Mathematics High School

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Answers

Answer 1

Answer:

Step-by-step explanation:

14.

x = 5.0081818181..

10x = 50.08181818181....

100x = 500.81818181818...

100x - x = 500.8181818... - 5. 008181818....

99x = 495.81

[tex]x = \frac{495.81}{99} = \frac{495.81 \times 100}{99 \times 100} \\\\\\x= \frac{49581}{9900}[/tex]

[tex]x = \frac{5509}{1100}[/tex]

14.

[tex]\sqrt{50} - \sqrt{98} + \sqrt{162} \\\\\sqrt{ 2 \times 25} - \sqrt{ 2 \times 49} + \sqrt{2 \times 81}\\\\\sqrt{ 2 \times 5^2} - \sqrt{ 2 \times 7^2} + \sqrt{2 \times 9^2}\\\\5\sqrt2 - 7 \sqrt 2 - 9 \sqrt 2\\\\\sqrt{2} ( 5 - 7 + 9 ) \\\\7\sqrt2[/tex]

15.

[tex]\frac{3 + \sqrt5}{4 - 2\sqrt 5} \\\\= \frac{3 + \sqrt5}{4 - 2\sqrt 5} \times \frac{4 + 2\sqrt5}{4 + 2\sqrt5}\\\\[/tex] [tex][ \ rationalizing \ the \ denominator \ ][/tex]

[tex]=\frac{(3 + \sqrt5)(4 + 2\sqrt5)}{(4 -2 \sqrt5)(4 + 2\sqrt5)}\\\\=\frac{12 + 6 \sqrt5 + 4\sqrt5 + 2(\sqrt5)^2}{(4)^2 - (2\sqrt5)^2}[/tex] [tex][ \ (a - b)(a +b) = a^2 - b^2 \ ][/tex]

[tex]=\frac{12 + 10 + 10\sqrt5}{16 - (4 \times 5)}\\\\=\frac{22 + 10\sqrt5}{16 - 20 }\\\\=\frac{22+ 10 \sqrt5 }{-4}[/tex]

[tex]= \frac{11}{-2} + \frac{5 \sqrt5}{-2}\\\\= -\frac{11}{2} + \frac{-5 }{2} \sqrt5\\\\[/tex]

[tex]a = - \frac{11}{2} , \ b = -\frac{5}{2}[/tex]

[tex]\frac{\sqrt7 + 1 }{\sqrt7 - 1} - \frac{\sqrt7 - 1}{\sqrt7 + 1}\\\\[/tex]

[tex]\frac{(\sqrt 7 + 1 )( \sqrt7 + 1)}{(\sqrt7 - 1 )(\sqrt7 + 1)} - \frac{(\sqrt7 - 1)(\sqrt 7 - 1)}{(\sqrt7 + 1)(\sqrt7 - 1)}[/tex] [tex][ \ LCM \ of \ denominators : (\sqrt7 -1)(\sqrt7 + 1) \ ][/tex]

[tex]\frac{(\sqrt 7 + 1 )^2 -( \sqrt7 - 1)^2}{(\sqrt7)^2 - 1^2}[/tex] [tex][ \ (a \pm b)(a \pm b) = (a \pm b)^2 \ (a-b)(a+b) = a^2 - b^2 \ ][/tex]

[tex]=\frac{(7 + 1 + 2\sqrt7) - ( 7 + 1 - 2\sqrt7)}{7 - 1}\\\\=\frac{8 + 2\sqrt7 - 8 + 2\sqrt7}{6}\\\\= \frac{4 \sqrt7}{6}\\\\= \frac{2 \sqrt 7}{3}[/tex]

Related Questions

There is a special offer at the book shop.
Ryan chooses 4 books that cost
£4.00
£3.80
£3.00
and £1.20
Special
offer
4 for the
price of 3.
Buy any 4 books and get
the cheapest one completely free!
What fraction of the normal total price does he save?
Choose the correct calculation.
£4.00 + £3.80 + £3.00 + £1.20
£1.20
£1.20
£4.00 + £3.80 + £3.00 + £1.20
£1.20
£4.00 + £3.80 + £3.00
x (£4.00 + £3.80 + £3.00 + £1.20)

Answers

price of 3Step-by-step explanation:

Can someone help and explain how to do these problems please

Answers

Step-by-step explanation:

1st one right angle

Right angle is of 90°

and 70° is given so subtract them

90-70=30 so y is 30°

2nd one

35° given and

[tex] \frac{35}{7} = 5[/tex]

so 7x5=35

t=5

What is the length of the side x?

Answers

Answer and Step-by-step explanation:

Solve for the middle side, then for x using Pythagorean Theorem.

[tex]A^2 + B^2 = C^2\\\\\\6^2 + 8^2 = C^2\\\\100 = C^2\\\\C = 10\\\\\\\\A^2 + 10^2 = 12^2\\\\A^2 + 100 = 144\\\\A^2 = 44\\\\A^2 = 2\sqrt{11} <-Answer[/tex]

#teamtrees #PAW (Plant And Water)

Pls help. What is the appropriate congruent for these triangles

Answers

Answer:

C. HL

Step-by-step explanation:

The diagram given shows that the hypotenuse length and the length of a leg of one right triangle is congruent to the hypotenuse and corresponding leg length of the other. Based on Hypotenus-Leg criterion, the two right triangles is proved to be congruent because it meets the criterion of HL.

16p⁷q⁸÷2p⁴q⁵
whats the answer?

Answers

Answer:

[tex]8 {p}^{3} {q}^{3} [/tex]

Step-by-step explanation:

Hope it is helpful....

Monique goes out for coffee once per week. She has already spent $40.86 this year on her coffees and each one is $4.54. There are 27 weeks left in this school year for Monique. If she continues getting coffee at this rate how much money will she have spent on coffee by the end of the year?

Answers

Firstly, 27 x 4.54
= $122.58

$ [tex]$163.44[/tex] money will she have spent on coffee by the end of the year.

What is PEDMAS rule?

PEDMAS rule states that the order of operation starts with the parentheses first or the calculation which is enclosed in brackets. Then the operation is performed on exponents(degree or square roots) and later we do operations on division & multiplication and at last addition and subtraction.

According to the question

Monique goes out for coffee once per week.

She has already spent $40.86 this year on her coffees and each one is $4.54.

There are 27 weeks left in this school year for Monique.

If she continues getting coffee at this rate, money will she have spent on coffee by the end of the year:

Based on the given conditions

[tex]40.86 + 27 \times 4.54[/tex]

By using PEDMAS rule, first we have to multiply 27 and 4.54

= [tex]40.86 + 122.58[/tex]

By using PEDMAS rule, first we have to add 40.86 and 122.58

= [tex]163.44[/tex]

Thus, $163.44 money will she have spent on coffee by the end of the year.

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Find the area of the figure below

Answers

Answer:

521

Step-by-step explanation:

1. Maggie currently has a balance of $-15 in her bank account, she deposits $11
into her account. How much money does Maggie have in her account? *

Answers

-15+11=-4 so Maggie has -4 in her account

Answer: Maggie now has $-4 in her bank account.

Explanation: The word “deposits” usually means “add”, so all you need to do is:

-15+11
=-4

Therefore, Maggie now has a balance of $-4 in her bank account.

Hope this helps シ

A quadratic monomial with a leading coefficient of 6

A linear binomial with a leading coefficient of 2

Answers

Given:

A quadratic monomial with a leading coefficient of 6.

A linear binomial with a leading coefficient of 2.

To find:

The mathematical terms for the given statements.

Solution:

Monomial: The expression with single term.

Binomial: The expression with two terms.

Quadratic: Highest power of the variable is 2.

Linear: Highest power of the variable is 1.

Coefficient: In the product of a number and a variable, the number is known as the coefficient of that variable.

The first statement is "A quadratic monomial with a leading coefficient of 6".

Quadratic monomial means single term with degree 2. The leading coefficient of 6. So, the term is [tex]6x^2[/tex].

The second statement is "A linear binomial with a leading coefficient of 2".

Linear binomial means [tex]ax+b[/tex], where a and b are real values. The leading coefficient is 2. So, [tex]a=2[/tex].

Let [tex]b=1[/tex], then the required linear binomial is [tex]2x+1[/tex].

Answer:

A. 0.4

B.0.9

C.0.7

Step-by-step explanation:

Answers:

a) 0.4b) 0.9c) 0.7

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

Explanation:

Part (a)

P(winning) = 0.6 is given

The probability of not winning is 1 - P(winning) = 1 - 0.6 = 0.4

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

Part (b)

P(losing) = 0.1 is given

The probability of not losing is 1 - P(losing) = 1 - 0.1 = 0.9

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

Part (c)

The probability of winning is 0.6 and the probability of losing is 0.1

This adds to 0.6+0.1 = 0.7, which must mean 0.3 is the probability of drawing (since 0.7+0.3 = 1)

So the probability of not drawing is 1 - P(draw) = 1 - 0.3 = 0.7, which is exactly the sum of the probabilities of winning and losing.

Given that A , B and C are the vertices of a triangle and that ∠ C B A = 80 ∘ and ∠ A C B = 35 ∘ , label the triangle with the correct vertices, A , B , or C . Select the correct answer from the options below.

Answers

Put in in order from least to Greatest 3,-18,5,4,-2,6

A)-2,3,4,5,6-18

B)-2,18,3,4,5,6

C)-18,-2,3,4,5,6

D)3,4,5,6-2,-18

Answers

smalsksleehekbskdnejeoejekd

Answer:

Step-by-step explanation:

-2,3,4,5,6-18 from least to greatest

What is the relationship between the values tand s plotted on the number line
below?
S
A. t= s
B. t>s
O c. tcs

Answers

Answer:

The answer should be t > s. (B) is the answer.

Which could be the graph of f(x) = |x -h| + k if h and k are both positive?

Answers

Step-by-step explanation:

The graph of the function y=|x| is as shown in the attached diagram. The only possible translation of this graph right and up is option A. (In option B graph is translated right and down, in option C- left and up and in option D - left and down). Answer: correct choice is A.

Answer:

Step-by-step explanation:

Just did it

It wants me to use division, but sadly I am not getting the answers I want with it. Please help!

Answers

Answer:

a. 70 gallons of water were leaked each month.

Step-by-step explanation:

Set up an equation:

Variable x = gallons leaked each month

210/3 = x/1

Cross multiply:

210 × 1 = 3 × x

210 = 3x

Divide by 3 to isolate the variable:

70 = x

The division part is only 210 ÷ 3 = x. I wrote it down this way so you can see how I came to this equation.

Check your work:

210/3 = 70/1

210 × 1 = 3 × 70

210 = 210

Correct!

The graph of f(x) is the solid black graph below. Which function represents the
dotted graph?

Answers

Answer: The answer is y= f(x+1)+5

Step-by-step explanation: The reason is that when you are translating the graph, the information in the parenthesis (In this case: (x+1)) is always on the x axis moving either left or right. You just go one in the opposite direction of what the sign is, so since the sign in the parenthesis is "+" you would go left in the opposite direction. Then, for the upward translation, you would have to move 5 units upward and this is done by just adding five to the end of it.

what is 0.06 divided by 8 working out

Answers

It’s an answer for your question

Answer:

0.0075

Step-by-step explanation:

0. 0 0 7 5

_______________________

8 ÷ 0. 0 6 0 0

− 0

_______________________

0 0

− 0

_______________________

0 6

− 0

_______________________

6 0

− 5 6

_______________________

4 0

− 4 0

_______________________

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

6.) Find the square root(s)

Answers

Answer:

the square root is 0.08/8

-2/5 or -0.4
Is the square root

Tollowing statement.
The type of rule in which you are given the first term and then your equation gives you a method for finding the
next term in a sequence.

Answers

Answer:

recursive

Step-by-step explanation:

recursive lets us find the next term using a formula of the term preceding it or coming before it.

The type of rule in which you are given the first term and then your equation gives you a method for finding the next term in a sequence is called Recursion

What is recursive function ?

Recursive function is a function that repeats or uses its own previous term to calculate subsequent terms and thus forms a sequence of terms . Example : Arithmetic progression , geometric progression etc

so, the type of rule in which you are given the first term and then your equation gives you a method for finding the next term in a sequence is called Recursion

Learn more about Recursion

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Find the area of a circle with radius 2cm, leave your answer in terms of pi

Answers

Answer:

[tex]Area = 4 \pi \ cm^2[/tex]

Step-by-step explanation:

[tex]Area = \pi r^2 = \pi \times 2^2 = 4 \pi \ cm^2[/tex]

Answer:

A = 4 cm squaree

this us because u multiply π r and square it. sorry if it's confusing

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Please answer these tree questions in detail... Will give Brainliest for the best... Want answer in detail ASAP

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Please answer these tree questions in detail...
Will give Brainliest for the best...
Want answer in detail ASAP