The sum of two consecutive numbers is n+1. What are the numbers?

1 answer:

5 0

Let, consecutive number is (n-1) & n
Then: n-1+n = n+1
2n-1 = n+1
2n-n = 1+1
n = 2
& (n-1) = 2-1 = 1

So, numbers are 1 & 2

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A point on the terminal side of an acute angle in standard position is (1, 2 √2). Find the cosine value of this angle.

kozerog [31]

Answer:

$cos\theta=1/3$

Step-by-step explanation:

The point at the terminal side of an acute angle is given by $(1, 2\sqrt{2} )$ .

That is,

$x = 1$ and $y= 2\sqrt{2}$ .

Let r be the length of line segment drawn from the origin to the point and is given by the formula:

$r = \sqrt{x^{2} + y^{2}}$

Substituting the values of x and y into r,

$r = \sqrt{1^{2} + (2\sqrt{2} )^{2}}$

$r = \sqrt{1 + 8}$

$r = \sqrt{9}$

Thus, $r=3$

Also, $cos\theta$ is given by:

$cos\theta = x/r\\$

Substituting values of x and r,

$cos\theta = 1/3\\$

4 0

3 years ago

Help, I need it fast! D:

patriot [66]

Let's solve this problem step-by-step.

STEP-BY-STEP SOLUTION:

Let's first establish the simple interest formula which we will require to solve this problem as displayed below:

Simple Interest = Principal × Rate of Interest × No. of Time Periods

I = PRN

Now let's substitute the values from the problem into this formula as displayed below:

I = $90

P = ?

R = 6%

N = 3 years

I = PRN

90 = P × 0.06 × 3

P = 90 / 0.06 × 3

P = 90 / 0.18

P = $500

ANSWER:

As the principal and the amount borrowed is the same, Claire borrowed $500. Therefore, the answer is:

D ) $500

Please mark as brainliest if you found this helpful! :)
Thank you <3

5 0

3 years ago

Circle A has an area of 452.16ft2. With a radius of 12 ft. If circle B has a radius of 17 ft, what is it’s area?

ehidna [41]

Answer: 907.92 ft²

Step-by-step explanation:

1. To solve this problem you must apply the formula for calculate the area of a circle, which is shown below:

$A=r^{2}\pi$