Solve the following equation for the variable.
x + 7 = 12

Step-by-step explanation:

(a + b)(5a – 3b) + (a – 3b)(a – b)

Expand each of the terms separately

That's

(a + b)(5a – 3b) = 5a² - 3ab + 5ab - 3b²

= 5a² + 2ab - 3b²

(a – 3b)(a – b) = a² - ab - 3ab + 3b²

= a² - 4ab + 3b²

Add the terms

That's

5a² + 2ab - 3b² + a² - 4ab + 3b²

Group like terms

5a² + a² + 2ab - 4ab - 3b² + 3b²

We have the answer as

(a – b) (a² + b² + ab) – (a + b) (a² + b²– ab)

Expand the terms separately

For (a – b) (a² + b² + ab)

Using the rule

x³ - y³ = (x - y)( x² + xy + y²) expand the expression

So we have

(a – b) (a² + b² + ab) = a³ - b³

For (a + b) (a² + b²– ab)

Using the rule

x³ + y³ = (x + y)( x² - xy + y²) expand the expression

We have

(a + b) (a² + b²– ab) = a³ + b³

Subtract the terms

That's

a³ - b³ - (a³ + b³)

Remove the parenthesis

a³ - b³ - a³ - b³

Group like terms

a³ - a³ - b³ - b³

We have the final answer as

(b² – 49) (b + 7) + 343

Expand the terms

That's

b³ + 7b² - 49b - 343 + 343

We have the final answer as

Hope this helps you

Answer:

this is a hard one can u explain it more

Step-by-step explanation:

Answer: Hi!

An exponent is is a number that represents how many times a number is being multiplied by itself. It is shown as either a small number positioned on the top tight of a term or the symbol ^ between the term and the exponent. For example, if you had 4 to the power of 2, you would multiply 4 by itself 2 times. 4 * 4 is equal to 16.

Hope this helps!

Answer:

What are the list of answers for this question? That would kind of help narrow some of my answers down.

Step-by-step explanation:

Answer:

Hey there!

The census never asks any questions about D. Spending Habits.

Let me know if this helps :)

Answer:

Your answer will be D

Answer:

0.1[tex]\frac{}{6}[/tex]

Step-by-step explanation:

When Juan cut a 1 lb loaf of banana bread into 6 slices, the weight of each slice forms a repeating decimal. A repeating decimal is a decimal number with repeating digit/s.

i.e [tex]\frac{1}{6}[/tex] = 0.166666666666666...

To express the total weight for each slice, he should write a bar over 6 to show that the number repeats.

i.e [tex]\frac{1}{6}[/tex] = 0.1[tex]\frac{}{6}[/tex]

Note that [tex]\frac{}{6}[/tex] has expressed that the division has 6 as the repeating digit in the decimal number.

Answer:

C. 64

Step-by-step explanation:

x° = 1/2[(360° - 2*58°) -2*58°]

x° = 1/2[(360° - 116°)- 116°]

x° = 1/2[244°- 116°]

x° = 1/2[128°]

x° = 64°

x = 64

Answer:

6

Step-by-step explanation:

Let thee number be x

Square of number: x²

Product of 6 and square of number = 6 *x² = 6x²

Expression: 6x² + 15

Coefficient of x² = 6

The value of the coefficient will be 6 for the expression.

A numerical or constant quantity placed before and multiplying the variable in an algebraic expression.

Let thee number be x

Square of number: x²

Product of 6 and square of number

[tex]= 6 \times x^2 = 6x^2[/tex]

Expression will be

[tex]6x^2 + 15[/tex]

Coefficient of x² will be = 6

hence the value of the coefficient will be 6 for the expression.

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Answer:

Hey there!

4a-3=D

4a=D+3

a=(D+3)/4

Let me know if this helps :)

a) n² + 6

n=1

1² + 6 = 1 + 6 =7

n=2

2² + 6 = 4 + 6 = 10

n=3

3² + 6 = 9 + 6 =15

n=4

4² + 6 = 16 + 6 =22

7, 10, 15, 22

n=10

10² + 6 = 100 + 6 =106

10 th term-106

b) 3n²

n=10

3 x 10² = 3 x 100= 300

10th term- 300

Hope this helps!

5(x + 2) is the product of a constant factor 5 and a 2-term factor (x + 2 )

It gets the result:   5(x+2) = 5•x + 5•2 = 5x + 10

Answer:

y = - 4x - 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 4, thus

y = - 4x + c ← is the partial equation

To find c substitute M(- 2, 1) into the partial equation

1 = 8 + c ⇒ c = 1 - 8 = - 7

y = - 4x - 7 ← equation of line

Answer:

y = 12

Step-by-step explanation:

The first step is to determine the perimeter of triangle TUV. We know side UV has a length of 20 cm and that the triangle is equilateral, so all sides have the same length. Thus the perimeter of the triangle must be 20 cm * 3 = 60 cm

The perimeter of PQRS is the sum of the lengths of sides PQ, QR, RS, and SP in cm.

PQ = y + 6

QR = 9 (given in diagram)

RS = 2y

SP = 9 (the diagram shows that it has the same length as QR)

Together they must add up to 60 cm to match the perimeter of the triangle, so:

PQ + QR + RS + SP = 60

(y + 6) + 9 + 2y + 9 = 60

3y + 24 = 60

3y = 36

y = 12

Answer:

B) monomial

Step-by-step explanation:

If there is only one term in an expression, then it is monomial

A monomial is a real number, a variable, or a product of

a real number and one or more variables.

Since -6 is a real number, it's a monomial.

Answer:

First, you fill the 6L cup.

Then you add everything to the 10L. There would be a difference of 4L.

You put a line on the 6L added. And then you fill it up until it completes the 10L. Repeat the process 2 times adding water up to 10L and adding the 4L difference to the recipe.

Step-by-step explanation:

- 8L are needed for a recipe.

- You have a 6L jug and a 10L jug without graduation.

- You fill the 6L of the jug and put it in the 10L jug, and put a line that marks the 6L.

- Then you complete the 10L, empty until the water is with the same 6L of water, and repeat the process.

- So you complete 4L without having graduated jugs.

Answer:

r = 1

Step-by-step explanation:

We can combine like terms, getting -3r = -3.

Then we can divide both sides by -3, and get r = 1.

Answer:

r = 1

Step-by-step explanation:

First, we'll simplify

-5r + 2r = -3

-3r = -3

Then, we divide

-3 divided by - 3 is equal to 1

Therefore, r = 1

Hope this helps!

==========================================================

Explanation:

There are two methods you could use. The first method involves the remote interior angle theorem. This says the remote interior angles (the two y angles) add to the exterior angle (130)

y+y = 130

2y = 130

y = 130/2

y = 65

--------

Or we could find the interior angle that is adjacent to the 130 degree angle. This is 180-130 = 50 degrees. So this is the top interior angle of the triangle. For any triangle, the three interior angles always add to 180

angle1+angle2+angle3 = 180

y+y+50 = 180

2y+50 = 180

2y = 180-50

2y = 130 ... from here on out, the steps are the same as above

y = 130/2

y = 65

So this helps show how the remote interior angle theorem is set up

Answer:

5 hours 22 minutes

Step-by-step explanation:

Let us represent the number of hours that Jeri worked as: h

Jeri's lawn service charges an initial fee of $4.50 plus $3 an hour

= $4.50 + $3 × h

= $4.50 + 3h

If she is asked to start before 7 a.m. Jeri charges 1.5 times the regular amount.

= 1.5 × ($4.50 + 3h)

If she made $29.25 on a job that began at 5 am, how many hours did Jeri work?

Hence, we have the final equation;

= 1.5 × ($4.50 + 3h) = $29.25

= 6.75 + 4.5h = 29.25

Collect like terms

= 4.5h = 29.25 - 6.75

4.5h = 22.5

h = 22.5/4.5

h = 5.3571428571

Approximately= 5.36 hours

1 hour = 60 minutes

0.36 hour =

60 × 0.36

= 21.6 minutes

Approximately ≈ 22 minutes

Therefore, Jeri worked for 5 hours 22 minutes

Answer:

4 full pages or 5 to use all the leaves

Step-by-step explanation:

26 leaves

6 per page

26/6 ≈ 4.33

4 full pages or 5 for all leaves

Answer:

f(2) = 1

Step-by-step explanation:

To calculate f(2), substitute x = 2 into f(x) , that is

f(2) = 2² - 5(2) + 7 = 4 - 10 + 7 = 1

Answer:

Step-by-step explanation:

Total calories in a granola bite= 27

The calories contained are from grams of carbohydrates and other ingredients

One gram of carbohydrate contains 4 calories

The equation 4c + 5 = 27 represents the relationship between these quantities.

1. 5 from the equation represent calories from other ingredients

2. Neither 8 nor 3 is the solution to the equation

4c + 5 = 27

When 8 is the solution

4(8)+5=27

32+5=27

37=27

When 3 is the solution

4(3)+5=27

12+5=27

17=27

Neither 8 nor 3 is the solution to the equation because 8 gives a higher calories in the granola bite and 3 gives a lower calories in the granola bite.

3. Solution to the equation

4c + 5 = 27

4c= 27-5

4c = 22

Divide both sides by 4

c=22/4

=5 2/4

=5 1/2

The solution to the equation is 5 1/2

Answer:

Step-by-step explanation:

if m and n are irrational number then the product of mn sometimes rational and sometime irrational

ex: √5 *√2=√10 irrational

ex: √8*√2=√16=4 rational

b-y=|x|+3

explain why |x|+3≥|x+3|

absolute value of any number is always positive

x           |x|+3          ≥            |x+3|

1              4              =               4             in this case equal

2             5                                5

-2             5             ≥                 1             in this case |x|+3≥|x+3|

in case of negative value of x then |x|+3>|x+3|

Answer:

(C) 100

Step-by-step explanation:

The average of a data set is just all the numbers added up divided by the amount of numbers.

If we already have 4 pieces of data and we're looking for one more, we have 5 data pieces.

This means that the sum of all of the numbers in the data set will be [tex]91\cdot5=455[/tex] if the mean is 91.

We can find the missing value by adding up what we know and subtracting from 455.

[tex]87+86+93+89=355\\\\455-355=100[/tex]

So Abby needs a 100% on her fifth history quiz to have an average of 91 on all her quizzes.

Hope this helped!

A score which Abby needs to get on her fifth quiz to have an average of exactly 91 is equal to: C. 100.

An average is also referred to as mean and it can be defined as a ratio of the sum of the total number in a data set to the frequency of each data.

In this exercise, we would assign a variable (S) to the unknown score from the fifth quiz with an average of exactly 91. Thus, the average for the fifth quiz is given by this mathematical expression:

91 = (87 + 86 + 93 + 89 + S)/5

91 = (355 + S)/5

Cross-multiplying, we have:

455 = 355 + S

S = 455 - 355

S = 100.

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Answer:

x = 2

Step-by-step explanation:

Solve for x:

12 - 3 x = 6

Hint: | Isolate terms with x to the left hand side.

Subtract 12 from both sides:

(12 - 12) - 3 x = 6 - 12

Hint: | Look for the difference of two identical terms.

12 - 12 = 0:

-3 x = 6 - 12

Hint: | Evaluate 6 - 12.

6 - 12 = -6:

-3 x = -6

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of -3 x = -6 by -3:

(-3 x)/(-3) = (-6)/(-3)

Hint: | Any nonzero number divided by itself is one.

(-3)/(-3) = 1:

x = (-6)/(-3)

Hint: | Reduce (-6)/(-3) to lowest terms. Start by finding the GCD of -6 and -3.

The gcd of -6 and -3 is -3, so (-6)/(-3) = (-3×2)/(-3×1) = (-3)/(-3)×2 = 2:

Answer:  x = 2

Answer:

(a) The median estimate is 450.

(b) The first and third quartiles are 300 and 750 respectively.

(c) The interquartile range is 450.

(d) The particular value which is less than 150 or it is more than 1200, is considered as an outlier.

(e) Yes, there is one outlier in our data which is the value of 1,500.

(f) The distribution is positively skewed.

Step-by-step explanation:

We are given that the box plot shows the undergraduate in-state tuition per credit hour at four-year public colleges. 0, 300, 600, 900, 1,200, 1,500.

(a) As we can see in the box plot that the middlemost data lies between 300 and 600, that means;

Median is given by the average of the two numbers, i.e;

             Median =  [tex]\frac{300+600}{2}[/tex]

                           =  [tex]\frac{900}{2}[/tex]  = 450

So, the median estimate is 450.

(b) As we know that the first quartile represents 25% of the data values and the third quartile represents 75% of the data values.

So, from the box plot given; we can observe that the first quartile, [tex]Q_1[/tex] = 300 and the third quartile lies between the values of 600 and 900, i.e;

Third quartile, [tex]Q_3[/tex] = [tex]\frac{600+900}{2}[/tex]

                             =  [tex]\frac{1500}{2}[/tex]  = 750

So, the first and third quartiles are 300 and 750 respectively.

(c) The interquartile range is given by the following formula;

          Interquartile range = Third quartile - First quartile

                                          =  [tex]Q_3-Q_1[/tex]

                                          =  750 - 300 = 450

(d) From the box plot; it is clear that if the particular value is less than 150 or it is more than 1200, then it is considered as an outlier.

(e) Yes, there is one outlier in our data which is the value of 1,500.

(f) The distribution is positively skewed because the more values are on the right side of the curve and it skewed towards the right.

Answer:

Step-by-step explanation:

6A = 60°

6B = 34°

Answer:

6a) 60 degree

6b) 27 degree

7a) b=60 degree and a=30 degree

7b) x=36 degree and x=36 degree

8a) 95 degree

8b) 100 degree

i posted the 9 th one and all the above ones with proper workout with your other question

Step-by-step explanation:

Answer:

sinA = 35/37 & cosA = 12/37

Step-by-step explanation:

Answer:

8.4 grams

Step-by-step explanation:

So if there are 1.2 grams of protein in a half cup serving, and you're trying to find how many grams in a 3.5 serving. Find the number of halves in 3.5

That would be 7, because 7 multiplied by 1/2 is 3.5

So then multiply 1.2 with 7

= 8.4 grams

Answer:

A, B and C

Step-by-step explanation:

A) 3 and 18 = has 3 as factor

B) 8 and 24 = has 3 as factor

C) 12 and 18 = has 3 as factor

D) 1 and 3 = has as factor of 1 and 3

so the answer is A, B and C

Answer:

Step-by-step explanation:

Given expression

7.50h + 0.20s + 40

A)

Coefficients are 7.50 and 0.20

Variables are h and s

Constant=40

B) if Corinne works for 25 hours and selling $300 in magazine

Weekly earnings = 7.50h + 0.20s + 40

=7.50(25) + 0.20(300) + 40

= 187.5 + 60 + 40

=$287.5

C)

If Corinne starts earning $9 per hour.

Original expression

7.50h + 0.20s + 40

New expression

9h + 0.20s + 40

The coefficient of h will change because of the increase in earnings per hour

Coefficients are 9 and 0.20