What is the area of this parallelogram?


4.9 cm²

12.25 cm²

17.15 cm²

24.01 cm²
Parallelogram A B C D is composed of a square and two triangles. The square has a length and height of 3.5 centimeters each. There are two identical triangles. Each triangle has a base of 1.4 centimeters and a height of 3.5 centimeters.

\(\\ \rm\Rrightarrow \dfrac{IJ}{IL}=\dfrac{MN}{MP}\)

\(\\ \rm\Rrightarrow \dfrac{24}{12}=\dfrac{MN}{3.8}\)

\(\\ \rm\Rrightarrow 2=\dfrac{MN}{3.8}\)

\(\\ \rm\Rrightarrow MN=3.8(2)\)

\(\\ \rm\Rrightarrow MN=7.6\)

The LCM of the set of numbers are:

1. {12,15} = 60

2. {16,24} = 48

3. {18,27} = 54

4. {20,28} = 140

5. {36,54} = 108

6. {9,12,24} = 72

7. {15, 20, 45} = 180

8. {6,8,12} = 24

9. {4,6,9} = 36

10. {8,9,12} = 72

The least common multiple of two or more numbers is the least multiple that is common to two or more numbers. A multiple of a number is the product of an integer and that number. For example, the multiples of 6 are 12 and 18.

Prime factors of 12 = 2 x 2 x 3

Prime factors of 15 = 3 x 5

LCM = 2 x 2  x 3 x 5 = 60

Prime factors of 16 = 2 x 2 x 2 x 2

Prime factors of 24 = 2 x 2 x 2 x 3

LCM = 2 x 2 x 2 x 2 x 3 = 48

Prime factors of 18  = 2 x 3 x 3

Prime factors of  27  = 3 x 3 x 3

LCM = 2 x 3 x 3 x 3 = 54

Prime factors of 20  = 2 x 2 x 5

Prime factors of 28  = 2 x 2 x 7

LCM = 2 x 2 x 5 x 7 = 140

Prime factors of 36  =2 x  2 x 3 x 3

Prime factors of 54  = 2 x 3 x 3 x 3

LCM = 2 x 2 x3 x 3 x3 = 108

Prime factors of 9  = 3 x 3

Prime factors of 12 = 2 x 2 x 3

Prime factors of 24 = 2 x 2 x 2 x 3

LCM = 2 x 2 x 2 x 3 x 3 = 72

Prime factors of 15 = 3 x 5

Prime factors of 20 = 2 x 2 x 5

Prime factors of  45 = 3 x 3 x 5

LCM = 2 x 2 x 3 x 3 x 5 = 180

Prime factors of 6  = 2 x 3

Prime factors of 8= 2 x 2 x 2

Prime factors of  12= 2 x 2 x 3

LCM = 2 x 2 x 2 x 3 = 24

Prime factors of 4  = 2 x 2

Prime factors of 6= 2 x 3

Prime factors of  9= 3 x 3

LCM = 2 x 2 x 3 x 3 = 36

Prime factors of 8 = 2 x 2 x 2

Prime factors of 9= 3 x 3

Prime factors of 12 = 2 x 2 x 3

LCM = 2 x 2 x 2 x 3 x 3 = 72

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Yes, if two angles are vertical angles, then they are congruent (have equal measures).

Vertical angles are two non-adjacent angles formed by the intersection of two lines. They are always congruent, meaning they have the same measure. This can be proven mathematically using the Vertical Angles Theorem which states that vertical angles are congruent.

If two angles are vertical angles, they are formed by intersecting lines and share a common vertex but do not share a common side. The angles are always equal in measure and are congruent. This is known as the Vertical Angles Theorem, and it can be proven mathematically. When working with geometry, understanding the properties of different angles is important to correctly solve problems and equations. By knowing that vertical angles are always congruent, we can simplify calculations and make geometric proofs easier.

In conclusion, vertical angles are always congruent, which is a fundamental concept in geometry. The Vertical Angles Theorem proves that two angles formed by intersecting lines are always equal in measure and are congruent. This knowledge is essential for solving geometry problems and is a useful tool for math students.

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Step-by-step explanation:

The graph that represents all values of x such that x > -3 and x < 2 is the graph of a vertical line segment located between -3 and 2 on the x-axis, but excluding these two points. This can be represented graphically as:

|

|

|

---------x---------

|

|

|

-3 2

Here, the open circles indicate that the points -3 and 2 are not included in the range of values for x.

Answer:

$130

Step-by-step explanation:

Answer:

$130

Step-by-step explanation:

1300×10%

$130

Answer:

4  months.

Step-by-step explanation:

So I added this "out" and the LCM (Least Common Multiple) is 12. So it'd take 4 months for both of them to hit 12 pounds.

Hope this helps and have a nice day!

Answer:

Step-by-step explanation:

-3x+10=21

-3x=21-10

-3x=11

x=11/-3

x=- 11/3

Answer:

1) a. Verticle angles are congruent

3) b. Same-side interior angles are supplementary

5) d. Alternate interior angles are congruent when the lines are parallel

6) c. Substitution

Step-by-step explanation:

1) ∠1 and ∠2 are vertical angles, they're congruent

3) ∠2 and ∠3 are same-side interior angles which are supplementary (add up to 180)

5) ∠3 and ∠4 are alternate interior angles meaning they're congruent

6) idrk how to explain it but its the last one so substitution goes with it :)

The probability of getting exactly 1 three, to the nearest thousandth is 0.347.

We have,

Binomial distribution is the distribution of a random variable X for which there are only two possibilities. The probability p for the success and the probability of 1-p for the failure, which consist of n trials.

The binomial distribution has the formula,

P(x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ

where x : number of times for a specific outcome within n trials

p : probability of success in each trial

n : number of trials

Given that a fair die is rolled 3 times.

Here, n = 3, x = 1

p = probability of getting three for 1 trial = 1/6

1 - p = 1 - 1/6 = 5/6

P(1) = ³C₁ (1/6)¹ (5/6)³⁻¹

    = 0.347

Hence the probability of getting exactly 1 three is 0.347.

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complete question:

If a fair die is rolled 3 times, what is the probability, to the nearest thousandth, of getting exactly 1 three?

Answer: whichever one is easiest to get by itself.

Step-by-step explanation:

Answer:

c = 70°

Step-by-step explanation:

The sum of the angles of a triangle is always 180°.

We can use the other two to solve for c:

57 + 53 + c = 180

110 + c = 180

c = 70

Therefore, angle c is 70°.

Answer:v = 9

Step-by-step explanation:

Simplifying

2(3v + 8) = 70

Reorder the terms:

2(8 + 3v) = 70

(8 * 2 + 3v * 2) = 70

(16 + 6v) = 70

Solving

16 + 6v = 70

Solving for variable 'v'.

Move all terms containing v to the left, all other terms to the right.

Add '-16' to each side of the equation.

16 + -16 + 6v = 70 + -16

Combine like terms: 16 + -16 = 0

0 + 6v = 70 + -16

6v = 70 + -16

Combine like terms: 70 + -16 = 54

6v = 54

Divide each side by '6'.

v = 9

Answer: the answer is 9

Step-by-step explanation:

1. open the bracket by multiplying: 2(3v+8)=70

6v+16=70

2. take the 16 over the equals sign.  note:(the plus sign in front of the 16 changes to a minus sign.)

6v=70-16

6v=54

3. divide both sides by 6

6v/6=54/6

final answer: v=9

Answer:

all you need to so is multiply 40 by .65 then you will get your answer of 26 miles left

Step-by-step explanation:

The value of the first term is 2, and the recursive definition for the sequence is: a(1) = 2

                      a(n) = a(n-1) - 5

To determine the value of the first term and write a recursive definition for the given sequence, let's analyze the pattern.

The given sequence is: 12, 7, 2, -3, -8, ...

Observing the sequence, we can see that each term is obtained by subtracting 5 from the previous term. Therefore, the first term can be found by subtracting 5 from the second term.

To find the value of the first term, we subtract 5 from 7:

7 - 5 = 2

So, the first term of the sequence is 2.

Now, let's write a recursive definition for the sequence. A recursive definition describes how each term is related to the previous terms.

In this case, each term is obtained by subtracting 5 from the previous term. Let's denote the nth term of the sequence as a(n).

Recursive definition:

a(1) = 2 (the first term is 2)

a(n) = a(n-1) - 5 (each term is obtained by subtracting 5 from the previous term)

Using this recursive definition, we can generate the terms of the sequence:

a(1) = 2

a(2) = a(1) - 5 = 2 - 5 = -3

a(3) = a(2) - 5 = -3 - 5 = -8

a(4) = a(3) - 5 = -8 - 5 = -13

...

By continuing this process, we can generate all the terms of the sequence.

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Answer:

∠2 = 41°

Step-by-step explanation:

This is because, all three interior angles in a triangle will have a sum of 180 degrees.

So given that we have two angles, 90 degrees(right angle) and 49 degrees, we can replace angle 2 as our unknown value(a variable) and make it equal to 180 degrees then solve for x;

49 + 90 + x = 180

139 + x = 180

-139        -139

x = 41°, ∠2 = 41°

Answer:

3.78%

Step-by-step explanation:

The formula for compound interest is given by:

A(t) = P(1 + r/n)^(nt), where

Thus, we can plug in 8500 for P, 11022 for A(t), 1 for n, and 7 for t to find r:

Step 1:  Plug in the values and simplify:

11022 = 8500 * ( 1 + r/1)^(7 * 1)

11022 = 8500 * (1 + r)^(7)

Step 2:  Divide both sides by 8500:

(11022 = 8500 * (1 + r)^(7)) / 8500

11022/8500 = (1 + r)^(7)

5511/4250 = (1 + r)^(7)

Step 3:  Raise both sides to the 1/7 power (this is the same as taking the 7th root of both sides):

(5511/4250 = (1 + r)^(7))^(1/7)

1.037815641 = 1 + r

Step 4:  Subtract 1 from both sides to find r:

(1.037815641 = 1 + r) - 1

0.0378154607 = r

Step 5:  Multiply 0.0378154607 by 100 to find the interest rate as a percentage:

0.0378154607 * 100

3.78156407 = %

Step 6:  Round to the nearest two decimal places:

3.78

Thus, the interest rate is about 3.78%

Answer:

XS-9, yes#####################

Answer:

The possible number of students in Mrs. Hayko's class is limited to 15 or 30, as higher multiples of 15 would exceed the desired class size.

Step-by-step explanation:

a)

Let 'x' be the total number of students in Mrs. Hayko's class.

One-third of the students walk to school: (1/3)x.

The remaining students who do not walk to school: (2/3)x.

Four-fifths of the non-walking students take the bus: (4/5) * (2/3)x.

Simplify to find the fraction of students taking the bus: (8/15)x.

b)

Consider different values for 'x' to find a whole number of students taking the bus.

Start with a small number, such as x = 15.

Calculate the number of students taking the bus using (8/15)x.

If the result is a whole number, it's a possible class size.

Repeat with different values of 'x' until a whole number is obtained.

The possible number of students in Mrs. Hayko's class could be 15, 30, or any other multiple of 15.

The series expansion for e z 1 z up to z 5 is obtained by multiplying the Maclaurin series for e z and 1 1 z. For |z| 1, this series converges.

The Maclaurin series for e^z is:

e^z = 1 + z + z^2/2! + z^3/3! + z^4/4! + ...

The Maclaurin series for 1/1-z is:

1/(1-z) = 1 + z + z^2 + z^3 + z^4 + ...

Multiplying these two series together gives:

e^z/(1-z) = (1 + z + z^2/2! + z^3/3! + z^4/4! + ...)(1 + z + z^2 + z^3 + z^4 + ...)

= 1 + (1+z) + (z + z^2/2! + z^2) + (z^2/2! + z^3 + z^3/3!) + (z^3/3! + z^4 + z^4/4!) + ...

= 1 + z + 2z^2 + 3z^3 + 5z^4 + ...

This series converges for |z| < 1

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Answer:

......

Step-by-step explanation:............

$25,000 of Geoffrey's income is subject to the net investment income tax.

The net investment income tax applies to certain types of income, including rental real estate income, and is calculated based on an individual's modified adjusted gross income (MAGI) and filing status. In the case of Geoffrey, his rental real estate income of $25,000 is subject to the net investment income tax.

To calculate the net investment income tax, we need to determine Geoffrey's MAGI. His total income for the year consists of $25,000 in rental real estate income and $180,000 in wages, totaling $205,000. Since he has no adjustments to income, his MAGI is equal to his total income of $205,000.

Therefore, the amount of Geoffrey's income subject to the net investment income tax is $25,000.

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Period 1 is with highest grade.

Given,

Histograms for three periods.

Now,

Period 1:

Total grade = 1 + 5 + 14 + 12

Total grade = 32

Period 2 :

Total grade = 0 + 4 + 19 + 8

Total grade = 31

Period 3 :

Total grade = 0 + 4 + 10 + 10

Total grade = 24

Hence the data from histogram shows that the highest grade is from period 1 that is 32.

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Answer:

36%, I'm fairly certian

Step-by-step explanation:

A. 90%

B. 60%

C. 30%

D. 36%

D. makes the most sense to me

The probability of going to the amusement park will be 60%.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Given that:-

The probability will be calculated as:-

\(P|A|B|=\dfrac{P(A\cap B)}{P(B)}\\\\\\P|A|B|=\dfrac{0.6\times 0.9}{0.9}=0.6=60\%\)

Therefore probability of going to the amusement park will be 60%.

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Step-by-step explanation:

If t and w are inversely proportional, it means that as one variable increases, the other variable will decrease by the same factor. In this case, we have the equation t = 4/w, which means that if we multiply w by a certain factor, t will be divided by the same factor.

If we multiply w by 6, the new value of w will be 6 times the original value:

w' = 6w

To find the new value of t, we can substitute w' into the equation:

t' = 4/w'

t' = 4/(6w)

t' = 2/3w

So we see that t has been divided by 6/1 = 6. Therefore, the value of t will decrease by a factor of 6 if the value of w is multiplied by 6.

Answer:

The surfacearea of the box would 140 length (14 times 10), 125 width (12.5 times 10), and 10 height(1 times 10). Therefore2ﾗ(140ﾗ125 + 140ﾗ10 + 125ﾗ10) = 40,300 centimeters^2