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3 years ago

What is the slope of the line represented by the equation f(x) = -3x + 7? A. -7 B. -3 C. 3 D. 7

Mathematics

2 answers:

Basile [38]3 years ago

4 0

Answer:

B. -3

Step-by-step explanation:

y = mx + b is slope intecept formula

m = slope

y = -3x + 7

-3 = m

aivan3 [116]3 years ago

3 0

Answer:

B. -3

Step-by-step explanation:

I got it right in a test.

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If tanA+sinA=m and tanA-sinA=n.prove that m^2-n^2=4√mn

mash [69]

Let $a=\tan A$ and $b=\sin A$ . Then

$m^2-n^2=(a+b)^2-(a-b)^2=(a^2+2ab+b^2)-(a^2-2ab+b^2)=4ab$

$\implies m^2-n^2=4\tan A\sin A$

and

$mn=(a+b)(a-b)=a^2-b^2$

$\implies4\sqrt{mn}=4\sqrt{\tan^2A-\sin^2A}$

The expression under the square root can be rewritten as

$\tan^2A-\sin^2A=\dfrac{\sin^2A}{\cos^2A}-\sin^2A=\sin^2A\left(\dfrac1{\cos^2A}-1\right)=\sin^2A(\sec^2A-1)$

Recall that

$\sin^2A+\cos^2A=1\implies\tan^2A+1=\sec^2A$

so that

$\tan^2A-\sin^2A=\sin^2A\tan^2A$

and assuming $\sin A>0$ and $\tan A>0$ , we end up with

$4\sqrt{\tan^2A-\sin^2A}=4\tan A\sin A$

so that

$m^2-n^2=4\sqrt{mn}$

as required.

5 0

2 years ago

The area of a circular sun spot is growing at a rate of 1,200 km2/s.

Tpy6a [65]

A)

$\bf \textit{area of a circle}\\\\
A=\pi r^2
\\\\\\
\cfrac{dA}{dt}=\pi \cdot 2r\cfrac{dr}{dt}\implies \cfrac{dA}{dt}=2\pi r\cfrac{dr}{dt}\implies \cfrac{\frac{dA}{dt}}{2\pi r}=\cfrac{dr}{dt}\\\\
-----------------------------\\\\
\left. \cfrac{dr}{dt} \right|_{r=3000}\implies \cfrac{1200}{2\pi \cdot 3000}=\cfrac{dr}{dt}\\\\$

B)

$\bf A=\pi r^2\qquad A=490000\implies 490000=\pi r^2\implies \sqrt{\cfrac{490000}{\pi }}=r
\\\\\\
\left. \cfrac{dr}{dt} \right|_{r=\sqrt{\frac{490000}{\pi }}}\implies \cfrac{1200}{2\pi \cdot \sqrt{\frac{490000}{\pi }}}=\cfrac{dr}{dt}
$

8 0

2 years ago

Which statement explains how the lines x + y = 2 and y = x + 4 are related?

zysi [14]

Answer: X = -1 and Y = 3
—————————————
X + Y = 2
X = 2 - Y
————————
Y = x + 4
Y = 2 - Y + 4
2Y = 2 + 4
2Y = 6
Y = 3
————————
X + Y = 2
X + 3 = 2
X = -1

8 0

2 years ago

Triangles P and Q are similar.

svp [43]

Answer:

if i labeled the triangle correctly BC= sqrt 97, ZX=32sqrt 2

Step-by-step explanation:

join my stream and tell me how to label the triangle

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2 years ago

1/4x - 3-4 > 4<br> PLEASE SHOW THE WORK

enot [183]

X>44

.25(x)-3-4>4
.25(x)-7>4
.25(x)>11
x>11

3 0

2 years ago