Simplifying two rational expressions, matching them with their equivalent simplified forms. Please helpppp! 23 pts.

Answer:

5.2

Step-by-step explanation:

= 3a - b / 2c + 3a - c / c - b

= 3(3) - (-4) / 2(-2) + 3(3) / -2 -(-4)

= 9 + 4 / -4 + 9 / -2+4

= 13 / 5 / 2

= 13 / 5 * 2

= 2.6 * 2

= 5.2

Answer:

Step-by-step explanation:

[tex]\frac{3a -b}{2c}+\frac{3a-c}{c-b}=\frac{3*3-[-4]}{2*(-2)}+\frac{3*3-[-2]}{-2-[-4]}\\\\=\frac{9+4}{-4}+\frac{9+2}{-2+4}\\\\=\frac{13}{-4}+\frac{11}{2}\\\\=\frac{-13}{4}+\frac{11*2}{2*2}\\\\=\frac{-13}{4}+\frac{22}{4}\\\\=\frac{-13+22}{4}\\\\=\frac{9}{4}\\\\=2\frac{1}{4}[/tex]

Answer:

x = 2

because we have the same question and i got it right its hard to explain but trust me its x = 2

The solution to the given equation is 2. Therefore, option B is the correct answer.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is x/6 = 4/12.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, x/6 = 4/12

By cross multiplication, we get

12x=24

⇒ x=2

The solution to the given equation is 2. Therefore, option B is the correct answer.

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Answer:

Hey there!

That would be 50,020,000, and choice B would be correct.

Let me know if this helps :)

Answer:

314.16 metres

Step-by-step explanation:

The answer to this problem is essentially just the circumference of the circle.

The circumference, or perimeter, is denoted by C = 2πr = πd, where r is the radius (and half the diameter) and d is the diameter.

Here, the diameter is 100 metres, so plug this in for d:

C = πd

C = π * 100 ≈ 314.16 metres

The answer is about 314.16 metres.

~ an aesthetics lover

Greetings from Brasil....

As stated in the statement of the question, EF is a bisector of CD, so point G is the median point of CD, so CG = GD

5X - 1 = 7X - 13

X = 6

EF = EG + GF

6X - 4 = EG + 13      x = 6, so

6·6 - 4 = EG + 13

(see attachment)

Answer:

[tex]\boxed{5 \cdot \sqrt{2} \cdot \sqrt[6]{5} }[/tex]

Step-by-step explanation:

[tex]\sqrt[3]{250} \cdot \sqrt{\sqrt[3]{10} }[/tex]

[tex]\sqrt{\sqrt[3]{10} } \implies (10^\frac{1}{3} )^\frac{1}{2} =10^\frac{1}{6} =\sqrt[6]{10}[/tex]

[tex]\therefore \sqrt{\sqrt[3]{10} }=\sqrt[6]{10}[/tex]

[tex]\text{Solving }\sqrt[3]{250} \cdot \sqrt{\sqrt[3]{10} }[/tex]

[tex]250=2 \cdot 5^3[/tex]

[tex]\sqrt[3]{250}=\sqrt[3]{2\cdot 5^3}=5 \sqrt[3]{2}[/tex]

Once

[tex]\sqrt[6]{2} \cdot \sqrt[6]{5} = \sqrt[6]{10}[/tex]

We have

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

We can proceed considering the common base of exponentials

[tex]\sqrt[3]{2} \cdot \sqrt[6]{2} = 2^{\frac{1}{3}} \cdot 2^{\frac{1}{6} } = 2^{\frac{3}{6} } = 2^{\frac{1}{2} }=\sqrt{2}[/tex]

Therefore,

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

Answer:

5/18

Step-by-step explanation:

Lets write an equation:

5/12*2/3=5*2/12*3.

5*2=10,

12*3=36.

10/36=5/18

The answer is 5/18.

Hope this helps!

Answer:

See Explanation

Step-by-step explanation:

1.

Standard Form: 2 * 10^8

The number is expanded as follows:

[tex]10^8 = 100,000,000[/tex]

So: [tex]2 * 10^8 = 2 * 100,000,000[/tex]

[tex]Expanded\ Form: 200,000,000[/tex]

Word Form: Two hundred million

2.

Standard Form: 3.5 * 10^7

The number is expanded as follows:

[tex]10^7 = 10,000,000[/tex]

So: [tex]3.5 * 10^7 = 3.5 * 10,000,000[/tex]

[tex]Expanded\ Form: 35,000,000[/tex]

Word Form: Thirty five million

3.

Standard Form: 9 * 10^9

The number is expanded as follows:

[tex]10^9 = 1000,000,000[/tex]

So: [tex]9 * 10^9 = 9 * 1000,000,000[/tex]

[tex]Expanded\ Form: 9,000,000,000[/tex]

Word Form: Nine billion

4.

Standard Form: 5.5 * 10^7

[tex]10^7 = 10,000,000[/tex]

So:

[tex]5.5 * 10^7 = 5.5 * 10,000,000[/tex]

[tex]Expanded\ Form: 55,000,000[/tex]

Word Form: Fifty five million

5.

Standard Form: 4.3 * 10^7

[tex]10^7 = 10,000,000[/tex]

So:

[tex]4.3 * 10^7 = 4.3 * 10,000,000[/tex]

[tex]Expanded\ Form: 43,000,000[/tex]

Word Form: Forty Three million

Answer:

a) The perimeter of a rectangle is written as:

P = 2*L + 2*W

where L is the length amd W is the width (broad in this case).

here we have:

L = 8cm and W = b

then the perimeter is:

P = 2*8cm + 2*b

And we know that:

18cm ≤ P ≤ 50cm

where ≤ is used because there is written "not more" and "not less", so the equalities are allowed

now we can replace P by the above equation:

18cm ≤ 16cm + 2*b ≤ 50cm

now we can subtract 16cm in each side and get:

18cm - 16cm ≤ 2*b ≤ 50cm - 16cm

2cm ≤ 2*b ≤ 34cm

Now we can divide each side by 2.

1cm ≤ b ≤ 34cm/2 = 17cm

1cm ≤ b ≤ 17cm.

b) Here we have missing information, so this can not be answered.

(only knowing that one side length is x, and another side length is x + 3cm, we can know that x > 0cm, so the minimum value of x is really close to 0cm)

Answer:

Addition and Subtraction of Fractions · 1. Add: (i) 7/ 10 + 2/15 (ii) 2²/₃ + 3¹/₂ · 2. Simplify: (i) 15/16 – 11/12 (ii) 11/15 – 7/20 · 3. Simplify: 4⁵/₆ – 2³/₈ + .

Answer:

7/10 + 2/15= 5/6

2 3/3 + 3 1/2= 6 1/2

15/16 - 11/12= 1/48

11/15 - 7/20= 23/60

Step-by-step explanation:

When adding or subtracting fraction with different denominators, we must find there LCM to be their new denominators. Then divide the new denominator by the old denominator, do for both fractions, then multiply the answer with the numerator, do for both fractions to get their new numerators. Then add or subtract the fractions. Then simplify the answer if needed.

Ex 1:

The LCM of 10 and 15 is 30

7/10 + 2/15

(30 ÷ 10=3, 3 × 7= 21)(30 ÷ 15= 2, 2 × 2=4)

=21/30 + 4/30= 25/30 or 5/6

With whole numbers, add the two whole numbers together. Then n add the fractions. Lastly add both of the answers together.

Ex:

The LCM of 3 and 2 is 6

2 3/3 + 3 1/2

=2 + 3= 5

= 3/3 + 1/2= 9/6 or 1 3/6 or 1 1/2

= 5 + 1 1/2

= 6 1/2

Always remember to simplify if possible or necessary.

I hope this helps! I'm sorry if it's wrong or too complicated.

Answer:

[tex]\huge \boxed{y=\sqrt{30} }[/tex]

Step-by-step explanation:

We can use ratios to solve for the problem.

y/5 = 6/y

Cross multiply.

y × y = 5 × 6

y² = 30

Take the square root of both sides.

y = [tex]\sqrt{30}[/tex]

Answer:

6x³y

Step-by-step explanation:

(2xy) * 3x²

We know that 2 * 3 = 6 and x * x² = x¹ * x² = x⁽¹⁺²) = x³ so the final answer is 6x³y.

Answer:

5,5,15

Step-by-step explanation:

Answer:

=−ab2+2ac2+2ac+2a−28b+3c

Step-by-step explanation:

a+2c−5b−c+a−b2a−6b+2c2a−6b+ca−6b+ca−5b+2c

=a+2c+−5b+−c+a+−ab2+−6b+2ac2+−6b+ac+−6b+ac+−5b+2c

Combine Like Terms:

=a+2c+−5b+−c+a+−ab2+−6b+2ac2+−6b+ac+−6b+ac+−5b+2c

=(−ab2)+(2ac2)+(ac+ac)+(a+a)+(−5b+−6b+−6b+−6b+−5b)+(2c+−c+2c)

=−ab2+2ac2+2ac+2a+−28b+3c

Answer:

=−ab2+2ac2+2ac+2a−28b+3c

Answer:

B. 2a − 6b + c

Step-by-step explanation:

Took the test :)

Answer:

Think of the double angle formula for

sin

2

x

Explanation:

sin

2

x

=

sin

x

2

sin

x

cos

x

=

sin

x

2

sin

x

cos

x

−

sin

x

=

0

sin

x

(

2

cos

x

−

1

)

=

0

Solution A:

sin

x

=

0

⇒

x

=

k

π

,

k

∈

Z

Solution B:

2

cos

x

=

1

⇒

cos

x

=

1

2

,

x

=

±

π

3

+

2

k

π

=

π

3

(

6

k

±

1

)

,

k

∈

Z

∴

x

=

k

π

or

x

=

π

3

(

6

k

±

1

)

,

k

∈

Z

Step-by-step explanation:

Answer:

       [tex]\bold{x=\frac\pi3+2k\pi\quad \vee\quad x=\frac{5\pi}3+2k\pi\quad \vee\quad x=k\pi\ ,\quad k\in\mathbb Z}[/tex]

Step-by-step explanation:

[tex]\sin 2x=\sin x\\\\\sin2x - \sin x=0\\\\2\sin x\cos x-\sin x=0\\\\(2\cos x-1)\sin x=0\\\\2\cos x-1=0\qquad\qquad\qquad\qquad or\qquad \sin x=0\\\\2\cos x=1\quad\qquad\qquad\qquad\qquad\ or\qquad \sin x=0\\\\\cos x=\frac12\qquad\qquad\qquad\qquad\qquad or\qquad \sin x=0\\\\x=\frac\pi3+2k\pi\quad \vee\ \ x=\frac{5\pi}3+2k\pi\quad\ \ \vee\ \ x=0+k\pi\ ,\quad k\in\mathbb Z[/tex]

Answer:

There are 20 cups of coffee in two pots of coffee and 36 donuts in 3 boxes of donuts

Step-by-step explanation:

The rule of three or is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them. That is, what is intended with it is to find the fourth term of a proportion knowing the other three.

If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other), the direct rule of three must be applied as follow:

a ⇒ b

c ⇒ x

So [tex]x=\frac{c*b}{a}[/tex]

In this case, the rule of three can be applied as follows:

[tex]amount of cups of coffe=\frac{2coffe pots*10 cups of coffee}{1 coffe pot}[/tex]

amount of cups of coffe= 20

[tex]amount of donuts=\frac{3 boxes*12 donuts}{1 box}[/tex]

amount of donuts= 36

There are 20 cups of coffee in two pots of coffee and 36 donuts in 3 boxes of donuts

Answer:

135

Step-by-step explanation:

From the given information:

The total number of handshakes can be represented by the combination of 18 combination 2, which can be mathematically expressed as:

[tex]\mathbf{^{18}C_2}[/tex] .

where;

[tex]\mathbf{^{18}C_2}[/tex] is the number of ways two people can shake themselves from a total of 28 people without much regard about the order of arrangement of the handshakes.

[tex]\mathbf{^{18}C_2 = \dfrac{18!}{2!(18-2)!}}[/tex]

[tex]\mathbf{= \dfrac{18!}{2!(16)!}}[/tex]

= 153

From these 6 companies, the possibility that there will be handshakes from within the company is [tex]\mathbf{^3 C_2}[/tex]

[tex]\mathbf{^3 C_2} = \dfrac{3!}{2!(3-2)!}[/tex]

[tex]= \mathbf{ \dfrac{3 \times 2!}{2!(1)!}}[/tex]

= 3

However, number of companies = 6

∴ the number of handshakes within companies = 3 × 6 = 18

But we are being told that :

If the representatives did not shake hands with people from their own company, how many handshakes took place

Therefore, the number of handshakes that took place in regard to the given criteria = 153 - 18

= 135

Answer:

35x+40y

Step-by-step explanation:

1. expand the terms by multiplying 5 by what's inside the parenthesis, so multiply by 7x and 8y and add them. So you get 35x+40y

Answer:

35x +40y

Step-by-step explanation:

5(7x+8y)

Distribute

5*7x + 5*8y

35x +40y

Answer:

0.8208 ; 0.8448

Step-by-step explanation:

Given the following :

Number of tosses = 4

Probability of head on any toss :

P(head) = 0.4

Therefore ;

(1 - p(head)) = (1 - 0.4) = 0.6

Binomial probability :

P(X) = nCx * P^x * (1 - P) ^(n-x)

Where:

n = number of trials ; x = number of success ; P = probability of success.

P(X≤2) = P(0) + P(1) + p(2)

using binomial probability calculator to ensure faster computation:

P(X≤2) = 0.1296 + 0.3456 + 0. 3456

= 0.8208

B)

P(1 ≤ X ≤ 3) = P(1) + P(2) + P(3)

P(1 ≤ X ≤ 3) = 0.3456 + 0.3456 + 0.1536

= 0.8448

Answer:

2x+8

Step-by-step explanation:

The mathematical expression will be;

⇒ 2x + 8

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

⇒ '' Eight more than the product of two and a number x''.

Now,

Since, The algebraic expression is,

⇒ '' Eight more than the product of two and a number x''.

Hence, We get the mathematical expression as;

⇒ Product of 2 and number x = 2x

And, 8 more than 2x = 2x + 8

Thus, We get the mathematical expression as;

⇒ 2x + 8

Learn more about the mathematical expression visit:

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Answer:

A square root of a number is a value that, when multiplied by itself, gives the number.

Example: 4 × 4 = 16, so a square root of 16 is 4.

The symbol for a square root is √ which always means the positive square root.

Example: √36 = 6 (because 6 x 6 = 36)

Answer:

Monday, at 12:15 AM

Step-by-step explanation:

Do this question in parts. First, add 2 days to Friday to get Sunday at 5:45 PM. Then, add 6 hours to 5:45 to get 11:45 PM. Finally, add 30 minutes to 11:45 PM. That takes you to 12:15, and since you passed midnight, Sunday is now Monday. That means the bus arrives Monday, at 12:15 AM.

Answer:

Reflection, Translation, and possibly Rotation

Answer:

1.8 hours.

Step-by-step explanation:

It is important to note that:

Speed = Distance ÷ Time

We have two trains.

Step 1

We have to find the distance that each train travelled.

Since Speed = Distance ÷ Time

Distance = Speed × Time

First train

It travels at 105 miles per hour

Distance travelled by first train =

105 × x hours

= 105x miles

Second Train

It travels at 85 miles per hour

Distance travelled by the second train = 85 miles × x hours

= 85x miles

We are told that: the two trains leave stations 342 miles apart at the same time and travel toward each other

Hence, the time it would take each train to meet each other is calculated as:

105x + 85x = 342 miles

190x = 342 miles

x = 342/190

x = 1.8 hours.

G'Day mate! Here's the answer:

53 1/3

1. 6(3 + 6) - 4/5

2. 6 x 3 is 18, and 6 x 8 is 48

3. 18 plus 48 is 66

4. 66 - 4/5 = 266/5

5. 266/5 as mixed number is 53 1/5

Answer:

[tex]\Large \boxed{\frac{326}{5}}[/tex]

Step-by-step explanation:

[tex]\displaystyle 6(3 + 8) - \frac{4}{5}[/tex]

Solving brackets.

[tex]\displaystyle 6(11) - \frac{4}{5}[/tex]

[tex]\displaystyle 66 - \frac{4}{5}[/tex]

Subtract.

[tex]\displaystyle \frac{66}{1} - \frac{4}{5}[/tex]

[tex]\displaystyle \frac{66 \times 5}{1 \times 5} - \frac{4}{5}[/tex]

[tex]\displaystyle \frac{330}{5} - \frac{4}{5}[/tex]

[tex]\displaystyle \frac{330-4}{5}[/tex]

[tex]\displaystyle \frac{326}{5}[/tex]

Answer:

The correct answer is 6000

Step-by-step explanation:

I disagree because 10 to the 3rd power = 1000 x 6 = 6000

The mistake he made was that George multiplied all of the number so, 6 x 10 x 3 = 60 x 3 = 180.

Answer:

-6.25

Step-by-step explanation:

The answer is -6.25.