2.2.3 quiz: angle theorems what is the value of y? OA.50

A.) Area = (1/2) × 7 × 6 × √(15)/4 = 21√(15)/4

B.) Angle C is 75 degrees.

C.) Sin(A) is 3√(255)/85 in simplest radical form.

Trigonometry is a branch of mathematics that examines triangle-related relationships and calculations, particularly the measurement of triangle sides and angles.

A.) We can apply the following formula to determine the triangle's area:

Area = (1/2) × b × a × sin(C)

Since we know b=7 and a=6, we have:

Area = (1/2) × 7 × 6 × sin(C)

To find sin(C), we can use the fact that cos(C) = 1/4 and the Pythagorean identity:

sin²(C) + cos²(C) = 1

sin(C) = √(1 - cos²(C)) = √(1 - 1/16) = √(15/16) = √(15)/4

B.) To find C, we can use the Law of Cosines:

c² = a² + b² - 2ab×cos(C)

c² = 6² + 7² - 2(6)(7)(1/4) = 85/2

c = √(85)/2

Now we can use the Law of Cosines again to find angle C:

cos(C) = (a² + b² - c²)/(2ab)

cos(C) = (6² + 7² - (√(85)/2)²)/(267) = 1/4

C.) To find sin(A), we can use the Law of Sines:

sin(A)/a = sin(C)/c

sin(A) = asin(C)/c = 6(√(15)/4)/(√(85)/2) = 3×√(15)/√(85) = √(255)/85

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Answer:

the second one is x= -1

*this stuff is genuinely easy. I'm in 10th grade and all you have to do is put it in the calculator. If you have a tinspire like me you could make the x into a 1 in the calculator, put the whole thing in graph and it'll trace the answer for you. If your teacher wants to see work then maybe don't do that but let me know and I'll send the work for you.

Answer: 3 meters

Step-by-step explanation:

The area of the rectangular region is given by:

(18 + 2x) * (30 + 2x) = 18*30 + 36x + 60x + 4x^2

Simplifying this expression, we get:

4x^2 + 96x - 1300 = 0

Dividing both sides by 4, we get:

x^2 + 24x - 325 = 0

Now we can solve for x using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = 24, and c = -325.

Plugging in these values, we get:

x = (-24 ± sqrt(24^2 - 4(1)(-325))) / 2(1)

x = (-24 ± sqrt(936)) / 2

x = (-24 ± 30) / 2

x = 3 or -27

Since the width of the path cannot be negative, the only possible solution is x = 3 meters. Therefore, the width of the path surrounding the pool is 3 meters.

The function is transformed by horizontal translation to the right is applied first, followed by the vertical translation downward

Given data ,

Let the parent function be represented as f ( x )

Now , the value of f ( x ) is

y = 3ˣ

Let the transformed function be f' ( x )

y' = 3⁽ˣ⁻²⁾ - 4

Horizontal Translation: When compared to the basic function, y = 3x, the function's "(x-2)" inside the exponent of 3 causes a horizontal translation to the right of 2 units.

This results in a 2 unit shift along the x-axis of the function's graph.

Vertical Translation: In comparison to the base function y = 3x, the "-4" at the end of the function causes a vertical translation downward of 4 units.

This results in a 4 unit downward shift of the function's y-axis graph.

Hence , the function is transformed

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The quadrilateral is inscribed inside the circle and x = 44

Given data ,

Let the quadrilateral be inscribed inside the circle as shown in the figure

Now , the measure of angles are

m∠CFE = (2x + 6)°

m∠CDE = (2x − 2)°

And , opposite sides of the angles of quadrilateral are supplementary

So , m∠CFE + m∠CDE = 180°

On simplifying , we get

2x + 6 + 2x - 2 = 180

4x + 4 = 180

4x = 176

x = 44

Hence , the angle is solved and x = 44

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The complete question is attached below :

Quadrilateral CDEF is inscribed in circle A.

If m∠CFE = (2x + 6)° and m∠CDE = (2x − 2)°, what is the value of x?

A) 22

B) 44

C) 46

D) 89

Answer: 44

Step-by-step explanation:

i took the test

The calculated value of the perimeter of the scaled rectangle is 120 inches

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

Perimeter =  48 in

Scale factor = 2.5

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

Perimeter of the scaled rectangle = Perimeter * Scale factor

Substitute the known values in the above equation

Perimeter of the scaled rectangle = 48 * 2.5

Evaluate

Perimeter of the scaled rectangle = 120

Hence, the perimeter of the scaled rectangle is 120

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Answer:

$97.50

Step-by-step explanation:

Purchase Price:

$150

Discount:

(150 x 35)/100 = $52.50

Final Price:

150 - 52.50 = $97.50

The missing dimensions of the triangular plot of land are:

i. b = 2.45

ii. A = 69.5

iii. C = 75.5^o

A cosine rule is a trigonometric function that can be used to determine the length of side, or measure of the internal angles of a none right angled triangle.

Cosine rule states that;

[tex]b^{2}[/tex] = [tex]a^{2}[/tex] + [tex]c^{2}[/tex] -2acCos B

To determine the missing values of the triangle in the attached diagram, we have;

[tex]b^{2}[/tex] = [tex]a^{2}[/tex] + [tex]c^{2}[/tex] -2acCos B

  = 4^2 + 7^2 - 2(4*7)Cos35^o

  = 16 + 49 -2(36*0.8192)

  = 65 - 58.9824

  = 6.0176

b = (6.0176)^1/2

  = 2.4531

b = 2.45

From sine rule,

a/ Sin A = b/Sin B = c/ Sin C

a/ Sin A = b/Sin B

4/Sin A = 2.45/ Sin 35

Sin A = 4* Sin 35/ 2.45

        = 0.9365

A = Sin^-1 0.9365

  = 69.47

A = 69.5

So to determine the value of C, we have;

A + B + C = 180^o

69.5 + 35 + C = 180

104.5 + C = 180

C = 180 - 104.5

   = 75.5

C = 75.5^o

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Angle or arc HGJ is measured at 275 for given figure.

Arcs may be created from the circumference of a circle. It is referred to as the curved line that connects two locations on a circle's perimeter and splits it into segments. The length of an arc is inversely proportional to the angle it makes at the centre of the circle.

When the central angle rises, so does the arc's length, and vice versa. Arcs are commonly used to depict and compute measurements of circles and circular objects in geometry, trigonometry, and physics.

For given problem,

mHGJ= 360° - mJH = 360°-( mJl + mlH ) =  360°-(30°+55°)

         = 360°-85° = 275°

Hence, arc or angle HGJ= 275 degrees

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Hailey goes to a store an buys an item that price of a dollars, so the expression that represents the total amount that Hailey paid at the register in terms of a is 0.702a.

The amount of discount that Hailey receives is 35% of the original price, which is 0.35a. Therefore, the discounted price she pays is a - 0.35a = 0.65a.

The amount of tax that is added to the discounted price is 8% of the discounted price, which is 0.08(0.65a) = 0.052a.

So the total amount that Hailey paid at the register is the discounted price plus the tax:

total amount = discounted price + tax

total amount = 0.65a + 0.052a

Simplifying this expression, we get:

total amount = 0.702a

Therefore, the expression that represents the total amount that Hailey paid at the register in terms of a is 0.702a.

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Step-by-step explanation:

A(n) discount is an amount returned after purchase or deducted from the purchase price.

Let's use the variable "x" to represent the number of 3-inch bolts that James bought.

We know that he bought a total of 16 bolts, so the number of 4-inch bolts he bought would be 16 - x.

The cost of the 3-inch bolts is 36 cents each, so the total cost of the 3-inch bolts would be 0.36x dollars.

Similarly, the cost of the 4-inch bolts is 42 cents each, so the total cost of the 4-inch bolts would be 0.42(16 - x) dollars.

We know that the total cost of all the bolts was $6.00, so we can set up the following equation:

0.36x + 0.42(16 - x) = 6.00

Simplifying and solving for x, we get:

0.36x + 6.72 - 0.42x = 6.00

-0.06x = -0.72

x = 12

Therefore, James bought 12 of the 3-inch bolts.

Answer:

The correct answer is D. purchase price: $117, advertised price: $293.

Step-by-step explanation:

Answer:

A data set of the least purchased menu items at a bakery is best shown as a (Report)

Step-by-step explanation:

Have A Good Day :)

Answer: x=-5,y=3

Step-by-step explanation: Add the 2 equations together, 3x+x=4x, y+(-y)=0, and -12-8=-20. This leaves us with 4x=-20, so x=-5. Plug x back into the equation, so -5-y=-8, add 5 to both sides  so -y=-3, and y=3.

The New Area based on the information will be 168ft

Expanding the above equation, we get:

120ft² + 22x + x² = 240ft²

Rearranging and simplifying, we get:

x² + 22x - 120 = 0

Since the increase cannot be negative, we take the positive value of x:

x = 2

Therefore, the increase in both the length and width of the patio should be 2ft to double its area.

New Length = 10ft + 2ft = 12ft

New Width = 12ft + 2ft = 14ft

New Area = 12ft x 14ft = 168ft²

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Answer:

? = 13.7

Step-by-step explanation:

Right triangle equation A^2 + B^2 = C^2

7.6^2 + 11.4^2 =

57.76 + 129.96 = 187.72

find the square root of 187.72 by putting it in the calculator

187.72 = 13.70109485^2

Estimate = 13.7^2

The building is, 246 feet tall.

Since, We know that;

Two or more triangles will always be referred to as similar if on comparing their corresponding properties, some common relations holds. Some of the relations are relations between their length of sides, relations among their internal angles etc.

To determine the height of the building, we have;

height of pole = 7 ft

total length of the building's shadow = 167 ft

the length of the shadow of the pole = 4.75 ft

Let the height of the building be represented by h. On comparison, we have;

4.75/ 167 = 7/h

4.75h = 167 x 7

        = 1169

h = 1169/ 4.75

h  = 246.11

Hence, The building is 246 ft. tall.

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Check the picture below.

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x_1=0\\ x_2=15 \end{cases}\implies \cfrac{f(15)-f(0)}{15 - 0}\implies \cfrac{11-5}{15}\implies \cfrac{6}{15}\implies \cfrac{2}{5}[/tex]

The volume of the leaning regular hexagonal prism, can be found to be 351. 89 inch ³.

A right triangle can be constructed in a regular hexagon by linking the midpoint of one side and a vertex to the center. This specially-crafted triangle comprises two legs, one of which is half the size of the primary side (acting as the hypotenuse) while the remaining leg lies parallel to the hexagon's apothem (height).

The height of the prism can be found with cosine to be:

h = slanted height x Cos (angle )

h = 11 x Cos ( 70 degrees )

h = 3. 762 inches

We can then find the volume of the leaning hexagonal prism to be:

= Area x Height

= 93. 528 x 3. 762

= 351. 89 inch ³

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The output for an input of n is given as follows:

f(n) = -4 - 2n.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

For this problem, we have that when x increases by one, y decays by two, hence the slope m is given as follows:

m = -2.

Hence:

f(n) = -2n + b.

When n = 1, f(n) = -6, hence the intercept b is obtained as follows:

-6 = -2 + b

b = -4.

Hence the equation is:

f(n) = -2n - 4.

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The end behavior of the given function is As x → –∞, f(x) → –∞, and as x → ∞, f(x) → –∞.

The term "end behavior" describes the behaviour or trend of a function's graph as its x-values go closer to positive or negative infinity. It explains how the function "ends" or acts when x is extremely large (positive infinity) or extremely small (negative infinity). The degree and leading coefficient of the polynomial formulation of the function can be used to predict the final behaviour. For instance, the left and right ends of the graph will both point upward for a function with an odd-degree polynomial and a positive leading coefficient (towards positive infinity).

For the function f(x) = -2∛x as x approaches negative infinity because the function has a negative coefficient in front of the cube root, which means that as x decreases significantly, the absolute value of the cube root increases. The function also approaches negative infinity as x approaches very big (positive) values and the cube root approaches very small absolute values. As a result, the function's final behaviour is that it approaches negative infinity as x gets closer to both negative and positive infinity.

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The end behavior of the given function is As x → –∞, f(x) → –∞, and as x → ∞, f(x) → –∞.

The term "end behavior" describes the behaviour or trend of a function's graph as its x-values go closer to positive or negative infinity. It explains how the function "ends" or acts when x is extremely large (positive infinity) or extremely small (negative infinity). The degree and leading coefficient of the polynomial formulation of the function can be used to predict the final behaviour. For instance, the left and right ends of the graph will both point upward for a function with an odd-degree polynomial and a positive leading coefficient (towards positive infinity).

For the function f(x) = -2∛x as x approaches negative infinity because the function has a negative coefficient in front of the cube root, which means that as x decreases significantly, the absolute value of the cube root increases. The function also approaches negative infinity as x approaches very big (positive) values and the cube root approaches very small absolute values. As a result, the function's final behaviour is that it approaches negative infinity as x gets closer to both negative and positive infinity.

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Answer:

The function f(x) = -2∛x represents a cube root function that is multiplied by -2.

As x approaches negative infinity, the cube root of x becomes more negative, and when it is multiplied by -2, it becomes more positive. Therefore, as x → –∞, f(x) → ∞.

As x approaches positive infinity, the cube root of x becomes more positive, and when it is multiplied by -2, it becomes more negative. Therefore, as x → ∞, f(x) → –∞.

Therefore, the correct answer is: As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞. D.

Answer:

The function f(x) = -2∛x represents a cube root function that is multiplied by -2.

As x approaches negative infinity, the cube root of x becomes more negative, and when it is multiplied by -2, it becomes more positive. Therefore, as x → –∞, f(x) → ∞.

As x approaches positive infinity, the cube root of x becomes more positive, and when it is multiplied by -2, it becomes more negative. Therefore, as x → ∞, f(x) → –∞.

Therefore, the correct answer is: As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞. D.

Answer:

Step-by-step explanation:

To solve this problem, we need to use the distance formula to find the length of each side of the triangle, and then apply the Pythagorean theorem to determine whether the triangle is a right triangle.

Let's label the three vertices of the triangle as A, B, and C, and their coordinates as follows:

A = (-2, 5)

B = (3, -1)

C = (1, 3)

The length of AB is:

AB = sqrt((3 - (-2))^2 + (-1 - 5)^2) = sqrt(25 + 36) = sqrt(61)

The length of AC is:

AC = sqrt((1 - (-2))^2 + (3 - 5)^2) = sqrt(9 + 4) = sqrt(13)

The length of BC is:

BC = sqrt((1 - 3)^2 + (3 - (-1))^2) = sqrt(4 + 16) = sqrt(20) = 2sqrt(5)

Now, we need to check whether the triangle is a right triangle. We can do this by checking whether the sum of the squares of the two shorter sides (AB and AC) is equal to the square of the longest side (BC). If it is, then the triangle is a right triangle.

AB^2 + AC^2 = 61 + 13 = 74

BC^2 = (2sqrt(5))^2 = 20

Since AB^2 + AC^2 is not equal to BC^2, the triangle is not a right triangle.

Therefore, the answer is: "The triangle is not a right triangle."

Answer:

Step-by-step explanation:

The surface area of a cube is given by the formula:

SA = 6s^2

where s is the length of an edge.

Substituting s = 6.44 cm into the formula, we get:

SA = 6(6.44 cm)^2

SA = 6(41.4736 cm^2)

SA = 248.8416 cm^2

Therefore, the surface area of the cube is 248.8416 cm^2.

Answer: 8.625

Step-by-step explanation:The eight stays an 8 snd 5:8 is .625. Add these together and you get 8.625.

Answer:

Step-by-step explanation:

1

The equation is Skateboard = Deck + Grip Tape + Trucks + Wheels + Bearings + Hardware + Assembly + Personalization.

Here's an equation that outlines my "recipe" for making a skateboard:

Skateboard = Deck + Grip Tape + Trucks + Wheels + Bearings + Hardware + Assembly + Personalization

Explanation of the equation:

Deck: The wooden or composite board that serves as the main body of the skateboard. It is typically made from layers of plywood or other materials, and its dimensions (length, width, concavity, etc.) can be customized based on personal preference.

Grip Tape: A sandpaper-like material that is applied to the top of the deck to provide traction for the rider's feet. It is usually made of adhesive-backed paper or fabric and comes in various designs and colors.

Trucks: Metal T-shaped components that are mounted on the underside of the deck and serve as the axle and suspension system of the skateboard. They consist of a baseplate, hanger, kingpin, bushings, and hardware, and are responsible for allowing the board to turn and pivot.

Wheels: Typically made of urethane or other durable materials, skateboard wheels come in various sizes, shapes, and hardness levels (durometer). They are attached to the trucks and provide smooth rolling and maneuverability.

Bearings: Small, round metal or ceramic components that fit inside the wheels and allow them to spin freely on the axle. They are crucial for reducing friction and enabling the wheels to roll smoothly.

Hardware: Nuts, bolts, and screws used to attach the trucks to the deck and assemble the skateboard. They are typically made of metal and come in different sizes and lengths.

Assembly: The process of putting together all the skateboard components to create a functional skateboard. It involves attaching the trucks to the deck using the hardware, installing the wheels and bearings, and applying the grip tape.

Personalization: This refers to any additional customization or personal touches that a skateboarder may choose to add to their skateboard, such as stickers, artwork, or modifications to the deck shape or truck settings, to make it unique and suited to their individual style.

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