The table shows the height of an object, h(t), in meters after t seconds. Use your calculator to find the quadratic function. Find the approximate time, to the nearest hundredth of a second, after which the object will reach its maximum height.

Final answer:

The value of y, which directly varies with x, is found by first determining the constant of variation when x = 9 and y = 5.4. Using this constant, we calculate the value of y for x = -10, resulting in y = -6.

Explanation:

The value of y directly varies with x, which means the relationship between x and y can be described by the equation y = kx, where k is the constant of variation. Since y = 5.4 when x = 9, we first find the constant of variation as follows: k = y/x = 5.4/9 = 0.6. Now, to find y when x is -10, we use the constant of variation k in the equation: y = kx = 0.6(-10) = -6.

The relationship between y and x is one of direct variation, represented by the equation y = kx, where k is the constant of variation. Given that y = 5.4 when x = 9, the constant k is calculated as 0.6. Applying this constant, when x = -10, the value of y is found to be -6. This process showcases the direct variation principle in determining y based on the given x values and the constant of variation.

Answer:

2475 cm

Step-by-step explanation:

We are given that Roberto's toy car travels 40 cm/sec at high speed and 25 cm/sec at low speed.

We have to find that the distance would have the car traveled

Speed of car at high speed=40 cm/sec

Speed of car at low speed=25 cm/sec

If car  takes time to travel at high speed=30 seconds

If car takes time to travel  at low speed=51 seconds

[tex]Distance=speed\times time[/tex]

Using this formula

Distance traveled by the car at high speed=[tex]40\times 30=1200 cm[/tex]

Distance traveled by the car at low speed=[tex]51\times 25=1275 cm[/tex]

Total distance traveled by the car =1200+1275=2475 cm

Hence, the distance  would have traveled by the car=2475 cm

We have been given that the formula for the force of gravity pulling on the bob is given by [tex] F=m\times g\times sin(\theta) [/tex]), where g is equal to[tex] 9.8m/s^2 [/tex].

Now, we have been given that the mass of the bob of the pendulum is 0.01 kg and that the pendulum makes 22.5 degree angle with the vertical.

Thus, applying the given values in the formula of the given in the question, we get the formula to be:

[tex] F=m\times g\times sin(\theta)=0.01\times9.8\times sin(22.5^{\circ}) [/tex]

[tex] \therefore F\approx0.0375 [/tex] N

Answer:

To estimate 179% of 41 by rounding, use the expression

✔ 180%(40)

.

Using the distributive property, the expression is equivalent to

✔ (100%)(40) + (80%)(40)

.

179% of 41 is about

✔ 72

.

Step-by-step explanation:

We have to find the missing value to the nearest whole number of tan x° =0.9.

Since, tan x° =0.9

To evaluate the missing value of 'x', we will take [tex] \arctan (0.9) [/tex]

So, [tex] x^{\circ}=\arctan (0.9) [/tex]

Now, we will find the value of [tex] \arctan (0.9) [/tex]using the calculator, we get,

[tex] x^{\circ}=\arctan (0.9)=41.9^{\circ}=42^{\circ} [/tex]

So, the missing value of 'x' to the nearest whole number is [tex] 42^{\circ} [/tex].

The length of AD is 18 units.

To find the length of AD, we can use the fact that the altitude from the right angle of a right triangle divides the triangle into two smaller similar triangles.

Let's denote the length of AD as x.

Since triangle ADC and triangle CDB are similar to triangle ACB, we can set up the following proportions:

For triangle ADC:

AD / AC = CD / AB

For triangle CDB:

BD / AC = CD / AB

We already know that AC = 12, AB = 36, and CD = x. So, let's substitute these values into the proportions:

For triangle ADC:

x / 12 = CD / 36

For triangle CDB:

(36 - x) / 12 = CD / 36

Now, let's solve these equations:

From the first equation:

x / 12 = CD / 36

x = (12 * CD) / 36

x = CD / 3

From the second equation:

(36 - x) / 12 = CD / 36

36 - x = (12 * CD) / 36

36 - x = CD / 3

Now, let's solve for CD using the second equation:

36 - x = CD / 3

36 - (CD / 3) = CD / 3

36 = (2 * CD) / 3

CD = (36 * 3) / 2

CD = 54

Now that we have found CD, we can substitute it into the first equation to find x:

x = CD / 3

x = 54 / 3

x = 18

So, the length of AD is 18 units.

Each economic term is matched with its appropriate description as follows:

OLIGOPOLY ||  There are no barriers to entry in the market.

MONOPOLY ||  There is a single seller in the market.

COLLUSION ||  Three companies secretly enter into a price agreement.

PERFECT COMPETITION ||  Every company in this market structure is aware of the actions of the other companies.

There are no barriers to entry in the market is the match of - Oligopoly (The market is shared by many sellers )

There is a single seller in the market is the match of - Monopoly

Three companies secretly enter into a price agreement is the match for - Collusion

Every company in this market structure is aware of the actions of the other companies is the match for Perfect Competition.

Answer:

[tex]114.8\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The area of a trapezoid is equal to

[tex]A=\frac{1}{2}(b1+b2)h[/tex]

In this problem we have

[tex]b1=12\ ft[/tex]

[tex]b2=15\ ft[/tex]

[tex]h=8.5\ ft[/tex] ----> the height of the trapezoid is the perpendicular distance between the bases

substitute the values

[tex]A=\frac{1}{2}(12+15)(8.5)[/tex]

[tex]A=\frac{1}{2}(27)(8.5)=114.75\ ft^{2}[/tex]

Round to the nearest tenth

[tex]114.75=114.8\ ft^{2}[/tex]

Answer:

114.8 is the answer

Step-by-step explanation:

got it on edgen

The sale price of the chair including tax is $185.5.

In mathematics, the tax calculation is related to the selling price and income of taxpayers. It is a charge imposed by the government on the citizens for the collection of funds for public welfare and expenditure activities. There are two types of taxes: direct tax and indirect tax.

Given that, Miles is buying a chair that regularly costs $250.

Today the chair is on sale for 30% off

So, the new cost is 250-30% of 250

= 250 - 30/100 ×250

= 250-75

= $175

The tax rate is 6%

Sale price = 175+6% of 175

= 175+6/100 ×175

= 175+0.06×175

= $185.5

Therefore, the sale price of the chair including tax is $185.5.

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Answer:

The correct option is:

Option: C

C valid; There is no bias in the survey.

Step-by-step explanation:

It is given that:

An organisation president  uses a list of 1008 members in alphabetical order and selects every 10th member to participate in the survey.

So, the sample used by her is a valid sample.

Since, she sets a random rule to choose the members  to participate in the survey.

The sample used by her is unbiased.

( Since, the aim of our survey questions are to capture an unbiased opinion to capture the true sentiments of the survey taker )

Hence, the correct statement regarding her survey is:

C. valid; There is no bias in the survey

The answer to this should be 13

Substitute the value of the variable into the expression and simplify

Substitute: |-2^2 + -3^2|

Simplify: |-2^2|= 4, |-3^2|= 9

Solve: 4 + 9 = 13

Given a = 5, b = -3, and c = -2, the absolute value of |c2 + b2| is calculated by squaring the values of c and b, adding them, then taking the absolute value, resulting in 13.

The question asks us to evaluate the expression |c2 + b2|, given that a = 5, b = -3, and c = -2. The vertical bars indicate that we are dealing with the absolute value, which means we want the positive result of the expression inside the bars.

First, substitute the given values into the expression, we get |-22 + (-3)2| which is |4+9|.

Second, add the squares of c and b together to get 13.

Finally, since the absolute value of 13 is still 13, this is our answer, corresponding to option D.

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Answer:

Option C is correct.

Step-by-step explanation:

Given is :

The value of Ari's rolls of coins is = $113

The coins are pennies, dimes, nickels and quarters.

Total money is represented by = penny + nickle + dime + quarter  All values in dollars are represented by:

113 = .01* pennies + .05* nickles + 0.1* dimes + 0.25* quarters  

Further calculating we get,

113 = .01* 50*penny rolls + .05 * 40*nickle rolls + .1 * 50*dime rolls + .25 * 40*quarter rolls  

[tex]113=.5p+2n+5d+10q[/tex]

where p is the number of penny rolls, n is the number of nickle rolls, d is the number of dime rolls, and q is the number of quarter rolls  

Now checking all the options by putting values.

A. [tex]113=.5(5)+2(8)+5(4)+10(7)[/tex]

[tex]113\neq 108.5[/tex]

B. [tex]113=.5(4)+2(8)+5(7)+10(5)[/tex]

[tex]113\neq 103[/tex]

C. [tex]113=.5(4)+2(8)+5(5)+10(7)[/tex]

[tex]113=113[/tex]

D. [tex]113=.5(5)+2(8)+5(7)+10(4)[/tex]

[tex]113\neq 93.5[/tex]

Therefore, option C is the right option.

Answer:

Larry has 1525 cents or 15.25 dollars.

Step-by-step explanation:

The following are the values for each of the coins:

1 Nickel=5 cents

1 Dime = 10 cents

1 Quarter = 25 cents

1 Fifity-cent = 50 cents

So the total value of the Larry's have is

Total money = 62*5 cents + 24*10 cents + 17*25 cents + 11*50 cents

Total money = 310 cents + 240 cents + 425 cents + 550 cents

Total money = 1525 cents

This is equal to 15.25 dollars.

Final answer:

The zeros of the equation -3x^4 + 27x^2 + 1200 = 0 can be found by substituting y = x^2 to create a quadratic equation, solving for y using the quadratic formula, and then solving for x for each y value found.

Explanation:

To find all the zeros of the equation -3x^4 + 27x^2 + 1200 = 0, we can treat the equation as a quadratic in form by substituting y = x^2, which reduces the equation to -3y^2 + 27y + 1200 = 0. This is now a standard quadratic equation that can be solved using the quadratic formula, y = (-b ± sqrt(b^2 - 4ac))/(2a), where a = -3, b = 27, and c = 1200. Once we find the values for y, we substitute back x^2 = y to get the values of x which are the zeros we are looking for.

The quadratic equation would provide us with two values for y, say y1 and y2. For each y value found, we solve for x by taking the square root, resulting in two x values for each y, giving us a total of four zeros for the original quartic equation.

we can re-write our expression as:

-3a^2+27a+1200=0

-3(a^2-9a-400)=0

a^2-9a-400=0

factorizing the above we have:

a^2+16a-25a-400=0

a(a+16)-25(a+16)=0

(a+16)(a-25)

thus replacing back x^2 we have:

(x^2+16)(x^2-25)

=(x^2+16)(x-5)(x+5)

factorizing (x^2+16) we get

x^2=+/-√-16

x=+/-4i

thus the zeros of the expression are:

x=-5, x=5 , x=-4i, x=4i

Answer:  The required equation of line BC is [tex] x=4.[/tex]

Step-by-step explanation:  As shown in the attached figure, lines AB and BC meet at right angle at the point B. The co-ordinates of point A and B are (-3, 4) and B(4, 4).

We are to find the equation of line BC.

We know that the slope of a line passing through the points (a, b) and (c, d) is given by

[tex]m=\dfrac{d-b}{c-a}.[/tex]

So, the slope of the line AB will be

[tex]m=\dfrac{4-4}{4-(-3)}\\\\\Rightarrow m=0.[/tex]

Therefore, the equation of the line AB is

[tex]y-4=m(x-4)\\\\\Rightarrow y-4=0\\\\\Rightarrow y=4.[/tex]

Since y = constant is the equation of a line parallel to X-axis, so its perpendicular line will be parallel to Y-axis.

So, its equation will be of the form

x = constant.

Since the line BC is perpendicular to AB passing through the point (4, 4), so we must have

[tex]x=4.[/tex]

Thus, the required equation of line BC is [tex] x=4.[/tex]

The statement "The value 3 is an upper bound for the zeros of the function f(x) = -3x^3 + 20x^2 - 36x + 16" is FALSE.

To determine whether the value 3 is an upper bound for the zeros of the function f(x) = -3x^3 + 20x^2 - 36x + 16, we need to check if the function has any real roots greater than 3.

One way to approach this is by analyzing the behavior of the function as x approaches infinity. We can check the sign of the leading coefficient (-3) and the constant term (16) to determine the overall behavior of the function.

Leading coefficient:

The leading coefficient of -3 indicates that the highest power of x in the function is negative. This means that as x approaches infinity, the function will decrease without bound.

Constant term:

The constant term of 16 indicates that the function intersects the y-axis at y = 16.

Considering these observations, we can infer that the function starts at a positive value (y = 16) and approaches negative infinity as x increases. This implies that the function f(x) = -3x^3 + 20x^2 - 36x + 16 will have at least one real root greater than 3.

Therefore, the statement "The value 3 is an upper bound for the zeros of the function f(x) = -3x^3 + 20x^2 - 36x + 16" is FALSE.

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Answer:

B. the y -intercept is (0,3)

Step-by-step explanation: