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2 years ago

Total Price: The sales tax rate is 5%. If the sales tax on a 10-speed bicycle is $9, what is the purchase price?

Mathematics

1 answer:

Lesechka [4]2 years ago

6 0

Answer:

The purchase price is $180

The total price is: $189

Step-by-step explanation:

Sales tax rate = 5\%

Sales tax on bike = $9

We need to find the purchase price.

Let purchase price = x

We know that Sales tax = 5% of x

and Total price = Purchase Price + Sales tax

So, we can write:

Sales tax = 5% of x

Putting values and finding x

$9 =5\% \:of\: x\\9=\frac{5}{100}\:of\:x \\x= \frac{9*100}{5}\\x=180$

So, the value of x i.e Purchase price = $180

The purchase price is $180

Now finding the total price of bicycle

Total price = Purchase Price + Sales tax

Total price = 180 + 9

Total price = $189

So, The total price is: $189

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The graph of an inverse trigonometric function passes through the point (1, pi/2). Which of the following could be the equation

rodikova [14]

Answer: C) $y=sin^-1 x$

Step-by-step explanation:

Since, the graph of an inverse trigonometric function will pass through the point $(1,\frac{\pi}{2})$ ,

If this point satisfies the function,

For the function $y=cos^{-1} x$

If x = 1

$y=cos^{-1}1=0$

Thus, $(1,\frac{\pi}{2})$ is not satisfying function $y=cos^{-1} x$ ,

⇒ The graph of $y=cos^{-1} x$ is not passing through the point $(1,\frac{\pi}{2})$

For the function $y=cot^{-1}x$

If x = 1

$y=cot^{-1}1=\frac{\pi}{4}$

Thus, $(1,\frac{\pi}{2})$ is not satisfying function $y=cot^{-1}x$ ,

⇒ The graph of $y=cot^{-1}x$ is not passing through the point $(1,\frac{\pi}{2})$

For the function $y=sin^{-1} x$

If x = 1

$y=sin^{-1}1=\frac{\pi}{2}$

Thus, $(1,\frac{\pi}{2})$ is satisfying function $y=sin^{-1} x$ ,

⇒ The graph of $y=sin^{-1} x$ is passing through the point $(1,\frac{\pi}{2})$ .

For the function $y=tan^{-1}x$

If x = 1

$y=tan^{-1}1=\frac{\pi}{4}$

Thus, $(1,\frac{\pi}{2})$ is not satisfying function $y=cos^{-1} x$ ,

⇒ The graph of $y=tan^{-1} x$ is not passing through the point $(1,\frac{\pi}{2})$ .

Hence, Option C is correct.

3 0

3 years ago

Consider firing a pumpkin from a canon at a target that is 17 meters away. The pumpkin follows a quadratic path as displayed to

bixtya [17]

A.
(0,00
(2.6,7.9)
(4.8,12.4)
(9.7,15.1)

b.
well, the points don't look like they are on the line but they actually are (plot twist)

so
since (0,0) is on th egarph

0=a(0)²+b(0)+c
0=c
so
f(x)=ax²+bx+0 or
f(x)=ax²+bx

find a and b
sub points

(2.6,7.9)
7.9=a(2.6)²+b(2.6)
7.9=6.76a+2.6b

(4.8,12.4)
12.4=a(4.8)²+b(4.8)
12.4=23.04a+4.8b

use those 2 equations
7.9=6.76a+2.6b
12.4=23.04a+4.8b

eliminate b
multiply first equation by -4.8 and 2nd by 2.6 and add them
-37.92=-32.448a-12.48b
32.24=59.904a-12.48b +
-5.68=27.456a+0b

-5.68=27.456a
divide both sides by 27.456
(-5.68/27.456)=a
find b

12.4=23.04a+4.8b
12.4=(-130.8672/27.456)+4.8b
12.4+(130.8672/27.456)=4.8b
(12.4+(130.8672/27.456))/4.8=b

da equation is
$y= \frac{-5.68}{27.456} x^2+ \frac{12.4+\frac{130.8672}{27.456}}{4.8}x$

c. the roots are found with your calculator
the roots are at x=0 and x=17.287323943662
so very close to the target but not exactly on it
if the target has a radius of 0.287323943662 or more then it will hit the target

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