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3 years ago

The x intercepts of the graph of f(x)= x(x+1)(x-5)(x-7) are {0 or 1}, {-1 or 1}, {5 or -5} & {7 or -7}?

1 answer:

7 0

X-intercepts if f(x) = 0
f(x) = x(x + 1)(x - 5)(x - 7)
f(x) = 0 if x = 0 or x +1 = 0 or x - 5 = 0 or x - 7 =0
Answer: {-1 or 0 or 5 or 7}

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Use completing the square to solve the equation x2 - 10x = -8.

Alenkasestr [34]

A. X^2-10x. =-8
To complete the square you get half of -10 and then square that number half of -10 is -5 and -5 times -5 equals positive 25 that would you add to each side

x^2-10x+25=-8+25
17

6 0

3 years ago

Read 2 more answers

Se tiene un rectángulo cuya base mide el doble que su altura y su área es 12

irina [24]

Answer:

Part 1) The perimeter is $P=6\sqrt{6}\ cm$

Part 2) The diagonal is $d=\sqrt{30}\ cm$

Step-by-step explanation:

The question in English is

You have a rectangle whose base is twice the height and its area is 12

square centimeters. Calculate the perimeter of the rectangle and its diagonal

step 1

Find the dimensions of rectangle

we know that

The area of rectangle is equal to

$A=bh$

$A=12\ cm^2$

$bh=12$ ----> equation A

The base is twice the height

$b=2h$ ----> equation B

substitute equation B in equation A

$(2h)h=12\\2h^2=12\\h^2=6\\h=\sqrt{6}\ cm$

Find the value of b

$b=2\sqrt{6}\ cm$

step 2

Find the perimeter of rectangle

The perimeter is given by

$P=2(b+h)$

substitute

$P=2(2\sqrt{6}+\sqrt{6})\\P=6\sqrt{6}\ cm$

step 3

Find the diagonal of rectangle

Applying the Pythagorean Theorem

$d^2=b^2+h^2$

substitute

$d^2=(2\sqrt{6})^2+(\sqrt{6})^2$

$d^2=30$

$d=\sqrt{30}\ cm$

3 0

3 years ago

A cooler has 12 apple juices and 15 grape juices. 9 of the apple juices are sugar free and 5 of the grape juices are sugar free.

Romashka-Z-Leto [24]

Answer:

The probability that it is grape juice, given that the juice is not sugar free is 0.769 or 76.9%

Step-by-step explanation:

$P(\text{Grape }|\text{ Not sugar free})=\dfrac{P(\text{Grape }\cap \text{ Not sugar free})}{P(\text{Not sugar free})}$

A cooler has 12 apple juices and 15 grape juices. So total 27 juices are there.

Out of 12 apple juices, 9 of the apple juices are sugar free, so 3 are not sugar free.

Out of 15 grape juices, 5 of the grape juices are sugar free, so 10 are not sugar free. So,

$P(\text{Grape }\cap \text{ Not sugar free})=\dfrac{10}{27}$

$P(\text{Not sugar free})=\dfrac{10+3}{27}=\dfrac{13}{27}$

Putting the values,

$P(\text{Grape }|\text{ Not sugar free})=\dfrac{P(\text{Grape }\cap \text{ Not sugar free})}{P(\text{Not sugar free})}=\dfrac{\frac{10}{27}}{\frac{13}{27}}=\dfrac{10}{13}=0.769$

5 0

3 years ago

Read 2 more answers

Plastic parts produced by an injection-molding operation are checked for conformance to specifications. Each tool contains 12 ca

Ksju [112]

Answer:

a) 45 possible outcomes

b) 55 possible outcomes

Step-by-step explanation:

Given:

- Total cavities = 12

- Selection = 3 parts

- Non-conforming cavities = 2

Find:

a) How many samples contain exactly 1 nonconforming part?

b) How many samples contain at least 1 nonconforming part?

Solution:

- The question asks for the use of combinations to express the outcomes for each scenario.

- For first part, we want the inspector to pick exactly one non-conforming part among 3 selected. So let us say that he has already chosen that one non conforming cavity. Now he has to make 2 more selections out of total conforming cavities = 12 - 2 = 10 conforming cavities. Hence, the total possible outcome is to chose 2 randomly from 10 conforming cavities.

( Exactly 1 ) 10C2 = 45 possible outcomes

- The second part entails that at-least 1 non-conforming cavity is selected. To choose exactly 1 non conforming we calculated above. In the similar way calculate for selecting exactly 2 non-conforming cavities. The total possible outcome would be to choose from 10 conforming and we choose 1 from it:

( Exactly 2 ) 10C1 = 10 possible outcomes

- Hence, for at-least 1 non conforming cavity being selected we same the above two cases calculated:

(At-least 1 ) = ( Exactly 1 ) + ( Exactly 2 )

(At-least 1 ) = 45 + 10 = 55 possible outcomes

4 0

3 years ago

Help me please don't know

dem82 [27]

1. 5 x 5
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3 years ago