f(x) =
x^2/
(x^2 − 9)

Where is the auction increasing and decreasing?
Critical numbers= 2

Answer:

x=3

Step-by-step explanation:

2x+3=9

2x=6

x=3

The answer is: 33.33%

Since we have the average number of accidents that occurs in 1 month, and it's equal to 3, we can calculate the probability of 1 accident occurs by dividing it into the average number of accidents, using the following formula:

[tex]Probability=\frac{FavorableOutcomes}{Outcomes}*100[/tex]

Where,

Favorable outcomes are the occurrence of the event, for this case, it's equal to 1.

Outcomes are the possible occurrence of the event, for this case, it's equal to 3.

So, by substituting we have:

[tex]Probability=\frac{1}{3}*100[/tex]

[tex]Probability=0.3333*100=33.33[/tex]

So, the probability will be equal to 33.33%

Have a nice day!

Answer:

x=-1/2

Step-by-step explanation:

4x-6=10x-3

Subtract 4x from each side

4x-4x-6=10x-4x-3

-6 =6x-3

Add 3 to each side

-6+3 =6x-3+3

-3 = 6x

Divide each side by 6

-3/6 = 6x/6

-1/2 =x

➷ 4x - 6 = 10x - 3

Add 3 to both sides:

4x - 3 = 10x

Subtract 4x from both sides:

- 3 = 6x

Divide both sides by 6:

x = -1/2

The correct answer would be B. x = -1/2

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Answer:

asfvbrgterwgwertbewgrq3geqgrewrgergergfergewrg

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

b^2 c^-1

Let b=-4 and c =2

(-4)^2 * (2)^-1

The negative exponent means it is in the denominator

(-4)^2 / (2)^1

16/2

8

Final Answer:

The population is the total number of students in the school.

Explanation:

The gym teacher's inquiry regarding the number of students playing a sport pertains to a subset of the larger student body. In statistical terms, the 20 students she questioned represent a sample.

The population, in this context, encapsulates the entirety of students attending the school, irrespective of whether they were asked about their sports participation or not.

When the gym teacher approached 20 students throughout the day, she was essentially drawing information from a limited group within the school. The population, however, extends beyond these 20 individuals to encompass every student enrolled in the institution.

This broader set includes students who might not have been present that day or were not approached by the teacher for their input. Determining the population aids in understanding the context and scale of the sampled data.

For instance, if the gym teacher's goal is to ascertain the percentage of students engaged in sports activities, the population figure (total number of students) becomes crucial for accurate statistical inference.

Consequently, the teacher can use this information to make informed decisions or implement strategies that cater to the entire student body, considering the interests and involvement in sports across the school.

Answer:

C and E repr. constant functions.

Step-by-step explanation:

C and E represent constant functions.  One can tell immediately by the fact that y remains the same even when x changes.

Answer:

The correct option is C and E.

Step-by-step explanation:

Constant functions is the function those output value(y) remains same for any input values(x).

Now consider the provided options.

Option A, B and D has different output value(y) for different the different input values(x)

Now consider the option C and E.

Option C and E has same output value(y) for different the different input values(x).

Therefore, the correct option is C and E.

Answer:

The simplified form of n to the -6th power times p to the 3rd power is p^3/n^6.

Step-by-step explanation:

For this case we have that by definition of properties of powers, it is fulfilled that:

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

We have the following expression:

[tex]n ^ {- 6} * p ^ 3[/tex]

We can rewrite it as:

[tex]\frac {p ^ 3} {n ^ 6}[/tex]

Finally:

[tex]n ^ {- 6} * p ^ 3 = \frac {p ^ 3} {n ^ 6}[/tex]

Answer:

Option C

Answer:

)x + 5)(x - 5)

Step-by-step explanation:

x² - 25 ← is a difference of squares and factors in general as

a² - b² = (a + b)(a - b), thus

x² - 25 = x² - 5² = (x + 5)(x - 5)

Answer:

x = 7

Step-by-step explanation:

Order of operations rules require that we do multiplication and division BEFORE addition and subtraction.

Let's start by simplifying the expression.  Adding 15 to both sides results in:

8,000÷(28x+4) = 40.

Multiplying both sides by (28x + 4) results in the simpler:

8000 = 40(28x + 4).

Dividing both sides by 40 results in:

200 = 28x + 4, or

196 = 28x

Solve for x by dividing both sides by 28:

x = 7

Answer:

m∠1 = (a + b) you will also need to divide the sum by 2

Step-by-step explanation:

The measures of angles formed by intersecting chord can be found by adding their arc measures and dividing in 2.

In this case, m< 1 = 1/2 ( a + b).

Based on the angle of intersecting chords theorem, the equation of that can be used to solve m∠1 is: m∠1 = 1/2(a + b).

The angle of intersecting chords theorem states that the measure of any of the vertical angles formed when two chords intersect equals half of the sum of the two intercepted arcs.

Therefore, based on the angle of intersecting chords theorem, the equation of that can be used to solve m∠1 is: m∠1 = 1/2(a + b).

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Answer:

D

Step-by-step explanation:

Since the triangle is right use the sine trig ratio to solve for x

noting that sin45° = [tex]\frac{1}{\sqrt{2} }[/tex] ← exact value

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{8}{x}[/tex]

Multiply both sides by x

x × sin45° = 8 ( divide both sides by sin45° )

x = [tex]\frac{8}{sin45}[/tex] = [tex]\frac{8}{\frac{1}{\sqrt{2} } }[/tex] = 8[tex]\sqrt{2}[/tex]

Answer:

The answer is 4y

Step-by-step explanation:

This is because when you have a variable and 2 numbers you work backwards to find the number of the x so you do the opposite of adding you subtract,  2 - 6 remember you are working backwards but now you have the answer 4 but there is a variable next to the two so you so you add that to the four.

100% - 25% = 75%

$35 x 75/100 = $26.25

The sale price should be $26.25.

a shirt was original $35 and is now 25% off.

Since it is 25% off

So, it should be

= 100% - 25%

= 75%

Now the 75% of $35 should be $26.25.

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Answer:

Step-by-step explanation:

Total Number of animals = 23 + 27 = 50

Number of Dogs = 27

Percentage of dogs = [tex]\frac{27}{50}[/tex] × 100 = 54%

The percentage of dogs will be 54%.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

Number of cats = 23

Number of dogs = 27

Now,

Total number of animals = 23 + 27

                                      = 50

And, Number of dogs = 27

Hence, The percentage of dogs = (27/50) × 100

                                                  = 54%

Thus, The percentage of dogs will be 54%.

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Answer:

208⅓ ft²

Step-by-step explanation:

The dimensions of Rachel's living room are 80 times the measurements on the scale drawing.

Calculate the width:

                                                                                     w = 80 × 1⅞

Convert the mixed number to an improper fraction     = 80 × 15/8

Cancel the 8s                                                                  = 10 × 15

                                                                                        = 150 in

Convert inches to feet                                                   = 150/12  

Convert the improper fraction to a mixed number      = (144 + 6)/12

                                                                                        = 12⁶/₁₂

Reduce the fraction to lowest terms                             = 12½ ft

Calculate the length

l = 80 × 2½  = 80 × 5/2 = 40 × 5 = 200 in = 200/12 = (192 + 8)/12

l = 16⁸/₁₂ = 16⅔ ft

Calculate the area

A = lw

A = 16⅔ × 12½

Convert the mixed numbers to improper fractions

A = 50/3× 25/2

Cancel the 2s

= 25/3 × 25

Multiply numerators and denominators                        

= 625/3

Convert the improper fraction to a mixed number    

= (624 + 1)/3

= 208⅓ ft²

The area of Rachel's living room is 208⅓ ft².

The tenth in 149.95 is 9. To round it to the nearest tenth, use the hundredth. The hundredth is 5. When rounding, always round up when it is a 5. 95 should be rounded to 100, but it is a decimal. 100 as a decimal is equal to 1. 149 + 1 = 150.

Answer:

149.95 becomes 150 when rounded to the nearest tenth because 149.95 is only .5 away from 150. If it was something like 149.4 it would be rounded to 149.

Answer:

x = 33

Step-by-step explanation:

There are 180 degrees in a triangle.

There are also 180 degrees in a straight line.

180 - 105 = 75.

Thus, 75+72+x=180.

x=33

Answer:

x=33

Step-by-step explanation:

Step one :

From the screen shot

The sum of angles on a straight line is 180° hence 180°-105°=75°

The unknown angle is 75°

Step two :

To find the angle x° the sum of angles in a triangle is 180°

Therefore

x°+72°+75°=180°

x+147=180

x=180-147

x=33°

Answer:

Step-by-step explanation:

If y = ax² + bx + c has negative value of a, then a parabola is open down.

Look at the picture.

Vertex  = (-4, -4)

Answer:

C)   (-4, -4)

Step-by-step explanation:

Answer:

1) The picture whose width = x and Length = (x + 8) feet

2) Width = 4 feet

   Length = 12 feet

Step-by-step explanation:

A rectangle has one side longer than the other.

Area of a rectangle = product of its sides.

                                  = length × width

Width = x feet

Length = (x + 8) feet

Area = 48

∴ x × (x + 8) = 48

   x² + 8x = 48

  x² + 8x + 4² = 48 + 4²

  (x + 4)² = 64

 x + 4 = √64

x = ±8 - 4

x = - 12        or x = 4

     Since length can not be negative, x = 4

∴ Width = 4 feet

   Length =4 + 8 = 12 feet

The dimensions of the rectangle where its area is 48 square feet and length is 8 feet more than width is 4 feet (width) and 12 feet (length). The question is set on algebra, calculation of area and understanding of shapes.

This problem falls under the category of algebra and involves understanding the concept of shapes, particularly rectangles, and calculation of their area.

We know, the area of a rectangle is calculated as the product of its length and width. Given that the area is 48 square feet and the length is 8 feet more than the width. Let's denote the width as 'w' and the length as 'w + 8'.

So, we can set up the equation as: w * (w + 8) = 48. Solving this quadratic equation will give us the values for 'w' and 'w + 8' or the dimensions of the rectangle.

If you factor the quadratic equation, you get (w - 4)(w + 12) = 0. Setting these factors to zero, we find that w = 4 or w = -12. Since width cannot be negative, the width is 4 feet. And the length, which is 8 feet more than the width, will be 4 + 8 = 12 feet.

For the picture representation, simply imagine or draw a rectangle. Label the shorter side as 4 feet (width) and longer side (length) as 12 feet.

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Answer: 1) [tex]A = 28ft^{2}[/tex]

2) 55 points

Step-by-step explanation:

1) A= 8w + 18, w=1.25

A = 8(1.25) + 18

A = 10 + 18

A = 28ft^2

2) 25 points to start with, additional 5 points per magazine they sell, m = number of magazines they sell

total points = 25 + 5m

How many if they sell 6?

total = 25 + 5(6)

= 25 + 30

total = 55

Answer:

D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

Answer (a): Area of garden [tex]= 4x^2+12x+9[/tex]

Answer (b): Area of the square garden and the walkway =  [tex]16x^2+24x+9[/tex]

Step-by-step explanation:

Answer (a):

From given picture we see that Length of the garden = 2x+3

Width of the garden = 2x+3

Then area of the square garden = (Length)(Width)

[tex]= (2x+3)(2x+3)[/tex]

[tex]= 4x^2+6x+6x+9[/tex]

[tex]= 4x^2+12x+9[/tex]

Answer (b):

From given picture we see that width of the walkway = x

Then length of the garden including walkway =x + (2x+3) +x=4x+3

Similarly width of the garden = 4x+3

Then area of the square garden and the walkway = (Length)(Width)

[tex]= (4x+3)(4x+3)[/tex]

[tex]= 16x^2+12x+12x+9[/tex]

[tex]= 16x^2+24x+9[/tex]

Answer:

option C

Step-by-step explanation:

Given table is a linear function when the change in y to change is x is a constant.

From the tables, difference of x is a constant 1

Lets look at the difference of y values

First table

We find the change in y values

[tex]-6+2=-4[/tex]

[tex]-2+6=+4[/tex]

the difference is not a constant. So it is not a linear

Second table

[tex]-5+2=3[/tex]

[tex]-9+5= 4[/tex]

the difference is not a constant. So it is not a linear

Third table

[tex]-10+2= -8[/tex]

[tex]-18+10=-8[/tex]

[tex]-26+18= -8[/tex]

the difference is a constant. So it is a linear function.

Answer:

False

Step-by-step explanation:

The measures of a right-angle are;

A right triangle has a 90° angle and two acute angles and the sum of angles should add up to 180°. The leg angles could be  45 to form an  °isosceles triangle.

Answer:

[tex]\large\boxed{B.\ \dfrac{7}{4}}[/tex]

Step-by-step explanation:

[tex]\dfrac{\Delta y}{\Delta x}=\dfrac{14}{8}=\dfrac{14:2}{8:2}=\dfrac{7}{4}[/tex]

Answer:

Count up however many squares are in the grip paper, and if it's not all the way full call it 1/2. Then add your half squares together, then add your whole squares to your half squares

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

A parallel line means equal m values, so the slope of the equation has to be 3.

Then, we can plug in the (1,6) to each of the equations with 3 as a slope and see if they are equal to each other.

B. 6 = 3 + 3

B. 6 = 6

So B is the correct equation.