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2 years ago

6. In the figure below, measure of angle 1 = 3x + 5, measure of angle 2 = 5x - 18, and measure of angle 3 = 7x-2

Mathematics

1 answer:

Lesechka [4]2 years ago

4 0

See photo for solution and mark me as brainliest if i helped :)

A: although it seems like they are forming a 90º angle, they actually add up to a 89 º angle and therefore are not complementary

B: see photo

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a) The curve with equation y2 = x3 + 3x2 is called the Tschirnhausen cubic. Find an equation of the tangent line to this curve a

Neporo4naja [7]

Answer:

Tangent at (1,2) has value $\frac{15}{4}$ . And (-2, 4) is the point of intersection of horizontal tangent.

Step-by-step explanation:

Given curve equation,

$y^2=x^3+3x^2\hfill (1)$

To find tangent at (x,y)=(1,2) and point of intersection of horizontal tangent, differentiate (1) withrespect to x we get,

$2y\frac{dy}{dx}=x^3+3x^2$

$\implies \frac{dy}{dx}=\frac{3(x^2+2x)}{2y}$

At (1, 2), tangent line is,

$\frac{dy}{dx}|_{(1,2)}}=\frac{15}{4}$

To find point of intersection of horizontal tangent we have to do,

$\frac{dy}{dx}=0$

$\implies x(x+2)=0\implies x=0 or -2$

Thus,

At x=0, y=0

but snce,

$\lim_{y\to 0}\frac{dy}{dx}\to \infty$

at (0,0) there exist a vertical tangent. And,

At x=-2, y=4.

Thus (-2, 4) is the point of intersection of horizontal tangent.

6 0

2 years ago

Anna bought 8 tetras and 2 rainbow fish for her aquarium. The rainbow fish cost $6 more than the tetras. She paid a total of $

____ [38]

Answer:

C, D, and E

Step-by-step explanation:

When trying to solve for the cost of each item you will find a rainbow fish is $8.50 and a tetra is $2.50. If you use that information to solve the other answer choices C, D, and E would be correct

5 0

2 years ago

Read 2 more answers

For three consecutive years, Sam invested some money at the start of the year. The first year, he invested x dollars. The second

nikitadnepr [17]

Year Sam Sally1: X (3/2)X-10002: (5/2)X-2000 2X-15003: X/5+1000 X/4+1400Total 37X/10-1000 15X/4-1100
Since their investments are known to be equal, we equate the two totals and solve for X.37X/10-1000=15X/4-1100(150-148)X/40 = 1100-1000X/20=100X=2000
So Sam invested $2000 the first year.Sally invested X/4+1400=1900 in the last year.

6 0

1 year ago

The owner of a manufacturing plant employs eighty people. As part of their personnel file, she asked each one to record to the n

wariber [46]

Answer:

Mean of the sample = 27.83

The variance of the the sample = 106.96

Standard deviation of the sample = 10.34

Step-by-step explanation:

Step(i):-

Given random sample of six employees

x 26 32 29 16 45 19

mean of the sample

$x^{-} = \frac{26+32+29+16+45+19}{6} = 27.83$

Mean of the given data = 27.83

Step(ii):-

Given data

x : 26 32 29 16 45 19

x - x⁻ : -1.83 4.17 1.17 -11.83 17.17 -8.83

(x - x⁻)² : 3.3489 17.3889 1.3689 139.9489 294.80 77.9689

∑ (x-x⁻)² = 534.8245

Given sample size 'n' =6

The variance of given data

S² = ∑(x-x⁻)² / n-1

$S^{2} = \frac{534.8245}{6-1} = 106.9649$

The variance of the given sample = 106.9649

Step(iii):-

Standard deviation of the given data

$S = \sqrt{variance} = \sqrt{106.9649} =10.3423$

Standard deviation of the sample = 10.3423

8 0

2 years ago

It takes one week for a crew of workers to pave 3/5 kilometer of a road. At that rate, how long will it take to pave 1 kilometer

kondaur [170]

1 kilometer =5/3 week

Step-by-step explanation:

Given that the crew paves 3/5 kilometer of a road in 1 week then this can be written as;

3/5 k = 1 week

For 1 kilometer of a road,

3/5k = 1 week

1k=?

perform cross product as;/multiplication equation

1*1 / 3/5

1*5/3

5/3, 1 2/3 weeks

A division equation will be'

3/5 kilometers = 1 week

Divide both sides by 3/5

1 kilometer =5/3 week

Learn More

Multiplication /Division :brainly.com/question/11892889

Keywords: kilometers, equation, multiplication.division

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4 0

2 years ago