How to change the format of the equation y-5=x

A loon is flying at a height of 10 feet above a lake. The lone dives into the water to catch a fish that is at a depth of 6 feet

Zielflug [23.3K]

I do believe that the answer is 16 feet (D)

5 0

3 years ago

the line joining A(a, 3) to B(2 -3) is perpendicular to the line joining C(10,1) to B. The value of a is?

RideAnS [48]

Well, first off, let's find what is the slope of BC

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
B&({{ 2}}\quad ,&{{ -3}})\quad 
% (c,d)
C&({{ 10}}\quad ,&{{ 1}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{1-(-3)}{10-2}\implies \cfrac{1+3}{10-2}
\\\\\\
\cfrac{4}{8}\implies \cfrac{1}{2}$

now, a line perpendicular to that one, will have a negative reciprocal slope, thus

$\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{1}{2}\\\\
slope=\cfrac{1}{{{ 2}}}\qquad negative\implies -\cfrac{1}{{{ 2}}}\qquad reciprocal\implies - \cfrac{{{ 2}}}{1}\implies \boxed{-2}$

now, we know the slope "m" of AB is -2 then, thus

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
A&({{ a}}\quad ,&{{ 3}})\quad 
% (c,d)
B&({{ 2}}\quad ,&{{ -3}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-3-3}{2-a}=\boxed{-2}
\\\\\\
\cfrac{-6}{2-a}=-2\implies -6=-4+2a\implies -2=2a\implies \cfrac{-2}{2}=a
\\\\\\
-1=a$

6 0

3 years ago

A sample with a mean of m = 40 and a variance of s2 = 20 has an estimated standard error of 1 point. how many scores are in the

tamaranim1 [39]

The correct option is 20.

The score found for the sample is 20.

<h3>What is Standard error?</h3>

A standard error is a statistic that is applied to test the distribution of data. This metric is comparable to standard deviation. We can calculate the standard error if we know the sample size & standard deviation. It assesses the mean's precision.

Now, according to the question;

Sample mean; $\bar{x}=40$

Sample variance; $s^{2}=20$

Thus, $s=\sqrt{20}=4.47$

Standard error SE = 1

The amount of scores with in sample must be determined here.

The standard error formula is as follows:

$S E=\frac{s}{\sqrt{n}}$

We might rearrange the formula as follows:

$\begin{aligned}\sqrt{n} &=\frac{s}{S E} \\n &=\left(\frac{s}{S E}\right)^{2}\end{aligned}$

Substituting the values;

$\begin{aligned}&n=\left(\frac{4.47}{1}\right)^{2} \\&n=19.98\end{aligned}$

The sample's number of scores n = 19.98 = 20 (round up)

Therefore, the scores are in the sample is 20.

To know more about the Standard error, here

brainly.com/question/14467769

#SPJ4

3 0

1 year ago

Use the Distributive Property to find (z−5)(z+3).

Anastasy [175]

Consider, $(z-5)(z+3)$ . Let's say $a = z-5$ then the problem reduces to $a(z+3)=za+3a$ . (Do you understand this step?)

So then replacing a again with our definition we get, $z(z-5)+3(z-5)=z^2-5z+3z-15=z^2-2z-15$ .

4 0

3 years ago

Solve the compound inequality: 4 < 3x – 1 < 20

Nataliya [291]

Answer:

x = (5/3 , 7)

Step-by-step explanation:

4 0

3 years ago