Line v passes through points (10, 9) and (1, 13). Line w is perpendicular to v. What is the slope of line w?

Answer:

Step-by-step explanation:

For the length of AC

cosθ = 14/17

θ = arcCos 14/17

θ = 34.56

Let x = opposite

cot34.56  = 14/x

1.45=14/x

x1.45 = 14

x = 9.66

therefore, the length of AC is 9.66

For angle B is 34.56  

For angle C is 55.44

For Angle C :

90 + c + 34.56   = 180

c = 180 - 124.56

c = 55.44

Answer:

There are a total of 144 students in soccer training.

Step-by-step explanation:

12x5=60

60-12=48

48=4/5

4/5=1/3

1/3 = 48

48x3= 144

Hey there!

12w = 102

DIVIDE 12 to BOTH SIDES

12w/12 = 102/12

SIMPLIFY IT!

w = 102/12

w = 102 ÷ 6 / 12 ÷ 6

w = 17 / 2

w = 8 1/2

Therefore, your answer should be:

w = 17/2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

b = 5 ± √5 / 5

Step-by-step explanation:

Given :

Subtract 10b from both sides :

Splitting the middle term :

Answer:

[tex]y = \frac{x - 3}{2}[/tex]

Step-by-step explanation:

To find the inverse of a function, simply 'switch' the x and y's and solve for y. [tex]y = 2x + 3[/tex] becomes [tex]x = 2y + 3[/tex]. Now, solving for y, we get [tex]y = \frac{x - 3}{2}[/tex].

hope this helped! :)

The probability that the next costumer will pay with a credit card is 0.07.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that the next costumer will pay with a credit card = number of customers that paid with a credit card / total number of customers

8 / ( 8 + 3 + 102)

= 8 / 113 = 0.07

Here is the complete question:

Owen owns a small business selling ice-cream.He knows that in the last week 102 customers paid cash, 3 costumers used a debit card, and 8 costumers used a credit card. Based on these results,express the probability that the next costumer will pay with a credit card as a decimal to the nearest hundredth

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Differential Calculus, or Differentiation

If we have a function of one variable, ie of the form [tex]y=f(x)[/tex], then in its most basic form differentiation is the study of how a small change in one variable [tex]x[/tex] affects the other variable [tex]y[/tex].

As an real life example, consider the average speed of a moving car:

average speed = distance travelled/ time taken

Obviously, this is an average by definition, but if there existed a formal mathematical link between distance and time, could we build a function that would tell us the instantaneous velocity at every given moment? The study of differential calculus gives strategies for calculating the ratio of a little change in distance to a small change in time, and then calculating the real instantaneous speed by making the small change infinitely small.

Similarly if we wanted to find the gradient of the tangent to a curve at some particular point [tex]A[/tex] we would estimate the gradient by using a chord to a nearby point [tex]B[/tex]. As we move this nearby point [tex]B[/tex]  closer to the tangent point [tex]A[/tex] the slope of the chord approaches the slope of the tangent with more and more accuracy. Again differential calculus provides techniques for us to make the point [tex]B[/tex] infinitesimally close to the point [tex]A[/tex] o that we can calculate the actual gradient of the tangent.

Integral Calculus, or Integration

Suppose we wanted to calculate the area under a curve, [tex]y=f(x)[/tex],  bounded the [tex]x[/tex] =axis, and two points [tex]a[/tex] and [tex]b.[/tex] We could start by splitting the interval  [tex][a,b][/tex]  into [tex]n[/tex] regular strips, and estimating the area under the curve using trapezia (this is the essence of the trapezium rule which provides an estimate of such an area). If we increase [tex]n[/tex] then generally we would hope for a better approximation. The study of integration provides techniques for us to take an infinitely large number of infinitesimally small strips to gain an exact solution.

The Fundamental Theorem of Calculus

Given the above two notions, it would appear that there is no connection between them at first., The Fundamental Theorem of Calculus, on the other hand, is a theorem that connects the rate of change of the area function (which determines the area under a curve) to the function itself. In other words, the area function's derivative equals the function itself.

Visual for  Fundamental Theorem of Calculus for integrals:

[tex]\int\limits^b_af {(x)} \, dx =F(b)-F(a).[/tex]

where F is an antiderivative of [tex]f[/tex]

Physics, Chemistry, all engineering sciences, statistics, economics, finance, biology, computer science, linguistics, to name but a few, are all areas that would be a desert without the use of calculus.

Leibnitz and Newton worked to define the velocity of a planet moving on a curved trajectory. That was not possible without calculus, and both had to invent differential calculus. Differential calculus allows to compare quantities along a curve, and thus their time rate of change.

All of classical physics can be summarized in this operation. Given second derivative (which is Force/mass), find the position as a function of time. This process is called integration. Half of calculus is made with integration, the other half with derivation. All of classical physics rests on these two parts of the calculus.

Quantum mechanics, quantum field theory, electromagnetism, fluid mechanics all use integration and derivation and much more. I rest my case. I hope this helps you gauge the place that calculus occupies in science.

Answer:

so what i think is that *friendship​Step-by-step explanation:

Answer:

  (x, y) = (12, 15)

Step-by-step explanation:

The given expression for y suggests that using substitution would be a good choice for the method of solution.

__

  x +(x +3) = 27 . . . . substitute for y using the second equation

  2x = 24 . . . . . . . subtract 3

  x = 12 . . . . . . . divide by 2

  y = 12 +3 = 15 . . . . use the second equation to find y

The solution is (x, y) = (12, 15).

Answer:

600.00

Step-by-step explanation:

Understanding :

600.00 is the actual price of the electric cooker.

Answer:

A is the answer

Step-by-step explanation:

because 3 is shaded

and there is 5 rows with three shaded

Answer:

output = - 68

Step-by-step explanation:

given

output = input × 17

when input = - 4 , then

output = - 4 × 17 = - 68

Answer:

Step-by-step explanation:

Remark

You are trying to convert the base function f(x) = x^2 into the child function g(x) = -(x + 3)^2 + 5

UP

Start with the simplest part of the transformations. + 5

If you have g(x) = f(x)+5 what you have done is move the function up 5 units on your grid.

Up side Down

Next is the - sign.

f(x) = x^2

g(x) = - f(x) = - x^2

This has the affect of turning x^2 upside down. It looks like a cup opening towards the counter or down.

Left right

The last step is left / right. This is the hard one. It moves in the opposite direction that you think it should. x +3 moves the parabola left, not right. If you want it to move right, use (x - 3)

Graph

I have enclosed a graph to show you exactly what is going on. The red  line is f(x)=x^2

The blue line is g(x) = -(x + 3)^2 + 5

Answer:

midpoint: (3.65, -3.65)

Explanation:

[tex]\sf (x_m, y_m) = (\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})[/tex]

where (x1, y1), (x2, y2) are points

[tex]\rightarrow \sf (\dfrac{2.9+4.4}{2}, \dfrac{-4.4-2.9}{2})[/tex]

[tex]\rightarrow \sf (\dfrac{7.3}{2}, \dfrac{-7.3}{2})[/tex]

[tex]\rightarrow \sf (3.65, \ - 3.65)[/tex]

Answer:

Doing something despite difficulty or delay in achieving success.

Step-by-step explanation:

Answer:

continued effort to do or achieve something despite difficulties, failure, or opposition

Step-by-step explanation:

Answer:

-1 - 4 i

Step-by-step explanation:

5 - (2 * i) - (2 * (3 + i)) =

-1 - 4 i

To solve this expression, we can use the mathematical operations: addition, multiplication and division. So the correct value, will be m = 1/24

This expression is an equation of the first fractional degree. To calculate, let's:

— move the negative - term to the other side of the positive equation, thus adding:

3/4m - 6 = 12

3/4m = 12 + 6

3/4m = 18

— Now, let's calculate without being fractional. We will isolate the variable multiply the terms with each other:

3/4m = 18

3 = 4m . 18

3 = 72m

— Finally, we'll turn this equation into a fraction, like this - simplifying the numerator and denominator by the same real number:

3 = 72m

m = 3/72

m = 3÷3 / 72÷3

m = 1/24

Therefore, the correct value of this expression is m = 1/24

Answer:

L=8cm W=5cm

Step-by-step explanation:

8+8=16

5+5=10

10+16=26cm

5x8=40cm

Answer:

20/39.

Step-by-step explanation:

There are a total of 13 students.

Prob(Boy is selected) = 8/13

Prob(Girl is then selected) = 5/12

So probability ( Boy selected then a girl)  = 8/13 * 5/12 = 10/39

- and the probability of Girl then a boy selected is also  10/39

So the required probability = 2 * 10/39

= 20/39.

Answer:

0.03

Step-by-step explanation:

the first thing you would do in this equation is to deal with the exponent

a negative exponent puts the number under 1

1/10^2

10^2 is also 100

1/100

3 * 1/100 is 3/100 so that is your answer

3/100 is also 0.03

Answer: [tex]\frac{3}{100}[/tex] or 0.03

Step-by-step explanation:

3×[tex]10^{-2}[/tex]

3 × [tex]\frac{1}{100}[/tex]

⇒ [tex]\frac{3}{100}[/tex]

⇒ 0.03

Answer:

3

Step-by-step explanation:

Find the sum of the data set and divide it by the number of data points in the set:

[tex]\text{Mean}=\frac{2+3+1+4+5+2+3+4+3}{9}=\frac{27}{9}=3[/tex]

Therefore, the mean of the data set is 3

The answer is...:

True

Answer:

3/8

Step-by-step explanation:

(3/4)/2=3/8

Answer:

270

Step-by-step explanation:

 x = k/y     This is an inverse relationship with k = constant of proportion (or variation)

-9 = k/(-30)

k = -9  *  -30 = 270

Answer:

Constant of variation  = 270.

Step-by-step explanation:

y = k/x

-30 = k / -9

k = -30 * -9

k = 270

The events A and B are independent events, and the values of P(A) and P(B) are 7/12 and 1/2, respectively

The event A is given as:

A : Sum greater than 6

In the sample space of a roll of two dice, there are 21 outcomes that are greater than 6, out of a total of 36 outcomes

This means that:

P(A) = 21/36

Simplify

P(A) = 7/12

The event B is given as:

B : Sum is divisible by 2

In the sample space of a roll of two dice, there are 18 outcomes that are divisible by 2, out of a total of 36 outcomes

This means that:

P(B) = 18/36

Simplify

P(B) = 1/2

Hence, the probability values of P(A) and P(B) are 7/12 and 1/2, respectively

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