The slope of a line is 2. The y-intercept of the line is -6. Which statements accurately describe how to graph the function

∠A and ∠C are right angles. m∠p = _???_ degrees.

iogann1982 [59]

Answer

Find out the m∠p .

To prove

As in ΔDAB is a right triangle

Apply pythagorean theorem

Hypotenuse ² = Perpendicular ² + Base²

DB² = AB² + AD²

AB = 5 units

AD = 6 units

Put in the above formula

DB² = 5² + 6²

= 25 + 36

= 61

$DB = \sqrt{61}\ units$

= 7.8 units (approx)

Now in ΔDCB is a right triangle .

By using the trignometric identity .

$cosp = \frac{Base}{Hypotenuse}$

$cosp = \frac{DC}{DB}$

As DC = 4 units

DB = 7.8 units (approx)

Put all the values in the trignometric identity .

$cos p = \frac{4}{7.8}$

$\angle p = cos^{-1}(\frac{4}{7.8})$

∠p = 59.15 ° (approx)

5 0

2 years ago

Read 2 more answers

The square of a number decreased by 3 times the number 28 find all possible values for the number

stealth61 [152]

Question:

The square of a number decreased by 3 times the number is 28 find all possible values for the number

Answer:

The possible values of number are 7 and -4

Solution:

Given that the square of a number decreased by 3 times the number is 28

To find: all possible values of number

Let "a" be the unknown number

From given information,

square of a number decreased by 3 times the number = 28

$a^2 - 3a = 28$

$a^2 - 3a - 28 = 0$

Let us solve the above quadratic equation

$\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0$

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Using the above formula,

$\text { For } a^{2}-3 a-28=0 \text { we have } a=1, b=-3, c=-28$

$\begin{aligned}&a=\frac{-(-3) \pm \sqrt{(-3)^{2}-4(1)(-28)}}{2 \times 1}\\\\&a=\frac{3 \pm \sqrt{9+112}}{2}\\\\&a=\frac{3 \pm \sqrt{121}}{2}=\frac{3 \pm 11}{2}\\\\&a=\frac{3+11}{2} \text { or } a=\frac{3-11}{2}\\\\&a=7 \text { or } a=-4\end{aligned}$

Thus the possible values of number are 7 and -4

5 0

2 years ago

A textbook has 500 pages on which typographical errors could occur. Suppose that there are exactly 10 such errors randomly locat

DiKsa [7]

Answer:

The probability of a selection of 50 pages will contain no errors is 0.368

The probability that the selection of the random pages will contain at least two errors is 0.2644

Step-by-step explanation:

From the information given:

Let q represent the no of typographical errors.

Suppose that there are exactly 10 such errors randomly located on a textbook of 500 pages. Let $\mu$ be the random variable that follows a Poisson distribution, then mean $\mu = \dfrac{10}{500}= 0.02$

and the mean that the random selection of 50 pages will contain no error is $\lambda = 50 \times 0.02 =1$

∴

$Pr(q= 0) = \dfrac{e^{-1} (1)^0}{0!}$

Pr(q =0) = 0.368

The probability of a selection of 50 pages will contain no errors is 0.368

The probability that 50 randomly page contains at least 2 errors is computed as follows:

P(X ≥ 2) = 1 - P( X < 2)

P(X ≥ 2) = 1 - [ P(X = 0) + P (X =1 )] since it is less than 2

$P(X \geq 2) = 1 - [ \dfrac{e^{-1} 1^0}{0!} +\dfrac{e^{-1} 1^1}{1!} ]$

$P(X \geq 2) = 1 - [0.3678 +0.3678]$

$P(X \geq 2) = 1 -0.7356$

P(X ≥ 2) = 0.2644

The probability that the selection of the random pages will contain at least two errors is 0.2644

6 0

2 years ago

Write and solve a quadratic equation for the situation below. Choose the answer that has both an equation that correctly models

Andreas93 [3]

Acceleration is:

a=g

Velocity is the integral of the above

v=gt+v0

And position is the integral of the above

h=gt^2/2+v0t+h0

You are given that v0=15ft/s and h0=0ft and let g≈-32 so

h(t)=-16t^2+15t

It will hit the ground when h(t)=0 so:

0=-16t^2+15t which is equal to

16t^2-15t=0 factor

t(16t-15)=0, since we are looking for the time other than zero...

t=15/16 of a second :)

So they obviously just rounded to one whole second. So C.) was the correct answer. (Although I would say they are all wrong because they didn't SAY to round the answer :P) Haha, not trying to confuse you, the answer is most likely C. because they had the correct equation.

7 0

2 years ago

The desired percentage of sio2 in a certain type of aluminous cement is 5.5. to test whether the true average percentage is 5.5

k0ka [10]

Wait...what??

uhh I have absolutely no idea

8 0

2 years ago