3.
In the figure. ABCD is a parallelogram. Find the area and the
perimeter of ABCD.
​

Answer:

Hey there!

4a-3=D

4a=D+3

a=(D+3)/4

Let me know if this helps :)

Answer:

height = 10 inches

base = 6 inches

The height and base width of the triangle will be 4 inches and 10 inches, respectively.

Assume 'h' is the height of the triangle and 'b' be the base of the triangle. Then the area of the triangle is given as,

A = (1/2) × h·b

The base of a triangle measures 6 inches less than its height. If the area of the triangle is 20 square inches. Then the equations are given as,

b = h - 6             ...1

20 = (1/2)bh

40 = bh             ...2

From equations 1 and 2, then we have

40 = (h - 6)h

40 = h² - 6h

h² - 6h - 40 = 0

h² - 10h + 4h - 40 = 0

h(h - 10) + 4(h - 10) = 0

(h - 10)(h + 4) = 0

h = 10, -4

The height can be negative, so neglect -4. Then the width of the triangle is given as,

b = 10 - 6

h = 4

The height and base width of the triangle will be 4 inches and 10 inches, respectively.

More about the area of the triangle link is given below.

https://brainly.com/question/19305981

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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!

Answer:

[tex]9m^2 + 17m- 9[/tex]

Step-by-step explanation:

Given

[tex]7m^2 + (2m - 1)(m + 9)[/tex]

Required:

Simplify

We start by opening the bracket

[tex]7m^2 + (2m(m + 9) - 1(m + 9))[/tex]

[tex]7m^2 + 2m^2 + 18m - m - 9[/tex]

Collect Like Terms

[tex]9m^2 + 17m- 9[/tex]

Hence, the equivalent expression is [tex]9m^2 + 17m- 9[/tex]

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

Step-by-step explanation:

[tex] \frac{x}{8} = \frac{9}{24} [/tex]

Cross multiply

We have

24x = 72

Divide both sides by 24

That's

[tex] \frac{24x}{24} = \frac{72}{24} [/tex]

We have the answer as

3x² + 2x - 10

when x = - 1

Substitute the value of x into the expression

That's

3(-1)² + 2(-1) - 10

= 3 - 2 - 10

We have the answer as

When x = 0

That's

3(0) + 2(0) - 10

When x = 1

That's

3(1)² + 2(1) - 10

= 3 + 2 - 10

= 5 - 10

[tex] \sqrt{( - 9)} [/tex]

First of all apply the radical rule

That's

[tex] \sqrt{ - a} = \sqrt{ - 1} \times \sqrt{a} [/tex]

So we have

[tex] \sqrt{ - 9} = \sqrt{ - 1} \times \sqrt{9} [/tex]

Using the imaginary rule

That's

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

We have

[tex] \sqrt{9} \times i[/tex]

We have the final answer as

[tex] \frac{1}{x} [/tex]

when x = 0

We have

[tex] \frac{1}{0} = 0[/tex]

when x = 1

[tex] \frac{1}{1} = 1[/tex]

when x = 2

We have

[tex] \frac{1}{2} [/tex]

Hope this helps you

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.

Read more on average here: https://brainly.com/question/9550536

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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

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:

63 inches

Step-by-step explanation:

the formula for the area of a triangle is

a = 1/2 bh

plug in the numbers

a = 1/2(9)(14)

9 times 14 is 126

a = 1/2(126)

half of 126 (or 126 divided by 2)

area = 63 inches

Answer:

Interval Ratio

Step-by-step explanation:

In statistics, the level of measurement used for a variable determines the what summary statistics and analysis are possible. There are three types of level of measurement.

Nominal

Ordinal

Interval/ Ratio

The nominal is the most basic level of measurement. It is known as categorical or qualitative. Examples includes, numbers,color, sex.  Nominal can be stored as a word or text  or given a numerical code.However, the number do not imply order. They are usually expressed in percentage

Ordinal  are variables based on ranks, they are usually have a meaningful order but the intervals between the variables may not be equal. They are usually expressed in frequencies.

The interval/ratio level of measurement  is the most precise level of measurement. Data can be measured and ordered. Examples include, number of customers, age, weight or size. Interval / Ratio data is also known as scale, parametric or quantitative. Interval / Ratio can be discrete  with whole numbers or continuous with fractional numbers.

Answer:

see below

Step-by-step explanation:

4c + 5 = 27

1.  5 is the calories that come from something else besides carbohydrates in the one bite.

2.

Test the values 8 and 3

4*8 +5 = 32+5 = 37  this does not equal 27

4*3+5 = 12+5 = 17   this does not equal 27

neither 8 nor 3 are solutions

3.  

4c + 5 = 27

Subtract 5 from each side

4c + 5-5 = 27-5

4c = 22

Divide each side by 4

4c/4 = 22/4

c =5.5

Answer:

A. The 5 would stand for the other ingredients.

B. She is correct since if you plug in those numbers for c they would be wrong

C. 5.5

Step-by-step explanation:

A. The 5 would stand for the other ingredients.

    The reason that it is the other ingredients since it is the only other possible answer

B. She is correct since if you plug in those numbers for c they would be wrong

C. 5.5

To do this you would just subtract 5 from both sides leaving you with 4c=22 then you would divide 4 from both sides so you get c= 22/4 and when you simplify you get 11/2 which as a number is 5.5

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

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:

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:

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:

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:

sinA = 35/37 & cosA = 12/37

Step-by-step explanation:

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

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:

B

Step-by-step explanation:

3.005 x 10 = 30.05

30.05 x 30.05 x 30.05 x 30.05 x 30.05 x 30.05 x 30.05 x 30.05 or 30.05 to the 8th power = 300,500,000

B = 300,500,000

Answer:

B

Step-by-step explanation:

● 3.005 × 10^8

10^8 is 100000000

● 3.005 × 100000000

● 300500000

Answer:

(-2, 8) and (5, -1)

slope: (y² - y¹) / (x² - x¹)

(-1 - 8) / (5 + 2) = -9/7

y = -9/7x + b

8 = -9/7(-2) + b

8 = 18/7 + b

8 = (2.57) + b

b = 5.43

y = -9/7x + 5.43

parallel = same slope

y = -9/7x

perpendicular = reciprocated slope

y = 7/9x

Answer:

37

Step-by-step explanation:

4x - 6 + x + 3 can be simplified to 5x - 3 by combining like terms.

substituting 8 for x, you get 5*8 - 3

evaluating, 40 - 3 = 37

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:

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:

12

Step-by-step explanation:

12         48........(2)

6           24........(2)

3           12.........(3)

1            4...........4

             4

Multiplication in the parentheses is our greatest common factor of 12 and 48

2 x 2 x 3 = 12

Answer:

12

Step-by-step explanation:

The greatest factor of 12 is 12

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!

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:

26

Step-by-step explanation:

5x³ - 21 + 7

x = 2

then:

5x³ - 14

5*2³ -14

5*8 - 14

40 - 14

26

Answer:

The simplified answer to the given equation is -54.

Step-by-step explanation:

For this problem, we are given the value of x.

x = -2

So, let's plug in this value into our expression soit can be easier to solve.

5(-2)³ - 21 + 7

First, simplify the exponents.

5(-8) - 21 + 7

Now, multiply 5 by -8.

-40 - 21 + 7

Subtract -40 from 21.

-61 + 7

Add 7 to -61.

-54

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