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2 years ago

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John starts a saving account with $100. Every week he adds $6 to his account. Which equation can be used to determine the number

of weeks, w, after which John's account reaches $220?
A: 6w + 100 = 220
B: 6w - 100 = 220
C: 6w + 220 = 100
D: 6 + w = 220

1 answer:

Artist 52 [7]2 years ago

5 0

A would be your answer. If we did 220-100 and divide that by 6, you'd get the equivalent of w.

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Read 2 more answers

Find the measure of the exterior angle in the following triangle. DUE SOON PLZ HELP WITH STEP BY STEP

PSYCHO15rus [73]

Answer:

The measure of an exterior angle = 125°

Hence, option A is correct.

Step-by-step explanation:

As the given triangle is a right-angled triangle ΔABC.

Given the angles

m∠A = 35°

m∠C = 90°

We know that the sum of angles in a triangle is 180°.

Thus,

m∠A + m∠B + m∠C = 180°

substituting m∠A = 35° and m∠C = 90° in the equation

35° + m∠B + 90° = 180°

125 + m∠B = 180°

subtract 125 from both sides

125 + m∠B - 125 = 180° - 125

m∠B = 55°

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m∠B = 55°

As the exterior angle of the given triangle is adjacent to m∠B = 55°.

We know that the exterior angle of a triangle is equal to the sum of two opposite interior angles.

Here,

∠A and ∠C are two opposite interior angles of the exterior angle.

Thus,

The measure of an exterior angle is equal to the sum of two opposite interior angles.

as

m∠A = 35°

m∠C = 90°

so

Exterior angle = m∠A + m∠C

= 35° + 90°

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2 years ago

Carmella is purchasing a $105,000 home and her bank is offering her a 30-

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Answer:

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Step-by-step explanation:

We will use annuity formula, which is:

$P=C[\frac{1-(1+r)^{-n}}{r}]$

Where P is the loan amount

C is the monthly payment

r is the rate of interest [monthly]

n is the time period [in months]

Firstly, let's calculate her normal monthly payment (without purchasing points):

P is 105,000

C is what we need to find

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n is 12*30 = 360

Now, we have:

$P=C[\frac{1-(1+r)^{-n}}{r}]\\105,000=C[\frac{1-(1+0.00375)^{-360}}{0.00375}]\\105,000=C[197.3612]\\C=532.02$

So <u>monthly payment would be around $532.02</u>

<u />

Now,

With each point purchase, the interest rate goes down by 0.25%, so for 2 points it will be 4.5% - 2(0.25) = 4%

Also, since 20% downpayment, the loan amount would be (0.8)(105,000) = 84,000.

Now, putting these values into the annuity formula we have:

$84,000=C[\frac{1-(1+0.0033)^{-360}}{0.0033}]\\84,000=C(210.4766)\\C=399.09$

The <u>monthly payment would be around $399.09</u>

<u />

The amount that is lower is 532.02 - 399.09 = $132.93

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