If the surface area of a cube is 160 in2, then which best describes the length of an edge of the cube?

(a) It is possible to form a triangle with the angle measures, 30°, 80°, 70°

It is not possible for all such triangles to be congruent.

(b) It is possible to form a triangle with the angle measures, 20°, 105°, 55°

It is not possible for all such triangles to be congruent.

(c) It is not possible to form a triangle with the side lengths, 4cm, 3cm, 8cm

(d) It is possible to form a triangle with these side lengths.

All such triangles are congruent

From the question, we are to determine if it is possible for a triangle to have the given angle measures or side lengths

(a) To determine if a triangle can have the angle measures 30°, 80°, and 70°, we add the angles together to see if they equal 180°, the total degrees of a triangle.

30° + 80° + 70° = 180°

Since the angle measures add up to 180°, it is possible to form a triangle with these angle measures.

It is not possible for all such triangles to be congruent, since triangles with the same angle measures can have different side lengths.

(b) To determine if a triangle can have the angle measures 20°, 105°, and 55°, we add the angles together to see if they equal 180°.

20° + 105° + 55° = 180°

Since the angle measures add up to 180°, it is possible to form a triangle with these angle measures. However, it is not possible for all such triangles to be congruent, since triangles with the same angle measures can have different side lengths.

(c) To determine if a triangle can have side lengths 4cm, 3cm, and 8cm, we apply the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

4cm + 3cm > 8cm

4cm + 8cm > 3cm

3cm + 8cm > 4cm

Since all three inequalities are not satisfied (4 + 3 = 7 is not greater than 8, which is the longest side), it is not possible to form a triangle with these side lengths.

(d) To determine if a triangle can have side lengths 8cm, 15cm, and 17cm, we apply the triangle inequality theorem.

8cm + 15cm > 17cm

8cm + 17cm > 15cm

15cm + 17cm > 8cm

Since all three inequalities are satisfied, it is possible to form a triangle with these side lengths.

All such triangles are congruent, since these side lengths satisfy the conditions for a unique triangle known as a Pythagorean triple.

Hence, the triangle with side lengths 8cm, 15cm, and 17cm is a right triangle, and all right triangles with these side lengths are congruent by the Pythagorean theorem.

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The ratio of the surface areas to cube A to cube B is 12 : 7 .

What is known as a cube?

Six faces, eight vertices, and twelve edges make up the three-dimensional shape of a cube. An example of a prism in particular is a cube. These are the calculations for the volume of the cube formula: Amount = (side) 3.

                      The cube's face's diagonal length is equal to 2. (edge) Cube's cube's diagonal length is three (edge) 12 is the perimeter (edge). Each number multiplied by itself is a square number. The squared sign is (insert square symbol). Up to the number 100, the square numbers are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. A number multiplied by itself three times is a cube number.

The ratio of the volumes of cube A to cube B is  =  1728 : 343

                                                                       = 12 : 7

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The sign of each of the functions in the given interval is positive.

Suppose \( \theta \) is in the interval \( \left(90^{\circ}, 180^{\circ}\right) \), we can find the sign of each of the following functions by using the unit circle and the reference angles.

77. \( \cos \frac{\theta}{2} \)
Since \( \theta \) is in the second quadrant, \( \frac{\theta}{2} \) will be in the first quadrant. Therefore, the sign of \( \cos \frac{\theta}{2} \) will be positive.

78. \( \sin \frac{\theta}{2} \)
Similarly, since \( \theta \) is in the second quadrant, \( \frac{\theta}{2} \) will be in the first quadrant. Therefore, the sign of \( \sin \frac{\theta}{2} \) will be positive.

79. \( \sec \frac{\theta}{2} \)
The secant function is the reciprocal of the cosine function, so the sign of \( \sec \frac{\theta}{2} \) will be the same as the sign of \( \cos \frac{\theta}{2} \), which is positive.

In conclusion, the sign of each of the functions in the given interval is positive.

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Answer:

The dilated image has half the dimensions of the pre-image

So the pre-image is dilated by a scale factor of 1/2 (0.5)

Step-by-step explanation:

The side lengths of the dilated image is related to the preimage by a division of 2

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

The figure

Where we have

Pre-Image = PQRS

Image = P''Q'R'S'

From the figure, we can see that

The side lengths of P''Q'R'S' is half of the side lengths of PQRS

This means that

(x, y) = 1/2(x, y)

Hence, the transformation is (x, y) = 1/2(x, y)

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Step-by-step explanation:

Since the new poison kills half the population every 2 months, we can say that the remaining half will survive for another 2 months. Therefore, after 2 months, the rodent population will be half of 1,000,000, which is 500,000.

After another 2 months, the remaining half of the 500,000 will survive, which is 250,000.

After another 2 months, the remaining half of the 250,000 will survive, which is 125,000.

After 6 months, the rodent population will be 125,000.

Since 12 months is six 2-month periods, we can repeat this process again. After another 2 months, the rodent population will be 62,500.

After another 2 months, the rodent population will be 31,250.

After another 2 months, the rodent population will be 15,625.

Therefore, after 12 months, the rodent population will be 15,625.

There are infinitely many expressions equivalent to 11x + 10, including 22x + 20, 11(x+1)-1, -11(-x)-10, and 11(x+2)-12.

What is expression ?

In mathematics, an expression is a combination of numbers, symbols, and/or variables that are put together in a meaningful way, usually to represent a quantity or a mathematical relationship.

There are infinitely many expressions that are equivalent to 11x + 10, because you can add or subtract any expression to both sides of the equation to get a new equivalent expression. Here are some examples:

22x + 20: This is equivalent to 11x + 10 because if you distribute 11 to x and 10, you get 11x + 10.

11(x + 1) - 1: This is also equivalent to 11x + 10 because if you distribute 11 to x and 1, you get 11x + 11 - 1, which simplifies to 11x + 10.

-11(-x) - 10: This is equivalent to 11x + 10 because if you distribute -11 to -x, you get 11x + 10.

11(x + 2) - 12: This is also equivalent to 11x + 10 because if you distribute 11 to x and 2, you get 11x + 22 - 12, which simplifies to 11x + 10.

In general, any expression of the form 11x + k, where k is a constant, is equivalent to 11x + 10.

Therefore, there are infinitely many expressions equivalent to 11x + 10, including 22x + 20, 11(x+1)-1, -11(-x)-10, and 11(x+2)-12.

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This is shorter than the path made up of the two shortest sides by 33%.

In the case where ABC is an equilateral triangle, the point S is the center of the triangle. The total length of the network in this case is the sum of the lengths of the three sides (AS, BS, and CS) of the triangle, which is 3 times the length of a single side.

This is shorter than the path made up of the two shortest sides by 33%,

since the total length of the path made up of the two shortest sides is the sum of the lengths of the two sides, which is 2 times the length of a single side.

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Answer:

y - 17 = - 5(x + 7)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = - 5 and (a, b ) = (- 7, 17 ) , then

y - 17 = - 5(x - (- 7) ) , that is

y - 17 = - 5(x + 7)

Answer:

y = -5x - 18.

Step-by-step explanation:

The point-slope form of the equation of a line is given by:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is a point on the line.

We are given that the line passes through the point (-7, 17) and has a slope of -5. Thus, we can substitute these values into the point-slope form equation to get:

y - 17 = -5(x - (-7))

Simplifying the right-hand side of the equation:

y - 17 = -5(x + 7)

y - 17 = -5x - 35

Finally, adding 17 to both sides of the equation, we get the slope-intercept form of the equation:

y = -5x - 18

Therefore, the equation of the line that passes through the point (-7,17) with slope -5 is y = -5x - 18.

Accοrding tο similarity οf triangles, the length οf CF is 8/3.

Similarity οf triangles is a cοncept in geοmetry that describes the relatiοnship between twο triangles that have the same shape but may be different in size. Twο triangles are cοnsidered similar if their cοrrespοnding angles are cοngruent and their cοrrespοnding sides are prοpοrtiοnal.

Since FG is parallel tο CD, we can use similar triangles tο find the length οf CF. Let's call the length οf CF x. Then we have:

FE/FG = CD/CF

Substituting the given values, we have:

5/(x-1) = 8/x

Crοss-multiplying, we get:

5x = 8(x-1)

Expanding the brackets, we get:

5x = 8x - 8

Subtracting 5x frοm bοth sides, we get:

3x = 8

Dividing bοth sides by 3, we get:

x = 8/3

Therefοre, the length οf CF is 8/3.

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Complete question:

Answer: 41 hours and 15 minutes

Step-by-step explanation:

First, we count the time duration from 7:30am to 4:30pm, which is 9 hours.

Next, we subtract 45 minutes from 9 hours, which equals 8 hours and 15 minutes.

Last, we multiply that by 5 which equals 41 hours and 15 minutes.

Step-by-step explanation:

How many cups of milk are in a gallon = 16

If a recipe uses 2 cups for 6 servings, then he will make 48 servings from a gallon.

1 quart is 4 cups of milk, a gallon contains 4 quarts

1 pint is 2cups, a gallon contains 8pints of milk

From the question 1 gallon is 4 quarts or 8pints or 48servings

Answer:

[tex]2 \sqrt{5} [/tex]

Is the simplified form

Step-by-step explanation:

Greetings!!!

Given expression

[tex] \frac{10}{ \sqrt{5} } [/tex]

factor the number 10:5.2

[tex] = \frac{5.2}{ \sqrt{5} } [/tex]

Apply radical rule

[tex]a = \sqrt{a} \sqrt{a} [/tex]

[tex]5 = \sqrt{5} \sqrt{5} \\ = \frac{ \sqrt{5} \sqrt{5}.2 }{ \sqrt{5} } [/tex]

Cancel the common factor :✓5

[tex] = \sqrt{5} .2 \\ = 2 \sqrt{5} [/tex]

If you have any questions tag me on comments

Hope it helps!!!

Answer:

2 * [tex]\sqrt{5}[/tex]

Step-by-step explanation:

Given: [tex]\frac{10}{\sqrt{5} }[/tex]

Using the basis formula, you simplify it to:

2×[tex]\sqrt{5}[/tex]

Answer:

a) The height of the building is 382 feet.

b) The rock is 382 feet above the ground at its highest point.

c) It takes the rock 3.25 seconds to reach a height of 200 feet.

d) Tt takes the rock 4.76 seconds to hit the ground.

Step-by-step explanation:

The function that models the distance (in feet) between the rock and the ground t seconds after it is thrown is a quadratic function.

As the leading coefficient of the quadratic function is negative, it is a parabola that opens downwards.

The rock is thrown from the top of the building. Therefore, the height of the building is the value of d(t) when t = 0. This is the y-intercept of the graphed function.

Substitute t = 0 into the given function:

[tex]\begin{aligned}\implies d(0)&=-16(0)^2-4(0)+382\\&=0+0+382\\&=382\; \sf feet \end{aligned}[/tex]

Therefore, the height of the building is 382 feet.

The highest point of the rock is the height of the building, since the rock is thrown down from the top.

Therefore, the rock is 382 feet above the ground at its highest point.

This can be proven by finding the vertex of the graph of the function.

The vertex (maximum point) of the graphed function is (-0.125, 382.25).

As the x-value of the vertex is negative, and time can only be positive, the path of the rock is on a downwards trajectory when t ≥ 0. Therefore, the highest point is the point at which the rock is thrown.

To calculate how long it takes for the rock to reach a height of 200 feet, substitute d(t) = 200 into the given function and solve for t.

[tex]\begin{aligned}\implies -16t^2-4t+382&=200\\-16t^2-4t+182&=0\\-2(8t^2+2t-91)&=0\\8t^2+2t-91&=0\\8t^2+28t-26t-91&=0\\4t(2t+7)-13(2t+7)&=0\\(4t-13)(2t+7)&=0\\\\\implies 4t-13&=0 \implies t=\dfrac{13}{4}=3.25\; \sf s\\\implies 2t+7&=0 \implies t=-\dfrac{7}{2}=-3.5\; \sf s\end{aligned}[/tex]

As time is positive, t = 3.25 s only.

Therefore, it takes the rock 3.25 seconds to reach a height of 200 feet.

The rock will hit the ground when d(t) = 0.

Therefore, to calculate how long it takes for the rock to hit the ground, substitute d(t) = 0 into the given function:

[tex]\implies -16t^2-4t+382=0[/tex]

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Solve for t using the quadratic formula.

[tex]\implies t=\dfrac{-(-4) \pm \sqrt{(-4)^2-4(-16)(382)}}{2(-16)}[/tex]

[tex]\implies t=\dfrac{4 \pm \sqrt{24464}}{-32}[/tex]

[tex]\implies t=-\dfrac{4 \pm \sqrt{16 \cdot 1529}}{32}[/tex]

[tex]\implies t=-\dfrac{4 \pm \sqrt{16} \sqrt{1529}}{32}[/tex]

[tex]\implies t=-\dfrac{4 \pm 4\sqrt{1529}}{32}[/tex]

[tex]\implies t=-\dfrac{1 \pm \sqrt{1529}}{8}[/tex]

[tex]\implies t=-5.01280...,4.76280...[/tex]

As time is positive, t = 4.76 s only.

Therefore, it takes the rock 4.76 seconds to hit the ground.

The structure has a 382-foot height. The rock's highest peak is 39 1/2 feet high, or 195.5 feet. The time it takes for the rock to touch the ground is roughly 6.289 seconds.

In arithmetic, we use angles and distance to determine an object's height. The distance between the items is measured horizontally, and the height of an object is determined by the angle of the top of the object with respect to the horizontal.

By setting t = 0, we can determine the rock's starting height:

d(0) = -16(0)^2 - 4(0) + 382

= 382

The highest point of the rock occurs at the vertex of the parabolic route, which is determined by the formula t = -b/2a

where a = -16 and b = -4.

t = -(-4) / 2(-16) = 1/8

d(1/8) = -16(1/8)^2 - 4(1/8) + 382

= 391/2

The equation d(t) = -16t^2 - 4t + 382 = 200 for t:

-16t^2 - 4t + 382 = 200

-16t^2 - 4t + 182 = 0

4t^2 + t - 45.5 = 0

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The statement "W1 (+) W2 if and only if the expression 0=0+0 is the only expression of the vector 0 as sum of a vector in W1 and another in W2" is equivalent to the statement "W1 (+) W2 if and only if W1 ∩ W2 = {0}".

Proof:

(⇒) Assume that W1 (+) W2. This means that for any vector v ∈ V, there exist unique vectors w1 ∈ W1 and w2 ∈ W2 such that v = w1 + w2. In particular, for the vector 0 ∈ V, there exist unique vectors w1 ∈ W1 and w2 ∈ W2 such that 0 = w1 + w2. Since 0 is the additive identity, we must have w1 = 0 and w2 = 0. Therefore, the only vector in the intersection of W1 and W2 is the zero vector, so W1 ∩ W2 = {0}.

(⇐) Assume that W1 ∩ W2 = {0}. Let v ∈ V be an arbitrary vector, and suppose that there exist vectors w1, w1' ∈ W1 and w2, w2' ∈ W2 such that v = w1 + w2 = w1' + w2'. Then we have w1 - w1' = w2' - w2 ∈ W1 ∩ W2. But since W1 ∩ W2 = {0}, we must have w1 - w1' = 0 and w2' - w2 = 0, which implies that w1 = w1' and w2 = w2'. Therefore, the expression v = w1 + w2 is unique, so W1 (+) W2.

Thus, we have shown that W1 (+) W2 if and only if W1 ∩ W2 = {0}.

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The measure of the 2 angle in the triangle is 55 degrees.

In geometry, a kite is a quadrilateral with two pairs of adjacent sides that are equal in length. This means that a kite is a special type of quadrilateral called a "tangential quadrilateral" because its sides can be inscribed in a circle.

If one angle of a triangle is a right angle (90 degrees) and another angle is 35 degrees, then the sum of the three angles in the triangle is 180 degrees.

Therefore, the measure of the third angle can be found by subtracting the sum of the other two angles from 180 degrees:

Third angle = 180 degrees - 90 degrees - 35 degrees

Third angle = 55 degrees

So the measure of the 2 angle in the triangle is 55 degrees.

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The value of n in the n-sided polygon, with sides AC and AD, where the external angle formed at the point the decagon touches the n-sided polygon is 60° is; n = 15

A polygon is a planar shape with three or more straight sides.

The sum of angles at a point property indicates that, the sum of angles at the point A can be presented as follows;

∠BAC + ∠CAD + ∠DAB = 360°

Angle ∠BAC = 60°

Angle ∠DAB is an interior angle of a 10-sided regular polygon, (a decagon),  therefore, the measure of angle ∠DAB is 144°

Plugging in the values of the measures of the angles ∠BAC and ∠DAB, in the equation, ∠BAC + ∠CAD + ∠DAB = 360°, we get;

+ ∠CAD + 144° = 360°

∠CAD = 360° - (144° + 60°) = 156°

∠CAD = 156°

The formula for finding the measure of the interior angle of an n-sided polygon, θ, can be presented as follows;

θ = (n - 2) × 180°/n

Where the interior angle, θ = 156°, which is the measure of ∠CAD, in the n-sided polygon, we get;

156° = (n - 2) × 180°/n

156·n = 180·n - 360

360 = 180·n - 156·n = 24·n

n = 360/24 = 15

The number of sides in the n-sided polygon is 15, therefore, AC and AD are adjacent to a 15-sided polygon

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The final solution to the inequality y>=-(7)/(6)x is the shaded region on the graph.

To solve the inequality y>=-(7)/(6)x, we will first graph the boundary line and then shade the appropriate region.

1. Begin by graphing the boundary line y=-(7)/(6)x. This line has a slope of -(7)/(6) and passes through the origin (0,0).

2. Since the inequality includes the "greater than or equal to" symbol (>=), the boundary line should be solid to indicate that points on the line are included in the solution.

3. Next, we need to determine which region to shade. To do this, we can choose a test point that is not on the boundary line. A common test point is (0,1), which is above the boundary line.

4. Substitute the coordinates of the test point into the inequality to see if it is true or false: 1>=-(7)/(6)(0)

5. Since the inequality is true, the region that includes the test point is the solution. This means we should shade the region above the boundary line.

6. The final graph should have a solid boundary line with the region above it shaded.

The solution to the inequality y>=-(7)/(6)x is the shaded region on the graph.

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The lengths of the two legs are 2 centimeters and 9 centimeters.

Let's call the shorter leg of the right triangle x and the other leg y. According to the given information, we can create the following equation:

x = y - 7

Since we know that the hypothenuse is 13 centimeters, we can use the Pythagorean theorem to create another equation:

x^2 + y^2 = 13^2

Substituting the first equation into the second equation, we get:

(y - 7)^2 + y^2 = 13^2

Simplifying and rearranging terms, we get:

2y^2 - 14y - 72 = 0

Using the quadratic formula, we can solve for y:

y = (14 ± √(14^2 - 4(2)(-72))) / (2(2))

y = (14 ± √484) / 4

y = (14 ± 22) / 4

y = 9 or y = -2

Since the length of a leg cannot be negative, we reject the negative solution and take y = 9 centimeters as the length of the other leg. Then, we can use the first equation to find the length of the shorter leg:

x = 9 - 7

x = 2 centimeters

Therefore, the lengths of the two legs are 2 centimeters and 9 centimeters.

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Step-by-step explanation:

The area A of a rectangle is given by multiplying its length and width. In this case, the length is 7x - 1 units and the width is 2x + 3 units. Therefore, the area of the rectangle is:

A = (7x - 1)(2x + 3)

= 14x^2 + 19x - 3

Hence, the area of the rectangle is 14x^2 + 19x - 3 square units.

Answer:

14x^2+19x-3

Step-by-step explanation:

you have to times them together so

(7x-1)(2x+3)

14x^2+21x-2x-3

=14x^2+19x-3

let's firstly convert the mixed fractions to improper fractions and them sum them up.

[tex]\stackrel{mixed}{7\frac{5}{12}}\implies \cfrac{7\cdot 12+5}{12}\implies \stackrel{improper}{\cfrac{89}{12}}~\hfill \stackrel{mixed}{11\frac{2}{3}} \implies \cfrac{11\cdot 3+2}{3} \implies \stackrel{improper}{\cfrac{35}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{89}{12}+\cfrac{35}{3}\implies \cfrac{(1)89~~ + ~~(4)35}{\underset{\textit{using this LCD}}{12}}\implies \cfrac{89+140}{12}\implies \cfrac{229}{12}\implies {\Large \begin{array}{llll} 19\frac{1}{12} \end{array}}[/tex]

B' is the reflection of the x-axis at position B(1,3) (1,-3) as a consequence of B (1, 3) being reflected over the x-axis.

A coordinate is a group of integers used to describe a point's location in space in mathematics. Cartesian coordinates are the most widely used form of coordinates. They are made up of an ordered pair of numbers (x, y) that represent a point's horizontal and vertical distances from a constant point of reference known as the origin. The y-coordinate indicates the point's vertical distance from the origin, while the x-coordinate represents the point's horizontal distance from it.

given

The x-coordinate remains constant while the sign of the y-coordinate varies when a point is reflected over the x-axis.

Therefore, we only need to alter the sign of the y-coordinate of B in order to determine the reflection B' of the point B(1,3) over the x-axis.

B' is the reflection of the x-axis at position B(1,3) (1,-3) as a consequence of B (1, 3) being reflected over the x-axis.

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Multiplying or dividing both sides by a positive number leaves the inequality symbol unchanged.

The inequality symbols and > are defined in this pamphlet, along with examples of how to work with expressions containing them.

The following guidelines should be followed when changing or rearranging statements that involve inequalities:

Rule 1: An inequality symbol remains unchanged when the same amount is added to or subtracted from both sides.

Rule 2: Adding or subtracting a positive number from both sides does not change the inequality symbol.

Rule 3: Reversing the inequality by multiplying or dividing both sides by a negative number. It follows that  changes to > and vice versa.

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1. False. The probabilities of two mutually exclusive events should add up to 1. In this case, the probability of it raining and not raining should add up to 1, but .4 + .52 = .92, which is not equal to 1.

2. False. The probabilities of all possible outcomes should add up to 1. In this case, the probabilities of the printer making 0, 1, 2, 3, or 4 or more mistakes should add up to 1, but .19 + .34 + -.25 + .43 + .29 = .97, which is not equal to 1. Additionally, the probability of an event cannot be negative, so -.25 is not a valid probability.

3. True. The probabilities of all possible outcomes add up to 1 (.19 + .38 + .29 + .15 = 1) and none of the probabilities are negative.

4. True. The probabilities of the three events add up to 1 (1/4 + 1/2 + 1/8 = 7/8) and none of the probabilities are negative.

5. The probability of getting a head on a fair coin toss is 1/2. The probability of getting either a head or a tail is 1, since those are the only two possible outcomes. The probability of getting neither a head nor a tail is 0, since there are no other possible outcomes.

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To evaluate det(A) by a cofactor expansion along a row or column of our choice, we will use the following formula:

det(A) = a11C11 + a12C12 + a13C13 + ... + a1nC1n

where aij is the element in the ith row and jth column of matrix A, and Cij is the cofactor of that element.

For simplicity, we will choose to expand along the first row of matrix A.

det(A) = 5C11 + 0C12 + 0C13 + 1C14 + 0C15 + 3C16 + 3C17 + 3C18 + (-1)C19 + 0C110

Now, we will find the cofactors of each element in the first row.

C11 = (-1)1+1det(M11) = det(M11) = (5)(4)(3)(54) - (3)(2)(4)(3) = 3240 - 72 = 3168

C12 = (-1)1+2det(M12) = -det(M12) = -(0)

C13 = (-1)1+3det(M13) = det(M13) = (0)

C14 = (-1)1+4det(M14) = det(M14) = (3)(4)(3)(54) - (2)(2)(4)(3) = 1944 - 48 = 1896

C15 = (-1)1+5det(M15) = -det(M15) = -(0)

C16 = (-1)1+6det(M16) = det(M16) = (2)(4)(3)(54) - (2)(2)(4)(3) = 1296 - 48 = 1248

C17 = (-1)1+7det(M17) = -det(M17) = -(2)(3)(3)(54) - (2)(2)(4)(3) = -972 - 48 = -1020

C18 = (-1)1+8det(M18) = det(M18) = (1)(3)(3)(54) - (2)(2)(4)(3) = 486 - 48 = 438

C19 = (-1)1+9det(M19) = -det(M19) = -(1)(4)(3)(54) - (2)(2)(4)(3) = -648 - 48 = -696

C110 = (-1)1+10det(M110) = det(M110) = (0)

Now, we will substitute the cofactors back into the formula and simplify.

det(A) = 5(3168) + 0(0) + 0(0) + 1(1896) + 0(0) + 3(1248) + 3(-1020) + 3(438) + (-1)(-696) + 0(0)

det(A) = 15840 + 1896 + 3744 - 3060 + 1314 + 696

det(A) = 19430

Therefore, det(A) = 19430.

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Answer: about 26.00

Step-by-step explanation:

not intersect.

To determine if two lines intersect in R3, we need to solve for both parameters (t and s) in the two equations and then check if the values are equal.

For Line 1: x = 2 - t, y = -3 + 5t, z = t. We can solve for t by setting all three equations equal to each other, giving t = x - 2 = y + 3 = z.

For Line 2: P = (4,-1,16) + s (1,4,-7). We can solve for s by setting the three equations equal to each other, giving s = (x - 4) / 1 = (y + 1) / 4 = (z - 16) / -7.

If the two values of t and s are equal, then the lines intersect at the point (x, y, z). If they are not equal, then the lines do not intersect.

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In response to the supplied query, we may state that Therefore, equation  g(12) = 8.

Using the equals symbol (=) to indicate equivalence, a math equation links two statements. Algebraic equations prove the equality of two mathematical expressions by a mathematical assertion. The equal sign, for example, provides a gap between the numbers 3x + 5 and 14 in the equation 3x + 5 = 14. You can use a mathematical formula to understand the connection between the two phrases that are written on opposite sides of a letter. Most of the time, the logo and the particular software match. e.g., 2x - 4 = 2 is an example.

To find g(3), we substitute x=3 into the function g(x):

g(3) = 2(3)/3

g(3) = 6/3

g(3) = 2

Therefore, g(3) = 2.

To find g(12), we substitute x=12 into the function g(x):

g(12) = 2(12)/3

g(12) = 24/3

g(12) = 8

Therefore, g(12) = 8.

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Step-by-step explanation:

remember,

100% = 1

1% = 100%/100 = 1/100 = 0.01

as decimal

2/5 % = 1% × 2/5 = 0.01 × 0.4 = 0.004

as fraction

1% × 2/5 = 1/100 × 2/5 = 2/500 = 1/250

Answer:

The solution of this system is the yellow region which is the area of overlap. In other words, the solution of the system is the region where both inequalities are true. The y coordinates of all points in the yellow region are both greater than x + 1 as well as less than x.

Answer: C. 1/2

Step-by-step explanation:

The coefficient is the number being multiplied by q. The sum is the additive total. To add fractions, they need a common denominator.

2/3 = 4/6

Adding a negative is the same as subtracting.

4/6 + (-1/6) = 4/6 - 1/6 = 3/6 = 1/2

Hope this helps!