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3 years ago

Find the value of r in(4,r) (r,3) so that the slope of the line containing them is 0

Mathematics

1 answer:

Pavel [41]3 years ago

8 0

Answer:

r = 3.

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

$y = mx + b$

In which m is the slope.

Finding the slope of a line, given two points:

When we are given two points of a line, the slope of the line is given by the change in y divided by the change in x.

Points (4,r), (r,3)

Change in y: 3 - r

Change in x: r - 4

Slope is 0, so:

$\frac{3 - r}{r - 4} = 0$

$3 - r = 0$

$r = 3$

The value is r = 3.

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What is x equal to ? Link down below.

scZoUnD [109]

Answer:

Step-by-step explanation:

Because of supplementary angles that line has to equal to 180

180-75 = 105

so 105 = (2x + 5)

you can subtract 5 from each side and get

100 = (2x)

then divide each side by 2 and you get

x = 50

you can check it by doing (2 x 50 + 5)

2 x 50 = 100 + 5 = 105 + 75 = 180

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3 years ago

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tekilochka [14]

Answer:

Step-by-step explanation:

I am not 100% sure but I hope this helps you.

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3 years ago

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If $8700 is invested at 3% annual simple interest, how much should be invested at 6% annual simple interest so that the total ye

True [87]

First off, see how much 8700 as principal, yields at 3% APR
that is $\bf \qquad \textit{Simple Interest Earned}\\\\
I = Prt\qquad 
\begin{cases}
I=\textit{interest earned}\\
P=\textit{original amount deposited}\to& \$8700\\
r=rate\to 3\%\to \frac{3}{100}\to &0.03\\
t=years\to &1
\end{cases}$

it will yield some amount

subtract that amount from 393
the difference is how much the yield will be on the 6% investment
so

$\bf \qquad \textit{Simple Interest Earned}\\\\
I = Prt\quad 
\begin{cases}
I=\textit{interest earned}\\
P=\textit{original amount deposited}\to& \$8700\\
r=rate\to 3\%\to \frac{3}{100}\to &0.03\\
t=years\to &1
\end{cases}
\\\\\\
\implies \boxed{?}\\\\
-----------------------------\\\\
\textit{how much to invest at 6\%?}
\\\\\\
$

$\bf \qquad \textit{Simple Interest Earned}\\\\
(393-\boxed{?}) = Prt\quad 
\begin{cases}
I=\textit{interest earned}\\
P=\textit{original amount deposited}\to& \$\\
r=rate\to 6\%\to \frac{6}{100}\to &0.06\\
t=years\to &1
\end{cases}
\\\\\\
\textit{solve for "P", to see how much should the Principal be}\\\\
\textit{keep in mind that }P+\boxed{?}=393\leftarrow \textit{both yields added}$

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3 years ago

Help me with my question please

Vikentia [17]

Answer:

i, iii and iv

Step-by-step explanation:

196 = 14²

400 = 20²

324 = 18²

6 0

3 years ago

Find the area of the shaded region given the radius of each circle is 4. Answer in exact form is preferred.

larisa [96]

In each circle, we have a sector that subtends an angle of 270 deg at the center, with a radius of 4

We can obtain the area of each sector as :

$\begin{gathered} \text{Area of sector = }\frac{\theta}{360^0}\text{ }\times\text{ }\pi r^2 \\ =\text{ }\frac{270^0}{360^0}\text{ }\times\text{ }\pi\text{ }\times4^2 \\ =\text{ 37.7 square units} \end{gathered}$

Given that there are 4 of such sectors, we have:

$\begin{gathered} \text{Area of shaded region = 4 }\times\text{ 37.7} \\ =\text{ }150.8\text{ square units} \\ =\text{ 151 square units} \end{gathered}$

Answer = 151 square units

5 0

1 year ago