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3 years ago

Ignore the mess... I need help with #20 please and thank you

Mathematics

1 answer:

enot [183]3 years ago

6 0

Because the triangle is isosceles, angle P and angle R are the same. Thus, your work would be:

$6x+4 + 2(98-4x) = 180$ . You then simplify this to 6x+4 + 196 - 8x = 180. Combine like terms, you get - 2x = - 20. x = 10.

Plug x = 10 back into the equation 98 - 4x to get 98 - 4(10) which becomes 98 - 40 = 58.

Angle P should be equal to 58 degrees.

To check your work add up the angles to see if they equal 180:

58 + 58 + 6(10) + 4 = 116 + 64 = 180.

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In the illustration below, the three cube-shaped tanks are identical. The spheres in any given tank

fredd [130]

Answer:

1) Volume occupied by the spheres are equal therefore the three tanks contains the same volume of water

2) $Amount \ of \, water \ remaining \ in \, the \ tank \ is \ \frac{x^3(6-\pi) }{6}$

Step-by-step explanation:

1) Here we have;

First tank A

Volume of tank = x³

The volume of the sphere = $\frac{4}{3} \pi r^3$

However, the diameter of the sphere = x therefore;

r = x/2 and the volume of the sphere is thus;

volume of the sphere = $\frac{4}{3} \pi \frac{x^3}{8}$ = $\frac{1}{6} \pi x^3$

For tank B

Volume of tank = x³

The volume of the spheres = $8 \times \frac{4}{3} \pi r^3$

However, the diameter of the spheres 2·D = x therefore;

r = x/4 and the volume of the sphere is thus;

volume of the spheres = $8 \times \frac{4}{3} \pi (\frac{x}{4})^3= \frac{x^3 \times \pi }{6}$

For tank C

Volume of tank = x³

The volume of the spheres = $64 \times \frac{4}{3} \pi r^3$

However, the diameter of the spheres 4·D = x therefore;

r = x/8 and the volume of the sphere is thus;

volume of the spheres = $64 \times \frac{4}{3} \pi (\frac{x}{8})^3= \frac{x^3 \times \pi }{6}$

Volume occupied by the spheres are equal therefore the three tanks contains the same volume of water

2) For the 4th tank, we have;

number of spheres on side of the tank, n is given thus;

n³ = 512

∴ n = ∛512 = 8

Hence we have;

Volume of tank = x³

The volume of the spheres = $512 \times \frac{4}{3} \pi r^3$

However, the diameter of the spheres 8·D = x therefore;

r = x/16 and the volume of the sphere is thus;

volume of the spheres = $512\times \frac{4}{3} \pi (\frac{x}{16})^3= \frac{x^3 \times \pi }{6}$

Amount of water remaining in the tank is given by the following expression;

Amount of water remaining in the tank = Volume of tank - volume of spheres

Amount of water remaining in the tank = $x^3 - \frac{x^3 \times \pi }{6} = \frac{x^3(6-\pi) }{6}$

$Amount \ of \ water \, remaining \, in \, the \ tank = \frac{x^3(6-\pi) }{6}$ .

5 0

3 years ago

Please help me find X

Zanzabum

Answer:

x = 2

Step-by-step explanation:

The product of distances from the intersection of secants to the near and far intersections with the circle are the same. For a tangent, the near and far points of intersection with the circle are the same. This relation tells us ...

(2√3)(2√3) = x(x +4)

12 = x² +4x

16 = x² +4x +4 . . . . . add the square of half the x-coefficient to complete the square

4² = (x +2)² . . . . . . . . write as squares

4 = x +2 . . . . . . . . . . positive square root

2 = x . . . . . . . . . . . . . subtract 2

_____

<em>Alternate solution</em>

If you believe x to be an integer, you can look for factors of 12 that differ by 4.

12 = 1×12 = 2×6 = 3×4

The factors 2 and 6 differ by 4, so x=2 and x+4=6.

6 0

3 years ago

HELP ME PLEASE REALLY IMPORTANT OR ILL GET IN TROUBLE!! WILL MARK AS BRAINLEST IF YOU GET IT CORRECT!!

dmitriy555 [2]

Answer:

2n + 11

Step-by-step explanation:

You can combine 4n and -2n.

You get 2n + 11

8 0

3 years ago

Ms. Mor ris has 35 tests to grade this weekend. Mrs. Cook has 80% more tests than that to grade this weekend. How many tests doe

Serga [27]

Answer:

Mrs. Cook has to grade 63 tests.

Step-by-step explanation:

In order to find the answer, first you have to calculate 80% of the number of tests Ms. Morris has:

35*80%= 28

Then, you have to add the number that represents 80% to the number of tests Ms. Morris has to grade:

35+28=63

According to this, the answer is that Mrs. Cook has to grade 63 tests.

8 0

3 years ago

Steve kicks a football into the air. The path that a ball takes can be described by the equation h=20t - 5t squared where h is t

FinnZ [79.3K]

Since h represents the height of the ball at any given time, t, let h = 25, such that the ball will be 25m high at t.

Now, we have 25 = 20t - 5t²
5t² - 20t + 25 = 0
t² - 4t + 5 = 0

$\frac{4 +- \sqrt{16 - 20}}{2}$

Since the discriminant is less than zero, there are no solutions.
Hence, the ball will never be 25m high.

4 0

2 years ago