16x+x =12 solve justify each step with algebraic property

Answers

Answer 1

Here are some things you should know when solving algebraic equations.
If you add an expression to both sides of an equation, the resulting equation will have the same solution set as the original equation. In other words, they will be equivalent. This is true for all operations. As long both sides are treated the same, the equation will stay balanced.
You will also need to know how to combine like terms. But what are like terms to begin with? Like terms are defined as two terms having the same variable(s) (or lack thereof) and are raised to the same power. In mathematics, something raised to the first power stays the same. So, 5x and 10x are like terms because they both have the same variable and are raised to the first power. You don’t see the exponents because it doesn’t change the value of the terms.
To combine like terms, simplify add the coefficients and keep the common variable(s) and exponent.
The distributive property is another important rule you will need to understand. The distributive property is used mostly for simplifying parentheses in expressions/equations.
For example, how would you get rid of the parentheses here?
6(x + 1)
If there wasn’t an unknown in between the parentheses, you could just add then multiply. That is what the distributive property solves. The distributive property states that a(b + c) = ab + ac
So, now we can simplify our expression.
6(x + 1) = 6x + 6

16x + x = 12
17x = 12 <-- Combine like terms
x = [tex]\frac{12}{17}[/tex]

So, x is equal to 12/17 or approximately to 0.7.

Related Questions

Jacks has 18 marbles,he loses 6 of them.

What fraction of the marbles does he lose?

Answers

6/18
1/3

Hope this helps!

The sample variance is 18.7. what is the sample standard deviation? answer to two decimal places.

Answers

I think that the sample standard might be 18.5 and 19, but, I might be very wrong.

find the Factor of
48m - 80n.

Answers

48m = 16(3m)
80n = 16(5n)

so
48m - 80n = 16(3m - 5n)

Distributive property of 68/4

Answers

Start with 68/4. Rewrite 68 as (4)(17)/4. Cancel the 4s. Result: 17.

The trick here is to rewrite 68 as 4(17).

What is the value of x?

6 + 8x
-------------- = 5x
2

A) -2
B) -1
C) 1/3
D) 3

Answers

The ans is choice D. since there nothing under 5x, imagine there is a 1 under. After that, you can simply cross multiply, so it would be 1(6+8x)= 2(5x). 6+8x= 10x now combine like terms so subtract 8x from both sides and divide 6 by 2 and you will get 3

I just took the test the answer is D.3

How do write 21,070 in standard form

Answers

2.107 times 10^4 is the answer to your question

Final answer:

The number 21,070 is already in standard form. Standard form is a straightforward expression of a number as commonly written, without the need for scientific notation for simple numbers like this one.

Explanation:

The number 21,070 written in standard form is simply 21,070 itself. In mathematics, standard form refers to the way a number is commonly written. This number is already in standard form because it is expressed in a direct and straightforward manner. There is no need for further simplification or conversion. When numbers are very large or very small, they can be cumbersome to write out in full, which is why scientists and mathematicians may use scientific notation to express them.

For instance, if we had a larger number like 77,123,450, we could write it in scientific notation as 7.712345 × 10⁷, emphasizing that it is 7.712345 times ten to the seventh power.

For the provided number 21,070, no such conversion is necessary, and it remains 21,070 in standard notation.

what is (9x^4-x^2y^2-5y^4)-(3x^4+2x^2y^2-7y^4)

Answers

(9x⁴ - x²y² - 5y⁴) - (3x⁴ + 2x²y² - 7y⁴)
9x⁴ - x²y² - 5y⁴ - 3x⁴ - 2x²y² + 7y⁴
6x⁴ - 3x²y² + 2y⁴

Solve the system using the elimination method.

2x + y − z =9

−x + 6y + 2z =−17

5x + 7y + z =4

Whats x, y, and z???

Answers

By adding the 1st and third equation together, you get rid of z and end with 7x+8y=13. The second equation will be the second equation and 2 times the first equation, so the will yield 3x+8y=1. Now, you solve this system of equations and get x3, y=-1, and z=-4

Final answer:

Using the elimination method, the given system of equations leads to a solution of x = -1, y = 1, and z = -2.

Explanation:Solving the SystemThe first step in solving this system of equations using the elimination method is to try and eliminate one of the variables. Let's start with eliminating 'z' by adding the first and the third equation: [tex](2x + y - z) + (5x + 7y + z) = 7x + 8y = 13.[/tex]Now we can eliminate 'z' from the second equation as well by subtracting from it twice the first one:[tex]-(-x + 6y + 2z) - 2(2x + y - z) = -3x + 4y = -5.[/tex]Then we solve the new system of two equations: 7x + 8y = 13 and -3x + 4y = -5. Using substitution or elimination on this will give y = 1Substituting y = 1 into the equation -3x + 4y = -5 gives x = -1.Finally, substituting x = -1 and y = 1 into the first original equation 2x + y - z = 9 gives z = -2. So, the solution is x = -1, y = 1, z = -2.

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There are six different sixth roots of 64. That is, there are six complex numbers that solve x^6=64

Please help

Answers

There are two possible solutions:

1)
When we know that:

[tex]\sqrt[n]{z}=\sqrt[n]{|z|}\Big(\cos\frac{\phi+2k\pi}{n}+i\sin\frac{\phi+2k\pi}{n}\Big)\qquad\text{for}\quad k=0,1,\ldots,n-1[/tex]

when [tex]z=|z|(\cos\phi+i\sin\phi)[/tex]

then:

[tex]x^6=64\quad|\sqrt[6]{(\ldots)}\\\\x=\sqrt[6]{64}[/tex]

For [tex]x=64[/tex] we have:

[tex]64=|64|(\cos0+i\sin0)\quad\Rightarrow\quad \phi=0[/tex]

and:

[tex]\sqrt[6]{64}=\sqrt[6]{64}\Big(\cos\frac{0+2k\pi}{6}+i\sin\frac{0+2k\pi}{6}\Big)\qquad\text{for}\quad k=0,1,\ldots,5\\\\\\ \sqrt[6]{64}=2\Big(\cos\frac{k\pi}{3}+i\sin\frac{k\pi}{3}\Big)\qquad\text{for}\quad k=0,1,\ldots,5 [/tex]

k = 0

[tex]2\Big(\cos\frac{0}{3}+i\sin\frac{0}{3}\Big)=2(1+0i)=2\cdot1=\boxed{2}[/tex]

k = 1

[tex]2\Big(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\Big)=2\Big(\frac{1}{2}+i\frac{\sqrt{3}}{2}\Big)=\boxed{1+i\sqrt{3}}[/tex]

k = 2

[tex]2\Big(\cos\frac{2\pi}{3}+i\sin\frac{2\pi}{3}\Big)=2\Big(-\frac{1}{2}+i\frac{\sqrt{3}}{2}\Big)=\boxed{-1+i\sqrt{3}}[/tex]

k = 3

[tex]2\Big(\cos\frac{3\pi}{3}+i\sin\frac{3\pi}{3}\Big)=2\Big(\cos\pi+i\sin\pi\Big)=2(-1+0i)=\boxed{-2}[/tex]

k = 4

[tex]2\Big(\cos\frac{4\pi}{3}+i\sin\frac{4\pi}{3}\Big)=2\Big(-\frac{1}{2}-i\frac{\sqrt{3}}{2}\Big)=\boxed{-1-i\sqrt{3}}[/tex]

k = 5

[tex]2\Big(\cos\frac{5\pi}{3}+i\sin\frac{5\pi}{3}\Big)=2\Big(\frac{1}{2}-i\frac{\sqrt{3}}{2}\Big)=\boxed{1-i\sqrt{3}}[/tex]

So the answer is:

[tex]x=\{2,\,1+i\sqrt{3},\,-1+i\sqrt{3},\,-2,\,-1-i\sqrt{3},\,1-i\sqrt{3}\}[/tex]

2)
We don't know method (1). If so, we could use following identities:

[tex](1)\quad a^2-b^2=(a+b)(a-b)\\\\(2)\quad a^3-b^3=(a-b)(a^2+ab+b^2)\\\\(3)\quad a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]

There will be:

[tex]x^6=64\\\\x^6-64=0\\\\(x^3)^2-8^2=0 \qquad\text{from (1)}\\\\(x^3+8)(x^3-8)=0\\\\(x^3+2^3)(x^3-2^3)=0\qquad\text{from (2) and (3)}\\\\ (x+2)(x^2-2x+4)(x-2)(x^2+2x+4)=0\qquad(\star)[/tex]

Now, we complete the square for:

[tex]x^2-2x+4=x^2-2x+1+3=(x^2-2x+1)+3=(x-1)^2+3=\\\\=(x-1)^2+(\sqrt{3})^2=(x-1)^2-(-1)(\sqrt{3})^2=(x-1)^2-i^2(\sqrt{3})^2=\\\\=(x-1)^2-(i\sqrt{3})^2=\text{from (1)}=\boxed{(x-1-i\sqrt{3})(x-1+i\sqrt{3})}[/tex]

and for:

[tex]x^2+2x+4=x^2-2x+1+3=(x^2+2x+1)+3=(x+1)^2+3=\\\\=(x+1)^2+(\sqrt{3})^2=(x+1)^2-(-1)(\sqrt{3})^2=(x+1)^2-i^2(\sqrt{3})^2=\\\\=(x+1)^2-(i\sqrt{3})^2=\text{from (1)}=\boxed{(x+1-i\sqrt{3})(x+1+i\sqrt{3})}[/tex]

When we return to [tex](\star)[/tex]:

[tex](x+2)(x^2-2x+4)(x-2)(x^2+2x+4)=0\\\\(x+2)(x-1-i\sqrt{3})(x-1+i\sqrt{3})(x-2)(x+1-i\sqrt{3})(x+1+i\sqrt{3})=\\=0[/tex]

And we have answer:

[tex]x=\{-2,\,1+i\sqrt{3},\,1-i\sqrt{3},\,2,\,-1+i\sqrt{3},\,-1-i\sqrt{3}\} [/tex]

To find the six sixth roots of 64, you can use polar form and De Moivre's Theorem to calculate the complex numbers. The roots are 2, 1+i√3, -1+i√3, -2, -1-i√3, and 1-i√3.

[tex]X^6 = 64[/tex]

The sixth roots of 64 are complex numbers and can be found by writing 64 in polar form and applying De Moivre's Theorem. Let's find the six roots:

First root: 2(cos(0) + i sin(0)) = 2

Second root: 2(cos(π/3) + i sin(π/3)) = 2(1/2 + i√3/2) = 1 + i√3

Third root: 2(cos(2π/3) + i sin(2π/3)) = 2(-1/2 + i√3/2) = -1 + i√3

Fourth root: -2

Fifth root: -2(cos(-π/3) + i sin(-π/3)) = -2(1/2 - i√3/2) = -1 - i√3

Sixth root: -2(cos(-2π/3) + i sin(-2π/3)) = -2(-1/2 - i√3/2) = 1 - i√3

I have 5 digits. My 4s are worth 4 [10,000s] and 4 * 10. One of my 3s is worth 3,000. The other is worth 1/10 as much. My other digit is a 2. What number am I?

Answers

The given information are actually the digits and their place values in multiples of 10. To know the identity of the number, simply multiply the digit with its place value. The solution is as follows:

4(10,000) + 4(10) + 3,000 + 3,000(1/10) + 2 = 43,342

Thus, the 5-digit number is 43,342.

domain of the function

Answers

hello :
y exist : x+6 ≥ 0
x ≥ -6

How many pairs of whole numbers have a sum of 99

Answers

does anyone know lol

44 pairs. I believe that's the right answer.

What is 8.038×108 in standard form?

80,308,000

80,380,000

83,800,000

803,800,000

Answers

Okay. I think what you mean by this is 8.038 * 10^8. 10^8 = 100,000,000. When you multiply that by 8.038, you get 803,800,000. The answer is D.

Answer:

803,800,000

Step-by-step explanation:

8.038×10^8 in standard form

To get standard form we multiply the decimal number by 10^8

10^8 is 100000000

Now we multiply

8.038×100000000

Move the decimal number 3 places to the right and add 5 more zeros

803800000

So the standard form of the given expression is

803,800,000

Use the function below to find f(4).

Answers

f(x) = 1/3 * 4^x.......f(4)....so we sub in 4 for x
f(4) = 1/3 * 4^4
f(4) = 1/3 * 256
f(4) = 256/3 <===

Answer: The correct option is (C) [tex]\dfrac{256}{3}.[/tex]

Step-by-step explanation: The given function is

[tex]f(x)=\dfrac{1}{3}\times 4^x.[/tex]

We are to find the value of f(4).

To find the value of f(4), we need to substitute the value of x as 4 in the given definition of function f(x).

Substituting x = 4 in f(x), we have

[tex]f(4)=\dfrac{1}{3}\times 4^4=\dfrac{1}{3}\times 256=\dfrac{256}{3}.[/tex]

Therefore, the value of f(4) is [tex]\dfrac{256}{3}.[/tex]

Option (C) is correct.

Which of the following is a true equation?

1) 10 + 3 + 1 = 13 + 6
2) 4 - 3 = 7
3) 4 + 3 - 3 = 7 - 3
4) 4 + 3 = 7 + 3

Answers

4 + 3 - 3 = 7 - 3
4 = 4

answer

3) 4 + 3 - 3 = 7 - 3

Tyquan uses the greatest common factor and the distributive property to rewrite this sum: 75 + 60 What expression does Tyquan write? 3(25 + 20) 5(15 + 12) 25(3 + 60) 15(5 + 4)

Answers

the GCF of 75 and 60 is 15

75/15 = 5
60/15 = 4

so ur expression is : 15(5 + 4) <==

The answer is 15(5+4)

Find the range of the graphed function?

Answers

for finding range pay attention to y axis max of function is 5 and its min is -9
B is true

B is the correct answer

Express each repeating decimal as a fraction.

1.
1.8[4]

2.
2.1[26]

Answers

Hello,

1.8444444....=1.8+1/10*0.44444....
=1.8+1/10*4/9
=1.8+4/90
=162/90+4/90
=166/90
=83/45

2.126262626...=2.1+1/10*0.262626...
=2.1+1/10*26/99
=2.1+26/990
=2079/990+26/990
=2105/990
=421/198

Answer:

1.8444444....=1.8+1/10*0.44444....

=1.8+1/10*4/9

=1.8+4/90

=162/90+4/90

=166/90

=83/45

2.126262626...=2.1+1/10*0.262626...

=2.1+1/10*26/99

=2.1+26/990

=2079/990+26/990

=2105/990

=421/198

Solve For L: A = L ⋅ W ⋅ H

L=aw/h

L=wh/a

L=a/wh

L=w/ha

Answers

Ok so what you're trying to do is get L by itself so to do this you move everything to the other side:
A=L*WH
[tex] \frac{A}{WH} [/tex]=L
So you answer would be: C

your answer would be the third one C

Store A advertises a sale for 3 loaves of bread for $5.94. Explain how to use an equivalent rate to find the unit price of the bread at Store A.

Answers

Answer: I wrote the rate, with $5.95 in the numerator and 3 loaves in the denominator. I needed to find an equivalent rate expressed as a fraction with the denominator of 1. I noticed 3 loaves divided by 3 gave a denominator of 1, so I divided $5.94 by 3 to find that each loaf costs $1.98.

Just did it on Edge 2021

Btw Can you mark me brainlest pls

The equivalent rate of the bread is $1.98.

Since the store advertises a sale for 3 loaves of bread for $5.94, in order to find the equivalent rate, the person has to divide $5.94 by 3. This will be:

= $5.94/3

= $1.98

Therefore, the equivalent rate of the loaves of bread will be $1.98

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What is the value of x? 58 92 121 63

Answers

(184-58)/2 = x
126/2 = x
63 = x

Answer:

Angle x = 63 °.

Step-by-step explanation:

Given : A circle larger arc angle 184° and smaller arc angle 58°.

To find: What is the value of x.

Solution : We have given that larger arc angle 184°

Smaller arc angle 58°.

Angle formed by tangent and chord = x

m∠x = [tex]\frac{1}{2}( 184 - 58 )[/tex].

m∠x = [tex]\frac{1}{2}( 126)[/tex].

m∠x = 63 °.

Therefore, Angle x = 63 °.

A right triangle has one angle that measure 23o. The adjacent leg measures 27.6 cm and the hypotenuse measures 30 cm. What is the approximate area of the triangle? Round to the nearest tenth. Area of a triangle = bh

Answers

Answer:

162.8 cm²

Step-by-step explanation:

The formula for the area of a triangle is

A = 1/2bh, where b is the base and h is the height.

The base can be represented as the given leg, 27.6 cm. We do not know the height. We must use the Pythagorean theorem to find this:

a²+b² = c²

27.6²+b² = 30²

761.76+b² = 900

Subtract 761.76 from each side:

761.76+b²-761.76 = 900-761.76

b² = 138.24

Take the square root of each side:

√(b²) = √(138.24)

b = 11.8

Now we use the area formula:

A = 1/2(11.8)(27.6) = 162.84 ≈ 162.8

The area of a given right triangle is 162.8 cm².

What is area?

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

Given that, the base can be represented as the given leg, 27.6 cm. We do not know the height.

Using Pythagorean theorem,

a²+b² = c²

27.6²+b² = 30²

761.76+b² = 900

761.76+b²-761.76 = 900-761.76

b² = 138.24

b = √(138.24)

b = 11.8

The formula for the area of a triangle is

A = 1/2bh, where b is the base and h is the height

A = 1/2(11.8)(27.6) = 162.84 ≈ 162.8

Therefore, the area of a given right triangle is 162.8 cm².

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Simplify the expression 3 1/3/3 1/3. Explain how the expression and its simplified form show that the set of irrational numbers is not closed under division

Answers

The expression given is ambiguous according to the standard rules of math (PEMDAS) due to the lack of appropriate parentheses and probably the exponentiation symbol ^.

From the context, I assume it to mean
(3^(1/3)) / (3^(1/3)) = 1

Since 3^(1/3) is the cube-root of 3, and is thus irrational.
However, the quotient is exactly 1, which is a rational number.

The example is therefore a counter-example for the statement that "set of irrational numbers is closed under division", or stated differently,
"the set of irrational numbers is not closed under division"

Besides the 90° angle measure, what are the other two angle measures of a right triangle with side lengths 5, 12, and 13? Round to the nearest degree.

Answers

In the right triangle, the longest side is the hypotenuse.
Let α be the angle opposite to the side with a length of 12 units, then according to the Law of sines:

[tex] \frac{13}{sin90^o}= \frac{12}{sin \alpha } \ \ \to \ \ sin \alpha = \frac{12 \cdot sin90^o}{13}= \frac{12*1}{13} \approx 0.923 \ \ \to \ m\angle \alpha \approx 67^o[/tex]

In a triangle, the three interior angles always add to 180° ⇒

third angle = 180 - 90 - 67 = 23°

Answer:
67° and 23° (to the nearest degree).

The other two angles are 23 degrees and 67 degrees.

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given,

Given a right angled triangle with one angle 90 degrees.

We need to find the other two angle measures of a right triangle with side lengths 5, 12, and 13

The relations in a right triangle are given as follows:

The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.

The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.

The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.

In this problem, the hypotenuse is the largest size of 13.

The angle opposite to the side of length 5 is found as follows:

sinθ=5/13

θ=sin⁻¹5/13

θ=23

By angle sum of 3 angles is of 180º, the other angle is of 67º.

Hence, the other two angles are 23 degrees and 67 degrees.

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A coin is tossed 10 timesWhat is the probability of getting all heads?

Answers

The probability of getting all heads is 1/2

there is two sides, one head an one tail, or 1/2 chance of getting heads

Tossed 10 times, it still has 1/2

hope this helps

In the numer 6,666.666 how does the 6 in the hundredths place compare to 6 in the place to its left

Answers

the six to the left is worth more than the six in the hundredths

hope

i helped

0.06 vs 0.6
the 6 in the hundreths place is 1/10 the value of the 6 in the place to the left

McDonald's is the king of the burger world, as it has more hamburger joints than any other restaurant chain. In 2013, McDonald's had 1427 locations in Canada. If the population of Canada was approximately 35.16 million citizens in 2013, what was the number of McDonald's restaurants per capita in Canada in 2013? Express your answer in scientific notation rounded correctly to three decimal places.

Answers

Sent you a picture of the solution.

In 2013, there were approximately 4.509 McDonald's restaurants per 100,000 people in the US.

To calculate the number of McDonald's restaurants per capita in the US in 2013, we divide the total number of McDonald's locations (14267) by the population of the US (316,500,000).

[tex]\[ \text{McDonald's per capita} = \frac{14267}{316500000} \][/tex]

Performing the division, we get [tex]$ 4.509 \times 10^{-5} $[/tex].

This means there were approximately 4.509 McDonald's restaurants per 100,000 people in the US in 2013.

So, the number of McDonald's restaurants per capita in the US in 2013 is [tex]$ 4.509 \times 10^{-5} $ or $ 4.509 \times 10^{-5} $[/tex] McDonald's per person.

Bess practices trumpet 1/2 hr on Monday and 1 3/5 hr on Wednesday.

How many hours does Bess practice trumpet?

Answers

She practice for 2.1 or 2 1/10

She practiced for 2.1 hours total

The tensile strength of paper is modeled by a normal distribution with a mean of 35 pounds per square inch and a standard deviation of 2 pounds per square inch. what is the probability that the strength of a sample is less than 38 lb/in2? round your answer to 4 decimal places.

Answers

Given
mean=35 psi
std dev=2 psi
distribution normal

For probability that X<38,
calculate
Z score = (X-mean)/std dev
=(38-35)/2=1.5
P(X<38)
=P(Z<1.5)
=0.9331928 from tables.

So probability that the strength of a random sample <38 pis = 0.9332

Joe has 310 baseball cards. He writes the number of cards in expanded form. How many ones will he write?

Answers

Uh,.... it's 310. Still.

Answer:

The expanded form of 310 is:

310 = 300 + 10.

Joe will write two numbers to form 310.

Step-by-step explanation:

The expanded form is used to write numbers and see the math value of individual digits. So, the numbers are separated into individual place values and decimal places and form a mathematical expression.

310 in expanded form is 300 + 10 = 310.

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