The base of a parallelogram is (2x + 3) units and the corresponding height is (3x – 2) units. Find the area of the parallelogram in terms of x. What will be the area of parallelogram if x = 30 units?please explain how you got the answer

Answer:

the answer is: [tex]\{3, 9\}[/tex]

Step-by-step explanation:

Given a set:

Let S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Two subsets,

One subset of odd numbers:

A = {1, 3, 5, 7, 9, 11, 13, 15, 17, ......}

Other subset of multiples of 3:

B = {3, 6, 9, 12, 15, .....}

To find:

Which number in set S are elements in both A and B.

So, we need to find intersection of A and B provided the number is between 1 to 10 (1 to 10 are the elements of S).

First of all, let us have intersection (i.e. common elements) of A and B:

[tex]A\cap B = \{3, 9, 15, 21, ......\}[/tex]

Now, the numbers between 1 to 10 are:

[tex]\{3, 9\}[/tex]

So, the answer is: [tex]\{3, 9\}[/tex]

Answer:

x = 21

Step-by-step explanation:

1. Write the equation

(18 + 2x) ÷ 5 = 12

2. Multiply both sides by 5

18 + 2x = 60

3. Subtract 18 from both sides

2x = 42

4. Solve for x by dividing both sides by 2

x = 21

Answer:

the equation is 18+2x/5 =12

Step-by-step explanation:

now

18+2x= 60

or 2x= 60-18

or 2x= 42

or x=21

so the no is 21 (ans)

thank u

Answer:

I would reject the null hypothesis because it falls outside of the 95% confidence interval.

Answer: 1st floor

Step-by-step explanation:

From the descriprion Tristan got in the elevator on the second floor   (2nd). He went five floors down toward the Parking garage this meant at the end of the journey he was on the seventh (7th) floor of the building. He went back of six (6) More floors before existing the elevator this would put Tristan on first (1st) floor of the building.

Answer:

The possible values are less than 4 but greater than –4

Step-by-step explanation:

If the absolute value of integer number is less than 4 then it is 0, 1, 2 or 3.

so the possible integer numbers are: -3, -2, -1, 0, 1, 2 or 3.

All of them are greater than -4 and less than 4

Answer:

Answer is C.

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

5x-5 = 2x+13

5x-2x = 13+5

     3x = 18

       x = 6

RT = 2(6) + 13 =25

Answer:

2000

Step-by-step explanation:

Salim will need to get 2000 clicks in order to get $50 per month or more.

First: 5 cents goes into one dollar 20 times.

Second: You multiply 20 times 50. This is how you get 2000. There is your answer.

Salim needs at least 700 clicks per month  in order to earn $50 per month or more

A linear equation is in the form:

y = mx + b;

where y, x is variable, m is the rate of change and b is the y intercept.

Let y represent the total pay Salim earns and x represent the number of clicks.

Salim's Website earns $15 per month plus $0.05 every time a visitor clicks, hence:

y = 0.05x + 15

To earn for than $50 per month:

0.05x + 15 > 50

0.05x > 35

x > 700

Salim needs at least 700 clicks per month  in order to earn $50 per month or more

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Answer:

2

Step-by-step explanation:

This depends on what type of graph, like quadratic, linear, etc. For linear it would be 2 points.

Answer:

-7(x+2)

Step-by-step explanation:

-3(2x+5)-(x-1)

↦ -6x+(-15)-x+1

↦-6x-x-15+1

↦7x-14

↦2(x-7)

Answer: the speed of the elevator is 4.6 miles per hour.

Step-by-step explanation:

Given, The elevator in the Washington Monument takes 75 seconds to travel 506 feet to the top floor.

Since 1 hour = 3600 seconds

⇒ 1 second = [tex]\dfrac{1}{3600}[/tex] hour

⇒ 75 seconds = [tex]\dfrac{75}{3600}[/tex] hour [tex]=\dfrac{1}{48}[/tex] hour

1 mile = 5280 feet

1 feet = [tex]\dfrac{1}{5280}[/tex] mile

506 feet = [tex]\dfrac{506}{5280}[/tex] miles [tex]=\dfrac{23}{240}[/tex] miles

Speed = [tex]\dfrac{Distance}{Time}[/tex]

[tex]=\dfrac{\dfrac{23}{240}}{\dfrac{1}{48}}\\\\=\dfrac{23\times48}{240}\\\\=\dfrac{23}{5}\\\\=4.6\text{ miles per hour}[/tex]

Hence, the speed of the elevator is 4.6 miles per hour.

Answer:

C. The statement is an equation because there is an equality symbol.

Step-by-step explanation:

Equation:

Combination of terms joined by the sign minus, plus, multiplication, and division and has equality sign.

Example

5x+45=-5

Term:

A Numbers. (Only)

Example:

9

Combination of a number and a variable joined by multiplication or division.

Example:

9x, 6ab, 10n

Variable:

a symbol that is written with a number or a term.

6ab

Expression:

Terms joined by the sign plus or minus

Hope this helps ;)❤❤❤

Answer:

Step-by-step explanation:

Firstly,open the brackets

ax -ab =[tex]a^{2}[/tex] + bx

collect like terms

ax-bx=[tex]a^{2}[/tex] +ab

factorise

x(a-b)=a(a+b)

x=[tex]\frac{a(a +b)}{a- b}[/tex]

She would use 9/7 of a bottle of conditioner for a full year.

A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.

We have been given that Martina used 3/4 of a bottle of conditioner in 7/12 of a year.

Let the amount of conditioner would be x she uses in a full year

As per the given condition, we can write a proportion as

3/4 of a bottle : 7/12 of a year = x : 1

⇒ (3/4) / (7/12) = x / 1

Reciprocal the terms of the denominators,

⇒ (3/4) × (12/7) = x

⇒ 36 / 28 = x

⇒ x = 9/7

Therefore, she would use 9/7 of a bottle of conditioner for a full year.

Learn more about the proportion here:

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#SPJ2

Answer:  No it does not .

Step-by-step explanation:

First use the coordinates of point A and B to write an equation.

A (-3,-2)

B(2,1)

We will need to use these points to find the slope first and by doing that we will find the difference in the y values and divide it by the difference in the x values.

-2-1= -3

-3-2 = -5

-3/-5= 3/5  

The slope is 3/5 and now we need to find the y intercept using the same points. As you can see the equation will have to be in slope intercept form which uses the formula y=mx+b  where m is the slope and b is the y-intercept.

We will plot the first points in and solve for b.

-2=3/5(-3) + b

-2= -9/5 + b  

+9/5  +9/5

b = -1/5  

We will now write the equation  y=3/5x - 1/5   .

Now using the equation try point c to see if it fits the graph.  

Point C is (5,3)  so again plot in the x and y coordinates and solve,

3= 3/5(5) - 1/5

3 = 3 - 1/5

3[tex]\neq[/tex] 14/5

In this case 3 does not equal 14 over 5 so Point c does not fit the graph

Greetings from Brasil...

Here's our problem:

[tex]\large{\frac{12^{16}}{12^{4}}}[/tex]

From potentiation properties:

Mᵃ ÷ Mᵇ = Mᵃ⁻ᵇ

division of power of the same base: I repeat the base and subtract the exponents

Bringing to our problem

12¹⁶ ÷ 12⁴

12¹⁶⁻⁴

Answer:

[tex]12^{12}[/tex]

Step-by-step explanation:

Answer:

Plane 'S'

Step-by-step explanation:

Since a plane is a two dimensional surface on which infinitely many points may lie.

In the picture attached, two planes (two dimensional) have been given.

Plane S

Plane T

Plane 'S' contains three points A, B and C and plane 'T' contains points D and E.

Therefore, the plane which contains points A, B and C is Plane 'S'.

The plane that contains points A, B and C is the plane S.

A plane is simply a 2-dimensional surface or figure.

The above definition of a plane means that, there are only two planes in the given figure.

These planes are:

Hence, the plane which contains points A, B and C is plane S.

Read more about planes at:

https://brainly.com/question/17268701

Answer: Hi!

To simplify this expression, we will combine like terms.

-5a - 12a + 2b - 3b

-5a - 12a = -17a

2b - 3b = -1b

Our equation now looks like this:

-17a - 1b

We have nothing left to simplify, so we're done!

Hope this helps!

Answer: -2b-4

Ok, so I assume you meant b-4-3b. If not, then B-4-3b is the best you can get, since B and b are different in math.

Anyways, we can rearrange b-4-3b into b-3b-4. Calculating b-3b = -2b. That means -2b-4 is the answer.

Hope that helped,

-sirswagger21

Answer:

B - 4 - 3B

=> -2B - 4

Answer:

The answer is A. The horizontal asymptote is y=0.50 because as Sophia does more and more extra chores, the average amount of money she earns can never be equal or less than $0.50 per extra chores.

Step-by-step explanation:

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

Let's simplify step-by-step.

[tex]-a - b + 1 + ab[/tex]

[tex]= -a + -b + 1 + ab[/tex]

So the answer is : [tex]\boxed {-a + -b + 1 + ab}[/tex]

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Have a great day/night!

❀*May*❀

Ok so we need to find out the different kinds of variables/constants.

1st kind: -a

2nd kind: -b

3rd kind: 1

4th kind: ab

-a and -b are different because they are different variables, and since their value is not known, you can't add or subtract them together.

-a, -b, and 1 are not the same because -a and -b are variables and their value is unknown. However, 1 is a constant, and it's value is constant and known.

-a, -b, and ab are different because ab are "fused together" (multiplied) and that means you cannot add them separately.

So this expression cannot be factorized.

♡ Hope this helps! ♡

❀ 0ranges ❀

Answer:

1/6 2/3x-4

Step-by-step explanation:

What you do to answer the problem is multiply everything in the parenthesis by 2/3.

2/3 of 1/4 = 1/6

With x, you just have 2/3x and leave it at that for now.

2/3 of -6 = -4

so you end up with, 1/6 2/3x-4

(Remember that of means multiplication in my answer)

I hope this helps!

Answer:

Crew: 32

Marty: 48

Blakely: 24

Step-by-step explanation:

I mainly just used guess and check. Crew is 32 years old. So, let's find Marty's age.

32 × 1. 5 = 48

Marty is 48. Now, let's find Blakely's age.

32 × 0.75 = 24

Add all the ages together.

32 + 48 + 24 = 104

Hope that helps.

Crew's age is 32, Marty's age is 48 and Blakey's age is 24

Let :

c represent Crew's age

m represent Marty's age

b represent Blakely's age

From the question, the following can be derived

m = 1.5c

b = 0.75c

m + b + c = 104

Substitute for m and b in the above equation

c + 1.5c + 0.75c = 104

3.25c = 104

divide both sides of the above equation by 3.25

c = 104 / 3.25

c = 32

Substitute for c in the equations that represent  Marty and Blakely's age

m = 1.5c

m = 1.5(32)

m = 48

b = 0.75c

0.75(32)

b = 24

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Answer:

The correct option is;

Triangle angle sum theorem

Step-by-step explanation:

Statement [tex]{}[/tex]                                                                        Reason

1. m∠H = 30° m∠J = 50°, m∠P = 50° m∠N = 100°[tex]{}[/tex]           Given

2. ∠H + m∠J + m∠K = 180° [tex]{}[/tex]                                  (Triangle angle sum theorem)

3. 30° + 50° + m∠K = 180° [tex]{}[/tex]                                                (Substitution property)

4. 80° + m∠K = 180° [tex]{}[/tex]                                                          (addition)

5. m∠K = 100° [tex]{}[/tex]                                                                    (subtraction property)

6. m∠J = m∠P; m∠K = m∠N [tex]{}[/tex]                                              (substitution)

7. m∠J ≅ m∠P; m∠K ≅ m∠N[tex]{}[/tex] If angles are equal then they are congruent

8. ΔHKJ ~ ΔLNP [tex]{}[/tex]   [tex]{}[/tex]    AA similarity theorem.

Answer:

Triangle angle sum theorem

Step-by-step explanation:

Answer:

The height of the pole is 167 m

Step-by-step explanation:

The given parameters are;

Increase  in the length of the shadow = 90 m

Initial angle of elevation of the Sun = 58°

Final angle of elevation of the Sun = 36°

We have a triangle formed by the change in the length of the shadow and the rays from the two angle of elevation to the top of the pole giving an angle 22° opposite to the increase  in the length of the shadow  

We have by sin rule;

90/(sin (22°)  = (Initial ray from the top of the pole to the end of the shadow's length)/(sin(122°)

Let the initial ray from the top of the pole to the end of the shadow's length = l₁

90/(sin (22°)  = l₁/(sin(122°)

l₁ = 90/(sin (22°) ×(sin(122°) = 283.3 m

Therefore;

The height of the pole = 283.3 m × sin(36°) = 166.52 m

The height of the pole= 167 m to three significant figures.

Answer:

height of pole = 121 m (to 3 significant figures

Step-by-step explanation:

From the diagram attached to this solution:

Let the length of the shadow = b

Let the height of the triangle = h

[tex]Triangle\ 1\\\\Tan\ (58)\ =\ \frac{h}{b}\\1.60\ =\ \frac{h}{b} - - - - - -(1)\\\\[/tex]

[tex]Tan\ (36) = \frac{h}{b+90} \\0.73\ =\ \frac{h}{b+90} - - - - (2)[/tex]

[tex]From\ equation\ (1)\\1.60 = \frac{h}{b}\\ cross-multiplying\\1.60b = h - - - - - (3)\\\\\\from\ equation\ (2)\\0.73\ =\ \frac{h}{b+90}\\ corss-multiplying\\0.73b\ +\ 65.7 = h\\h\ =\ 0.73b\ +\ 65.7- - - - - -(4)\\[/tex]

Notice that equation (3) = equation (4) = h

[tex]1.60b = 0.73b\ + 65.7\\1.60b\ -\ 0.73b\ = 65.7\\0.87b\ =\ 65.7\\b\ =\ \frac{65.7}{0.87} = 75.52\ m\\[/tex]

Now let us find the height of pole from equation (3)

1.60b = h - - - - - - (3)

where b = 75.52

h = 1.60 × 75.52

h = 120.83 m

= 121 m (to three significant figure

Answer:

The correct options are;

A. 1·2 = 2

B. 1·1 = 1

E. 1 + 1 = 2

Step-by-step explanation:

Given that the equations 1.2 = 2 and 1.1 = 1 are correctly written as 1·2 = 2 and 1·1 = 2, we have;

The product of any number and one is equal the same number, that is a × 1 = a

Whereby we have the expression 1·2 which is 1 × 2,  we therefore have;

1 × 2 = 1 · 2= 2

B. Similarly we have;

1 · 1 = 1 × 1 = 1

Also, 1 + 1 = 2 is correct as the sum of two numbers is equal to the sum of the count of the numbers, therefore;

E. 1 + 1 = 2 is correct.

Answer:

2 meters

Step-by-step explanation:

The formula for finding the volume of a triangular prism is:

V = 1/2ba * h where b = base length, a = height of base and h = height of prism. In this case, we're solving for a. We know that V = 4.5, b = 1.5 and h = 3 so:

4.5 = 1/2 * 1.5 * a * 3

4.5 = 2.25a

a = 2 meters

Answer:

First of all snog can you please say something in comments man you the best mod out there.

1.5 m because that is the height of the tent. It says so as a measurement.

Step-by-step explanation:

Answer:

95.44%

Step-by-step explanation:

We can find the percentage of area lies within 2 standard deviations of mean by computing P(-2<Z<2).

So,

P(-2<Z<2)=P(-2<Z<0)+P(0<Z<2)

Using normal area table P(0<Z<2)=0.4472. So,

P(-2<Z<2)=0.4472+0.4772

P(-2<Z<2)=0.9544

Thus, the 95.44% of area lies within 2 standard deviations of mean.

Answer:

[tex] ST = 5\sqrt{2} [/tex]

Step-by-step explanation:

Given:

S(-3, 10)

T(-2, 3)

Required:

ST

SOLUTION:

Use the distance formula, [tex] \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex], to find ST.

Where,

[tex] S(-3, 10) = (x_1, y_1) [/tex]

[tex] T(-2, 3) = (x_2, y_2) [/tex]

[tex] ST = \sqrt{(-2 -(-3))^2 + (3 - 10)^2} [/tex]

[tex] ST = \sqrt{(1)^2 + (-7)^2} [/tex]

[tex] = \sqrt{1 + 49} [/tex]

[tex] = \sqrt{50} = \sqrt{25*2} [/tex]

[tex] ST = 5\sqrt{2} [/tex]

Answer:

0.0000375, 3.75x10^-3, 37.5x10^5, 37,500,000, 3.75x10^9

Step-by-step explanation:

0.0000375

37.5x10^5  = 37.5 * 100,000 = 3,750,000

3.75x10^9  = 3.75 * 1,000,000,000 = 3,750,000,000

3.75x10^-3  = 3.75 * 0.001 = 0.00375

37,500,000

Answer:

0.0000375

3.75x10^-3

37.5x10^5

37,500,000

3.75x10^9

Answer:

=x3 - 8x + 3x2-24

=X(x2- 8) + 3(x2- 8)

=(X+3) (x2- 8)

Answer:

x^(3)-3x^(2)+8x-24

x2 (x-3) +8 (x-3)

Factor the polynomial by factoring out the greatest common factor,

x-3 (x-3) (x2+8)