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3 years ago

PLEASE ANSWER FAST this is homework and my teacher is giving us time to do it even if the deadline passed I don't know fractions

Mathematics

2 answers:

cluponka [151]3 years ago

7 0

For this the answer for 6. Is 5/1 and 7. Is 9/1

Marysya12 [62]3 years ago

5 0

Answer:

Step-by-step explanation:

5/7

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Given quadrilateral RSTU, determine if each pair of sides (if any) are parallel and which are perpendicular for the coordinates

WINSTONCH [101]

Check the picture below.

so, clearly UR is not parallel to ST, but is likely that UT is parallel to RS.

keeping in mind that parallel lines, have the same exact slope, let's check the slope for UT as well as RS, if they are the same, then indeed both are parallel,

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&R&(~ 1 &,& -3~) 
% (c,d)
&S&(~ 4 &,& -1~)
\end{array}
\\\\\\
% slope = m
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-(-3)}{4-1}\implies \cfrac{-1+3}{4-1}\implies \cfrac{2}{3}\\\\
-------------------------------$

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&U&(~ -4 &,& -2~) 
% (c,d)
&T&(~ 2 &,& 2~)
\end{array}
\\\\\\
% slope = m
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-(-2)}{2-(-4)}\implies \cfrac{2+2}{2+4}\implies \cfrac{4}{6}\implies \cfrac{2}{3}$

there you have it, notice the slopes of each.

from the picture, clearly there are no right-angles at vertices U and R, however at S and T, it looks like, but we dunno.

well, we know UT || RS, now if ST ⟂ RS, then ST will have a negative reciprocal slope to RS, namely whatever the slope of RS is, ST will be the negative reciprocal of that, so let's check what is the slope of ST then,

$\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{2}{3}\\\\
negative\implies -\cfrac{2}{ 3}\qquad reciprocal\implies \boxed{- \cfrac{ 3}{2}}\\\\
-------------------------------\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&S&(~ 4 &,& -1~) 
% (c,d)
&T&(~ 2 &,& 2~)
\end{array}
\\\\\\
% slope = m
slope = m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-(-1)}{2-4}\implies \cfrac{2+1}{2-4}\implies \boxed{-\cfrac{3}{2}}$

and if ST ⟂ RS, then ST ⟂ UT.

8 0

3 years ago

Anna invests $7,000 in an account that compounds interest continuously and earns 7.5%. How long will it take for her

NeX [460]

Answer:

It will take 36.1 years for her money to reach $105,000.

Step-by-step explanation:

The amount of money earned after t years in continuous interest is given by:

$P(t) = P(0)e^{rt}$

In which P(0) is the initial investment and r is the interest rate, as a decimal.

Anna invests $7,000 in an account that compounds interest continuously and earns 7.5%.

This means that $P(0) = 7000, r = 0.075$

How long will it take for her money to reach $105,000?

This is t for which P(t) = 105000.

$P(t) = P(0)e^{rt}$

$105000 = 7000e^{0.075t}$

$e^{0.075t} = \frac{105000}{7000}$

$e^{0.075t} = 15$

$\ln{e^{0.075t}} = \ln{15}$

$0.075t = \ln{15}$

$t = \frac{\ln{15}}{0.075}$

$t = 36.1$

It will take 36.1 years for her money to reach $105,000.

6 0

3 years ago

9. There are 56 children who need to be divided into teams of 8. How many children will

anyanavicka [17]

Answer:

Your answer is 7 children on each team

Step-by-step explanation:

The question clearly states "divided," so divide 56 by 8.

The question is asking you how many kids are on each team.

If I didn't understand the question properly, let me know. :) good luck!

5 0

3 years ago

Use the position function s(t) = –4.9t2 + 500, which gives the height (in meters) of an object that has fallen for t seconds fro

weqwewe [10]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The value is $v(3) = 29.4 \ m/s$

Step-by-step explanation:

From the question we are told that

$s(t) = -4.9t^2 + 500$

And

$\lim_{t \to a} \frac{s(a) - s(t)}{a-t}$

Generally s(t) at t = a is mathematically evaluated as

$s(a) = -4.9a^2+ 500$

$s(a) - s(t) = -4.9a^2 + 500 - ( -4.9t^2+500)$

$s(a) - s(t) = -4.9a^2 + 500 +4.9t^2-500)$

$s(a) - s(t) = 4.9(t^2 - a^2)$

Thus the velocity is represented as

$v(t) =\lim_{t \to a} \frac{s(a) - s(t)}{a-t} \equiv \lim_{t \to a} \frac{4.9(t^2 - a^2 )}{ a-t}$

=> $v(t) = \lim_{t \to a} - 4.9(a + t )$

=> $v(t) = -4.9 (a + a )$

=> $v(t) = -9.8a$

Now at t = 3

=> $v(3) = -9.8 (3)$

=> $v(3) = 29.4 \ m/s$

3 0

4 years ago

6. Would the amount of dissolved oxygen in the Missouri River increase or decrease if large amounts of chemical waste were dumpe

WARRIOR [948]

<span>The amount of dissolved oxygen in the Missouri River would decrease if large amounts of chemical waste were dumped into it. It would decrease because the chemical waste would feed on the microorganisms and reduce the amount of oxygen in the river.</span>

7 0

3 years ago