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3 years ago

The difference of two supplemtary angles is 58 degrees. Find the measures of the angles

Mathematics

1 answer:

erik [133]3 years ago

4 0

Answer:

The measure of the angles are 61° and 119°

Step-by-step explanation:

Let the first angle = x°

let the second angle = y°

The sum of two supplementary angles = 180°

x° + y° = 180° ----- equation (1)

based on the given question; "the difference of two supplementary angles is 58 degrees."

x° - y° = 58° ------- equation (2)

from equation (2), x° = 58° + y°

Substitute the value of x into equation (1)

(58° + y°) + y° = 180°

58 + 2y = 180

2y = 180 -58

2y = 122

y = 122 / 2

y = 61°

The second angle is given by;

x° = 58° + y°

x = 58° + 61°

x = 119°

Thus, the measure of the angles are 61° and 119°

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1. Find the vertex of the following: y = (x - 4)(x - 10) *

horsena [70]

Answer:

1. (7,-9)

2. (4,0) and (10,0)

3. (3,0) and (-3,0)

4. (0,-9)

5. (-1,-32)

Step-by-step explanation:

To find the vertex use the formula

$\frac{-b}{2a}$

First make the equation into a quadratic equation.

$(x-4)(x-10)\\x^{2} -10x-4x+40\\x^{2} -14x+40$

Now it is in the form

$ax^{2} +bx+c=0$

Now we can substitute the values

$\frac{-(-14)}{2(1)} \\\frac{14}{2} \\7$

Now we have 7 as our x value for the vertex we can substitute for y,

$x^{2} -14x+40=y\\(7)^{2} -14(7)+40=y\\49-98+4=y\\y=-9$

So the vertex for 1 is (7,-9)

To find the intercepts for 2 & 3, they basically already give it to you. You just need to find a value for x for x-4 that will equal it to 0 and another for x for x-10 that will equal it to 0.

$x-4=0\\x=4\\\\x-10=0\\x=10$

4 is slightly different but start the same,

$(x-3)(x+3)\\x^{2}+3x-3x-9\\x^{2}-9$

Here, c (9) just shows the graph move down 9, so the y intercept = 9.

5 is the same process as 1,

$2(x-3)(x+5)\\2(x^{2}+5x-3x-15)\\2(x^{2}+2x-15)\\2x^{2}+4x-30$

Vertex,

$\frac{-(4)}{2(2)} \\\frac{-4}{4} \\-1$

Substitute,

$2x^{2}+4x-30\\2(-1)^{2}+4(-1)-30\\2-4-30\\-32$

So the vertex is (-1,-32)

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OverLord2011 [107]

5x + 10 10
---------- = -------
121 11

make the bottom have same common denominator

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