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3 years ago

7

Robert earns $300 each week. What equation shows the relationship between salary per week (s), number of weeks worked (w), and t

otal income (t).

2 answers:

zvonat [6]3 years ago

7 0

The equation is: T=S x W

astraxan [27]3 years ago

5 0

Answer:

t = 300w

t = total income

w = number of weeks worked

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Suppose a principal amount of $2079 were invested into a simple interest account that pays an annual rate of 2.31% then the amou

Anna35 [415]

Answer:

The amount of interest earned at the end of 14 years would be $672.3486

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

$E = P*I*t$

In which E are the earnings, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

In this problem, we have that:

$P = 2079, I = 0.0231, t = 14$

So

$E = 2079*0.0231*14 = 672.3486$

The amount of interest earned at the end of 14 years would be $672.3486

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3 years ago

Looking at the top of tower A and base of tower B from points C and D, we find that ∠ACD = 60°, ∠ADC = 75° and ∠ADB = 30°. Let t

katrin2010 [14]

Answer:

$\text{Exact: }AB=25\sqrt{6},\\\text{Rounded: }AB\approx 61.24$

Step-by-step explanation:

We can use the Law of Sines to find segment AD, which happens to be a leg of $\triangle ACD$ and the hypotenuse of $\triangle ADB$ .

The Law of Sines states that the ratio of any angle of a triangle and its opposite side is maintained through the triangle:

$\frac{a}{\sin \alpha}=\frac{b}{\sin \beta}=\frac{c}{\sin \gamma}$

Since we're given the length of CD, we want to find the measure of the angle opposite to CD, which is $\angle CAD$ . The sum of the interior angles in a triangle is equal to 180 degrees. Thus, we have:

$\angle CAD+\angle ACD+\angle CDA=180^{\circ},\\\angle CAD+60^{\circ}+75^{\circ}=180^{\circ},\\\angle CAD=180^{\circ}-75^{\circ}-60^{\circ},\\\angle CAD=45^{\circ}$

Now use this value in the Law of Sines to find AD:

$\frac{AD}{\sin 60^{\circ}}=\frac{100}{\sin 45^{\circ}},\\\\AD=\sin 60^{\circ}\cdot \frac{100}{\sin 45^{\circ}}$

Recall that $\sin 45^{\circ}=\frac{\sqrt{2}}{2}$ and $\sin 60^{\circ}=\frac{\sqrt{3}}{2}$ :

$AD=\frac{\frac{\sqrt{3}}{2}\cdot 100}{\frac{\sqrt{2}}{2}},\\\\AD=\frac{50\sqrt{3}}{\frac{\sqrt{2}}{2}},\\\\AD=50\sqrt{3}\cdot \frac{2}{\sqrt{2}},\\\\AD=\frac{100\sqrt{3}}{\sqrt{2}}\cdot\frac{ \sqrt{2}}{\sqrt{2}}=\frac{100\sqrt{6}}{2}={50\sqrt{6}}$

Now that we have the length of AD, we can find the length of AB. The right triangle $\triangle ADB$ is a 30-60-90 triangle. In all 30-60-90 triangles, the side lengths are in the ratio $x:x\sqrt{3}:2x$ , where $x$ is the side opposite to the 30 degree angle and $2x$ is the length of the hypotenuse.

Since AD is the hypotenuse, it must represent $2x$ in this ratio and since AB is the side opposite to the 30 degree angle, it must represent $x$ in this ratio (Derive from basic trig for a right triangle and $\sin 30^{\circ}=\frac{1}{2}$ ).

Therefore, AB must be exactly half of AD:

$AB=\frac{1}{2}AD,\\AB=\frac{1}{2}\cdot 50\sqrt{6},\\AB=\frac{50\sqrt{6}}{2}=\boxed{25\sqrt{6}}\approx 61.24$

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3 years ago

Read 2 more answers

Solve this inequality 5 x + 2 < 32

Hatshy [7]

Answer:

Here is your answer:

5x + 2 < 32

solution:

5x+ 2 < 32

or, 5x < 32-2

or, 5x < 30

or, 5x < 30/2

or, 5x < 15

or, x < 15/3

or, x < 5

therefore, x < 5 <u>ans</u>

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3 years ago

What is square root of 64?

3241004551 [841]

Answer:

8

Step-by-step explanation:

8*8=64

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The inequality log8(2x) < log2(x – 2) can be graphed on the graphing calculator by using the inequalities log8(2x) < y and

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Answer:

c - (4, ∞)

Step-by-step explanation:

answer on edg

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