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3 years ago

Find measure of angle BED

Mathematics

1 answer:

Mila [183]3 years ago

3 0

The angles all form vertical angles. The ones labeled are vertical to each other and the ones not labeled are vertical to each other. Vertical angles are congruent, therefore, 2x + 50 = 7x. Solving for x you get 50 = 5x and x = 10. That means that that set of vertical angles each have a measure of 70. That's 140 so far. Around the "circle" created by those angles is a total degree measure of 360. So 360 - 140 = 220. Divide that in half to get the measure of angle BED and its vertical angle AEC. So your angle measure, BED is 110.

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√₂

snow_lady [41]

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$2000 was invested at 5% and $5000 was invested at 8%.

Step-by-step explanation:

Assuming the interest is simple interest.

<u>Simple Interest Formula</u>

I = Prt

where:

I = interest earned.
P = principal invested.
r = interest rate (in decimal form).
t = time (in years).

Given:

Total P = $7000
P₁ = principal invested at 5%
P₂ = principal invested at 8%
Total interest = $500
r₁ = 5% = 0.05
r₂ = 8% = 0.08
t = 1 year

Create two equations from the given information:

$\textsf{Equation 1}: \quad \sf P_1+P_2=7000$

$\textsf{Equation 2}: \quad \sf P_1r_1t+P_2r_2t=I\implies 0.05P_1+0.08P_2=500$

Rewrite Equation 1 to make P₁ the subject:

$\implies \sf P_1=7000-P_2$

Substitute this into Equation 2 and solve for P₂:

$\implies \sf 0.05(7000-P_2)+0.08P_2=500$

$\implies \sf 350-0.05P_2+0.08P_2=500$

$\implies \sf 0.03P_2=150$

$\implies \sf P_2=\dfrac{150}{0.03}$

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Substitute the found value of P₂ into Equation 1 and solve for P₁:

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$\implies \sf P_1=7000-5000$

$\implies \sf P_1 = 2000$

$2000 was invested at 5% and $5000 was invested at 8%.

Learn more about simple interest here:

brainly.com/question/27743947

brainly.com/question/28350785

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1 year ago

What is the nth term for the sequence 5 , 14 , 29 , 50 , 77

Marina86 [1]

The answer would be 3n^2 + 2.

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I hope this helps!

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3 years ago