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3 years ago

What is the measure of 1? 90° 80° 85° 95°

Mathematics

2 answers:

Leokris [45]3 years ago

5 0

Answer:

C. 85

Step-by-step explanation;

You know that that sum of the angle measures in a quadrilateral is 360°, so you can solve for the missing angle measure.

So, you can see the bottom left corner equals 90 degrees because of the right angle. The other degrees plus 90 equals 275. So we would subtract 275 from 360 and get 85.

This means that "1" equals 85 degrees.

I hope this helps!

Morgarella [4.7K]3 years ago

3 0

Answer:90

Step-by-step explanation:

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Do you know. How to solve these?

trapecia [35]

It is E. 25:10 simplifies to 5:2.

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3 years ago

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A tangent from point P to a circle of radius 4 cm is 10 cm long. Find: <br>a the distance of P from the centre of the circle <br

d1i1m1o1n [39]

Answer:

see explanation

Step-by-step explanation:

The tangent and the radius at the point of contact form a right angle

Using Pythagoras' identity on the right triangle formed.

Let x be the distance from the centre to P, then

x² = 4² + 10² = 16 + 100 = 116 ( take the square root of both sides )

x = $\sqrt{116}$ ≈ 10.77 cm (to 2 dec. places )

let the required angle be Θ, then

Using the sine or cosine ratio in the right triangle.

cosΘ = $\frac{adjacent}{hypotenuse}$ = $\frac{10}{\sqrt{116} }$

Θ = $cos^{-1}$ ( $\frac{10}{\sqrt{116} }$ ) ≈ 21.8°

7 0

3 years ago

You go outside and step on a frog, the sand is yellow because the grass was 42, therefore the rabbit hopped 39 degrees upwards.

Zina [86]

Answer:

Step-by-step explanation:

its 40 because bob is orange.

8 0

2 years ago

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what is the distance between the points (4, 5) and (10, 13) on a coordinte plane a. 12 units b. 8 units c. 10 units d. 14 units

qaws [65]

Answer:

<h2>10 units</h2>

Option C is the correct option

Step-by-step explanation:

Let the points be A and B

A ( 4 , 5 ) ------> ( x1 , y1 )

B ( 10 , 13 ) ------> ( x2 , y2 )

Now, let's find the distance between these points:

$\sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} }$

plug the values

$= \: \sqrt{(10 - 4) ^{2} + {(13 - 5)}^{2} }$

Calculate the difference

$= \sqrt{ {(6)}^{2} + {(8)}^{2} }$

Evaluate the power

$= \sqrt{36 + 64}$

Add the numbers

$= \sqrt{100}$

Write the number in exponential form with. base of 10

$= \sqrt{ {(10)}^{2} }$

Reduce the index of the radical and exponent with 2

$= 10 \: units$

Hope this helps..

Best regards!!

7 0

3 years ago

Integral of 17/(x^3-125)

daser333 [38]

Answer:

17/75 ln│x − 5│− 17/150 ln(x² + 5x + 25) − 17/(5√75) tan⁻¹((2x + 5) / √75) + C

Step-by-step explanation:

∫ 17 / (x³ − 125) dx

= 17 ∫ 1 / (x³ − 125) dx

= 17 ∫ 1 / ((x − 5) (x² + 5x + 25)) dx

Use partial fraction decomposition:

= 17 ∫ [ A / (x − 5) + (Bx + C) / (x² + 5x + 25) ] dx

Use common denominator to find the missing coefficients.

A (x² + 5x + 25) + (Bx + C) (x − 5) = 1

Ax² + 5Ax + 25A + Bx² − 5Bx + Cx − 5C = 1

(A + B) x² + (5A − 5B + C) x + 25A − 5C = 1

Match the coefficients and solve the system of equations.

A + B = 0

5A − 5B + C = 0

25A − 5C = 1

A = 1/75

B = -1/75

C = -2/15

So the integral is:

= 17 ∫ [ 1/75 / (x − 5) + (-1/75 x − 2/15) / (x² + 5x + 25) ] dx

Simplify:

= 17/75 ∫ [ 1 / (x − 5) − (x + 10) / (x² + 5x + 25) ] dx

Factor ½ from the numerator of the second fraction:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 20) / (x² + 5x + 25) ] dx

Split the fraction:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 5) / (x² + 5x + 25) − ½ (15) / (x² + 5x + 25) ] dx

Multiply the last fraction by 4/4:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 5) / (x² + 5x + 25) − 30 / (4x² + 20x + 100) ] dx

Complete the square:

= 17/75 ∫ [ 1 / (x − 5) − ½ (2x + 5) / (x² + 5x + 25) − 15 / ((2x + 5)² + 75) ] dx

Split the integral:

= 17/75 ∫ 1 / (x − 5) dx − 17/150 ∫ (2x + 5) / (x² + 5x + 25) dx − 17/5 ∫ 1 / ((2x + 5)² + 75) dx

The first integral is:

∫ 1 / (x − 5) dx = ln│x − 5│

The second integral is:

∫ (2x + 5) / (x² + 5x + 25) dx = ln(x² + 5x + 25)

The third integral is:

∫ 1 / ((2x + 5)² + 75) dx = 1/√75 tan⁻¹((2x + 5) / √75)

Plug in:

= 17/75 ln│x − 5│− 17/150 ln(x² + 5x + 25) − 17/(5√75) tan⁻¹((2x + 5) / √75) + C

4 0

3 years ago