The sum of 3 times a number and -2, added to 5 times the number

Mathematics

1 answer:

givi [52]2 years ago

3 0

Answer:

3x + (5x -2)

Step-by-step explanation:

X is any number so 3 times a number is 3x. -2 plus 5 times a number is the same as 5 times a number minus 2. And the sum would be 3x + (5x - 2)

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Find the x intercepts of the parabola with vertex (-1,-16) and y intercept (0,-15)

Arlecino [84]

first, write the equation of the parabola in the required form: 
(y - k) = a·(x - h)² 

Here, (h, k) is given as (-1, -16). 
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(y + 16) = a · (x + 1)² 

Unfortunately, a is not given. However, you do know one additional point on the parabola: (0, -15): 

-15 + 16 = a· (0 + 1)² 
.·. a = 1 

.·. the equation of the parabola in vertex form is 
y + 16 = (x + 1)² 

The x-intercepts are the values of x that make y = 0. So, let y = 0: 

0 + 16 = (x + 1)² 
16 = (x + 1)² 

We are trying to solve for x, so take the square root of both sides - but be CAREFUL! 

± 4 = x + 1 ...... remember both the positive and negative roots of 16...... 

Solving for x: 
x = -1 + 4, x = -1 - 4 
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Or, if you prefer, (3, 0), (-5, 0).

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3 years ago

Work out the size of one of the exterior angles

hodyreva [135]

Given Information :-

⠀

A polygon with 10 sides ( Decagon )

⠀

To Find :-

⠀

The value of one of the exterior angles

⠀

Formula Used :-

⠀

$\qquad \diamond \: \underline{ \boxed{ \pink{ \sf Exterior ~angle = \dfrac {360^\circ}{no. ~of~sides}}}} \: \star$

⠀

Solution :-

⠀

Putting the given values, we get,

⠀

$\sf \dashrightarrow Exterior ~angle = \dfrac{360 ^\circ}{10} \: \: \\ \\ \\ \sf \dashrightarrow Exterior ~angle = \frac{36 \cancel{0}^\circ}{ \cancel{10}} \: \: \\ \\ \\ \sf \dashrightarrow Exterior ~angle = \underline{ \boxed{ \frak{ \red{36^\circ}}}} \: \star \\ \\$