A line that passes through the origin also passes through the point (6,2). What is the slope of the line?

please answer with an explanation

Answer:

y=4√3 units

Step-by-step explanation:

Hi there!

We are given ΔABC, which is a right triangle (m<C=90°), m<A=60°, AB=8, and BC=y

We need to find the value of y (BC)

The side AB is the hypotenuse of the  (the side opposite from the right angle).

BC is a leg, which is a side that makes up the right angle.

Now, if we have a right triangle that has one of the acute angles as 60°, the side OPPOSITE from that 60° angle (in this case, BC) is equal to [tex]\frac{a\sqrt{3}}{2}[/tex], where a is the length of the hypotenuse

Since we have the hypotenuse given as 8, the length of BC (y) is [tex]\frac{8\sqrt{3}}{2}[/tex], or 4√3

so y=4√3 units

Hope this helps!

Answer:

13 miles

Step-by-step explanation:

He hikes 4 mph downhill and it takes 30 minutes or 0.5 hours lesser than the trip uphill at 2 mph.

Thus, if the distance upward is x and we are told the distance downhill is 3 miles longer.

Then, since time = distance/speed, we have;

((x + 3)/4) + 0.5 = x/2

Multiply through by 4 to get;

x + 3 + (0.5 × 4) = 2x

x + 5 = 2x

2x - x = 5

x = 5 miles

Now, it means distance uphill = 5 miles and distance downhill = 5 + 3 = 8 miles

Thus, total distance covered = 8 + 5 = 13 miles

Answer:

2x + 2y = 4 and 4x + 4y = 16

Step-by-step explanation:

For two lines to be parallel, they must have the same slope.

To determine the correct answer to the question, we shall determine the slope of each equation in the given options to see which have the same slope. This can be obtained as follow:

1st option:

3x + 2y = 45 and 8x + 4y = 135

We shall rearrange the above equations to look like y = mx + c

NOTE: m is the slope.

3x + 2y = 45

rearrange

2y = –3x + 45

Divide both side by 2

y = –3x/2 + 45/2

Slope (m) = –3/2

8x + 4y = 135

Rearrange

4y = –8x + 135

Divide both side by 4

y = –8x/4 + 135/4

Slope (m) = –8/4 = –2

The two equation has different slopes. Thus, they are not parallel.

2nd option:

x + y = 25 and 2x + y = 15

x + y = 25

Rearrange

y = –x + 25

Slope (m) = –1

2x + y = 15

Rearrange

y = –2x + 15

Slope (m) = –2

The two equations has different slopes. Thus, they are not parallel.

3rd option:

2x + 2y = 50 and 4x + 2y = 90

2x + 2y = 50

Rearrange

2y = –2x + 50

Divide both side by 2

y = –2x/2 + 50/2

Slope (m) = –2/2 = –1

4x + 2y = 90

Rearrange

2y = –4x + 90

Divide both side by 2

y = –4x/2 + 90/2

Slope (m) = –4/2 = –2

The two equations has different slopes. Thus, they are not parallel.

4th option:

2x + 2y = 4 and 4x + 4y = 16

2x + 2y = 4

Rearrange

2y = –2x + 4

Divide both side by 2

y = –2x/2 + 4/2

Slope (m) = –2/2 = –1

4x + 4y = 16

Rearrange

4y = –4x + 16

Divide both side by 4

y = –4x/4 + 16/4

Slope (m) = –4/4 = –1

The two equations have the same slopes. Thus, they are parallel.

Answer:

547 500

Step-by-step explanation:

Interest for 1 year:

0.01%×365=3.65 a year

3.65×10=36.5% for 10 years

36.5×1,500,000÷100=547 500

The interest paid after 10 years is 547 ,500 Baht.

Interest is the amount paid or earned when a loan is taken or an investment is done respectively.

It is given that

Principal = 1,500,000 Baht

Rate = 0.01 % per day

Time period = 10 years

Interest = ?

Interest = P *R *T/100

Interest = 1500000 * 0.01 *365* 10 / 100

Interest = 547,500 Baht

Therefore the interest paid after 10 years is 547 ,500 Baht.

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Answer:

x = 14/3

Step-by-step explanation:

9.

The given equation is:

(x-2)+(x-3)+(x-9)=0

After opening the brackets,

x-2+x-3+x-9=0

3x+(-2-3-9) = 0

3x-14=0

x = 14/3

So, the value of x is equal to 14/3.

Step-by-step explanation:

D(.10) + Q(.25) = 4

I think

Answer:

D(.10) + Q(.25) = 4

Step-by-step explanation:

Answer:

The point estimate for the number of pieces per package is of 18.72.

Step-by-step explanation:

Point estimate of a population mean:

The mean of the sample gives an estimate for the population mean.

They find that the sample mean number of pieces is 18.72.

This means that the point estimate for the number of pieces per package is of 18.72.

Let the <C=x

We know in a triangle

☆Sum of angles=180°

[tex]\\ \sf\longmapsto 51+26+x=180[/tex]

[tex]\\ \sf\longmapsto 77+x=180[/tex]

[tex]\\ \sf\longmapsto x=180-77[/tex]

[tex]\\ \sf\longmapsto x=103°[/tex]

Answer:

(d) 7

Step-by-step explanation:

The total number of subsets that can be derived from a set with n elements is given by;

2ⁿ

Out of these subsets, there is one empty set. Therefore, the total number of non-empty subsets is given by;

2ⁿ - 1

Given:

A = {x, y, z}

Set A has 3 elements. This means that n = 3

Therefore, the total number of subsets that can be derived from set A is

2ⁿ = 2³ = 8

One of these 8 subsets is an empty set, therefore, the total number of non-empty subsets of A is;

2ⁿ - 1 = 2³ - 1

8 - 1 = 7

This can be checked by writing all the possible subsets of A as follows;

∅

{x}

{y}

{z}

{x, y}

{y, z}

{x, z}

{x, y, z}

Removing the empty set ∅, the non-empty subsets of A are;

{x}

{y}

{z}

{x, y}

{y, z}

{x, z}

{x, y, z}

Answer:

Step-by-step explanation:

Solution of the equation [tex]\sqrt{3} (cosec\theta) -2=0[/tex]in the  [ 0, 2π) is [tex]\frac{\pi }{3}[/tex] and [tex]\frac{2\pi }{3}[/tex].

" Trigonometric ratios are defined as relation of the ratio of the sides of the triangle to the acute angle of the given triangle enclosed in it."

Formula used

[tex]cosec\theta = \frac{1}{sin\theta}[/tex]

According to the question,

Given trigonometric ratio equation,

[tex]\sqrt{3} (cosec\theta) -2=0[/tex]

Replace trigonometric ratio [tex]cosec\theta[/tex] by [tex]sin\theta[/tex]  in the above equation we get,

[tex]\sqrt{3} (\frac{1}{sin\theta} ) -2=0\\\\\implies \sqrt{3} (\frac{1}{sin\theta} ) = 2\\\\\implies sin\theta=\frac{\sqrt{3} }{2}[/tex]

As per given condition of the interval [ 0, 2π) we have,

[tex]\theta = sin^{-1} \frac{\sqrt{3} }{2} \\\\\ implies \theta = \frac{\pi }{3} or \frac{2\pi }{3}[/tex]

Hence, solution of the equation [tex]\sqrt{3} (cosec\theta) -2=0[/tex]in the  [ 0, 2π) is

[tex]\frac{\pi }{3}[/tex] and [tex]\frac{2\pi }{3}[/tex].

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Answer:

Her food cost as a percentage of sales is 33.58%.

Step-by-step explanation:

Since Chef Amy does beginning inventory on Thursday night and finds that she has $ 4697 in food products in the restaurant, and throughout the week she purchases:

$ 668 produces

$ 2206 meat

$ 2488 dry goods

$ 3755 dairy

The following Thursday she does ending inventory and finds that she has $ 3518 in food.

She looks at her sales de ella and finds that she made $ 30658 over the same 7 day period.

To determine what her food cost is as a percentage of sales (her food cost percentage), the following calculation must be performed:

4,697 + 668 + 2,206 + 2,488 + 3,755 = 13,814

13,814 - 3,518 = 10,296

30,658 = 100

10,296 = X

10,296 x 100 / 30,658 = X

1,029,600 / 30,658 = X

33.58 = X

Therefore, her food cost as a percentage of sales is 33.58%.

Answer:

it would be 1/4(60)

Step-by-step explanation:

30 percent of 61 is 18.3 and 1/4 of 60 is 15 which is closest to 18.3

Answer:

18x2 is 36 but you have to minus it so the answer is 28.

Answer:

8 are bad in math and 16 in physics

Step-by-step explanation:

Answer: The answer is b

Answer:

Step-by-step explanation:

Volume of the 3d composite figure is,

(7×6×5)+(7×6×5)/3

= 210+70

= 280 cm³

Relationship between the two volumes,

Volume of the rectangular prism is 3 times the volume of the pyramid.

Answered by GAUTHMATH

Answer:

I was gonna anwer it but somone already did.

Step-by-step explanation:

Answer:

[tex]\int (x+ 1) \sqrt{2x-1} dx = \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{15}(2x-1)^{\frac{5}{2}} + C[/tex]

Step-by-step explanation:

[tex]\int (x+1)\sqrt {(2x-1)} dx\\Integrate \ using \ integration \ by\ parts \\\\u = x + 1, v'= \sqrt{2x - 1}\\\\v'= \sqrt{2x - 1}\\\\integrate \ both \ sides \\\\\int v'= \int \sqrt{2x- 1}dx\\\\v = \int ( 2x - 1)^{\frac{1}{2} } \ dx\\\\v = \frac{(2x - 1)^{\frac{1}{2} + 1}}{\frac{1}{2} + 1}} \times \frac{1}{2}\\\\v= \frac{(2x - 1)^{\frac{3}{2}}}{\frac{3}{2}} \times \frac{1}{2}\\\\v = \frac{2 \times (2x - 1)^{\frac{3}{2}}}{3} \times \frac{1}{2}\\\\v = \frac{(2x - 1)^{\frac{3}{2}}}{3}[/tex]

[tex]\int (x+1)\sqrt(2x-1)dx\\\\ = uv - \int v du[/tex]                              

[tex]= (x +1 ) \cdot \frac{(2x - 1)^{\frac{3}{2}}}{3} - \int \frac{(2x - 1)^{\frac{3}{2}}}{3} dx \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ u = x + 1 => du = dx \ ][/tex]    

[tex]= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \int (2x - 1)^{\frac{3}{2}}} dx\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \times ( \frac{(2x-1)^{\frac{3}{2} + 1}}{\frac{3}{2} + 1}) \times \frac{1}{2}\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \times ( \frac{(2x-1)^{\frac{5}{2}}}{\frac{5}{2} }) \times \frac{1}{2}\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{15} \times (2x-1)^{\frac{5}{2}} + C\\\\[/tex]

Answer:

7 brown M&Ms.

Step-by-step explanation:

This question is not complete, but I will assume that the final question is how many brown M&Ms will be in this package.

0.14 × 52 is our equation.

The answer is 7.28. We cannot have .28 of a brown M&M in a package (unless you count the broken ones) so there will be, on average, 7 brown M&Ms in a package.

(again, the question is incomplete, so this may not be the answer)

Answer:

The number of ways = 151200

Step-by-step explanation:

Below is the calculation of the number of ways:

Total number of people = 10

Total number of posts = 6

The number of ways = 10P6

The number of ways = [tex]\frac{10!}{10! - 6!}[/tex]

The number of ways = 10 x 9 x 8 x 7 x 6 x 5

The number of ways = 151200

Answer:

The 3rd

Step-by-step explanation:

If x goes to infinity, f(x) goes to infinity too:

[tex]lim \: \frac{2 {x}^{2} }{3x - 1} = lim \frac{2x}{3 - \frac{1}{x} } = \frac{ 2 \times \infty }{3 - 0} = \infty [/tex]

1.

X = 0

2x + 1 = 0

X = 0

X = - ½ (Because we brought the numbers from one side to the other)

2.

Not sure for number 2.

Answer:

r= 17.73174

Step-by-step explanation:

calculations

Step-by-step explanation:

Given: [tex]y = -\dfrac{2}{x}[/tex]

Derivative of a power function [tex]x^n[/tex]:

[tex]\dfrac{d}{dx}(x^n) = nx^{n-1}[/tex]

Therefore,

[tex]\dfrac{dy}{dx}=-2(-1)x^{-2} = \dfrac{2}{x^2}[/tex]

Answer:

[tex]A=603.18\ cm^2[/tex]

Step-by-step explanation:

The length of a blade, r = 24 cm

The sweeping angle is 120°.

We need to find the total area cleaned at one sweep of the blade. The area of sector is given by :

[tex]A=\dfrac{\theta}{360}\times \pi r^2[/tex]

[tex]A=\dfrac{120}{360}\times \pi \times 24^2\\\\=603.18\ cm^2[/tex]

So, the total area cleaned at one sweep of the blade is [tex]603.18\ cm^2[/tex].

9514 1404 393

Answer:

  a-b

Step-by-step explanation:

Add the two equations together:

  (ax +by) +(bx +ay) = (a² -b²) +(0)

  x(a +b) +y(a +b) = (a +b)(a -b)

  x + y = a - b . . . . . divide by (a+b), assuming a+b ≠ 0

Answer:

It will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.

Step-by-step explanation:

We can write a half-life function to model our function.

A half-life function has the form:

[tex]\displaystyle A=A_0\left(\frac{1}{2}\right)^{t/d}[/tex]

Where A₀ is the initial amount, t is the time that has passes (in this case seconds), d is the half-life, and A is the amount after t seconds.

Since the half-life of the element is 30 seconds, d = 30. Our initial sample has nine grams, so A₀ is 9. Substitute:

[tex]\displaystyle A=9\left(\frac{1}{2}\right)^{t/30}[/tex]

We want to find the time it will take for the element to decay to 0.72 grams. So, we can let A = 0.72 and solve for t:

[tex]\displaystyle 0.72=9\left(\frac{1}{2}\right)^{t/30}[/tex]

Divide both sides by 9:

[tex]\displaystyle 0.08=\left(\frac{1}{2}\right)^{t/30}[/tex]

We can take the natural log of both sides:

[tex]\displaystyle \ln(0.08)=\ln\left(\left(\frac{1}{2}\right)^{t/30}\right)[/tex]

By logarithm properties:

[tex]\displaystyle \ln(0.08)=\frac{t}{30}\ln(0.5)[/tex]

Solve for t:

[tex]\displaystyle t=\frac{30\ln(0.08)}{\ln(0.5)}\approx109.3\text{ seconds}[/tex]

So, it will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.

Answer:

C

Step-by-step explanation:

tracing paper is your friend

Answer:

504 arrangements are possible

Step-by-step explanation:

Arrangements of n elements:

The number of arrangements of n elements is given by:

[tex]A_{n} = n![/tex]

Arrangements of n elements, divided into groups:

The number of arrangements of n elements, divided into groups of [tex]n_1, n_2,...,n_n[/tex] elements is given by:

[tex]A_{n}^{n_1,n_2,...,n_n} = \frac{n!}{n_1!n_2!...n_n!}[/tex]

In this case:

9 pens, into groups of 5, 3 and 1. So

[tex]A_{9}^{5,3,1} = \frac{9!}{5!3!1!} = 504[/tex]

504 arrangements are possible

Answer:

25 goat and 15 chicken

Step-by-step explanation:

Say the number of goats is G, then the number of chickens is 40 - G as there are 40 heads and each chicken and each goat has one head.

The number of feet is 130

So 2(40 - G) + 4G = 130

So 80 - 2G + 4G = 130

2G = 50

G = 25

25 goats and 15 chickens