Mathematics High School

What is the value of X?

Answers

Answer 1

Answer:

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is

x² = 40² + 9² = 1600 + 81 = 1681 ( take square root of both sides )

x = [tex]\sqrt{1681}[/tex] = 41

Related Questions

Prove that an integer consisting of 3n ones is divisible by 3n (e.g. 111 is divisible by 3, 111,111,111 is divisible by 9, etc.) Prove it by induction. Notice, that while the number with a sum of digits divisible by 3 is itself a multiple of 3 and the number with a sum of digits divisible by 9 is itself a multiple of 9, it is NOT true that the number with a sum of digits divisible by 27 is necessarily a multiple of 27.

Answers

For proof of 3 divisibility, abc is a divisible by 3 if the sum of abc (a + b + c) is a multiple of 3.

Integers divisible by 3

The proof for divisibility of 3 implies that an integer is divisible by 3 if the sum of the digits is a multiple of 3.

Proof for the divisibility

111 = 1 + 1 + 1 = 3 (the sum is multiple of 3 = 3 x 1) (111/3 = 37)

222 = 2 + 2 + 2 = 6 (the sum is multiple of 3 = 3 x 2) (222/3 = 74)

213 = 2 + 1 + 3 = 6 ( (the sum is multiple of 3 = 3 x 2) (213/3 = 71)

27 = 2 + 7 = 9 (the sum is multiple of 3 = 3 x 3) (27/3 = 9)

Thus, abc is a divisible by 3 if the sum of abc (a + b + c) is a multiple of 3.

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√x-1=4
I need the answer for this question

Answers

Answer:

Step-by-step explanation:

First we add 1 to both sides :

√x = 5

Now we square both sides :

x = 5²

x = 25

To check this answer we substitute our answer back into the original equation:

√25 - 1 = 4

5 - 1 = 4

4 = 4

✅

Hope this helped and brainliest please

If f(x )= 3/x-3, what is (fof)(x)?

Answers

Answer:

the second option is correct.

Step-by-step explanation:

that is the solution above.

The two tables show the number of copies of albums x, y, and z sold in outlets a, b, c, and d of a company. which outlet sold the greatest number of copies of album x in july and august?

Answers

Outlet A sold the greatest number of copies of album x in July and August

How to determine the outlet?

The tables of values are given as:

July

Album X Album Y Album Z

Outlet A 14 8 6

Outlet B 7 13 4

Outlet C 2 11 1

August

Album X Album Y Album Z

Outlet A 12 14 10

Outlet B 5 12 8

Outlet C 16 12 7

In July, the total sales of album x are:

Outlet A = 14

Outlet B = 7

Outlet C = 2

In August, the total sales of album x are:

Outlet A = 12

Outlet B = 5

Outlet C = 16

Add both sales

A = 14 + 12 = 26

B = 7 + 5 = 12

C = 2 + 16 = 18

26 (in outlet A) is greater than 12 and 18

Hence, outlet A sold the greatest number of copies of album x in July and August

Answers

Answer:

i can't see the question i would love to help though

Step-by-step explanation:

The difference between two numbers is 17 and twice the smaller of these is 26. What are the numbers?
Does anyone know the answer?

Answers

Answer:

13 and 30

Step-by-step explanation:

the smaller of the two numbers is 13.

If there is a 17 number difference, then that means that the second number is 30.

give brainliest, please!
hope this helps :)

a 4 1/2 inch candle burns down in 9 hours. after how many hours will it have burned 4 1/4 inches? use the drop down menu to state your answer as a decimal, mixed number, or improper fraction.

Answers

The number of hours it will take to burn 4 1/4 inches of candle is 8.5 hours in decimal.

How to solve fractions?

Using ratio to solve, find the ratio of candle length to the time taken to burn down

let

x = time taken by 4 1/4 inches candle

4 1/2 : 9 = 4 1/4 : x

9/2 ÷ 9 = 17/4 ÷ x

9/2 × 1/9 = 17/4 × 1/x

1/2 = 17/4x

cross product

1 × 4x = 2 × 17

4x = 34

x = 34/4

x = 8.5 hours

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1,8,27; 64; Rule Missing numbers

Answers

Answer:

rule: f(n) = n³

missing numbers: 125, 216, 343, 512, 729

Step-by-step explanation:

Your familiarity with the cubes of small integers helps you recognize each of these numbers is a cube. Their sequence is the sequence of cubes of increasing natural numbers.

1 = 1·1·1 = 1³

8 = 2·2·2 = 2³

27 = 3·3·3 = 3³

64 = 4·4·4 = 4³

The rule is ...

f(n) = n³

The cubes of 5 through 9 will complete the set of numbers ...

1, 8, 27, 64, 125, 216, 343, 512, 729

Wich inequality represents the phrase “a number b is atleast 16”?

Answers

Answer: B

Explanation: Key word: Atleast. This shows that you can still get 16 but it's the lowest you can get. Meaning, if you were to say, atleast get a 16% done. It'll mean that getting 16% is good but also, you'll want to get a higher number of course.

Enlarge the triangle by scale factor of -1/3
Please help me on this question I will mark you as the brainiest

Answers

The attached image represents the triangle after it has been enlarged

How to enlarge the triangle?

The given parameters are:

Scale factor, k = -1/3Center, (a,b) = (-1,2)

From the graph, the coordinates of the triangle are:

A = (-4,2)

B = (-4,-4)

C = (-1,-4)

The rule of dilation is calculated using:

[tex](x,y) \to (k(x - a) + a, k(y - b) + b)[/tex]

So, we have:

[tex]A' = (-\frac 13(-4 +1) - 1, -\frac 13(2 - 2) + 2)[/tex]

A' = (0, 2)

[tex]B' = (-\frac 13(-4 +1) - 1, -\frac 13(-4 - 2) + 2)[/tex]

B' = (0, 4)

[tex]C' = (-\frac 13(-1 +1) - 1, -\frac 13(-4 - 2) + 2)[/tex]

C' = (-1, 4)

See attachment for the image of the triangle, after it has been enlarged

Answers

Answer:

x = - 1

Step by step explanation:

The rational expression will be undefined if the denominator is zero.

x+1 = 0

x = -1

Hence, for x = -1, the given expression will be undefined.

If x is a positive integer, for how many different values of x is the square root of 48/x a whole number?

Answers

The number of values x for which the square root of 48/x a whole number are two.

What is the number?

The square root of a number can be described as number that when multiplied with itself yields the number.

The first step is to determine the factors of 48. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

The factors of 48 that will yield a perfect square when divided by 48: 3 and 12.

48 divided by 3 would give a value of 16.

48 divided by 12 would give a value of 4.

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evaluate q-r if q= -14 and r=-6

Answers

Answer:

- 8

Step-by-step explanation:

substitute q = - 14 and r = - 6 into the expression

q - r

= - 14 - (- 6)

= - 14 + 6

= - 8

Answer: -8

Step-by-Step Explanation:

=> q - r, where q = -14 and r = -6

Therefore,
= q - r
= -14 - (-6)
= -14 + 6
= -8

A toy giraffe was made using
a scale factor of 1:8. If the toy
giraffe is 2 feet long, how many
feet long is the real giraffe?

Answers

The real giraffe would be 8 times larger than the toy giraffe, since it’s a ratio of 1:8.
The toy is 2 feet, so we multiply that by 8, and 2x8 = 16.
The real giraffe is 16 feet long.

A regular pentagon and a regular hexagon are both inscribed in the circle below. Which shape has a bigger area? Explain your reasoning. 4

Answers

Answer:

Pentagon

Step-by-step explanation:

Because as you can see, a regular pentagon is bigger than then the hexagon. If it's both in the circle below, the pentagon will most likely have an big advantage in this.

[tex]\sqrt{29-12\sqrt{5}[/tex] simplify this

Answers

[tex] \sqrt{29 \: - \: 12 \sqrt{5} } [/tex]

Factor the indicated expression:

[tex] \sqrt{(3 \: - \: 2 \sqrt{5}) ^{2} } [/tex]

Simplified the index the root and also the exponent using the number 2.

[tex] \boxed{ \bold{2 \sqrt{5} \: - \: 3}}[/tex]

MissSpanish

[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{29-12\sqrt{5}} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{20-12\sqrt{5}+9} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{4\cdot \:5-12\sqrt{5}+9} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{\left(\sqrt{4}\right)^2\left(\sqrt{5}\right)^2-12\sqrt{5}+\left(\sqrt{9}\right)^2} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{4}=2 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{9}=3 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf 2\cdot2\cdot3\sqrt{5}=12\sqrt{5} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{2^2\left(\sqrt{5}\right)^2-2\cdot \:2\cdot \:3\sqrt{5}+3^2} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Apply\:the\:formula\:from\:binomial\:to\:square:(a-b)^2=a^2-2ab+b^2 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf 2^{2}(\sqrt{5})^{2}-2\cdot2\cdot3\sqrt{5}+3^{2}=(2\sqrt{5}-3)^{2} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{\left(2\sqrt{5}-3\right)^2} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Apply \ the \ laws \ of \ exponents:\sqrt[n]{a^{2} }=a \end{gathered}$}[/tex]

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

[tex]\red{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \red{=2\sqrt{5}-3 } \end{gathered}$}}} \ \ \red{\Rightarrow} \ \ \bf{\red{Answer}}[/tex]

↓

[tex]\red{\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\red{MyHeritage}} \end{gathered}$}}}}[/tex]

10 out of 15
Which is the equation of the line passing through (0, 8) and (4, 0)?

Answers

Answer:

y=-2x+8

Step-by-step explanation:

We want an equation of the form y=mx + b, where m is the slope and b is the value of y when x=0.

The slope of a line through the two given points:

(4,0) and (0,8)

Rise = (8-0) = 8

Run = (0-4) = -4

Slope = 8/-4 = -2

The y-intercept is given by the point (0,8), which tells us that b=8.

The equation is y = -2x + 8

Answer:

Which is the equation of the line passing through (0, 8) and (4, 0)?

The one that you are on is correct

y = -2x + 8

Step-by-step explanation:

You're welcome.

The graph shows the functions f(x), p(x), and g(x): 6.98 Ax) 1 p(x) 8(xx) US -9.06 10.94 -6.35 Courtesy of Texas Instruments Part A: What is the solution to the pair of equations represented by p(x) and f(x)? (3 points) Part B: Write any two solutions for f(x). (3 points) Part C: What is the solution to the equation p(x) = g(x)? Justify your answer.

Answers

Answer:

See the attached graph.

Step-by-step explanation:

A standard die is rolled and a month
of the year is chosen at random.
What is the probability of rolling a
number that is at least
then
choosing a month that does not
begin with the letter M?
200

Answers

Answer:

The probability is [tex]\frac{5}{9}[/tex]

Step-by-step explanation:

First we will find the probability of having a roll that is at least 3

1 2 3 4 5 6

this means there is a [tex]\frac{4}{6}[/tex] chance we will roll at least 3

Next we will find which months of the year are applicable

January February March April May June July August September October November December

This means there is a [tex]\frac{5}{6}[/tex] chance we will pick a month that does not begin with the letter M.

Now we can multiply these chances together to see what the total probability is.

[tex]\frac{4}{6} * \frac{5}{6} = \frac{20}{36} \rightarrow \boxed{\frac{5}{9}}[/tex]

That is the answer

- Kan Academy Advance

Type the correct answer in the box. Use numerals instead of words.
What is the length of the diagonal shown in the rectangular prism? Round your answer to the nearest tenth.

Answers

The length of the diagonal shown in the rectangular prism is; 9.5 ft

How to Use Pythagoras Theorem?

First of all, we have to find the length of the diagonal base to get;

x = √(4² + 7²)

x = √65

Thus;

Length of the diagonal shown = √(5² + (√65)²)

Length of the diagonal shown = √90

Length of diagonal shown = 9.4868

Length of diagonal shown ≈ 9.5 ft

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Answer:

got 100% on Plato

Step-by-step explanation:

If c = 64-d, what is the value of C when D = -1/6

Answers

The equation c = 64 - d is a linear equation, and the value of c in the equation is 64 1/6

How to solve the equation?

The equation is given as:

c = 64 - d

The value of d is given as:

d = -1/6

Substitute -1/6 for d in c = 64 - d

c = 64 - -1/6

Evaluate the difference

c = 64 1/6

Hence, the value of c in the equation is 64 1/6

Answers

Answer:

B. The function is nonlinear.

Step-by-step explanation:

A linear function graphs as a straight line. It is a polynomial function of degree 1. Any function that is not a linear function is a nonlinear function.

degree

The function given is a polynomial function of degree 2. (Its highest-degree term is x^2, which has an exponent of 2.)

categorization

Since the degree is not 1, the function is nonlinear.

_____

Additional comment

A polynomial function will never be "linear at some points and nonlinear at other points." Such a description might apply to a piecewise-defined function.

Hi can anybody answer this please !

Answers

Answer:

7ft; 8 minutes

Step-by-step explanation:

a. to find the height the person boarded at, plug in t=0 since this is right when the person got on the Ferris wheel. we then get:

h(0) = -45 * cos ((pi/4)*0) + 52 = 7 ft

b. to find the period, we have pi/4 * t = 2*pi, solve for t to get t=8

A radioactive isotope has a rate of decay of 84%. that is, every day,
84% of the isotope remains. how many days is its half-life? round to
the nearest tenth.

Answers

The half life of the radioactive isotope to the nearest tenth is 0.83 days.

What is rate of radioactive decay?

The rate of radioactive decay is the rate at which a radioactive isotope is disintegrated. The half life is the time taken for half of the original amount of radioactive isotope to remain.

Given that;

t/12 = 0.693/k

Where;

t1/2 - half life

k =decay constant

t/12 = 0.693/0.84

t/12 = 0.83 days

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Which expression is equivalent to 18x^2√14x^8 / 6√7x^4, if x ≠ 0?

Answers

The equivalent expression of [tex]18x^2\sqrt{14x^8} \div 6\sqrt{7x^4}[/tex] is [tex]3x^4\sqrt{2}[/tex]

How to determine the equivalent expression?

The expression is given as:

[tex]18x^2\sqrt{14x^8} \div 6\sqrt{7x^4}[/tex]

Start by dividing 18 by 6

[tex]3x^2\sqrt{14x^8} \div \sqrt{7x^4}[/tex]

Next, divide 14 by 7

[tex]3x^2\sqrt{2x^8} \div \sqrt{x^4}[/tex]

Take the square root of x^8 and x^4

[tex]3x^2 * x^4\sqrt{2} \div x^2[/tex]

Divide x^2 by x^2

[tex]3* x^4\sqrt{2}[/tex]

Evaluate

[tex]3x^4\sqrt{2}[/tex]

Hence, the equivalent expression of [tex]18x^2\sqrt{14x^8} \div 6\sqrt{7x^4}[/tex] is [tex]3x^4\sqrt{2}[/tex]

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Answer: B or 3x^4 sqrt 2

explanation: only simplified answer above

Given the pattern rule Tn=n2-1

what are the first 3 terms of the pattern

Answers

Answer:

0, 3 , 8

Step-by-step explanation:

substitute n = 1, 2, 3 into the pattern rule

T₁ = 1² - 1 = 1 - 1 = 0

T₂ = 2² - 1 = 4 - 1 = 3

T₃ = 3² - 1 = 9 - 1 = 8

How do I solve and find x?

Answers

Answer:

x=60

Step-by-step explanation:

First get x all alone on 1 side of the equation. Add 14.5 to both sides of the equation to cancel out the negative. You will then be left with

x/5= 12

Multiply both sides of the equation by 5 to cancel out the division and you'll get x=60

3b - c +5 if c= - 4, b=2.

Answers

Answer:

Step-by-step explanation:

To find the answer, plug the values of each variable into the equation and simplify. It may be easiest to plug one variable in at a time, simplify, then plug the next variable in. Remember, if the equation is asking you to subtract a negative number, the negatives cancel and you want to add the numbers.

b = 2 c = -4

3b - c + 5 <----- Original expression

3(2) - c + 5 <----- Plug 2 in for "b"