Solve |2x + 6|<16

A {x|-11 B {x<-11 or x>5}
C {x|-5

Answer:

leg 1= 36  feet

leg2 = 15  feet

Step-by-step explanation:

Hi, we have to apply the Pythagorean Theorem:  

c^2 = a^2 + b^2  

Where c is the hypotenuse of the triangle (in this case the distance between Doreen’s house and the tower) and a and b are the other legs.  

leg1 = x

leg2 = x-21 (21 feet less than the other leg)

Replacing with the values given:  

39^2 = x^2 + (x-21)^2  

1,521 = x^2 + x^2 -42x +441

0 = 2x^2 -42x +441-1,521

0= 2x^2 -42x -1,080

For: ax2+ bx + c  

x =[ -b ± √b²-4ac] /2a  (quadratic formula)

Replacing with the values given:  

x=-(-42)± √(-42)²-4(2)-1080] /2(2)  

x= 42± √10,404] /4

x = 42± 102 /4

Positive:

x = 42+102 /4 = 36

leg 1= 36

leg2 = 36-21 =15

Feel free to ask for more if needed or if you did not understand something.  

The length of shorter leg is 15 feet and other leg is 36 feet.

Let us consider that, length of shorter leg is x feet.

So that, length of other leg is [tex](x+21)[/tex] feet.

It is given that, the hypotenuse is 39 feet.

Apply Pythagoras theorem,

                 [tex]x^{2} +(x+21)^{2} =(39)^{2}\\ \\x^{2} +x^{2} +441+42x=1521\\\\2x^{2} +42x-1080=0\\\\x=15 ,-36[/tex]

Since, side can not be negative.

So that, we have to consider x=15 feet.

Length of other leg[tex]=x+21=15+21=36feet[/tex]

Learn more about the Pythagoras theorem here:

https://brainly.com/question/343682

Answer:

Options (3), (4) and (5)

Step-by-step explanation:

1). a² - 9a + 7ab + 63b

  = a(a - 9) + 7b(a + 9)

  Now we can not solve this problem further.

  Therefore, can't be factored by grouping.

2). 3a + 4ab - b - 12

   = a(3 + 4b) - 1(b - 12)

   We can't solve it further.

   Therefore, can't be factored by grouping.

3). ab + 6b - 2a - 12

   = b(a + 6) - 2(a + 6)

   = (b - 2)(a + 6)

  We can be factored this expression by grouping.

4). x³ + 9x²+ 7x + 63

   = x²(x + 9) + 7(x + 9)

   = (x² + 7)(x + 9)

   Therefore, the given expression can be factored by grouping.

5). ay² + a - y² - 1

  = a(y² + 1) - 1(y² + 1)

  = (a - 1)(y² + 1)

  This expression can be factored by the grouping method.

Options (3), (4) and (5) are the correct answers.

Answer:

Option (2)

Step-by-step explanation:

Parent function has been given as,

f(x) = [tex]\sqrt{x}[/tex]

When translated by 3 units left,

f(x + 3) = [tex]\sqrt{(x+3)}[/tex]

g(x) = [tex]\sqrt{(x+3)}[/tex]

If the translated function is stretched vertically by a scale factor = k

New function will be,

g'(x) = [tex]k\sqrt{(x+3)}[/tex]

Since a point (1, 4) passes lies on the transformed function.

g'(1) = [tex]k\sqrt{(1+3)}[/tex]

4 = 2k

k = 2

Therefore, transformed function represents the translation by 3 units in the negative side of the x-axis and stretched vertically by 2 units.

Option (2) will be the answer.

Answer:

x=27

Step-by-step explanation:

So let's look at the ratio

3:9

x:81

x is proportional to 3 the same way that 81 is to 9

How would we get 9 to 81?

We would multiply by 9

So what is 3*9?

27

Answer:

Your in middle school you should know this figure this by now FIGURE IT OUT ON YOUR OWN.....

Step-by-step explanation: yeah

Answer:

i dont know the volume but if it tells you what each book measures. Ive left a guide below to distribution.

Step-by-step explanation:

volume = 1

0.5 +0.5 = 1

volume 2

1+1 = 2

you just need to use the word distribution and show like this

(V): amount  / 2 =  new amount (adding cm^3)

To work out volume you take the length and width and height of the shelf of the books. you show your workings like this.

(V): L x Wx H =

You then multiply the amount of books if you was not given the measure of the bookcase shelf.

IF the bookcase is double like the picture and doesnt show the shelf measure than you half the hieght only and keep the same length and width.

H/2 =   first and enter below the new height.

(V): L xWx H  = this is the whole shelf

(V) =     / 2   you enter the Volume amount infront of the /2 and this way you see the volume for the math textbooks being 1/2 of 1  by (/2)  

Use the found answer

LAbel

MAth text books (V) =

Bounty paper towells (V) =

Then see how many cubic sheets fit.

ie) if they measure 30cm x 1cm x 30xm

and the shelf measures 30cm x 60 x 60

you can count up from the second values as the first values fit the length

The width = 1 x 60 - 60 books.  (example 1cm Width thickness)

Then see the height does not change to the height of the books.

IF it does change then for every 2cm change you divide the height of the bookcase by 60-1, 60-2 or 60-3, 60-4cm etc. just one of these that fits the indifference of height

then multiply if 60-58cm = 58 we know this is 2 / 60 x 100 = 3.33%

To calculate percentage decrease: see above

First: work out the difference (decrease) between the two numbers you are comparing. Then: divide the decrease by the original number and multiply the answer by 100. If your answer is a negative number, then this is a percentage increase.

You then apply (V) of shelf number x 0.03 and then subtract from that shelf volume to show your workings or reapply the same technique to see how many fit as decrease ie) 0.50% =  amount x 0.50 = 1/2 new amount.

Hey mate!!

Answer:

n(A)=12

Solution,

A={3,6,9,12,15,18,21,24,27,30,33,36}

Just count the elements,

There are 12 elements in the set.

So the cardinal number of the set is 12.

Answer:

[tex]12[/tex]

Step-by-step explanation:

A = {3,6,9,12,15,18,21,24,27,30,33,36}

To find the cardinal number,

So, according to that,

there are 12 numbers in this set.

So, it's clear for us that, the cardinal number of this set is 12

n (A)= 12

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

[tex]\frac{25}{9}[/tex]

Step-by-step explanation:

[tex]4+\frac{5}{3} ^2-2^2=\frac{5}{3}^2=\frac{25}{9}[/tex]

Answer: 6a. 3 1/3, 6b. 2 2/5, 6c. 1/4, 6d. 9/10

Step-by-step explanation: You can use math/way or Soc/ratic to find the answers. Math/way is a website, Socr/atic is an app.

Answer:

it is 3/y.

Step-by-step explanation:

the answer is 3/y because 3 comes before y in the question.

Answer:

The answer is Graph III.

Step-by-step explanation:

Given that the linear equation is y = mx + c where m represents gradient and c is y-intercept.So firstly, we have to make y the subject :

[tex]3x - 36 + 2y = 0[/tex]

[tex]2y = - 3x + 36[/tex]

[tex]y = - \frac{3}{2} x + 18[/tex]

Next, by looking at the graph, we know that the line has a negative gradient and touches y-axis at 18 which suits the equation.

Answer:

Step-by-step explanation:

Same side interior angles refers to the pair of angles which are inside the two "parallel" lines and at the same side of the transversal line.

Notice that angles BGH and DHG are same side interior angles. Similarly, angles AGH and CHG are also same side interior angles.

Therefore, the right answer is ∠DHG.

Answer:

0

Step-by-step explanation:

The discriminant is

12^2 - 4*11*4 = -32

Since it is negative, there are 0 real solutions

Answer:

{x ∈ R: x<6}

Step-by-step explanation:

Given

Required

Write the set using set builder notation

The very first thing to do is to list out the range of x, using inequalities;

x is less than 6 implies that -infiniti < x < 6

The next step is to translate this to set builder. This is done as follows

x ∈ R - > This means that x is a real number

x < 6 -> where x is less than 6.

Bringing these two together, it gives:

{x ∈ R: x<6}

Hence, the set of real numbers x less than 6 is equivalent to {x ∈ R: x<6} using set builder notation

Answer:

1`. y = 4x+6

2. y = -6x + 29

3. y= 3x+1

4. y = x -2

5. y = 11.5x+ 3

6. y = -2x -4

Step-by-step explanation:

Answer:

There are 40 windows on the 10th floor

Step-by-step explanation:

Since we know one cube has 4 "windows" (each hole on its side not counting top and bottom) we can calculate that for each "floor" 4 more windows are added. So in other words, if "x" equals the amount of "floors" the equation for solving this would be 4x = # of windows.

Answer:

The length of side A is 12 cm

Step-by-step explanation:

This question is best answered when there's an attachment; however, the absence of an attachment doesn't mean it can't be solved.

Given

Side A corresponds to 24 cm

Length 6 cm corresponds to Length 12 cm

Required

Find A

The given parameters can be represented mathematically as;

[tex]\frac{A}{24} = \frac{6}{12}[/tex]

With this expression, the value of A can be easily solved

First; multiply both sides by 24

[tex]24 * \frac{A}{24} = \frac{6}{12} * 24[/tex]

[tex]\frac{24 *A}{24} = \frac{6}{12} * 24[/tex]

[tex]\frac{24A}{24} = \frac{6}{12} * 24[/tex]

[tex]A = \frac{6}{12} * 24[/tex]

[tex]A = \frac{6 * 24}{12}[/tex]

[tex]A = \frac{144}{12}[/tex]

[tex]A =12[/tex]

Hence, the length of side A is 12 cm

Answer:

ANSWER:A

Step-by-step explanation:

ANSWER IS A!SAVE YOURSELF! RUN! DON'T FAIL UR TEST!

byeeeeee:)

<3

I think you can multiply how many are defective in a sample by how much more stuff there is

Answer:

I'm glad you asked!I couldn't fully understand it so I made it the best of my ability.

Step-by-step explanation:

1.(Please,I cannot understand it .I think it is incomplete.)

2.18 out of 270 students speak 3 languages or more.So [tex]30,330[/tex] x [tex]\frac{18}{270}[/tex] = [tex]2,002.2,002[/tex] students.

3.We would do 5,000 x [tex]\frac{2}{10}[/tex] = 1,000.

4.No, the manufacturer cannot assume the prediction is valid.

The sample size of 10 is too small compared to the size of the shipment.

5.You can use random samples by using them for graphs which numbers are too big.

Answer:

D

Step-by-step explanation:

Took it on Ed but it might be different

Answer:

D

Step-by-step explanation:

I did the math :)

Answer:

Step-by-step explanation:

Angles: 45°: 45°: 90°

Ratio of sides: 1:1:√2

Given c= 55

a =c/√2

a=55/√2 = 38.9

b=a+2 = 38.9+2 =41.9

The length of the legs of the triangle is 41.9

A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.

Angles are: 45°: 45°: 90°

The ratio of sides: 1:1:√2

Given c = 55

a = c/√2

a = 55/√2

a = 38.9

b = a+2

b = 38.9+2

b =41.9

Thus, the length of the legs of the triangle is 41.9

Learn more about a right angle;

https://brainly.com/question/7116550

#SPJ2

Answer:

[tex]\sqrt{\frac{153.86}{3.14} } = r[/tex]

Step-by-step explanation:

a=pir^2

153.86 = 3.14*r^2

[tex]\sqrt{\frac{153.86}{3.14} } = r[/tex]

You're welcome and don't forget to click THANKS

Answer:

\sqrt{\frac{153.86}{3.14} } = r

Step-by-step explanation:

a=pir^2

153.86 = 3.14*r^2

\sqrt{\frac{153.86}{3.14} } = r

Answer: $47.83

Step-by-step explanation: Let's turn the percentage into a decimal, move the decimal two times to the right...

6% ⇒ 0.06

0.06 * $50.88 = $3.05

$50.88 - $3.05 = $47.83

Remember x = price before tax...

x = $47.83

___________________________________

Total number of students=2200

Total percent of male=52.5%

Total percent of female=100%-52.5%

=47.5%

Total number of female= 47.5% of 2200

=47.5/100*2200

=1045

So the total number of female is 1045

hope it helps

Good luck on your assignment

________________________________

Answer:

[tex]1045[/tex]

Step-by-step explanation:

[tex]no. \: \: of \: \: students = 2200[/tex]

First let's find the percentage of female.

[tex]100\% - 52.5\% = 47.5\%[/tex]

So now let's find how many female students are there in the class

[tex]2200 \times47.5\% \\ 2200 \times \frac{47.5}{100} \% \\ = 1045[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

$20.30

Step-by-step explanation:

There are 4 people so 81.20/4 = 20.30

Answer: $20.30

Step-by-step explanation:

There are 4 people and so you need to divide the cost by the amount of people to see what each person owes

Answer:

BC = 24

Step-by-step explanation:

In the picture attached, the missing triangles are shown:

Data

As a consequence of the "Side Splitter" Theorem:

AD/DE = AB/BC

Replacing with data and solving for BC

5/12 = 10/BC

BC = 10*12/5 = 24

The length of BC is 8 units.

The given figure is image 1.

From the image: AD = AB + BD = 10 + 5 = 15.

From the image triangle ABC and ADE are similar.

So their sides will be in the same ratio.

[tex]\frac{10}{15}=\frac{BC}{12}\\\\BC=\frac{10}{15}\cdot12\\\\BC=8[/tex]

Learn more: https://brainly.com/question/13769924

Answer:

1

Step-by-step explanation:

Answer:

2.

Step-by-step explanation:

Rational numbers can be written as a/b where a and b are integers ( b not zero) and a and b are co-prime ( no common factors)

A whole number is rational (2 for example can be written as 2/1).

It could have been 2 or 3 or 33.

Answer:

y = kxz²

k= y/xz²

x= 3 y = 60 z= 2

k = 60/3(2)²

k=60/12

k= 5

Hope this helps.

Step-by-step explanation:

The circumference of the clock will be 8.6π because its hand is the radius. In 15 minutes the hand moves a quarter of the circumference which is 2.15π or 6.571.

Answer:

1. 88 degrees

2. x=8

Step-by-step explanation:

1.

In a hexagon, all of the interior angles must add up to 720 degrees. Therefore:

x+125+120+95+120+172=720

x=88

2.

Since opposite sides of a parallelogram are equal:

2x=x+8

x=3x-16

Let's go with the first equation.

2x=x+8

Subtract x from both sides:

x=8

You can plug this into the second equation to ensure it works:

3(8)-16=8

24-16=8

8=8

Hope this helps!

Answer:

1. 88

2. 48

Step-by-step explanation:

1. The total of the inner angles of the hexagon is 720

95+120+120+172+125=632

720-632=88

2. 2x=x+8

x=8

If we put all the x's in place and add them, the result is: 48