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Mathematics

1 answer:

mr_godi [17]4 years ago

5 0

Description:

x^2 to mean x squared

f(x) = x^2+3x-10

f(x+5) = (x+5)^2+3(x+5)-10 replace every x with x+5

f(x+5) = (x^2+10x+25)+3(x+5)-10

f(x+5) = x^2+10x+25+3x+15-10

f(x+5) =x^2+13x+30

Compare this with x^2+kx+30 and we see that k = 13

Factor and solve the equation below

x^2+13x+30 = 0

(x+10)(x+3) = 0

x+10 = 0 or x+3 = 0

x = -10 or x = -3

The smallest zero is x = -10 as its the left-most value on a number line

Answer: k = 13The smallest zero or root is x = -10

Please mark brainliest

<em><u>Hope this helps.</u></em>

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Does anybody know how to do question 2 please show working out

Natalija [7]

2a.
Since BC = 10m and M is the midpoint, we can find CM by : 10÷2 = 5m
So, CM = 5m

2b. Now, you have the base ( 5m) & hypotenuse (13m). Pythagoras' Theorem:

$c {}^{2} = {a}^{2} + {b}^{2}$
Where c is the hypotenuse, a & b are sides.

${13}^{2} = {5}^{2} + b {}^{2} \\ {5}^{2} + {b}^{2} = 13 {}^{2} \\ {b}^{2} = 13 {}^{2} - {5}^{2} \\ b = \sqrt{144} \\ b = 12$
b here refers to the height.

2c.
Area of a right-angled triangle =
$\frac{base \times height}{2}$
So,
$\frac{10 \times 12}{2} \\ = 60 {m}^{2}$

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3 years ago

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Use the diagram to complete the statements.

Ksenya-84 [330]

Answer: The answers are: 3, 4, point R to point Q, depression from point Q to point R

Step-by-step explanation:

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3 years ago

1. Using the formula for the probability of one event or another event, calculate the probability of drawing a card from a stand

ddd [48]

A standard deck has 52 cards.
A standard deck has 4 jacks.
A standard deck has 13 clubs.

From this, we can derive the following:
The probability of drawing a jack is 4/52 or 1/13
The probability of drawing a club is 13/52 or 1/4

But since the problem asks for drawing jack or club, therefore we should add the 2 probabilities, making 17/52. This is not the final answer yet. We know that there is a jack of clubs, therefore we need to subtract 1 from the probabilities since jack of clubs were considered in the 2 categories of probability.

With that being said, the probability of drawing a club or a jack is 16/52 or 4/13

Bonus Question:

The first thing you need to do here is find the probability of each scenario. First let's do what is given, the probability of drawing 2 aces. Since there are 4 aces in a deck of 52, we can easily say that the probability of drawing an ace is 4/52. However for our second draw, the probability of drawing a different ace is 3/51. This is so since we already drew a card that is an ace, hence we need to subtract one from the total aces (4-1) and from the total cards in the deck (52-1). In getting the probability of drawing two aces, we need to multiply the said probabilities: 4/52 and 3/51, resulting to 1/221.

For the second scenario, the drawing of 2 red cards, we just use the same concept but in this, we are already considering the 2 red cards in the first scenario, therefore the chance of drawing a red on our first draw is 24/52. For our second, we just need to subtract one card, therefore 23/51. Multiply these two and we will get 46/221.

Now, the problem asks for the chance of drawing either 2 reds or 2 aces, therefore we add the probabilities of the 2 scenarios:
46/222 + 1/221 = 47/221

Summary:
First Scenario:
4/52 + 3/51 = 1/221
Second Scenario:
24/52 + 23/51 = 46/221
Chances of drawing 2 red cards or 2 aces:
1/221 + 46/221 = 47/221

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3 years ago

EXAMPLE 2 Prove that 9ex is equal to the sum of its Maclaurin series. SOLUTION If f(x) = 9ex, then f (n + 1)(x) = for all n. If

amm1812

Answer:

To Prove: $9e^x$ is equal to the sum of its Maclaurin series.