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3 years ago

What is the y intercept of the line 5x – 3y + 30 = 0

Mathematics

1 answer:

Sliva [168]3 years ago

8 0

Answer:

The y-intercept would be -10/3 but in y-intercept form, it would be 'y=-5/3x-10/3'

Step-by-step explanation:

5x-3y+10=0

first, you would want to subtract '5x' and '10' from both sides.

-3y = -5x -10

Next, you want to divide '-3' from both sides, but you do not take the 'y' with it because you want to keep the 'y' by itself.

y = -5/3x - 10/3

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Prove: cot(x) sec^4(x) = cot(x) +2tan(x) + tan^3(x)

masha68 [24]

$\bf cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}
\qquad\qquad 
sec(\theta)=\cfrac{1}{cos(\theta)}\quad\qquad 1+tan^2(\theta)=sec^2(\theta)\\\\\\
tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}
\qquad \qquad cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)}
\\\\
-------------------------------\\\\
cot(x)sec^4(x)=cot(x)+2tan(x)+tan^3(x)\\\\
-------------------------------\\\\$

$\bf \textit{so, let's do the left-hand-side}\\\\
cot(x)sec^2(x)sec^2(x)\implies cot(x)[1+tan^2(x)][1+tan^2(x)]
\\\\\\
cot(x)[1^2+2tan^2(x)+tan^4(x)]
\\\\\\
cot(x)+2tan^2(x)cot(x)+tan^4(x)cot(x)
\\\\\\
cot(x)+2\cdot \cfrac{sin^2(x)}{cos^2(x)}\cdot \cfrac{cos(x)}{sin(x)}+\cfrac{sin^4(x)}{cos^4(x)}\cdot \cfrac{cos(x)}{sin(x)}
\\\\\\
cot(x)+2\cdot \cfrac{sin(x)}{cos(x)}+\cfrac{sin^3(x)}{cos^3(x)}\implies \boxed{cot(x)+2tan(x)+tan^3(x)}$

8 0

3 years ago

Please answer quick!!

Anon25 [30]

Answer:

if u answer my question i will answer your

Step-by-step explanation:

7 0

3 years ago

In an all boys school, the heights of the student body are normally distributed with a mean of 71 inches and a standard deviatio

muminat

Answer:

15.87%

Step-by-step explanation:

First thing here is that we calculate the z-score which corresponds to 76

mathematically;

z-score = (x-mean)/SD

mean = 71 and SD = 5

plugging these values, we have;

z = (76-71)/5 = 5/5 = 1

Now, we want to firstly get the probability that we have a student shorter than 76 inches

The probability we want to calculate is P(z<1)

we can get this using the z-score table directly

That would be 0.15866

In percentage that is 15.866% which is 15.87% to the nearest tenth

7 0

3 years ago

Find the missing values of the variables. The diagram is not to scale.

Paul [167]

Answer:

y = 64 and x =99

Step-by-step explanation:

y+116 =180

y=64

and

x+y+72+135=360

x=99

5 0

3 years ago

Geometry question for homework.

mars1129 [50]

So remember that the distance formula is $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$ .

$\sqrt{(4-4)^2+(-2-(-5))^2}\\ \sqrt{0^2+3^2}\\ \sqrt{0+9}\\ \sqrt{9}\\ 3$

Distance between (4,-5) and (4,-2) is 3 units.

$\sqrt{(1-(-1))^2+(1-4)^2}\\ \sqrt{2^2+(-3)^2}\\ \sqrt{4+9}\\ \sqrt{13}$

Distance between (1,1) and (-1,4) is √13 (or 3.61 rounded to the hundreths) units.

3 0

3 years ago