Which equation does NOT represent a function?
O A. Y= 3x^2– 5
O B. x = y^2– 9
O C. Y = 12
O D. 3x + 4y = 6

There is no real value of x that satisfies the condition for g(x) = x + 6 to be a tangent to the curve f(x) = k√x.

To find the value of the constant k, we need to determine the point of tangency between the curve f(x) and the tangent line g(x).

The given equation for the tangent line is g(x) = x + 6. We know that the tangent line and the curve are tangent at a specific point, which means they have the same slope at that point.

To find the slope of the curve f(x), we need to differentiate it with respect to x. The derivative of f(x) = k√x is given by:

f'(x) = (1/2)(k/x^0.5) = k/(2√x)

Since the slope of the tangent line g(x) is 1, we can set the derivative of f(x) equal to 1 and solve for x:

k/(2√x) = 1

Multiplying both sides by 2√x, we get:

k = 2√x

Now we have the expression for k in terms of x. To find the value of x, we need to substitute this expression into the equation of the tangent line:

g(x) = x + 6

Substituting k = 2√x, we have:

x + 6 = 2√x

To solve this equation for x, we can square both sides:

(x + 6)^2 = (2√x)^2

Expanding the left side:

x^2 + 12x + 36 = 4x

Bringing all terms to one side:

x^2 + 12x + 36 - 4x = 0

Simplifying:

x^2 + 8x + 36 = 0

This is a quadratic equation. We can solve it by factoring or using the quadratic formula. However, upon closer inspection, we notice that the discriminant (b^2 - 4ac) is negative, indicating that the equation has no real solutions.

Therefore, there is no real value of x that satisfies the condition for g(x) = x + 6 to be a tangent to the curve f(x) = k√x.

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Answer:

1: No, x is raised to a power

2: Yes, can be solved in the form of y = mx + b

3: If this is supposed to be x + y = 45, then yes because it can be solved in the form of y = mx + b

4: Yes, it is in the form of y = mx + b

5: Yes, it is in the form of y = mx +b, it has a slope of zero and will be a horizontal line, which will pass the vertical line test

6: No, x is raised to a power.

7: No, x is raised to a power.

8: No, x is raised to a power

9: Is that supposed to be pi? If so, yes, it is in the form of y = mx + b

Step-by-step explanation:

The value of angle t as shown in the diagram below is 38°.

An angle is formed when two straight lines or rays meet at a common endpoint.

To calculate the value of angle t, we use the formula below

Formula:

∠OXZ+∠OZX+∠XOZ = 180° (Sum of the angle in a triangle).............. Equation 1

From the angle,

Given:

Substitute these values into equation 1

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Answer:

The answer is "angle".

Step-by-step explanation:

There will be two legs as well as a hypotenuse inside the right triangle. Its legs are both at an angle of 90° as well as the length of a right triangle upon on hypotenuse half is the opposite side of a right angle. When you have the two-angle measurement as well as the right triangle height on one side, you can find equal measurements of two angles on another and the lengths for two sides on another.

The answer to this question is 5h + 4.

Laplace transforms are an essential mathematical tool used to solve differential equations. These transforms transform differential equations to algebraic equations that can be solved easily.

To solve the differential equations given in the question, we will use Laplace transforms. So let's start:Solution:a) y" – y = t y(0) = 1, y'(0) = 1First, we take the Laplace transform of the given differential equation.L{y" - y} = L{ty}

Taking the Laplace transform of both sides gives:L{y"} - L{y} = L{ty}Using the formula, L{y"} = s²Y(s) - s*y(0) - y'(0), and L{y} = Y(s) then we get:s²Y(s) - s - 1 = (1/s²) + (1/s³)Rearranging the above equation, we get:Y(s) = [1/(s²*(s² + 1))] + [1/(s³*(s² + 1))]Now, we apply the inverse Laplace transform to find the solution.y(t) = (t/2)sin(t) + (cos(t)/2)

The solution of the differential equation y" – y = t, with initial conditions y(0) = 1, y'(0) = 1 is y(t) = (t/2)sin(t) + (cos(t)/2).

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Answer:

6.06

Percentage Calculator: 20 is what percent of 330? = 6.06.

Multiplying the beats in a year by the number of years in a lifetime:

Total heartbeats in a lifetime = Beats in a year × Average lifetime

To calculate the total mass of mercury in the tank, we need to find the volume of the tank and then multiply it by the concentration of mercury.

Given:

Length of tank (L) = 105 m

Width of tank (W) = 50 m

Depth of tank (D) = 11 m

Concentration of mercury = 80 mg/L

First, calculate the volume of the tank:

Volume = Length × Width × Depth

Volume = 105 m × 50 m × 11 m

Now, convert the concentration from mg/L to kg/m³:

Concentration = 80 mg/L = 80 × 10⁻⁶ kg/m³

Multiply the volume by the concentration to find the mass of mercury:

Mass of mercury = Volume × Concentration

Note: The resulting mass will be in kilograms.

To find the mass of water required to fill a circular hot tub, we need to calculate the volume of the hot tub and then multiply it by the density of water.

Given:

Diameter of hot tub (d) = 3.4 m

Depth of hot tub (h) = 1.3 m

The radius of the hot tub (r) can be calculated as half of the diameter:

Radius = d/2 = 3.4 m/2

Now, calculate the volume of the hot tub:

Volume = π × radius² × depth

The density of water is approximately 1000 kg/m³.

Finally, multiply the volume by the density of water to find the mass:

Mass of water = Volume × Density

To estimate the total number of times a human heart beats in an average lifetime, we need to multiply the heart rate (in beats per minute) by the number of minutes in a year and then multiply it by the number of years in a lifetime.

Given:

Heart rate = 65.1 beats/minute

Average lifetime = 57.2 years

Number of days in a year = 365.25

First, calculate the number of minutes in a year:

Minutes in a year = 60 minutes/hour × 24 hours/day × 365.25 days/year

Next, multiply the heart rate by the number of minutes in a year:

Beats in a year = Heart rate × Minutes in a year

Finally, multiply the beats in a year by the number of years in a lifetime:

Total heartbeats in a lifetime = Beats in a year × Average lifetime

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Answer: 10 - 4x

Step-by-step explanation:

Answer:

1(a)1,030,000+0.13x

(b)$1,030,026

2. (a)Base and Index

(b)See Explanation

Ste-by-Step Explanation

(a)Total Amount to be paid to the four actors

=500,000+(300,000+0.02x)+(150,000+0.03x)+(80,000+0.08x)

Collect like terms

=500,000+300,000+150,000+80,000+0.02x+0.03x+0.08x

\(\text{Total Amount Paid= }1,030,000+0.13x\)

(b)When x=200

\(\text{Total Amount Paid= }1,030,000+0.13(200)\\=1,030,000+26\\=$1,030,026\)

Question 2

(a)The two parts of a power are the base and index.

Take, for example, the expression: \(a^b\\\)

\(a$ is the base\\b is the index\)

Another example using numbers is: \(10^3\)

In this case:

\(10$ is the base\\3 is the index\)

(b)Like terms are terms that have the same letter/variable attached to them.

For example, the following pairs are like terms

These, however, are not like terms

Based on the given sample of job applicants' years of experience (1, 3, 3, 1, 2), we can conclude that the sample contains a range of values and does not exhibit a uniform pattern. Further statistical analysis would be required to draw more specific conclusions about the sample.

The sample of job applicants' years of experience consists of the values 1, 3, 3, 1, and 2. From this information, we can observe that the sample includes different values, ranging from 1 to 3. This suggests that there is some variation in the years of experience among the job applicants.

However, with a sample size of only five, it is challenging to draw definitive conclusions about the entire population of job applicants. The sample might not be fully representative of the entire applicant pool, and there is limited information to assess the overall distribution or any underlying patterns in the data.

To gain more insights and make more robust conclusions, further statistical analysis would be necessary. Techniques such as calculating measures of central tendency (e.g., mean, median) and measures of dispersion (e.g., standard deviation, range) could provide a more comprehensive understanding of the sample and its characteristics.

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Answer:

number of $8 sold= 200

Number of $10 tickets sold= $150

Number of $12 tickets sold = $50

Step-by-step explanation:

Let the quantity of $8 ticket be represented as  x

Let the quantity of $10 ticket be represented as  y

Let the quantity of $12 ticket be represented as  z

Such that total tikets sold = 400 can be represented as x+y+z= 400

Prices of$8, $10 and $12 gave a total income of $3,700  such that it can be represented as

8x +10y + 12z =$3,700

Also given that combined number of $8 and $10 priced tickets sold was 7 times the number of $12 tickets sold, we have that

x+y = 7z

Giving us the equations to solve to  be

x+y+z= 400------ equation 1

8x +10y + 12z =$3,700---- equation 2

x+y = 7z------equation 3

Step 2- solving

Putting equation 3 i n equation 1, we have that

7z+z = 400

8z= 400

z= 400/8= 50

also puting the value of z= 50 in equation 1

x+y+z= 400

x+y+50= 400

x+y = 350---- equation 4

putting z= 50 into equaton 2 and solving out

8x +10y + 12z =$3,700

8x +10y + 12x 50 =$3,700

8x +10y + 600 =$3,700

8x +10y =3,700 - 600

8x +10y=3,100---------equation 5

Multiplying equation 4 by 8  and subtracting from equation 5

8x +10y=3,100

-8x+8y= 2,800

2y=300

y= 300/2

y=150

to find x, when y= 150 using equation 4

x+y = 350

x= 350-150

x= 200

Therefore number of $8 sold= 200

Number of $10 tickets sold= $150

Number of $12 tickets sold = $50

The centers of the circles are 15 units apart, if two circles have radii 15 and 95 and if the two external tangents to the circles intersect at 60 degrees.

Let O1 and O2 be the centers of the circles with radii 15 and 95, respectively. Let T1 and T2 be the points of tangency of the external tangent lines with the circles.

Since the tangent lines are external to the circles, we can draw radii perpendicular to the tangent lines from the centers of the circles to the points of tangency. Let T1' and T2' be the points where these radii intersect the tangent lines.

Then, we have:

OT1' = 15

OT2' = 95

T1'T2' = 2*OT1'*cos(60) = OT1'

Note that T1'T2' is equal to the distance between the centers of the circles. Therefore, we have:

Distance between the centers = T1'T2' = OT1' = 15

Hence, the centers of the circles are 15 units apart.

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Hello There! :)

3 Negative numbers that are less than -1:

And it goes on and on for ever. Hope it helps you! :)

Do ask me if you have any question.

~An excited gal

\(MagicalNature\) here to help

Answer:

-4,-9,-10

Step-by-step explanation:

Answer:

\(=\frac{1}{2}\)

Step-by-step explanation:

\(\frac{x^{3+3} }{8x} \\\\\frac{1+3}{8} \\\\\frac{4}{8} \\\\\frac{1}{2}\)

Answer:

1/2

Step-by-step explanation:

Answer:

1- The range of the runner's heart rate is 60 to 110.

2- The interval where the runner's heart rate is increasing is from second 0 to second 2.

3- The interval where the runner's heart rate is decreasing is not mentioned in the given information.

4- The interval where the runner's heart rate is staying the same is from second 2 to second 4.

5- To create an equation to represent the linear portions between 2 and 3 minutes, we need to first determine the slope of the line. The slope is the change in heart rate (y-value) divided by the change in time (x-value). In this case, the change in heart rate is 80 - 60 = 20 and the change in time is 2 - 0 = 2. Therefore, the slope of the line is 20/2 = 10.

To find the equation of the line, we can use the point-slope form of a linear equation, which is: y - y1 = m(x - x1). In this case, y1 is the starting heart rate of 60 at time x1 = 0. Substituting these values into the equation, we get: y - 60 = 10(x - 0). Simplifying this equation, we get: y = 10x + 60.

To find the equation of the range between 3 and 4 minutes, we can use the same method. The starting heart rate at time x1 = 3 is 80 and the ending heart rate at time x2 = 4 is above 110. The change in heart rate is 110 - 80 = 30 and the change in time is 4 - 3 = 1. Therefore, the slope of the line is 30/1 = 30. Using the point-slope form of a linear equation, we get: y - 80 = 30(x - 3). Simplifying this equation, we get: y = 30x + 50.

6- It is difficult to determine what is causing the changes in heart rate without more information. Heart rate can be affected by many factors, including physical activity level, age, fitness level, and underlying medical conditions. It is possible that the runner's heart rate increased at the beginning of the interval due to the increased physical activity, and remained constant for the next two minutes because the activity level was sustained. The sudden increase in heart rate at the end of the interval could be due to a variety of factors, such as a burst of energy or a reaction to some external stimulus.

the yardstick is typically 1 yard

and 1 yard is basically 3 feet

and 1 yard can also be 0.9144 meters

so,

1 yard = 1 meters (approximately)

The measurement that the length of a yardstick ruler is closest in length is 1 meter

so the correct option is the last option which is 1 meter.

The triangle is a right-angled triangle with a perpendicular side of 5 and a hypotenuse of 8.3.

\(\theta = sin^{-1}\dfrac{5}{8.3}\)

as we know that sine for any angle is the ratio of its perpendicular to the hypotenuse,  and trigonometry is only applicable to a right-angled triangle.

therefore,

\(\theta = sin^{-1}\dfrac{5}{8.3}\\\\sin \theta=\dfrac{5}{8.3}=\dfrac{Perpendicular}{Hypotenuse}\\\)

Hence, the triangle is a right-angled triangle with a perpendicular side of 5 and a hypotenuse of 8.3.

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Answer:

8<16x-2

--------

4

Step-by-step explanation:

that proves that that is the answer

Kiera's actions reveal a combination of options A, B, and D. Firstly, Kiera demonstrates her belief in her mother's abilities by taking charge and handling a problematic situation independently.

When her mother's campaign video fails to load, Kiera promptly steps in and manages to get the content loaded, exhibiting her resourcefulness and support for her mother's cause. Furthermore, Kiera attends the luncheon despite feeling uneasy and out of place, indicating her willingness to show up and support her mother's endeavors. However, Kiera's discomfort highlights her struggles with her mother's newfound political fame, and the changes that come with it, such as the exclusive event that she attends. Lastly, Kiera's decision to seek out friends and social connections suggests her recognition of the shifting dynamics in her household and her need for companionship amidst the family's political spotlight. Therefore, Kiera's actions in chapter 2 reveal her loyalty and support for her mother's campaign, but also her internal conflict and search for stability amidst the changes in her life.

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The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)

Here,

σ1 = 15%

σ2 = 10%

w1 = 50%,

w2 = 50%

Substituting the values in the above formula:

σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158 = 1.58%σB

= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158

= 1.58%

Hence, the correct option is

D. σ(A) = 14.14%;

σ(B) = 16.33%.

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Answer:

4x

Step-by-step explanation:

bcoz

y = 6 - 2x

6-2x = 4x

y=4x

Answer:

\(4^{4}\) and \(6^{2}\)

Step-by-step explanation:

1. The base numbers are 4 and six in this question

2. There are four #4s and two #6

3. 4 and 2 would be the exponents

Answer:

Take two points and connect them with a line.

Step-by-step explanation:

We can take the points (0,-4) and (1,-\(\frac{5}{3}\)). Now we can connect the two points with a line and we get our graph.

Answer:

(See the third picture)

Step-by-step explanation:

Start by turning everything to slope-intercept form:

\(7x-3y=12\\-3y=-7x+12\\y=\frac{7}{3}x-4\)

Next, plot down the y-intercept on the graph (which in this case is -4):

(The y-intercept is the point where a line crosses the y-axis, thus, the y-intercept must be (0, y))

(See the first picture)

Next up, plot down the next point with the slope, recall that the graph is rise over run, or more specifically, y over x.

The slope is 7/3, the rise is 7 and the run is 3, so to draw the next point, start at your y-intercept, and go 7 units up, and 3 to the right, the next point should look like this:

(See the second picture)

And finally, draw a straight line across both points:

(See the third picture)

Answer:

I use to know this

Step-by-step explanation:

there a app the can help you do it

Answer:

√y+4÷3=p

Step-by-step explanation:

y=3p²-4

y+4=3p²

y+4/3=p²

p=√y+4÷3

Answer:

\(p = \pm\sqrt{\dfrac{y+4}{3}\)

Step by step explanation:

\(~~~~~y = 3p^2 -4\\\\\implies 3p^2 = y+4\\ \\\implies p^2 = \dfrac{y+4}{3}\\\\\implies p = \pm\sqrt{\dfrac{y+4}{3}\)

Answer:

Below

Step-by-step explanation:

Radians =  degrees * pi /180

Radians * 180/pi   =  degrees

Step-by-step explanation:

you can look it up

This equation 16t² - 9t - 29 = 0 he hits the water.

To write an equation describing when the diver hits the water, we need to consider the vertical motion of the diver. We can use the equation:

y = y₀ + v₀t + (1/2)gt²

where:

y is the vertical position at time t

y₀ is the initial vertical position

v₀ is the initial vertical velocity

g is the acceleration due to gravity

t is the time

Given the information:

y₀ = 29 ft (height of the platform above the water)

v₀ = 9 ft/s (initial upward velocity)

g = 32 ft/s² (acceleration due to gravity, assuming downward is positive)

Plugging in these values, we have:

y = 29 + 9t - (1/2)(32)t²

To find when the diver hits the water, we set y equal to zero:

0 = 29 + 9t - (1/2)(32)t²

Simplifying the equation, we get:

16t² - 9t - 29 = 0

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