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Hitman42 [59]
3 years ago
7

The sum of the angles of a triangle is 180°. If one angle of a triangle measures x and the second angle measures (5x +19)º

Mathematics
1 answer:
lapo4ka [179]3 years ago
8 0

Answer:

third angle = (-6x + 161)°

Step-by-step explanation:

180° = (x)° + (5x + 19)° + third angle →

180° = (6x + 19)° + third angle →

180° – (6x + 19)° = (6x + 19)° + third angle – (6x + 19)° →

180° – (6x + 19)° = third angle →

180° + -(6x + 19)° = third angle →

180° + (-6x)° + (-19)° = third angle

180° – 6x° – 19° = third angle

(180° – 19°) – 6x° = third angle

161° – 6x° = third angle

third angle = 161 – 6x°

third angle = -6x° + 161°

third angle = (-6x + 161)°

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aleksandrvk [35]

Answer:

4) VW= 23

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Step-by-step explanation:

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VU= 31

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subtract 8 from 31

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UW= 18

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subtract 6 from 18

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Is 9.78083 a rational number
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in a week karry ran 9.3 miles and Tricia ran 4.4 miles. Use mental math to find how much farther Karry ran than Tricia. Explain
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Find the number b such that the line y = b divides the region bounded by the curves y = 36x2 and y = 25 into two regions with eq
Gemiola [76]

Answer:

b = 15.75

Step-by-step explanation:

Lets find the interception points of the curves

36 x² = 25

x² = 25/36 = 0.69444

|x| = √(25/36) = 5/6

thus the interception points are 5/6 and -5/6. By evaluating in 0, we can conclude that the curve y=25 is above the other curve and b should be between 0 and 25 (note that 0 is the smallest value of 36 x²).

The area of the bounded region is given by the integral

\int\limits^{5/6}_{-5/6} {(25-36 \, x^2)} \, dx = (25x - 12 \, x^3)\, |_{x=-5/6}^{x=5/6} = 25*5/6 - 12*(5/6)^3 - (25*(-5/6) - 12*(-5/6)^3) = 250/9

The whole region has an area of 250/9. We need b such as the area of the region below the curve y =b and above y=36x^2 is 125/9. The region would be bounded by the points z and -z, for certain z (this is for the symmetry). Also for the symmetry, this region can be splitted into 2 regions with equal area: between -z and 0, and between 0 and z. The area between 0 and z should be 125/18. Note that 36 z² = b, then z = √b/6.

125/18 = \int\limits^{\sqrt{b}/6}_0 {(b - 36 \, x^2)} \, dx = (bx - 12 \, x^3)\, |_{x = 0}^{x=\sqrt{b}/6} = b^{1.5}/6 - b^{1.5}/18 = b^{1.5}/9

125/18 = b^{1.5}/9

b = (62.5²)^{1/3} = 15.75

8 0
3 years ago
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