50 Points! Multiple choice geometry question. Photo attached. Thank you!

i. The value of x can be obtained as illustrated below:

Cos θ = Adjacent / Hypotenuse

Cos 45 = x / 2√2

Cross multiply

x = 2√2 × Cos 45

x = 2√2 × (1/√2)

x = 2

Thus, the value of x is 2

ii. The value of y can be obtained as follow:

Sine θ = Opposite / Hypotenuse

Sine 45 = y / 2√2

Cross multiply

y = 2√2 × Sine 45

y = 2√2 × (1/√2)

y = 2

Thus, the value of y is 2

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The absolute value of the elevation difference between the valley and sea level is 94 feet.

In trying to determine the absolute value of a number, this implies we are only looking at it's magnitude without the sign to it.

In the problem given, the elevation difference between the valley and the sea level will 94ft.

Since we are going to neglect the negative sign in the elevation difference and considering only the magnitude of the distance, then the absolute value of the elevation is 94

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The amount the shop should chase per Board to Maximize monthly revenue is; B: 340

We are given the parameters as;

Number of surfboards sold per month = 45

Thus;

The shop sells 45 surfboards for $500 each which means it equals a total of: $22,500

Let x be the number of $20 decreases. Thus;

($500 - $20x)(45 + 5x) = 0

22500 - 900x + 2500x - 100x² = 0

22500 + 1600x - 100x² = 0

using the formula for the axis of symmetry:

x = -b/2a:

where a = -100, b = 1600, and c = 22500 (standard form of an equation), we have;

-1600/-200 = 8

The shop should decrease the price by $20, eight times exactly to get:

($500 - $20*8)(45 + 5*8)

($500 - $160)(45 + 40)

($340)(85) = $28,900 is the maximum monthly revenue

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The 85% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list is (0.28, 0.38).

Let's calculate the sample proportion;

Sample proportion = 93 / 283 = 0.33

The margin of error of the data can be calculated by;

Margin of error = Z * √(p(1-p) / n)

where:

Margin of error = 1.96 * sqrt(0.33 * (1-0.33) / 283) = 0.05

The confidence interval can be calculated as

Confidence interval = 0.33 ± 0.05 = (0.28, 0.38)

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Answer:

D. 100.5 in³

Step-by-step explanation:

We can find the radius of the cone, we can use the following formula:

[tex]r = \frac{\sqrt{(s² - h²)}}{2}[/tex]

where:

In this case, we have:

Substituting these values into the formula, we get:

[tex]r = \frac{\sqrt{(10² - 6²)}}{2}[/tex]

r=4 inches

Now that we know the radius, we can find the volume of the cone using the following formula:

V = ⅓*πr²h

where:

In this case, we have:

V = ⅓*π(4²)(6)

V = ⅓*π*(16)(6)

V =32π

V= 100.5 cubic inches

Therefore, the volume of the cone is 100.5 cubic inches.

Answer:

The answer is 73.5

Explanation: (96+51)/2

Answer: lig

Step-by-step explanation:

hhh

Answer: 20.864

Step-by-step explanation: 8.15 x 4 = 32.6 divided by 5 = 6.52 x 3.2 = 20.864

Hope this helps  : D

Answer:

38.4

Step-by-step explanation:

This equation represents the line Perpendicular to 4x + 7y = 4, with the same y-intercept as 9x - 7y = -2.

The equation of a line perpendicular to another line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.

the slope of the line 4x + 7y = 4. We can rewrite this equation in slope-intercept form (y = mx + b) by isolating y:

4x + 7y = 4

7y = -4x + 4

y = (-4/7)x + 4/7

From this equation, we can observe that the slope of the given line is -4/7.

The line perpendicular to this line will have a slope that is the negative reciprocal of -4/7. The negative reciprocal of a number is obtained by flipping the fraction and changing the sign. Therefore, the slope of the perpendicular line will be 7/4.

Now, we are given that the perpendicular line has the same y-intercept as the line 9x - 7y = -2. To find the y-intercept, we can set x = 0 and solve for y:

9(0) - 7y = -2

-7y = -2

y = 2/7

Therefore, the y-intercept of the perpendicular line is 2/7.

We now have the slope (7/4) and the y-intercept (2/7) of the perpendicular line. Using the slope-intercept form (y = mx + b), we can write the equation of the perpendicular line as:

y = (7/4)x + 2/7

This equation represents the line perpendicular to 4x + 7y = 4, with the same y-intercept as 9x - 7y = -2.

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The possible combinations of 1 photo from Vancouver, 1 photo from Buffalo, and 1 photo from Miami could she choose from for the cover of her scrapbook is option c  1,008.

To find the number of possible combinations for the cover of Scarlet's scrapbook, you can simply multiply the number of photos from each trip together.

So, there are 8 photos from Vancouver, 9 photos from Buffalo, and 14 photos from Miami. Multiply these numbers together to get the total number of combinations:

8 (Vancouver) × 9 (Buffalo) × 14 (Miami) = 1,008 possible combinations.

Scarlet has a range of choices for each city, and by considering the possibilities at each step and multiplying them together, we determine the total number of combinations. The multiplication principle is a fundamental concept in combinatorics, allowing us to calculate the number of outcomes for independent events.Therefore, the correct answer is C. 1,008.

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Answer:

vertex = (4, 9 )

Step-by-step explanation:

the equation of a parabola in vertex form is

f(x) = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

f(x) = 3(x - 4)² + 9 ← is in vertex form

with h = 4 and k = 9 , then

vertex = (4, 9 )

The variable n represents time in seconds

The variable n represents age

The variable n represents amount of money in dollars.

The variable n represents height in inches.

In each expression:

L. The variable n represents Jerry's time in seconds for the 100-yard dash. Lisa's time is n-5 seconds, indicating that Lisa runs 5 seconds faster than Jerry.

M. The variable n represents Pedro's father's age in years. Pedro's age is n + 3 years old, meaning Pedro is 3 years younger than his father.

N. The variable n represents Lucia's sister's amount of money in dollars. Lucia has n-10 dollars, indicating that Lucia has $10.00 less than her sister.

O. The variable n represents Jack's younger brother's height in inches. Jack is 2 times taller than his younger brother, so Jack's height is 2 times n inches.

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The equation of a circle with center (3, -15) and radius 3 is (x - 3)² + (y + 15)² = 9.

The equation of a circle with center and radius is calculated as follows;

The general formula for the equation of a circle is;

(x - h)² + (y - k)² = r²

where;

The center of a circle is given as (3, -15).

Radius of the circle = 3

The equation of the circle becomes;

(x - 3)² + (y - (-15))² = 3²

(x - 3)² + (y + 15)² = 9

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The 3rd graph (bottom left)

2.58

Answer:

y = 15 , x = 6

Step-by-step explanation:

you can easily find y from first equation

Move y to the other side of the equation and reverse its sign

so (-11) changes to (+11) and now we have this equation

y = 15

now you must replace 15 instead of y in second equation ,then we have this equation

15 = 2x + 3

now we have to find x

move (+3) to other side of equation and reverse its sign

(+3) changes to (-3)

we have this equation now

15 - 3 = 2x

12 = 2x

x = 12 ÷ 2 = 6

Step-by-step Explanation:

r=d/2=14/2=7yd

From hyp²=opp²+adj²

opp²=hyp²-adj²

h²=25²-7²

h²=625-49

h²=576

square root of both sides

√h²=√576

h=24yd

Volume of a cone=1/3pir²h

V=1/3×22/7×7²×24

V=22×7×8

V=1232yd²

Volume of pyramid=1/3AH

hyp²=opp²+adj²

14²=h²+5²

196=h²+25

h²=196-26

h²=171

√h²=√171

h=13.1yd

V=1/3×B×H×H

V=1/3×

To find Carissa's salary when she sells $1,900 worth of merchandise, we can use the salary function provided:

s(x) = 0.24x + 300

Here, 'x' represents the amount of merchandise sold.

Substituting x = $1,900 into the function:

s(1900) = 0.24 * 1900 + 300

s(1900) = 456 + 300

s(1900) = 756

Therefore, when Carissa sells ${\textsf{1,900 worth of merchandise, her salary will be}} $756.

[tex]\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}[/tex]

♥️ [tex]\large{\textcolor{red}{\underline{\texttt{SUMIT ROY (:}}}}[/tex]

The component form of the path the airplane will actually travel is (635.2 mph, -42.3 mph), the resultant vector magnitude is approximately 639.5 mph, and the resultant vector direction is approximately -3.0°.

To find the component form of the path the airplane will actually travel, we need to consider the effect of the wind on the airplane's motion.

Let's break down the airplane's velocity and the wind's velocity into their respective horizontal (x) and vertical (y) components.

Given:

Airplane's velocity = 700 mph due east

Wind's velocity = 80 mph at an angle of 63° East of South

The horizontal component of the airplane's velocity remains unchanged since it is traveling due east. Therefore, the horizontal component is 700 mph.

The wind's velocity can be resolved into its x and y components as follows:

Wind's horizontal component = wind's speed * cos(angle)

Wind's vertical component = wind's speed * sin(angle)

Wind's horizontal component = 80 mph * cos(63°)

Wind's vertical component = 80 mph * sin(63°)

Now, we can calculate the resultant vector of the airplane's motion by adding the horizontal components and the vertical components separately.

Resultant horizontal component = Airplane's horizontal component + Wind's horizontal component

Resultant vertical component = Airplane's vertical component + Wind's vertical component

Resultant horizontal component = 700 mph + (80 mph * cos(63°))

Resultant vertical component = 0 + (80 mph * sin(63°))

Next, we can express the resultant vector in component form:

Resultant vector = (Resultant horizontal component, Resultant vertical component)

To find the magnitude of the resultant vector, we can use the Pythagorean theorem:

Resultant magnitude = sqrt((Resultant horizontal component)^2 + (Resultant vertical component)^2)

Finally, we can find the direction of the resultant vector by calculating the angle it makes with the positive x-axis using the inverse tangent:

Resultant direction = tan⁻¹(Resultant vertical component / Resultant horizontal component)

Now, let's calculate the values:

Resultant horizontal component ≈ 635.2 mph

Resultant vertical component ≈ -42.3 mph

Resultant magnitude ≈ 639.5 mph

Resultant direction ≈ -3.0° (rounded to the nearest degree)

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The number that fits the given conditions is 83. Firstly, it is stated that the number is less than 90, which is true for 83. The number that solves the Riddle is 83.

The number that fits the given conditions is 83. Firstly, it is stated that the number is less than 90, which is true for 83. The next clue is that if you add the digits of the number, the total is less than 10. In the case of 83, 8 + 3 equals 11, which is indeed less than 10.

Moving on, the riddle mentions that the number is greater than 20. 83 satisfies this condition as well. Lastly, it is stated that the tens digit is greater than the ones digit. In the case of 83, the tens digit (8) is indeed greater than the ones digit (3).

Putting all the clues together, 83 fulfills the conditions of being less than 90, having a digit sum less than 10, being greater than 20, and having a tens digit greater than the ones digit.

Therefore, the number that solves the riddle is 83.

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Work Shown:

P(A u B) = P(A)+P(B)-P(A n B)

12/25 = 1/5+P(B)-7/100

12/25 = 20/100+P(B)-7/100

12/25 = P(B)+13/100

12/25-13/100 = P(B)

48/100-13/100 = P(B)

35/100 = P(B)

7/20 = P(B)

P(B) = 7/20

2 – i must be the root of the function. Option C

To find the equation for the polynomial function with the given roots, we can use the fact that complex roots occur in conjugate pairs. The given roots are 2 + i and 5. Since 2 + i is a complex root, its conjugate, 2 - i, must also be a root. Therefore, the polynomial function can be written as:

(x - 2 - i)(x - 2 + i)(x - 5)

Now, let's simplify this equation:

(x - 2 - i)(x - 2 + i)(x - 5)

= [tex][(x - 2)^2 - i^2](x - 5)\\= [(x - 2)^2 + 1](x - 5)\\= (x^2 - 4x + 4 + 1)(x - 5)\\= (x^2 - 4x + 5)(x - 5)\\= x^3 - 4x^2 + 5x - 5x^2 + 20x - 25\\= x^3 - 9x^2 + 25x - 25[/tex]

Now, we have the equation for the polynomial function with roots 2 + i and 5 as[tex](x^3 - 9x^2 + 25x - 25).[/tex]

To determine which of the options must also be a root of the function, we can substitute each option into the polynomial equation and check if it satisfies the equation.

A) –3:

[tex](-3)^3 - 9(-3)^2 + 25(-3) - 25 = -27 - 81 - 75 - 25 = -208[/tex]

Since the result is not zero, -3 is not a root of the function.

B) –5:

[tex](-5)^3 - 9(-5)^2 + 25(-5) - 25 = -125 - 225 - 125 - 25 = -500[/tex]

Since the result is not zero, -5 is not a root of the function.

C) 2 – i:

[tex][(2 - i)^3 - 9(2 - i)^2 + 25(2 - i) - 25] = 0[/tex]

When evaluating this expression, it will simplify to zero. Therefore, 2 - i is a root of the function.

D) 2i:

[tex](2i)^3 - 9(2i)^2 + 25(2i) - 25 = -8i - 36 - 50i - 25 = -61 - 58i[/tex]

Since the result is not zero, 2i is not a root of the function.

Based on the calculations, the option C) 2 – i must also be a root of the function.

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The equation modeling the data will depend on the specific context and meaning of X and Y. Once this information is known, it will be possible to write an accurate equation that models the data.

In order to write an equation modeling the data using the given terms X and Y, we need to have a clear understanding of what X and Y represent. Without this information, it is not possible to write an equation that accurately models the data.

X and Y could represent a variety of things depending on the context in which they are used. For example, X could represent time and Y could represent distance traveled.

In this case, we could use the equation Y = mx + b, where m is the slope and b is the y-intercept, to model the data. The slope would represent the speed at which the object is traveling, and the y-intercept would represent the initial position of the object.

Another example could be that X represents the number of workers in a factory and Y represents the number of products produced. In this case, we could use the equation Y = kX,

where k is a constant representing the productivity of each worker. This equation would model the data by showing the relationship between the number of workers and the number of products produced.

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Answer:

Step-by-step explanation:

Angles <5 and <1 are adjacent to <6.

Adjacent angles refer to those angles that share a common side and common vertex but at the same time, not overlap with each other. In this question , angle <6 is sharing a side and a common vertex  with <5 and <1 without overlapping each other. Therefore, we can say that the angles are adjacent to each other.

Similarly, if we were supposed to find the adjacent angles of <1, then, the adjacent angles would be angles <6 and <2, as they are sharing the same side and common vertex with that of <1, and are not overlapping each other.

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The given information, we have two Functions: f(x) = (x + 7)^2 g(x) = (x + a)^2  the correct choice is: g(x) = (x - 9)^2.

The given information, we have two functions:

f(x) = (x + 7)^2

g(x) = (x + a)^2

The graph of function f(x) opens upward and has its vertex at (-7, 0). This means that the vertex of f(x) is obtained by shifting the graph of the parent function (x)^2 to the left by 7 units. Therefore, the value of "a" in g(x) should be the same as the shift applied to f(x), but in the opposite direction.

Since the vertex of f(x) is at (-7, 0), we need to shift the graph to the left by 2 units to obtain the vertex of g(x). Therefore, "a" should be -9.

So, g(x) = (x - 9)^2.

Therefore, the correct choice is: g(x) = (x - 9)^2.

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The value of x is 14.

We know in an isosceles triangle an isosceles polygon is a polygon with at least two sides of equal length.

We have two sides measured 2x-9 and x+ 5.

From the figure the length of sides are equal then

2x-9 = x+ 5

2x- 9- x = 5

x-9 = 5

Add 9 to both sides of the equation:

x - 9 + 9 = 5 + 9

x= 14

Thus, the value of x is 14.

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Answer:

Equation 3: 4y + (y - 1) = 29 (y = 6)

Equation 1: (2y + 3) - 4 = 9 (y = 5)

Equation 2: 4y - y + 1 = 13 (y = 4)

Step-by-step explanation:

An example of a negative linear equation is y = -2x + 6.

A negative linear equation is an equation of the form ax + b = 0, where a and b are constants and a is a negative number.

A negative linear equation would be written as:

y = -2x + 6

This equation shows a linear relationship between y and x in the form of a straight line. The slope of the line is negative which can be seen by the "-2" coefficient of the x term. The y-intercept of the line is 6, which is found by setting x=0 and solving for y. This means that the line crosses the y-axis at y=6.

Therefore, an example of a negative linear equation is y = -2x + 6.

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Answer:

The slope of the line is 14.

Step-by-step explanation:

To find the slope of the line that intersects the points (8, -10) and (9, 4), we can use the slope formula:

m = (y2 - y1) / (x2 - x1)

Where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using the coordinates (8, -10) as (x1, y1) and (9, 4) as (x2, y2), we can substitute the values into the slope formula:

m = (4 - (-10)) / (9 - 8)

= (4 + 10) / (9 - 8)

= 14 / 1

= 14