what is the slope of a line with one point at (6,3) and another point at (8,2)

Step-by-step explanation:

We have cartisean points. We are trying to find polar points.

We can find r by applying the pythagorean theorem to the x value and y values.

[tex]r {}^{2} = {x}^{2} + {y}^{2} [/tex]

And to find theta, notice how a right triangle is created if we draw the base(the x value) and the height(y value). We also just found our r( hypotenuse) so ignore that. We know the opposite side and the adjacent side originally. so we can use the tangent function.

[tex] \tan(x) = \frac{y}{x} [/tex]

Remeber since we are trying to find the angle measure, use inverse tan function

[tex] \tan {}^{ - 1} ( \frac{y}{x} ) = [/tex]

Answers For 2,5

[tex] {2}^{2} + {5}^{2} = \sqrt{29} = 5.4[/tex]

So r=sqr root of 29

[tex] \tan {}^{ - 1} ( \frac{5}{2} ) = 68[/tex]

So the answer is (sqr root of 29,68).

For -3,3

[tex] { -3 }^{2} + {3}^{2} = \sqrt{18} = 3 \sqrt{2} [/tex]

[tex] \tan {}^{ - 1} ( \frac{3}{ - 3} ) = - 45[/tex]

Use the identity

[tex] \tan(x) = \tan(x + \pi) [/tex]

So that means

[tex] \tan(x) = 135[/tex]

So our points are

(3 times sqr root of 2, 135)

For 5,-3.5

[tex] {5}^{2} + {3.5}^{2} = \sqrt{37.25} [/tex]

[tex] \tan {}^{ - 1} ( \frac{ - 3.5}{ - 5} ) = 35[/tex]

So our points are (sqr root of 37.25, 35)

For (0,-5.4)

[tex] {0}^{2} + { - 5.4}^{2} = \sqrt{} 29.16 = 5.4[/tex]

So r=5.4

[tex] \tan {}^{ - 1} (0) = undefined[/tex]

So our points are (5.4, undefined)

Answer:

V = 260.2 m^3

Step-by-step explanation:

The area of the circular base is (pi)(r)^2, where r is the radius and half the diameter.

In this case the volume of the cone is V = (1/3)(pi)(5 m)^2*(10 m) = 260.2 m^3

Answer: 262

...........................

Answer:

252

Step-by-step explanation:

60+61+11

Answer:

The value of log 8 is 0.9030

Step-by-step explanation:

To find:

Value of log 8

Solution:

Let we take,

x=log8

x=log (2)^3

x=3log2

x=3*0.3010

x=0.9030

Hence, the value of log 8 is 0.90.

Answer:

6

Step-by-step explanation:

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Answer:

Option B.

Step-by-step explanation:

We have the equation:

x^2 + 6*x - 2 = 0

Remember that:

(a*x + b)^2 = (a*x)^2 + 2*a*b*x + b^2

Because the term with x^2 has a coefficient equal to 1, then a = 1.

(x + b)^2 = x^2 + 2*b*x + b^2

The ter with x is: 6*x

then:

2*b*x = 6*X

2*b = 6

b = 6/2 = 3

we have:

(x + 3)^2 = x^2 + 6*x + 9

Now, our equation is:

x^2 + 6*x - 2 = 0

Now we can add the term (11 - 11) = 0

x^2 + 6*x - 2 + (11 - 11) = 0

x^2 + 6*x - 2 + 11 - 11 = 0

x^2 + 6*x + (11 - 2) - 11 = 0

x^2 + 6*x + 9 - 11 = 0

And we know that:

x^2 + 6*x + 9  = (x + 3)^2

Then we can rewrite our equation as:

(x + 3)^2 - 11 = 0

Then the correct option is B.

The equation that matches our result is option B. (x+3)² - 11. Therefore, rewriting x² + 6x - 2 = 0 by completing the square gives us (x+3)² - 11 = 0.

To rewrite the equation x² + 6x - 2 = 0 by completing the square, we need to follow these steps:

Move the constant term (-2) to the other side of the equation:

x² + 6x = 2

Take half of the coefficient of x (which is 6) and square it. Add the result to both sides of the equation:

x² + 6x + (6/2)² = 2 + (6/2)²

x² + 6x + 9 = 2 + 9

x² + 6x + 9 = 11

Now, let's look at the answer choices:

A. (x+3)² = 18

B. (x+3)² - 11

C. (x+3)² - 2

D. (x+3)² - 9

Among the answer choices, the equation that matches our result is option B. (x+3)² - 11. Therefore, rewriting x² + 6x - 2 = 0 by completing the square gives us (x+3)² - 11 = 0.

To know more about equation:

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Answer:

the length of side X is 37

Answer

[tex]f(t) = 91000 *1.0376^t[/tex]

Explanation

Given

[tex]a = 91000[/tex] -- initial

[tex]r = 3.76\%[/tex]

Required

The exponential equation

The exponential equation is:

[tex]y =ab^t[/tex]

Where

[tex]b=1 +r[/tex]

We used minus, because the rate increases..

So, we have:

[tex]b=1 +3.76\%[/tex]

[tex]b=1 +0.0376[/tex]

[tex]b=1.0376[/tex]

So:

[tex]y =ab^t[/tex]

[tex]y = 91000 *1.0376^t[/tex]

Hence:

[tex]f(t) = 91000 *1.0376^t[/tex]

Answer:

75.5 cm

Step-by-step explanation:

S = (a+b)*h/2

h = 2 * S / (a+b) = 2 * 7701 / 204 = 75.5 cm

I hope this helps you

tgM=39/80

sinM=39/89

cosM=80/89

Answer:

[tex]y=-\frac{1}{5} x-1[/tex]

Step-by-step explanation:

Hi! Welcome to brainly!

So slope intercept form - y = mx + b

where m = slope and b = y intercept

First lets find the y intercept

The y intercept is at (0,-1)

B would equal the y value of the y intercept so b = -1

now lets find the slope

To do so we can pick 2 points on the line and use the slope formula

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

the points can vary but i chose the points (5,-2) and (10,-3)

having found the points we plug them into the formula

[tex]m = \frac{-3-(-2)}{10-5} \\-3-(-2)=-1\\10-5=5\\m=-\frac{1}{5}[/tex]

now that we have found all of the information we plug the values into the equation and get that the answer is

[tex]y=-\frac{1}{5} x-1[/tex]

9514 1404 393

Answer:

  20%

Step-by-step explanation:

The discount was $35 -28 = $7. As a percentage of the original price, that is ...

  $7/$35 × 100% = 20%

Mai's coupon was for a 20% discount.

Answer:

B. Yes, all the conditions are met.

Step-by-step explanation:

According to the question

There is a random sample of 111 people also these people are independent

The population size is also not given so we assume that it should be on infinity i.e. it should be more than 10 times higher as compared with the sample size

And, the number of success in the sample is 93

So, the number of failure would be

= 111 - 93

= 18

So, the 93 and 18 would be higher than 10

Therefore, the option b is correct

Answer:

[tex]x^2 + (y-60)^2 = 30,625[/tex]

Step-by-step explanation:

There are 42 carts, so there is 42 spaces in between them; if one of those spaces are 25pi/3 feet long, then 42 of them would be 25*42*pi/3 = 350pi (Perfect! no fractions)

350pi is the circumference. Now if we plug that into the circumference equation we get:

C = 2pi*r

350pi = 2pi*r

Divide both sides by pi to get rid of it

350 = 2r

Divide both sides by 2

r = 175 feet

So the new equation to graph it is:

x^2+y^2 = 175^2 = 30,625

We also know that the center of the Ferris wheel has to be at least 60 feet from the ground. Since the radius is more than that, a good bit of the Ferris wheel has to be underground OR we can make it higher (keyword: at least) if we want it to be above ground. I'll do the equation for underground since it more closely represents the question.

subtracting a number from y, shifts the graph up that much so:

[tex]x^2 + (y-60)^2 = 30,625[/tex]

I can't really draw it electronically but I can graph it:

Answer:

hmmm................chupapu

Answer:

5

Step-by-step explanation:

when finding a y intercept thevalue of x must be0,,,,,,when xis changed to 0the answer left is 5

Answer:

409 i would say

Step-by-step explanation:

very sorry is its wrong!!! :(

Answer:

prob d im guessing :^)

Step-by-step explanation:

tell me if i got it right or wrong i will fix if needed

Answer:

14.4

Step-by-step explanation:

6 x (t1/3 + t1/2) = 12(6)

2t + 3t = 72

5t = 72 /5

t= 14.4

Answer:

This triangle is an isosceles acute

Step-by-step explanation:

First lets define each classification

scalene - no equal sides

isosceles - two equal sides

equilateral - all equal sides

acute - all angles have a measure of less than 90 degrees

right - has a right angle (90 degree angle)

obtuse - has an angle that has a measure of more than 90 degrees

Now lets classify

The triangle has two equal sides (indicated by the little line on the top and bottom side) therefore it is an isosceles triangle

We know its an acute triangle because the one angle given is not a right angle nor a obtuse angle meaning that the other two angles are going to have  a measure of less than 90 degrees

So we can conclude that this is an isosceles acute triangle

Answer:

x = 26.4°

Step-by-step explanation:

Defence angle = x

Side length Opposite to reference angle = 4

Hypotenuse length = 9

Apply trigonometric ratio, SOH. Thus:

Sin x = Opp/Hyp

Sin x = 4/9

[tex] x = sin^{-1}(\frac{4}{9} [/tex]

x = 26.3878° = 26.4° (nearest tenth)

Answer:

(3 x 4) - 1    and  3 x 4 - 1

Step-by-step explanation:

Hope this helps!

Answer:

I got 678.58401 but i think it is C. 648n cubic units

Step-by-step explanation:

Answer:

d.) 1/12

Step-by-step explanation:

As it is equal to 0.083 and it is nearest to zero

Answer:

d. 1/12

Step-by-step explanation:

Since all of the fractions are positive and you want the one closest to 0, you need to find the smallest fraction. With fractions, especially when all of the numerators are 1, the larger the denominator becomes, the smaller the fraction. 12 is the largest denominator; therefore, 1/12 must be the smallest fraction. Which makes 1/12 the closest to 0.

Answer:

True

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Answer:

Step-by-step explanation:

6x4=24+1=25 75/25=3 .

oh and btw go back to high school

12 pieces ! ( > < )

for future reference, this will be a lot easier to do than using points !! so simple :))

use your calculator to divide the large number by the small number !! that should give your answer

and remember if a fraction is out of four think of it like quarters or 25 cents :3

so 75 divided by 6.25 is 12 !!

good job !!! ♡♡

Answer:

lateral surface area of cone =

[tex]\pi rl[/tex]

where, l = slant height, and r = radius

then

[tex]l.a = \pi \times 8 \times 17[/tex]

[tex]l.a = 136\pi[/tex]

The lateral area of this cone will be 136 π. Lateral area is found as the product of pi ,radius and slant height.

It is defined as the three-dimensional shape in which the base is a circular shape and if we go from circular base to top the diameter of the circle reduces and at the vertex, it becomes almost zero.

lateral area of this cone is found as;

L=πrl

L=π×8×17

L=136π

Hence,the lateral area of this cone will be 136 π.

To learn more about the cone refer to the link;

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