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ivanzaharov [21]

3 years ago

14

What do the following two equations represent? y-8 +5) y-8- +5) Choose 1 answer: The same line Distinct parallel lines Perpendic

ular lines Intersecting, but not perpendicular lines

1 answer:

Over [174]3 years ago

7 0

Answer:

I think it would be y-3-m

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The expression 1500(1.07)^t represents the value of a $1500 investment that earns 7% interest per year, compounded annually for

fomenos

Total = Principal * (1 + rate) ^ years
Total = 1,500 * (1.07) ^ 2
Total = 1,717.35

6 0

3 years ago

Erin had 6 pens Justin gave her some more now she has 9 pens how many did Justin give her

Katyanochek1 [597]

Answer:

3

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Anna enjoys having dinner at a restaurant in a town where the sales tax on meals is 10%. She leaves 15% tip before the sales tax

vitfil [10]

Answer:

The cost of her dinner without tax or tip is <u>$22</u>.

Step-by-step explanation:

Given:

Anna enjoys having dinner at a restaurant in a town where the sales tax on meals is 10%.

She leaves 15% tip before the sales tax is applied, and the tax is calculated on the pre-tip amount.

She spends a total of $27.50 on her dinner.

Now, to find the cost of her dinner without tax or tip.

Let the cost of dinner without tax or tip be $x.$

So, the tax is:

$10\%\ of\ x.$

$=\frac{10}{100} \times x$

$=0.10\times x$

$=0.10x.$

And, the tip is:

$15\%\ of \ x.$

$=\frac{15}{100} \times x$

$=0.15\times x$

$=0.15x.$

<u><em>As given, she spends a total $27.50 on her dinner.</em></u>

Now, to get the cost of her dinner without tax or tip:

$x+0.15x+0.10x=27.50$

$x+0.25x=27.50$

$1.25x=27.50$

<em>Dividing both sides by 1.25 we get:</em>

$x=22$

$x=\$22.$

Therefore, the cost of her dinner without tax or tip is <u>$22</u>.

5 0

3 years ago

Dan is watching The Birds in his backyard. Of the birds he watches, 9. Of them,or 45%, are sparrows. How many birds are in his b

ra1l [238]

If 9 of the sparrows is 45% of the birds in the backyard, 9/x = 45/100.

Cross multiply to get 9 * 100 = 45x; simplified is 900 = 45x or 20.

This means that there are 20 birds in the backyard. You can check this by dividing 9/20 which equals 45%

5 0

3 years ago

Need help with trig problem in pic

Sidana [21]

Answer:

a) $cos(\alpha)=-\frac{3}{5}\\$

b) $\sin(\beta)= \frac{\sqrt{3} }{2}$

c) $\frac{4+3\sqrt{3} }{10}\\$

d) $\alpha\approx 53.1^o$

Step-by-step explanation:

a) The problem tells us that angle $\alpha$ is in the second quadrant. We know that in that quadrant the cosine is negative.

We can use the Pythagorean identity:

$tan^2(\alpha)+1=sec^2(\alpha)\\(-\frac{4}{3})^2 +1=sec^2(\alpha)\\sec^2(\alpha)=\frac{16}{9} +1\\sec^2(\alpha)=\frac{25}{9} \\sec(\alpha) =+/- \frac{5}{3}\\cos(\alpha)=+/- \frac{3}{5}$

Where we have used that the secant of an angle is the reciprocal of the cos of the angle.

Since we know that the cosine must be negative because the angle is in the second quadrant, then we take the negative answer:

$cos(\alpha)=-\frac{3}{5}$

b) This angle is in the first quadrant (where the sine function is positive. They give us the value of the cosine of the angle, so we can use the Pythagorean identity to find the value of the sine of that angle:

$cos (\beta)=\frac{1}{2} \\\\sin^2(\beta)=1-cos^2(\beta)\\sin^2(\beta)=1-\frac{1}{4} \\\\sin^2(\beta)=\frac{3}{4} \\sin(\beta)=+/- \frac{\sqrt{3} }{2} \\sin(\beta)= \frac{\sqrt{3} }{2}$

where we took the positive value, since we know that the angle is in the first quadrant.

c) We can now find $sin(\alpha -\beta)$ by using the identity:

$sin(\alpha -\beta)=sin(\alpha)\,cos(\beta)-cos(\alpha)\,sin(\beta)\\$

Notice that we need to find $sin(\alpha)$ , which we do via the Pythagorean identity and knowing the value of the cosine found in part a) above:

$sin(\alpha)=\sqrt{1-cos^2(\alpha)} \\sin(\alpha)=\sqrt{1-\frac{9}{25} )} \\sin(\alpha)=\sqrt{\frac{16}{25} )} \\sin(\alpha)=\frac{4}{5}$

Then:

$sin(\alpha -\beta)=\frac{4}{5}\,\frac{1}{2} -(-\frac{3}{5}) \,\frac{\sqrt{3} }{2} \\sin(\alpha -\beta)=\frac{2}{5}+\frac{3\sqrt{3} }{10}=\frac{4+3\sqrt{3} }{10}$

d)

Since $sin(\alpha)=\frac{4}{5}$

then $\alpha=arcsin(\frac{4}{5} )\approx 53.1^o$

4 0

3 years ago