The value of m ∠ RPS is 64. 7°
<h3>What are collinear angles?</h3>
Collinear angles are angles formed when three or more points lie on the same straight line.
Note that angles on a straight line sum up to 180 degrees.
From the diagram given, we can see that the angles are collinear angles and thus sum up to 180 degrees;
- m ∠QPS = 88°
- m ∠ RPS = 5x + 34°
- m ∠ QPR = 8x + 15°
m ∠QPS + m ∠ RPS + m ∠ QPR = 180°
88° + 5x + 34° + 8x + 15° = 180
collect like terms
5x + 8x = 180 - 137
Add like terms
13x = 43
Make 'x' the subject of formula
x = 43/ 7
x = 6. 14
m ∠ RPS = 5x + 34 = 5 ( 6. 14) + 34 = 30. 7 + 34 = 64. 7°
Thus, the value of m ∠ RPS is 64. 7°
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Kira's time exercising every day can be represented as t ≥ 40 because she exercises for 40 minutes or more.
<h3>How can this situation be represented?</h3>
This situation can be represented with an inequality. An inequality is an expression that is used to represent variables. This type of expression uses symbols such as >, < or ≥ to represent different variable values.
<h3>What inequality is represented in this situation?</h3>
- The expression is: t ≥ 40
The inequality represented in this situation implies that Kira exercises is equal or more time than 40 minutes every day.
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Answer:
- 5x² - 11x + 2
Step-by-step explanation:
(f + g)(x) = f(x) + g(x)
f(x) + g(x)
= - 4x² - 6x - 1 + (- x² - 5x + 3)
= - 4x² - 6x - 1 - x² - 5x + 3 ← collect like terms
= - 5x² - 11x + 2
Answer:
300
Step-by-step explanation:
The area of the rectangle can be calculated as follows
15√ 25^2 - 15^2
= 15√625-225
= 15√400
= 15 × 20
= 300
Hence the area of the rectangle is 300
The length and width of the toolbox given the diagonal is 45 inches and 15 inches respectively.
<h3>Triangle</h3>
- Width of the triangle = w
- Length of the triangle = 3w
- Diagonal = 30 inches
Hypotenuse ² = opposite ² + adjacent ²
30² = w² + (3w²)
30² = 4w²
900 = 4w²
w² = 900/4
= 225
w = √225
w = 15
Therefore,
Width of the triangle = w
= 15 inches
Length of the triangle = 3w
= 3(15)
= 45 inches
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