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Ann [662]
3 years ago
9

Triangle ABC is a right triangle. Point D is the midpoint of side AB and point E is the midpoint of side AC. The measure of angl

e ADE is 36°. The proof, with a missing reason, proves that the measure of angle ECB is 54°. Statement Reason m∠ADE = 36° Given m∠DAE = 90° Definition of a right angle m∠AED = 54° Triangle Sum Theorem segment DE joins the midpoints of segment AB and segment AC Given segment DE is parallel to segment BC ? ∠ECB ≅ ∠AED Corresponding angles are congruent m∠ECB = 54° Substitution property Which theorem can be used to fill in the missing reason? Concurrency of Medians Theorem Isosceles Triangle Theorem Midsegment of a Triangle Theorem Triangle Inequality Theorem

Mathematics
1 answer:
butalik [34]3 years ago
7 0

Answer:

Midsegment of a Triangle Theorem

Step-by-step explanation:

Midsegment of a Triangle Theorem - is the right choice

  • <em>The Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long.</em>

<u></u>

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Kamran wins the big game lottery. He invests part of his winnings in treasury bonds promising a 5% annual return and he deposits
Ostrovityanka [42]

Answer:

Amount won by Kamran = $21,450

Step-by-step explanation:

This can be calculated using the following 3 steps:

Step 1: Calculation of the amount invested in treasury bonds

Since the limit to the duration of investment is not stated, the amount invested can be calculated using the formula for calculating the present value of a perpetuity as follows:

PV = P / r …………………………………. (1)

Where;

PV = Present value or the amount invested treasury bonds = ?

P = Annual return on his investments = $661.25

r = Annual rate of return = 5%, or 0.05

Substitute the values into equation (1), we have:

PV = $661.25 / 0.05 = $13,225

Step 2: Calculation of the amount deposited in the money market account

From Step 1 above, we have:

Amount invested treasury bonds = $13,225

Since he invests $5000 more in treasury bonds than he deposits in the money market account, the amount deposited in the money market account can be calculated as follows:

Amount deposited in the money market account = Amount invested treasury bonds - $5,000 = $13,225 - $5,000 = $8,225

Step 3: Calculation of the amount won by Kamran

Amount won by Kamran = Amount invested treasury bonds + Amount deposited in the money market account = $13,225 + $8,225 = $21,450

7 0
3 years ago
If m angle ECD is six less than five times m angle BCE, and mangle BCD = 162º. find each
Usimov [2.4K]

Answer:

see explanation

Step-by-step explanation:

let ∠BCE = x then ∠ECD = 5x - 6 and

∠BCE + ∠ECD = ∠BCD, substitute values

x + 5x - 6 = 162, that is

6x - 6 = 162 ( add 6 to both sides )

6x = 168 ( divide both sides by 6 )

x = 28

Hence

∠BCE = x = 28°

∠ECD = 5x - 6 = (5 × 28) - 6 = 140 - 6 = 134°

5 0
3 years ago
Read 2 more answers
In a market research survey of 29012901 ​motorists, 255255 said that they made an obscene gesture in the previous month. complet
harina [27]
A. 1-255255/29012901=0.991202017 is the probability of not making an obscene gesture.
b. The probability of none of 5050 making an obscene gesture is (a) raised to the power of 5050: 4.1591E-20 approx. We have not used the 5% rule in this binomial distribution.
8 0
3 years ago
What is the extraneous solution?
8_murik_8 [283]
<h3>Answer:</h3>

  x = 1

<h3>Step-by-step explanation:</h3>

<em>The only solution is an extraneous solution</em>, which is to say the equation has no solution.

The rational expression reduces to -1 (for x≠1), which makes the equation ...

  1 = 1/x

The only solution to this is x=1, which is specifically disallowed.

___

If you subtract the right side, the equation becomes ...

  ((-x+1)(x) +2(x)(x -1) -(x -1))/(x -1) = 0

  (-x^2 +x +2x^2 -2x -x +1)/(x -1) = 0 . . . . eliminate parentheses in the numerator

  (x^2 -2x +1)/(x -1) = 0 . . . . . . . . . . . . . . . collect terms

  (x -1)^2/(x -1) = 0 . . . . . . . . . . . . . . . . . . . factor

This is undefined for the only value of x that could possibly be a solution, x=1.

8 0
3 years ago
Arithmetic and Geometric Sequences (Context)
V125BC [204]

The formula for compound interest

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

A is the amount in the account at the end

P is the principal balance or the amount initially invested

r is the annual interest rate in decimal form

n is the number of times it is coupounded per year

t is the number of years

A = 1800 ( 1+ .0375/1) ^ (1*6)

A = 1800 ( 1.0375)^6

A = 2244.92138

Rounding to the nearest cent

A = 2244.92

7 0
1 year ago
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