Is the product of a rational number and an irrational number always irrational?

9514 1404 393

Answer:

  7.28

Step-by-step explanation:

Consider the attachment. There, we have identified a point C that makes ABC a right triangle with the right angle at C.

The Pythagorean theorem gives you the relationship between side lengths of a right triangle. The square of the hypotenuse (longest side) is equal to the sum of the squares of the other two sides.

  AB² = AC² +BC²

We can count grid squares to find the lengths of AC and BC. They are 2 units and 7 units, respectively. This means ...

  AB² = 2² +7²

  AB² = 2·2 +7·7 = 4 +49 = 53

When we know the square, we can find what it is the square of by taking the square root. Generally, a calculator is required for this.

  AB = √53 ≈ 7.2801099

When we round this number to two decimal places (the nearest hundredth), we get ...

  AB ≈ 7.28 . . . units

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Additional comments

You will notice that the length AC in the diagram is the difference of the x-coordinates of points A and B. Similarly, the length BC in the diagram is the difference of y-coordinates. Then the square AB² is the sum of the squares of these differences. The length AB is the square root of that sum.

In general, this is how you find the length of a line segment from its end point coordinates.

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A little magic, perhaps: You may find that repeating the 11-digit number on the first line several times a day for a few days will help to moderate your difficulty understanding this. The numbers convey an energy that is intended to counteract the brain block that often arises when seeing a math problem.

Answer:

6,000

Step-by-step explanation:

60 hundreds.

600 tens.

Answer:

100

Step-by-step explanation:

if SP>CP,

It is profit [SP - CP = Profit]

if CP>SP,

It is loss   [CP - SP = Loss]

Here in the question CP>SP so,

loss = CP - SP

       =200 - 100

       = 100

f(x) *g(x) = (x-3)(x+11) = x^2 +11x -3x -33 = x^2 +8x -33

Sorry if its wrong :(

Answer:

g(x) = [tex]\frac{1}{x+11}-9[/tex] is my choice

Step-by-step explanation:

I. If move right is +x and move down is -y

               then f(x) = [tex]\frac{1}{x}[/tex]

               +x = 11, -y = -9

                so g(x) = [tex]\frac{1}{x+11}-9[/tex]

Hope that help :D

Answer: H. 20%

Step-by-step explanation: if 4/5 got 100 then 80% got 100 so the other 20% did not get a 100

9514 1404 393

Answer:

  the number is 1

Step-by-step explanation:

First of all, you need to know what you're solving. Here, we assume you're trying to find "the number."

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Let n represent "some number." The given relation can be written using math symbols as ...

  5n +8 = 10 +3n

Subtract 3n +8 from both sides to separate the variable and the constant terms.

  2n = 2

  n = 1 . . . . . . . divide by 2

The number is 1.

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Check

  5 times 1, added to 8 is 13. This amounts to the same thing as 10 added to the product of 3 and 1.

Answer:

C. 4

Step-by-step explanation:

We have the equation [tex]\sqrt[x]{81} =3[/tex] and are asked to find the value of x.

To find x, we need to find how many times 3 can go into 81 but as an exponent, instead of saying 3 * x it would be [tex]3^x[/tex].

So find the value of each exponent by replacing it with each answer choice :

[tex]3^8 = 6561[/tex]

[tex]3^{27} = 7.6255975e+12[/tex]

[tex]3^4 = 81[/tex]

[tex]3^2 = 9[/tex]

Since to the power of 4 equals the cube root in the original equation, therefore B. is the answer.

The absolute value of a number returns the positive value of the given number. Ruben will be at exactly 90 miles in 2 hours or 5 hours

Given that:

[tex]d = |210 - 60t|[/tex]

To calculate t when [tex]d = 90[/tex], we have:

[tex]90 = |210 - 60t|[/tex]

Rewrite as:

[tex]|210 - 60t| = 90[/tex]

Remove absolute bracket

[tex]210 - 60t = 90 \ or\ 210 - 60t = -90[/tex]

Collect like terms

[tex]- 60t = -210 + 90 \ or\ - 60t = -210 -90[/tex]

[tex]- 60t = -120 \ or\ - 60t = -300[/tex]

Divide through by -60

[tex]t = 2 \ or\ t = 5[/tex]

Hence, Ruben will be at exactly 90 miles in 2 hours or 5 hours

Read more about absolute values at:

https://brainly.com/question/1301718

Answer:

It is a function and 0to^2 shows your function dt.c and 4c-3 shows your function is wrong and the answer is 0 and 31/4 to the power of 25 and shows that the function is 8.

Step-by-step explanation:

Answer:

166,67

Step-by-step explanation:

We want to find a number x which 12% is 20:

x * 0.12 = 20

x = 20 / 0.12

x = 166,67

Answer:

true

Step-by-step explanation: true

Answer:

The distance is always the opposite of the difference.The distance is the absolute value of the difference.

Answer:

The distance is the absolute value of the difference

Step-by-step explanation:

Sum is the when 2 or more numbers are added . Difference is the quantity at which 2 numbers differ i.e difference between 9 and 7 is 2. If you are talking about distance in reference to segment the distance ishow far apart two points are.

9514 1404 393

Answer:

  $321.99

Step-by-step explanation:

Use the annuity formula and solve for P.

  A = P(12/r)((1 +r/12)^(12t) -1) . . . . value of a series of deposits P earning rate r compounded monthly for t years.

  50,000 = P(12/0.05)((1 +0.05/12)^(12·10) -1) = P(240)(0.64700950)

  P = 50,000/155.282279 = 321.99

You would need to deposit $321.99 in the account each month to have $50,000 in 10 years.

Answer:

D

Step-by-step explanation:

hhgxhsbjxkxjebdibfhejx

The expression 4x + 6 -y^2  when evaluated has a value of -22

From the question, we have the following parameters that can be used in our computation:

4x + 6 -y^2

Also, we have

x=-3 and y=4

Substitute the known values in the above equation, so, we have the following representation

4x + 6 -y^2 = 4 * -3 + 6 - 4^2

Evaluate

4x + 6 -y^2 = -22

Hence, the solution is -22

Read more about expression at

https://brainly.com/question/30492964

#SPJ6

Answer:

7

Step-by-step explanation:

15ft - 8ft

Answer : 2604 can be divided into 1736 and 868 in the ratio of 2:1.

Step-by-step explanation:

2x + x = 2604

or, 3x = 2604

or, x = 2604/3 = 868

so

2x = 2*868 = 1736

now

x = 868

Answer:

5 units

Subtract -6 and -1, and you get -5. -5 can't be the answer since we are asked to find the distance, so it is the absolute value of -5, 5.

Answer:

D) 6 units

Explanation:

Point A is 5 units away from 0 (the middle)

Point B is 1 unit away from 0

5 + 1 = 6

Distance between two points cannot be negative

Answer:

4.1145

Step-by-step explanation:

You can use the following formula to solve this kind of problems,

[tex] log_{a}(b) + log_{a}(c) = log_{a}(bc) [/tex]

So, let's start of with log4_(300). Since the question have already gave log4_(3) =0.7925 and log4_(5) =1.1610. It means that you have to split the 300 into the simplest form where almost all of the numbers are 3 and 5.

[tex] log_{4}(300) = log_{4}(4 \times 5 \times 3 \times 5) \\ = log_{4}(4) + log_{4}(5) + log_{4}(3) + log_{4}(5) \\ = 1 + 1.1610 + 0.7925 + 1.1610 \\ = 4.1145[/tex]

Answer:

B) [tex]A=4x+8[/tex]

Step-by-step explanation:

Hi there!

Area of a trapezoid: [tex]A=\displaystyle\frac{1}{2}h(b_1+b_2)[/tex]

⇒ b₁ = x-3

⇒ b₂ = x+7

⇒ h = 4

Plug the given information into the equation:

[tex]A=\displaystyle\frac{1}{2}(4)[(x-3)+(x+7)]\\\\A=\displaystyle\frac{1}{2}(4)(x-3+x+7)\\\\A=2(2x+4)\\\\A=4x+8[/tex]

Therefore, the area of the trapezoid is [tex]4x+8[/tex].

I hope this helps!

Step-by-step explanation:

steps are in the picture above.

Use the formula y2-y1/x2-x1

That gives you

5 - (-2) / -1 - 1 = -7/2

-7/2 should be your slope.

(Or it could be -3.5 in decimal form)

Answer:

Step-by-step explanation:

Answer:

8%

Step-by-step explanation:

Ok, there is 52 cards per deck, 13 per suit ( club, diamond, heart, and spade)

if you multiply 13 by 4 ( 4 is dependent on the number of suit, and 4 will always be the number of suit )

The probability is 8%.

Why, because 25 would be pulling a random card and your saying you want the suit to be diamond the probability of you getting a random diamond card would be 25%. But were not doing that. So cross out 31% and 25%.

Also, 4% would be as your counting 100 cards. So that leaves me with 8%.

Answer:

the number will vary the answer

Step-by-step explanation:

3×1=3

3×2=6

Answer:

14.

JIm can solve 4/7 math problems in a minute. that is the unit rate. how did i get that? 7/7 = 1 and thats what we need for a unit rate, the number one. that means we have to divide 4 by 7 too. therefore, 4/7.

we aren't done. we multiply 4/7 * 25 to find out how many math problems jim can solve in 25 minutes.

about.. 14.29 and we need a whole number since you cant solve a decimal of a math problem so he can solve 14 math problems in 25 minutes.

Step-by-step explanation:

Answer:

43.57

Step-by-step explanation:

divide 4/4 and 7/4 to get the base amount of minutes per question then multiply 1.75 by 25 minutes

The measure of angle DAC must be 60 degrees. Since a right angle is 90 degrees, the sum of the degrees of both of the angles must be that amount. If angle BAD is 30 degrees, the measure of angle DAC must be 60 degrees.