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2 years ago

Solve the following quadratic by completing the square.

Mathematics

1 answer:

lianna [129]2 years ago

4 0

Answer:

$x = -5 \pm \sqrt{26}$

Step-by-step explanation:

$x^2+10x-1=0\\\\\implies x^2+2\cdot 5 x +5^2-5^2-1=0\\\\\implies (x+5)^2-25-1=0\\\\\implies (x+5)^2 -26=0\\\\\implies (x+5)^2 = 26\\\\\implies x +5 = \pm\sqrt{26}\\\\\implies x = -5 \pm \sqrt{26}$

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There are 12 students in a classroom, including the triplets Joey, Chloe, and Zoe. If 3 of the 12 are randomly selected to give

lesya692 [45]

we know that

The probability of an event is the ratio of the size of the event space to the size of the sample space.

The size of the sample space is the total number of possible outcomes

The event space is the number of outcomes in the event you are interested in.

P=size of the event space/size of the sample space

step 1

find the probability that Joey will be first

size of the sample size=12

size of the event space=1

P=1/12

step 2

find the probability that Chloe will be second

size of the sample size=12-1=11

size of the event space=1

P=1/11

step 3

find the probability that Zoe will be third

size of the sample size=11-1=10

size of the event space=1

P=1/10

step 4

Find the probability that Joey will be first, Chloe will be second, and Zoe will be third

P=(1/12)*(1/11)*(1/10)-----> P=1/1320-----> 0.00075------> 0.076%

the answer is

the probability that Joey will be first, Chloe will be second, and Zoe will be third is 0.00075 (0.076%)

4 0

3 years ago

The graph shows a fir tree's diameter growth over a 50 year period.

Brilliant_brown [7]

Answer:

The answer is B.) The diameter of the fir tree when planted and 20 inches

Step-by-step explanation:

The y-intercept is the initial diameter of the fir tree (10 inches). At the end of 50 years, the tree's diameter is 30 inches. Therefore, 30 − 10 = 20 inches of growth occurred over the 50 year period. The diameter of the fir tree when planted. The fir tree's diameter was 10 inches when it was planted.

6 0

3 years ago

Yea thank for the answer

kolbaska11 [484]

Answer:

Step-by-step explanation:

Hello!

10*17 = > 170 cm²

(3,14 * 8)/4 =>6,28cm²

170 + 6,28 => 176,28cm²

4 0

2 years ago

Read 2 more answers

Average Inventory The Yasuko Okada Fragrance Company (YOFC) receives a shipment of 400 cases of specialty perfume early Monday m

Ksenya-84 [330]

Answer:

Step-by-step explanation:

At the end of any given business day, CFFC has 400-80t cases of perfume on hand, where t = 1 represents Monday, t = 2 represents Tuesday and so on. The inventory becomes nil on Friday evening. So,

The values of a and b are

a = 0

b = 5

Using the formular for average value, we have the average value as

$\frac{1}{5-0}\int\limits^5_0 {(400-80t)}dt\\\\=\frac{1}{5}(400t-\frac{80t^2}{2})\limits^5_0\\\\=\frac{1}{5}(400t-40t^2)\limits^5_0\\\\=\frac{1}{5}(2000-1000)\\\\=200$

Average inventory is 200 cases

8 0

3 years ago

On top of a hill, a rocket is launched from a distance 80 feet above a lake. The rocket will fall into the lake after its engine

Free_Kalibri [48]

The maximum height is 144 feet.

The maximum height is the y-coordinate of the vertex. To find the vertex, we first use x = -b/2a. For our information, that is x=-64/2(-16) = -64/-32 = 2.

Now we substitute this into the equation:
y = -16(2²) + 64(2) + 80 = -64 + 128 + 80 = 144

3 0

3 years ago