Solving equations-variables on both sides!

Answer:

C.

Step-by-step explanation:

The area of the triangle is

[tex]\text{Area}=\dfrac{1}{2}\cdot \text{Base}\cdot \text{Height}[/tex]

You know that

Area - irrational number

[tex]\dfrac{1}{2}[/tex] - rational number (rational numbers are those that can be written as a fraction)

Base = 18 inches - rational number (actually, 18 is a natural number and each natural number is rational)

Height - unknown

You can rewrite previous formula as

[tex]\text{Area}=\dfrac{1}{2}\cdot 18\cdot \text{Height}\\ \\\text{Area}=9\cdot \text{Height}[/tex]

Now consider all options:

A. If height is a whole number then area is a whole number as a product of two whole numbers. False

B. If height is a rational number, then area is rational number as a product of two rational numbers. False

C. If height is a irrational number, then area is irrational number as a product of rational and irrational numbers. True

D. If height is a non-real complex number, then area is non-real complex number as a product of rational and non-real complex numbers. False

Option C. An irrational number.

The area of a triangle is given by the formula A = 1/2 × base × height. In this problem, the base of the triangle is 18 inches. Since the problem states that the area is an irrational number, we need to determine what the height (or altitude) of the triangle must be.

To have an irrational area, either the base or the height (or both) must be irrational. Given that the base is a whole number (18 inches), the height must be an irrational number to produce an irrational value for the area. We can set up the formula as follows:

A = 1/2 × 18 × h, where h is the height.

For A to be irrational, h must be an irrational number.

Therefore, the best answer to fill in the blank is:

Step-by-step explanation:

Converting all the numbers to decimals,

1) -0.5

2) 1/2 = 0.5

3) 0.7

4) -4/4 = -1

We see that order of numbers from least to greatest is -1 < -0.5 < 0.5 < 0.7

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Answer:

20 - 2n

Step-by-step explanation:

The sequence is arithmetic since the difference between consecutive terms is constant, that is

d = 16 - 18 = 14 - 16 = 12 - 14 = - 2

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 18 and d = - 2, thus

[tex]a_{n}[/tex] = 18 - 2(n - 1) = 18 - 2n + 2 = 20 - 2n

[tex]a_{n}[/tex] = 20 - 2n

If we know that [tex]x_{1} = 18[/tex] and [tex]r = -2[/tex], then the n-th term of the number sequence is [tex]f(n) = 18 -2\cdot (n-1)[/tex].

This sequence is an example of an arithmetic sequence, since each consecutive pair of elements has one and only one difference, that is to say:

[tex]r = x_{i+1}-x_{i}[/tex], [tex]\forall\,i\in \mathbb{N}[/tex] (1)

The expression for any arithmetic sequence is described by the following formula:

[tex]f(n) = x_{1} + r\cdot (n-1)[/tex], [tex]n \ge 1[/tex] (2)

Where:

If we know that [tex]x_{1} = 18[/tex] and [tex]r = -2[/tex], then the n-th term of the number sequence is [tex]f(n) = 18 -2\cdot (n-1)[/tex].

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Answer:

42

Step-by-step explanation:

if you divide 546 with 13 it will give you 42 mostly because 546 is the total of miles that he drove so if you dive by how many days he has been driving you will get your answer.

Troy drove 546 miles over 13 days, resulting in an average of 42 miles driven each day after dividing the total miles by the number of days.

To find out how many miles Troy drove each day, we need to divide the total number of miles driven by the number of days. Troy drove a total of 546 miles over the course of 13 days.

Divide the total miles (546) by the number of days (13).

The calculation is:

546 miles / 13 days = 42 miles per day.

Therefore, Troy drove 42 miles each day.

Answer:

Step-by-step explanation:

11:45 + 1 hour = 12:45

12:45 + 1 hour = 1:45

1:45 + 30 minutes = 2:15

Answer: 1050 miles in 5 hours

Step-By-Step explanation: there are 20 1/20 per hour

10 1/2 x 20 = 210 miles per hour

210 * 5 =1050 miles in 5 hours

[tex]\text{Hello there!}\\\\\text{We're trying to find how many miles he can drive in 5 hours}\\\\\text{We know that he drives 10.5 miles in 1/20 of an hour}\\\\\text{We need to find how much he drives in an hour, so you have to}\\\text{multiply 10.5 by 20}\\\\10.5\cdot20=210\\\\\text{In 1 hour, he drives 210 miles}\\\\\text{Now, multiply 210 by 5 to see how much he drives in 5 hours}\\ \\210\cdot5=1050\\\\\large\boxed{\text{John drives 1,050 mile in 5 hours}}[/tex]

Answer:

Find the area of two sides (Length*Height)*2 sides.

Find the area of adjacent sides (Width*Height)*2 sides.

Find the area of ends (Length*Width)*2 ends.

Add the three areas together to find the surface area.

Example: The surface area of a rectangular prism 5 cm long, 3 cm.

Answer:

The way to do this is multiplying all the 3 dimensional sides Then adding them.

Step-by-step explanation:

What i mean by this is by, Multiplying the Length and height together .

Next is Multiplying the Width and Height together

Next would to multiply the Length And Width together.

Lastly would to add all your solutions together.

If you have any questions feel free to ask in the comments.

Answer:

b

Step-by-step explanation:

Answer:

The nth term of this number sequence 18, 16, 14, 12,... will be -2n + 20.

First term = 18

Second term = 16

Common difference = 16 - 18 = -2

It should be noted that the formula for finding the next term of an arithmetic sequence will be:

= a + (n - 1)d

= 18 + (n - 1) × -2

= 18 - 2n + 2

= -2n + 20

Therefore, the nth term of this number sequence 18, 16, 14, 12,... will be -2n + 20.

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Answer:

Step-by-step explanation:

y = 4x + 1

We can see that for each value of x substituted into this equation will give us a value for y .

For example , if we take x to be 4 , and put the value in this equation we get 4(4) + 1 = y

We get y = 17

Final answer:

The expression that represents the mass of two grains of salt, approximately one microgram or 0.000001g, in scientific notation is 1 x 10-6g.

Explanation:

The expression that represents the mass of two grains of salt, approximately one microgram or 0.000001g, in scientific notation is 1 x 10-6g.

Scientific notation is a way to express numbers that are extremely large or small in a more manageable format. In scientific notation, a number is written as a coefficient multiplied by a power of 10. The coefficient must be greater than or equal to 1 and less than 10, and the power of 10 represents how many places the decimal point needs to be moved to get the original number.

Answer:

two solutions

Step-by-step explanation:

it could be 5 or -5

Step-by-step explanation:

We need to write the following ratios with its simplest form.

1. [tex]\dfrac{21}{28}[/tex]    

Factors of 21 = 3, 7

Factors of 28 = 2, 7, 2  

[tex]\dfrac{21}{28}=\dfrac{3}{4}[/tex]  

2. [tex]\dfrac{96}{32}[/tex]    

Factors of 96 =  1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

Factors of 32 =  1, 2, 4, 8, 16, 32

[tex]\dfrac{96}{32}=\dfrac{3}{1}[/tex]

3. [tex]\dfrac{22}{33}[/tex]    

Factors of 22 = 1, 2, 11, 22

Factors of 33 =  1, 3, 11, 33

[tex]\dfrac{22}{33}=\dfrac{2}{3}[/tex]

4. [tex]\dfrac{12}{36}[/tex]    

Factors of 12 = 1, 2, 3, 4, 6, 12

Factors of 36 =  1, 2, 3, 4, 6, 9, 12, 18, 36

[tex]\dfrac{12}{36}=\dfrac{1}{3}[/tex]

5. [tex]\dfrac{72}{56}[/tex]    

Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56

[tex]\dfrac{72}{56}=\dfrac{9}{7}[/tex]

6. [tex]\dfrac{54}{63}[/tex]    

Factors of 54 = 1, 2, 3, 6, 9, 18, 27, 54

Factors of 63 = 1, 3, 7, 9, 21, 63

[tex]\dfrac{54}{63}=\dfrac{6}{7}[/tex]

Hence, this is the required solution.

Algebraic expression for three times the sum of a and b, then the expression would be; 3(a+b).

Simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.

Algebraic expression for three times the sum of a and b, then the expression;

Now put a + b in brackets because your multiplying a and b three times;

= 3(a+b)

Algebraic expression for three times the sum of a and b, then the expression would be; 3(a+b).

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Since it is in a 180 degrees... Flat line then we will 50 minus 180= 130.

this is your answer. D.) y=130

Answer:

As you remember from pre-algebra a coordinate plane is a two-dimensional number line where the vertical line is called the y-axis and the horizontal is called the x-axis. These lines are perpendicular and intersect at their zero points. This point is called the origin.

Step-by-step explanation:

Answer:

mhmmmmm

i need help on this too

Answer:

To calculate probability you have to understand that P = favorable cases / possible cases. So, your probability is 7/10 (Consider all the cards, have the same probability when you pick one).

Step-by-step explanation:

Which are your favorables cases

card 4, card 5, card 6, card 7, card 8, card 9, card 10

Which are you possible cases

The 10 cards.

Answer:

Step-by-step explanation:

This would be called the range.

Answer: Range describes the set of all possible output values for a function.

Step-by-step explanation:

Since we denote values for dependent variable as output values.

Thus , we call Range is the  set of all possible output values for a function.

Therefore, the term describes the set of all possible output values for a function : Range

Answer:you do 15 divided by 8

Step-by-step explanation:

Answer:  276 miles in 5 hours and 45 minutes

 5 x 48 = 240

240 + 36 = 276

Answer:

You would be able to travel 276 miles

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For this case we must represent the following expression algebraically:

"eight more than the product of a number and two"

Let "x" be the variable that represents the unknown number

We have to:

the product of a number and two is represented as: [tex]2x[/tex]

Then, the full expression will be:

[tex]2x + 8[/tex]

Thus, we use multiplication and addition.

ANswer:

Option C

Answer: multiplication and addition

Step-by-step explanation:

In mathematics we use addition(+) operation to show "sum", subtraction (-) to show "difference" , multiplication (×) operation to show "product" and divide (÷) to show "quotient".

Given mathematical statement : eight more than the product of a number and two

Here, we use addition(+) operation to show "more than" and multiplication (×) operation to show "product" .

Hence, the two operations are needed to write the expression that represents are : multiplication and addition

Answer:

Step-by-step explanation:

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Answer:

6i[tex]\sqrt{21}[/tex]

Step-by-step explanation:

Note that [tex]\sqrt{-1}[/tex] = i

Using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

Simplifying the radical, that is

[tex]\sqrt{-84}[/tex]

= [tex]\sqrt{4(21)(-1)}[/tex]

= [tex]\sqrt{4}[/tex] × [tex]\sqrt{21}[/tex] × [tex]\sqrt{-1}[/tex]

= 2 × [tex]\sqrt{21}[/tex] × i

= 2i[tex]\sqrt{21}[/tex]

Hence

3[tex]\sqrt{-84}[/tex]

= 3 × 2i[tex]\sqrt{21}[/tex]

= 6i[tex]\sqrt{21}[/tex]

Answer:

true

Step-by-step explanation:

Because as it go's down the other go's up

Answer:

5 inches

Step-by-step explanation:

a^2 + b^2 = c^2

12^2 + b^2 = 13^2

144 + b^2 = 169

b^2 = 25

b = 5

Jeremiah should start his cut 5 inches from P.

In the figure PQRS,

QR= 12 in. & PS = 13 in.

∠Q=∠R=90°

Now, Jeremiah will make exactly one straight cut from the top edge of the cardboard to point S in order to cut the cardboard into a rectangle.

Let, Jeremiah cut PQ at point M, where SM⊥PQ

∴ ∠SMP = 90°, so ΔSMP is a right angle triangle.

After draw SM, SMQR will a rectangle.

Then, SM = QR = 12 in.

By pythagoras theorem,

PS²= SM²+PM²

⇒ PM²= PS²-SM²

⇒ PM²= 13²-12²

⇒ PM²= 169-144

⇒ PM = √ (25)

⇒ PM = 5   (Negative value is not possible)

So, PM = 5 inches

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Answer:

B

Step-by-step explanation:

x^3-2x^2-5x+6

Answer:

its b

Step-by-step explanation:

Answer:

Option A is the correct answer.

Step-by-step explanation:

Here we need to factorize  x²+3x−18

The coefficient of x is 3 and the constant is -18

Which means

           The sum of factors is 3

           The product of factors is -18

The factors satisfying are  6 and -3

Here the factors are given in the type (x+)(x−)

     So the value after plus is 6 and value after - is 3

Option A is the correct answer.            

Answer:

6 and 3

Step-by-step explanation:

Answer:  6m

Step-by-step explanation:

GCF is Greatest Common Factor.

In other words, what is the biggest factor they have in common?

You can factor both terms down to their primes and compare them:

               24m                                     18m

                 ∧                                          ∧

             4    6    m                               2   9    m

            ∧     ∧    ↓                               ↓   ∧    ↓  

          2  2   2 3  m                             2  3 3   m  

24m: 2 · 2 · 2 · 3 · m

18m:  2 · 3 · 3 · m

What do they have in common?

24m: 2 · 2 · 2 · 3 · m         Common is 6m, leftover is 4

18m:  2 · 3 · 3 · m              Common is 6m, leftover is 3

I showed the leftover because you need that to find the LCM