Is x = 6 a solution to the equation 5(x – 3) = x + 13?
Follow the steps to find out.

1. Rewrite the equation 5(x – 3) = x + 13 with 6 substituted for x. Write a question mark over the equal sign to show that you're testing to see if the equation is true.

Write your answer in the space below.


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Answer:

A

Step-by-step explanation:

Given :

2x + 4y = 14  ---------- eq 1

4x + y = 20 ---------- eq 2

if you multiply eq 2 by -4 on both sides, you get

-4 (4x + y = 20) = -4 (20)

-16x -4y = -80 --------- eq3

we can see that eq. 1 and eq 2 together forms the system of equations presented in option A, Hence A is equvalent to the orginal system of equations given in the question.

The system of equations which is equivalent to the [tex]2x + 4y = 14[/tex],[tex]4x + y = 20[/tex]  is given in option [tex](A)[/tex] i.e. [tex]2x + 4y = 14[/tex] and [tex]-16x - 4y = -80[/tex].

System of equations comprises of two or more equations and seeks common solutions to the equations.

We have,

[tex]2x + 4y = 14[/tex]   [tex]........(i)[/tex]

  [tex]4x + y = 20[/tex]    [tex]........(ii)[/tex]

Now,

To check that which option suits best for system of equation,

Lets multiply equation [tex](ii)[/tex] by [tex](-4)[/tex],

  [tex](-4) (4x + y) = (-4)*(20)[/tex]

[tex]-16x-4y=-80[/tex],

So, this above obtained equation is in option  [tex](A)[/tex].

Hence, we can say that the system of equations which is equivalent to the [tex]2x + 4y = 14[/tex] ,[tex]4x + y = 20[/tex] is given in option [tex](A)[/tex] i.e. [tex]2x + 4y = 14[/tex] and [tex]-16x - 4y = -80[/tex].

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Answer:

The product is;

(80x^2-560x+ 980)/9

Step-by-step explanation:

Here, we want to get the product of the two smaller numbers

let the mid number be y

3/4 = 2x-7/y

3y = 8x-28

y = (8x-28)/3

Let the biggest be z

3/5 = 2x-7/z

3z = 10x -35

z = (10x-35)/3

The product of the two other numbers is thus;

(10x-35)/3 * (8x-28)/3

= (10x-35)(8x-28)/9

(80x^2-280x - 280x + 980)9

= (80x^2 - 560x + 980)/9

Answer: A is the right angle

Step-by-step explanation:

a. 20^2 + 15^2 = 25^2

400 + 225 = 625

625 = 625

hope this helps :)

I've attached an image showing the data relationship.

Answer:

1) y does not change based on changes in x: no-correlation

2) y tends to increase as x increases: positive correlation

3) y tends to decrease as x increases: negative correlation

Step-by-step explanation:

1) y does not change based on changes in x: This means that there is no correlation between y and x since change in x doesn't affect y.

2) y tends to increase as x increases: This implies positive correlation because the output increases with increase in input.

3) y tends to decrease as x increases: This implies negative correlation because the output decreases with increase in input values.

Answer:

y tends to decrease as x increases: negative!

y tends to increase as x decreases: positive!

y does not change based on changes in x: no correlation!

Step-by-step explanation:

:))

We know that m ║ n.

Let's first find the value 'x'.

When two lines are parallel, and a transversal is drawn, the angles on the same side of the transversal are equivalent.

This means that (5x + 16)° and (7x + 4)° are equivalent.

Equating them,

5x + 16 = 7x + 4

16 - 4 = 7x - 5x

12 = 2x

x = 12/2

x = 6°

Since we know the value of 'x', let's substitute them into the angles and find out the actual measurements.

5x + 16 = 5 × 6 + 16 = 30 + 16 = 46°.

7x + 4 = 7 × 6 + 4 = 42 + 4 = 46°.

Now let's find the value of 'y'.

If you observe carefully, (7x + 4)° and (y + 6)° form a linear pair.

This means that both those angles should add upto 180°.

Using that theory, the following equation can be framed:

(y + 6)°+ (7x + 4)° = 180°

Since we know the actual value of (7x + 4)°, let's substitute that value and move ahead.

(y + 6)° + 46° = 180°

y + 6 + 46° = 180

y + 52° = 180°

y = 180° - 52°

y = 128°

Therefore, the values of 'x' and 'y' are 46° and 128° respectively.

Hope it helps. :)

Answer:

Noah mistakenly added 25 and 7 in denominator instead of subtracting in the third step.

Step-by-step explanation:

Noah had to rationalize the denominator of [tex]\frac{32}{5-\sqrt{7}}[/tex]

According to him,

[tex]\frac{32}{5-\sqrt{7} = \frac{32(5+\sqrt{7}{(5-\sqrt{7})(5+\sqrt{7}[/tex]

Solving the nominator and denominator

[tex]= \frac{160-32\sqrt{7}}{25+5\sqrt{7}-5\sqrt{7}-7}[/tex]

Noah did correctly till this point.

In the next step he add 25 and 7 in the denominator, whereas, it should be subtracted.

Hence,

Noah mistakenly added 25 and 7 in denominator instead of subtracting in the third step.

Answer:

YD=6.9

Step-by-step explanation:

In an isosceles trapezoid both diagonals have an equal length. Given this, since diagonal AC is equal to 17.2, diagonal BD must be equal to 17.2. Diagonal BD is made up of segments BY and YD, so the lengths of BY and YD must add to equal 17.2. Since BY is 10.3, the equation YD+10.3=17.2 can be used to find the value of YD. To solve this, subtract 10.3 from both sides of the equation to find that YD is equal to 6.9.

Answer:

20,000

Decay

8%

Step-by-step explanation:

The inital value is the value at time = 0

The equation represents decay which is shown because as t approaches infinity the equation equals 0

It changes by 8 percent (1-.92)

If you have any questions please let me know.

Answer:

Initial value at t=0 is 20,000

Function represent decay with time

Changing 8%/year

Step-by-step explanation:

[tex]v(o)=20000(0.92)^{0}=20000[/tex]

Answer:

1.875

Step-by-step explanation:

Answer:

15/8 simplified = 1 7/8

Step-by-step explanation:

an easier way to divide fractions is to convert all into a improper fraction like this 1 1/4 > 1x4+1= 5/4 since 2/3 isnt mixed keep it ok so now you have 5/4 divided by 2/3 next you take the fraction on the right and flip then multiply it to get 5/4 x 3/2 then you multiply across to get 15/8 then change that to a mixed number by dividing 15 by 8 to get 1 with a remainder of 7 so 1 7/8 is your answer

hope this helps you in the future have a blessed day!

Answer:

37%

Step-by-step explanation:

Use the general addition rule for any two events:

(32 + 28) - 23

60 - 23

= 37

So, the probability that someone has a dog or cat is 37%

Answer:

37%

Step-by-step explanation:

32 + 28 = 60

60 - 23 = 37

Answer:

2√133

Step-by-step explanation:

a²+b²=c²

8²+12²=c²

c²=208

208+18²=532

√532=23

Answer:

[tex]2 \sqrt{ - 2 } [/tex]

maybe?

Answer: x^15

Step-by-step explanation:

You multiply 5 times 3

Answer:

The answer is B

Step-by-step explanation:

Answer:

x = 13

Step-by-step explanation:

54 divided by (13 + 5) = 3

Answer:

x = 13

Step-by-step explanation:

Answer:

y= -4

Step-by-step explanation:

y=3x-1

y=3(-1)-1

y=-3-1

y= -4

Answer: 508.68 inches

Step-by-step explanation:

The volume of a cylinder is written as:

= πr²h

where,

π = 3.14

r = 9

h = 2

Volume = πr²h

= 3.14 × (9²) × 2

= 3.14 × 81 × 2

= 508.68

Answer:

No, P(A) ≠ P(A|B)

Step-by-step explanation:

Condition must be held in order to two events be independent of each other:

[tex]P(A B) = P(A)P(B) => P(A) = P(A|B)\\Or\\P(B) = P(B|A)[/tex]

[tex]P(A)=\frac{42}{81}\\P(B) =\frac{46}{81}\\P(A B) = \frac{20}{81}\\P(A|B) =\frac{P(A B)}{P(B)} = \frac{20}{46} \neq P(A) => P(AB) = \frac{20}{81} \neq P(A)P(B) = \frac{23}{81}\\\\P(B|A)=\frac{P(AB)}{P(A)}=\frac{20}{42} \neq P(B) => P(AB) = \frac{20}{81} \neq P(A)P(B)= \frac{23}{81}\\\\[/tex]

Note: (AB) means (A ∩ B)

The probability of P(A) is not equal to the probability of P(A|B) option third No, P(A) ≠ P(A|B) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.

Two events must be independent of each other, condition must be maintained:

P(A and B) = P(A) × P(B)

The probability:

P(A) = 42/81

P(B) = 46/81

P(AB) = 20/81

P(A|B) = P(AB)/P(B) = 20/46 ≠ P(A) = 20/81 ≠ P(A)P(B) = 23/81

P(B|A) = P(AB)/P(A) = 20/42 ≠ P(B) = 20/81 ≠ P(A)P(B) = 23/81

Thus, the probability of P(A) is not equal to the probability of P(A|B) option third No, P(A) ≠ P(A|B) is correct.

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Answer:

30cm^2

Step-by-step explanation:

area of triangle- 1/2xAxB

1/2(5x12)

0.5x60=30

Answer:

It is the last one

Step-by-step explanation:

To find the price for one you would divide 36.90 by 9 and to find the equation it is asking for you do the opposite which is 9p=36.90

Answer:

The answer is 9p=36.90

Step-by-step explanation:

Hope this helps!

Answer:

x=2

Step-by-step explanation:

2x - 6= -2

   +6    +6

2x= 4

/2    /2

x=2

Answer:

Answer: x^2 +14x+49

Step-by-step explanation:

Answer:

ok 120

Step-by-step explanation:

Answer:

The slope is [tex] \frac{7}{10} [/tex]

Step-by-step explanation:

☆Remember:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]

☆We just plug in now!

[tex]m = \frac{8 - 1}{4 - ( - 6)} = \frac{7}{10} [/tex]

Answer:A

Step-by-step explanation:I took the test already trust me

Answer:

The answer is C

Step-by-step explanation: