Given the definitions of f(x) and g(x) below,
find the value of (gof)(-7).
f(x)
13
g(x) = 2x² - 6x – 10
=
- 2x

A table representing the transactions based on the question prompt is given below:

Date Transaction Type Check No. Description Debit (-) Credit (+) Balance

10/01 Starting Balance - - - - $1,863.90

10/03 Check 621 Telephone Company $71.10 - $1,792.80

10/07 Check 622 Banner Reality (Rent) $500.00 - $1,292.80

10/08 Check 623 Electric Company $51.12 - $1,241.68

10/10 Check 624 Cathy Santoro (Piano) $25.00 - $1,216.68

10/15 Deposit - Paycheck - $650.00 $1,866.68

10/16 Check 625 Don's Day Camp $200.00 - $1,666.68

10/18 Check 626 Ed's Sporting Goods $90.00 - $1,576.68

10/21 Check 627 Maple Place Garage $49.00 - $1,527.68

11/15 Deposit - Paycheck - $400.00 $1,927.68

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Hey!

For any graphing calculator problems I would recommend using desmos if your teacher allows it or getting a graphing calculator such as a ti-nspire :)

This way, it will be able to graph and get the answers quicker!

The answers to this question is (37.5,15) and (0,60). To find your answers when you graph always look for where the lines intersect. If the lines do not intersect then it is not one of your answer choices. (examples are below).

The discriminant is positive for all values of k, thus, the roots are always real.

For a quadratic equation:

0 = ax^2 + bx +c

The discriminant is defined as:

D = b^2 - 4ac

If the discriminant is positive, then the roots are real.

Here we have:

x^2 +(1-k)x+k-3

Then:

a = 1

b = (1 - k)

c = k - 3

The discriminant is:

D = (1 - k)^2 - 4(k - 3)

D = 1^2 - 2k + k^2 - 4k + 12

D = k^2 - 6k + 13

Now notice that the vertex of this quadratic is at:

k = 6/2 = 3

Evaluating there we get:

D = 3^2 - 6*3 + 13

D = 9 - 18 + 13 = 4

So the discriminant is positive for all values of k, meaning that all the roots are real.

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Applying the triangle sum theorem, the value of x in the image given is:

x = 33°;   x = 45°

Recall that according to the triangle sum theorem, all three interior angles of a triangle is equal to 180 degrees.

a. x + 21 + (180 - 54) = 180 [triangle sum theorem]

x + 147 = 180

x = 180 - 147

x = 33°

b. (180 - 102) + x + 57 = 180 [triangle sum theorem]

x + 135 = 180

x = 180 - 135

x = 45°

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The indicated probability for the given mean and standard deviation for  P(7 ≤ x ≤ 10) is equal to 0.6915 approximately.

Mean = 8

Standard deviation = 2

Standardize the distribution using the formula,

z = (x - μ) / σ

where μ is the mean and σ is the standard deviation.

Substituting the given values, we get,

z = (x - 8) / 2

We want to find P(7 ≤ x ≤ 10),

which is the same as finding the probability that z is between,

z = (7 - 8) / 2

  = -0.5

and

z = (10 - 8) / 2

  = 1

Using a standard normal table .

Find the area under the standard normal distribution curve between -0.5 and 1.

P(-0.5 ≤ z ≤ 1) ≈ 0.6915

Attached table.

This implies,

P(7 ≤ x ≤ 10) ≈ 0.6915.

Therefore, the probability that x is between 7 and 10 is approximately 0.6915.

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The above question is incomplete, the complete question is:

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.)

μ = 8; σ = 2

P(7 ≤ x ≤ 10) =

The preceding polynomial equation has three solutions: z = 0, z = 3/4, and z = -1/5.

First, we can factor out a common factor of z:

z(20z² - 11z - 3) = 0

Now we need to factor the quadratic expression in the parentheses.

We can use the quadratic formula or factor by grouping to do this. Factoring by grouping yields:

z(20z² - 11z - 3) = 0

z(4z - 3)(5z + 1) = 0

Setting each of the factored terms equal to zero, we have:

z = 0, 3/4, -1/5

Therefore, the solutions to the given polynomial equation are z = 0, z = 3/4, and z = -1/5.

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Answer: B) The report accurately stated the results because the sample size was sufficient.

Step-by-step explanation:

The given statement in the report about a possible causal relationship between age and responses cannot be determined solely based on the information provided. However, the statement can be considered accurate because the sample size of 100 people from a local high school was sufficient to provide reliable results. The fact that the majority of those surveyed were teenagers does not make the report inaccurate or unreliable. The mean response score of 1.5 and the standard deviation of 0.3 are valid indicators of the attitudes of the surveyed group towards the age at which an individual can receive a driver's license.

The approach employed in this specific instance is a non-probability sampling technique labeled as convenience sampling.

It involves selecting the participants based on convenience or, in other words, selecting those who are readily available to take part in the study. Hence the school district has decided to dispatch the survey to all parents whose children have access to the online questionnaire.

The selected sample principally arises from considerations of the ease with which it can be attained, thus making convenience rather than randomness the dominant factor informing the selection process.

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A school district sends an online survey to all parents of students in the district asking for feedback on props educational changes on recent tax cuts

What is the sampling method used here

Answer: 1/5

Step-by-step explanation:

In this case, you multiple the exponents together because you are raising a power to a power:

25^(-3/2 * 1/3)

25^(-3/6)

25^(-1/2)

Next, when the power is negative, we can get rid of it by changing the whole number to its reciprocal (divide the number by one):

1/(25^(1/2))

Now, when an exponent is a fraction, the numerator is what the base is raised to and the denominator is what the base is rooted to:

1/(sqrt(25))

Now, simplify:

1/5

The polar coordinates in rectangular coordinates are (3√2, 2√6)

Given are polar coordinates (6√2, 7π/3), we need to convert it into, rectangular coordinates.

so, (r, θ) = (6√2, 7π/3)

x = rcosθ

y = rsinθ

r = 6√2, θ = 7π/3

x = 6√2 cos 7π/3 = 3√2

y = 6√2 sin 7π/3 = 2√6

Hence, the polar coordinates in rectangular coordinates are (3√2, 2√6)

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The cost of one hour of television each day is $1.

We have,

The average electricity bill reduced to $130 to $40.

Number of days in month= 30 days

So, the cost of one hour of television is

= (130- 40) /30

= 90 /30

= $30

Thus, the cost of one hour of television is $ 30.

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The function f(x)* = 1 + x^2 is defined for all real numbers x, so the domain is all real numbers, or (-∞, ∞).

In determining the function's output values, one must consider its collection of feasible results to extract the range. Reviewing f(x)* exhibits a minimum value of 1 due to x^2 being perpetually non-negative, while adding another factor merely preserves positivity.

Concurrently as x skyrockets, so too does the value of f(x)* given that approaching infinity generates infinitely larger powers than any constant coefficient subordinated by it. Consequently, the overall range of f(x)* becomes [1, ∞), enwrapping all feasible solutions equivalent or superior to 1.

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The x and y values in the triangle are:

x = 58°

y = 26°

Trigonometry deals with the relationship between the ratios of the sides of a triangle with its angles.

To find the x and y values in the triangle, check the attached image for labeling.

In the image:

Triangle ABC is isosceles. Thus,

t = 61° (base angles of isosceles triangles are equal)

x + t + 61 = 180  (sum of angles in a triangle is 180°)

x + 61 + 61 = 180

x = 180 - 61 - 61

x = 58°

x + v = 180 (sum of angles on a straight line is 180°)

58 + v = 180

v = 180 - 58

v = 122°

In triangle ACD:

32 + v + y = 180  (sum of angles in a triangle is 180°)

32 + 122 + y = 180

y = 180 - 32 - 122

y = 26°

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The effect of increasing the distance e between charged object is that , the electric force decreases because the distance has an indirect relationship to the force.

Coulomb's law states that the force between two charged bodies is directly proportional to the product of the charge and inversely proportional to the square of the distance between them.

Coulomb's law can therefore be expressed mathematical as;

F = Q1Q2/r²

where r is the distance between charge Q1 and Q2

This means that since the force is inversely proportional to the square of distance, force will decrease as distance is increasing.

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The volume of the rectangular prism is 90 units³

We have,

The figure shown has the dimensions:

L = Length = 5 units

W = Width = 6 units

H = Height = 3 units

Now,

The volume of the rectangular prism.

= L x W x H

= 5 x 6 x 3

= 90 units³

Thus,

The volume of the rectangular prism is 90 units³

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The expression is simplified to √5

From the information given, we have that;

logₐ x = 3

logₐ y = 4

logₐ z = 5

Given that the expression is;

logₐ [tex]\sqrt[4]{\frac{y^3z^6}{x^4z^-^2} }[/tex]

Now, we have to substitute the value of the logarithm into the expression.

We have;

[tex]\sqrt[4]{\frac{4^35^6}{3^45^-^2} }[/tex]

Find the value of the index forms and substitute;

[tex]\sqrt[4]{\frac{64(625)}{81(1/25)} }[/tex]

Multiply the values and expand the bracket

3(5)/3(5^⁻²/4)

multiply the values

15/3(5^-1/2)

Find the square root of the denominator, we have

15/3(√5)⁻¹

5/√5

Rationalize the surd form, we get;

5√5/5

Then, we have;√5

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The value of -5/6 ÷( -1/4) is 3 1/3

A fraction is a part of a whole. it consist of upper part( numerator) and lower part denominator.

In a simple fraction, both numerator and denominator are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Solving -5/6 ÷( -1/4)

-5/6 × -4/1

= 20/6

= 10/3

= 3 1/3

therefore the value of the expression is 3 1/3

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To find the variability in the distribution of the means, we need to calculate a measure of spread, such as the standard deviation. We can use the dot plot to estimate the standard deviation of the distribution.

From the dot plot, we see that the range of the means is from 0 to 150 bags of dog food sold per day. The midpoint of this range is 75, which we can use as an estimate of the population median. We can estimate the standard deviation by calculating the distance between the median and the quartiles.

From the dot plot, we can see that the lower quartile (Q1) is around 60, and the upper quartile (Q3) is around 110. Therefore, the interquartile range (IQR) is:

IQR = Q3 - Q1 = 110 - 60 = 50

We can use the IQR to estimate the standard deviation by assuming that the distribution is approximately normal and using the empirical rule, which states that:

Approximately 68% of the data falls within one standard deviation of the mean.

Approximately 95% of the data falls within two standard deviations of the mean.

Approximately 99.7% of the data falls within three standard deviations of the mean.

Since the IQR is about half of the range, we can estimate the standard deviation as:

SD ≈ IQR / 1.35 ≈ 50 / 1.35 ≈ 37

Therefore, an appropriate estimate of the standard deviation of the distribution of means is 37, rounded to the nearest whole number.

Interpretation: The variability in the distribution of means is relatively large, with a standard deviation of approximately 37 bags of dog food sold per day. This means that the mean number of bags sold per day can vary by as much as 37 bags from one sample to another.

Answer:

3x = 6y

Step-by-step explanation:

8 - 2y = 6y and 3x is by itself so it would be 3x is equal to 6y.

The angle measure explained in the solution.

Given that, a || b, we need to find the missing angles,

∠1 = 42° [vertically opposite angles]

∠3 = 62° [vertically opposite angles]

∠2 = 180°-(∠1+62°) [angle in a straight line]

∠2 = 76°

∠4 = ∠2 [vertically opposite angle]

∠4 = 76°

∠4 = ∠9 = 76° [alternate angles]

∠9 = ∠12 = 76° [vertically opposite angle]

∠3 = ∠ 6 = 62° [alternate angles]

∠ 6 = ∠7 = 62° [vertically opposite angle]

∠3 + ∠5 = 180° [consecutive angles]

∠5 = 118°

∠5 = ∠8 = 118° [vertically opposite angle]

∠4 + ∠10 = 180° [consecutive angles]

∠10 = 104°

∠10 = ∠11 [vertically opposite angle]

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The implementing of subtraction as a money lesson need a starting with concrete examples and building students' understanding of the concept in scenarios.

As a mathematical concept, subtraction is useful in real-life scenarios including managing money. To implement it, we must note that it important to start with concrete examples that students can relate to like making purchases or earning an allowance.

We can provide the students with a set amount of money and ask them to subtract the cost of various items from it to determine how much they have left. For example, if a student has $10 and wants to buy a $3 toy, they would need to subtract $3 from $10 to determine that they have $7 remaining.

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A polynomial function f(x) of degree 3 with given zeros, 2, -3 , 5 and condition f(3)=6 is given by f(x) = -1/2 (x-2)(x+3)(x-5).

Degree of the polynomial function is equal to 3.

Zero's of the polynomial function is equal to 2, -3 , 5 .

And f(3) = 6

If 2, -3, and 5 are zeros of f(x), then we can write function as,

f(x) = a(x-2)(x+3)(x-5)

where a is some constant.

To determine the value of a, we can use the fact that f(3) = 6.

Substituting x = 3 into the equation above, we get,

f(3) = a(3-2)(3+3)(3-5)

     = -12a

Here we have,

f(3) = 6, so we can set these two expressions equal to each other and solve for a,

⇒ -12a = 6

⇒ a = -1/2

Now we can substitute this value of a back into the equation for f(x) that we found earlier,

⇒ f(x) = -1/2 (x-2)(x+3)(x-5)

Therefore, a polynomial function f(x) of degree 3 with zeros 2, -3, 5, and f(3) = 6 is equal to f(x) = -1/2 (x-2)(x+3)(x-5).

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The line equations according to its features are, respectively:

Case C: y = - 2

Case D: x = - 7

Case E: y = - x + 1 / 2

Case F: y = - (1 / 3) · x + 20 / 3

Case G: y = 4 · x + 17

In this question we must determine five line equations based on its features. The equation of the line can be found by understanding the following features:

There are two forms of the equation of the line:

Slope-intercept

y = m · x + k

Standard

a · x + b · y + c = 0

Where:

Now we proceed to determine the equation of each line:

Case C: m = 0, (x, y) = (- 7, - 2)

- 2 = 0 · (- 7) + k

k = - 2

y = - 2

Case D: m = 0, (x, y) = (- 7, - 2)

x = - 7

Case E: k = 1 / 2, m = - 1

y = - x + 1 / 2

Case F: Parallel to x - 3 · y = 9, (x, y) = (2, 6)

x - 3 · y = 9

3 · y = 9 - x

y = 3 - (1 / 3) · x

m = - 1 / 3

6 = - (1 / 3) · 2 + k

6 = - 2 / 3 + k

k = 20 / 3

y = - (1 / 3) · x + 20 / 3

Case G: Perpendicular to y + (1 / 4) · x - 5 = 0, (x, y) = (- 3, 5)

y + (1 / 4) · x - 5 = 0

y = - (1 / 4) · x + 5

m = - 1 / 4

m' = 4

5 = 4 · (- 3) + k

5 = - 12 + k

k =  17

y = 4 · x + 17

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One way Olivia might have moved ABCDE onto A"B"C"D"E" is by first reflecting ABCDE over the x-axis, and then translating it 4 units to the left and 6 units down.

1) This would map point A to A", B to B", C to C", D to D", and E to E", creating A"B"C"D"E".

2) Angelica's transformation does not result in a figure that matches A"B"C"D"E". Reflecting ABCDE over the y-axis would map point A to A", B to E", C to D", D to C", and E to B", so the shape would be flipped horizontally. Translating it up 8 units would then shift the shape up, but it would still be horizontally flipped, so it would not match A"B"C"D"E".

3) Michael's claim is not correct. Translating ABCDE diagonally 8 units up and 10 units right would move point A to point J, which is not on A"B"C"D"E". The other points would also not be in their correct positions, so the resulting shape would not match A"B"C"D"E". To get to A"B"C"D"E" with one transformation, Michael would need to use a combination of translation, rotation, and/or reflection.

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Answer:

What do we have to do in this? Find x? Let me know I'll explain it in the comment section

Note that the graph of WXY when reflected to W'X'Y' is attached accordingly.

A reflection in mathematics is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a fixed point set; this set is known as the axis or plane of reflection. A figure's reflection image is its mirror image in the axis or plane of reflection.

A line of reflection is required to accomplish a geometric reflection; the resulting orientation of the two figures is opposite.

The distance between the corresponding portions of the figures is the same. Ordered pair rules reflect along the x-axis (x, -y), the y-axis (-x, y), and the line y=x (y, x).

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The volume of the resulting solid revolved around the x-axis is equal to  28.274 cubic units (round to the nearest thousandth).

Vertices of the right triangle are,

(0, 0), (0, 3) and (-4, 0)

To obtain the solid formed by revolving the given right triangle about the x-axis, use the disk method.

The cross-sectional area of the solid at a given height is a circle with radius = distance between the x-axis and the upper edge of the triangle at that height.

The height of the triangle is 3 units,

and the base of the triangle is 4 units.

So, the equation of the hypotenuse of the right triangle can be found as follows,

y = (3/4)x + 3

Now, let us consider a horizontal slice of the solid at a distance y units above the x-axis.

The radius of the circle at this height is ,

r = y - 3

The area of the circle at this height is ,

A = πr²

   = π(y - 3)²

The limits of integration are y = 0 the x-axis to y = 3 the height of the triangle.

Using the disk method, the volume of the solid is,

V = [tex]\int_{0}^{3}[/tex] π(y - 3)²dy

Evaluating the integral, we get,

⇒ V = π /3 ( y - 3 )³[tex]|_{0}^{3}[/tex]

⇒ V = π/3 [( 3- 3 )³ - ( 0 -3)³ ]

⇒ V = (π /3) ( 27)

⇒V  = 9π

⇒V  = 9 (3.1415)

Rounding to the nearest thousandth gives,

V ≈ 28.274

Therefore, the volume of the solid formed by revolving the given right triangle about the x-axis is approximately 28.274 cubic units.

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Car Make and Model that i choose is Toyota RAV4

The Cost of this car as of today is about $27,000

To know the value of car after one year will be:

20% of $27,000

= $5,400.

So the car  value will be:

$27,000 - $5,400

= $21,600 after year 1

3.  Value of car after second year of ownership:

15% of $27,000

= $4,050.

So, the car  value will be:

$21,600 - $4,050

= $17,550 after year 2.

4 The Exponential Function If the car continues to decrease in value by 15% each yea will be

V(x) = 27,000 x (0.85)ˣ

V(5) = 27,000 x (0.85)⁵

= 27,000  x  0.44370

= $11979.9

Therefore, the value of the car after owning it for five years is  $11979.9

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See text below



Car Value: Exponential

1. Pick a car that you would be interested in buying someday. Research the cost of buying this car.

Car Make and Model:

Cost of this car as of today:

2. Cars depreciate in value over time, which means they lose a certain percent of their value each year. A car typically decreases in value by 20% within the first year. If the car you picked above decreased in value by 20% in its first year, how much will it be worth one year after owning it?

Value of car after one year:

3. Each year after the first year, a car typically decreases around 15% in value. How much will your car be worth after owning it for 2 years?

Value of car after second year of ownership:

4. If your car continues to decrease in value by 15% each year, write the equation of the exponential function that models its value x years after you purchased it.

Exponential Function:

Use your exponential function to calculate the predicted value of your car after you own it for five years.

Value after five years of ownership:

The angle of elevation from the ground to the top of a 45 foot tree from 65 feet away is 33.41 degrees.

To find the angle of elevation from the ground to the top of a tree, we need to use some trigonometry. We can use the tangent function, which relates the opposite and adjacent sides of a right triangle.

Let's call the angle of elevation θ. We can draw a right triangle with the height of the tree (45 feet) as the opposite side and the distance from the tree to the observer (65 feet) as the adjacent side. Then, we can use the formula:

tan(θ) = opposite / adjacent

Plugging in the values we have:

tan(θ) = 45 / 65

We can solve for θ by taking the inverse tangent of both sides:

θ = arctan(45 / 65)

Using a calculator, we get:

θ ≈ 33.41 degrees

Therefore, the angle of elevation from the ground to the top of the tree is approximately 33.41 degrees.

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