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3 years ago

HELP! 7th grade math! GIVE CORRECT ANSWER AND YOU WILL GET BRAINLIEST!!

Mathematics

1 answer:

Ksenya-84 [330]3 years ago

3 0

Answer:

ED = 4 units

Step-by-step explanation:

Observing the figure given to us, we can deduce the following:

=>CE = EA (because point E is the midpoint of CA)

Therefore, if CE = EA = x unit, CA = 2x

=>Also, CD = DB (because point D is the midpoint of CB)

Therefore, if CD = DB = y, CB = 2y

Thus, CA/CE = CB/CD = 2 (2x/x = 2y/y)

Going by the above ration we got comparing the ratio of the corresponding sides of ∆CAB and ∆CED (2:1), we can conclude that ∆CAB ~ ∆CED

Using the ratio of the corresponding sides of ∆CAB to ∆CED = (2:1), measure of segment ED is calculated below:

AB/ED = 2/1

8/ED = 2/1

Cross multiply

8 × 1 = 2 × ED

Divide both sides by 2

8/2 = ED

ED = 4 units

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The order of the ______________ in the congruence statement for two congruent triangles tells you the correspondence.

goblinko [34]

Letters

If ABC is congruent to DEF
Then angle A = angle D
angle B = angle E
angle C = angle F
Sides:
AB = DE
BC = EF
AC = DF

4 0

3 years ago

Read 2 more answers

How Much Have I Saved? Portfolio

avanturin [10]

The time value of money calculation can be performed using formula equations or online calculators.

The correct responses are;

1) Option 3

2) Option 2

3) The difference in principal is approximately $8,000

The difference in interest earned is approximately $2,977.87

4) It is better to invest more money at the beginning of the 30 years

Reasons:

Option 1: Present value = 0

Amount invested per month, A = $25/month

The Annual Percentage Rate, APR, r = 3.25%

Number of years = 30

The future value of an annuity is given by the formula;

$\displaystyle FV_{A} = \mathbf{A \cdot \left (\frac{ \left(1 + \frac{r}{m} \right)^{m\cdot t} - 1}{\frac{r}{m} } \right)}$

In option 1, m = 12 periods per year

Therefore;

$\displaystyle FV_{A} = 25 \times \left (\frac{ \left(1 + \frac{0.0325}{12} \right)^{12 \times 30} - 1}{\frac{0.0325}{12} } \right) \approx \mathbf{15,209.3}$

Contribution = $25 × 12 × 30 = $9,000

Total interest earned = $15,209.3 - $9,000 = $6,209.3

Final balance = $15,209.3

Option 2: Present value = 0

Amount, A = $75/quarter

m = 4 periods per year

The Annual Percentage Rate, APR = 4.00%

Therefore;

The effective interest rate is therefore;

$\displaystyle r_{eff} = \left(1 + \frac{0.04}{4} \right)^4 - 1 \approx \mathbf{0.04060401}$

$\displaystyle FV_{A} = 75 \times \left (\frac{ \left(1 + \frac{0.04060401}{4} \right)^{4 \times 30} - 1}{\frac{0.04060401}{4} } \right) \approx 17,437.7$

Using an online calculator, FV = $17,467.04

Contribution = $75 × 4 × 30 = $9,000

Total interest earned = $17,467.04 - $9,000 = $8,467.04

Final balance = $17,467.04

Option 3: Present value = $1,000

APR = 6.25%

m = 12 period per year

Number of years, t = 30 years

Therefore;

$\displaystyle FV = \left (1 + \frac{0.0625}{12} \right)^{12 \times 30} \approx \mathbf{6,489.17}$

Contribution = $1,000

Total interest earned = $6,489.17 - $1,000 = $5,489.17

Final balance = $6,489.17

The table of values is therefore;

$\begin{tabular}{|c|c|c|c|}Option \# &Contribution &Total Interest Earned&Final Balance\\1&\$9,000&\$6,209.3 & \$15,209.3\\2&\$9,000&\$8,467.04 &\$17,467.04\\3&\$1,000&\$5,489.17&\$6,489.17\end{array}\right]$

1) The option that has the least amount invested are option 3

Option 3 investment plan is a present value of $1,000, invested for 30 years at 6.25% APR compounded monthly.

2) Option 2 yielded the highest amount at the end of 30 years, given that the APR is higher than the APR for option 1, although the amount invested over the period are the same.

The basis of option 2 investment plan is $75 invested quarterly at 4.00% APR compounded monthly for 30 years.

3) The difference in the principal invested for the highest and lowest final balance is $9,000 - $1,000 = $8,000

The difference in the interest earned is; $8,467.04 - $5,489.17 = $2,977.87

4) In option 1 the present value is zero, therefore zero amount was invested at the beginning.

The interest to investment ration is 6,209.3:9,000 ≈ 0.7:1

In option 3, all the money was invested at the beginning.

The interest to investment ratio of option 3 is; 5,489.17:1,000 ≈ 5.5:1

Given that the interest to investment ratio, which is the return on investment is larger when more money is saved at the beginning as in option 3, it is better to invest more money at the beginning.

Learn more about future value of an annuity here:

brainly.com/question/8243704

3 0

3 years ago

One number is 2 more than 3 times another. Their sum is 22. Find the numbers. 8, 14 5, 17 2, 20 4, 18 10, 12

xxTIMURxx [149]

9514 1404 393

Answer:

(b) 5, 17

Step-by-step explanation:

You can try the answer choices easily enough.

2 +3×8 ≠ 14

2 +3×5 = 17 . . . . this choice works (5, 17)

2 +3×2 ≠ 20

2 +3×4 ≠ 18

2 +3×10 ≠ 12

Or, you can solve the equation:

x + (2 +3x) = 22

4x = 20 . . . . . . . . subtract 2

x = 5 . . . . . . . . . . divide by 4

The numbers are 5 and (22 -5) = 17.

5 0

3 years ago

24 is 40% of what number? please show me the steps also.

ella [17]

Answer:

1) 24 is 40% of 60

2) (.4)100x=24

3) 25x=24

4) 25x⋅5=24⋅5

5) 2x=120

6) 2x/2=120/2

7) x=60

4 0

2 years ago

A storage container consists of a box of length 90cm, width 42 cm and height 34 cm, and a lid

Ivanshal [37]

Answer:

20079.05 cm^2,

Step-by-step explanation:

Surface area of the box without the lid

= 90*42 + 2(90*34) + 2(42*34) = 12756.

Now find Surface area of the half cylinder:

The diameter of the 2 half circles = 42 so the radius = 21.

The area of the lid

= 2 + 1/2 π (21)^2 + π r * 90

= 7323,052

Total = 20079.052

7 0

2 years ago