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3 years ago

I have 3/5 marbles. Emily gave me 4/3 marble. how many marbles do I have?

1 answer:

5 0

If you have 3/5 marbles and you got 4/3more marbles then all you have to do is:3/5 x 3/3 and get 9/15.For 4/3 you multiply 4/3 x 5/5 and get 20/15.You simplify this and get 1 5/15.Now all you do is add them and get 1 14/15. Hope this helped you :-).

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2. Consider the circle x² + y2 = 1, given in figure. Let OP makes an angle 30° with the x axis.

PolarNik [594]

The equation of the tangent line to the circle passing through the point P is; y = (1/√3)x ± 2/√3

<h3>How to find the equation of the tangent?</h3>

I) We are given the equation of the circle as;

x² + y² = 1

Since angle of inclination is 30°, then slope is;

m = tan 30 = 1/√3

Then equation of the tangent will be;

y = (1/√3)x + c

Put (√3)x + c into the given circle equation to get;

x² + ((1/√3)x + c)² = 1

x² + ¹/₃x² + (2/√3)cx + c² = 1

⁴/₃x² + (2/√3)x + (c² - 1) = 0

Since we need to find value of c for equation to become tangent, then the above quadratic equation must have real and equal roots.

Thus;

((2/√3)c)² - 4(⁴/₃)(c² - 1) = 0

⁴/₃c² - ¹⁶/₃(c² - 1) = 0

⁴/₃c² - ¹⁶/₃c² + ¹⁶/₃ = 0

4c² = ¹⁶/₃

c² = ⁴/₃

c = √⁴/₃

c = ±²/√3

Thus, equation of tangent is;

y = (1/√3)x ± 2/√3

II) Radius from the given equation is 1. Thus, we will use trigonometric ratio to find the x and y intercept;

x-intercept is at y = 0;

0 = (1/√3)x ± 2/√3

-(1/√3)x = ±2/√3

Intercept is positive. Thus;

x = (2/√3)/(1/√3)

x = 1

y - intercept is positive at x = 0;

y = (1/√3)0 ± 2/√3

y = 2/√3

Read more about Equation of tangent at; brainly.com/question/17040970

#SPJ1

6 0

1 year ago

Write the answer in numeric form?

kondor19780726 [428]

Answer:

x=11. 38 degrees; 52 degrees

Step-by-step explanation:

90+6x-14+3x+5=180

81+9x=180

9x=99

x=11

38 degrees, 52 degrees

8 0

3 years ago

4.6363 as fraction using long division

nirvana33 [79]

Answer:

459/99

Step-by-step explanation:

0.6363... is equal to 63/99.

We want to add 4.

4 = 396/99

396/99 + 63/99 = 459/99

We can double check with a calc.

5 0

3 years ago

Please help! Urgent! Will mark brainliest!

Wewaii [24]

Answer:

Fun Fact: The shortest teletubbie is 6,6 the tallest one is 10 feet

Step-by-step explanation:

7 0

3 years ago

Please answer one question asap <br>A(-4,3) B(2,-1) D(-4,-1) C(2,-5)

Leni [432]

Answer:

Step-by-step explanation:

Vertices of the given quadrilateral are A(-4, 3), B(2, -1), C(2, -5) and D(-4, -1)

Since, slope of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by,

Slope = $\frac{y_2-y_1}{x_2-x_1}$

Slope of AB = $\frac{3+1}{-4-2}$

= $-\frac{2}{3}$

Slope of AD = $\frac{3+1}{-4+4}$

= Not defined (Parallel to y-axis)

Slope of DC = $\frac{-5+1}{2+4}$

= $-\frac{2}{3}$

Slope of BC = $\frac{-1+5}{2-2}$

= Not defined (Parallel to y-axis)

Slope of AB = slope of DC = $-\frac{2}{3}$

Slope of BC = slope of AD = Not defined (parallel to y-axis)

As per property of a parallelogram,

"Opposite sides of a parallelogram are parallel and equal in measure"

Therefore, ABCD is a parallelogram.

8 0

3 years ago