match the simplified expressions to an equivalent expression

The quadratic functions are: f(x) = 0.03x² for Design A and g(x) = 0.024x² for Design B.

A quadratic function is a type of polynomial function of the form f(x) = ax² + bx + c, where a, b, and c are constants and x is the variable. In a quadratic function, the highest power of the variable is 2.

The graph of a quadratic function is a parabola, which is a U-shaped curve that opens either upwards or downwards depending on the sign of the coefficient a. If a > 0, the parabola opens upwards, and if a < 0, the parabola opens downwards. The vertex of the parabola, which is the point where the curve changes direction, is given by the coordinates (-b/2a, f(-b/2a)).

Quadratic functions have a wide range of applications in various fields such as physics, engineering, economics, and finance. For example, they can be used to model the motion of projectiles, the trajectory of a rocket, the shape of a bridge arch, the optimization of business profits, and the behavior of financial markets.

Let's assume that each side of the cube has a length of x inches. Then, the surface area of the cube is 6x² square inches.

a. For Design A with a cost of $0.005 per square inch, the total cardboard cost can be calculated using the quadratic function:

f(x) = 0.005(6x²) = 0.03x²

b. For Design B with a cost of $0.004 per square inch, the total cardboard cost can be calculated using the quadratic function:

g(x) = 0.004(6x²) = 0.024x²

Therefore, the quadratic functions are:

f(x) = 0.03x² for Design A

g(x) = 0.024x² for Design B

To know more about cube visit:

https://brainly.com/question/29023639

#SPJ1

The complete question is:

Answer:

✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️✔️

Answer:

x^2 - 9 = 0

Step-by-step explanation:

its right one.......

answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

The two integers are equal to 1 and 7 respectively.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Let x represent the smaller number. Then the given relationships say ...

1/x + 2/(x+6) = 9/7

Multiplying by 7x(x+6), we have ...

7(x+6) +14x = 9x(x+6)

9x² +54x = 21x +42 . . . . .eliminate parentheses, swap sides

9x² +33x = 42 . . . . . . . . ...subtract 21x

3x² +11 -14 = 0 . . . . . . . . . .subtract 42 and divide by 3

(3x +14)(x -1) = 0 . . . . . . . . factor

Values of x that make this true are x = 1 and x = -14/3. Then for the positive integer x=1, the other integer is x+6=7.

Therefore, the two integers are equal to 1 and 7 respectively.

To know more about an expression follow

https://brainly.com/question/4686531

#SPJ1

The distance between the coordinates R and S is 4 units and the distance between T and U is √26 units.

The distance formula is a formula used to find the distance between two points in a two- or three-dimensional space. The formula is:

\(d = \sqrt{((x_2-x_1)^2+(y_2-y_1)^2)}\)

Where d is the distance between the two points (x1,y1) and (2, 2),

Using the distance formula, we can find the distance between any two points in a two-dimensional space.

For example, to find the distance between points R(-1.0) and S(3.0), we can use the distance formula:

\(d= \sqrt{(3-(-1))^2+(0-0)^2)} = \sqrt{(16+0)}\\= \sqrt{(16)}\\=4\)

Therefore, the distance between R(-1,0) and S(3,0) is 4 units. Similarly, we can find the distances between any other pair of points using the distance formula.

Distance between T and U is -

T(2, -3), U(-3, -2)

\(=\sqrt{(-3-2)^2 + (-2 - (-3))^2} \\=\sqrt{25 + 1}\\= \sqrt{26}\\\)

Learn more about coordinates here:

brainly.com/question/16634867

#SPJ1

Find the distance between following points -

R(-1,0), S(3, 0)

T(2, -3), U(-3, -2);

Answer:

C

Step-by-step explanation:

one-sixth of a number = 1/6 ·n

one-sixth of a number, decreased by 7 = (1/6 ·n) - 7

'at most 45' means values equal to 45 or less: ≤

~Brainly ACE

If you have questions ask

The speed of the plane is equal to 120 mph.

In Mathematics and Geometry, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using miles per hour (mph).

Mathematically, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

Time = distance/speed

Let the variable s represent the speed of the plane in miles per hour. Therefore, an equation that models the situation can be written as follows;

240/s = 80/s - 80

80s = 240s - 19200

19200 = 160s

s = 19200/160

s = 120 mph.

Read more on speed here: https://brainly.com/question/29445231

#SPJ1

Answer:

30.5

Step-by-step explanation:

This sequence is defined by f(n)=6.5 + 4.5

The term inside the parentheses (n) is the value you should input to get an output.

n varies from 0 to infinity

Now to find the fifth term put in mind that 0 is the first term.

This means that f(5) isn't the fifth term. In fact, it's the sixth term. So f(4) is the fifth term.

To find f(4) replace n by 4.

f(4) = 6.5 *4 +4.5 = 26+4.5=30.5

The relationship in this problem is not proportional, as there are different ratios between the number of people and the number of cars washed.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

The ratios between the output and the inputs are given as follows:

Different ratios, hence the relationship is not proportional.

A similar problem, also featuring proportional relationships, is presented at https://brainly.com/question/7723640

#SPJ1

Answer:

20

Step-by-step explanation:

5 times 4 = 20

Answer:

H

Step-by-step explanation:

This is because a rectangle can be divided into two triangles.

Answer:

are u asking what is 70 divided by 200? cause its 0.35

Step-by-step explanation:

30 gallons of 28% butterfat and 30 gallons of 16% butterfat should be combined to create a 60-gallon mixture that is 22 % butterfat.

Let x gallon of 28% butterfat mixed with the y gallon of 16% butterfat to obtain 60 gallons of 22.5% butterfat,

⇒ x + y = 60 ⇒ x = 60 - y ----(1),

Quantity of butterfat in x gallon + quantity of butterfat in y gallon = total quantity of butterfat,

⇒ 28% of x + 16% of y = 22% of 60

⇒ 0.28x + 0.16y = 0.22 × 60

⇒ 0.28x + 0.16y = 13.2

⇒ 28x + 16y = 1320

⇒ 14x + 8y = 660

From equation (1),

14(60-y) + 8y = 660

840 - 14y + 8y = 660

6y = 180

y = 30

Again from equation (1),

x = 60 - y

= 60 - 30

= 30

Hence, 30 gallons of 28% butterfat and 30 gallons of 16% butterfat are combined to create a 60-gallon mixture that is 22%

To learn more about percentages;

https://brainly.com/question/28773949

#SPJ1

Answer:

42

Step-by-step explanation:

2,​4,6,10,​16,26,​___

The pattern is adding the previous two numbers to get the next number

2+4 = 6

4+6 = 10

6+10 = 16

10+16 = 26

16+26 =42

Answer:

Step-by-step explanation:

you take away 1 from 2 and that leaves you with 1

Answer:

Let's say I have two apples. You want one too! I give you one, and how many do I have left? 1

What I am explaining here is that if you take one away from two, it becomes one.

Answer:

its 40

Step-by-step explanation:

i think

Integration is the process of combining the quantitative and qualitative data collecting and analysis strands of a mixed methods study for comparison and analysis, or for one strand to inform the other.

Let, 1 + x = t

differentiate the assumption

dx = dt

Substitute the values

=> ∫dt/t

=> ln t

In terms of x

=> ln(1 + x)²

Let, x = tan A

differentiate the assumption

dx = sec²A dA

Substitute the values

=>∫(sec²A dA)/(1 + tan²A)

=> ∫ dA

=> A

In terms of x

=> tan⁻¹x

Let, 1 + x² = t

differentiate the assumption

2xdx = dt

Substitute the values

=> ∫dt/2t

=> ln 2t²

In terms of x

=> ln(1 + x²)²

=> ∫(x² +1 - 1)dx/(1 + x²)

=> ∫dx + ∫dx/(1 + x²)

Now we can solve this as problem 2

= ∫sin x.(1 - cos²x) dx

= ∫sin x dx - ∫sin x. cos²x dx --- (1)

= I₁ - I₂ , where I₁ = ∫sin x dx and I₂ = ∫sin x. cos²x dx

Now, I₁ = ∫sin x dx = -cos x + C₁, where C₁ is the constant of integration ---- (2)

For I₂ = ∫sin x. cos²x dx, assume cos x = u ⇒ -sin x dx = du ⇒ sin x dx = -du

I₂ = ∫sin x. cos²x dx

= ∫u² (-du)

= - ∫u² du

= - u³/3 + C₂, where C₂ is the constant of integration

= (-1/3) cos³x + C2 ---- (3)

Substitute the values from (2) and (3) in (1),

∫sin³x dx = (-cos x + C₁) - ((-1/3) cos³x + C₂)

= -cos x + (1/3) cos³x + C₁ - C₂

= -cos x + (1/3) cos³x + C, where C = C₁ - C₂

⇒ ∫sin³x dx = -cos x + (1/3) cos³x + C

Learn more about mixed integration here:

https://brainly.com/question/14406088

#SPJ1

The straight-line distance between Akira's house and Cooper's house is 6.13 kilometers (rounded to the nearest tenth)

Given that,To get from home to his friend Akira's house, Jaden would have to walk 2.8 kilometers due east.The straight-line distance between Akira's house and Cooper's house is given by the distance between two points in a coordinate plane. Let the home be the origin (0, 0) of the coordinate plane and Akira's house be represented by the point (2.8, 4.7). Similarly, let Cooper's house be represented by the point (8.3, 7.4).The distance formula between the two points (2.8, 4.7) and (8.3, 7.4) is given by:distance = √[(8.3 - 2.8)² + (7.4 - 4.7)²]= √[5.5² + 2.7²]= √(30.25 + 7.29)= √37.54= 6.13 km (rounded to the nearest tenth)

for more search question distance

https://brainly.com/question/30395212

#SPJ8

The function shown on the graph is a sine function.

In the question, we are asked to identify the function that has been shown in the graph.

A trigonometric function called sin x, where x is the angle under discussion, stands for the sine of an angle. The sine function is the proportion between the perpendicular and hypotenuse of a right-angled triangle. In other words, it is the ratio of the hypotenuse to the side opposite the angle under examination, and its value changes as the angle changes. In the study of physics, sound and light waves are represented by the sine function.

Since sin x is defined for any x in (-∞, ∞) the domain of the sine function is all real integers. As the value of sin x does not exceed this, its range is [-1, 1], in contrast. The sine function's graph resembles an oscillating wave between -1 and 1. Additionally, sin x has a period of 2π since its value repeats every 2π radians. The domain and range of sine function can also be observed via its graph.

The graph shown in the figure satisfies all the conditions of being a sine graph.

Thus, the function shown on the graph is a sine function

.

Learn more about the sine function at

https://brainly.com/question/9565966

#SPJ9

The statements that are true regarding the expression with the exponents -1, -3, and 1 are;

An exponent is a quantity or power to which a value, expression or number is to be raised.

The specified expression can be presented as follows;

8⁻¹ × 8⁻³ × 8

Therefore; 8⁻¹ × 8⁻³ × 8 = 8⁽⁻¹ ⁺ ⁻³ ⁺ ¹⁾ = 8⁻³ = 1/8³

1/8³ = 1/512

Similarly, we get; 8⁷ × 8⁻¹⁰ = 8⁽⁷ ⁻ ¹⁰⁾ = 8⁻³ = 1/8³

Learn more on exponents here: https://brainly.com/question/29831670

#SPJ1

Answer:

Question  5

    correct option is  A

Question 6

    correct option is  D

Question 7  

      correct option is  A  

Step-by-step explanation:

Considering question 5

From the question we are told that

     The population proportion considered is  \(p = 0.25\)

      The sample size is  n  =  200

      The number that had a personal computer at home is  \(k = 65\)

      The  level of significance is  \(\alpha = 0.01\)

The null hypothesis is  \(H_o : p = 0.25\)

The alternative hypothesis is  \(H_a : p > 0.25\)

Generally from the z-table the critical value of  \(\alpha = 0.01\)  to the right of the curve is

          \(z_{\alpha } = 2.33\)

Generally given that it is a right-tailed test , the rejection region is  

      z > 2.33

Considering question 6

  The sample size is  n = 20

  The standard deviation is  \(s = 2\)

   The sample mean is  \(\=x = 6.3\)

   The  population mean   \(\mu = 6.7\)

Generally the test statistics is mathematically represented as

          \(t = \frac{ \= x - \mu }{\frac{s}{\sqrt{n} } }\)

=>       \(t = \frac{ 6.3 - 6.7 }{ \frac{ 2}{ \sqrt{20} } }\)

=>       \(t = -0.894\)

Considering question 7

  The sample size is  n = 60

   The sample mean is  \(x = 39\)

   The  population proportion    \(p = 0.85\)

Gnerally the sample proportion is mathematically represented as  

           \(\^ p = \frac{x}{n}\)

=>       \(\^ p = \frac{39}{60}\)  

=>       \(\^ p = 0.65\)

Generally the standard error of this distribution is mathematically represented as

     \(SE = \sqrt{ \frac{ p(1 - p ) }{ n } }\)

=> \(SE = \sqrt{ \frac{ 0.85 (1 - 0.85 ) }{ 60 } }\)

=> \(SE = 0.0461\)

Generally the test statistics is mathematically represented as

          \(z = \frac{ \^ p - p }{SE}\)

=>       \(z = \frac{ 0.65 - 0.85 }{0.0461}\)

=>       \(z = -4.34\)

The given values into the equation AE = 2a + 10. Therefore, The value of AE is 3 - x.

To find the value of AE, we can substitute the given values into the equation AE = 2a + 10.

Given:

AB = 10

AE = 2a + 10

ED = x + 3

CD = 4

Since AB is a segment on the line, it can be divided into AE and ED. Therefore, AB = AE + ED.

We know that AB = 10 and CD = 4. So, if we subtract CD from AB, we get AE + ED = 10 - 4.

AE + ED = 6.

Now, we can substitute the value of ED, which is x + 3, into the equation: AE + x + 3 = 6.

To find the value of AE, we need to isolate it on one side of the equation. Let's subtract x and 3 from both sides:

AE = 6 - x - 3.

Simplifying further, we get;

AE = 3 - x.

Therefore, the value of AE is 3 - x.

for such more question on value

https://brainly.com/question/27746495

#SPJ8

Answer:

Step-by-step explanation:

U={1,2,3,4,5,6,7,8,9,10}

A={2,4,6,8,10}

A'={1,3,5,7,9}

B={3,6,7,8,9}

C={1,3,4,5,6,10}

(A'UC)={1,3,4,5,6,7,9,10}

(A∩B)={6,8}

(A'∪C)∪(A∩B)={1,3,4,5,6,7,8,9,10}

Answer:

E'(-2,2)

J'(-1,-2)

R'(-3,-3)

S'(-5,-2)

Step-by-step explanation:

(x,y) → (-x,-y)

Answer:

15 people at each table

Step-by-step explanation:

1) divide total number of people by number of tables

240/16

2) solve

15 people at each table

all work should be in the picture, lmk if theres anything confusing