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3 years ago

Which expression represents "2 less than the product of 5 and a number"?

Mathematics

2 answers:

diamong [38]3 years ago

7 0

Two less ( means minus 2) the product of (means multiply) 5 and a number.
so you get (5n) -2

USPshnik [31]3 years ago

4 0

Answer:

it can also just be 5n-2 without ( )

Step-by-step explanation:

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Quadrilateral KLMN is a rectangle. The coordinates of L are L(1,-4), and the coordinates of Mare M(3,-2). Find the slopes of sid

lozanna [386]

L(1, -4)=(xL, yL)→xL=1, yL=-4
M(3, -2)=(xM, yM)→xM=3, yM=-2

Slope of side LM: m LM = (yM-yL) / (xM-xL)
m LM = ( -2 - (-4) ) / (3-1)
m LM = ( -2+4) / (2)
m LM = (2) / (2)
m LM = 1

The quadrilateral is the rectangle KLMN
The oposite sides are: LM with NK, and KL with NK
In a rectangle the opposite sides are parallel, and parallel lines have the same slope, then:
Slope of side LM = m LM = 1 = m NK = Slope of side NK
Slope of side NK = m NK = 1

Slope of side KL = m KL = m MN = Slope of side MN

The sides KL and LM (consecutive sides) are perpendicular (form an angle of 90°), then the product of their slopes is equal to -1:
(m KL) (m LM) = -1
Replacing m LM = 1
(m KL) (1) = -1
m KL = -1 = m MN

Answer:
Slope of side LM =1
Slope of side NK =1
Slope of side KL = -1
Slope of side MN = -1

3 0

3 years ago

A segment with endpoints A (2, 1) and C (4, 7) is partitioned by a point B such that AB and BC form a 3:2 ratio. Find B.

sdas [7]

$\bf ~~~~~~~~~~~~\textit{internal division of a line segment} \\\\\\ A(2,1)\qquad C(4,7)\qquad \qquad \stackrel{\textit{ratio from A to C}}{3:2} \\\\\\ \cfrac{A\underline{B}}{\underline{B} C} = \cfrac{3}{2}\implies \cfrac{A}{C} = \cfrac{3}{2}\implies 2A=3C\implies 2(2,1)=3(4,7)\\\\[-0.35em] ~\dotfill\\\\ B=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill$

$\bf B=\left(\cfrac{(2\cdot 2)+(3\cdot 4)}{3+2}\quad ,\quad \cfrac{(2\cdot 1)+(3\cdot 7)}{3+2}\right)\implies B=\left( \cfrac{4+12}{5}~,~\cfrac{2+21}{5} \right) \\\\\\ B=\left(\cfrac{16}{5}~~,~~\cfrac{23}{5} \right)\implies B=\left( 3\frac{1}{5}~~,~~4\frac{3}{5} \right)$

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3 years ago

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The table shows the time in

docker41 [41]

30 seconds, half a minute.

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3 years ago

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Let c be parametrized by x = et sin (10t) and y = et cos (10t) for 0 ≤ t ≤ 2. find the length l of

marysya [2.9K]

$C:x(t)=e^t\sin10t;\,y(t)=e^t\cos10t;\,0\le t\le2$

$\displaystyle\int_0^2\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt$
$\displaystyle=\int_0^2\sqrt{(e^t\sin10t+10e^t\cos10t)^2+(e^t\cos10t-10e^t\sin10t)^2}\,\mathrm dt$
$\displaystyle=\int_0^2e^t\sqrt{\sin^210t+20\sin10t\cos10t+100\cos^210t+\cos^210t-20\sin10t\cos10t+100\sin^210t}\,\mathrm dt$
$=\displaystyle\int_0^2e^t\sqrt{1+100}\,\mathrm dt$
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7 0

3 years ago

There are 6 red marbles, 9 blue marbles, and 10 green marbles in a bag.

Nat2105 [25]

Answer:

I think 64%

Step-by-step explanation:

6+9+10 = 25

25x4 = 100

6x4 = 24

10x4 = 40

24+40 = 64

64/100 = 64%

Sry if this is wrong but I think this should be correct

7 0

2 years ago

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