Kathryn draws three pairs of intersecting lines. In each figure, she measures a pair of angles. What is a reasonable conjecture for Kathryn to make by recognizing a pattern and using inductive reasoning? When a pair of lines intersect, the vertical angles are acute. When a pair of lines intersect, all of the angles formed are right angles. When a pair of lines intersect, the vertical angles are congruent. When a pair of lines intersect, all of the angles formed are congruent.

Answer: Each face would have an area of 22 * 22 = 484 square inches.

Since a cube has 6 faces, then the total area = 6 * 484 = 2,904 square inches.

Step-by-step explanation:

To find the area under the normal distribution curve for a range of z-values, you refer to a z-table and possibly subtract two areas to find the area between two z-values. The areas above were calculated as examples.

The subject in question involves finding the area under the standard normal distribution curve for various z-values. This is a concept in statistics that evaluates the probability which a particular range of values under the normal distribution curve might occur.

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the three inside angels need to equal 180, so first find the missing inside angle:

86.5 + 41.4 = 127.9

180-127.9 = 52.1

now that angle and y need to equal 180 degrees

 so 180 - 52.1 = 127.9

y = 127.9 degrees

Answer: [tex]m= -\frac{1}{26}[/tex]

(19,-16) = (x1,y1)

(-7-15) = (x2,y2)

Slope= [tex]\frac{y2-y1}{x2-x1}[/tex]

         = [tex]\frac{-15-(-16)}{-7-19}[/tex]

         = [tex]\frac{-15+16}{-7-19}[/tex]

         = [tex]\frac{-15+16}{-26}[/tex]

         = [tex]-\frac{1}{26}[/tex]

Answer:

2x+ 5 expression represents the amount of time jim reads

Step-by-step explanation:

As per the statement:

Kelly reads x hours a week.

⇒Kelly read in a week = x hours

Also, tim reads two times more than kelly

⇒tim read in a week= 2x

It is also given that:

jim reads five hours more than tim.

⇒Jim = tim read + 5

⇒Jim read in a week = 2x +5

Therefore, expression represents the amount of time jim reads is, 2x+ 5

Answer: "Use the straightedge to draw a line through points X and Y." is the right answer.

Step-by-step explanation:

To perpendicular bisector of line segment AB. There are following steps:

1) Draw arcs from points A and B on the both sides of AB.

2) Name the intersection points as X and Y.

3) Use the straightedge to draw a line through points X and Y.

4) Name the point as O

hence we have construct perpendicular bisector XY of AB which bisects at O.

Skip counting by ten from 350 to 240 involves starting at 350 and counting backwards by subtracting ten each time until you reach 240. The sequence would look as follows: 350, 340, 330, 320, 310, 300, 290, 280, 270, 260, 250, 240.

In Mathematics, when asked to 'skip count' it means that you are counting up or down by a specified number, in this case, by ten. However, the student's question asks to skip count by ten from 350 to 240, which would require counting backwards or decreasing the count by ten each time.

To skip count by ten from 350 to 240, you would start at 350 and then subtract 10 each time, like this: 350, 340, 330, 320, 310, 300, 290, 280, 270, 260, 250, 240. Note: 240 is included in the sequence as it is the final number we're skip counting down to.

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Mickey has 3 cards.

To determine how many cards Mickey has, we can set up a proportion using the information given. We know that for every five cards Mickey has, Mike has 3 cards. So the proportion would be: (Mickey's cards) / 5 = 3 / (Mike's cards).

Given that Mike has 72 cards, we can plug that into the proportion: (Mickey's cards) / 5 = 3 / 72.

To solve for Mickey's cards, we can cross multiply: (Mickey's cards) = (3 / 72) * 5.

After simplifying, we find that Mickey has 3.125 cards. However, since we can't have a fraction of a card, we know that Mickey has 3 cards.

Answer:

CPCTC; JP≅MI; SAS

Step-by-step explanation:

For the first question, we use the congruence statement.  When we are using the congruence statement to match corresponding pieces, the justification is that Congruent Parts of Congruent Triangles are Congruent, or CPCTC.

For the second question, we again use CPCTC and the congruence statement.  P matches T and B matches I, so PB = TI and B = I.  J matches M also, so BJP = IMT.  However, P does not match I, so JP does not equal MI.

For the third question, we have two sides (AM matching ZD and BD matching itself) and an included angle (AMD and ZDM).   This is Side-Angle-Side, or SAS.

The distributive property of multiplication involves multiplying a number with each term inside a bracket, then adding or subtracting the results. To find a missing number, set up an equation based on the distributed multiplication and solve for the unknown.

The distributive property of multiplication can be simply defined as a(b + c) = ab + ac. In this equation, 'a' is distributed over 'b' and 'c', which means we multiply 'a' individually with 'b' and 'c', and then add the results.

Let's consider an example: 2(3 + 4) = ? Here, applying the distributive property, we multiply 2 with 3 and 2 with 4 separately. Hence, 2*3 + 2*4 = 6 + 8 = 14. So, the result is 14.

To solve distribution problems with a missing number, you would set up the equation and solve for the unknown. For example, if we have 3(x+5) = 21, we can first distribute the 3 to get 3x + 15 = 21. Then, you'd subtract 15 from both sides to isolate the 'x'. So, 3x = 21 - 15, which simplifies to 3x = 6. Finally, dividing both sides by 3 gives x = 2. So, the missing number is 2.

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The point-slope equation of the line through (1,3) and (5,1) is y - 3 = -0.5(x - 1), where the slope m= -0.5 was calculated using the formula m = (y2 - y1) / (x2 - x1).

To complete the point-slope equation of the line through points (1,3) and (5,1), we first need to find the slope of the line, which can be calculated using the formula: m = (y2 - y1) / (x2 - x1), here (x1,y1) and (x2,y2) are the coordinates of two points on the line.

Substituting in the given coordinate values gives us m = (1 - 3) / (5 - 1), which simplifies to m = -0.5, indicating a downward slope.

The point-slope form of the equation of a line is y - y1 = m(x - x1). So, substituting one of the given points (1, 3) and the calculated slope into the point-slope form gives us y - 3 = -0.5(x - 1).

Therefore, the point-slope equation of the line through (1,3) and (5,1) is y - 3 = -0.5(x - 1).

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The equation for the total number of miles m that Ana has traveled after d days is m = 240 + 350d.

What is an equation?

An equation is an equality relationship between two expressions written on both sides of the equal to sign.

Ana travels 240 miles on the first day.

Her cousin and she travel 350 miles everyday.

If d is the number of days, then to find the equation for the total number of miles covered m,

m = 240 + 350d miles in d days.

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The midpoint of the line segment is [tex](\frac{-21}{2} ,5)[/tex].

Midpoint is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.

[tex](x,y)=(\frac{x_{1}+x_{2} }{2} ,\frac{y_{1} +y_{2} }{2} )[/tex]

Where,

[tex](x, y)[/tex] is the midpoint of the line segment.

[tex](x_{1},y_{1}) and (x_{2} ,y_{2} )[/tex] are the endpoints of the line segment.

Let (x, y) be the midpoint of the line segment.

According to the given question

We have

(-8, 12) and (-13, -2) are the endpoints of the line segment.

Therefore, the midpoint of the line segment is given by

[tex](x,y)=(\frac{-8-13}{2} ,\frac{12-2}{2} )[/tex]

⇒[tex](x, y) = (\frac{-21}{2} ,\frac{10}{2})[/tex]

⇒[tex](x,y)=(\frac{-21}{2} ,5)[/tex]

Hence, the midpoint of the line segment is [tex](\frac{-21}{2} ,5)[/tex].

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The rate of change of length of the Clupea harengus (Atlantic herring) at t = 7 years is approximately 2.8 cm per year.

To determine how fast the length of Clupea harengus (Atlantic herring) is changing at age t = 7 years, you need to calculate the derivative of the given function, l(t) = 32(1 − e−0.37t), with respect to time. The derivative measures the rate of change of a function, which in this case corresponds to the speed of growth of the herring.

The derivative of l(t) with respect to t is given by: l'(t) = 32 * 0.37e^(-0.37t).

Substitute t = 7 into this derivative function to get: l'(7) = 32 * 0.37e^(-0.37*7) ≈ 2.8 cm/year.

So, the length of the Atlantic herring is increasing at approximately 2.8 cm per year when the herring is 7 years old.

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To find the rate at which the length of the Atlantic herring is changing at age t = 7 years, we need to take the derivative of the length function and evaluate it at t = 7.

To find the rate at which the length of the Atlantic herring is changing at age t = 7 years, we need to find the derivative of the length function with respect to time. The function l(t) = 32(1 − e−0.37t) represents the average length of the herring at age t. Taking the derivative of this function gives us:

l'(t) = 32 * (-0.37) * e−0.37t

Now, we can substitute t = 7 into the derivative to find the rate of change at that age:

l'(7) = 32 * (-0.37) * e−0.37(7)

This expression can be simplified further to find the exact value of the rate of change.

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In 24 ways the first, second, third, and fourth place be assigned

A permutation is an arrangement of objects in a definite order. .

Given that, for a spelling contest awards four prizes Tim, Sam, Jen, and Kate all made it to the final round.

We need to find in how many ways can first, second, third, and fourth place be assigned.

This can be arranged in 4! ways.

4!=4×3×2×1

4!=24

Hence in 24 ways the first, second, third, and fourth place be assigned.

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the answer is A x=15 and y =12

The area of the front cover of the square notebook is A = 400 cm²

A square is a four sided quadrilateral with all of the side having equal lengths. The total internal angle of a square is 360° with each side perpendicular to each other.

A square is a 4 sided polygon where all the sides are of equal length.

The area of the square is the square of any one of its side

Let a be the side of the square

Area of the square = a²

Given data ,

Let the area of the square be represented as A

Now , the side length of the notebook a = 20 cm

And , the area of the front cover of the notebook = area of square

On simplifying , we get

The area of front cover A = a²

The area of the front cover of the notebook A = 20 x 20

The area of the front cover of the notebook A = 400 cm²

Hence , the area of the square notebook is 400 cm²

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