. Multiply (5x2 + x − 4)(x + 2).

''All prime numbers are odd."

That is incorrect because if we consider the smallest odd number, 2, is an even number. We can say that except 2, all prime numbers are odd.

14. section is wrong. For example, both numbers can be negative, so when we multiple these two, it will equals a positive value.

Answer:

w = 11.25

Step-by-step explanation:

To solve this problem, we are going to move all of the terms containing the variable w to the left side of the equation and all of the constant terms (ones with numbers only) to the right side of the equation.

w - 24 = -3w + 21

To do this, we should first add 24 to both sides of the equation.

w - 24 + 24 = -3w +21 + 24

If we simplify, we get:

w =  -3w + 45

Next, we should add 3w to both sides of the equation.

w + 3w = -3w + 3w + 45

4w = 45

Finally, we can divide both sides by 4.

4w/4 = 45/4

w = 11.25

Hope this helps!

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:

Here, 5x + 10 = 24 + 6x - 3x

or, 5x  + 10 = 24 + 3x ( 6x-3x )

or, 5x - 3x = 24 - 10

or, 2x = 14

or, x = 14/2

Hence answer is 7.

Answer:

x = -6

Step-by-step explanation:

36 + x = 12 - 3x

36 + x - 36 = 12 - 3x - 36

x = -3x - 24

x + 3x = -3x - 24 + 3x

4x = -24

4x / 4 = -24 / 4

x = -6

Answer:

x = -6

Step-by-step explanation:

36 + x = 12 - 3x

We need all terms with x on the left side.

Add 3x to both sides.

36 + x + 3x = 12 - 3x + 3x

36 + 4x = 12

We need all terms that are just numbers on the right side. Subtract 36 from both sides.

36 - 36 + 4x = 12 - 36

4x = -24

We have 4x, which means 4 multiplied by x, on the left side. We want x alone. Divide both sides by 4.

x = -6

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:

x = -5

Step-by-step explanation:

Solve for x:

(x + 5)^2 = 0

Take the square root of both sides:

x + 5 = 0

Subtract 5 from both sides:

Answer:  x = -5

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:

see explanation

Step-by-step explanation:

Given the 2 equations

2r + 3s = - 5 → (1)

6s = 2r → (2) ( divide both sides by 2 ), then

r = 3s

Substitute r = 3s into (1)

2(3s) + 3s = - 5

6s + 3s = - 5

9s = - 5 ( divide both sides by 9 )

s = - [tex]\frac{5}{9}[/tex]

Substitute this value into either of the 2 equations and evaluate for r

Substituting into r = 3s, then

r = 3 × - [tex]\frac{5}{9}[/tex] = - [tex]\frac{5}{3}[/tex]

Solution is r = - [tex]\frac{5}{3}[/tex] and s = - [tex]\frac{5}{9}[/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:

=−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:

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:

[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:

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

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:

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.

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:

Hey there!

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

Let me know if this helps :)

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:

brainly.com/question/1859113

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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:

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.

To learn more about the solution of an equation visit:

https://brainly.com/question/14506845.

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Answer:

-6.25

Step-by-step explanation:

The answer is -6.25.

Answer:

The answer to this question is pentagonal prism or pentagonal pyramid.

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]

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:

f (x) = 1

substitute 1 for x

f (1) = 3 (1) - 4

= 3 - 4

= -1

Answer:

[tex]y = \frac{ x + 4}{3} [/tex]

Step-by-step explanation:

Let f(x) =y

y= 3x-4

[interchanging variables]

x=3y-4

[making y the subject]

3y=x+4

Therefore the inverse of the function is

[tex]y = \frac{x + 4}{3} [/tex]

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:

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.