Please help me with this math question!

The range of the function f (x) = (x - 1)² when the domain is {-5,0,5} is,

⇒ {36, 1, 16}

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable

Given that;

The function is,

⇒ f (x) = (x - 1)²

And, domain is {-5,0,5}.

Now, We can find the value of range as;

Put x = - 5 in above function,

⇒ f (x) = (x - 1)²

⇒ f (x) = (- 5 - 1)²

⇒ f (x) = (- 6)²

⇒ f (x) = 36

Put x = 0 in above function,

⇒ f (x) = (x - 1)²

⇒ f (x) = (0 - 1)²

⇒ f (x) = (- 1)²

⇒ f (x) = 1

Put x =  5 in above function,

⇒ f (x) = (x - 1)²

⇒ f (x) = ( 5 - 1)²

⇒ f (x) = ( 4)²

⇒ f (x) = 16

Thus, The range of the function f (x) = (x - 1)² when the domain is {-5,0,5} is,

⇒ {36, 1, 16}

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Answer:

1. 64cm² , 2. 240yd² , 3.≈220.5cm² , 4.≈193.4m² , 5. 38.6ft² , 6. ≈78.1yd² , 7. ≈120.7

Step-by-step explanation:

1. A=12x4.5+2x5 , 2. A=24x8+0.5x12x8 3. A=0.5x16x15+0.5x8²π ,4. A=7x15+0.5(15/2)² 12 ,5. A=3.6(16/2)+0.5x7x2.8 ,6. A=8(16/2)+0.5x9π ,7. A=(8/4)x5²xcot(180/8)

Answer:

[tex]P (t) = 580e ^ {0.18t}[/tex]   or  [tex]P (t) = 580 (1.18) ^ t[/tex]

Step-by-step explanation:

There are two models of exponential growth that you can use to predict the population of bacteria after t hours.

I) [tex]P (t) = pe ^ {rt}[/tex]

II) [tex]P (t) = p (1 + r) ^ t[/tex]

Where

p is the initial population of bacteria

r is the growth rate

t is the time in hours.

In this case we know that:

[tex]p = 580\\\\r = \frac{18}{100}\\\\r = 0.18[/tex]

Then the equations that can be used to predict the population of bacteria after t hours are:

I) [tex]P (t) = 580e ^ {0.18t}[/tex]

II)[tex]P (t) = 580 (1 + 0.18) ^ t[/tex]

Answer:

The EOC is an exam that is more logical, what I can recommend is to study the packages the teacher gave you and also study at USATESTPREP that can help you a lot

Answer:

The equation of the line is y = 7x - 10

Step-by-step explanation:

* Lets revise the form of the equation

- The form of the equation of a line is y = mx + c , where m is the slope

  of the line and c is the y-intercept

- The y-intercept means the line intersect the y-axis at point (0 , c)

- The slope of the line which passes through points (x1 , y1) , (x2 , y2)

 is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

* Lets solve the problem

∵ The y-intercept is y = -10

∴ The line intersects the y-axis at point (0 , -10)

∵ The line passes through the points (2 , 4) and (0 , -10)

- Lets find the slope of the line using the rule of the slope above

∵ [tex]m=\frac{-10-4}{0-2}=\frac{-14}{-2}=7[/tex]

∴ The slope of the line is 7

∵ c is the y-intercept

∵ The y-intercept is y = -10

∴ c = -10

∵ y = mx + c

∴ y = 7x + -10

∴ y = 7x - 10

* The equation of the line is y = 7x - 10

Answer: Assuming a unit of apples is one pound, the answer is .69 cents

Step-by-step explanation:

3.45 / 5 = .69

Answer:

One point:  (2/3, 0)

Step-by-step explanation:

The fastest way to determine this is to find the discriminant, b^2-4ac:

discriminant = (-12)^2 - 4(9)(4) = 144 - 144 = 0

The rule here states that if the discriminant is 0, the function has two real, equal roots.  Those roots are

       -(-12) ± √0

x =   ---------------- = 12/18, or 2/3.

             2(9)

The graph touches the x-axis at x = 2/3, but does not cross it.  In other words, the graph intersects the x-axis at only one x value:  2/3.

x = ------------------

The graph of the function y = 9x² - 12x + 4 intersect the x-axis at [tex]x = \frac{2}{3}[/tex] only.

The x-intercepts are the points where the graph intersects the x-axis. The vertex is the point that defines the minimum or maximum of a parabola.

We have,

y = 9x² - 12x + 4

Now,

So, to get the x-intercept,

Put y = 0,

i.e.

0 = 9x² - 12x + 4

Now,

Using the mid term splitting method,

0 = 9x² - 12x + 4

0 = 9x² - 6x - 6x + 4

0 = 3x(3x - 2) -23(x - 2)

i.e.

0 = (3x - 2) (3x - 2)

Now,

3x - 2 = 0

⇒ [tex]x = \frac{2}{3}[/tex]

And,

Now,

3x - 2 = 0

⇒ [tex]x = \frac{2}{3}[/tex] ,

So,

The x -intercept is only at one point, i.e. [tex]x = \frac{2}{3}[/tex].

Hence, we can say that the graph of the function y = 9x² - 12x + 4 intersect the x-axis at [tex]x = \frac{2}{3}[/tex] only.

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Answer:

3 and 1/2

Step-by-step explanation:

because if one can holds 10 liters of gas, three cans would hold 30 because 10 times 3 is 30 plus the extra 5 liters in the remaining can

Answer:

7/10

Step-by-step explanation:

We have  liters of gas, and we need to figure out how many cans we can fill.

Hint #22 / 4

We need to divide the 7 liters by the 10 liters that each can holds.

Answer:

21.325 is the correct answer

Answer: 21.325

Explanation: 12.195+9.13

Answer:3360

Step-by-step explanation:

Answer:

The correct answer option is H. 4374.

Step-by-step explanation:

We are given the following geometric sequence and we are to find its 8th term:

[tex]\frac{2}{9}, \frac{2}{3}, 2,...[/tex]

Here [tex]a_1=\frac{2}{9}[/tex] and common ratio [tex](r) = \frac{\frac{2}{3} }{\frac{2}{9} } =3[/tex].

The formula we will use to find the 10th term is:

nth term = [tex]a_1 \times r^{(n-1)}[/tex]

Substituting the values in the formula to get:

10th term = [tex]\frac{2}{9} \times 3^{(10-1)}[/tex]

10th term = 4374

Answer:

B.  17%.

Step-by-step explanation:

The General Probability Addition Rule is

P(A∪B) = P(A) + P(B) − P(A∩B)   where P(A∪B) = P(A) or P(B)  and P(A∩B) = P(A) and P(B).

So applying this to our problem we have:

0.57 = 0.43 + 0.31 - P( household has a cat and a dog)

so the answer is 0.43 + 0.31 - 0.57

= 0.17 or 17%.

The probability that the household own both a cat and a dog will be 17%.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

The General Probability Addition Rule is

P(A∪B) = P(A) + P(B) − P(A∩B)   where P(A∪B) = P(A) or P(B)  and P(A∩B) = P(A) and P(B).

So applying this to our problem we have:

0.57 = 0.43 + 0.31 - P( household has a cat and a dog)

so the answer is 0.43 + 0.31 - 0.57

= 0.17 or 17%.

Hence the probability that the household own both a cat and a dog will be 17%.

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Answer:

b

Step-by-step explanation:

todo lol que tienes que hacer es hacer la cosa ricola sexta

Answer:

it is very simple -5 =(5)(-1)=(x+4)(2x-3).so compare( 5)=(x+4) and (x=1) it can be solved by mind.....(2x^2)+5x-7=0 then

These are the steps.

1. Write out the equation.

2. FInd any whole numbers and put them together and find any variables and put them together, both in parentheses.

3. Solve both equations in parentheses.

4. Divide -5 by 3 to find x. The answer is on step 5.

[tex]1. (2x - 3)(x + 4) = -5\\2. (-3 + 4)(2x + x) = -5\\3. (1)(3x) = -5\\4. 3x = -5\\5. x = -1.66[/tex]

The number line for the inequality n < -3 would have an open circle at -3 and be shaded to the left, representing all numbers less than -3.

When considering the inequality n < -3, the number line that represents the solutions to this inequality would show all the numbers that are less than -3. This means that any point to the left of -3 on the number line would be shaded to indicate that it is part of the solution set. Additionally, the number -3 would typically be represented with an open circle, indicating that -3 is not included in the set of solutions because the inequality is strictly less than, not less than or equal to.

If you were to graph this inequality on a number line, you would start at the point -3 and shade everything to the left of -3 going towards negative infinity. This visualization shows that n can take any value that is less than -3. Therefore, the number line for the solutions of n < -3 would look like a horizontal line with an open circle at -3 and a shaded region extending to the left from -3.

Answer:

25.13

Step-by-step explanation:

Since the Diameter is 8 the equation to find the Circumference is pi time D

3.14 x 8 equals 25.13274...

let's recall that the radius of a circle is half of the diameter, now, if the diameter say "d" got enlarged 8 times, to it became 8d, then the radius "r" got enlarged 8 times as well, namely 8r.

[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} r=8r \end{cases}\implies \stackrel{\textit{is 8 times larger than that of the original}}{C=2\pi (8r)\implies C=\stackrel{\downarrow }{8}[2\pi r]}[/tex]

Answer:

64 inches  : cross-section, cube, 16 inches

26 inches  : right rectangular prism, 10x 3 x 14 inches

48 inches  : cube with 12-inches edges

34 inches : rectangular prism, 5x12x4 diagonal of 13 inches

Step-by-step explanation:

right rectangular prism, 10x 3 x 14 inches

The cross-section is parallel to the base, so it cuts the height, maintaining the length and width.  So, we have:

P = 10 + 3 + 10 + 3 = 26 inches

cube with 12-inches edges

This time, the cross-section is done perpendicular to the base, but in this case it doesn't matter since it's a cube... so it could be done in any direction and it wouldn't change the result.

P = 12 + 12+ 12 + 12 = 48 inches

rectangular prism, 5x12x4 diagonal of 13 inches

The cut is done perpendicular to the base, but along a diagonal of 13 inches, so the height is preserved, and the diagonal length becomes the new side other than height.

P = 13 + 4 + 13 + 4 = 34 inches

cross-section, cube, 16 inches

Again, the cross-section is done parallel to the base, but in this case it doesn't matter since it's a cube... so it could be done in any direction and it wouldn't change the result.

P = 16 + 16 + 16 + 16 = 64 inches.

Answer:

points

Step-by-step explanation:

Answer:

The radius = 18 cm

Step-by-step explanation:

* Lets take about the inscribed triangle in a circle

- If the three vertices of a triangle lie on the circumference of a circle,

 then this triangle is inscribed in the circle

- The vertices of the triangle are inscribed angles in the circle

- The inscribed angle opposite to a circle's diameter is always a

  right angle (its measure is 90°)

- Now lets solve the problem

∵ Δ ABC is a right triangle at C

∴ m∠C = 90°

∵ Δ ABC is inscribed in a circle

∴ A , B , C lie on the circumference of the circle

∴ ∠A , ∠B , ∠C are inscribed angles in the circle

∴ m∠C = 90°

∵ ∠C is opposite to the side AB

∴ AB is the diameter of the circle ⇒ from the bold note above

∵ m∠B = 30°

∵ AC = 18 cm

- Lets use the trigonometry function to find the length of AB

* In Δ ABC

∵ AC is opposite to angle B

∵ AB is the hypotenuse

∵ sin Ф = opposite/hypotenuse

∴ sin B = AC/AB

∴ sin (30)° = 18/AB ⇒ using cross multiplication

∴ AB sin (30)° = 18 ⇒ divide both sides by sin (30)°

∴ AB = 18/sin(30)°

∵ sin(30)° = 1/2

∴ AB = 18/(1/2) = 36 cm

∵ AB is the diameter of the circle

∵ The length of the radius of a circle = 1/2 the length of the diameter

∴ The radius = 1/2 × 36 = 18 cm

Answer:

5

Step-by-step explanation:

8 quizzes / 2 weeks = 20 quizzes / x weeks

Cross multiply:

8x = 40

Divide:

x = 5

Harold will have to attend 5 weeks.

Answer:

Paul is taller

2 meters is 6.5 feet.

Answer:Paul is taller the answer will be 6.5.

Step-by-step explanation:You had to convert the meters into feet to see which one will be taller.

Answer: flower vase

Step-by-step explanation:

A container that has a liquid volume of about 1 liter at home is typically a soda bottle. A liter is a metric unit of capacity and is equivalent to 1,000 cubic centimeters or milliliters, making it a convenient measure for everyday use.

An example of a container that you might find at home which, when filled, has a liquid volume of about 1 liter is a soda bottle. Liters and milliliters are metric units for measuring capacity. A liter is a convenient measure for everyday liquid volumes and is commonly used for beverages and other liquids in the home. Since a liter is equal to 1,000 milliliters, and taking into account that a juice box holds about 25 centiliters, which is 250 milliliters, a soda bottle's capacity is approximately four times that of a typical juice box. It's interesting to note that the liter can also be connected to cubic meters, as 1 liter is the same as 1,000 cubic centimeters (1,000 cm³), making these units interchangeable.

For this case we must factor the following expression:

[tex]m ^ 2-14m + 48[/tex]

We must look for two numbers that when multiplied give as a result "48", and when summed, give as a result "-12". These numbers are:

-6 and -8

[tex]-6 * -8 = 48\\-6-8 = -14[/tex]

So, we have:

[tex](m-6) (m-8)[/tex]

ANswer:

Option D

Answer:

Step-by-step explanation:

DDDDDDDDDDDDDDDDDD

Answer:

y = 1/4 x - 12.5

Step-by-step explanation:

8x + 2y = -8 (rewrite in y = mx + b form)

2y = -8x -8 (divide both sides by 2)

y = -4x -2 for first line

Perpendicular line L has "opposite/inverse" slope

y = -4x + b becomes y = 1/4 x + b

What's b (the y-intercept)?

Plug the point (2, -12) into the equation y = 1/4 x  + b to solve for b

-12 = 1/4 (2) + b

-12 = 1/2 + b (subtract 1/2 from both sides)

-12.5 =b (rewrite equation)

y = 1/4 x - 12.5

Answer:

4

te ayudara en las ecuaciones

The value of  [tex]8^(^2^/^3^)[/tex]  is equal to 4 by exponent property

To simplify the number [tex]8^(^2^/^3^)[/tex]

we can apply the property of exponents which states that [tex](a^m)^n = a^(^m^\times^n^).[/tex]

Now [tex]8^(^2^/^3^)[/tex], which means we need to raise 8 to the power of 2/3.

Now, let's rewrite 8 as a power of a base that is a perfect cube:

8 = 2³

[tex](2^3)^(^2^/^3^)[/tex]

Applying the exponent property mentioned earlier, we multiply the exponents:

[tex]2^(^3 ^\times^2^/^3^)[/tex]

2²

we get four, 4

Therefore,  [tex]8^(^2^/^3^)[/tex]  is equal to 4.

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Multiply the given dimensions by the scale factor of 4:

2 x 4 = 8

3 x 4 = 12

6 x 4 = 24

The volume of a pyramid is found by multiplying the Length x the width x the height and dividing by 3:

Volume = (8 x 12 x 24) / 3

Volume = 2304 / 3

Volume = 768 cubic units.

The answer is D.

The volume of the larger pyramid is 768 units³.

Scale factor is the ratio of the dimension of the given original object and the dimension of the new object from the original.

Given that,

A machine assembly requires two pyramid-shaped parts.

Volume of the pyramid = 1/3 × base area × height

If the larger pyramid has a scale factor of 4, each dimension is 4 times this pyramid.3

Base area of the larger pyramid = (4 × 3) × (4 × 2)

                                                     = 96 units²

Volume of the larger pyramid = 1/3 × 96 × (6 × 4)

                                                 = 768 units³

Hence the required volume is 768 units³.

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Answer:

no solution

Step-by-step explanation:

The solution to a system of equations given graphically is at the point of intersection of the 2 lines.

The 2 lines shown here are parallel and never intersect

Hence the system has no solution

Answer:

8-3r

Step-by-step explanation:

we know that

The conjugate is where we change the sign in the middle of two terms

In this problem

we have

8+3r

so

The conjugate is

8-3r

Answer:

8-3sqrt

Step-by-step explanation:

The correct answer is C. 12

If you were to line up all the numbers in chronological order, the order would be: 5, 8, 8, 10, 10, 10, 11, 12, 12, 14, 17, 17, 19, 20, 20, 21. Twelve is the center of all the numbers. There's eight numbers on each side of 12. Hope this helps! Please mark brainliest! Thank you v much! :)

Answer:

C) 12

Step-by-step explanation:

Step 1: List the numbers in order from least to greatest. Take a look at the data and cross out numbers as you place them. There are 16 numbers. The order of these numbers are:

5, 8, 8, 10, 10, 10, 11, 12, 12, 14, 17, 17, 19, 20, 20, 21

Step 2: Cross out numbers from each side to the furthest left and right. By the time you do this, the remaining numbers should be 12 and 12.

Step 3: Find the median. Because there are two numbers left, you do this by adding the two remaining numbers and divinding them by 2. However, because they are the same number, you can safely say that the median is 12.

Answer:

The correct answer option is A. positive.

Step-by-step explanation:

When an exponent or a power is an even number and the base is a negative number, the value is always positive.

Suppose we have a negative base [tex] - 3 [/tex] and a power which is even, lets say, [tex] 6 [/tex] so what we get is a positive value.

[tex](-3)^6=729[/tex]

Therefore, a negative base with even power is always a positive value.

Answer: A. positive

Step-by-step explanation:

We know that powers are written in this form:

[tex]b^m[/tex]

Where "b" is the base and "m" is the exponent.

By definition, the exponent indicates how many times to base must be multiplied by itself. Then, if the base is negative and the exponent is an even number, you get:

[tex](-3)^4=(-3)(-3)(-3)(-3)=81\\\\\\(-2)^2=(-2)(-2)=2\\\\\\(-5)^6=(-5)(-5)(-5)(-5)(-5)(-5)=15,625[/tex]

Therefore, when an exponent of a power is an even number and the base is a negative number, the value is always positive.

Answer:

A =  617 yd², to the nearest yard

That distance is called the "circumference," and its formula is C = 2πr.

We need r to find the area of the park.  So we solve C = 2πr for r:

          C

r   = -------    

        2π

Substituting 88 yd for C, we get r = (88 yd) / (6.28) = 14.01 yd

The formula for the area of this circular park is A = πr².

Here, r = 14.01 yd, so the area of this park is:

A = π(14.01 yd)² = 3.14(196.36 yd²) = 617 yd², to the nearest yard.

The area of the park is [tex]A = 617 yd^2[/tex], to the nearest yard.

That distance is called the circumference and

We have to determine the area of the park

The circumference of the circle is C = 2πr.

We need r to find the area of the park.

So we solve C = 2πr for r:

[tex]r=\frac{C}{2\pi}[/tex]

Substituting 88 yd for C,

We get r = (88 yd) / (6.28)

r= 14.01 yd

The formula for the area of this circular park is

A = πr².

Here, r = 14.01 yd, so the area of this park is,

[tex]A = \pi (14.01 yd)^2[/tex]

[tex]A = 3.14(196.36 yd^2)[/tex]

[tex]A = 617 yd^2[/tex], to the nearest yard.

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