Solve and show your work for each equation.

What is 0.36... (36 repeating) expressed as a fraction in its simplest form?
What is 0.36... (6 repeating) expressed as a fraction in its simplest form?

Note that

[tex]x^2 - y^2 = (x - y) (x + y)[/tex]

and

[tex]x^2 + 2xy + y^2 = (x + y)^2[/tex]

Then their LCM is [tex]\boxed{x + y}[/tex].

Answer:

The slope is undefined

Step-by-step explanation:

[tex]m=\frac{9-3}{2-2}[/tex]

The denominator leads to 0 so it would not be possible to find the answer

Answer:

undefined

Step-by-step explanation:

anything divided by zero is undefined since you cant logically give (for example) 2 apples to 0 people.

For slopes not so obvious, the formula is (slope)m= (rise)y/(run)x

Answer:

in the attachment

Step-by-step explanation:

Given: Piece-wise function graph.

We need to find the function.

In the graph, we can see a two-piece

For -3≤x≤0

Endpoints on graph (-3,-6) and (0,0)

It is the horizontal line. The equation of the horizontal line is y=k.

Equation: y=3

Now, we write as a piecewise function.

First blank = 2x

Second Blank = 3

hope this helps:)

Answer:

in the pic...

Step-by-step explanation:

Hope it Helps!!!

Answer:

a. y = 2(x + 3)² - 17

b. y = 4(x + 6)² - 154

Step-by-step explanation:

a. y = 2x² + 12x + 1

y = 2[(x² + 6x)] + 1

y = 2[(x + 3)² - 9] + 1

y = 2(x + 3)² - 18 + 1

y = 2(x + 3)² - 17

b. y = 4x² + 48x - 10

y = 4[(x² + 12x)] - 10

y = 4[(x + 6)² - 36)] - 10

y = 4(x + 6)² - 144 - 10

y = 4(x + 6)² - 154

Volume = PI x r*2 x h/3

r = radius which is shown as 8

h is the height which is shown as 63

Volume = 3.14 x 8^2 x 63/3

Volume = 3.14 x 64 x 21

Volume = 4,220.16 cubic units.

Based on the key features, the end behavior and the zeros of function h [h(x) = -x³ - 9x² +4x +96], the statement that is true of the above graph is: "The graph is positive on the intervals (-8, -4) and (3, infinity) (Option B)"

A function's "end behavior" refers to how the function's graph behaves at its "ends" on the x-axis.

In other words, if we look at the right end of the x-axis (as x approaches + ∞) and the left end of the x-axis (as x approaches - ∞ ), the end behavior of a function represents the trend of the graph.

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Answer:

The answer is (-84)

putting the value of X =(- 3)

2) X = 216

Hello!

We are going to evaluate the expression with our given x-value for question 2.

We know that our expression is: x^4 + 5x^3 - 3x^2 + 11x - 6

We also know that our x-value = 3

We will simply plug in "3" to "x" in our expression and solve.

Solve:

x^4 + 5x^3 - 3x^2 + 11x - 6

Plug in 3 to x:

(3)^4 + 5(3)^3 - 3(3)^2 + 11(3) - 6

Simplify:

(3)^4 + 5(3)^3 - 3(3)^2 + 11(3) - 6

81 + 5(3)^3 - 3(3)^2 + 11(3) - 6

81 + 135 - 3(3)^2 + 11(3) - 6

81 + 135 - 27 + 33 - 6

216 - 27 + 33 - 6

189 + 33 - 6

222 - 6 = 216

Therefore, our final answer would be 216.

Answer:

216

Answer:

3:1

Step-by-step explanation:

3 and 1 is not divisible by any number

Answer:

You need 2 numbers whose product is 45 and whose difference is 4.

so the length is 9 and the width is 5.

Hope this helps.

Answer:

132ft^2

Step-by-step explanation:

Answer:

y = 4x - 17

Step-by-step explanation:

y - 3 = 4(x - 5) ← distribute parenthesis by 4

y - 3 = 4x - 20 ( add 3 to both sides )

y = 4x - 17

the answer would be 9.88372093e-7

1 )Simplify.

[tex]\frac{850000000000000000}{8.6E}[/tex]+23

2 )Answer

9.88372093e-7

When a given function is written with factors in the form of ( x - r ), then r is a zero of the function.

We're given:

Therefore, the zeros of the function are 7 and -6.

-6, 7

The zeroes of the function will be equal to ( 7, -6 ).

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given function:-

As we can see that the quadratic equation in the factorized form is ( x - 7 ) ( x+ 6 ) so we will equate each factor to zero.

( x- 7 )  = 0

x = 7

( x+ 6 ) = 0

x = -6

Therefore zeroes of the function will be equal to ( 7, -6 ).

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Answer:

Maybe the answer will be C. P ( A and B )

explanation:

I think it is OPTION C , P(A and B)

as this is the only option which has the value of 80, which we got from the table...

Answer:

B. shifting

Step-by-step explanation:

When the price is rising or shifting higher, the demand curve moves to the left. But, t here is a corresponding change in the demand curve in that scenario while the cost stays unchanged. Since it relies on variables other than price, the simultaneous shift might go either left or right. However, the upward-pointing line depicts a rise in price and a fall in supply. 

Answer:

4 rows

Step-by-step explanation:

First set:

unknown rows, 5 tiles each

meaning old total is divisible by 5

Second set:

3 additional rows, 3 tiles each

meaning that the new total is divisible by 3

so, our total number of tiles is divisible by 5, add 1 and it is divisible by 3 when added 1

{another way I solved it : [and when it is divided by 3, it has 8 that fit into the original pattern; which is another way of knowing that each of the rows of 5 [each have 2 removed when turned into rows of 3] add up to having a remainder of 8 tiles; 8 / 2 = 4; so there were four rows in the original pattern contributing to the change--there were four rows] }

x is divisible by 5, x + 1 is divisible by 3

essentially, we are looking for a number that ends in 5 or 0, and the next number [ending in 6 or 1] is divisible by 3

I know that 5 goes into 20, and that 21 is divisible by 3, so let's test it out:

4 (rows of 5) turns into 7 [4 + 3] rows of 3

because 21 can be split into 7 rows, this number of tiles is possible

so, in the original pattern, there must have been 4 rows

hope this helps!! {so sorry if this confuses you, please let me know if I should explain my reasoning further}

have a lovely day :)

Answer: 72

Step-by-step explanation:

Step 1: Divide 18 and 2, which is 9

Step 2: Divide 56 and 7, which is 8

Step 3: Multiply 9x8 and get 72

The required piecewise function that represents the graph is given as:

[tex]f(x)=\left \{ {{y = -3x-10} \atop y=-\frac{1}{2}x-3 } \atop y=-2x-6 }} \right.[/tex]

The graph consists of 3 lines with different equations and slopes. In order to determine the function it represents, we will create a piecewise function.

For the line crossing the negative x-axis

Using the coordinate points (-4, 2) and (-2, -4)

Slope = -6/2

Slope = -3

2 = -3(-4) + b
2 - 12 = b

b = -10

The equation of the line will be y = -3x-10

For the line crossing the negative y-axis

Using the coordinate points (-2, -4) and  (2,-2)

Slope = 2/4

Slope = 1/2

-2 = 1/2(2) + b
-2 - 1 = b

b = -3

The equation of the line will be y = -1/2x-3

For the line crossing the positive x-axis

Using the coordinate points (2, -2) and (3, 0)

Slope = 2/1

Slope = 2

0 = 2(3) + b
0 - 6 = b

b = -6

The equation of the line will be y = 2x-6

The required piecewise function that represents the graph is given as:

[tex]f(x)=\left \{ {{y = -3x-10} \atop y=-\frac{1}{2}x-3 } \atop y=-2x-6 }} \right.[/tex]

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Answer: The answer for this problem is all real numbers or R.

Step-by-step explanation: In order to solve first you must deal with what's inside the parenthesis.

[tex]8(4x+2)=8*4x + 8*2= 32x +16[/tex]

Now that the parenthesis is out of the picture, now proceed to subtract the 16 that was outside of the parenthesis.

[tex]32x+16-16=32x[/tex]

You should then have an equation set up like so.

32x = 32x

Now you need to move one of the 32x's to the other side of the equation.

[tex]32x-32x=0[/tex]

Your final equation should be.

0 = 0

So, all real numbers (R) will work for this equation.

Answer:

a

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 )

then the discriminant

Δ = b² - 4ac

• if b² - 4ac > 0 then 2 real solutions

• if b² - 4ac = 0 then 2 real and equal solutions

• if b² - 4ac < 0 then no real solutions

given

[tex]\frac{3}{4}[/tex] x² - 3x = - 4 ( add 4 to both sides )

[tex]\frac{3}{4}[/tex] x² - 3x + 4 = 0 ← in standard form

with a = [tex]\frac{3}{4}[/tex] b = - 3 , c = 4

then

b² - 4ac = (- 3)² - ( 4 × [tex]\frac{3}{4}[/tex] × 4) = 9 - 12 = - 3

since b² - 4ac < 0 then equation has no real solutions

Answer:

a.  -3; no real solutions.

Step-by-step explanation:

Discriminant

[tex]\boxed{b^2-4ac }\quad\textsf{when}\:ax^2+bx+c=0[/tex]

[tex]\textsf{When }\:b^2-4ac > 0 \implies \textsf{two real solutions}.[/tex]

[tex]\textsf{When }\:b^2-4ac=0 \implies \textsf{one real solution}.[/tex]

[tex]\textsf{When }\:b^2-4ac < 0 \implies \textsf{no real solutions}.[/tex]

Given equation:

[tex]\dfrac{3}{4}x^2-3x=-4[/tex]

Add 4 to both sides of the equation so that it is in standard form:

[tex]\implies \dfrac{3}{4}x^2-3x+4=-4+4[/tex]

[tex]\implies \dfrac{3}{4}x^2-3x+4=0[/tex]

Therefore, the variables are:

[tex]a=\dfrac{3}{4}, \quad b=-3, \quad c=4[/tex]

Substitute these values into the discriminant formula to find the value of the discriminant:

[tex]\begin{aligned}\implies b^2-4ac&=(-3)^2-4\left(\dfrac{3}{4}\right)(4)\\&=9-(3)(4)\\&=9-12\\&=-3\\\end{aligned}[/tex]

Therefore, as -3 < 0, the discriminant is less than zero.

This means there are no real solutions.

Answer:

well not sure but I think it is 8° or 17.8°

Answer:

1. 3/14

2. 2/7

3. 1/7

4. 5/14

5. 11/14

6. 9/14

Step-by-step explanation:

first get the total number of pens

3 red pens + 4 blue pens + 2 black pens + 5 green pens =

14 total number of pens

1. What is the probability that the pen chosen red?

3 red pens out of a total of 14 pens = 3/14

2. What is the probability that the pen chosen is blue?

4 blue pens out of a total of 14 pens = 4/14 -> simplified -> 2/7

3. What is the probability that the pen chosen is black?

2 black pens out of a total of 14 pens = 2/14 -> simplified -> 1/7

4. What is the probability that the pen chosen is green?

5 green pens out of a total of 14 pens = 5/14

5. What is the probability that the pen chosen is NOT red?

of the 3 red pens, 4 blue pens, 2 black pens and 5 green pens

4 blue pens, 2 black pens and 5 green pens are NOT red

4 blue pens + 2 black pens + 5 green pens =

11 total number of pens that are NOT red

11 total number of pens that are NOT red out of a total of 14 pens = 11/14

6. What is the probability that the pen chosen is NOT green?

of the 3 red pens, 4 blue pens, 2 black pens and 5 green pens

the 3 red pens, 4 blue pens, 2 black pens are NOT green

3 red pens + 4 blue pens + 2 black pens =

9 total number of pens that are NOT green

9 total number of pens that are NOT green out of a total of 14 pens = 9/14

gathmath.com

Given :-

>> Total no. of outcomes = 3 + 4 + 2 + 5

>> Total no. of outcomes = 3 + 4 + 7

>> Total no. of outcomes = 10 + 4

>> Total no. of outcomes = 14

Solution 1 :-

We know,

As there are three red pens. Therefore,

Solution 2 :-

We know,

As there are four blue pens. Therefore,

Solution 3 :-

We know,

As there are two black pens. Therefore,

Solution 4 :-

We know,

As there are five green pens. Therefore,

Solution 5 :-

We know,

As there 11 pens that are not red (Green + black + blue).

Solution 6 :-

We know,

As there are 9 pens that are not green (Red + blue + black).

The height of the shorter cone is 6.81cm

A cone is hollow three-dimensional shape with side lengths that tappers from the base to a point at the vertex.

Analysis:

Let the radius of the first cone be = r

radius of shorter cone = R

height of first cone = h

height of shorter cone = H

if volume of the two cones are same

1/3π[tex]r^{2}[/tex]h = 1/3π[tex]R^{2}[/tex]H

[tex]r^{2}[/tex]h = [tex]R^{2}[/tex]H

H =  [tex]r^{2}[/tex]h /  [tex]R^{2}[/tex]

H = [tex](8.5)^{2}[/tex]x 10 / [tex](10.3)^{2}[/tex] = 6.81cm

In conclusion, the height of the shorter cone is 6.81cm

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Answer:

centre (5,0)

radius:9

I hope it will be helpfulness

The new equation will become f(x) = 3([tex]2^{x}[/tex]).

The given information is the stretch factor which is 3 and the equation f(x)=[tex]2^{x}[/tex].

When there is a vertical strecth factor, you need to multiply the equation by the stretch factor.

By stretching the function, the value of y has to be multiplied by 3, will now be equal to 3f(x)

The new equation will become f(x) = 3([tex]2^{x}[/tex]).

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Answer: a) 46 minutes
               b) 10:47

The basic knowledge for this is that 60 minutes = 1 hour

a) Question a asks for how long it took from a 10:34 bus from Mosley to reach Bamford. From the table you can see that the 10:34 bus reaches Bamford at 11:20. All you have to do is count from 10:34 to 11:20.
10:34 will become 11:00 at 10:60 right? Clock's generally don't show 10:60 but goes directly to 11:00 after 1 minute is passed at 10:59. So from 10:34 to 11:00, it takes 26 minutes. Remember the bus reaches at 11:20 so from 11:00 to 11:20, it takes 20 minutes. Now add them up:
26 minutes + 20 minutes = 46 minutes

Here you go! Total 46 minutes from Mosley to Bamford.

b) From question b, we can see that Trina did not ride the first bus or by any chance missed it because the bus left at 10:14 and she is at the station at 10:15. Now think it from your perspective! You missed the first bus and you are in a big rush. So to reach your destination as early as possible, you will obviously take the next earliest bus. The next bus is at 10:24 (Belton). So if we take the 10:24 bus in Belton, it reaches at 10:47 in Garton.

 ∩_∩
(„• ֊ •„)♡
┏━∪∪━━━━┓
   hope it helped
┗━━━━━━━┛

Answer:

C. -2

Step-by-step explanation:

Use A-P-E-X

How I solved it:

3/4(1/5÷3/5)(-8)

3/4(1/5×5/3)(-8)

3/4(1/3)(-8)

1/4(-8)=-2

Hope this helps!

If not, I am sorry.

Answer:

10 cm is 20% of 50 cm.

Step-by-step explanation:

1) Put the "question" into fraction form: 10/50

2) Divide the numerator by the denominator (essentially changing the fraction into the decimal form): 10 ÷ 50 = 0.2

3) Multiply the quotient by 100: 0.2 × 100 = 20

4) Slap a "%" on the end and you're good to go!! : 20%

Answer:

35 miles per hour

Step-by-step explanation:

Speed of a car or any other object is given by distance divided by time taken.

therefore,

according to the given data in the table :

speed = miles covered/ time taken

           =  140/4 = 35 miles per hour

           =  175/5 = 35 miles per hour

           =  210/6 = 35 miles per hour

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