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3 years ago

Plz help its due today and I don't understand its asking for the measurement of angle DEF

Mathematics

1 answer:

tatyana61 [14]3 years ago

6 0

Answer:

m∠DEF = 135º

Step-by-step explanation:

1. I will find the answer to X by writing what ∠FEA, ∠AEB, ∠BEC by doing

(2x+5) + (4x) + (3x-5) = 180, all simplified it will give me x=20

2. I want to figure out what ∠AEB and ∠BEC are

since x=20 and ∠AEB is 4x, we substitute x as 20 as : 4(20) which is 80.

We then figure out ∠BEC since x=20 and ∠BEC is 3x-5 we substitute the 20 in place of x, which will be 3(20) - 5= 55.

3. I want to add ∠AEB + ∠BEC to get the vertical angle of ∠DEF

(the vertical angel of ∠DEF is ∠AEB + ∠BEC)

∠AEB + ∠BEC = ∠DEF

80 + 55 = ∠DEF

135 = ∠DEF

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natulia [17]

Answer:

diagonal = = 12.8 inches (to the nearest tenth of an inch)

Step-by-step explanation:

As shown in the diagram attached to this solution:

Let the Length of the rectangular board = a

Let the width = b

Let the diagonal = d

where:

a = 10 inches

b = 8 inches

d = ?

Triangle ABC in the diagram is a right-angled triangle, therefore, applying Pythagoras theorem:

(hypotenuse)² = (Adjacent)² + (Opposite)²

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d² = 164

∴ d = √(164)

d = 12.806 inches

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<em>N:B Rounding off to the nearest tenth of an inch is the same as rounding off to 1 decimal place.</em>

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3 years ago

Laura goes to a bank and opens a new account. She deposits $5,500. The bank pays 1. 6% interest compounded annually on this acco

HACTEHA [7]

The amount that is the closest to the account balance at the end of 4 years is given by: Option B: $5,860. 53 (approx)

<h3>How to calculate compound interest's amount?</h3>

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

$CI = P(1 +\dfrac{R}{100})^T - P$

The final amount becomes:

$A = CI + P\\A = P(1 +\dfrac{R}{100})^T$

For the considered case, we're given that:

Initial amount Laura deposited = $5,500 = P
Type of interest: Compound interest
Unit of time: Annually
Rate of interest = 1.6% annually = R
Total unit of time for which amount is to be calculated: 4 years = T

The final amount at the end of 4 years in the considered account of Laura is evaluated as:

$A = 5500(1 + \dfrac{1.6}{100})^4 = 5500(1.016)^4 \approx 5860.53 \: \rm (in \: dollars)$

Thus, he amount that is the closest to the account balance at the end of 4 years is given by: Option B: $5,860. 53 (approx)

Learn more about compound interest here:

brainly.com/question/11897800

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2 years ago

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yuradex [85]

Answer:

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Step-by-step explanation:

the difference between 96 and 68 is 28 bucks

28 is what percent of 96

is over of

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3 years ago

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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