100 Points! Geometry question. Photo attached. Find x and y. Please show as much work as possible. Thank you!

The solution after resolving into factors are,

⇒ 8 (a - 3b) (a - b)

We have to given that,

Resolve into factors the expression,

⇒ (3a - 5b)² - (a + b)²

Now, We can simplify for resolving the factors as,

⇒ (3a - 5b)² - (a + b)²

Since, WE know that,

⇒ x² - y² = (x - y) (x + y)

Hence,

⇒ (3a - 5b)² - (a + b)²

⇒ [(3a - 5b) - (a + b)] [ (3a - 5b) + (a + b)]

⇒ [3a - 5b - a - b] [4a - 4b]

⇒ (2a - 6b) (4a - 4b)

⇒ 2 (a - 3b) × 4 (a - b)

⇒ 8 (a - 3b) (a - b)

Thus, The solution after resolving into factors are,

⇒ 8 (a - 3b) (a - b)

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8. Option (A) is correct as line XB is a radius

9. Option (D) is correct as line BD is a tangent line

The radius is the straight line from the center of the circle to the circumference and according to the tangent to a circle theorem, a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency

8. The only option that represents a radius is the line from the center X to the point B on the circle circumference.

9. The line from the point B to the point D is called is a tangent to the circle

Therefore, line XB is a radius and line BD is a tangent line.

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The correct classification for this triangle is an acute triangle.

The angle measures given are 51, 89, and 40 degrees.

There are no angles that are either equal to or greater than 90 degrees among those mentioned. Consequently, the triangle does not contain any angles that are either right or obtuse.

To categorize a triangle according to its angles, the total of the angles within the triangle, which is invariably 180 degrees, is taken into account.

51 + 89 + 40 = 180

Given that the total of the angles is 180 degrees, we can deduce that this particular triangle is acute in nature. An acute-angled triangle is a type of triangle that has three angles which are each smaller than 90 degrees.

Therefore, the correct classification for this triangle is an acute triangle.

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The value of X is 7.

Given that the set of number are in pattern,
X, 5, 9, 27, 15, 21.

To find the value of X such that given numbers are in pattern.

The next three number are three times of first three numbers respectively.

Let a, b, c is the first three numbers then 3a, 3b, 3c are next three numbers.

Consider the given set of numbers,  X, 5, 9, 9 × 3, 5 × 3, 21.

By using the data and the pattern set gives,

3X = 21.

Divide by 7 on both sides,

X = 7.

Hence, the value of X is 3

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The required acceleration is 0.0666 [tex]m^{2}[/tex]/s.

Given that the velocity of the object is 2m/s and time is 30s.

Acceleration is the rate of change of velocity with respect to time.

To find the acceleration by using the  formula.

acceleration (a) = velocity (v) / time (t).

By using data and formula gives,

acceleration (a) = velocity (v) / time (t).

acceleration (a) = 2 / 30

acceleration (a) = 0.0666 [tex]m^{2}[/tex]/s.

Hence, the required acceleration is 0.0666 [tex]m^{2}[/tex]/s.

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The base 10 equivalent of the base 7 number 463421 is 83174.

To convert a number from base 7 to base 10, we multiply each digit of the base 7 number by the corresponding power of 7 and sum up the results.

For the number 463421 in base 7:

= 4 x 7⁵ + 6 x 7⁴ + 3 x 7³ + 4 x 7² + 2 x 7¹ + 1 x 7⁰

= 4 x 16807 + 6 x 2401 + 3 x 343 + 4 x 49 + 2 x 7 + 1 x 1

= 67228 + 14406 + 1029 + 196 + 14 + 1

= 83174

Therefore, the base 10 equivalent of the base 7 number 463421 is 83174.

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The probability of not rolling factors of 5 on both dice is 25/36

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

Rolling two number cubes

Using the above as a guide, we have the following:

Sample space,  S = {1, 2, 3, 4, 5, 6}

In the above sample space, we have

Not factors of 5 = {1, 2, 3, 4, 6}

So, we have

P(Not rolling factor of 5) = 5/6 * 5/6

Evaluate

P(Not rolling factor of 5) = 25/36

Hence, the probability is 25/36

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Question

Two six sided dice are rolled.

Find the probability of not rolling factors of 5 on both dice

The coordinate of vertices of DEF are;

D = ( -4, -3)

E = ( -7, 4)

F =( -7, -3)

Here, we have,

Reflection in the y-axis: The reflection of point (x, y) across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse  (x,y)→( -x,y) .

First, triangle ABC is reflected across the y axes.

So, we have:

(x,y)→( -x,y)

then, translated down 5 units.

so, transformation rule on ABC, we have:

(x,y)→( -x , y - 5)

so, the coordinate of vertices of DEF are;

D = ( - 4, 2 - 5) = ( -4, -3)

E = ( -7, 9 - 5) = ( -7, 4)

F = (-7 , 2 - 5) = ( -7, -3)

Hence, the coordinate of vertices of DEF are;

D = ( -4, -3)

E = ( -7, 4)

F =( -7, -3)

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The answer choice which belongs in the green box and is the longest side of the triangle as required is; 11.06.

It follows from the task content that since the sum of angles in a triangle is; 180°, the missing angle measure is; 180 - 51 - 109° = 20°.

Consequently, it follows from the sine law that;

4 / sin 20° = x / sin 109°

x = 4 sin 109° / sin 20°

x = 11.06.

Ultimately, the number that belongs in the green box is; 11.06.

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The given histogram is bimodal, which is the last option/ option E, as bimodal distribution means that the data set has two distinct peaks or modes. In a bimodal histogram, the bars are grouped in a way that shows two prominent peaks or modes in the data.

Each bar in the histogram represents a specific range of values, and the height of the bar indicates the frequency or count of data points falling within that range. In a bimodal histogram, there will be two relatively high bars that correspond to the two modes of the data. The bimodal histogram is useful for visualizing and analyzing data sets that exhibit two distinct groups or clusters. It provides a clear visual representation of the two modes and their frequencies, which can help in identifying patterns and understanding the underlying characteristics of the data.

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The slope of line AD will be 4/3

Given,

ABCD is a square.

AB ⇒ y = -3/4 x + 7

Now,

AB is straight line.

Straight line equation ⇒ y =mx + c

m = slope of line

c = y intercept

Here,

m = -3/4 ( slope of line AB )

Now for slope of line AD,

ABCD is a square. Thus AB and AD are perpendicular to each other.

According the relation,

[tex]m_{1} m_{2} = -1[/tex]

[tex]m_{1}[/tex] = slope of line 1

[tex]m_{2}[/tex] = slope of line 2

So,

-3/4 [tex]m_{2}[/tex] = -1

[tex]m_{2}[/tex] = 4/3.

Hence slope of AD is 4/3 .

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Answer:

10

Step-by-step explanation:

[tex]2\frac{3}{8}[/tex]+[tex]1\frac{3}{4}[/tex]+[tex]5\frac{7}{8}[/tex]=

[tex]2\frac{3}{8} +1\frac{6}{8} +5\frac{7}{8}[/tex]=

[tex]8\frac{16}{8} =10[/tex]

Answer:  D

Step-by-step explanation: -135

The angles in the triangle are as follows:

∠X = 58°

Exterior angle of ∠X = 122°

The sum of angles in a triangle is 180 degrees. The sum of the exterior angle and the interior angle of a triangle is 180 degrees.

Therefore, let's find the measure of ∠X in the triangle XYZ.

Hence,

m∠X = (2g + 16)°

The exterior angle of m∠X  measures 4g + 38 degrees.

Hence,

2g + 16 + 4g + 38 = 180

6g + 54 = 180

6g = 180 - 54

6g = 126

g = 126 / 6

g = 21

Therefore,

∠X = (2(21) + 16)°  = 42 + 16 = 58 degrees

Exterior angle of ∠X =  4(21) + 38 = 84 + 38 = 122

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The ability of the twins to divide the oddly shaped plot into two Identical plots along the grid lines depends on the presence of a line of symmetry.

To determine whether the set of twins can divide the oddly shaped plot of land into two identical plots along the grid lines, we need to consider the characteristics of the plot and the conditions required for the division.

For the division to be possible, the plot needs to have a line of symmetry that can be used to create two identical halves. A line of symmetry divides an object into two equal and mirrored parts.

If the plot of land has a line of symmetry, the twins can divide it by drawing a line along the symmetry axis. This line should cut the plot into two equal halves, ensuring that both plots are identical.

However, if the plot does not have a line of symmetry, it may not be possible to divide it into two identical plots along the grid lines. In this case, the twins would need to consider alternative methods of division or compromise on the goal of having two identical plots.

To determine if the plot has a line of symmetry, the twins can examine its shape and characteristics. They can look for any symmetrical patterns, such as equal sides or mirrored shapes, that indicate the presence of a line of symmetry.

If the plot does not have an obvious line of symmetry, the twins might need to explore other options, such as dividing the plot into two equal areas based on other criteria, such as the length or width of each half.

the ability of the twins to divide the oddly shaped plot into two identical plots along the grid lines depends on the presence of a line of symmetry. If such a line exists, they can divide the plot by drawing a line along the symmetry axis. However, if the plot lacks symmetry, they may need to consider alternative methods of division or adjust their expectations.

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Note the full question may be :

To determine whether the twins can divide the oddly shaped plot of land into two identical plots along the grid lines, we need more specific information about the shape and dimensions of the plot. the shape of the plot (rectangular, triangular, irregular), the lengths of its sides, any existing grid lines or divisions within the plot.

The greater number of packages that can fit in the truck is 24000.

The volume of the part of the truck that is being filled is 375 cubic feet.

We have,

To determine the greater number of packages that can fit in the truck, we need to calculate the volume of both the packages and the part of the truck that is being filled.

The volume of a cube-shaped package:

The side length of the cube-shaped package is 1/4 feet.

The volume of a cube is given by V = s³, where s is the side length.

Therefore, the volume of each package is (1/4)³ = 1/64 cubic feet.

The volume of the part of the truck being filled:

The dimensions of the rectangular prism-shaped part of the truck are:

Length = 8 feet

Width = 6(1/4) feet = 6.25 feet

Height = 7(1/2) feet = 7.5 feet

The volume of a rectangular prism is given by V = length × width × height.

Therefore, the volume of the part of the truck being filled is:

8 × 6.25 × 7.5

= 375 cubic feet.

To calculate the greater number of packages that can fit in the truck, we divide the volume of the part of the truck by the volume of each package:

= 375 cubic feet / (1/64 cubic feet)

= 375 × 64

= 24000 packages.

Therefore,

The greater number of packages that can fit in the truck is 24000.

The volume of the part of the truck that is being filled is 375 cubic feet.

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y=2/3x-4 is the equation of the line where 2/3 is the slope.

We have to find the equation of line which is passing through points (0, -4) and (3, -2).

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁.

Slope = -2+4/3-0

=2/3

Now let us find the y intercept.

-4=2/3(0)+b

b=-4

The equation of line is y=2/3x-4.

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The graph that best represents these characteristics is the one that shows an increasing curve with a flattened slope and is shifted upward. Option C

The function C(x) = (1/4)√x + 2 represents the side length of the smaller granola bar, where x is the area of the larger granola bar in square inches. To determine which graph shows C(x), we need to analyze the characteristics of the function.

First, let's consider the behavior of the function C(x) = (1/4)√x + 2:

Square Root Function: The term √x indicates that the function involves the square root of x. This means that as x increases, C(x) will also increase, but at a decreasing rate.

Scaling Factor: The coefficient (1/4) scales the square root of x. It affects the steepness of the function and causes C(x) to increase more slowly compared to a simple square root function.

Vertical Shift: The constant term (+2) shifts the entire function vertically upward by 2 units. This means that the graph will be raised by 2 units compared to a standard square root function.

Based on these characteristics, we can conclude that the graph of C(x) will be an increasing curve with a flattened slope compared to a simple square root function, and it will be shifted upward by 2 units.

Among the answer choices, the graph that best represents these characteristics is the one that shows an increasing curve with a flattened slope and is shifted upward. Without the actual graphs provided, it is difficult to specify the exact choice, but it should exhibit these features described above.

It is essential to refer to the available graphs or visually analyze the functions to determine the correct graph that shows C(x). Option C is correct.

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a. The variables are x and y which represents 2 shots and 3 shots respectively.

b. The system of equations are;

x + y = 11

2x + 3y = 29

a. Let's define the variables to write the system of equations:

Let x be the number of two-point shots Noah made.

Let y be the number of three-point shots Noah made.

b. We can write a system of equations that model this problem.

Equation 1: x + y = 11

This equation represents the total number of shots Noah made, which is 11.

Equation 2: 2x + 3y = 29

This equation represents the total number of points Noah scored, which is 29. Since each two-point shot is worth 2 points and each three-point shot is worth 3 points, we can multiply the number of two-point shots (x) by 2 and the number of three-point shots (y) by 3 and sum them up to get the total score of 29.

The system of equations that can be used to determine the number of two-point shots Noah made and the number of three-point shots he made is:

x + y = 11

2x + 3y = 29

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The coordinates of the Triangle RST after it is translated 4 units down and 3 units to the left is the option;

R¢(-7, -2), S¢(2, -1), T¢(-1, -9)

A translation transformation is one in which the location of the pre-image is transformed from its initial location to the destination location.

The coordinates of the vertices of the triangle RST are; R(-4, 2), S(5, 3), T(2, -5)

The translation transformation that is applied on the triangle RST includes;

A vertical translation 4 units downwards

An horizontal translation 3 units to the left

The translation transformation is therefore; T₍₋₃, ₋₄₎

Therefore, applying each transformation, we get;

R(-4, 2) ⇒ T₍₋₃, ₋₄₎ ⇒ R¢(-4 -3, 2 - 4) = R¢(-7, -2)

S(5, 3) ⇒ T₍₋₃, ₋₄₎ ⇒S¢(5 - 3, 3 - 4) = S¢(2, -1)

T(2, -5) ⇒ T₍₋₃, ₋₄₎ ⇒ T¢(2 - 3, -5 - 4) = T¢(-1, -9)

The correct option is therefore, the first option

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The angles of the triangle are ordered as follows:

<B, <C and <A.

We consider a triangle with side lengths and angles related as follows:

Then the lengths and the sines of the angles are related as follows:

sin(A)/a = sin(B)/b = sin(C)/c.

By the law of sines, we have that the greater angle measures are opposite to the greater side lengths.

Hence the angle measures for this problem are ordered as follows:

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The angles of triangle ABC is arranged below

angle b - smallest

angle c

angle a - largest

To determine the angles of triangle ABC in order from smallest to largest, we can use use the knowledge that the side with higest length will face the largest angle.

Let the angles be

angle c is opposite AB = 12

angle b is opposite AC = 11

angle a is opposite BC = 19

Using the knowledge as introduced we have that

angle a > angle c > angle b

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ABC forms a right-angled triangle

Let the distance between AB = x

Using Pythagoras theorem

Sin 30 = Opposite / Hypoteneuse

Sin 30 = 12 in/ x

However, From the equilateral triangle, all sides are = 2 and the angles are all = 60 degrees. Then we take a right-angled triangle out of it. This means that the base equals 1, and the top side is halved and equals 30 degrees.

Using Pythagoras' theorem, Sin 30 = 1/ 2

Substituting back into the equation, we get:

1/ 2 = 12 in / x

Cross multiplying, we get:

x = 24 in

Recall x = AB

AB = 24 inches

To remember the angles and their respective formula, use SOHCAHTOA

Where sin x = Opposite / Hypoteneuse

Cos x = Adjacent / Hypoteneuse

Tan x = Opposite / Adjacent

Answer: Area = = 38.5 - Perimeter - 29.6819.

Step-by-step explanation:

To find the perimeter and area of a triangle with vertices L(5,5), M(-2,-4), and N(5,-6), we can use the distance formula and the formula for the area of a triangle.

Perimeter:

The perimeter of a triangle is the sum of the lengths of its sides. We can find the lengths of each side using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

Using this formula, we can calculate the lengths of LM, MN, and NL:

LM = √((-2 - 5)^2 + (-4 - 5)^2)

= √((-7)^2 + (-9)^2)

= √(49 + 81)

= √130

MN = √((5 - (-2))^2 + (-6 - (-4))^2)

= √((7)^2 + (-2)^2)

= √(49 + 4)

= √53

NL = √((5 - 5)^2 + (-6 - 5)^2)

= √((0)^2 + (-11)^2)

= √(0 + 121)

= √121

= 11

The perimeter of the triangle is the sum of these three sides:

Perimeter = LM + MN + NL

= √130 + √53 + 11 = 29.6819

Area:

To calculate the area of the triangle, we can use the formula for the area of a triangle using the coordinates of its vertices. The formula is given by:

Area = 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

Using the coordinates of L(5,5), M(-2,-4), and N(5,-6), we can calculate the area:

Area = 0.5 * |5(-4 - (-6)) + (-2)(-6 - 5) + 5(5 - (-4))|

= 0.5 * |5(2) + (-2)(-11) + 5(9)|

= 0.5 * |10 + 22 + 45|

= 0.5 * |77|

= 38.5

Therefore, the perimeter of the triangle is given by √130 + √53 + 11 = 29.6819 units, and the area of the triangle is 38.5 square units.

The graph shows the solution set for -4.4 ≥ 1.6x - 3.6 is Graph I.

To solve the inequality -4.4 ≥ 1.6x - 3.6, we can follow these steps:

Add 3.6 to both sides of the inequality to isolate the term with x:

-4.4 + 3.6 ≥ 1.6x - 3.6 + 3.6

-0.8 ≥ 1.6x

Divide both sides of the inequality by 1.6

-0.8 / 1.6 ≥ 1.6x / 1.6

-0.5 ≥ x

So, the solution to the inequality is x ≤ -0.5.

Now, from the solution the graph for the inequality start with closed dot from 0.5 and move towards the points -0.6, -0.7, -0.8, ....

Thus, the graph shows the solution set for -4.4 ≥ 1.6x - 3.6 is Graph I.

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1. The t-value of the data is 1.833

2. The margin of error is 1.66

3. The confidence interval is between 11.66 to 8.34

From the question given;

sample size = 11

sample mean = 10 inches

standard deviation = 3 inches

1.The t-value of the data with a degree of freedom equal to 10 at 0.05 significance level = 1.833

2. Using the formula below, the margin of error is;

[tex]ME = t * \frac{SD}{\sqrt{n} }[/tex]

Substituting the values into the formula above;

ME = 1.833 * 3/√11

ME = 1.66

3. The confidence interval of the data is;

CI = mean ± ME

where CI is the confidence interval, mean is the sample mean, and ME is the margin of error. In this case, the confidence interval is calculated as follows:

CI = 10 +/- 0.96 = 9.04 to 10.96 inches

CI = 10 ± 1.66 = 11.66 to 8.34

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The meaning of the sentence is that for an one-to-one function, each input makes an unique output.

Here we want to find the meaning of  "A function f is one-to-one if f(x) = f(y) implies x = y"

That is a definition of an one-to-one function.

In simpler words, an one to one function is a function that for each input x, the output y is unique.

So the sentence says that if:

f(x) = f(y)  (we have two equal outputs)

Then x = y  (then the inputs must be equal)

So that is the meaning of the sentence.

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The statement is saying that a class R is considered an n-ary relation if all its elements are n-tuples.

The symbol R⊂Vⁿ represents that the class R is a subset of Vⁿ, which is the class of all n-tuples.

Here, Vⁿ represents the set of all possible n-tuples, and R is a subset of that set.

The notation Cⁿ is used to denote the set of n-tuples with elements from the set C, and C×D represents the Cartesian product of sets C and D.

The statement defines an n-ary relation as a class where all its elements are n-tuples, and it establishes a connection between the class R and the set of all n-tuples (Vⁿ).

The notation Cⁿ and C×D are used to describe sets of n-tuples and Cartesian products, respectively, in a mathematical context.

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