The length if a photograph is 6 inches less than twice the width. The photograph is mounted in a frame that is 3 inches wide on all sides. If the area of the framed picture is 270 square inches, find the dimensions of the unframed photograph.​

The solutions to the trigonometric equation 2 cos²0-2sin²0= √3 is option C.

It should be noted that a trigonometric equation is one that contains a trigonometric function with a variable. For example, sin x + 2 = 1 is an example of a trigonometric equation.

The equations can be something as simple as this or more complex like sin2 x – 2 cos x – 2 = 0.

In this case, solutions to the trigonometric equation 2 cos²0-2sin²0= √3 is π/12 + πn and 11x/12 + πn

The correct option is C.

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Answer:

Step-by-step explanation:

in question no. 17

base=x

perpendicular=9

hipotanus=15

by applying pythagorus

(x)² + (9)² = (15)²

x=√(15)²-(9)²

x= √225-81

x=√144 = 12

now area of triangle = 1/2 ×base×height

= 1/2 × 12 × 9 = 54

area of figure 17 = 54 × 2 = 108

Examining the graph it can be deduced that

The domain is

The range is

The graph is not a function

To qualify as a function, any input (x-value) of a graph must be linked to a single output (y-value). Therefore, each x-value ought to have one and only one y-value that matches it.

A method for identifying whether or not a given graph is representative of a function is by conducting a vertical line test. To achieve this, vertically draw lines through the graph. When every vertical line hits the graph at just one point, then the illustration aptly presents a function. Conversely, if the graph forms multiple intersection points with any vertical line, it isn't classified as a functional representation.

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Answer:

Step-by-step explanation:

A

The solution to the system of linear equations graphed below is (3, -1).

Given are two graphs of linear equations.

The solution of a system of linear equations can be solved either numerically or graphically.

In the graphical method, the solution of a system of linear equations is the point where all the lines intersect.

Here the lines of both the equations intersect at (3, -1).

This means that the intersecting point is (3, -1).

Solution is (3, -1).

Hence the required solution is (3, -1).

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The probability of the TPMS triggering a warning is 0.0198 or about 0.02, rounded to four decimal places.

It is used to predict and estimate the likelihood of future events and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Let's assume that the tire pressure follows a normal distribution with a mean of 32 psi and a standard deviation of 3 psi.

Let's also assume that the TPMS warning is triggered when the tire pressure falls below 25 psi or rises above 39 psi.

Using a standard normal distribution table or calculator, we can find the z-scores corresponding to 25 psi and 39 psi:

z₁ = (25 - 32) / 3 = -2.3333

z₂ = (39 - 32) / 3 = 2.3333

Then, we can find the probabilities associated with these z-scores:

P (z < -2.3333) = 0.0099

P (z > 2.3333) = 0.0099

The total probability of the TPMS triggering a warning is the sum of these two probabilities:

P(TPMS warning) = P(z < -2.3333) + P(z > 2.3333) = 0.0099 + 0.0099 = 0.0198

Therefore, the probability of the TPMS triggering a warning is 0.0198 or about 0.02, rounded to four decimal places.

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The correct answer is "not enough information to prove any parallel lines."

If two lines in a two-dimensional plane are parallel, then the corresponding angles formed by a transversal (a line that intersects both lines) are congruent (i.e., they have the same measure).

Additionally, the alternate interior angles (angles that are on opposite sides of the transversal and inside the pair of parallel lines), as well as the corresponding angles (angles that are in the same position relative to the transversal on the two parallel lines), are also congruent.

In the given diagram, line k is parallel to m, while line a is also parallel to line b but forming a transverse line to line k and line m. Also line k and line m form a transverse line to lines a and b.

So we can conclude that not enough information to prove any parallel lines.

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The mathematical expression is -12x³[tex]y^8[/tex].

We have,

-12x to the power of 3 y to the power of 8

Now, writing the mathematical expression

-12x to the power of 3  = -12x³

and, y to the power of 8 = [tex]y^8[/tex]

So, the expression can be written as

= -12x³[tex]y^8[/tex]

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Answer:

Step-by-step explanation:

To find the answer, we can use the formula for combinations:

nCr = n! / r!(n-r)!

where n is the total number of games, r is the number of losses, and n-r-1 is the number of ties (since we already know there are 9 wins).

Substituting the values, we get:

13C3 * 10C1

= (13! / 3!10!) * (10! / 1!9!)

= (13*12*11 / 3*2*1) * 10

= 2860

Therefore, there are 2860 ways the schedule can end with 9 wins, 3 losses, and 1 tie.

The value of the trigonometric ratios  are;

sin A = 2/5

cos A = 3/5

tan A = 2/3

It is important to note that there are six different trigonometric identities and their ratios.

We have;

From the diagram shown, we have;

sin θ = opposite/hypotenuse

cos θ = adjacant/hypotenuse

tan θ = opposite/adjacent

Then,

sin A = 6/15 = 2/5

cos A = 9/15 = 3/5

tan A = 6/9 = 2/3

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The value of the trigonometric ratios  are;

sin A = 2/5

cos A = 3/5

tan A = 2/3

It is important to note that there are six different trigonometric identities and their ratios.

We have;

From the diagram shown, we have;

sin θ = opposite/hypotenuse

cos θ = adjacant/hypotenuse

tan θ = opposite/adjacent

Then,

sin A = 6/15 = 2/5

cos A = 9/15 = 3/5

tan A = 6/9 = 2/3

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S-62 degrees

T-76 degrees

Step-by-step explanation:

IJ and KJ are congruent, so s would have the same measurement as I.

You would simply subtract from both s and i to get t.

Answer:

is the answer A????????????

to be honest I’m only here for the answers but I also need the points

[tex]f(x) = x^2 + 6x - 7[/tex] is the equation of the function.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

To find the equation of the quadratic function, we need to use the vertex form of the equation:

[tex]f(x) = a(x - h)^2 + k[/tex]

where (h, k) is the vertex of the parabola.

We know that the vertex is (-3, 16), so h = -3 and k = 16. We also know that the x-intercepts are at -7 and 1, which means that the factors of the quadratic function are (x + 7) and (x - 1).

To find the value of 'a', we can use either of the x-intercepts:

[tex]f(-7) = a(-7 + 3)^2 + 16 = 0\\\\16a = 16\\\\a = 1[/tex]

Therefore, the equation of the quadratic function is:

[tex]f(x) = (x + 7)(x - 1)\\\\f(x) = x^2 + 6x - 7[/tex]

So the answer is (A)[tex]f(x) = x^2 + 6x - 7[/tex].

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The solution of the equation is [tex]z = \frac{[-9 \±9\sqrt{3 i}]}{2}[/tex]

Given is an equation, [tex]\frac{1}{z+9} -\frac{1}{z} = \frac{1}{9}[/tex], we need to solve it,

[tex]\frac{1}{z+9} -\frac{1}{z} = \frac{1}{9}[/tex]

[tex]\frac{z-(z+9)}{z(z+9)} = \frac{1}{9}[/tex]

[tex]\frac{-9}{z^2+9z} =\frac{1}{9}[/tex]

[tex]z^2+9z = -81\\\\z^2+9z+81 = 0[/tex]

Using the quadratic formula,

[tex]x = \frac{[-b \±\sqrt{(b^2-4ac)}]}{2a}[/tex]

here, a = 1, b = 9 and c = 81.

So,

[tex]z = \frac{[-9 \±\sqrt{(81-4(81))}]}{2}\\\\z = \frac{[-9 \±\sqrt{(-243)}]}{2}\\\\\\\\\z[/tex]

[tex]z = \frac{[-9 \±9\sqrt{3 i}]}{2}[/tex]

Hence, the solution of the equation is [tex]z = \frac{[-9 \±9\sqrt{3 i}]}{2}[/tex]

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The reflection of the figure over y = -2x - 1 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.

Because the line of reflection has a slope of -1/2, each image point will be on a line with a slope of 2 that passes through the associated pre-image point.

It might be simplest to count the grid squares between the pre-image point and the line, then from the line to the image point's location. Those measurements will be the same.

The second attachment shows the mirrored image.

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Answer:

  see attached

Step-by-step explanation:

You want the 2-way table filled based on the descriptions of its contents.

The total number of students surveyed (240) goes in blank 9, where row and column headings are both "Total".

The number 35% × 240 = 84 goes in blank 7, the total number interested in athletics.

The number 3/5 × 240 = 144 goes in blank 3, the total number interested in academic clubs.

The number 26 goes in blank 1, which is in row 1 (interested in academic clubs) and in column 1 (interested in athletics). It is the number interested in both.

Blank 2 is the difference between blank 3 and blank 1. It makes the total for the line be correct.

Blank 4 is the difference between blank 7 and blank 1. It makes the total for the column be correct.

Similarly, blanks 8 and 6 are differences that make the row and column totals (respectively) be correct.

Finally, blank 5 is the value that makes its row and column totals be correct. The fact that the one number makes two correct totals gives you a check on that number.

The filled table is shown in the first attachment. The calculations are shown in the second attachment.

The number of volumes of the encyclopedia on the bottom shelf is given as follows:

H) 19.

The number of volumes of the encyclopedia on the bottom shelf obtained as the subtraction between the highest number and the lowest number identifying the numbers, adding one.

We add one as the amount of numbers between n and n + 1, inclusive, is of n + 2. For example, between 12 and 13, we have two numbers.

Then the number of volumes of the encyclopedia on the bottom shelf is given as follows:7

30 - 12 + 1 = 19.

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To transform the left-hand side of the given identity "1 + cos(2x)" into the right-hand side "[tex]2cos^2(x)[/tex]", the expression "1" should be changed to "[tex]2sin^2(x)[/tex]" and the left-hand side should be simplified.

Trigonometric identities are mathematical equations that may be used to express trigonometric functions. These identities, which are also used to solve trigonometric equations, can be utilised to simplify and manage trigonometric expressions.

Trigonometric identities, which are derived from the geometric properties of triangles and the unit circle, provide a way to describe trigonometric functions in terms of other trigonometric functions or constants. In many areas of mathematics, physics, engineering, and other fields where trigonometry is used, they are commonly used.

Replacing  "1" with "[tex]2sin^2(x)[/tex]".

[tex]1 + cos(2x) -- > 2sin^2(x) + cos(2x)[/tex]

Using the double angle formula for cosine

The double angle formula for cosine is: cos(2x) = [tex]2cos^2(x) - 1[/tex]

Substitute the double angle formula into the expression for cos(2x) on the left-hand side.

[tex]2sin^2(x) + cos(2x) -- > 2sin^2(x) + (2cos^2(x) - 1)[/tex]  [Substitute cos(2x) with [tex]2cos^2(x) - 1[/tex]]

Simplify the expression on the left-hand side.

[tex]2sin^2(x) + (2cos^2(x) - 1) -- > 2sin^2(x) + 2cos^2(x) - 1[/tex] [Simplify using distributive property]

[tex]2sin^2(x) + 2cos^2(x) - 1 -- > 2(sin^2(x) + cos^2(x)) - 1[/tex] [Apply trigonometric identity [tex]sin^2(x) + cos^2(x) = 1[/tex]]

[tex]2(sin^2(x) + cos^2(x)) - 1 -- > 2(1) - 1[/tex] [Substitute [tex]sin^2(x) + cos^2(x)[/tex]with 1]

[tex]2(1) - 1 -- > 2 - 1\\2 - 1 -- > 1[/tex]

So, following simplification, the left-hand side equation "1 + cos(2x)" may be changed into "1." As a result, "1" in the equation needs to be altered to "2sin(x)" and the left side should be simplified to "1".

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The number of tests Rick has taken are 7.

The average of given numbers is equal to the sum of all the values divided by the total number of values. It  generally refers to a measure of central tendency or the typical value within a set of data points.

The mean, or arithmetic mean, is the most commonly used type of average. It is calculated by adding up all the values in a data set and dividing by the total number of data points. Mathematically, the mean is represented as:

Mean = (Sum of all values) / (Total number of data points)

Based on the given conditions, formulate:

581/83 =7

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The length of the hypotenuse is 4√2.

What is the Pythagoras theorem?

A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem or Pythagoras' theorem. According to this rule, the area of the square with the hypotenuse side is equal to the sum of the areas of the squares with the other two sides.

Here, we have

Given: base = 4

perpendicular = 4

We have to find the length of the hypotenuse.

We apply here Pythagoras theorem and we get

b² + p² = h²

(4)² + (4)² = h²

16 + 16 =  h²

32 =  h²

h = 4√2

Hence, the length of the hypotenuse is 4√2.

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The actual distance between the two cities is equal to 288 miles.

In Geometry and Mathematics, a scale factor simply refers to the ratio of two corresponding side lengths in two similar geometric figures, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.

In Geometry, the scale factor of a geometric figure can be calculated by dividing the side lengths of the image by the side lengths of the pre-image:

Scale factor = length of image (new figure)/length of pre-image (actual figure).

Scale:

0.25 inch = 24 miles

0.25/24 = New distance/Actual distance

0.25/24 = 3/Actual distance

Actual distance = (24 × 3)/0.25

Actual distance = 288 miles.

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The slope of a line given the table is equal to 0.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the slope formula, we have the following;

Slope (m) = (9 - 9)/(3 - 1)

Slope (m) = 0/2

Slope (m) = 0.

Based on the table, the slope is the change in y-axis with respect to the x-axis and it is equal to 0.

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Answer:

f(x) = 16*0.75^x

Step-by-step explanation:

first off let's use this coordinate (the one given) :

(0,16)

let's substitute this into the equation with x being 0 and f(x) being 16

16 = a*b^0

*anything to the power of 0 is 1*

so:

a = 16

now use the second coordinate :

(1,12)

and do the same by substituting 1 for x and 12 for f(x), we also know what 'a' is:

12 = 16*b^1

12 = 16 * b

b = 3/4

so :

f(x) = 16*0.75^x

The total surface area of the cuboid with 7cm,5cm, and 10cm as dimensions is 310 square. cm and the volume is 350 cubic. cm.

Given dimensions of the figure are 7cm,5cm, and 10cm.

Length = 7cm.

Width = 5cm.

Height = 10cm.

The surface area of the cuboid = 2(lw+wh+lh).

Now, let us substitute the given values in the above formula.

2(7*5+5*10+7*10)

2(35+50+70)

2(155) = 310.

Therefore, the surface area of the figure is 310 square. cm.

Now, we have to find the volume of the figure.

Volume = Length x Width x Height.

Volume = 7*5*10

Volume = 350.

Therefore, the volume of the figure is 350 cubic. cm.

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A. The cash flow would be $91,400 if the depreciation were $48,000.

B. The cash flow would be $81,800 if the depreciation were $16,000.

C. The lost cash flow due to the reduced depreciation from $48,000 to $16,000 is $9,600.

Earnings before depreciation and taxes = $110,000

Depreciation = $48,000

Earnings before taxes = $62,000 ($110,000 - $48,000)

Taxes (30%) = $18,600 ($62,000 x 30%)

Earnings after taxes =  $43,400 ($62,000 - $18,600)

Depreciation $48,000

Cash flow = $91,400 ($43,400 + $48,000)

Earnings before depreciation and taxes = $110,000

Depreciation = $16,000

Earnings before taxes = $94,000 ($110,000 - $16,000)

Taxes (30%) = $28,200 ($94,000 x 30%)

Earnings after taxes =  $65,800 ($94,000 - $28,200)

Depreciation $16,000

Cash flow = $81,800 ($65,800 + $16,000)

Cash flow at $48,000 depreciation = $91,400

Cash flow at $16,000 depreciation = $81,800

Lost cash flow = $9,600 ($91,400 - $81,800)

Thus, we can learn that reduced depreciation increases the tax liability, thereby reducing the cash flow.

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A. The cash flow would be $91,400 if the depreciation were $48,000.

B. The cash flow would be $81,800 if the depreciation were $16,000.

C. The lost cash flow due to the reduced depreciation from $48,000 to $16,000 is $9,600.

Earnings before depreciation and taxes = $110,000

Depreciation = $48,000

Earnings before taxes = $62,000 ($110,000 - $48,000)

Taxes (30%) = $18,600 ($62,000 x 30%)

Earnings after taxes =  $43,400 ($62,000 - $18,600)

Depreciation $48,000

Cash flow = $91,400 ($43,400 + $48,000)

Earnings before depreciation and taxes = $110,000

Depreciation = $16,000

Earnings before taxes = $94,000 ($110,000 - $16,000)

Taxes (30%) = $28,200 ($94,000 x 30%)

Earnings after taxes =  $65,800 ($94,000 - $28,200)

Depreciation $16,000

Cash flow = $81,800 ($65,800 + $16,000)

Cash flow at $48,000 depreciation = $91,400

Cash flow at $16,000 depreciation = $81,800

Lost cash flow = $9,600 ($91,400 - $81,800)

Thus, we can learn that reduced depreciation increases the tax liability, thereby reducing the cash flow.

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Answer:

40%

Step-by-step explanation: