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3 years ago

If C, D, and E are midpoints of triangle ZAB, find ZA.

Mathematics

1 answer:

DanielleElmas [232]3 years ago

6 0

Well that doesn't even look right are you sure this is how it says

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The triangle shown below has an area of 20 units.

harina [27]

Happy anniversary birthday to you happy birthday to happy mama mama ghar ko happy anniversary birthday

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3 years ago

In the figure, the measure of angle 9 is 80 degrees and the measure of angle 5 is 68. Find the measure of each angle.

murzikaleks [220]

Answer/Step-by-step explanation:

Given:

m<9 = 80°,

m<5 = 68°

Lines w and v are parallel to each other.

m<1 = m<9 (corresponding angles theorem)

m<1 = 80°

m<2 + m<1 = 180° (linear pair)

m<2 + 80° = 180° (substitution)

m<2 = 180° - 80°

m<2 = 100°

m<3 = m<1 (vertical angles are congruent)

m<3 = 80°

m<4 = m<2 (vertical angles are congruent)

m<4 = 100°

m<6 + m<5 = 180° (linear pair)

m<6 + 68° = 180° (substitution)

m<6 = 180° - 68°

m<6 = 112°

m<7 = m<5 (vertical angles)

m<7 = 68°

m<8 = m<6 (vertical angles)

m<8 = 112°

m<10 = m<2 (corresponding angles)

m<10 = 100°

m<11 = m<9 (vertical angles)

m<7 = 80°

m<12 = m<10 (vertical angles)

m<12 = 100°

m<13 = m<5 (corresponding angles)

m<13 = 68°

m<14 = m<6 (corresponding angles)

m<14 = 112°

m<15 = m<13 (vertical angles)

m<15 = 68°

m<16 = m<14 (vertical angles)

m<16 = 112°

6 0

3 years ago

A couple needs $55,000 as a down payment for a home. If they invest the $40,000 they have at 4% compounded quarterly, how long w

slava [35]

Answer:

8 years

Step-by-step explanation:

Compound interest formula

$A(t)= A_0(1+\frac{r}{n})^{nt}$

A(t) is the final amount 55000

A_0= 40000, r= 4% = 0.04, for quarterly n=4

$55000=40000(1+\frac{0.04}{4})^{4t}$

divide both sides by 40000

$1375=(1+\frac{0.04}{4})^{4t}$

$1375=(1.01)^{4t}$

Take ln on both sides

$ln(1375)=4tln(1.01)$

divide both sides by ln(1.01)

$\frac{ln 1375}{ln 1.01}=4t$

Divide both sides by 4

t=8.00108

So it takes 8 years

8 0

4 years ago

Each side on a sticky note measures 9 centimeters. what is the srea of the sticky note?

Zielflug [23.3K]

Answer:

Step-by-step explanation:

All sides are equal. So sticky note is in the shape of square.

Area = side * side = 9 * 9 = 81 sq.cm

4 0

3 years ago

Show that 2^2n-1 +1 is divisible by 3 for all n > 1.

lakkis [162]

Step-by-step explanation:

Let's assume that

$P(n)\ =\ 2^{2n-1}+1$ is divisible by 3.

for n= 1

$P(1)\ =\ 2^{2.(1)-1}+1$

= 3

Hence, P(1) is true for n=1

for n=2

$P(2)\ =\ 2^{2.(2)-1}+1$

= 9, which is divisible by 3.

As we can see, P(n) is also true for n= 2.

Let's say P(n) is true for n = k

So,

$P(k)\ =\ 2^{2k-1}+1$ is divisible by 3.

$=>\ P(k+1)\ =\ 2^{2(k+1)-1}+1$

$=\ 2^{2k+1}+1$

For P(n) should be true, the difference of P(k+1) and P(k) must will have divisible by 3.

So,

$P(k+1)-P(k)\ =\ 2^{2k+1}+1-(2^{2k-1}+1)$

$=\ 2^{2k-1}(2^2-1)$

$=\ 3\times 2^{2k-1}$

as P(k+1)-P(k) is divisible by 3.

As a result, P(n) is true for all n>1.

8 0

3 years ago