Function rule that represents 5 less than one fourth of x is y

Find the lengths of g, h, and j. Round answers to the nearest tenth. (marking brainliest for correct)

Bezzdna [24]

Answer:

j=13, g=20.8, h=24

Step-by-step explanation:

The overall shape given and the shape within, are both right triangles. With right triangles, you are allowed to use the pythagorean theorem formula ( $a^{2} + b^{2} = c^{2}$ ) in order to solve for some sides. In this case, that would be j and h. The five in the smaller triangle is represented by b and the 12 is the hypotenuse so it is represented by c. When you plug in those numbers in the pythagorean theorem formula, you will find the value of j to be 13. When looking at this, we see that 12 is the second greatest value in the right triangle values that we just found, so we know the the opposing angle for that one will be 60 degrees. The 5's opposing side is therefore 30 degrees. When subtracting 90 and 30, we get 60, so therefore you can use the 30 60 90 formula to find the sides of the bigger triangle. The 60 degrees represents g. This formula will be $a\sqrt{3}$ . The a is 12 since it is the smallest value. So therefore, g is $12\sqrt{3}$ , which is 20.8. Now that we have this side, we can just use the pythagorean theorem formula to find the remaining side. Therefore, h is going to be 24

4 0

3 years ago

Linkin Corporation is considering purchasing a new delivery truck. The truck has many advantages over the company’s current truc

Romashka [77]

Answer:

Payback is 7.3 years

NPV $3,099

Step-by-step explanation:

The formula for payback period period=initial investment/annual cost savings

The initial investment is the amount of cash outflow that would be required to purchase the new delivery truck,which is $54,750,while on the other hand the annual cost savings is $7,500

cash payback period=$54,750/$7,500=7.3 years

Ordinarily,the expected payback is 1/2 of 8 years=4 years.

The net present is the present worth of the future cost savings as well as the scrap value of the truck in year 8,calculated by multiplying the cash flows with the discounted factors for relevant years as below:

Years cash flow DCF at 8% Present values

0 -$54,750 1 -$54,750

1-7 years $7500 5.2064 $39,048

8 $34,800 0.54027 $18,801

NPV $3,099

Note that the $34,800 =$7500+$27300

The year 1-7 factor is annuity factor for 8% 7 years

3 0

3 years ago

Remy was on vacation in New France, Canada. He went to the Ratatouille restaurant and had an excellent dinner. How much did

SashulF [63]

Answer:

See both answers in the explanation

Step-by-step explanation:

Given data

Cost of dinner= $32

TIp=18%

Let us find the amount of the tip

=18/100*32

=0.18*32

=$5.76

Hence the total amount paid is

=5.76+32

=$37.76

The Tip is

=$5.76

4 0

3 years ago

1. Let a; b; c; d; n belong to Z with n > 0. Suppose a congruent b (mod n) and c congruent d (mod n). Use the definition

lukranit [14]

Answer:

Proofs are in the explantion.

Step-by-step explanation:

We are given the following:

1) $a \equi b (mod n) \rightarrow a-b=kn$ for integer $k$ .

1) $c \equi d (mod n) \rightarrow c-d=mn$ for integer $m$ .

a)

Proof:

We want to show $a+c \equiv b+d (mod n)$ .

So we have the two equations:

a-b=kn and c-d=mn and we want to show for some integer r that we have

(a+c)-(b+d)=rn. If we do that we would have shown that $a+c \equiv b+d (mod n)$ .

kn+mn = (a-b)+(c-d)

(k+m)n = a-b+ c-d

(k+m)n = (a+c)+(-b-d)

(k+m)n = (a+c)-(b+d)

k+m is is just an integer

So we found integer r such that (a+c)-(b+d)=rn.

Therefore, $a+c \equiv b+d (mod n)$ .

//

b) Proof:

We want to show $ac \equiv bd (mod n)$ .

So we have the two equations:

a-b=kn and c-d=mn and we want to show for some integer r that we have

(ac)-(bd)=tn. If we do that we would have shown that $ac \equiv bd (mod n)$ .

If a-b=kn, then a=b+kn.

If c-d=mn, then c=d+mn.

ac-bd = (b+kn)(d+mn)-bd

= bd+bmn+dkn+kmn^2-bd

= bmn+dkn+kmn^2

= n(bm+dk+kmn)

So the integer t such that (ac)-(bd)=tn is bm+dk+kmn.

Therefore, $ac \equiv bd (mod n)$ .

//

3 0

3 years ago

If 5 n · 5 3 = 5 6 , then n is _____.

OLga [1]

Answer:

n = 109/ 5 if the expression is 5n - 5.3 = 56

7 0

3 years ago