Anyone knows about this ?.

Draw graphs of the following lines: The line through (-5, 2) having the slope of -3

Ivanshal [37]

What you want to do here is take this information and plug it into point-slope form. any time you're given a point and a slope, you generally want to plug it into this equation: y - y1 = m(x - x1).

in this equation, m is your slope and (x1, y1) is a given point. plug in your info--slope of -3 and (-5, 2).

y - 2 = -3(x + 5)

that is the equation of your line. however, if you want to graph it, this doesn't really make much sense to you. convert it to slope-intercept form, y = mx + b, by solving for y.

y - 2 = -3(x + 5) ... distribute -3
y - 2 = -3x - 15 ... add 2
y = -3x - 13 is your equation.

to graph this, and any other y = mx + b equation, you want to start with your y-intercept if it's present. your y intercept here is -13, which means the line you wasn't to graph crosses the y-axis at y = -13, or (0, -13). put a point there.

after you've plotted that point, you use your slope to graph more. remember that your slope is "rise over run"--you rise up/go down however many units, you run left/right however many units. if your slope is -3, you want to go down 3 units, then go to the right 1 unit. remember that whole numbers have a 1 beneath them as a fraction. -3/1 is your rise over 1.

6 0

2 years ago

Read 2 more answers

Ricardo comes up with his own casino game.You draw a card from a standard deck.If you pick a heart, you win $10.If you pick a fa

avanturin [10]

Answer:

Total number of cards in a standard deck of card=52

As deck of card contain 13 club +13 heart +13 spade+13 Diamond.

P(Diamond)=13/52 =1/4

If the card is not diamond then

P(not diamond)=39/52=3/4

Since after drawing card is not replaced

P ( second Diamond)=12/51

now if second card is not Diamond.then

P(non diamond)=39/51

Chances of your winning i.e both cards are diamonds=1/4×12/51=1/17=0.0588..(approx)

chances of your friend winning=1/4×39/51=[1/4]×[13/17]=13/68=0.1911..(approx)

Your friend has got better chance to win because there are more chances that both the cards are not Diamonds.

5 0

2 years ago

A circle with a radius of 5 cm has an area of 78.54 cm2. What constant, rounded to the nearest hundredth, do you get when the ar

Naily [24]

Answer:

3.14

Step-by-step explanation:

Area of a corcle is sexpressed as';

A = πr²

π = A/r²

π = 78.54/5²

π = 78.54/25

π = 3.1416

When the area is divided by radius the required constant is 3.14

3 0

2 years ago

Solve the following:

IrinaVladis [17]

Answer:

−4

Step-by-step explanation:

7 0

2 years ago

Trig proofs with Pythagorean Identities.

lorasvet [3.4K]

To prove:

$$\frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}=2 \cot ^{2} x+1$

Solution:

$$LHS = \frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}$

Multiply first term by $\frac{1+cos x}{1+cos x}$ and second term by $\frac{1-cos x}{1-cos x}$ .

$$= \frac{1(1+\cos x)}{(1-\cos x)(1+\cos x)}-\frac{\cos x(1-\cos x)}{(1+\cos x)(1-\cos x)}$

Using the identity: $(a-b)(a+b)=(a^2-b^2)$

$$= \frac{1+\cos x}{(1^2-\cos^2 x)}-\frac{\cos x-\cos^2 x}{(1^2-\cos^2 x)}$

Denominators are same, you can subtract the fractions.

$$= \frac{1+\cos x-\cos x+\cos^2 x}{(1^2-\cos^2 x)}$

Using the identity: $1-\cos ^{2}(x)=\sin ^{2}(x)$

$$= \frac{1+\cos^2 x}{\sin^2x}$

Using the identity: $1=\cos ^{2}(x)+\sin ^{2}(x)$

$$=\frac{\cos ^{2}x+\cos ^{2}x+\sin ^{2}x}{\sin ^{2}x}$

$$=\frac{\sin ^{2}x+2 \cos ^{2}x}{\sin ^{2}x}$ ------------ (1)

$RHS=2 \cot ^{2} x+1$

Using the identity: $\cot (x)=\frac{\cos (x)}{\sin (x)}$

$$=1+2\left(\frac{\cos x}{\sin x}\right)^{2}$

$$=1+2\frac{\cos^{2} x}{\sin^{2} x}$

$$=\frac{\sin^2 x + 2\cos^{2} x}{\sin^2 x}$ ------------ (2)

Equation (1) = Equation (2)

LHS = RHS

$$\frac{1}{1-\cos x}-\frac{\cos x}{1+\cos x}=2 \cot ^{2} x+1$

Hence proved.

5 0

3 years ago