A rectangular garden has a total area of 48 square yards. What are two possible side lengths for this garden?

The quadratic function f(x)= 3x2 - 2x + 5 has an average rate of change from x = -2 to x = 0 of - 14.

Qualities and their permutations, theorems and surrounding structures, morphologies and their placements, and locations where they can be encountered are all included in the study of mathematics. The association between a group of inputs, of which each has a related output, is referred to as a "function." A function is a relationship between inputs and outputs where each input produces a single, unique result. Every function has a domain and a requires great, often known as a scope. F is typically used to denote functions (x). An x is the input. Based on the following criteria, there are four primary categories of functions that are available: on procedures, one-to-one functions, several more functions, within functions, and on functions.

given

The slope formula, (y2-y1)/, states that the average rate of change is the ratio of the change in y to the change in x.

(x2-x1) We have f(x), which is equivalent to byt but instead of y.

f(-2) - f (0)  /   -2

= f(14+4 + 5 ) + 5 / -2

28 / - 2

= -14

The quadratic function f(x)= 3x2 - 2x + 5 has an average rate of change from x = -2 to x = 0 of - 14.

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The greatest acceleration when the unbalanced force is applied will be experienced by the least weighted box ( i.e., the mass of 2 kg)

Acceleration: it is defined as rate of change of velocity with respect to time.

Unbalanced Force:  it means that the force applied in one direction is greatest than the force applied in the opposite direction.

Given that, F = 8n.

let us assume that the boxes are of 2kg, 4 kg, 6 kg and 8 kg.

According to the 2nd law of motion: the external unbalanced force is directly proportional to rate of change of momentum or Force is equal to the product of mass and acceleration.

                         F = m × a

                 ⇒     a = F/ m

where,  F is Force, m is mass and a is acceleration.

Now, acceleration of the box of 2kg = 8÷2 = 4 m/s²

         acceleration of the box of 4kg = 8÷ 4 = 2 m/m²

         acceleration of the box of 6 kg = 8÷ 6 = 1.34 m/s²

         acceleration of the box of 8kg = 8÷ 8 = 1 m/s²

∴ the box with mass of 2kg experience the greatest acceleration.

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Given:

Height of the tree

To find the height of the tree, we use ratio/proportion.

So, we let x be the height of the tree and use the formula:

Height of man/length of man's shadow = x/length of the tree's shadow

Therefore ,the height of the tree is 20 ft.

Answer:

$5,500

Step-by-step explanation:

Steve is Darrlyn house for $360,000

Steve loan amount $275,000

He agreed to pay 2 points at closing

Therefore the amount steve will pay for points can be calculated as follow

= 275,000 × 2/100

= 275,000 × 0.02

= 5,500

Hence Steve will pay $5,500

Answer:

area of the circle,

radius=10m

diameter=20m

πr²

3.14×100

314m²

area of the triangle=1/2×20×10

=100

area of the shaded area=314-100=214 m²

the answer is option H

As per the function represented by the table, the correct function notation is f(5) = 9.

Given a function represented by a table is shown as follows:

x| 2 | 5 | 9

y| 9 | 14| 5

We can say that the ordered pair given in the bottom row can be written using function notation as f(5) = 9.

Function notation is a method to represent functions, and it is usually used in mathematics to make it easier to work with functions.

It helps to identify the input, the function, and the output of a function.

Using function notation:In function notation, the input is represented by the variable x, and the output is represented by the variable y.

Therefore, we can say that f(x) = y.

Using the table, we can see that when x = 5, y = 14.

So, f(5) = 14 is the correct answer to the given question.

Here, we see that the x and y coordinates are swapped from what we are used to.

The correct function notation is f(5) = 9.

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Answer:

x = 33.2

Step-by-step explanation:

Use Sine

Sine 56 = x / 40

Sine of 56 is 0.829

0.829 = x / 40

Multiply 40 on both sides

33.16 = x

Round to the nearest tenth

33.2

Trigonometry -

\( \frac{x}{40} = \frac{ \sin(56) }{1} \)

Cross multiply!

\(40 \sin(56) = x\)

Use your calculator to determine x.

Answer: X is approximately 33.2

Answer:

- 8°

Step-by-step explanation:

Step 1:

40° + x + 58° + 90° = 180°       Sum of a Δ

Step 2:

188° + x = 180°       Combine Like Terms

Step 3:

x = 180° - 188°     Subtract 188 on both sides

Answer:

x = - 8°

Hope This Helps :)

There are 70 different types of pizzas could be ordered

A permutation is an act of arranging the objects or numbers in order.

Combinations are the way of selecting the objects or numbers from a group of objects or collection, in such a way that the order of the objects does not matter

Given,

Number of options on crust=2

Number of options on topping= 7

Number of options on size= 5

Therefore for each type of crust there are 7 different topping, for each toppings there are 5 different sizes

The total number ways of ordering pizza=2×7×5=70

Hence, there are 70 different types of pizzas could be ordered

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Answer:

(a) The volume of the pyramid 440.44 cube units

(b) No she doesn't

(c) The volume of the larger pyramid is 1,486.485 cube units

Step-by-step explanation:

The given parameters are;

The scale factor of the pyramids, S.F. = 2:3

The base area of the small pyramid, \(A_{b1}\) = 110.11 square units

The height of the small pyramid, h₁ = 12 units

(a) The volume of a pyramid, V = (1/3) × Area of base × The height of the pyramid

Therefore;

The volume of the small pyramid, V₁ = (1/3) × 110.11 square units × 12 units

V₁ = 440.44 cube units

The volume of the small pyramid, V₁ = 440.44 cube units

(b) No she does not have to go through all the hard work again to find the volume of the larger pyramid

She only has to make use of the scale factor relationships of the two pyramid to calculate the volume of the larger pyramid

The volume scale factor = (The linear scale factor)³

(c) The linear scale factor of the pyramids = 2:3 = 2/3

Therefore;

The volume scale factor of the pyramids = (2/3)³ = 8/27

To find the volume of the larger pyramid, V₂, from the volume of the smaller pyramid, V₁, we multiply the volume of the smaller pyramid, V₁,  by 27/8 as follows;

V₂ = V₁ × (27/8)

Therefore;

The volume of the larger pyramid, V₂ = 440.44 cube units × (27/8) = 1,486.485 cube units

The volume of the larger pyramid, V₂ = 1,486.485 cube units.

The answer to the given question would be as follows:

a). The volume of the pyramid would be:

\(440.44\) cube units

b). No, she doesn't have to do the hard work to find the larger pyramid's volume would be:

c). The volume for the larger pyramid would be:

\(1,486.485\) cube units

a). As we know,

The volume of pyramid \(=\) \((1/3)\) × Area of base × The height of the pyramid

The volume of Sarah's pyramid \(=\) \((1/3)\) × \(110.11\) square units × \(12\) units

∵ V₁ \(= 440.44\) cube units

b). No, Sarah will not have to repeat the hard work to determine the area of the larger pyramid.

The only thing she will have to consider is:

The volume scale factor \(= (The linearscalefactor)^3\)

c). The volume of a larger pyramid would be:

The pyramid's linear scale factor \(= 2:3 = 2/3\)

Thus,

The pyramid's volume scale \(= (2/3)^3 = 8/27\)

So,

The volume of a larger pyramid \(= V_{1}\) × (27/8)

\(= 440.44 cube units\) × \((27/8)\)

\(= 1,486.485\) cube units

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Answer: a) 7        b) -4         c) 15         d) -1        e) -8

Step-by-step explanation:

7x + 9 = 58

     -9   -9

7x       =  49

÷7         ÷7  

  x      =   7

x/2 - 12 =  -14

      +12   +12

x/2       =   -2

×2          ×2  

  x      =    -4

-3x + 33 =  -12

       -33   -33

-3x         =  -45

÷-3         ÷-3  

  x         =   15

8x + 16 =    8

      -16   -16

8x        =   -8

÷8          ÷8  

  x      =    -1

2x - 2 = -18

     +2   +2

2x       = -16

÷2         ÷2  

  x      =  -8

Constant of variation for given quadratic equation is 2/3

Correct option is a.

The ratio between two variables in a direct variation or the product of two variables in an inverse variation.

In the direct variation equations = k and y = k x,

and the inverse variation equations x y = k and

k is the constant of variation.

Given,

quadratic equation,

15y = 10x²

y = (10/15)x²

y = (2/3)x²

Comparing it with general form y = kx²

k = 2/3

Hence, 2/3 is constant of variation for the quadratic equation.

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The series to 10 term is

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512

An equation that represents a sequence based on a rule is called a recurrence relation.

Finding the following term, which is dependent upon the prior phrase, is made easier (previous term). We can readily predict the following term in a series if we know the preceding term.

The term is predicted by multiplying the preceding term by 2

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Answer:

s >= 150 and h>= 52

Step-by-step explanation:

1. 129 mph < S mph

2. h > 50 inches

Answer:

x = 2 and x = -1

Step-by-step explanation:

The zeroes of the function are found by setting g(x) equal to 0:

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

By the Zero Product Property, in order for this equation to be equal to 0, each of (x - 2) or (3x + 3) or both has to equal 0. So, set each equal:

x - 2 = 0

x = 2

3x + 3 = 0

3x = -3

x = -3/3 = -1

The zeroes are thus x = 2 and x = -1.

~ an aesthetics lover

Answer:

x=2 x=(-1)

Step-by-step:

Solve: (x-2)(3x+3)=0

= x-2=0                   3x+3=0

=x-2(+2)=0(+2)       =3x-3(-3)=0(-3)

=x=2                      =3x=(-3)

                              =3x/3=(-3)/3

                              =x=(-1)

Answer:

Step-by-step explanation:

Halie,  find angle EAD.... see it?   next think about the definition of vertical angles: each of the pairs of opposite angles made by two intersecting lines.

which angle is EAD  an opposite pair of?   ∠IAH  looks like a good one.  

The determinants for the given linear system are |A| = -19, |Ax| = -74, and |Ay| = 57.

A linear system is a collection of one or more linear equations involving one or more variables.

The given linear system's determinants are:

The coefficient matrix determinant, denoted by |A|

The x variable matrix determinant, denoted by |Ax|

The y variable matrix determinant, denoted by |Ay|

To find these determinants, we first need to write the coefficient matrix and the x and y variable matrices.

The coefficient matrix is the matrix of the coefficients of the variables

| 5 2 |

|-3 -5 |

The x variable matrix is obtained by replacing the x column in the coefficient matrix with the constants on the right-hand side of the equations:

| 14 2 |

| 3 -5 |

The y variable matrix is obtained by replacing the y column in the coefficient matrix with the constants:

| 5 14 |

|-3 3 |

Now we can calculate the determinants:

|A| = determinant of the coefficient matrix = (5)(-5) - (-3)(2) = -19

|Ax| = determinant of the x variable matrix = (14)(-5) - (2)(3) = -74

|Ay| = determinant of the y variable matrix = (5)(3) - (14)(-3) = 57

Therefore, the determinants for the given linear system are |A| = -19, |Ax| = -74, and |Ay| = 57.

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Answer:

x = -7/b

Step-by-step explanation:

bx = -7

Divide each side by b

bx/b = -7/b

x =-7/b

Solve the equation for x : bx = -7

Here we are provided to find for x so from the equation by cross multiplying we will remove b to the right hand side of the equation and then we can get x

bx = -7

Now, to cross multiply

x = -7/b

Therefore, the required answer is -7/b

Answer:

Josh has played 12 MORE matches then her. Not 12 TIMES as many matches. The correct answer would be he haas played 12 more matches then her or 3 times as many matches as her.

Step-by-step explanation:

ANSWER

320π ft³

EXPLANATION

The volume of a cylinder with a radius r and a height h is,

Where B is the area of the base, which is a circle, so the volume is,

In this case, r = 4 feet and h = 20 feet,

Hence, the volume of this cylinder is 320π cubic feet.

Answer:

\( - 2m - 5m = 9m - 12 \\ ⟶ - 2m - 5m - 9m = - 12 \\ ⟶ - 16m = - 12 \\ ⟶ - m = \frac{ - 12}{16} \\ ⟶ - m = \frac{ - 6}{8} \\ ⟶ m = - ( - \frac{6}{8} ) \\ ⟶m = \frac{6}{8} \)

\(m=0.75\)

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{m = 0.75}}}}}\)

Step-by-step explanation:

\( \sf{ - 2m - 5m = 9m - 12}\)

Collect like terms

⇒\( \sf{ - 7m = 9m - 12}\)

Move 9m to left hand side and change it's sign

⇒\( \sf{ - 7m - 9m = - 12}\)

Collect like terms

⇒\( \sf{ - 16m = - 12}\)

Divide both sides of the equation by -16

⇒\( \sf{ \frac{ - 16m}{ - 16} = \frac{ - 12}{ - 16} }\)

Calculate

⇒\( \sf{ m = 0.75}\)

Hope I helped!

Best regards!!

When you are doing calculations, you can usually tell when you need to change base by looking at the problem. If the problem includes fractions, a base other than 10 may be more efficient. If the problem includes exponents, a base other than 10 may be necessary.

When working with numbers, it is important to know what base the numbers are in in order to correctly perform calculations. The base of a number is the number of digits used to express it, meaning that the base of a number can range from base 2 (binary) to base 36 (base 36 uses the numbers 0-9 and the letters A-Z).

Changing the base of a number can be helpful when dealing with fractions, exponents, and other complex calculations. To change the base of a number, divide the number by the base and then divide the remainder by the base, continuing to divide until the remainder equals 0.

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The magnitude of the x-component of this vector is 9.05m.

The angle of inclination of the vector is calculated as;

θ = 90 ⁰ - 48.4 ⁰

θ = 41.6 ⁰

The magnitude of the x-component of the vector is calculated as;

Vx = 12.1 m x cos ( 41.6 )

Vx = 9.05 m

A vector can be represented by an ordered set of numbers, called components, that indicate the magnitude and direction of the vector in a particular coordinate system. The components of a vector can be added or subtracted using vector addition and subtraction, and multiplied by a scalar (a real number) using scalar multiplication.

Vectors can be visualized as arrows in a two- or three-dimensional space, where the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector. Vectors can also be represented as matrices, which can be used to perform various operations on vectors, such as dot product and cross product.

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Complete Question:-

Answer:

−18b+6

Step-by-step explanation:

6(−3b+1)

Use the distributive property to multiply 6 by −3b+1.

−18b+6

The cost function for the company is C(x) = 32,000 + (1/3)x + 444x, and the revenue function is R(x) = (1,476 - (2/3)x)x. The break-even points can be found by setting C(x) equal to R(x) and solving for x.

The cost function C(x) represents the total cost incurred by the company, which consists of fixed costs and variable costs per unit. The fixed costs are $32,000, and the variable cost per unit is given by (1/3)x + 444. Therefore, the cost function is C(x) = 32,000 + (1/3)x + 444x.

The revenue function R(x) represents the total revenue generated by selling x units of the product. The selling price per unit is given by 1,476 - (2/3)x. Therefore, the revenue function is R(x) = (1,476 - (2/3)x)x.

To find the break-even points, we set the cost function equal to the revenue function and solve for x. Therefore, we have the equation C(x) = R(x):

32,000 + (1/3)x + 444x = (1,476 - (2/3)x)x.

Simplifying and rearranging the equation will give us the break-even points, which are the values of x that make the cost equal to the revenue.

In conclusion, the cost function is C(x) = 32,000 + (1/3)x + 444x, and the revenue function is R(x) = (1,476 - (2/3)x)x. The break-even points can be found by setting C(x) equal to R(x) and solving for x.

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The circumstance that the score is located 5 points above the mean a central value, relatively close to the mean is when the population standard deviation is much greater than 5.

Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean. It is a popular measure of variability because it returns to the original units of measure of the data set.

Here, we have

We have to find under what circumstances is a score that is 5 points above the mean considered a central value--meaning it is relatively close to the mean.

We concluded from the above statement that when the population standard deviation is much greater than 5.

Hence, when the population standard deviation is much greater than 5 then, the score that is 5 points above the mean is considered a central value.

Therefore, the correct option is D.

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Answer:

Step-by-step explanation:

5x+5

Answer:

the first option will the correct answer

The average velocity for the [3,4] is 27m/s and for [4,5] is 37m/s

The average velocity can be found by taking the derivative of the position function and evaluating it at the midpoint of the interval.

The average velocity on the interval [3,4] is given by (s(4) - s(3)) / (4 - 3), which is equal to (s(4) - s(3)) / 1. Using the position function, s(t) = 5t^2 - 8t + 13, we find that s(4) = 5(4²) - 8(4) + 13 = 61 and s(3) = 5(3²) - 8(3) + 13 = 34. Therefore, the average velocity on the interval [3,4] is (61 - 34) / 1 = 27 m/s.

The average velocity on the interval [4,5] is given by (s(5) - s(4)) / (5 - 4), which is equal to (s(5) - s(4)) / 1. Using the position function, s(t) = 5t² - 8t + 13, we find that s(5) = 5(5²) - 8(5) + 13 = 98 and s(4) = 5(4²) - 8(4) + 13 = 61. Therefore, the average velocity on the interval [4,5] is (98 - 61) / 1 = 37 m/s.

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