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balandron [24]
3 years ago
8

P(a) = 2a -3; find p(a) = 15

Mathematics
1 answer:
Andrei [34K]3 years ago
8 0
Since both is equal to p(a), you can set them as equal to each other:

15 = 2a - 3
18 = 2a
9 = a
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Determine whether parallelogram JKLM with vertices J(-7, -2), K(0, 4), L(9, 2) and M(2, -4) is a rhombus, square, rectangle or a
White raven [17]
Check the picture below

now, we know is a parallelogram, so the diagonals will bisect

looking at the picture, the interior angles are not right-angles, and thus is not a rectangle, and is not a square either, due to the same reason

is it a rhombus?  well, a rhombus, is a parallelogram, that's "slanted" per se, but regardless of how slanted it may be, the sides are all equal

now, we don't need to check the length of both pairs, just one of the segments of each pair, let's check only then JK and KL, the ones in red in the picture, since each pair of segments are twin, if JK = KL, then that means all sides are equal

\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
J&({{-7 }}\quad ,&{{ -2}})\quad 
%  (c,d)
K&({{ 0}}\quad ,&{{ 4}})\\\\
K&({{ 0}}\quad ,&{{ 4}})\quad 
%  (c,d)
L&({{ 9}}\quad ,&{{ 2}})
\end{array}\qquad 
%  distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
JK=\sqrt{[0-(-7)]^2+[4-(-2)]^2}\implies JK=\sqrt{(0+7)^2+(4+2)^2}
\\\\\\
JK=\sqrt{7^2+6^2}
\\\\\\
KL=\sqrt{(9-0)^2+(2-4)^2}\implies KL=\sqrt{9^2+(-2)^2}

now... another characteristic of a rhombus is, the diagonals, meet at right-angle, that means KM ⟂ JL

and that simply means, if you get the slope of KM and the slope of JL, the product of their slope is -1

\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%   (a,b)
K&({{ 0}}\quad ,&{{ 4}})\quad 
%   (c,d)
M&({{ 2}}\quad ,&{{ -4}})
\end{array}
\\\\\\
% slope  = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{-4-4}{2-0}

\bf -------------------------------\\\\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%   (a,b)
J&({{ -7}}\quad ,&{{ -2}})\quad 
%   (c,d)
L&({{ 9}}\quad ,&{{ 2}})
\end{array}
\\\\\\
% slope  = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{2-(-2)}{9-(-7)}\implies \cfrac{2+2}{9+7}

then multiply both slopes, if their product is -1, that means, they're perpendicular to each other, and it IS a rhombus only, then.

7 0
3 years ago
Read 2 more answers
3. An aspirin tablet weights 0.5 grams. How many ounces does it weigh?
maksim [4K]
3. An aspirin weighs 0.018 ounces.
1 gram = 0.035 ounces

4. An aspirin is 500 milligrams.
1,000 milligrams = 1 gram
7 0
3 years ago
PLS HELP!!!! WILL GIVE BRAINLIEST!!!!
Marysya12 [62]
(3,0) (-4,0)

not for sure but still mark brainliest cause i need it ✋ im doing bad rn
3 0
2 years ago
9. The longitude of a geographic location is measured in degrees east (E) or west (W) from the
alexandr402 [8]

Based on the longitudes of Quito and Singapore, the shortest distance between the two areas is 19,702.5 km .

<h3>How far is Quito from Singapore?</h3>

Because both cities are close to the equator, you use the longitudinal difference method to find the shortest distance.

First find the difference in longitudes:

= Singapore - Quito

= 104 - (-78.5) because Quito is west

= 104 + 78.5

= 182.5°

Then subtract this from 360°:
= 360 - 182.5

= 177.5°

Every 1° longitude along the Equator is 111 km so the shortest distance is:

= 177.5 x 111

= 19,702.5 km

Find out more on longitudes at brainly.com/question/23425958.

#SPJ1

8 0
1 year ago
What percent of 100 is 30?<br> a. 30%<br> b. 333%<br> c. 3.33%<br> d. 0.3%
alexdok [17]
If you would like to know what percent of 100 is 30, you can calculate this using the following steps:

x% of 100 is 30
x% * 100 = 30
x/100 * 100 = 30
x = 30%

The correct result would be a. 30%.
4 0
3 years ago
Read 2 more answers
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