Fill in the table using this function rule.

y=5x+3

The value of x for which (f - g)(x) = 0 is x = 12.

To find the value of x for which (f - g)(x) = 0, we need to subtract g(x) from f(x) and set the resulting expression equal to zero. Let's perform the subtraction:

(f - g)(x) = f(x) - g(x)

= (16x - 30) - (14x - 6)

= 16x - 30 - 14x + 6

= 2x - 24

Now, we can set the expression equal to zero and solve for x:

2x - 24 = 0

Adding 24 to both sides:

2x = 24

Dividing both sides by 2:

x = 12

Therefore, the value of x for which (f - g)(x) = 0 is x = 12.

Know more about the expression click here:

https://brainly.com/question/15034631

#SPJ11

Answer: 22

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

(36 x8-204)

multiply first

36(8)=288

then subtract

288-204=84

8+84 ÷6

divide first

84 ÷6=14

8+14=22

Step-by-step explanation:

Magnitude = sqrt ( (-12)^2 + (-4)^2 ) = sqrt 160 = 12.649

Angle = arctan(-4/-12) = 198 degrees

The Magnitude: 12.649 and Direction: 18° (option c).

To find the magnitude and direction of the vector v = (-12, -4), we can use the following formulas:

Magnitude (or magnitude) of v = |v| = √(vₓ² + \(v_y\)²)

Direction (or angle) of v = θ = arctan(\(v_y\) / vₓ)

where vₓ is the x-component of the vector and \(v_y\) is the y-component of the vector.

Let's calculate:

Magnitude of v = √((-12)² + (-4)²) = √(144 + 16) = √160 ≈ 12.649 (rounded to the thousandths place)

Direction of v = arctan((-4) / (-12)) = arctan(1/3) ≈ 18.435°

Since we need to round the direction to the nearest degree, the direction is approximately 18°.

So, the correct answer is:

Magnitude: 12.649 (rounded to the thousandths place)

Direction: 18° (rounded to the nearest degree)

The correct option is: 12.649; 18°

To know more about Magnitude:

https://brainly.com/question/31022175

#SPJ2

Answer:

-2+10=8

Step-by-step explanation:

subtracting a negative is the same as adding a positive

(also they are like terms so this could be written as 10-2 but use the first one bc that's what they want)

In order for a set of numbers to represent three sides of a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem. Only option C represents three sides of a triangle.

Now let's check each option to see which one satisfies the triangle inequality theorem:

a. 5, 3, and 2

The sum of 5 and 3 is 8, which is greater than 2. The sum of 5 and 2 is 7, which is also greater than 3. The sum of 3 and 2 is 5, which is not greater than 5. Therefore, this set of numbers does not represents three sides of a triangle.

b. 9, 5, and 15

The sum of 9 and 5 is 14, which is less than 15. Therefore, this set of numbers does not represent three sides of a triangle.

c. 8, 10, and 6

The sum of 8 and 10 is 18, which is greater than 6. The sum of 8 and 6 is 14, which is also greater than 10. The sum of 10 and 6 is 16, which is greater than 8. Therefore, this set of numbers represents three sides of a triangle.

d. 4, 6, and 10

The sum of 4 and 6 is 10, which is less than 10. Therefore, this set of numbers does not represent three sides of a triangle. Therefore, only option C represents three sides of a triangle.

For more questions on triangle

https://brainly.com/question/28470545

#SPJ8

From the graph, it looks like the tangent line at 20 minutes has a slope that is close to 0.55°C/minute. So, the estimate of the rate of change of the temperature of the cookies after 20 minutes is approximately 0.55°C/minute.

To learn more about rate of change refer to:

brainly.com/question/25184007

#SPJ1

The rays of the angle from the measure 1/2 turn is 180 degrees

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

Angle measure = 1/2 turn

By definition, rays have two endpoints where they extend indefinitely on  one of the endpoints

As a general rule, we have

Substitute the known values in the above equation, so, we have the following representation

Angle measure = 1/2 * 360

Evaluate

Angle measure = 180

Hence, the angle measure is 180 degrees

Read more about angle at

https://brainly.com/question/25716982

#SPJ1

The parent would have to earn at least $4.166

$2,475 * 12 months = $29,700

$4,000 savings goal to the family's yearly income

$29,700 + $4,000 = $33,700

yearly income for second parent

80 hours/month * 12 months = 960 hours/year

If offer of daycare is accepted

$33,700 (total income) - $29,700 (first parent's income)

= $4,000

$4,000 / 960 hours = $4.166

this is the minimum wage

The parent would have to earn at least $4.166

Read more on earnings here:https://brainly.com/question/28920245

#SPJ1

The correct answer is option C.Which is the inequalities that show the graphs are y < x and y > 2.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The inequality which is shown in the figure is y < x and y > 2.We can see in the graph when you plot y > 2 then it will cover all the values greater than 2 in the graph.

Similarly, if we plot the inequality y < x on the graph it will cover all the values of y which are less than x and intersect at the point ( 2, 2).

Therefore the correct answer is option C.Which is the inequalities that show the graphs are y < x and y > 2. The graph is attached with the answer below.

To know more about graphs follow

https://brainly.com/question/25020119

#SPJ1

Answer:

1. (5·sin(A) - 3·cos(A)/(4·cos(A) + 5·sin(A))  = 1/8

2. θ = 30°

3. tan(θ) - cot(θ) = (2·sin²(θ) -1)/((cos(θ)×sin(θ))

from tan(θ) - 1/tan(θ) = sin(θ)/cos(θ) - cos(θ)/sin(θ) and sin²(θ) +  cos²(θ) = 1

4. tan10°·tan15°·tan75°·tan80°= 1 from;

sin(α)·sin(β) = 1/2[cos(α - β) - cos(α + β)]

cos(α)·cos(β) = 1/2[cos(α - β) + cos(α + β)]

5. x² + y² = a² + b² where x = a·cosθ - b·sinθ and y = a·sinθ + b·cosθ from;

cos²θ + sin²θ = 1

Step-by-step explanation:

1. Here we have 5·tan(A) = 5·sin(A)/cos(A) = 4

∴ 5·sin(A) = 4·cos(A)

Hence to find the value of (5·sin(A) - 3·cos(A)/(4·cos(A) + 5·sin(A)) we have;

Substituting the value for 5·sin(A) = 4·cos(A) into the above equation in both the numerator and denominator we have;

(4·cos(A) - 3·cos(A)/(4·cos(A) + 4·cos(A)) = cos(A)/(8·cos(A)) = 1/8

Therefore, (5·sin(A) - 3·cos(A)/(4·cos(A) + 5·sin(A)) = 1/8

2. For the equation as follows, we have

\(\frac{sin \theta}{1 + cos \theta} + \frac{1 + cos \theta}{sin \theta} = 4\) this gives

\(\frac{2sin (\theta/2) cos (\theta/2) }{2 cos^2 (\theta/2)} + \frac{2 cos^2 (\theta/2)}{2sin (\theta/2) cos (\theta/2) } = 4\)

\(tan\frac{\theta}{2} + \frac{1}{tan\frac{\theta}{2} } = 4\)

\(tan^2\frac{\theta}{2} + 1 = 4\times tan\frac{\theta}{2}\)

\(tan^2\frac{\theta}{2} - 4\cdot tan\frac{\theta}{2} + 1 = 0\)

We place;

\(tan\frac{\theta}{2} = x\)

∴ x² - 4·x + 1 = 0

Factorizing we have

(x - (2 - √3))·(x - (2 + √3))

Therefore, tan(θ/2) = (2 - √3) or (2 + √3)

Solving, we have;

θ/2 = tan⁻¹(2 - √3) or tan⁻¹(2 + √3)

Which gives, θ/2 = 15° or 75°

Hence, θ = 30° or 150°

Since 0° < θ < 90°, therefore, θ = 30°

3. We have tan(θ) - cot(θ) = tan(θ) - 1/tan(θ)

Hence, tan(θ) - 1/tan(θ) = sin(θ)/cos(θ) - cos(θ)/sin(θ)

∴  tan(θ) - 1/tan(θ) = (sin²(θ) -  cos²(θ))/(cos(θ)×sin(θ))...........(1)

From sin²(θ) +  cos²(θ) = 1, we have;

cos²(θ) = 1 - sin²(θ), substituting the value of sin²(θ) in the equation (1) above, we have;

(sin²(θ) -  (1 - sin²(θ)))/(cos(θ)×sin(θ)) = (2·sin²(θ) -1)/((cos(θ)×sin(θ))

Therefore;

tan(θ) - cot(θ) = (2·sin²(θ) -1)/((cos(θ)×sin(θ))

4. tan10°·tan15°·tan75°·tan80°= 1

Here we have since;

sin(α)·sin(β) = 1/2[cos(α - β) - cos(α + β)]

cos(α)·cos(β) = 1/2[cos(α - β) + cos(α + β)]

Then;

tan 10°·tan15°·tan75°·tan80° = tan 10°·tan80°·tan15°·tan75°

tan 10°·tan80°·tan15°·tan75° = \(\frac{sin(10^{\circ})}{cos(10^{\circ})} \times \frac{sin(80^{\circ})}{cos(80^{\circ})} \times \frac{sin(15^{\circ})}{cos(15^{\circ})} \times \frac{sin(75^{\circ})}{cos(75^{\circ})}\)

Which gives;

\(\frac{sin(10^{\circ}) \cdot sin(80^{\circ})}{cos(10^{\circ})\cdot cos(80^{\circ})} \times \frac{sin(15^{\circ}) \cdot sin(75^{\circ})}{cos(15^{\circ})\cdot cos(75^{\circ})}\)

\(=\frac{1/2[cos(80 - 10) - cos(80 + 10)]}{1/2[cos(80 - 10) + cos(80 + 10)]} \times \frac{1/2[cos(75 - 15) - cos(75 + 15)]}{1/2[cos(75 - 15) + cos(75 + 15)]}\)

\(=\frac{1/2[cos(70) - cos(90)]}{1/2[cos(70) + cos(90)]} \times \frac{1/2[cos(60) - cos(90)]}{1/2[cos(60) + cos(90)]}\)

\(=\frac{[cos(70)]}{[cos(70) ]} \times \frac{[cos(60)]}{[cos(60) ]} =1\)

5. If x = a·cosθ - b·sinθ and y = a·sinθ + b·cosθ

∴ x² + y² = (a·cosθ - b·sinθ)² + (a·sinθ + b·cosθ)²

= a²·cos²θ - 2·a·cosθ·b·sinθ +b²·sin²θ + a²·sin²θ + 2·a·sinθ·b·cosθ + b²·cos²θ

= a²·cos²θ + b²·sin²θ + a²·sin²θ + b²·cos²θ

= a²·cos²θ + b²·cos²θ + b²·sin²θ + a²·sin²θ

= (a² + b²)·cos²θ + (a² + b²)·sin²θ

= (a² + b²)·(cos²θ + sin²θ) since cos²θ + sin²θ = 1, we have

= (a² + b²)×1 = a² + b²

TheThe z-score of an observation of 4, with a sample mean of 4, is 0, indicating that the observation is at the same value as the mean.

The z-score measures how many standard deviations an observation is away from the mean. In this case, the sample mean is 4, and the observation value is also 4. To calculate the z-score, we use the formula: z = (x - μ) / σ, where x is the observation value, μ is the mean, and σ is the standard deviation.

Since the observation value (4) is equal to the mean (4), the numerator of the formula becomes 0. Dividing 0 by any number does not change its value. Therefore, the z-score of the observation value of 4, given a sample mean of 4, is 0.

Learn more about Standard deviation here: brainly.com/question/13498201

#SPJ11

Answer: 80

Step-by-step explanation:

Answer:

16910

Step-by-step explanation:

BIDMAS
1402 x 12 = 16824 +100 = 16924
16924-14 = 16910

Answer:

y=3x-7

Step-by-step explanation:

Equation of a Line: y=mx + b

Slope: 3/1 or 3

Y-int: -7

The equation of a line is a form of representing the set of points, which form a line in a coordinate system. 

The equation of a line that passes through the point (1, -4) and (2, -1) is

y = 3x - 7

The equation of a line is a form of representing the set of points, which form a line in a coordinate system. 

The general equation of a straight line is given as:

y = mx + c,

where m = slope of the line and c = y-intercept.

We have,

Two points:

(1, -4) = (a, b) and (2, -1) = (c, d)

The equation of a line can be written in the form:

y = mx + c

Slope:

m = (d - b) / (c - a) = -1 + 4 / 2 - 1 = 3 / 1 = 3

y-intercept:

Take a point (1, -4).

-4 = 3x1 + c

-4 - 3 = c

c = -7

Now,

The equation of a line is y = 3x - 7

Thus the equation of a line that passes through the point (1, -4) and (2, -1) is

y = 3x - 7

Learn more about equation of a line here:

https://brainly.com/question/14200719

#SPJ2

An electric circuit is a closed course that consists of all of the additives linked to finish the go with the drift of modern-day.

The circuit underneath is composed of:

A battery as a supply of direct modern-day which materials electricity within side the circuit for modern-day to go with the drift. Direct modern-day affords uni-directional modern-day. Here it has cells. Here 4 cells are linked in collection for the battery.

Two bulbs A and B linked in parallel connection. Each bulb has been parallel connected with a voltmeter.

A voltmeter measures the voltage throughout the element that it's miles linked with. It is continually linked in parallel with the additives.

Main circuit has an ammeter in collection with the battery and connection of bulb.

An ammeter measures the modern-day flowing within side the circuit. It is continually linked in collection.

Therefore, an electric circuit is a closed course that consists of all of the additives linked to finish the go with the drift of modern-day.

Learn more about electric circuit here:

https://brainly.com/question/2969220

#SPJ9

In order for f(x) to be a linear function, determine the value of k in the data set.

x = {-7, -2, 2, 5}

f(x) = {-15, k, 3, 9}

The value of k is {-5}.

Given that to find the value of k in the data set such that the data set represents a linear function.

Linear Function is a straight line on the coordinate plane is represented by a linear function. The formula for a linear function is f(x) = mx + b, where m and b are real values.

Here, f(x) or y is the dependent variable, m is a slope of the line, x is the independent variable and b is the y-intercept.

Here,(x,f(x)) are {(-7,-15),(-2,k),(2,3),(5,9)}

The slope of the function,

(x, f(x)) = (2,3) and (5,9)

Slope formula is m=\(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\).

Slope m= \(\frac{9-3 }{5-2}\)

Slope m=\(\frac{6}{3}\)

Slope m=2.

Using the point slope form, determine the linear function's equation.

\(y-y_{1} =m(x-x_{1})\)

Here, \((x_{1},y_{1})=(-7,-15)\) and m=2

We get

y + 15 = 2 (x + 7)

y = 2x - 1

Now at x = -2 and f(x) = k

k = 2(-2) - 1

k = -4-1

k=-5

Therefore, the value of k is -5.

To learn more about linear function visit: https://brainly.com/question/21107621

#SPJ9

Answer:

12−pack of 1.8 ounce bars has the better price per bar

Step-by-step explanation:

a) 10−pack of 2.5 ounce bars $ 19.50

10 pack = $19.50

1 pack = x

10 packs × x = $19.50 × 1

x = $19.50 × 1/10 packs

x = $1.950

12−pack of 1.8 ounce bars 18.75

12 pack = 18.75

1 pack= x

12 packs × x = 1 pack × 18.75

x = 18.75/12

x =$ 1.5625

From the calculation above:

12−pack of 1.8 ounce bars has the better price per because it cost $1.5625

Answer:

Step-by-step explanation:

(5 + 4)/2 = 9/2

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

The polynomial expression when expressed in standard form is; A: n6 + 7mn5 + 14m2n4 – 5m3n3 – 6m6

The polynomial expression to be simplified is expressed as;

8mn⁵ - 2m⁶ + 5m²n⁴ - m³n³ + n⁶ - 4m⁶ + 9m²n⁴ - mn⁵ - 4m³n³

Grouping like terms gives;

8mn⁵ - mn⁵ - m³n³ - 4m³n³ - 2m⁶ - 4m⁶ + 5m²n⁴ + 9m²n⁴ + n⁶

This would be simplified to get;

7mn⁵ - 5m³n³ - 6m⁶ + 14m²n⁴ + n⁶

Looking at the given options, we can conclude that the only correct one is option A because it is well arranged according to their powers.

Read more about Polynomial expressions at; https://brainly.com/question/4142886

#SPJ1

To find the simple interest payable, we can use the formula:

Simple Interest = Principal × Rate × Time

where:

Principal = $28,800

Rate = 3.75% per annum (expressed as a decimal, so 3.75% = 0.0375)

Time = 4 years

(a) The simple interest payable is $4,320.

Simple Interest payable:

Simple Interest = $28,800 × 0.0375 × 4

Simple Interest = $4,320

Therefore, the simple interest payable is $4,320.

(b) The monthly repayment amount is approximately $690.

To find the monthly repayment, we need to calculate the total amount to be repaid and then divide it by the number of months in the loan term.

Total amount to be repaid = Principal + Simple Interest

Total amount to be repaid = $28,800 + $4,320

Total amount to be repaid = $33,120

The loan term is 4 years, which is equivalent to 4 × 12 = 48 months.

Monthly repayment = Total amount to be repaid / Number of months

Monthly repayment = $33,120 / 48

Monthly repayment ≈ $690

Therefore, the monthly repayment amount is approximately $690.

To know more about simple interest:

https://brainly.com/question/30964674

#SPJ11

The equation of the line that is parallel to x = 3 and goes through (4, -3) is: x = 4).

The slopes or parallel lines are always the same.

Given the equation of a vertical line, x = 3, the slope is undefined. So also, the slope of the line that is parallel to x = 3 is undefined.

If the line passes through the point (4, -3), it means it intercepts the x-axis at x = 4.

Therefore, the equation of the line that passes through (4, -3) and is parallel to x = 3 is: x = 4.

Learn more about the slope of parallel lines on:

https://brainly.com/question/10790818

#SPJ1

The equation that can be used to solve for the unknown number is option A: n - 7 = 13.

To solve for the unknown number, we need to set up an equation that represents the given information. The given information states that "seven less than a number is thirteen." This means that when we subtract 7 from the number, the result is 13. Therefore, we can write the equation as n - 7 = 13, where n represents the unknown number.

Option A, n - 7 = 13, correctly represents this equation. Option B, 7 - n = 13, has the unknown number subtracted from 7 instead of 7 being subtracted from the unknown number. Option C, n7 = 13, does not have the subtraction operation needed to represent "seven less than." Option D, n13 = 7, has the unknown number multiplied by 13 instead of subtracted by 7. Therefore, option A is the correct equation to solve for the unknown number.

You can learn more about  equation at

https://brainly.com/question/22688504

#SPJ11

Answer:

Dear user,

Answer to your query is provided below

Pages full = 13

Card on last page = 1

Step-by-step explanation:

Rafael has 118 baseball cards.

Each album can hold 9.

So, using multiples of 9 or by dividing 118/9

That 1 is remainder.

So, cards on last page is 1

Verify ,

Pages full = (118-1)/9 = 13

1. The rate of change is -1 and the initial value is 1.

2. The graph represents Ava’s travel plans is graph (I).

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx. So the change in y coordinate with respect to the change in x coordinate can be written as,

m = Δy/Δx

where, m is the slope

Note that tan θ = Δy/Δx

We also refer this tan θ to be the slope of the line.

1. We have the coordinates as C(3, -2) and D(-2, 3).

So, the rate of change of linear function is

= 3 - (-2) / (-2 -3)

= 3+ 2 / (-5)

= 5/ (-5)

= -1.

and, the initial values is where the independent variable is zero which is (1, 0).

2. The graph represented for Ava journey is (A).

This, is because the speed of Ava car and speed of taxi is equal which is shown in graph 1 clearly.

Learn more about Graphs at:

https://brainly.com/question/17267403

#SPJ1

The given question is incomplete, complete question is:

1. A relation is plotted as a linear function on a coordinate plane starting at point C at (3, –2) and ending at point D at (–2, 3). What is the rate of change for the linear function and what is its initial value?

The rate of change is ______ and the initial value is ______.

A. 1 and -1

B. -1 and 1

C. 5 and -2

D. -2 and 5

2. Ava drove her car at a constant rate to the train station. At the train station, she waited for the train to arrive. After she boarded the train, she traveled at a constant rate, faster than she drove her car. She entered the taxi and traveled at a constant speed. This speed was equal to the speed at which she had driven her car earlier. After some time, she arrived at her destination.

Which graph represents Ava’s travel plans? (First 3 graphs are the options to this question.)

For the function f(x, y, z) = xyz and the solid region Q defined as Q = {(x, y, z): 0 ≤ x ≤ 1, 0 ≤ y ≤ 7x, 0 ≤ z ≤ 3}, we can write the triple integral in six different orders of integration.

Each order represents a different sequence of integrating with respect to the variables x, y, and z. One of the triple integrals will be evaluated.

The six possible orders of integration for the triple integral of f(x, y, z) = xyz over the solid region Q = {(x, y, z): 0 ≤ x ≤ 1, 0 ≤ y ≤ 7x, 0 ≤ z ≤ 3} are as follows:

dz dy dx: Integrate first with respect to z, then y, and finally x. The limits of integration are z = 0 to z = 3, y = 0 to y = 7x, and x = 0 to x = 1.

dz dx dy: Integrate first with respect to z, then x, and finally y. The limits of integration are z = 0 to z = 3, x = 0 to x = 1, and y = 0 to y = 7x.

dx dz dy: Integrate first with respect to x, then z, and finally y. The limits of integration are x = 0 to x = 1, z = 0 to z = 3, and y = 0 to y = 7x.

dx dy dz: Integrate first with respect to x, then y, and finally z. The limits of integration are x = 0 to x = 1, y = 0 to y = 7x, and z = 0 to z = 3.

dy dz dx: Integrate first with respect to y, then z, and finally x. The limits of integration are y = 0 to y = 7x, z = 0 to z = 3, and x = 0 to x = 1.

dy dx dz: Integrate first with respect to y, then x, and finally z. The limits of integration are y = 0 to y = 7x, x = 0 to x = 1, and z = 0 to z = 3.

Now, let's evaluate one of the triple integrals, specifically the one with the order of integration dz dy dx:

∫∫∫xyz dz dy dx over the limits z = 0 to 3, y = 0 to 7x, and x = 0 to 1.

By evaluating this triple integral, we can find the numerical value of the integral and hence the answer to the specific computation.

To learn more about variables click here:

brainly.com/question/15078630

#SPJ11

Answer:

i know that y and z are both 53 degrees

Step-by-step explanation:

Answer:

x and y are both 53 degrees

I am pretty sure z is 106. tell me if it's not because I have two different answers it could be.

Answer:

12 adults

Step-by-step explanation:

We can solve this in a couple of simple steps. First, since there are 3 adults for every 8 students we add these two numbers together

3+8 = 11

Now we simply divide this number by the total amount of people that went to the trip in order to get how many times this set of adults and students repeats itself.

44 / 11 = 4

Finally, we multiply this number by the set of 3 adults in order to find out how many adults went to the trip.

4 * 3 = 12 adults

8 * 3 = 32 Students