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1 year ago

Solve for x in the equation x^2+10x+12=36

Mathematics

2 answers:

yulyashka [42]1 year ago

5 0

Answer: The required value of x is 2 or -12.

Step-by-step explanation: We are given to solve for x in the following equation :

$x^2+10x+12=36~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be solving the given equation by the method of factorization.

From equation (i), we have

$x^2+10x+12=36\\\\\Rightarrow x^2+10x+12-36=0\\\\\Rightarrow x^2+10x-24=0\\\\\Rightarrow x^2+12x-2x-24=0\\\\\Rightarrow x(x+12)-2(x+12)=0\\\\\Rightarrow (x-2)(x+12)=0\\\\\Rightarrow x-2=0,~~~~~~x+12=0\\\\\Rightarrow x=2,~-12.$

Thus, the required value of x is 2 or -12.

Elan Coil [88]1 year ago

4 0

I am going to put the all math work for the answer of this question, but if you need an explanation for how i got each step let me know and i will provide that for you
x^2 +10x + 12 = 36
x^2 + 10x + 12 - 36 = 0
x^2 +12x - 2x - 24 = 0
x(x + 12) - 2(x +12) = 0
(x + 12) x (x - 2) = 0
x + 12 = 0
x - 2 = 0
x = -12
x = 2
your answer for the first x is x = -12, and your answer for the second x will be
x = 2
let me know if you have any further questions
:)

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Josh travels frequently. For a particular airline, it takes 20 minutes for the first bag to arrive in baggage claim after a flig

Orlov [11]

Using the uniform distribution, it is found that:

A,B) 0.3 of the time does it take longer than 27 minutes for Josh’s bag to arrive in baggage claim.

C) 20% of the time does Josh’s bag arrive in less than 22 minutes.

--------------------------

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

$P(X < x) = \frac{x - a}{b - a}$

The probability of finding a value between c and d is:

$P(c \leq X \leq d) = \frac{d - c}{b - a}$

The probability of finding a value above x is:

$P(X > x) = \frac{b - x}{b - a}$

--------------------------

In the graph, we have that the distribution is uniform between 20 and 30 minutes, thus $a = 20, b = 30$

--------------------------

Itens a and b:

Above 27 minutes, thus:

$P(X > 27) = \frac{30 - 27}{30 - 20} = 0.3$

0.3 of the time does it take longer than 27 minutes for Josh’s bag to arrive in baggage claim.

--------------------------

Item c:

Less than 22 minutes, thus:

$P(X < 2) = \frac{22 - 20}{30 - 20} = 0.2$

0.2*100 = 20%

20% of the time does Josh’s bag arrive in less than 22 minutes.

A similar problem is given at brainly.com/question/15855314

6 0

1 year ago

A. The average yearly salary of a lawyer is $24 thousand less than twice that of an architect.

erastovalidia [21]

Answer:

The average yearly salary of the architect is $62,000 and the lawyer is $100,000.

Step-by-step explanation:

Given:

The average yearly salary of a lawyer is $24 thousand less than twice that of an architect.

Combined, an architect and a lawyer earn $ 210 thousand.

Now, to find the average yearly salary of an architect and a lawyer.

Let the average yearly salary of an architect be $x.$

So, the average yearly salary of the lawyer = $2x-24,000.$

Combined, architect and lawyer earn = $\$210,000.$

Now, to get the average salary of the architect and lawyer:

$x+(2x-24000)=210000$

$x+2x-24000=210000\\\\3x-24000=210000$

Adding both sides 24000 we get:

$3x=186,000\\\\Dividing\ both\ sides\ by\ 3\ we\ get:\\\\x=62000.$

The average salary of architect = $62,000.

Now, to get the average salary of lawyer by substituting the value of $x$ :

$2x-24000\\\\=2(62000)-24000\\\\=124000-24000\\\\=\$100,000.$

The average salary of lawyer = $100,000.

Therefore, the average yearly salary of the architect is $62,000 and the lawyer is $100,000.

4 0

2 years ago

Manuela solved the equation 3−2|0.5x+1.5|=2 for one solution. Her work is shown below. 3−2|0.5x+1.5|=2 −2|0.5x+1.5|=−1 |0.5x+1.5

lions [1.4K]

Answer:

Step-by-step explanation:

We'll just work on solving both so you can see what's involved in solving an absolute value equation. Because an absolute value is a distance, we can have that distance being both to the right on the number line of the number in question or to the left. For example, from 2 on the number line, the numbers that are 5 units away are 7 and -3. Using that logic, we will simplify the equation down so we can set up the 2 basic equations needed to solve for x.

If $3-2|.5x+1.5|=2$ then

$-2|.5x+1.5|=-1$ What you need to remember here is that you cannot distribute into a set of absolute values like you would a set of parenthesis. The -2 needs to be divided away:

$|.5x+1.5|=.5$

Now we can set up the 2 main equations for this which are

.5x + 1.5 = .5 and .5x + 1.5 = -.5

Knowing that an absolute value will never equal a negative number (because absolute values are distances and distances will NEVER be negative), once we remove the absolute value signs we can in fact state that the expression on the left can be equal to a negative number on the right, like in the second equation above.

Solving the first one:

.5x = -1 so

x = -2

Solving the second one:

.5x = -2 so

x = -4

7 0

2 years ago

Read 2 more answers

Maria has a cube-shaped box that measures 9 inches along each edge. Can she fit 1,000 1-cubic-inch cubes inside the box?

morpeh [17]

Answer:

Step-by-step explanation:

She would be able to fit 729 cubes but not 1000.

3 0

1 year ago

Choose the option that best completes the statement below. In finding the number of permutations for a given number of items, __

vodomira [7]

Let’s look at the permutations of the letters “ABC.” We can write the letters in any of the following ways:
ABC
ACB
BAC
BCA
CBA
CAB
Since there are 3 choices for the first spot, two for the next and 1 for the last we end up with (3)(2)(1) = 6 permutations. Using the symbolism of permutations we have: $3 P_{3}=(3)(2)(1)=6$ . Note that the first 3 should also be small and low like the second one but I couldn’t get that to look right.

Now let’s see how this changes if the letters are AAB. Since the two As are identical, we end up with fewer permutations.
AAB
ABA
BAA
To make the point a bit better let’s think of one A are regular and one as bold A.
ABA and ABA look different now because we used bold for one of the As but if we don’t do this we see that these are actual the same. If they represented a word they would be the same exact word.

So in this case the formula would be $\frac{3 P_{3} }{2!}= \frac{(3)(2)(1)}{(2)(1)}= \frac{6}{2}=3$ . We use 2! In the denominator because there are 2 repeating letters. If there were three we would use 3!

Hopefully, this is enough to let you see that the answer is A. The number of permutations is limited by the number of items that are identical.

7 0

2 years ago