Choose the expression that represents a quadratic expression. 9x − 2 5x2 9x − 1 −2x3 8x2 − 7x 1 x4 − 12x3 8x2 − 7x 1

EachEach value of time elapsed (in seconds) corresponding instantaneous velocity (in feet/second) are:2s= 96, 3s = 64, 4s= 32, 5s = 0, 6s = -32, 7s = -64. 8s= -96, 9s= -128.

Given equation:

f(t) = -16t² +160t

Velocity (v)=df(t)/dt

=-2×16t²+ 160t

=-32t+160

Hence:

-32t+160

1.     -32×(1) + 160 =    128ft/s

2.    -32×(2) + 160 =    96ft/s

3.    -32×(3) + 160 =    64ft/s

4.    -32×(4) + 160 =     32m/s

5.    -32×(5) + 160 =     0m/s

6.   -32×(6) + 160 =   -32m/s

7.    -32×(7) + 160 =    -64m/s

8.   -32×(8) + 160 =    -96m/s

9.    -32×(9) + 160 =   -128m/s

The pairs are;

2s= 96

3s = 64

4s= 32

5s = 0

6s = -32

7s = -64

8s= -96

9s= -128

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The diagonals of the qudrilateral will not be perpendicular to each other.

A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. If two segments are perpendicular, the multiplication of their slopes is -1.

The slope of a coordinate pair is given by the change in y divided by the change in x, that is:

For the diagonal AD the slope will be:-

Slope = ( -5 + 3 ) / ( -2 - 4) = ( 1 / 3 )

For the diagonal BC, the slope will be:-

Slope= ( 1 - 3) / ( 4 - 2 ) = ( -2 / 2) = -1

The multiplication of the two slopes will be,

M  =  ( 1 / 3 ) x -1 = ( - 1 / 3 )

Therefore,  the diagonals of the quadrilateral will not be perpendicular to each other. Because the product of the slope is not equal to -1.

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Answer:

The product of the slopes of the diagonals is -1.

Step-by-step explanation:

I had the question and got it right.

Answer:

20 and 35 dollars.

Step-by-step explanation:

x + x + 15 = 55

2x + 15 = 55

2x = 55 - 15

2x = 40

x = 40/2

x = 20

One of the brothers has saved 20 dollars, while the other has 35 dollars.

Step-by-step explanation:

2 equations with 2 variables.

the most common approach is

1. use one equation to express one variable by the other.

2. use this expression in the second equation and solve for the second variable.

3. use that solution in the original first equation and solve for the first variable.

the end.

0.05N + 0.10D = 2.20

N + D = 23

1. N = 23 - D

2. 0.05(23 - D) + 0.10D = 2.20

1.15 - 0.05D + 0.10D = 2.20

0.05D = 1.05

D = 1.05/0.05 = 21

3. N = 23 - D = 23 - 21 = 2

2 Nickels, 21 Dimes

The equation be 20.10 = X × 3 × 5/100 then, the value of X = 134.

To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.

The formula for Simple Interest exists PTR/100,

where, P = Principal

T = Time period in years

R = Rate of interest per annum.

Simple interest = PTR / 100

20.10 = X × 3 × 5/100

simplifying the above equation, we get

20.10 = 15X / 100

15X = 20.10 × 100 = 2010

X = 2010/15 = 134

X = 134.

Therefore, the value of X exists at 134.

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Answer: 6328723894

Step-by-step explanation:

The minimum cost to produce the product is $7.

What are functions?

To determine the minimum cost:

We have to determine the minimum cost of producing this product.

Since [tex]f(x) = 5x^{2} -70x+258[/tex].

Now, consider the equation [tex]5x^{2} -70x+258= 0[/tex].

Dividing the above equation by 5, we get

[tex]x^{2} -70x/5+258/5=0\\x^{2} -14x+258/5=0[/tex]

Now, considering the coefficient of 'x', dividing it by '2' and then adding and subtracting the square of the number which we got after dividing.

Since the coefficient of 'x' is 14, and half of 14 is '7'.

So, adding and subtracting from the above equation.

[tex]x^{2} -14x+(7)^{2} -(7)^{2}+258/5=0\\x^{2} -14x+49 -49+258/5=0\\(x-7)^{2} -49+258/5=0\\(x-7)^{2} +258-245/5=0\\(x-7)^{2} +13/5=0\\5(x-7)^{2} +13=0[/tex]

Now, we have to determine the minimum cost to produce the product.

Since [tex]f(x) = 5x^{2} -70x+258[/tex].

[tex]f'(x) = 10x-70[/tex]

Now, let f'(x)=0

[tex]10x-70=0\\10x=70[/tex]

Therefore, x=7

Now, consider which is greater than 0.

Therefore, x= 7 is the minimum cost.

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Answer: The minimum cost to produce the product is $13.

I apologize for the late answer, hope this helps in the future!

Step-by-step explanation:

To complete the square, we need to rewrite the given function in the form:

f(x) = a(x - h)^2 + k

where (h, k) is the coordinates of the vertex of the parabola defined by the function, and a is a positive constant that determines the shape of the parabola.

We start by factoring out the coefficient of x^2:

f(x) = 5(x^2 - 14x + 51.6)

To complete the square, we need to add and subtract a constant inside the parentheses that will allow us to write the expression inside the parentheses as a perfect square. The constant we need to add and subtract is half of the coefficient of x, squared:

f(x) = 5(x^2 - 14x + 51.6 + (7)^2 - (7)^2)

= 5((x - 7)^2 + 13)

Now we have the function in the desired form, with a = 5, h = 7, and k = 13. Since a is positive, we know that the vertex of the parabola is a minimum. Therefore, the minimum cost of producing the product is $13. So the correct answer is:

5(x − 7)2 + 13

Answer:

In mathematics, a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. For example, −3/7 is a rational number, as is every integer.

Answer:

Use the distance formula on both points AC and AB.

Distance formula is this:

\begin{gathered}d=\sqrt{(x2-x1)^2+(y2-y1)^2} \\\\d=\sqrt{(1--5)^2+(8--7)^2} \\\\d=\sqrt{(6)^2+(15)^2} \\\\d=\sqrt{36+225} \\\\d=\sqrt{261} \\\\\end{gathered}d=(x2−x1)2+(y2−y1)2d=(1−−5)2+(8−−7)2d=(6)2+(15)2d=36+225d=261

Distance for AC  is  16.16

Now do the same with the numbers for AB and get the distance of 5.39

2. To get the area, use the formula 1/2 x base x height

AB is the base and AC is the height.

1/2 x 16.16 x 5.39 = 43.55

the answer is 43.5

Answer:

Given:

Mass of the tennis ball=56.5 g

wavelength=5400 Angstroms

De-Broglie Wavelength = 5400 Angstrom.

= 5400 × 10⁻¹⁰ m.

Now, Using the Formula,

λ = h/mv

here,

h is the Planck's constant = 6.62 × 10⁻³⁴ J-s.

and v is the velocity of the tennis balls.

∴ 5400 × 10⁻¹⁰ = (6.62 × 10⁻³⁴)/ (0.054 × v)

⇒ 0.054v = (6.62 × 10⁻³⁴)/ (5400 × 10⁻¹⁰)

⇒ 0.054v = 0.0012 × 10⁻²⁴

⇒ v = 0.0012 × 10⁻²⁴/0.054

⇒ v = 0.023 × 10⁻²⁴ m/s.

Hence, the velocity of the tennis balls is 0.023 × 10⁻²⁴ m/s.

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The term that must be added to the equation x2+4x=1 to make it into a perfect square is 4.

Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. Since there is no ax2 term, the equation is linear if a = 0, not quadratic.

This is true because the Latin word quadratum, which means "square," plus the fact that the area of a square with side length x is equal to x2, make up what is known as the quadratic (or "square-like") definition of a polynomial equation with exponent two.

x²+4x=1

as, the x has coefficient 4.

so,

half the coefficient of x and add and subtract the square of the remaining.

x²+4x + 2 ² - 2² =1

Now,

make the whole square term

x²+4x + 2 ² - 4 - 1=0

( x + 2)² -5= 0

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The answer choice which is correct regarding the two functions is; For any value of x, g(x) will always be greater than h(x).

It follows from the task content that the functions given are; g(x) = x² and h(x) = –x².

On this note, since all values of x return a positive value for g(x) due to the square, it follows that the corresponding value of h(x) is always lesser.

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The probability of not choosing red when choosing one marble from the bag is 90%.

S = {1, 2, 3, 4, 5, 7}

Flipping a fair, two-sided coin.

probability that a student studied for exactly 1 hour is 0.23.

The probability of landing on yellow is less than the probability of landing on blue.

Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.

The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.

The experimental probability of drawing a spade is 0.15.

The probability of not choosing red when choosing one marble from the bag will be:

= (3 + 15 + 9)/30

= 27/30

= 90%

The sample space for rolling a fair seven-sided die will be S = {1, 2, 3, 4, 5, 7}.

The event that will have a sample space of S = {h, t} will be flipping a fair, two-sided coin.

The probability that a student studied for exactly 1 hour will be:

= 8/(1+8+2+5+9+7+3)

= 8/35

= 0.23

The true statement is that the probability of landing on yellow is less than the probability of landing on blue.

Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.

The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%. This was 13/40 = 32.5%.

The experimental probability of drawing a spade will be:

= 3/(7+3+6+4)

= 3/20

= 0.15.

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Answer: the sample space of the experiment from simultaneously flipping a coin and rolling a die consisted of: 2 × 6 = 12 possible outcomes.

Step-by-step explanation:

The sample space of 52 cards is all 52 possible outcomes, which is {Ace of Hearts, two of hearts, three of hearts...etc}.

The functions f(x) and g(x) are different functions

The function f(x) is a cubic function, while the function g(x) is a logarithmic function.

The common feature in both functions is their range

According to the statement

we have given that the some functions and we have to justify these functions.

The functions are given as:

f(x) = x³ + x² - 2x + 3 and g(x) = log(x) + 2

This means that the function f(x) is a cubic function, while the function g(x) is a logarithmic function.

The common key features of the functions

To do this, we plot the graphs of both functions

From the attached graph, we have the following features:

Function f(x)

Domain: -∞ < x < ∞

Range: -∞ < y < ∞

y - intercept = 3

x - intercepts = -2.37

Function g(x)

Domain: x > 0

Range: -∞ < y < ∞

y - intercept = None

x - intercepts = 0.01

By comparing the key features above, we can conclude that the common features in both functions is their range.

The functions f(x) and g(x) are different functions

The function f(x) is a cubic function, while the function g(x) is a logarithmic function.

The common feature in both functions is their range

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A statement which best defines an output is: B. an output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.

A function can be defined as a mathematical expression that defines and represents the relationship between two or more variable, which is typically modelled as input (x-values) and output (y-values).

In Mathematics, there are different types of functions and these include the following;

In this context, we can infer and logically deduce that a statement which best defines an output is that it's the result of a relation or the function rule, which usually are the y-values in a set of ordered pairs, on a table or a graph.

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Complete Question:

Which of the following best defines an output?

A. An output is the value that determines another based on the relation or the function rule, usually the x-values in a set of ordered pairs or on a table or graph.

B. An output is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.

C. An output is a special type of relation for which there is a rule that pairs each input with exactly one output.

D. An output is a set of ordered pairs in which no y-value repeats.

Answer: its C

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

The regression sum of squares (RSS) represents: a. The amount of variation in Y around its mean that the regression function can account for.

The regression sum of squares serves as the  sum of the differences that exist between the predicted value and the mean of the variable.

The Sum of Squared Error  however states the difference between the observed  and the predictive value.

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The weight of a 36-inch piece of PVC pipe is 0.20 pounds

The given parameters about the 36-inch piece of PVC pipe are

Height, h = 36 inches

Outside diameter, D = 0.82 inches

Inside diameter, d= 0.75 inches

The volume of the PVC pipe is then calculated as:

V = πh(D/2)^2 - πh(d/2)^2

Substitute the known parameters in the above equation

V = 3.14 * 36 * (0.82/2)^2 - 3.14 * 36 * (0.75/2)^2

Evaluate the quotients

V = 3.14 * 36 * 0.41^2 - 3.14 * 36 * 0.375^2

Evaluate the exponents

V = 3.14 * 36 * 0.1681 - 3.14 * 36 * 0.140625

Evaluate the products

V = 19.002024 - 15.89625

Evaluate the difference

V = 3.105774 cubic inches

From the question, we have:

Weight =  0.063 pounds per cubic inch

So, the total weight is

Total weight = 3.105774 cubic inches * 0.063 pounds per cubic inch

Evaluate the product

Total weight = 0.195663762 pounds

Approximate

Total weight = 0.20 pounds

Hence, the weight of a 36-inch piece of PVC pipe is 0.20 pounds

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The surface area of the cylinder is 18.84 square feet

The given parameters are

Height, h = 2 ft

Diameter, d = 2 ft

The radius (r) is half of the diameter (d)

This is calculated as:

Radius = Diameter/2

So, we have:

r = d/2

Substitute 2 for d

r = 2/2

Evaluate the quotient i.e. divide 2 by 1

r = 1

The surface area is then calculated using the following formula

A = 2πr² + 2πrh

Substitute the given values in the above equation

So, we have:

A = 2 * 3.14 * 1^2 + 2 * 3.14 * 1 * 2

Evaluate the exponents

A = 2 * 3.14 * 1 + 2 * 3.14 * 1 * 2

Evaluate the products

A = 6.28 + 12.56

Evaluate the sum

A = 18.84

Hence, the surface area of the cylinder with the given height and radius is 18.84 square feet

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The graph is in the attached image.

The value of (f - g)(x) is as follows:

(f - g)(x)  =  4x³ + 6x² - 7x - 1

f(x) = 4x³ + 6x² - 3x - 4

g(x) = 4x - 3

Let's find the function:

(f - g)(x)

Therefore,

(f - g)(x)  = 4x³ + 6x² - 3x - 4 - ( 4x - 3)

Hence, let's open the bracket

(f - g)(x)  = 4x³ + 6x² - 3x - 4 - 4x + 3

Let's combine like terms

(f - g)(x)  =  4x³ + 6x²  - 3x - 4x - 4 + 3

Therefore,

(f - g)(x)  =  4x³ + 6x² - 7x - 1

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Answer:

An arc of a circumference or of a circle mostly is a portion of the circumference. The length of an arc for all intents and purposes is simply the length of this portion of the circumference in a definitely major way. The circumference itself can particularly be considered an arc that goes around the circle in a fairly major way.

Answer:

  j = 19.6

  k = 25.9

  J = 49°

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationships between sides and angles in a right triangle.

The given side is opposite the given angle. We want to find the other acute angle and the missing sides: the hypotenuse, and the adjacent side. The relations involving the opposite side are ...

  Sin = Opposite/Hypotenuse   ⇒   Hypotenuse = Opposite/Sin

  Tan = Opposite/Adjacent   ⇒   Adjacent = Opposite/Tan

Of course, the acute angles in a right triangle are complementary, so we can use that fact to find the missing angle.

  Hypotenuse = Opposite/Sin

  IJ = 17/sin(41°) ≈ 25.9

  Adjacent = Opposite/Tan

 IK = 17/tan(41°) ≈ 19.6

  Angle J = 90° -41° = 49°

In summary, ...

  j = 19.6

  k = 25.9

  J = 49°

Answer:

x = 4, y = 1

Step-by-step explanation:

y = (1/4)x  

2x + 4y = 12

replace y with something x

2x + 4(1/4)x = 12

3x = 12

x = 4

so y = 1

Answer:

C

Step-by-step explanation:

Givens

r = 2 cm

h = 15 cm

pi = 3.14                                    The question does not expect a number for pi

Formula

V = (1/3) pi r^2 h                       Substitute givens into formula

Solution

V = 1/3 * pi * 2^2 * 15               Combine. Remember pi is left as it is

V = 1/3 * pi * 4 * 15                    

V = 1/3 pi * 60                         Divide 60 by 3

V = 20 pi

Based on the various costs resulting from the lease terms at the local dealership, the total cash to pay at signing is $5,480

This can be found by the formula:

= Down payment + Monthly payment + Security deposit + Acquisition fee

Solving gives:

= 4,100 + 475 + 415 + 490

= $5,480

In conclusion, option A is correct.

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Answer: B. $5005

Step-by-step explanation:

The car speed measurements that represent the same level of accuracy compared to the speed limit sign is 64mph (option D).

Accuracy is the exact conformity to truth or the degree of conformity of a measure to a true or standard value.

Accuracy is different from precision as precision deals with the closeness of an observed value with a true value.

According to this question, a highway sign shows a speed limit of 65 miles per hour. This suggests that a car speed measurement that will represent the same level of accuracy compared to the speed limit sign is 64mph.

64mph is the closest speed measurement to 65mph that does not exceed this speed limit. However, 66 mph is also close but exceeds the true value for the speed limit.

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The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

The graph of f(x) = x + 3 and g(x) = x is sketched using the geogebra tool. The way of determining the graph of f(x) + g(x) is by adding the y-coordinate of g(x) to the y-coordinate of f(x).

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Using the total weight the number of red, green and yellow colour are 2, 4 and 3 respectively.

The total number of reds, yellows, and greens on a scale is 9.

The reds weighed 3 pounds each, the yellows weighed 6 pounds each, and the greens weighed 5 pounds each. The total weight is 44

pounds. There are 2 more greens than reds.

Therefore,

let

x = number of reds

number of greens = x + 2

y = number of yellow

Therefore,

x + x + 2 + y = 9

2x + y = 7

3x + 6y + 5(x + 2) = 44

3x + 6y + 5x + 10 = 44

8x + 6y = 34

Hence,

2x + y = 7

8x + 6y = 34

8x + 4y = 28

8x + 6y = 34

2y = 6

y = 6 / 2

y = 3

2x + 3 = 7

2x = 7 - 3

2x  = 4

x = 4 / 2

x = 2

Therefore,

the number red colour = 2

the number of green colour = 2 + 2 = 4

the number of yellow colour = 3

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