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LUCKY_DIMON [66]
2 years ago
14

Need help asap i’ll vote brain liest

Mathematics
1 answer:
seropon [69]2 years ago
6 0

Answer:

The answer is y=3x+1

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2. Consider the circle x^2−4x+y^2+10y+13=0. There are two lines tangent to this circle having a slope of 2/3.
likoan [24]

Answer:

a) The coordinates are (0.431, -2.646) and (3.568,-7.354)

b) The tangent lines are

l₁ = (x-0.431)*2/3 - 2.646

l₂ = (x-3.568)2/3 - 7.354

Step-by-step explanation:

First, lets complete squares, by taking for each cordinate the square of a linear expression

0= x²−4x+y²+10y+13 = (x-2)²+ 4  + (y+5)²-25+13 = (x-2)²+(y+5)² - 8

Hence (x-2)² + (y+5)² = 8

Lets put y in function of x. We should obtain 2 functions f and g that represent the circle.

(y+5)² = 8 - (x-2)² = -x² + 4x + 4

y = ^+_- \sqrt{-x^2+4x+4} -5

Thus

f(x) = \sqrt{-x^2+4x+4} - 5

g(x) = -\sqrt{-x^2+4x+4} - 5

Lets find the derivate of each function and the points in which they reach the value 2/3. In those points the tangent line will have a slope of 2/3.

We may just find the values of x which the derivate of f is either 2/3 or -2/3.

\frac{-x+2}{\sqrt{-x^2+4x+4}} = ^+_-\frac{2}{3} \Leftrightarrow \frac{x^2-4x+4}{-x^2+4x+4} = \frac{4}{9} \Leftrightarrow 9(x^2-4x+4) = 4(-x^2+4x+4) \\\Leftrightarrow 13x^2-52x+20 = 0

The quadratic has roots

\frac{52 ^+_-\sqrt{1664}}{26}

one root is 3.568, which corresponds with g, and the other root is 0.431, corresponding to f.

Also g(3.568) = - 7.354 and f(0.431) = -2.646

This means that the coordinates are (0.431 , -2.646), (3.568 , -7.354) and the tangent lines are

l₁ = (x-0.431)*2/3 - 2.646

l₂ = (x-3.568)2/3 - 7.354

5 0
3 years ago
Is the percent increase from 50 to 70 equal to the percent decrease from 70 to 50? Explain.
Galina-37 [17]

Answer

No. The amounts of change are the same, but the original amounts are different. The ratio for the percent increase from 50 to 70 is 20/50, or 40%. The ratio for the percent decrease from 70 to 50 is 20/70, or about 29%.

8 0
3 years ago
Read 2 more answers
A Pyramid is placed inside a prism as shown in the pyramid has the same base area B as a prison but half the height H of the pri
guajiro [1.7K]

Answer:

D) V= 1/6 bh

Step-by-step explanation:

The expression that provides the volume of the pyramid is as follows;

As mentioned in the question

It is given that the pyramid put inside a prism

Also the pyramid contains the similar base area but the height is half of the prism

so the base area of the pyramid is b

And, the Height of the pyramid = h ÷ 2

Now as we know that  

The volume of the pyramid is

V = 1 ÷3 × base ares × height

= 1 ÷ 3 × b × h ÷ 2

V = 1 ÷ 6 bh

So, the volume is 1 ÷6 bh cube unit.

8 0
2 years ago
Read 2 more answers
Simplify<br>6(2 - 7v) - 4(-6v + 7)​
FrozenT [24]

6(2 - 7v) - 4(-6v + 7)​

multiply the first bracket by 6

(6)(2)=-12

(6)(-7v)=-42v

multiply the second bracket by -4

(-4)(-6v)=-24v

(-4)(7)=-28

12-42v+24v-28

-16-18v

Answer:

-16-18v or -18v-16

6 0
3 years ago
Read 2 more answers
Drag Each expression to show whether it is equivalent to 6.7-(-2.5), 6.7+(-2.5), or neither.
iogann1982 [59]

Answer:

Step-by-step explanation:

6.7 – (-2.5)

2.5+6.7

6.7 + (-2.5)

-2.5+6.7

6.7-2.5

neither

-2.5-6.7

2.5-6.7

-6.7+2.5

4 0
3 years ago
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