For Questions 2-5, determine whether each expression is a polynomial: (Questions are in image)

1. Write out the law of cosines and find the hypotenuse of triangle with 2 sides lengths equal to three and the included angle m

LUCKY_DIMON [66]

Answer:

1.) $\sqrt{13.341}$ ≈ 3.652

2.) I would say something about how the A in front of cos in the equation would change to 90, rather than stay 75 (in the equation for the step by step), but it would be easier to just use the Pythagorean theorem.

Step-by-step explanation:

I think we may have the same class so hopefully this helps:

1.) $a^2 = b^2 + c^2 - 2bccosA$ --> law of cosines formula.

$a^2 = 3^2 + 3^2 - 2(3)(3)cos(75)$ --> plugged in numbers; when you draw the triangle, the included angle would be A, and the opposite side would be a. B and b, and C and c are opposite each other. In this case, a is the hypotenuse.

$a^2 = 18 - 18cos75$ --> in between steps.

$a^2 = 13.341$ --> more simplifying.

$a(hypotenuse) = \sqrt{13.341} or 3.652$ --> answer

2.) This one is just an explanation: The 75 in the equation is the given angle, which is a. If this changes, it would just change in the equation too. And obviously, if it's 90 degrees, you can just use Pythagorean theorem a^2+b^2=c^2.

Good luck! :)

6 0

3 years ago

Write the equation for the quadratic function in standard form

Ede4ka [16]

Answer:

$y=x^2+6x+7$

Step-by-step explanation:

To write the quadratic in standard form, begin by writing it in vertex form

$y = a(x-h)^2+k$

Where (h,k) is the vertex of the parabola.

Here the vertex is (-3,-2). Substitute and write:

$y=a(x--3)^2+-2\\y=a(x+3)^2-2$

To find a, substitute one point (x,y) from the parabola into the equation and solve for a. Plug in (0,7) a y-intercept of the parabola.

$7=a((0)+3)^2-2\\7=a(3)^2-2\\7=9a-2\\9=9a\\1=a$

The vertex form of the equation is $y=(x+3)^2-2$ .

To write in standard form, convert vertex form through the distributive property.

$y=(x+3)^2-2\\y=(x^2+6x+9)-2\\y=x^2+6x+7$

8 0

4 years ago

What is StartFraction negative 23 over 6 EndFraction minus StartFraction 7 over 3 EndFraction

creativ13 [48]

Answer: $\frac{16}{3}$

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Simplify the expression, cos x cotx + sinx

olya-2409 [2.1K]

Answer:

cosec x

Step-by-step explanation:

$\cos x \: \cot x + \sin x \\ \\ = \cos x \times \frac{\cos x }{ \sin x } + \sin x \\ \\ = \frac{\cos^{2} x +\sin^{2} x }{ \sin x } \\ \\ = \frac{1}{ \sin x } \\ \\ = cosec x \\ \\ \red{ \boxed{ \bold{\therefore \: \cos x \: \cot x + \sin x = cosec \: x}}}$

8 0

3 years ago

Read 2 more answers

The time it takes me to wash the dishes is uniformly distributed between 10 minutes and 15 minutes. What is the probability that

mario62 [17]

Answer:

The probability that washing dishes tonight will take me between 12 and 14 minutes is 0.1333.

Step-by-step explanation:

Let the random variable X represent the time it takes to wash the dishes.

The random variable X is uniformly distributed with parameters a = 10 minutes and b = 15 minutes.

The probability density function of X is as follows:

$f_{X}(x)=\frac{1}{b-a};\ a$

Compute the probability that washing dishes will take between 12 and 14 minutes as follows:

$P(12\leq X\leq 14)=\int\limits^{12}_{14} {\frac{1}{15-10} \, dx$

$=\frac{1}{5}\int\limits^{12}_{14} {1} \, dx \\\\=\frac{1}{5}\times [x]^{14}_{12}\\\\=\frac{1}{15}\times [14-12]\\\\=\frac{2}{15}\\\\=0.1333$

Thus, the probability that washing dishes tonight will take me between 12 and 14 minutes is 0.1333.

5 0

3 years ago