Solving by Completing the Square

Answer:

nos   agoi o se

Step-by-step explanation:

Answer:

[tex]\boxed{\bold{\huge{\boxed{x = 10}}}}[/tex]

Step-by-step explanation:

=> [tex]\sf \frac{3}{4} x + \frac{5}{6} = 5x - \frac{125}{3}[/tex]

Combining like terms

=> [tex]\sf \frac{3x}{4} - 5x = -\frac{125}{3} - \frac{5}{6}[/tex]

Taking LCM to make the denominator same

=> [tex]\sf \large{\frac{3x-20x}{4} = \frac{-250-5}{6} }[/tex]

=> [tex]\sf \frac{-17x }{4} = \frac{-255}{6}[/tex]

=> [tex]\sf \frac{17x }{4} = \frac{255}{6}[/tex]

Cross Multiplying

=> [tex]\sf 17x * 6 = 4 * 255[/tex]

=> [tex]\sf 102x = 1020[/tex]

Dividing both sides by 102

=> x = 10

Answer:

Y=- 6

3(y-5)+2=5

multiply

3y-15+2=5

add

3y-13=5

add pos 13 to the neg 13 to

cancel it out and add +13 to 5

3y=18

divide -3 to pos 3 and 18 to cancel it out

y= -6

(h + k)(2) = 5

(h - k)(3) = 9

evaluate 3h(2) + 2k(3) = 17

The composition of functions is solved

a) ( h + k ) ( 2 ) = 5

b) ( h - k ) ( 3 ) = 9

c) 3h ( 2 ) + 2k ( 3 ) = 17

Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

Given data ,

Let the first function be represented as f ( x )

Now , the value of f ( x ) is

h ( x ) = x² + 1

Let the second function be represented as g ( x )

Now , the value of g ( x ) is

k ( x ) = x - 2

Now , the composition of function is

To calculate (h+k)(2), we substitute x = 2 in both h(x) and k(x), add them together and simplify:

h(2) = 2² + 1 = 5

k(2) = 2 - 2 = 0

(h+k)(2) = h(2) + k(2) = 5 + 0 = 5

To calculate (h-k)(3), we substitute x = 3 in both h(x) and k(x), subtract k(x) from h(x), and simplify:

h(3) = 3² + 1 = 10

k(3) = 3 - 2 = 1

(h-k)(3) = h(3) - k(3) = 10 - 1 = 9

To evaluate 3h(2)+2k(3), we substitute x = 2 and x = 3 in h(x) and k(x), respectively, and simplify:

3h(2) + 2k(3) = 3(5) + 2(3-2) = 15 + 2 = 17

Therefore , ( h + k ) ( 2 ) = 5 , ( h - k ) ( 3 ) = 9, and 3h( 2 ) + 2k( 3 ) = 17

Hence , the composition of functions is solved

To learn more about composition of functions click :

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Answer:

The sideways E is used for indcating that a point, object, or number belongs to a certian set.

Step-by-step explanation:

Answer:

Total length of shoes in feet = 2 feet

Length of each shoe = 1 feet

Step-by-step explanation:

Given:

Length of each shoe = 12 inches

Find:

Total length of shoes in feet

Computation:

Total length of shoes = [12 + 12] inches

Total length of shoes = 24 inches

12 inches = 1 feet

Total length of shoes in feet = 24 / 12

Total length of shoes in feet = 2 feet

Length of each shoe = 1 feet

Answer:

-3/2

Step-by-step explanation:

You are going a distance of 3/2 to the right, to get 3/2. You are going the same distance of 3/2 to the left, to get -3/2. Same distance traveled on a number line, just in different directions making it positive/negative.

Answer:

The answer is 3

Step-by-step explanation:

Answer:

mZCAD=310°

Step-by-step explanation:

M2BAC=1,m2DAE=3 and m-BAE=0 therefore solution will be 310°

Answer

about 15 min to 1 hour

Answer:

50

Step-by-step explanation:

When parethesis are next to each other than you need to multiply them.

- times - is positive so -5*--10 would be 50.

Answer:

two raised to the power of -3

Two to the power of negative 3

Step-by-step explanation:

[tex]2^-^3 = \frac{1}{2^3}[/tex]

1 divided by 2 to the power of 3

Answer:

115°

Step-by-step explanation:

Measure of the degree of the angle represented by section B on the chart = percentage in the pie chart ÷ 100 × 360. A full circle makes 360°.

Section B represents 32% of the pie chart, therefore, number of degrees for section B = [tex] \frac{32}{100}*360 = \frac{32*360}{100} [/tex]

[tex] = 115.2 [/tex]

Section B = 115° (to the nearest whole number)

Answer:

x = 17/15 or 1 2/15

Step-by-step explanation:

I got it directly from Khan

Answer:

<8 and <6 are congruent to each other.

Step-by-step explanation:

A protractor was used to determine the answer.  They both measured to 140 degrees.  

Answer:

12.5in.

x=.5t+11

Step-by-step explanation:

First of all, create the equation so you can solve both questions at once. We know that Sydney had eleven inches of snow on her lawn, and it doesn't dissapear, so it starts with x=11. Then every hour she gets .5 inches per hour, and the amount of hours is t, so that will translate to .5t. that makes the equation x=.5t+11. To find out how much she would have in three hours, substitute 3 for t, which which goes like this: x=.5(3)+11

x=1.5+11

x=12.5

Answer:

Snow after 3 hours: 12.5

Snow after t hours: 11+0.5t

Answer:

[tex]x = 1.28[/tex]

Step-by-step explanation:

Given

[tex]95 = 35^x[/tex]

Required

Solve for x

[tex]95 = 35^x[/tex]

Take Log of both sides

[tex]Log95 = Log35^x[/tex]

Apply law of logarithm

[tex]Log95 = xLog35[/tex]

Divide both sides by Log35

[tex]x = \frac{Log95}{Log35}[/tex]

[tex]x = \frac{1.97772360529}{1.54406804435}[/tex]

[tex]x = 1.28085262338[/tex]

Approximate

[tex]x = 1.28[/tex]

Answer:

The answer is

Step-by-step explanation:

To find an equation of a line in point slope form when given the slope and a point we use the formula

[tex]y - y_1 = m(x - x_1)[/tex]

where

m is the slope

( x1 , y1) is the point

From the question the point is (-2,-2) and slope 42

The equation of the line is

[tex]y + 2 = 42(x + 2) \\ y + 2 = 42x + 84 \\ y = 42x + 84 - 2[/tex]

We have the final answer as

[tex]y = 42x + 82[/tex]

Hope this helps you

Answer:

Multiplying integers is similar to multiplying whole numbers because integers are whole numbers. An integer is a whole number that is not a fraction.

Hope This Helps :)

Answer: The answer is D

Step-by-step explanation:

I divided 24 by 3 and it gave me 8 which is a whole number.

Answer:

4

Step-by-step explanation:

Answer:

  22

Step-by-step explanation:

In order to get one of the answer choices, it appears we need to interpret your input as ...

  [tex](q^{16}q^{-5})^2 = (q^{16-5})^2=q^{11\cdot 2}=q^{22}[/tex]

The value of n is 22.

__

The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  (a^b)^c = a^(bc)

Answer:

6

Step-by-step explanation:

Answer:

[tex]x<-\frac{1}{2}\text{ or } x>1[/tex]

Step-by-step explanation:

So we have the equation:

[tex]|-4x+1|>3[/tex]

First, note that since the sign is greater than, this is an or inequality (not an "and" inequality). This is the student's first mistake.

So, let's solve this inequality.

Case 1:

[tex]-4x+1>3[/tex]

Subtract 1 from both sides:

[tex]-4x>2[/tex]

Divide both sides by -4:

[tex]x<-\frac{1}{2}[/tex]

The student did not flip the sign when doing this step, hence the incorrect answer.

You correctly spotted the student's mistake. Nicely done!

Case 2:

[tex]-4x+1<-3[/tex]

This is what you're missing: for this second instance, we must flip the sign to less than right away. This is because we are essentially multiplying the 3 by a negative. So, we must flip the sign in order to be correct.

Now solve. Subtract 1 from both sides:

[tex]-4x<-4[/tex]

Divide both sides by -4. Since we're dividing by a negative, flip the sign:

[tex]x>1[/tex]

So, our solutions are:

[tex]x<-\frac{1}{2}, x>1[/tex]

As mentioned previously, this is an or inequality. Therefore, our final answer is:

[tex]x<-\frac{1}{2}\text{ or } x>1[/tex]

Edit: Improved Answer

Answer:

The answer is "Option b".

Step-by-step explanation:

In the calculation of engineering or modeling, it is used to assess its necessary system, that performance, and also used to evaluate the distribution network adjustments, which is used to accommodate the slew of other distribution network adjustments, that's why except "choice b" all were incorrect.

Answer:it is the tens place

Step-by-step explanation:

Answer:

2 represents the the tenths place

Step-by-step explanation:

You have 168,526 remember your tenth hundred and thousands 2 is in the tenth place that is what represents

Hope that answers ur question

Answer: 2

Step-by-step explanation:            

Answer:

A) 0.2967

B) 0.0747

C) 0.2637

D)0.6933

Step-by-step explanation:

We are told the box contains four 40-watt light bulbs, five 60-watt bulbs, and six 75-watt bulbs.

Thus, total number of bulbs = 4 + 5 + 6 = 15 bulbs

This is a combination problem.

Thus;

A) probability that exactly one of the selected bulbs are rated 75-watt will be = ((6C2) × (9C1))/(15C3)

= (15 × 9)/455

= 0.2967

B) probability that all three of the elected bulbs have the same rating;

Number of ways to select three 40 watt bulbs out of the 4 in the box = 4C1 = 4!/(3! × 1!) = 4

Number of ways to select three 60 watt bulbs out of the 5 in the box = 5C1 =

5!/(3! × 2!) = 10

Number of ways to select 75 watt bulbs out of the 6 in the box = 6C1 = 6!/(3! × 3!) = 20

Total number of ways = 4 + 10 + 20 = 34.

Thus, probability that all three of the elected bulbs have the same rating = 34/15C3 = 34/455

= 0.0747

C) probability that one bulb of each type is selected =

[(4C1) × (5C1) × (6C1)]/(15C3)

= (4 × 5 × 6)/455

= 0.2637

D) probability that at least two of the selected bulbs are rated 75-watt =

[(4C1 × 5C1 × 6C2)/15C3] + 6C3/15C3

= (4 × 5 × 15/455) + 20/455

= 0.6493 + 0.044

= 0.6933

Answer:

27

Step-by-step explanation:

15+7=22+7=22

Answer: 27

Step-by-step explanation:

15+7=22

22+5=27

I hope this helped!!

Answer:

1.5 MPH

Step-by-step explanation:

3/4 = 0.75

3/4 x 2 = 0.75 x 2 = 1.5

Answer:

-16

Step-by-step explanation:

-5(4)+2

-18+2

-16

Difference means subtract.

Set up the equation:

K - 8.1 > 24

Solve for k by adding 8.1 to both sides:

K > 32.1