What is the equation of the line that passes through the point (-6,8) and has a slope of -5/3?

Answer:

  √3 is irrational

Step-by-step explanation:

The location of the third point of a triangle can be found using a rotation matrix to transform the coordinates of the given points.

With reference to the attached figure, the slope of line AC is √3, an irrational number. This means the line AC never passes through a point with integer coordinates. (Any point with integer coordinates would be on a line with rational slope.)

The line segments making up an equilateral triangle are separated by an angle of 60°. If two vertices are on grid squares, the third must be a rotation of one of them about the other through an angle of 60°. The rotation matrix is irrational, so the rotated point must have irrational coordinates.

The math of it is this. For rotation of (x, y) counterclockwise 60° about the origin, the transformation matrix is ...

  [tex]\left[\begin{array}{cc}\cos(60^\circ)&\sin(60^\circ)\\-\sin(60^\circ)&\cos(60^\circ)\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}x'\\y'\end{array}\right][/tex]

Cos(60°) is rational, but sin(60°) is not. For any non-zero rational values of x and y, the sum ...

  cos(60°)·x + sin(60°)·y

will be irrational.

As in the attached diagram, if one of the coordinates of the rotated point (B) is zero, then one of the coordinates of its image (C) will be rational. The other image point coordinate cannot be rational.

0.8926 percent of the time, the shipment will be rejected.

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

A delivery of 50 cheap digital watches, 10 of which are flawed.

A digital watch's likelihood of malfunctioning

P = 10/50

= 0.2

Size of sample: n = 10

Additionally, if they find one or more samples to be defective, they reject the entire cargo.

Making use of the binomial probability formula:

[tex]P(x)={ }^{n} C_{x} p^{x}(1-p)^{n-x}[/tex]

The random variable x should stand in for the quantity of defective watches.

The chance that the delivery will be refused is:

[tex]P(x \geq 1)=1-P(0)[/tex]

= [tex]1-{ }^{10} C_{0}(0.2)^{0}(0.8)^{10}[/tex]

= 1 - (0.8)[tex]^{10}[/tex]

= 0.8926

As a result, 0.8926 percent of the time, the shipment will be rejected.

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I understand that the question you are looking for is:

A shipment of 50 inexpensive digital​ watches, including 10 that are​ defective, is sent to a department store. The receiving department selects 10 at random for testing and rejects the whole shipment if 1 or more in the sample are found defective. What is the probability that the shipment will be​ rejected

Using the z-distribution, it is found that the maximum error of the estimate is of 0.0475 hours.

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

The margin of error is given by:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

For this problem, the values of the parameters are given as follows:

[tex]\sigma = 0.5, n = 300[/tex]

We have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

Thus the maximum error of the estimate in hours is found as follows:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]M = 1.645\frac{0.5}{\sqrt{300}}[/tex]

M = 0.0475 hours

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Answer:

4.75%

Step-by-step explanation:

Given:     μ=z     σ=0.5     ∩=300     CL=90%

Maximum error  [tex]=Za/2*\frac{6}{\sqrt{n} } \\[/tex]

                          [tex]=1.645*\frac{0.5}{\sqrt{300} } \\=0.0475\\[/tex]

                          = 4.75%

The surface area of this pyramid with a regular pentagon as its base is equal to 851.09 square units.

In Mathematics, a complete circle has a magnitude of 360° and when it is divided by the 10 triangles, the angle formed at the center of the pentagon would always be equal to 36°.

Also, the length of the apothem of a pentagon can be calculated by using this formula:

a = s/2tan(36)

Where:

Substituting the given parameters into the formula, we have;

a = 10/2tan(36)

a = 10/1.45

a = 6.90 units.

Next, we would determine the slant height of this pyramid by applying Pythagorean theorem:

c² = a² + b²

c² = 6.9² + 13²

c² = 47.61 + 169

c² = 216.1

c = √216.1

c = 14.72 units.

For the surface area, we have:

Mathematically, the surface area of a pyramid with a regular pentagon as its base can be calculated by using this formula:

SA = 1.72l² × (5/2 × l × h)

SA = 1.72(14.72)² × (5/2 × 14.72 × 13)

SA = 372.69 + 478.4

SA = 851.09 square units.

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Cheetahs population will be more affected by genetic drift

Genetic drift is the change in a population's frequency of an existing gene variant brought on by chance. Gene variations may totally vanish due to genetic drift, hence reducing genetic variation. Additionally, it may lead to the considerably greater frequency and even fixation of previously rare alleles.

Random drift is a result of recurrently small populations, drastic population reductions known as "bottlenecks," and founder events in which a new population is created from a small number of individuals.

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Events A and B are dependent (option B).

Dependent events are events that can occur together. If event A occurs then event B would occur. In a standard deck of cards, cards that are hearts are red in colour. If a heart card is picked, then it would be red in colour.

Independents events are events whose occurrence do not depend on each other. They are random events.

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Assumed that sides are equal

CB

In (A) statistics class Wilson's students earn a higher ratio of a's to b's.

To find the higher ratio:

Given -

As we can observe that 3:5 < 11:15.

Therefore, in (A) statistics class Wilson's students earn a higher ratio of a's to b's.

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Answer:

1 hour

Step-by-step explanation:

The domain of the relation shown in the graph is -4 <= x <= 4

The complete question is added as an attachment

The relation on the graph is an ellipse function.

The domain is the set of x values the function can take

From the graph, we have the following x values

This means that the domain of x in the graph is -4 <= x <= 4

Hence, the domain of the relation shown in the graph is -4 <= x <= 4

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Let C(x) = -0.75x + 20,000 and R(x)= -1.50x then the profit function exists noted as P(x) = R(x) - C(x)

P(x) = -1.50x - (-0.75)x + 20,000

P(x)  = -0.75x + 20000

Therefore, the profit function exists -0.75x + 20000.

The profit function can be estimated by subtracting the cost function from the revenue function. Let profit be expressed as P(x), the revenue as R(x), the cost as C(x), and x as the number of items traded. Then the profit function exists noted as P(x) = R(x) - C(x).

Given:

C(x) = -0.75x+20,000 and R(x)= -1.50x

P(x) = R(x) - C(x)

= -1.50x - (-0.75)x + 20,000

= -1.50x + 0.75x + 20,000

Apply rule -(-a) = a

= -1.5x + 0.75x + 20000

Add similar elements:

-1.5 x + 0.75x = -0.75x

P(x)  = -0.75x + 20000

Therefore, the profit function exists -0.75x + 20000.

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The conclusion based on the hypothesis is that do not reject the null hypothesis as the row an column factors are independent.

From the information given, the null hypothesis is that the row and the column factors are independent. The alternative hypothesis is that they're dependent.

This was run by using the Chi square test and the following information was gotten:

Test statistic = 2.5234

P- value = 0.1122

Degree of freedom = (2-1)(2-1) = 1

Since the p value is equal to 1%, do not reject the null hypothesis as the row an column factors are independent.

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Answer and explanation in the attached file.

Answer: -8.

Step-by-step explanation:

-(2021.0,7+19,75)+2021.0,7-(8-19,75)=-2021.0,7-19,75+2021.0,7-8+19,75=-8.

The value of tanθ = ±∞ or tanθ = ±√(7/5)

The question is a trigonometric equation

A trigonometric equation is an equation that has unknowns that contain trigonometric ratios.

Given the trigonometric equation 7cosec²θ - 9cot²θ = 7, we require tanθ.

So, 7cosec²θ - 9cot²θ = 7

using the trigonometric identity 1 + cot²θ = cosec²θ.

Substituting this into the equation, we have

7cosec²θ - 9cot²θ = 7

7(1 + cot²θ)² - 9cot²θ = 7

7(1 + 2cot²θ + cot⁴θ) - 9cot²θ = 7

7 + 14cot²θ + 7cot⁴θ - 9cot²θ = 7

14cot²θ + 7cot⁴θ - 9cot²θ = 7 - 7

14cot²θ + 7cot⁴θ - 9cot²θ = 0

7cot⁴θ + 14cot²θ - 9cot²θ = 0

7cot⁴θ + 5cot²θ = 0

Factorizing out cot²θ, we have

cot²θ(7cot²θ - 5) = 0

⇒ cot²θ = 0 or 7cot²θ - 5 = 0

⇒ cotθ = ±√0 or 7cot²θ = 5

⇒ cotθ = ±0 or cot²θ = 5/7

⇒ cotθ = ±0 or cotθ = ±√(5/7)

⇒ 1/tanθ = ±0 or 1/tanθ = ±√(5/7)

⇒ tanθ = ±1/0 or tanθ = ±√(7/5)

⇒ tanθ = ±∞ or tanθ = ±√(7/5)

So, the value of tanθ = ±∞ or tanθ = ±√(7/5)

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Answer:

x = 36

Step-by-step explanation:

3x and 2x are a linear pair and sum to 180° , that is

3x + 2x = 180

5x = 180 ( divide both sides by 5 )

x = 36

Answer:

The "point-slope" form of the equation of a straight line is:

\begin{gathered}y-y_1=m(x-x_1)\\\\(x_1;\ y_1)\ is\ a\ known\ point\\\\m\ is\ the\ slope\ of\ the\ line\end{gathered}y−y1=m(x−x1)(x1; y1) is a known pointm is the slope of the line

We have:

m=-3;\ (x_1;\ y_1)=(2;-2)m=−3; (x1; y1)=(2;−2)

Substitute

\begin{gathered}y-(-2)=-3(x-2)\\\\y+2=-3(x-2)\end{gathered}y−(−2)=−3(x−2)y+2=−3(x−2)

Answer: B. y + 2 = -3(x - 2

The angles and lengths of each of the given triangles are;

5) m∠B = 57.52°

6) B = 70.81°

7) AB = 55.43 Km

8) AC = 39.06 ft

The cosine rule is expressed as;

c = √[a² + b² - 2ab(cos C)]

5) Using cosine rule;

BC = √[21² + 13² - 2(21*13)(cos 91)]

BC = 24.89

Using sine rule, we can find angle B as;

21/sin m∠B = 24.89/sin 91

sin m∠B = (21 * sin 91)/24.89

sin m∠B = 0.8436

m∠B = sin⁻¹0.8436

m∠B = 57.52°

6) Using cosine rule;

14² = 11² + 13² - 2(11*13)(cos B)]

196 = 121 + 169 - 286(cos B)

cos B = (121 + 169 - 196)/286

cos B = 0.3287

B = cos⁻¹0.3287

B = 70.81°

7) Using cosine rule;

AB = √[24² + 36² - 2(24*36)(cos 134)]

AB = 55.43 Km

8) Using cosine rule;

AC = √[21² + 26² - 2(21*26)(cos 112)]

AC = 39.06 ft

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The correct option is B.

The value will be  = 25

What is the Angles of the triangle?

The sum of the two interior angles that are not adjacent to it equals the exterior angles of a triangle, but the interior angles of a triangle always add up to 180°. Subtracting the angle of the desired vertex from 180° is another method for determining a triangle's exterior angle.

∠ACE = (2x+2)°

∠ECB = (5x+ 3)°

Angles ACE and ECB are additional angles according to the linear postulate, as seen in the attached diagram.

Therefore:

∠ACE+∠ECB = 180°

(2x+2)+(5x+3) = 180

2x+ 5x+ 2+ 3 = 180

7x + 5 = 180

7x = 175

x= 175/7

x = 25

Thus the value will be  = 25

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I understand that the question you are lookin for is :

Lines de and ab intersect at point c. lines d e and a b intersect at point c. angle a c e is (2 x 2) degrees. angle e c b is (5 x 3) degrees. what is the value of x?

A.12

B. 25

C. 38

D. 52

Answer:

6450.35/90.85 = 71 yards.

Step-by-step explanation:

Answer:

dave needs 3/5

Step-by-step explanation:

Step-by-step explanation:

what is the question ?

what problem needs to be solved ?

is it to find the ratio between fruit and nuts ?

then remember, a ratio is a fraction.

so, the ratio fruit : nuts is

1/5 / 1/3 = 1×3 / 5×1 = 3/5 or 3 : 5

or is it about any fraction problems and we need to bring them to the same denominator to add our compare them ?

to compare the 1/5 cup of fruit with the 1/3 cup of nuts, the smallest common multiple of 5 and 3 is 15. so we need to bring all to .../15.

how to make 15 out of 5 ? by multiplying 5 by 3. and we need to do this on the top of the fraction as well to keep the original value of the fraction.

1/5 = 1/5 × 3/3 = 3/15.

and with the same line of thinking :

1/3 = 1/3 × 5/5 = 5/15.

so, when mixing 1/5 cup of fruit with 1/3 cup of nuts, we get 3/15 + 5/15 = 8/15 cup of trail mix.

here you can clearly see the ratio again : 3/15 : 5/15 = 3:5

the first solution to get only full cups of trail mix is

3 cups of fruit and 5 cups of nuts = 8 cups of trail mix.

anything less will always end up with parts of cups (since 3/5 can't be simplified anymore).

Answer:  $34.32

Step-by-step explanation: We first calculate the price of the dress that was on sale. 30% of 35 is 35/10 x3. This is equal to 3.5x3 which is 7+3.5 = 10.5 We subtract this from 35 to get $24.5. So, the dress cost $24.5. Next 1/2 of 17 is 8.5. In total, the items cost $24.5+$8.5 = $33. Then, there is a 4% sales tax we have to add on to 33. 1% of 33 is 33/100 which is 0.33. This time 4 is 1.32. 33+1.32 is 34.32.

Answer:

x>-3

Step-by-step explanation:

7x+18>-3

transpose 18 to the other side to group the like terms

7x>-3-18

7x>-21

You divide bother sides by a 7 to get the value of x

7x/7>-21/7

therefore x>-3

Answer:

[tex] \sqrt{3} [/tex]

Step-by-step explanation:

27 is 3×3×3 from square root we can take 3 out as 3^2 elimate square root and remaining 3 is under root

Using the Fundamental Counting Theorem, there are 20 possibilities for their big night out.

It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

For this problem, we have that:

The number of possibilities is given by:

N = 5 x 4 = 20.

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The area of the grass that will be watered is given by  800/9 pi ft^2.

What is the area of a circle?

The area of a circle of radius r is given by:

A = πr²

In this problem, a rotating sprinkler head sprays water as far as 20 feet, hence the radius is of r = 20 ft.

It covers a central angle of 80º, while an entire circle has 360º, hence the area of grass that will be watered corresponds to 80/360 = 2/9 of the area of the circle.

Hence the watered area in ft² is given by-

A = 2/9 π × (20)²

   = 800π/ 9

Therefore, the area of the grass that will be watered is given by  800/9 pi ft^2.

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F = ma is [tex]a=\frac{F}{m}[/tex]

The following formula relates three quantities: Force (F), mass (m), and acceleration (a). F = ma

F = ma

F= force

m= mass

a= acceleration

[tex]F = ma[/tex]

Divide both sides by the mass

[tex]a=\frac{F}{m}[/tex]

F = ma is [tex]a=\frac{F}{m}[/tex]

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The option that's true about the plane illustrated is E. None of these.

From the information given, it should be noted that DBC isn't an isosceles triangle.

Also, from the figure, one can see that DAB isn't similar to DAC.

Likewise, BD and DC aren't perpendicular.

In conclusion, the correct option is E.

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The distance on map exists 32 cm and actual area exists 37.5 km².

Given: Scale of the map exists at 1:250000.

(a) Distance between two cities = 80 km

= 80000 m

= 8000000 cm

Distance on map = 8000000 [tex]*[/tex] 1/ 250000

= 32 cm

(b) Area of map = 6 cm²

Actual area = [tex]6(250000)^2[/tex] cm²

[tex]= 6 * 625 * 10^8[/tex] cm²

[tex]= 3750 * 10^8/ 10^{10}[/tex]

= 37.5 km²

Therefore, the distance on map exists 32 cm and actual area exists 37.5 km².

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Answer:

y=3x-5

Step-by-step explanation:

they are parallel meaning that only the constant is changing

-2 = 3(1) - (something)

-2 = 3 - (something)

something = 5.   - > that was 3+2

so y=3x+(-5)

Answer:

24/25

Step-by-step explanation:

use tan^-1 to find the angle

tan^-1(3/4)=36.86989765°

A =36.86989765°

2A= 2×36.86989765

=73.73979529°

sin2A>>>>sin(73.73979529°)

=24/25 or 0.96

Answer:

sin2A = [tex]\frac{24}{25}[/tex]

Step-by-step explanation:

using the identity

sin2A = 2sinAcosA

given

tan2A = [tex]\frac{3}{4}[/tex] = [tex]\frac{opposite}{adjacent}[/tex]

then this is a 3- 4- 5 right triangle with

hypotenuse = 5, opposite = 3 , adjacent = 4 , then

sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{5}[/tex] and cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{5}[/tex]

Then

sin2A = 2 × [tex]\frac{3}{5}[/tex] × [tex]\frac{4}{5}[/tex] = [tex]\frac{2(3)(4)}{5(5)}[/tex] = [tex]\frac{24}{25}[/tex]