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3 years ago

PLEASE HELP MEEEEEEEEDetermine the internal and external angles of the triangle below

Mathematics

1 answer:

zloy xaker [14]3 years ago

6 0

Answer:

The internal angles are 78°, 72°, 30°, and the external angle is 150°

Step-by-step explanation:

In a triangle, the measure of an external angle at one vertex equals the sum of the measures of the opposite internal angles to this vertex

In the given figure

∵ The angle of measure (4x + 22) is an exterior angle

∵ The angles of measures (3x - 18) and (2x + 8) are the opposite

interior angles

→ By using the rule above

∴ (3x - 18) + (2x + 8) = (4x + 22)

→ Add the like terms in the left side

∵ (3x + 2x) + (-18 + 8) = 4x + 22

∴ 5x + (-10) = 4x + 22

→ Remember (+)(-) = (-)

∴ 5x - 10 = 4x + 22

→ Add 10 to both sides

∵ 5x - 10 + 10 = 4x + 22 + 10

∴ 5x = 4x + 32

→ Subtract 4x from both sides

∵ 5x - 4x = 4x - 4x + 32

∴ x = 32

→ Substitute the value of x in the external and internal angles to find them

∵ The external angle = 4(32) + 22 = 128 + 22

∴ The external angle = 150°

∵ One of the internal angle = 3(32) - 18 = 96 - 18

∴ One of the internal angle = 78°

∵ Other internal angle = 2(32) + 8 = 64 + 8

∴ Other internal angle = 72°

→ The sum of the measure of the internal angles of a Δ is 180°

∵ The third internal angle of the triangle = 180° - 78° - 72°

∴ The third internal angle of the triangle = 30°

∴ The internal angles are 78°, 72°, 30°, and the external angle is 150°

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Step-by-step explanation:

11x^2 is a monomial because it contains one term.

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3 years ago

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The measure of angle 1 is (3x + 10)° and the measure of angle 4 is (4x – 15)°. Vertical and parallel lines c, d, and e are cut b

Nikitich [7]

Answer:

95 degrees

Step-by-step explanation:

since angles 1 and 4 are vertical angles, they are congruent

3x+10=4x-15

3x-4x=-15-10

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x=25

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angles 4 and 7 are supplementary due to them being alternate exterior angles

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Now, lets find the angle measure of angle 7:

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So, the angle measure of angle 7 is 95 degrees

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3 years ago

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Find f(a), f(a+h), and 71. f(x) = 7x - 3 f(a+h)-f(a) h if h = 0. 72. f(x) = 5x²

Leni [432]

Answer:

$71. \ \ \ f(a) \ = \ 7a \ - \ 3; \ f(a+h) \ = \ 7a \ + \ 7h \ - \ 3; \ \displaystyle\frac{f(a+h) \ - \ f(a)}{h} \ = \ 7$

$72. \ \ \ f(a) \ = \ 5a^{2}; \ f(a+h) \ = \ {5a}^{2} \ + \ 10ah \ + \ {5h}^{2}; \ \displaystyle\frac{f(a+h) \ - \ f(a)}{h} \ = \ 10a \ + \ 5h$

Step-by-step explanation:

In single-variable calculus, the difference quotient is the expression

$\displaystyle\frac{f(x+h) \ - \ f(x)}{h}$ ,

which its name comes from the fact that it is the quotient of the difference of the evaluated values of the function by the difference of its corresponding input values (as shown in the figure below).

This expression looks similar to the method of evaluating the slope of a line. Indeed, the difference quotient provides the slope of a secant line (in blue) that passes through two coordinate points on a curve.

$m \ \ = \ \ \displaystyle\frac{\Delta y}{\Delta x} \ \ = \ \ \displaystyle\frac{rise}{run}$ .

Similarly, the difference quotient is a measure of the average rate of change of the function over an interval. When the limit of the difference quotient is taken as h approaches 0 gives the instantaneous rate of change (rate of change in an instant) or the derivative of the function.

Therefore,

$71. \ \ \ \ \ \displaystyle\frac{f(a \ + \ h) \ - \ f(a)}{h} \ \ = \ \ \displaystyle\frac{(7a \ + \ 7h \ - \ 3) \ - \ (7a \ - \ 3)}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{7h}{h} \\ \\ \-\hspace{4.25cm} = \ \ 7$

$72. \ \ \ \ \ \displaystyle\frac{f(a \ + \ h) \ - \ f(a)}{h} \ \ = \ \ \displaystyle\frac{{5(a \ + \ h)}^{2} \ - \ {5(a)}^{2}}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{{5a}^{2} \ + \ 10ah \ + \ {5h}^{2} \ - \ {5a}^{2}}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{h(10a \ + \ 5h)}{h} \\ \\ \-\hspace{4.25cm} = \ \ 10a \ + \ 5h$

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2 years ago

1. What is a perfect square? 2. What is the square root of 4x²? 3. What is the square root of 25? 4. Factor 4x² + 20x + 25.

Ulleksa [173]

Answer:

Step-by-step explanation:

1) A perfect square is a whole number which is a product of a smaller whole number and itself. Examples of perfect squares are

4(2 × 2)

9(3 × 3)

16(4 × 4)

25(5 × 5)

36(6 × 6)

2) Square root of 4x² is 2x(product of square root of 4 and square root of x²)

3) square of 25 is 5

4) 4x² + 20x + 25

The general formula for solving quadratic equations is expressed as

x = [- b ± √(b² - 4ac)]/2a

From the equation given,

a = 4

b = 20

c = 25

Therefore,

x = [- 20 ± √(20² - 4 × 4 × 25)]/2 × 4

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x = [- 20 ± 0]/8

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3 0

3 years ago

Could anyone help me? this is hard i dont understand

emmainna [20.7K]

Answer:

can you please give me an example?

i will help you but give me your teacher's example

Step-by-step explanation:

let me know if it's done

3 0

2 years ago

PLEASE HELP MEEEEEEEEDetermine the internal and external angles of the triangle below​

PLEASE HELP MEEEEEEEEDetermine the internal and external angles of the triangle below