explanation: You can set pi as 3.14. Then, you get 123.836576. Round to the nearest hundredth to get 123.84.

Answer

I don’t quite understand what your asking but I hope this helps

y=3x-13

Step-by-step explanation:

Using the binomial distribution, it is found that there is a 0.7447 = 74.47% probability that fewer than 7 of them show up.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem, the values of the parameters are given as follows:

p = 0.7, n = 8.

The probability that fewer than 7 of them show up is given by:

[tec]P(X < 7) = 1 - P(X \geq 7)[/tex]

In which:

[tex]P(X \geq 7) = P(X = 7) + P(X = 8)[/tex]

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 7) = C_{8,7}.(0.7)^{7}.(0.3)^{1} = 0.1977[/tex]

[tex]P(X = 8) = C_{8,8}.(0.7)^{8}.(0.3)^{0} = 0.0576[/tex]

Then:

[tex]P(X \geq 7) = P(X = 7) + P(X = 8) = 0.1977 + 0.0576 = 0.2553[/tex]

[tec]P(X < 7) = 1 - P(X \geq 7) = 1 - 0.2553 = 0.7447[/tex]

0.7447 = 74.47% probability that fewer than 7 of them show up.

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Answer:

Step-by-step explanation:

Answer:

a) 15:7

b) 1950 ml

c) There were 10 people in the group

Step-by-step explanation:

a) In its basic form, the ratio would be 750:350. However, to get it to it's most basic form, we must find the greatest common factor (GCF) of 750 and 350, which is 50. Then, we divide both numbers by the GCF so that 750 is 15 and 350 is 7. Therefore, the basic form of the ratio is 15:7.

b) First, we can find the amount of chicken stock needed for 12 people, which is just double of the recipe since the recipe is for 6 people. (900 * 2 = 1800). Then, we need to figure out how much chicken stock is required for one person since there are 13 and not 12. We can do this by multiplying 900 by 1/6 (since it's for 1 person out of the 6 people recipe) to get 150. Then, add the amount of chicken stock needed for 12 people and 1 person together. 1800 + 150 = 1950.

c) First, we must figure out how many grams of leeks are required for just one person. We can do this by taking the amount needed in the recipe (for 6 people) and dividing it by 6 to get the amount needed for 1 person. 750 divide by 6 is 125, so 125 g of leeks are required to make soup for 1 person. Then, we take the total amount of leeks that Delia used (1250) and divide that by 125 to get 10.

The area of a regular polygon is one-half the product of its apothem and its perimeter. Often the formula is written like this: Area=1/2(ap), where a denotes the length of an apothem, and p denotes the perimeter.

Step-by-step explanation:

#Hopeithelps

Answer:

It's A

Step-by-step explanation:

Thx to the guy in the comments above

Answer:

It's A

Step-by-step explanation:

It's right

Answer:

here we have to divide the number of words per hour to the number of minutes per hour.

Step-by-step explanation:

5400÷60

=90.

therefore in a minute she types 90 words.

[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ 2^3~~ = ~~8\implies \log_2(8)~~ = ~~3[/tex]

60/4= 15

15 x 3 =45 minutes

[tex]g(x) =3x^2 -1\\\\g(-3)=3(-3)^2 -1 \\ \\~~~~~~~~~=3(9) -1 \\\\~~~~~~~~~=27-1\\\\~~~~~~~~~=26[/tex]

Answer:

g(26)

Step-by-step explanation:

substitute -3 for x.

g(x)=3[tex]x^{2}[/tex]-1

[tex]g(-3)=3(-3)^{2} -1\\g(-3)= 3(9)-1\\g(-3)= 27-1\\g(-3)=26[/tex]

========================================================

Reason:

Ari hasn't considered the case of "red and yellow" which is almost identical to "yellow and red".

It helps to lay out a two by two table. Along the rows and columns, you'll have "red" and "yellow". See below.

Then inside the table are the list of all outcomes in the form (x,y) where x is the horizontal component along the columns, and y is the vertical component along the rows.

Example: if x = red and y = red, then we have the outcome (x,y) = (red, red)

As the table shows, we have 4 outcomes. Therefore the probability of getting two yellows is 1/4

Technically the (red, yellow) = (yellow, red) since ultimately order doesn't matter in this case. For some probability problems, order will matter. But again, order doesn't matter here and it means that we can treat these two situations the same. So I can see why Ari thinks there are only three outcomes.

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

Here's another way to look at it:

The probability of landing on yellow is 1/2 assuming red and yellow are equally likely.

This means the probability of two yellow in a row is (1/2)*(1/2) = 1/4

Each is spin is independent of any other.

Answer: Heyaa! ~

Your Answer would be.. =4

Step-by-step explanation:

Hopefully this helps you ! ^^

The area of the triangle AOB is 9√3 square units

The triangle AOB is an equilateral triangle with the following parameters:

Side length, x = 6

Angle, y = 60

The area of the triangle is then calculated using:

Area = 0.5 * x^2 * sin(y)

So, we have:

Area = 0.5 * 6^2 * sin(60)

Evaluate

Area = 18 * 0.5√3

Evaluate the product

Area = 9√3

Hence, the area of the triangle AOB is 9√3 square units

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Students claim is correct. We can convert tan²θ + 1 = sec²θ to (sin²θ + cos²θ) = 1.

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles.

Here,

tan²θ + 1 = sec²θ

sin²θ/cos²θ + 1 = 1/cos²θ

By taking LCM, we get

(sin²θ + cos²θ)/cos²θ = 1/cos²θ

(sin²θ + cos²θ) = cos²θ/cos²θ

(sin²θ + cos²θ) = 1

Thus, Students claim is correct. We can convert tan²θ + 1 = sec²θ to (sin²θ + cos²θ) = 1.

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Answer:

Given function:

[tex]f(x)=2(3)^x[/tex]

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

[tex]\begin{aligned}\textsf{Average rate of change - Section A} & =\dfrac{f(1)-f(0)}{1-0}\\\\& =\dfrac{2(3)^1-2(3)^0}{1-0}\\\\& =\dfrac{6-2}{1}\\\\& =4 \end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Average rate of change - Section B} & =\dfrac{f(3)-f(2)}{3-2}\\\\& =\dfrac{2(3)^3-2(3)^2}{3-2}\\\\& =\dfrac{54-18}{1}\\\\& =36 \end{aligned}[/tex]

[tex]\dfrac{\textsf{Average rate of change of Section B}}{\textsf{Average rate of change of Section A}}=\dfrac{36}{4}=9[/tex]

Therefore, the average rate of change of Section B is 9 times greater than Section A.

The function is an exponential function (with 3 as the growth factor) so the rate of change increases over time.

Answer: [tex]2-5\sqrt{6}-3\sqrt{2}[/tex]

Step-by-step explanation:

= [tex](2-5\sqrt{6} )-3\sqrt{2}[/tex]

= [tex]2-5\sqrt{6}-3\sqrt{2}[/tex]

This expression is simplified already