MATHEMATICS HIGH SCHOOL

Simplify: –3(y + 2)2 – 5 + 6y
What is the simplified product in standard form?

Answers

Answer 1

Answer: The answer is -17

Hope this helps!

Answer 2

Answer:

-3

-6

-17

in the blanks in that order

Have a nice day

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Where would the square root of 130 be located on the number line

Answers

$√(130)=\boxed{11.40175425099138}\ it\ would\ be\ located\ in\ between\ 11\ and\ 12.$

Classify the following as rational or irrational: a) -1/5

Answers

Answer:irrational

Step-by-step explanation:its a negative fraction

Which of the following describes the domain of the function?

Answers

I think it's A but I'm not sure. The domain of a relation is simply the input, or x-values of the relation

Use integration by parts to integrate sin2x between pi and 0

Answers

Answer:

$\displaystyle \int\limits^0_(\pi) {\sin (2x)} \, dx = 0$

General Formulas and Concepts:

Calculus

Integration

Integrals

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

U-Substitution

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \int\limits^0_(\pi) {\sin (2x)} \, dx$

Step 2: Integrate Pt. 1

Identify variables for u-substitution.

Set u: $\displaystyle u = 2x$
[u] Differentiate: $\displaystyle du = 2 \ dx$
[Bounds] Switch: $\displaystyle \left \{ {{x = 0 ,\ u = 2(0) = 0} \atop {x = \pi ,\ u = 2 \pi}} \right.$

Step 3: Integrate Pt. 2

[Integral] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle \int\limits^0_(\pi) {\sin (2x)} \, dx = (1)/(2) \int\limits^0_(\pi) {2 \sin (2x)} \, dx$
[Integral] U-Substitution: $\displaystyle \int\limits^0_(\pi) {\sin (2x)} \, dx = (1)/(2) \int\limits^0_(2 \pi) {\sin u} \, du$
Trigonometric Integration: $\displaystyle \int\limits^0_(\pi) {\sin (2x)} \, dx = (1)/(2)(-\cos u) \bigg| \limits^0_(2 \pi)$
Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^0_(\pi) {\sin (2x)} \, dx = (1)/(2)(0)$
Simplify: $\displaystyle \int\limits^0_(\pi) {\sin (2x)} \, dx = 0$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Graph 3x + 2y = 6. Can someone help with this

Answers

Here are two ways to graph it. You can decide which one seems easier to understand or easier to do:

==> Manipulate the equation into the "slope-intercept" form, where 'y' is
all alone on one side and everything else is on the other side:

3x + 2y = 6

Subtract 3x from each side:   2y = -3x + 6

Divide each side by 2 : y = -3/2 x +3

This is the form you want. Just looking at it, it tells you that the slope
of the line on the graph is (-3/2), and it crosses the y-axis at +3 .
That's enough information to draw the line.
===============================================

=> Another way:

Look at the x-axis and the y-axis on the graph paper ... without any graph drawn on it yet. Just look at the 2 axes.

With an 'x'-number and a 'y'-number, you can find any point on it. Right ?

OK. Notice that at every point on the y-axis, x = 0 . And at every point
on the x-axis, y = 0. This can be very very helpful.

Now take your equation: 3x + 2y = 6 .

You know that the graph is going to be a straight line. And it's pretty obvious that if the line isn't horizontal or vertical, then it has to cross both the x-axis and the y-axis somewhere. If you had an easy way to find the two points where it crosses the axes, you could join those 2 points and you'd have your line !

You DO have an easy way to find those points !

If x=0, then the point is on the y-axis. Take your equation, make x=0, and it'll show you where the line crosses the y-axis:

   3(0) + 2y = 6 .

    2y = 6 .

Divide each side by 2 : y = 3 .

There's one point on the line: (0, 3)

Now remember that if y=0 the point is on the x-axis. So take your equation
and make y=0:

      3x + 2(0) = 6

3x = 6

Divide each side by 3 :    x = 2

There's another point on the line, where it crosses the x-axis: (2, 0) .

Shazam ! You have the 2 points where the line crosses the x- and
y- axes. Mark each one with a little dot, put your ruler down along
them, draw a line between them, and extend it as far in each direction
as you want to. That's the graph of your equation.

Plot these coordinates then draw a line through them and that is the line.

(2,0) x intercept
(0,3) y intercept

At LaGuardia Airport for a certain nightly flight, the probability that it will rain is 0.19 and the probability that the flight will be delayed is 0.15. The probability that it will not rain and the flight will leave on time is 0.74. What is the probability that the flight would be delayed when it is not raining? Round your answer to the nearest thousandth.

Answers

The probability that the flight would be delayed when it is not raining is 12.15%.

Since at LaGuardia Airport, for a certain nightly flight, the probability that it will rain is 0.19 and the probability that the flight will be delayed is 0.15, while the probability that it will not rain and the flight will leave on time is 0.74 , to determine what is the probability that the flight would be delayed when it is not raining, the following calculation must be performed:

Probability that it will not rain = 1 - probability that it will rain
X = 1 - 0.19
X = 0.81

Probability that the flight would be delayed when it is not raining = probability that it is not raining x probability that the flight will be delayed
X = 0.81 x 0.15
X = 0.1215
0.1215 x 100 = 12.15

Therefore, the probability that the flight would be delayed when it is not raining is 12.15%.

Learn more in brainly.com/question/795909

Final answer:

Explanation:

To find the probability that the flight would be delayed when it is not raining, we can use conditional probability. The probability that the flight will be delayed given that it is not raining can be calculated using the formula:
P(delayed | not raining) = P(delayed and not raining) / P(not raining)
We are given that P(delayed and not raining) = 0.74 and P(not raining) = 1 - 0.19 = 0.81. Substituting these values into the formula:
P(delayed | not raining) = 0.74 / 0.81 ≈ 0.914. Therefore, the probability that the flight would be delayed when it is not raining is approximately 0.914.