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3 years ago

The measure of an obtuse angle is given as (3x-42). What inequality describes all the possible values if x for the angel

Mathematics

1 answer:

Masteriza [31]3 years ago

8 0

Answer: x > 74

Step-by-step explanation:

An obtuse angle is greater than 180°. So, 3x - 42 must be greater than 180.

3x - 42 > 180
+42 +42
3x > 222
÷3 ÷3
x > 74

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You draw 4 cards from a deck of 52 cards with replacement. What are the probabilities of drawing a black card on each of your fo

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Solution:

As, in a pack of cards, there are 26 black cards and 26 red cards.

Probability of an event = $\frac{\text{total favorable outcome}}{\text{total possible outcome}}$

Probability of drawing a black card from a pack of 52 cards = $\frac{26}{52}=\frac{1}{2}$

As each card drawn is replaced,Each black card draw is an independent with another black card draw.

Probabilities of drawing a black card on each of four trial=

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3 years ago

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A pile of 15 boxes is 3 metres high. What is the depth of each box?

Vikentia [17]

200mm is the right answer

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3 years ago

What is the solution set of the equation 6x^2 - 18x - 18 =6?

dybincka [34]

Answer:

The solution set is {4, -1}

Step-by-step explanation:

6x²- 18x -18 = 6

6x²- 18x -18 - 6 = 0

6x²- 18x -24 = 0

6(x² - 3x - 4) = 0

6(x - 4)(x + 1) = 0

6 = 0 not true

x - 4 = 0 ; x + 1 = 0

x = 4 x = - 1

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3 years ago

A road map has a scale of 1:20000 on the map a road has a length of 4cm work out the actual distance five your answer in metre

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4 years ago

Circle P is described by the equation (x−1)2+(y+6)2=9 and circle Q is described by the equation (x+4)2+(y+14)2=4. Select from th

xeze [42]

Answer:

(a) Circle Q is 9.4 units to the center of circle P

(b) Circle Q has a smaller radius

Step-by-step explanation:

Given

$P:(x - 1)^2 + (y + 6)^2 = 9$

$Q:(x + 4)^2 + (y + 14)^2 = 4$

Solving (a): The distance between both

The equation of a circle is:

$(x - h)^2 + (y - k)^2 = r^2$

Where

$Center: (h,k)$

$Radius:r$

P and Q can be rewritten as:

$P:(x - 1)^2 + (y + 6)^2 = 3^2$

$Q:(x + 4)^2 + (y + 14)^2 = 2^2$

So, for P:

$Center = (1,-6)$

$r = 3$

For Q:

$Center = (-4,-14)$

$r = 2$

The distance between them is:

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2$

Where:

$Center = (1,-6)$ --- $(x_1,y_1)$

$Center = (-4,-14)$ --- $(x_2,y_2)$

So:

$d = \sqrt{(1 - -4)^2 + (-6 - -14)^2$

$d = \sqrt{(5)^2 + (8)^2$

$d = \sqrt{25 + 64$

$d = \sqrt{89$

$d = 9.4$

Solving (b): The radius;

In (a), we have:

$r = 3$ --- circle P

$r = 2$ --- circle Q

By comparison

$2 < 3$

Hence, circle Q has a smaller radius

4 0

3 years ago