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3 years ago

Please help! Thank you!

Mathematics

1 answer:

alexandr402 [8]3 years ago

4 0

Answer:

y=-1/3x+10

Step-by-step explanation:

y=3x+1

The line perpendicular would have a negative reciprocal of the slope of 3 which means that you would add a negative sign and then flip 3/1 into 1/3 resulting in -1/3 as the slope.

To find the line that passes through the point (6,8) you would plug the values into the equation y=mx+b

m=-1/3x as found above

6 is the x-value and 8 is the y-value

8=(-1/3)(6)+b

8=-2+b

Add 2 on both sides and you get b to equal 10

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Find the complement and the supplement of the given angle. 23°

e-lub [12.9K]

Answer:

Complement: 67°

Supplement: 157°

Step-by-step explanation:

Complementary angles = 90°

90-23=67°

Supplementary angles = 180°

180-23=157°

7 0

3 years ago

Round 8,349.0054 to the nearest thousands place.

pentagon [3]

To round this we have to go to the thousands place since the thousands place in this question is 8 its closer to 10 so the answer is 10k or 10,000

3 0

3 years ago

Read 2 more answers

What is the equation of the line that is parallel to the given line and passes theought the point (12, -2)

Nesterboy [21]

Answer:

Option D (y = 5/6x -12).

Step-by-step explanation:

Hey there!

The equation of the line which passes through the point (12,-2) is (y+2) = m2(x-12)………(i) [Using one point formula].

According to the question, the first line passes through point (12,6) and (0,-4).

So,

$slope(m1) = \frac{y2 - y1}{x2 - x1}$

$or \: m1 = \frac{ - 4 - 6}{0 - 12}$

$or \: m1 = \frac{5}{6}$

Therefore, the slope of the line is 5/6.

Now as per the condition of parallel lines, m1 =m2 = 5/6.

So, keeping the value of m2 in equation (i), we get;

(y+2) = 5/6(x-12)

$y + 2 = \frac{5}{6} x - 10$

or, y = 5/6x - 12.

Therefore, the required equation is y = 5/6 X - 12.

Hope it helps!

3 0

3 years ago

Christina earns $250 a week. To budget money, she pays $135 in bills each week. How much money does Christina have left at the e

Rama09 [41]

Answer:

460 USD

Step-by-step explanation:

monthly earnings = 250 x 4 = 1000

monthly bills = 135 x 4 = 540

end of month = 1000 - 540 = 460 USD

7 0

3 years ago

A closed, rectangular-faced box with a square base is to be constructed using only 36 m2 of material. What should the height h a

kkurt [141]

Answer:

$b=h=\sqrt{6}$ m

Step-by-step explanation:

Let

Bas length of box=b

Height of box=h

Material used in constructing of box=36 square m

We have to find the height h and base length b of the box to maximize the volume of box.

Surface area of box= $2b^2+4bh$

$2b^2+4bh=36$

$b^2+2bh=18$

$2bh=18-b^2$

$h=\frac{18-b^2}{2b}$

Volume of box, V= $b^2h$

Substitute the values

$V=b^2\times \frac{18-b^2}{2b}$

$V=\frac{1}{2}(18b-b^3)$

Differentiate w. r.t b

$\frac{dV}{db}=\frac{1}{2}(18-3b^2)$

$\frac{dV}{db}=0$

$\frac{1}{2}(18-3b^2)=0$

$\implies 18-3b^2=0$

$\implies 3b^2=18$

$b^2=6$

$b=\pm \sqrt{6}$

$b=\sqrt{6}$

The negative value of b is not possible because length cannot be negative.

Again differentiate w.r.t b

$\frac{d^2V}{db^2}=-3b$

At $b=\sqrt{6}$

$\frac{d^2V}{db^2}=-3\sqrt{6}$

Hence, the volume of box is maximum at $b=\sqrt{6}$ .

$h=\frac{18-(\sqrt{6})^2}{2\sqrt{6}}$

$h=\frac{18-6}{2\sqrt{6}}$

$h=\frac{12}{2\sqrt{6}}$

$h=\sqrt{6}$

$b=h=\sqrt{6}$ m

7 0

3 years ago