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AleksAgata [21]

3 years ago

10

12. Zac wil spend $185.00, or 5%, of his budget on gasoline. Gas prices have increased, and he needs to adjust his budget. If he

needs to increase his gas budget by $78.00 per month.by what percentage must he reduce his other expenses?

1 answer:

weqwewe [10]3 years ago

6 0

156 but a point in-between 15 and 6

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If line GH is perpendicular to line HJ, then GJ is ____ HJ.

valentinak56 [21]

Option A: >

Solution:

Given a triangle GHJ.

The line GH is perpendicular to line HJ.

This means the triangle is a right angled triangle.

In ΔGHJ, GH is the base of the triangle and

HJ is a height of the triangle.

Then the third side must be the hypotenuse of the right triangle.

We know that by the Pythagoras theorem,

$(\text {Hypotenuse})^2=(\text{Base})^2+(\text{Height})^2$

$(\text {GJ})^2=(\text {GH})^2+(\text {HJ})^2$

This clearly shows that the hypotenuse is greater than the height.

⇒ GJ > HJ

Option A: > is the correct answer.

If line GH is perpendicular to line HJ, then GJ is > HJ.

3 0

3 years ago

Give the first ten terms of the following sequences. You can assume that the sequences start with an index of 1. Logs are to bas

Vitek1552 [10]

Answer:

a)

a1 = log(1) = 0 (2⁰ = 1)

a2 = log(2) = 1 (2¹ = 2)

a3 = log(3) = ln(3)/ln(2) = 1.098/0.693 = 1.5849

a4 = log(4) = 2 (2² = 4)

a5 = log(5) = ln(5)/ln(2) = 1.610/0.693 = 2.322

a6 = log(6) = log(3*2) = log(3)+log(2) = 1.5849+1 = 2.5849 (here I use the property log(a*b) = log(a)+log(b)

a7 = log(7) = ln(7)/ln(2) = 1.9459/0.6932 = 2.807

a8 = log(8) = 3 (2³ = 8)

a9 = log(9) = log(3²) = 2*log(3) = 2*1.5849 = 3.1699 (I use the property log(a^k) = k*log(a) )

a10 = log(10) = log(2*5) = log(2)+log(5) = 1+ 2.322= 3.322

b) I can take the results of log n we previously computed above to calculate 2^log(n), however the idea of this exercise is to learn about the definition of log_2:

log(x) is the number L such that 2^L = x. Therefore 2^log(n) = n if we take the log in base 2. This means that

a1 = 1

a2 = 2

a3 = 3

a4 = 4

a5 = 5

a6 = 6

a7 = 7

a8 = 8

a9 = 9

a10 = 10

I hope this works for you!!

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Cint%5Climits%5E4_3%7Bx%5E%7B2%7D-x%20%7D%20%5C%2C%20dx" id="TexFormula1" title="\int\limits

melisa1 [442]

Answer:

$\frac{53}{6}$

Step-by-step explanation:

$\int\limits^4_3 {x^2-x} \, dx$

= [ $\frac{x^3}{3}$ - $\frac{x^2}{2}$ ] ← evaluate for upper limit - lower limit

= ( $\frac{64}{3}$ - $\frac{16}{2}$ ) - ( $\frac{27}{3}$ - $\frac{9}{2}$ )

= $\frac{64}{3}$ - 8 - 9 + $\frac{9}{2}$

= $\frac{155}{6}$ - 17

= $\frac{53}{6}$

5 0

3 years ago

Chet is camping with his after school club.They have 9 tents and 72 people.the same number of campers will be in each tent. How

Vesna [10]

The answer is 8 campers per tent

8 0

3 years ago

Read 2 more answers

What is 1/6d+2/3 = 1/4(d-2)

GenaCL600 [577]

1/6d + 2/3 = 1/4(d - 2)

First, simplify $\frac{1}{6} d$ to $\frac{d}{6}$ / Your problem should look like: $\frac{d}{6}$ + $\frac{2}{3}$ = $\frac{1}{4}$ (d - 2)
Second, simplify $\frac{1}{4} (d - 2)$ to $\frac{d-2}{4}$ / Your problem should look like: $\frac{d}{6}$ + $\frac{2}{3}$ = $\frac{d-2}{4}$
Third, multiply both sides by 12 (the LCM of 6,4) / Your problem should look like: 2d + 8 = 3(d - 2)
Fourth, expand. / Your problem should look like: 2d + 8 = 3d - 6
Fifth, subtract 2d from both sides. / Your problem should look like: 8 = 3d - 6 - 2d
Sixth, simplify 3d - 6 - 2d to d - 6 / Your problem should look like: 8 = d - 6
Seventh,add 6 to both sides. / Your problem should look like: 8 + 6 = d
Eighth, simplify 8 + 6 to 14 / Your problem should look like:14 = d
Ninth, switch sides. / Your problem should look like: d = 14

Answer: d = 14

3 0

3 years ago