Alisa can ride her bike 2 miles in 7 minutes, how long would it take her to ride 10miles if she rides at the same rate?

Leo works at McDonalds, and gets paid $8.50 hr. He passed his store’s inspection and received a $100 bonus.

Semmy [17]

Answer:

$8.50hr+ $100=x

Step-by-step explanation:

His $8.50 per hour is given to him plus $100 bonus.

7 0

3 years ago

Read 2 more answers

How much simple interest rate would earn if had $10,000 and you were being paid 5% for 15 months?

lakkis [162]

Here is the interest equation: I=prt
Where I is interest, p is principal, r is rate and t is time(in years).
Substitute with known values.

I= prt
I= 10000(.05)(1 and 1 over 4)
I= 625
Answer: $625 for 15 months.

4 0

3 years ago

For positive acute angles A and B, it is known that tan A = 35/12 and sin B = 20/29. Find the value of sin(A - B ) in the simple

almond37 [142]

Answer:

$\displaystyle \sin(A-B)=\frac{495}{1073}$

Step-by-step explanation:

We are given that:

$\displaystyle \tan(A)=\frac{35}{12}\text{ and } \sin(B)=\frac{20}{29}$

Where both A and B are positive acute angles.

And we want to find he value of sin(A-B).

Using the first ratio, we can conclude that the opposite side is 35 and the adjacent side is 12.

Then by the Pythagorean Theorem, the hypotenuse is:

$h = \sqrt{35^2 + 12^2} =37$

Using the second ratio, we can likewise conclude that the opposite side is 20 and the hypotenuse is 29.

Then by the Pythagorean Theorem, the adjacent is:

$a=\sqrt{29^2-20^2}=21$

Therefore, we can conclude that:

So, for A, the adjacent is 12, opposite is 35, and the hypotenuse is 37.

For B, the adjacent is 21, opposite is 20, and the hypotenuse is 29.

We can rewrite sin(A-B) as:

$\sin(A-B)=\sin(A)\cos(B)-\cos(A)\sin(B)$

Using the above conclusions, this yields: (Note that since A and B are positive acute angles, all resulting ratios will be positive.)

$\displaystyle \sin(A-B)=\Big(\frac{35}{37}\Big)\Big(\frac{21}{29}\Big)-\Big(\frac{12}{37}\Big)\Big(\frac{20}{29}\Big)$

Evaluate:

$\displaystyle \sin(A-B)=\frac{735-240}{1073}=\frac{495}{1073}$

6 0

3 years ago

Find the value of a and of b for which<br>(a) the solution of x2 + ax < b is<br>-2<x < 4

KengaRu [80]

Answer: $a = -2$

$b = 8$

Step-by-step explanation:

Given :

$x^{2} +ax$

re - writing the equation , we have

$x^{2} +ax-b$

we need to find the value of a and b for which -2<x < 4 , this means that the roots of the quadratic equation are -2<x < 4.

The formula for finding the quadratic equation when the roots are known is :

$x^{2}$ - sum of roots(x) + product of root = 0

sum of roots = -2 + 4 = 2

product of roots = -2 x 4 = -8

substituting into the formula , we have:

$x^{2} -2x-8=0$ , which could be written in inequality form as

$x^{2} -2x-8$

comparing with $x^{2} +ax-b$ , it means that :

$a = -2$

$b = 8$

3 0

3 years ago

A portion of a roller coaster track is shown in the figure above. the roller coaster track is shown at ground level at point S a

eimsori [14]

Answer:

Step-by-step explanation:

This is classic right triangle trig. The height of the hill is 78.4 which serves as the side opposite the reference angle of 23 degrees. The side we are looking for is the hypotenuse of that triangle. The trig ratio that relates the side opposite a reference angle to the hypotenuse of the right triangle is the sin ratio. Setting it up using our values:

$sin(23)=\frac{78.4}{x}$ , where x is the unknown length of the hypotenuse. Solving for x:

$x=\frac{78.4}{sin(23)}$

Make sure your calculator is in degree mode before entering this in. You will get a length of the hypotenuse as 200.649 feet, so choice A.

4 0

4 years ago