If $300 is invested at an interest rate of 3.5% per year , find the amount of the investment at the end of 15 years for the following compounding methods

A two column proof for ΔAEC ≅ ΔDEB  is as shown below.

"Two triangles are congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure."

"These angles formed on the inside of two straight lines when crossed by a transversal."

"It is point which divides a line segment into two equal parts."

"AAS (Angle Angle Side) theorem states that in the two triangles, if two angles and one side of a triangle are congruent to two angles and one side of a second triangle, then the two triangles are congruent."

For given question,

Given that CA is parallel to DB and E is the midpoint of AD.

CA is parallel to DB

CB is transversal.

∠ACB and ∠CBD are alternate interior angles.

We know that when a transversal intersects a parallel line then alternate interior angles formed are congruent.

So, ∠ACB ≅ ∠CBD                       ................(i)

Similarly for CA || DB and AD is transversal.

∠CAD ≅ ∠ADB                             ..................(ii)

Also,  E is the midpoint of AD.

By definition of midpoint,

⇒ AE = ED                                      ..................(iii)

From (i), (ii) and (iii),

By AAS postulate of triangle congruence,

ΔAEC ≅ ΔDEB      

Therefore, a two column proof for ΔAEC ≅ ΔDEB  is as shown below.

Learn more about AAS postulate of triangle congruence here:

https://brainly.com/question/1593616

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Answer:

(2, -4)

Step-by-step explanation:

Answer:

(2, -4)

Step-by-step explanation:

The solution to a system of equations is always going to be the point(s) where they intersect. To solve, use substitution and find each variable, x and y. Our final answer will be a set of coordinates (x, y). To plot this system, see the help image attached.

y = -x - 2

2x - y = 8

Substitute y to find x

2x - (-x - 2) = 8

2x + x + 2 = 8

3x = 6

x = 2

Substitute x to find y

y = -(2) - 2

y = -2 - 2

y = -4

Solution: (2, -4)

I hope this helps and God bless!

The Ruiz family using a rounded figure for exchange rate will not give the correct exchange.

Exchange rate:

1 euro = 1.35261 USD

1.35261 rounded to the nearest hundredth = 1.35

If Ruiz family is exchanging 50 euros for instance

Original exchange rate

1 euro = 1.35261 USD

50 euro = 67.6305

Rounded exchange rate:

1 euro = 1.35 USD

50 euro = 67.5 USD

Therefore, the Ruiz family using a rounded figure for exchange rate will not give the correct exchange.

Read more:

https://brainly.com/question/17985441

Answer:

The answer is 3054.8

Step-by-step explanation:

V = 4/3 × 22/7 × 9 × 9 × 9

V = 4 × 22/7 × 3 × 81

V = 4 × 22 × 243/7

V = 21384/7

V = 3054.8

Thus, The answer is 3054.8

Answer:

3054

Step-by-step explanation:

V=4/3 π9³ = 3054

hope it helps

Answer:

I dont know

Step-by-step explanation: I hope someone can help you

Answer:12 1/8

Step-by-step explanation:

you add the denomunator in order to get your answer

Answer:

a fraction whos denominator is a power of ten and whose numerator is expressed by figures placed to the right of the decimal point and the decimal point is always suppose to be right in the place where the other number is there suppose to line up hope this helps :)

Step-by-step explanation:

12-(-8)=20

x axis = 20:2 = 10

There would be 413 frozen dinners in the next 16 years.

Let y represent the amount of frozen dinners after x years.

If a certain quantity of money can buy 940 frozen dinners this year, and it decreases by 5% every year, hence:

y = 940(0.95)ˣ

In 16 years:

y = 940(0.95)¹⁶

y = 413.71

There would be 413 frozen dinners in the next 16 years.

Find out more on exponential function at: https://brainly.com/question/12940982

Answer:

x=1

Step-by-step explanation:

1) Distribute 3x+9=12

2) Subtract 9 from both sides 3x=3

3) Divide by three x=1

Answer:

  $65,139,000

Step-by-step explanation:

Integration of the given function involves straightforward application of the power rule. It can also be done easily by a modern calculator.

  [tex]\displaystyle \int_{1000}^{1300}{(190x-1370)}\,dx=95(1300^2-1000^2)-1370(1300-1000)\\\\=95(300)(2300)-1370(300)=300(95\cdot2300-1370)\\\\=65\,139\,000[/tex]

Revenue from the sale of those 300 tickets will be $65,139,000.

Step-by-step explanation:

The centroid O cuts every median in the ratio 2:1. The distance between a vertex and the centroid is twice the distance between the centroid and the midpoint of the opposite side.

Therefore: |OB| = 2|OF|

|BF| = |OF| + |OB| = |OF| + 2|OF| = 3|OF|

3x+3=3(2x-8)

3x+3=6x-24

3x=27

x=9

Answer:

Area of the shaded polygon= 372

Answer:

D. 4.5 and 12 seconds

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

It was correct on the quiz

Answer:

75%

Im happy to help you

Answer:

1/8

Step-by-step explanation:

I think so

Answer:

D. is correct.

[tex]2 * 1 = 2[/tex]

[tex]4 * 1=4[/tex]

[tex]4 + 2 = 6[/tex]

________________________________________________________

The product of answer choice D.(6) is not equal to the product of [tex]\frac{2}{3}[/tex] × 4, because [tex]\frac{2}{3}[/tex] × 4 is actually [tex]2\frac{2}{3}[/tex]

________________________________________________________

We learned how to find whole numbers through an expression with fractions.

Questions related to the topic? Ask me in the comments box.

Answer: 20v+5

Step-by-step explanation:

5(4v+1)

Use the distributive property to multiply 5 by 4v+1.

20v+5

Answer:

20v+5

Step-by-step explanation:

You would multiply using the distributive property

Distributive property formula examples:

AB=BA

A+B=B+A

(AB)C=A(BC)

(A+B)+C=A+(B+C)

A(B+C)=AB+AC

Answer:

4000

Step-by-step explanation:

Product just means multiply!

40 × 100 = 4000

Answer:

4000

Step-by-step explanation:

40 times 100 is 4000

take the 4 and put the amount of 0's in the equation behind it ( there are 3 in total, 2 from the 100 and 1 from the 40): 4000

Typically, linear equations are written in slope-intercept form:

[tex]y=mx+b[/tex]

To find the equation of a line given a point and the slope:

We're given:

[tex]y=mx+b[/tex]

⇒ Plug in the slope, [tex]\dfrac{1}{5}[/tex]:

[tex]y=\dfrac{1}{5}x+b[/tex]

⇒ Plug in the point (-5,-4) and solve for b:

[tex]-4=\dfrac{1}{5}(-5)+b\\\\-4=-1+b\\\\b=-3[/tex]

⇒ Therefore, the y-intercept of the line is -3. Plug this back into our original equation as b:

[tex]y=\dfrac{1}{5}x-3[/tex]

[tex]y=\dfrac{1}{5}x-3[/tex]

Answer: -x(x-4)(2x-49)

Step-by-step explanation:

Add and subtract the second term to the expression and factor by grouping.

Answer:

-x (x-4) (2x-49)

Step-by-step explanation:

take out -x

you then have

2x^2-57x+196

then factor the remaining

multiply number next to x^2 which is a with 196 which is c

(-57 is b)

multiply 2 with 196 which = 392

then find out what 2 factors of 392 add up to -57

they are -8 and -49

2(x-8/2)(x-49/2)=0

2(x-49/2)(x-8/2)=0

(-x)(2x-49)(x-4)=0

Answer:

9/70

Step-by-step explanation:

Given that:

70 students choose to attend one of three after school activities: football, tennis or running.

There are 30 boys. 13 students choose football, of which 9 are girls. 31 students choose tennis. 9 girls choose running.

A student is selected at random.

What is the probability this student chose running?

Since it asking for the probability of this student (randomly select) chose running. And we can see that there are 9 girls choose running.

Therefore, we also know 70 students is the total

Hence, the answer is 9/70

9/70 is in simplest form already.

~lenvy~

Answer:

9/70

Step-by-step explanation:

Important info:

Solution:

Probability of this student (randomly select) chose running. And we can see that there are 9 girls choose running.

Thus, 70 students is the total

Therefore, the answer is 9/70

9/70 can't be simplify.

[RevyBreeze]

Answer:

y<3/2x-5/2

Step-by-step explanation:

You just have to know how to get y on one side and the rest of the problem on the other.

First you would subtract 3x from both sides, which leaves you with -2y>5-3x.

Lastly you would divide both sides by -2.

To get the final answer of y<3/2x-5/2

Answer:

x = 10

Step-by-step explanation:

Both right triangles are similar.

-> Corresponding sides of similar triangles are in proportion.

[tex] \implies \: \frac{x + 6}{16} = \frac{x}{10} \\ \\ \implies \: 10(x + 6) = 16x \\ \\ \implies \: 10x + 60= 16x \\ \\ \implies \: 10x - 16x = - 60 \\ \\ \implies \: - 6x = - 60 \\ \\ \implies \: x = \frac{ - 60}{ - 6} \\ \\ \implies \: x = 10[/tex]

y=6x-20

Hope it helps.

Do comment if you have any query.

Answer:

y = m x + b       is the standard form for a straight line

you have

y = 6 x + b       if m = 6

Now when x = 2, y = -8          this is given

- 8 = 6 * 2 + b       substituting given values

b = -8 - 12 = -20

y = 6 x -20            is the equation requested

Check;

-8 = 6 * 2 - 20      

12 = 12         so this agrees

Answer:

Linear with a positive correlation

Step-by-step explanation:

This is because the data is linear and upwards sloping from which we can infer is a positive correlation.

Answer:

anywhere around 420-450

Step-by-step explanation:

the actual answer is 434, a good estimation would be in that range

Answer:

i believe it's 48

Step-by-step explanation:

7x^2 - 3x - 6

7(3)^2 - 3(3) - 6

63 - 9 - 6

54 - 6

48

$0.7

Given sentence:

Writing as an equation:

[tex]\implies 2.4 \ \text{pounds} = \$1.68[/tex]

To obtain the cost per pound of peas, divide 2.4 both sides. This will convert the value on the L.H.S to 1 pound. The value obtained on the R.H.S will be the the cost (answer).

[tex]\implies \dfrac{2.4 \ \text{pounds}}{2.4} = \$\dfrac{1.68}{2.4}[/tex]

[tex]\implies 1 \ \text{pounds}}= \$\dfrac{1.68}{2.4}[/tex]

[tex]\implies 1 \ \text{pound} = \$0.7[/tex]