Vue wonders how long the ball was in the air when it was 54 feet in the air so he writes the equation 54=-16s2+96s. Solve the equation for time(s) to determine how long the ball was in the air when it was 54 feet above the ground . Round your answer to the nearest hundredth of a second . On a piece of paper , Identify which of the following methods you used to solve this question : factoring , completing the square, the Quadratic Formula, using a graph. Then explain how your solution helps Vue answer his question

The area of the sector and length of the arc are 4.7 unit squared and 3.14 units respectively.

A sector is a portion of a circle which is enclosed between its two radii and the arc adjoining them.

The area of sector of a circle is the amount of space enclosed within the boundary of the sector.

Therefore,

area of the sector = 1 / 2 r²∅

area of the sector = 1 / 2 × 3² × π / 3

area of the sector = 9π / 6

area of the sector = 3 / 2 × 3.14

area of the sector = 4.71 units²

Length of the arc = r∅

where

Therefore,

Length of the arc =  3 × π / 3

Length of the arc = π

Length of the arc = 3.14 units

Therefore, the area of the sector is 4.71 units² and the length of the arc is  3.14 units.

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The statement about the functions that is true is (a) only g(x) is an even function.

From the question, we have the following parameters that can be used in our computation:

f(x) = √(x + 1) - 3

The graph of g(x)

The graph of g(x) is an even function

This is so because the graph remains unchanged under reflection in the y-axis.

However, the function f(x) is neither even nor odd

This is so because

Hence, the true statement is (a)

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The combined area of the shaded triangles in figure one is 2ab. We have four congruent right triangles given, with legs a and b. The formula to calculate the area of a right triangle is (leg * leg) / 2. So the area of one of the triangles is ab/2. We have four of these triangles, so ab/2 * 4 = 2ab.

The area of the unshaded square in figure one can be represented as c^2. Since the side of the square is given as c, its area must be c^2 (calculate the area of a square by multiplying its side length by itself).

The combined area of the unshaded squares in figure 2 can be represented by a^2 + b^2. Again, we find the areas of each square by multiplying the side lengths togther: (a * a) + (b * b) = a^2 + b^2.

Finally the areas of the squares in figure one and figure two show that a^2 + b^2 = c^2. This is because the shaded triangles in figure one take up the same area as that of figure two. And since the total figure areas are the same, the unshaded parts of each figure must be equal to each other. Therefore, we have a^2 + b^2 = c^2. This is also known as the Pythagorean Theorem.

Angle K has  a value of 63 degrees.

Given,

The triangle KLM

Angle L = 4x + 7

Angle K = 6x - 9

Angle M = 118° (Exterior)

We have to find the value of angle K.

Here,

Angle M (Interior) = 180 - 118 = 62° (linear pair of angles)

Now,

Angle L + Angle K + Angle M = 180° (Sum of interior angles of a triangle)

Then,

4x + 7 + 6x - 9 + 62 = 180

10x - 2 + 62 = 180

10x  + 60 = 180

10x = 180 - 60

x = 120/10

x = 12

Now,

Angle K = 6x - 9  = 6 × 12 - 9 = 72 - 9 = 63

That is,

The value of Angle K is 63 degrees.

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Answer:

To simplify this expression, we need to combine like terms. To do that, we need to combine terms that have the same variables raised to the same powers.

First, we will combine the terms in the first set of parentheses:

(4m²n² + 6m²n)

We see that the terms have the same variables, m and n, and the same powers, 2 and 1, respectively. We can combine these terms by adding their coefficients:

(4m²n² + 6m²n) = (4 + 6)m²n = 10m²n

Next, we will combine the terms in the second set of parentheses:

(8m²n^ - 7m²n² - 13m²n)

In this case, we see that the first two terms have the same variables and powers, so we can combine them by adding their coefficients:

(8m²n^ - 7m²n² - 13m²n) = (8 - 7)m²n^ - 13m²n = m²n^ - 13m²n

We can then combine the remaining term with the first term in the expression:

m²n^ - 13m²n + 10m²n = m²n^ + (-13 + 10)m²n = m²n^ - 3m²n

Finally, we will combine the terms in the third set of parentheses:

(14m²n - 2m^n² + 9m²n)

In this case, we see that the first two terms have the same variable and power for the m variable, but the powers of the n variable are different. Since we cannot combine these terms, we will need to leave them as is. We can, however, combine the remaining term with one of the other terms:

(14m²n - 2m^n² + 9m²n) = 14m²n - 2m^n² + (9 + (-14))m²n = 14m²n - 2m^n² - 5m²n

We can then combine this expression with the previous one:

14m²n - 2m^n² - 5m²n + m²n^ - 3m²n = (14 - 1)m²n - 2m^n² - (5 - 3)m²n = 13m²n - 2m^n² - 2m²n

Finally, we have simplified the expression as much as possible:

(4m²n² + 6m²n) - (8m²n^ - 7m²n² - 13m²n) - (14m²n - 2m^n² + 9m²n) = 13m²n - 2m^n² - 2m²n

Answer:

Mr. Conners will use 144 fence posts.

Step-by-step explanation:

Given question is incomplete; please find the question attached herewith.

As we can see from the attachment, Mr Corner's yard is in the rectangular shape.

Total distance around the yard = Perimeter of a rectangle = 2(Length + width)

Length of the yard = 330 ft

And width of the yard = 102 ft

So perimeter of the yard = 2(330 + 102                                         = 864 f

Mr. Conners wants to put a fence post at every 6 feet.

So number of posts used =

                                   =

                                         = 144

At two points [tex]x_{1}[/tex] = π/6 and [tex]x_{2}[/tex] = 5π/6 (using trigonometric function)

sinx =[tex]\frac{1}{2}[/tex]

⇒[tex]x_{1}[/tex] = π[tex](2n + \frac{1}{6} )[/tex] or [tex]x_{2}[/tex] = π[tex](2n + \frac{5}{6} )[/tex]

where n is an integer

But hence x belongs to [-3π , 3π]

the acceptable solutions are

[tex]x_{1}[/tex] = π/6 and [tex]x_{2}[/tex] = 5π/6

What are Trigonometric Functions?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides.

There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Function of Sine

The ratio of the opposing side's length to the hypotenuse is known as an angle's sine function. According to the diagram above, sin is worth:

Sin a =Opp/Hypo = CB/CA

Function of Cosine

The cosine of an angle is the ratio of the neighbouring side's length to the hypotenuse's length. The cos function will be derived as follows from the diagram up top.

Cos a = Adjacent/Hypotenuse = AB/CA

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Answer: look it up how to pronounce the word

Step-by-step explanation: go to goggle translate or an app.

Answer: the answer is try hard and if you don’t succeed try try again

Step-by-step explanation:

The point zero represents option (A) the location of the starting line

Here, -35 represents the starting location of a race car that is 35 yards behind the starting line.

Therefore, the location of the starting line = starting location of a race car that is 35 yards behind the starting line + 35

Substitute the values in the equation

The location of the starting line =  -35 + 35

Add the numbers

= 0

The ending location of a race car = 35

Thar is 35 yards in front of the starting line

Therefore, the zero represents the location of the starting line

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Proportionately, the sorting machine will take 100 minutes (1 hour and 40 minutes) to process 720 tons if it takes 50 minutes to process 360 tons.

Proportion is the ratio or numerical relationship that one quantity bears to another.

Proportions are equated to each other to find missing variables.

Proportions are fractional values, usually depicted as fractions, decimals, or percentages.

The total number of oranges to sort = 720 tons

Machine processing speed = 360 tons per 50 minutes

Proportionately, the machine can process 7.2 tons per minute (360/50).

The time to sort 720 tons = 100 minutes (720/360 x 50) or (720/7.2)

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Answer:

9/56

Step-by-step explanation:

Area of a rectangle = width x length

Area = (3/8) x (3/7) = 9/56

Mutiplying fractions is easy, just multiply the numerator, then multiply the denominator.

Factor the following questions is.6 m(x+2 n+2),

What is factor?

In mathematics, an integer m that can be multiplied by another integer to create n is known as a divisor of an integer n, also known as a factor of n. One can also state that n is a multiple of m in this situation.

[tex]6 x m+12 m+12 m n[/tex]

Factor out common term[tex]$6 m$ : $6 m(x+2+2 n)$[/tex]

[tex]\begin{aligned}& =6 m(x+2+2 n) \\& =6 m(x+2 n+2)\end{aligned}[/tex]

[tex]13 r+r+9 x r[/tex]

Add similar elements: [tex]$13 r+r=14 r$[/tex]

[tex]=14 r+9 x r[/tex]

[tex]15 x y+45 y+3 m y[/tex]

Factor out common term [tex]3y: $\quad 3 y(5 x+15+m)$[/tex]

[tex]\begin{aligned}& =3 y(5 x+15+m) \\& =3 y(5 x+m+15)\end{aligned}[/tex]

[tex]$7 m n+13 m n+8 m n$[/tex]

Add similar elements: [tex]$7 m n+13 m n+8 m n=28 m n$[/tex][tex]$=28 \mathrm{mn}$[/tex]

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Answer:

Step-by-step explanation:

Thank you

The expression of the inequality is -0.96 ≤ 0.3x and the solution will be x ≥ -3.2 thus, option (D) is correct.

A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

As per the given,

-0.96 ≤ 0.3x

Divide by 0.3 into both sides of the above equation,

-0.96/0.3 ≤ x

x ≥ -3.2

The number line goes from -3.2 to the positive or greater than -3.2 in the last option.

Hence "The solution of the inequality -0.96 ≤ 0.3x is x ≥ -3.2".

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Answer:

Then it is a circle!

The possible ethical issues of testing are given below.

What is drug?

Any chemical that, when consumed, alters the physiology or psychology of an organism qualifies as a drug. Usually, foods and other substances that support nutrition are distinguished from drugs.

(A)

Possible ethical problems: Since animals are able to perceive their surroundings, they have the right to exist free from human interference.

Therefore, animal research should not be done by humans. It is wrong to use animals only as stools to advance scientific understanding.

The right for an animal to live a full life without pain or suffering should be equal to that of humans.

Part B:

For the following reason, this is a bad assumption.

It does not follow that just because a drug causes the blood pressure levels in monkeys to return to normal after consumption that the drug will do the same for humans. This is because how humans and monkeys react to drugs differ.

Furthermore, it's unclear whether the drug's return to normal blood pressure was caused by it or by some other confounding variables that the researcher neglected to take into account.

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The value of x is  x < 2

What is inequality?

An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

-x-7> -9

Add 7 on both the sides

-x -7 + 7 > -9 +7

-x > -2

divide by -1 and change inequality sign

x < 2

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Vertex form of x-int: y-int: is .(2,3)

f(x)=−2x2+8x−5

Write

f(x)=−2x2+8x−5

as an equation.

y=−2x2+8x−5

Rewrite the equation in vertex form.

Tap for more steps...

y=−2(x−2)2+3

Use the vertex form,

y=a(x−y)2+k

, to determine the values of

a, h, and k.a=−2h=2k=3

Since the value of

a

is negative, the parabola opens down.

Opens Down

Find the vertex

(x,y).(2,3)

x-int: y-int: is .(2,3)

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The solution is 120 ounces

An average man can lift the weight of $ 150 in quarters

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total weight an average man can lift be = A

Now , the weight of an average quarter = 0.2 ounces

Now , Number of quarters in $ 1 = 4 quarters

Let the total amount be = $ 150

So , the number of quarters in $ 150 is given by the equation

Number of quarters in $ 150 = 150 x 4

Substituting the values in the equation , we get

Number of quarters in $ 150 = 600 quarters

And , the weight of 600 quarters = 600 x weight of an average quarter

Substituting the values in the equation , we get

Number of quarters in $ 150 = 600 quarters

The weight of 600 quarters = 600 x 0.2

The weight of 600 quarters = 120 ounces

Therefore , the value of A is 120 ounces

Hence , an average man can lift the weight of $ 150 in quarters

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Answer:

  $20.07

Step-by-step explanation:

You want Marissa's total bill when she bought three cartons of ice cream at $4.59 each and two packages of plastic bowls at $3.00 each, with the plastic being taxed at 5%.

The amount for each item will be the product of the cost per unit and the number of units.

  ice cream total = 3 × $4.59 = $13.77

  plastic total = 2 × $3.00 = $6.00

The tax is applied only to the plastic, so the amount of tax is ...

  5% × $6.00 = $0.30

The total bill is the sum of the item costs and the tax:

  $13.77 +6.00 +0.30 = $20.07

Marissa's total bill was $20.07.

Answer:

4

Step-by-step explanation:

Angles in a triangle add to [tex]180^{\circ}[/tex].

[tex]7x+2+60+90=180 \\ \\ 7x+152=180 \\ \\ 7x=28 \\ \\ x=4[/tex]

Answer:

write the equation of the line shown on the graph 0,3 3,1

Step-by-step explanation:

ano ba slope of variables

The amount of each type of table that will seat everyone is given as follows:

The combination is obtained with a system of equations, in which the variables of the system are given as follows:

There is a total of 52 tables, hence:

x + y = 52.

There will be a total of 280 people, hence:

4x + 10y = 280.

Hence the system is:

Multiplying the first equation by -4 and then adding them, the variable y is obtained as follows:

6y = 280 - 52 x 4

y = (280 - 52 x 4)/6

y = 12 tables.

Hence the variable x is obtained as follows:

x + y = 52

x + 12 = 52

x = 40 tables.

The problem is given as follows:

Mina's Catering Service is organizing a formal dinner for 280 people. The hall has two kinds of tables, one that seats 4 people and one that seats 10 people. The hall can contain up to a total of 52 tables. Which combination of tables sits everyone?

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Answer:

∠ 2 = 66°

Step-by-step explanation:

∠ 1 and ∠ 2 are same- side interior angles and sum to 180° , then

∠ 2 + 114° = 180° ( subtract 114° from both sides )

∠ 2 = 66°

The figure has three planes with three system of linear equations and three variables, we would definitely have three solutions

System of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.

In the given problem, we have a figure with three planes and it is a three variable system of linear equation.

Assuming the planes are x, y and z, we would expect three solutions because we have three variables.

Looking at the image again, from the three system of linear equations with three variables, we will have three solutions.

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Answer:

it is y=kx

Step-by-step explanation:

The cost of 6 bottle juice is $4.26.

What is cost?

A cost is the value of money that has been expended to produce something or provide a service and is therefore no longer available for use in production, research, retail, and accounting. In the case of an acquisition cost, the money spent on the acquisition is considered the cost.

Given:

Andrew buys 8 bottles of cranberry juice at the corner store for a total cost of $5.68.

So, the cost of each bottle is,

$5.68/8 = $0.71

Now to find the cost of 6 bottle of juice.

6 x $0.71 = $4.26

Hence, the cost of 6 bottle juice is $4.26.

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