Find the length of side

x in simplest radical form with a rational denominator.



Thanks in advance

Answer:

Yes,

Step-by-step explananation

The quotient of two rational numbers is always rational, and the reason for this lies in the fact that the product of two integers is always an rational number.

The Quotient of two Rational Numbers is a Rational Number if and only if Numerator and Denominator are Multiples.

From Algebra, we know that a Rational Number is a Real Number of the form:

[tex]x = \frac{a}{b}[/tex], [tex]a, b\in \mathbb{N}[/tex], [tex]x \in \mathbb{R}[/tex] (1)

Where:

The Quotient can be an Integer or not. In the first case, all Quotients have their equivalent Rational Numbers.

Now, if we divide a Rational Number by another Rational Number, then we have the following expression:

[tex]x' = \frac{x_{1}}{x_{2}}[/tex]

If [tex]x'[/tex] is a Rational Number, then it must also an Integer and if [tex]x'[/tex] is an Integer, then [tex]x_{1}[/tex] and [tex]x_{2}[/tex] must be Multiples of each other.

The Quotient of two Rational Numbers is a Rational Number if and only if Numerator and Denominator are Multiples.

Please see this question related to Rational Numbers: https://brainly.com/question/24398433

Step-by-step explanation:

3n-5=(-8*6)+(-8*5n) distributive property

3n-5=-48-40n

3n+40n=-48+5 add property

43n=-43 add property

43n/43=-43/43 division property

n=-1

Answer:

a)2/7

b)1/2

c)9/14

d)6/7

Step-by-step explanation:

The jar contains 4 red marbles, numbered 1 to 4 which means

Red marbles = (R1) , (R2) , (R3) , (R4)

It also contains 10 blue marbles numbered 1 to 10 which means

Blue marbles = (B1) , (B2) , (B3) , (B4) , (B5) , (B6) , (B7) , (B8) , (B9) , (B10) .

We can calculate total marbles = 4red +10 blues

=14marbled

Therefore, total marbles= 14

The marbles that has even number = (R2) , (R4) ,(B2) , (B4) , (B6) , (B8) , (B10) =7

Total number of Blue marbles = 10

Blue and even marbles = 5

(a) The marble is red

P(The marble is red)=total number of red marbles/Total number of marbles

=4/14

=2/7

(b) The marble is odd-numbered

Blue marbles with odd number= (B1) , (B3) , (B5) , (B7) , (B9) ,

Red marbles with odd number = (R1) , (R3)

Number of odd numbered =(5+2)=7

P(marble is odd-numbered )= Number of odd numbered/ Total number of marbles

P(marble is odd-numbered )=7/14

=1/2

(C) The marble is red or odd-numbered?

Total number of red marbles = 14

Number of red and odd marbles = 2

The marbles that has odd number = (R1) , (R3) ,(B1) , (B3) , (B5) , (B7) , (B9) =7

n(red or even )= n(red) + n(odd)- n(red and odd)

=4+7-2

=9

P(red or odd numbered)= (number of red or odd)/(total number of the marble)

= 9/14

(d) The marble is blue or even-numbered?

Number of Blue and even marbles = 5

Total number of Blue marbles = 10

Number of blue that are even= 5

The marbles that has even number = (R2) , (R4) ,(B2) , (B4) , (B6) , (B8) , (B10)

=7

n(Blue or even )= n(Blue) + n(even)- n(Blue and even)

= 10+7-5 =12

Now , the probability the marble is blue or even numbered can be calculated as

P(blue or even numbered)= (number of Blue or even)/(total number of the marble)

= 12/14

= 6/7

Answer:

[tex]\boxed{\sf B. \ All \ real \ numbers}[/tex]

Step-by-step explanation:

The domain is all possible values for x.

[tex]f(x)=(\frac{1}{4} )^x[/tex]

There are no restrictions on x.

The domain is all real numbers.

Answer:

B.All real number

hope you have unterstand

Total weight of the gravel, in tons used for the driveway is 8.6 tons

Weight of first load = 8 tons

Weight of second load = 1200 pounds

Convert pounds to tons:

1 pound = 0.0005 ton

1200 pounds = 0.6 ton

Then,

Weight of second load = 0.6 ton

Total weight of the gravel, in tons = Weight of first load + Weight of second load

= 8 tons + 0.6 tons

= 8.6 tons

https://brainly.com/question/24370065

Answer:

[tex]y=43[/tex]

Step-by-step explanation:

[tex]y=2(90-46)/2[/tex]

[tex]y=43[/tex]

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

OAmalOHopeO

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

Step-by-step explanation:

The value of the numerical expression 1 + 32 – 10 ÷ 2 will be 28.

Algebra is the study of graphic formulas, while logic is the interpretation among those signs.

The numerical expression is given below.

⇒ 1 + 32 – 10 ÷ 2

According to the PEMDAS rule, the computation wrapped in quotes or the parenthesis comes first in the sequence of operation.

This rule is used to solve the equation in a proper and correct manner.

PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction.

⇒ 1 + 32 – (10 ÷ 2)

Simplify the numerical expression, then the expression will be

⇒ 1 + 32 – 5

⇒ 33 – 5

⇒ 28

Then the value of the numerical expression 1 + 32 – 10 ÷ 2 will be 28.

More about the Algebra link is given below.

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Answer:

Slope passes through (-6, 5) and (-2, 7)

[tex]m_1=\frac{y_2-y_1}{x_2-x_1} =m_1=\frac{7-5}{-2+6}[/tex]

[tex]m_1=\frac{2}{4} =\frac{1}{2}[/tex]

Slope passes through (4, 2) and (6, 6)

[tex]m_2=\frac{6-2}{6-4}[/tex]

[tex]\frac{4}{2} =2[/tex]

[tex]m_1\times m_2 \neq -1[/tex] [tex]m_1\neq m_2[/tex]

Answer:- A) neither perpendicular nor parallel.

OAmalOHopeO

We know that,

[tex]EF=\dfrac{AD+BC}{2}[/tex]

which is

[tex]x=\dfrac{x-5+2x-4}{2}[/tex]

Now solve for x,

[tex]x=\dfrac{3x-9}{2}[/tex]

[tex]2x=3x-9[/tex]

[tex]x=9[/tex]

Since x is 9, the lengths are,

[tex]AD=x-5=9-5=\boxed{4}[/tex]

[tex]EF=x=\boxed{9}[/tex]

[tex]BC=2x-4=18-4=\boxed{14}[/tex]

Hope this helps :)

Answer:

D  [tex]\sqrt{x} +11=15[/tex]

Step-by-step explanation:

Edge 2020

For the given expression √x + 11 = 15 the value of x will be equal to 16.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression √x + 11 =15. The expression will be solved as below,

√x + 11 =15

√x = 15 - 11

√x = 4

Squaring on both sides of the equation,

x = 4²

x = 16

To know more about an expression follow

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Answer:

114 cm²

Step-by-step explanation:

Surface area of the rectangular prism,

2×(wl+hl+hw)

=2×(3×8+3×8+3×3)

= 2×(24+24+9)

= 2×(57)

=114 cm²

Answer:

Hope this helps :)

Step-by-step explanation:

A scatter plot is a two-dimensional diagram that displays individual data points based on the intersection of two variables, shown as vertical and horizontal axes. Individual data points or values are plotted at particular coordinates of the two variables being studied. Patterns of data points provide a visual representation of relationship between the two variables. A wide range of jobs and careers use this valuable analytical tool for data analysis and decision making.

My conclusion,

They help organize important data for future occurences.

Answer:

sorry gave wrong answer

Step-by-step explanation:

Answer:

If the perimeter of the rectangle is 30cm , find its area. W=5 FOR THE WIDTH. 5*10=50 FOR THE AREA.

Step-by-step explanation:

The area of the Rectangle is 50 sq.m

The area of rectangle for a rectangle of length L and width W is given by

                                              A =  L* W

It is measured in square units.

Let the length of the rectangle be L

The width of the rectangle is W

The length of a rectangle is twice its width

L = 2W

Perimeter of the Rectangle is 2( Length + Width)

30 = 2 (L +W)

15 = L + W

15 = 2W +W

15 = 3W

W = 5m

L = 10m

The area of the rectangle is Length * Width

Area = 10 *5

Area = 50 sq.m

To know more about Area of Rectangle

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Answer:

355/12

Step-by-step explanation:

Answer:

355/12mi

Step-by-step explanation:

9 1/2 = 19/2

20 1/12 = 241/12

19/2 + 241/12 = 355/12mi

Answer:

The expression = [tex] \frac{40}{y - 16} [/tex]

Value of the expression = 4 (when y is 20)

Step-by-step explanation:

Quotient simply means the result you get when you divide two numbers. Thus, dividend (the numerator) ÷ divisor (the denominator) = quotient.

From the information given to us here,

the dividend = 40

the divisor = y - 16

The quotient = [tex] \frac{40}{y - 16} [/tex]

There, the expression would be [tex] \frac{40}{y - 16} [/tex]

Find the value of the expression when y = 20.

Plug in 20 for y in the expression and evaluate.

[tex] \frac{40}{y - 16} [/tex]

[tex] = \frac{40}{20 - 16} [/tex]

[tex] = \frac{40}{4} = 10 [/tex]

The value of the expression, when y is 20, is 4.

Answer:5

Step-by-step explanation:

Answer:

D. (25π - 50) sq m

Step-by-step explanation:

Since ABCD is a square with the area of 100, we know that the dimensions are 10 by 10. With that, we can find that triangle ABC = 50 sq m because of (h*l)/2. Since A is the center of the circle that contains arc BD, we know that 10 is the radius of the quarter-circle ABC. Using (πr^2)/4 to get the area of the quarter-circle, we get that the quarter-circle ABC = 25π sq m. But the original triangle ABC in the quarter-circle is not shaded. Therefore, we subtract 50 from 25π, which leads to (25π - 50) sq m.

I hope this helped! :D

A(t)=P(1+r)t

A = accrued amount = what you are solving for

P = principle investment = $400

r = rate of growth = 5% = 0.05

t = time = 10 years

A(10) = 400(1.05)10 (use calculator to solve)

A(10) ≈ 4,200

Answer: 0.584

Step-by-step explanation:

We have:

5 discs

6 jump ropes

3 balls

12 pieces of sidewalk.

5 + 6 + 3 + 12 = 26

If all of them have exactly the same probability of being removed, then:

in the first selection, we do not want to remove a jump rope, so we can remove one disc, one ball or one piece of sidewalk.

The total number of those objects is:

5 + 3 + 12 = 20.

Then the probability of removing one of those objects is:

P1 = 20/26 = 0.769

Now in the second selection, we have the same situation, but now we have 25 objects in total, and because in the previous selection we removed one ball, or one disc, or one piece of sidewalk, the total number of these things now is 19.

So the probability of removing another object of that set is:

P2 = 19/25 = 0.76

The joint probability is equal to the product of the individual probabilities, so we have:

P = P1*P2 = 0.769*0.76 = 0.584

$121 and $12 ok isn't available in your ma er bishal bishal bishal

The process of copying an angle through construction involve ensuring

that the distance between the two rays forming the angle is the same or

equal in the original and copy of the angle at a given equal distance from

the vertex of both angles

The step where the error occur is step 4. She measured the incorrect length

The reason for the above selection is as follows:

The steps to copy an angle are as follows;

A critical step in the copying process involves the finding the distance

between the initial line and the terminal line EF at a given distance DG =

AE from the angle vertex

The step where the error occur is in step 4. by opening the compass

between points A and E which are points on the same line and placing the

compass at point G on line l to draw an arc intersecting the arc created

from point D at H, thereby making the radial distance between the two lines

forming the angle, in the copied angle at a distance E from the vertex,

equal to AE rather than EF

Therefore, the error occurred in step 4. She measured the incorrect length

Learn more about the steps to copy an angle here:

https://brainly.com/question/4292471

Answer:

it is 9%

Step-by-step explanation: the socks persent is the correct answer

Answer: D. 61%

Step-by-step explanation:

Answer:

168

Step-by-step explanation:

first, split both 840 and 24 into there primes.

840=2×2×2×3×5×7

24=2×2×2×3

therefore any multiples of 24 must have those factor.

so, factors of 840 that are multiples of 24 are

2×2×2×3=24

2×2×2×3×5=120

2×2×2×3×7=168

2×2×2×3×5×7=840

there the answer is 168

Using the concept of probability, it is found that there is a 0.0592 = 5.92% probability that you get a total of 17 given on the first spin you spin a 2.

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

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

In each trial, there are 13 possible outcomes(pockets numbered from 0 to 12), so the total number of outcomes is:

[tex]T = 13^2 = 169[/tex]

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

The desired outcomes are those who result in a sum of 15. Thus, they are:

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

Thus, the probability is:

[tex]p = \frac{D}{T} = \frac{10}{169} = 0.0592[/tex]

0.0592 = 5.92% probability that you get a total of 17 given on the first spin you spin a 2.

A similar problem is given at https://brainly.com/question/21444373

Answer:

x has to be less than 3

Step-by-step explanation:

Answer:

x < 3

I hope this helps!

Answer:

6 or 5 or 4...........

Step-by-step explanation:

Answer:

x=N :x<7

Step-by-step explanation:

123456

hope it's helpful

Answer:B the amount of money in a bank account never changes.

Step-by-step explanation:

Answer:

B. The amount of money in a bank account never changes.

Step-by-step explanation:

Equilibrium is achieved when the state of a reversible reaction of opposing forces cancel each other out. While in a state of equilibrium, the competing influences are balanced out. Imagine a cup with a hole in it being filled with water from a tap. The level of water in this cup would stay the same if the rate at which the water that flows inside is the same as the water that flows outside. Option B will be the correct answer because the amount of money going into the account is at the same rate of money coming out of the account.

Answer:

Step-by-step explanation:

34.375 Liters of milk make 11 tins of cheese. Assuming that milk is available in whole liters only, 35 Liters of milk are needed.

(A) The blue line has a slope of 5/2, red has slope 4/4 = 1, and purple has slope 3/9 = 1/3.

To find the slope, take any two points (a, b) and (c, d) on the line, then

slope = (d - b)/(c - a)

i.e. the ratio between the changes in the y and x coordinates.

(B) Each line has equation

• blue: y = 5/2 x

• red: y = x

• purple: y = 1/3 x

This follows from the general equation for a line with slope m and y-intercept b,

y = mx + b

or from the more general equation for a line with slope m passing through a point (a, b),

y - b = m (x - a)

(C) Consider the blue line. If you take units into account, its slope is

(5 units of distance)/(2 units of time) = 5/2 (units of distance/time)

which means, per unit time, some object travels a 5/2 units of distance, and this is the definition of speed.

(D) The competitor with the blue line, Mary, would win the race because their speed is the highest (5/2 > 1 > 1/3).

(E) Average velocity is defined as

v (ave) = ∆d/∆t = (change in distance)/(change in time)

At time 0, no one has moved yet. At time 4,

• Mary has covered a distance of 5/2 × 4 = 10, giving her an average velocity of (10 - 0)/(4 - 0) = 5/2

• Mike has covered a distance of 4, so his average velocity is (4 - 0)/(4 - 0) = 1

• Sam has covered a distance of 1/3 × 4 = 4/3, so his average velocity is (4/3 - 0)/(4 - 0) = 1/3

It's not a coincidence that the average velocities are the same as the slopes, because each racer travels at a constant speed.

(F) The racers' instantaneous velocities are the same as their respective average velocities, again because they are each moving at a constant speed.