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SSSSS [86.1K]
3 years ago
12

Solve x2 + 20x + 100 = 36 for x. Use completing the sqaure

Mathematics
1 answer:
Papessa [141]3 years ago
7 0
X^2+20x+100=36
-subtract 100 and move to other side
x^2+20x____=36-100
-divide 20 by 2 which gives you 10.
-square 10= (10)^2 which gives you 100.
-add the 100 to the right side of the equation.
(x+10)^2 = 36-100+100
(x+10)^2=36
-cancel out the square root and square root 36
(x+10)= 6
-subtract 10
x=-4

*Plug in (-4) into the equation to check your work*
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Whole page for 81! Good luck!
OLEGan [10]

Answer:

Prime number: A prime number has factor of only 1 and itself.

Ex: 3: 1 and 3 are the only ways to compose 3.

A whole number that has factors other than 1 and itself is called a composite number.

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To determine the prime factorization of a number, you must break down a number into its factors. (im not sure?)

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30= 2^1 3^1 5^1

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6 0
3 years ago
The number X of days in the summer months that a construction crew cannot work because of the weather has the probability distri
Ronch [10]

Answer:

a.)The probability of losing no more than ten days next summer is    

    0.65

b.) The probability that 8 - 12 days will be lost next summer  is 0.8

c.)  The probability there will be no days lost next summer is 0.

Step-by-step explanation:

The probability distribution for the number X of days in the summer that a construction crew cannot work because of the weather is given below:

x                    P(x)

6                   0.03

7                   0.08

8                   0.15

9                   0.2

10                  0.19

11                   0.16

12                   0.1

13                   0.07

14                   0.02

a.) To find the probability that no more than 10 days will lost next summer can be found by adding the values of probability of the days lost which are 10 days or less, that is to say we can write

 

p( x ≤ 10 )  = p(x=6) + p(x =7) + p(x=8) + p(x=9) + p(x=10)

                = 0.03     + 0.08    + 0.15     + 0.2     + 0.19

                = 0.65

b.) To find the probability that 8 to 12 days will be lost next summer will be given by taking into account and adding the probabilities starting form the probability when 8 days are lost to the probability when 12 days are lost

   p( 8 ≤ x ≤ 12)  = p(x=8) + p(x=9) + p(x=10) + p(x=11) + p(x=12)

                          = 0.15 +    0.2     + 0.19    +   0.16  + 0.1

                          = 0.8

c.) The probability that no days will be lost next summer will be given by

    = 1 - ( p(x=6) + p(x=7) +  p(x=8) + p(x=9) + p(10) + p(11) + p(12))

    = 1 -  1

    = 0  

   The probability that will be no days lost next summer is zero. We can conclude that there will be some days lost next summer.

4 0
3 years ago
What is the correct name for the angle shown
Vesna [10]

Answer:

i dont see no angle

Step-by-step explanation:

4 0
3 years ago
Which operations is the following set closed under: {... , -3, -1, 1, 3, ...}?
Ganezh [65]
Not addition, since -1+1=0 and 0 doesn't belong to the set.

Not subtraction, since 1-1=0.

It is closed under multiplication. The set appears to contain all non-zero multiples of 3.

Not division, since dividing some of the numbers results in rationals which do not belong to the set.

What other operations are you supposed to consider?
5 0
3 years ago
Read 2 more answers
Can you help me with my homework
goldfiish [28.3K]

Answer:

4. Option C (3a+2) inches

5. Extraneous solution x=-5/6 because we get for width and length negative values.

Solution: Value of x is 3

Length of the box: 5 ft

Width of the box: 4 ft

Step-by-step explanation:

4. Area of a rectangle: A=12a^2-a-6 square inches

Width: w=4a-3

Length: l=?

A=w l

Replacing A by 12a^2-a-6 and w by 4a-3

12a^2-a-6 = (4a-3) l

Solving for l: Dividing both sides of the equation by 4a-3:

(12a^2-a-6) / (4a-3) = (4a-3) l / (4a-3)

Simplifying:

(12a^2-a-6) / (4a-3) = l

l = (12a^2-a-6) / (4a-3)

Factoring the numerator:

12a^2-a-6 = (4a-3)(3a+2)

Let's check it:

(4a-3)(3a+2)=4a(3a)+4a(2)-3(3a)-3(2)=12a^2+8a-9a-6→(4a-3)(3a+2)=12a^2-a-6

Replacing the numerator:

l = (4a-3)(3a+2) / (4a-3)

Simplifying:

l = (3a+2) inches


5. Length: l=(3x-5) ft

Width: w=(2x-1) ft

Height: h=2 ft

Volumen of the box: V=40 ft^3

x=?

Length: l=?

Width: w=?

V = l w h

Replacing the given:

40 ft^3 = (3x-5) ft (2x-1) ft 2 ft

40 ft^3 = 2 (3x-5)(2x-1) ft^3

40=2(3x-5)(2x-1)

Dividing both sides of the equation by 2:

40/2=2(3x-5)(2x-1)/2

Simplifying:

20=(3x-5)(2x-1)

Eliminating the parentheses on the right side of the equation applying the distributive property:

20=3x(2x)+3x(-1)-5(2x)-5(-1)

20=6x^2-3x-10x+5

Adding like terms:

20=6x^2-13x+5

Equaling to zero: Subtracting 20 from both sides of the equation:

20-20=6x^2-13x+5-20

0=6x^2-13x-15

6x^2-13x-15=0

ax^2+bx+c=0; a=6, b=-13, c=-15

Using the quadratic formula:

x=[-b+-sqrt(b^2-4ac)]/(2a)

x=[-(-13)+-sqrt((-13)^2-4(6)(-15))]/(2(6))

x=[13+-sqrt(169+360)]/12

x=[13+-sqrt(529)]/12

x=[13+-23]/12

x1=(13-23)/12=(-10)/12=-10/12=-(10/2)/(12/2)→x1=-5/6

x2=(13+23)/12=36/12→x2=3


With x=-5/6

l=(3x-5) ft

l=(3(-5/6)-5) ft

l=(-5/2-5) ft

l=-(5/2+5) ft

l=-(5+2(5))/2 ft

l=-(5+10)/2 ft

l=-15/2 ft < 0. The length cannot be a negative number then x=-5/6 is a extraneous solution.

w=(2x-1) ft

w=(2(-5/6)-1) ft

w=(-5/3-1) ft

w=-(5/3+1) ft

w=-(5+3(1))/3 ft

w=-(5+3)/3 ft

w=-8/3 ft <0. The width cannot be a negative number then x=-5/6 is a extraneous solution.


With x=3

l=(3x-5) ft

l=(3(3)-5) ft

l=(9-5) ft

l=4 ft

w=(2x-1) ft

w=(2(3)-1) ft

w=(6-1) ft

w=5 ft

and h=2 ft

Let's check the volume

V= w l h

V=(5 ft)(4 ft)(2 ft)

V=40 ft^3 Correct

7 0
3 years ago
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