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

Sin(2x) = 20 x cos²(x), cos(2x) = -99 x cos²(x), and tan(2x) = -20/99.

To find the values of sin(2x), cos(2x), and tan(2x) using the given information, use trigonometric identities to express them in terms of tan(x) and sin(x).

Given that tan(x) = 10 and sin(x) is negative. Since tan(x) = sin(x)/cos(x), find cos(x) using the given information.

Let's solve for cos(x) first:

tan(x) = sin(x)/cos(x)

10 = sin(x)/cos(x)

Now, let's find sin(x) using the given information that sin(x) is negative:

Since tan(x) = sin(x)/cos(x) and tan(x) = 10, substitute 10 for sin(x)/cos(x):

10 = sin(x)/cos(x)

Multiplying both sides by cos(x):

10 x cos(x) = sin(x)

Now, sin(x) = 10 x cos(x).

Since sin(x) is negative, conclude that cos(x) must be positive.

Now, let's use the double-angle identities to find sin(2x), cos(2x), and tan(2x):

sin(2x) = 2 x sin(x) x cos(x)

cos(2x) = cos²(x) - sin²(x)

tan(2x) = sin(2x) / cos(2x)

Substituting sin(x) = 10 x cos(x) into the above formulas, express sin(2x), cos(2x), and tan(2x) in terms of cos(x):

sin(2x) = 2 x (10 x cos(x)) x cos(x) = 20 x cos²(x)

cos(2x) = cos²(x) - (10 x cos(x))² = cos²(x) - 100 x cos²(x) = -99 x cos²(x)

tan(2x) = sin(2x) / cos(2x) = (20 x cos²(x)) / (-99 x cos²(x)) = -20/99

Therefore, sin(2x) = 20 x cos²(x), cos(2x) = -99 x cos²(x), and tan(2x) = -20/99.

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The required equation that represent the hanger is 10 + 5x = 11 and the value of x is 1/5.

Given the diagram of the hanger which one side has 10 + 5x  and other side has 11.

To find the equation, equate the expression of one side to the numerical value of the other side. On solving the equation gives the value of x.

Thus, the equation is 10 + 5x = 11.

Consider the equation 10 + 5x = 11

On subtracting 10 from each side gives,

5x = 1

Divide each side by 5 gives,

x = 1/5.

Hence,  the required equation that represent the hanger is 10 + 5x = 11 and the value of x is 1/5.

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Answer:

The Law of Sines can be used to solve triangles when you have two angles and a side (AAS or ASA) or two sides and a non-included angle (SSA). In this case, triangle A can be solved using the Law of Sines because it has two angles and a side (AAS).

The x- and y-intercepts of the graph are:

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

-4x + 2y = 28.

For the x-intercepts, we set y to 0

So, we have

-4x = 28

Evaluate

x = -7

For the y-intercepts, we set x to 0

So, we have

2y = 28

Evaluate

y = 14

Hence, the x- and y-intercepts of the graph are -7 and 14, respectively

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Question

Find the x-intercept and the y-intercept of the line below. Click on "None" if applicable.

-4x + 2y = 28.

The total amplitude of the tip of King Arthur's sword is s +  [tex]\sqrt{3}[/tex]t/2.

Given that the length of the line segment connecting the centre of the regular hexagon to one of its vertices as  the length of the line segment connecting centre of the regular pentagon to one of its vertices.

To find the amplitude by adding these two lengths.

For the regular hexagon, the distance from the centre to a vertex is equal to the radius of the circumscribed circle. The radius  of the circumscribed circle is equal to length of a side.

Therefore, the amplitude of the hexagon is s.

For a regular pentagon, divide it into three triangles. One of these triangles is an isosceles triangle where the base is the side of the pentagon and the other two sides are radii of the circumscribed circle.

The amplitude of pentagon is the height of the isosceles triangle.

In an isosceles triangle, the height(h) is calculated from formula

h =  [tex]\sqrt{3}[/tex]t/2.

Therefore, the amplitude of the pentagon is   [tex]\sqrt{3}[/tex]t/2.

Hence, the total amplitude of the tip of King Arthur's sword is s +  [tex]\sqrt{3}[/tex]t/2.

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Answer: 39 ft2

Step-by-step explanation:

The area of the trapezoid is 39 square feet.

To find the area of a trapezoid, you can use the formula:

Area = (1/2) × (base1 + base2) × height

Given that the bases of the trapezoid are 16 feet and 10 feet, and the height is 3 feet, we can substitute these values into the formula:

Area = (1/2) × (16 + 10) × 3

Area = (1/2) × 26 × 3

Area = (1/2) × 78

Area = 39 ft^2

Therefore, the area of the trapezoid is 39 square feet.

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To find the area of a parallelogram in the coordinate plane, we need to determine the base and the height of the parallelogram.

Using the given coordinates, we can find the length of one side of the parallelogram as the distance between points A and B.

The length of AB = sqrt((6 - 7)^2 + (5 - 5)^2) = sqrt((-1)^2 + 0^2) = sqrt(1) = 1

The height of the parallelogram can be found as the distance between point D and the line passing through points A and B. We can use the formula for the distance between a point and a line to find the perpendicular distance.

The equation of the line passing through A and B can be found using the point-slope form:

y - 5 = (5 - 5)/(7 - 6) * (x - 7)

y - 5 = 0 * (x - 7)

y - 5 = 0

y = 5

The perpendicular distance from point D(-9, -2) to the line y = 5 is the difference in their y-coordinates:

Perpendicular distance = |-2 - 5| = 7

Now, we have the base length AB = 1 and the height = 7.

The area of the parallelogram is given by the formula: Area = base * height.

Area = 1 * 7 = 7 square units.

Check the picture below.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=1\\ b=13\\ h=7 \end{cases}\implies A=\cfrac{7(1+13)}{2}\implies A=49[/tex]

The measure of angle AEC is 225 degree.

Given ABCD square then all sides are equal and all angles are of 90°

AB=BC=CD=DA

and also CDE is an equilateral triangle

CD=DE=EC and all angles are of 60°

Now, In ΔADE, ∵AD=AE ⇒ ∠DAE=∠AED

∠ADE=∠ADC-∠EDC=90°-60°=30°

By angle sum property of triangle

∠ADE+∠DAE+∠AED=180°

30°+2∠AED=180°

2∠AED=150°

∠AED=75°

and, ∠EAB = ∠DAB-∠DAE = 90°-75° = 15°

Reflex angle ∠AEC= 360°-∠AED-∠DEC

=360° - 75° -60°

=225°

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The complete and correct question is attached below:

Answer:

Therefore, the expression becomes:

7/1 - 2/6

Now, we need to find a common denominator for the fractions, which is 6:

7/1 - 2/6 = (76)/(16) - 2/6

= 42/6 - 2/6

= (42 - 2)/6

= 40/6

Finally, we can simplify the fraction:

40/6 = 20/3

So, the difference between 5 2/6 and -2 4/6 is 20/3.

Step-by-step explanation:

First, let's subtract the whole numbers: 5 - (-2) = 5 + 2 = 7.

Next, let's subtract the fractions: 2/6 - 4/6 = (2 - 4)/6 = -2/6.

Combining the whole number and fraction results, we have:

7 - 2/6

Now, to simplify this result further, we can express 7 as a fraction with a common denominator of 6:

7 = 7/1

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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The equivalent fractions for the mixed numbers, with the same denominator, are given as follows:

32/12 and 27/12.

The mixed numbers in the context of this problem are given as follows:

The fractions that represent each number are given as follows:

The least common factor of 3 and 4 is given as follows:

3 x 4 = 12.

Hence the equivalent fractions are given as follows:

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To determine which box can hold all the cubes, we need to calculate the volume of each box and compare it to the volume occupied by the cubes.

The volume of a rectangular box is calculated by multiplying its length, width, and height.

Box A:

Volume = 4" x 6" x 8" = 192 cubic inches

Box B:

Volume = 6" x 3" x 12" = 216 cubic inches

Box C:

Volume = 6" x 6" x 4" = 144 cubic inches

Since the cubes have a side length of 1 inch, the volume occupied by 200 cubes would be:

Volume of cubes = 200 cubic inches

Comparing the volumes, we find that:

- Box A has a volume of 192 cubic inches, which is less than the volume of the cubes.

- Box B has a volume of 216 cubic inches, which is greater than the volume of the cubes.

- Box C has a volume of 144 cubic inches, which is less than the volume of the cubes.

Therefore, the box that would be able to hold all 200 cubes is Box B: 6" x 3" x 12".

Answer:

Naomi will need to score at least 89% on her fourth test to have an average of 90% in her math class.

Step-by-step explanation:

To find out what score Naomi needs to earn on her fourth test in order to have an average of 90%, we can set up an equation.

Let's denote the score on the fourth test as "x". Naomi has taken three tests, and their scores are 87%, 98%, and 86%. To find the average, we sum up all the scores and divide by the number of tests:

(87 + 98 + 86 + x) / 4 = 90

Now we can solve for x:

(87 + 98 + 86 + x) = 4 * 90

271 + x = 360

x = 360 - 271

x = 89

Naomi will need to score at least 89% on her fourth test to have an average of 90% in her math class.

The correct option is b, the pair of consecutive interior angles is 1 and 7.

First, we can see that the interior angles are the angles that are "interior" to the intersections.

These are 1, 4, 6, and 7.

Because the two lines are parallel, the consecutive interior angles are angles that would be adjacent (add up to 180°) but that are in different intersections.

Then the consecutive interior angles are:

3 and 6

1 and 7

The correct option is b.

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Answer:

Step-by-step explanation:

please what grade this if you answer i will help you

Answer:

16x + [tex]3y^{2}[/tex] - 26xy

Step-by-step explanation:
PEMDAS

(2x - 3y)(8x - y)
= 16x - 2xy - 24xy + [tex]3y^{2}[/tex]
= 16x + [tex]3y^{2}[/tex] - 26xy

Answer:

Step-by-step explanation:

Answer:

32 inches Aprox

Step-by-step explanation:

To find the size of a rectangular television screen given its height and width, we can use the Pythagorean theorem. The diagonal measurement (size) is the hypotenuse of a right triangle formed by the height and width.

Given:

Height of the television screen (h) = 20 inches

Width of the television screen (w) = 25 inches

Using the Pythagorean theorem:

diagonal² = height² + width²

diagonal² = 20² + 25²

diagonal² = 400 + 625

diagonal² = 1025

Taking the square root of both sides:

diagonal ≈ √1025

diagonal ≈ 32.02

Rounding to the nearest inch, the size of the television screen is approximately 32 inches.

Therefore, the size of the rectangular television screen, rounded to the nearest inch, is 32 inches.

The monthly payment on the 15-year fixed rate mortgage is $515.27.

The bank requires a 10% down payment on the condo price of $80,000.

Down Payment = 10% of $80,000

Down Payment = 0.1 * $80,000

Down Payment = $8,000

Therefore, the required down payment is $8,000.

Amount of the Mortgage:

To find the amount of the mortgage, we subtract the down payment from the condo price.

Amount of Mortgage = Condo Price - Down Payment

Amount of Mortgage = $80,000 - $8,000

Amount of Mortgage = $72,000

Therefore, the amount of the mortgage is $72,000.

Now, Monthly Payment = (Loan Amount x Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate) ^ (-Number of Months))

Monthly Interest Rate = Annual Interest Rate / 12

= 3.5% / 12 = 0.035 / 12

= 0.002917

and, Number of Months = 15 years x 12 months = 180 months

So, Monthly Payment = ($72,000 x 0.002917) / (1 - (1 + 0.002917) ^ (-180))

Monthly Payment ≈ $515.27

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Answer:

[tex]x=\frac{\pi}{4}+\frac{\pi n}{2}[/tex]

Step-by-step explanation:

[tex]\displaystyle \tan^2x-1=0\\\tan^2x=1\\\tan x=\pm 1\\\\x=\frac{\pi}{4}+\frac{\pi n}{2}[/tex]

Answer:

-----------------

Given function:

We know that absolute value is non-negative, hence |x + 3| has a minimum value of 0 when x = - 3. Then the function has a minimum value of 2.

The range is the set of output values. As we see given function has a minimum value of 2 and no maximum value.

It can be shown as:

The matching choice is C.

The width of the rectangle is 5k² and the length of the rectangle is 3k² + 7k + 4.

The greatest common monomial factor of 15k⁴, 35k³, and 20k² is 5k². So the width of the rectangle is 5k².

The area of the rectangle is the product of its length and width. So the length of the rectangle is the area divided by the width. The area is 15k⁴ + 35k³ + 20k² and the width is 5k². So the length is:

= (15k⁴ + 35k³ + 20k²) / (5k²)

= 3k² + 7k + 4.

Therefore, the width of the rectangle is 5k² and the length of the rectangle is 3k² + 7k + 4.

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Step-by-step explanation:

To solve this problem, we need to find the circumference of the circular playground and then multiply it by the number of rounds the runner completes.

The circumference of a circle can be calculated using the formula:

Circumference = 2 * π * radius

Given that the radius of the playground is 77m, we can substitute this value into the formula to find the circumference:

Circumference = 2 * π * 77

Now, we need to calculate the distance covered by the runner in 5 complete rounds. Since one round is equal to the circumference, the distance covered in 5 rounds would be:

Distance = 5 * Circumference

Substituting the value of the circumference, we have:

Distance = 5 * (2 * π * 77)

To simplify, we can use an approximation of π as 3.14:

Distance ≈ 5 * (2 * 3.14 * 77)

Calculating further:

Distance ≈ 5 * (6.28 * 77)

Distance ≈ 5 * 483.56

Distance ≈ 2417.8

Therefore, the distance covered by the runner in 5 complete rounds around the circular playground is approximately 2417.8 meters, which can be rounded to 2420 meters (as given in the answer).

Hope this helps!

Answer:

2420

Step-by-step explanation:

Circumference = 2πr

One complete round will be equal to the circumference = 2πr

Five rounds will be five times the circumference

= 5*2πr

= 10πr

[tex]= 10 *\frac{22}{7}*77 \\\\= 10* 22* 11\\\\= 2420[/tex]

The value of x is approximately 34.02.

Given that in a rectangle with length 31 and width is 14 and the diagonal length is x.

To find the value of x using the Pythagorean Theorem, we can consider the rectangle as a right triangle, where the length and width of the rectangle form the two sides of the triangle, and the diagonal length (x) is the hypotenuse.

According to the Pythagorean Theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Applying the given data gives,

[tex]x^2 = length^2 + width^2[/tex]

Substituting the given values into the equation:

diagonal length [tex]x^2 = 31^2 + 14^2[/tex]

diagonal length [tex]x^2[/tex] = 961 + 196

diagonal length [tex]x^2[/tex] = 1157

To find x, we take the square root of both sides:

diagonal length x = [tex]\sqrt{1157}[/tex]

diagonal length x = 34.02

Therefore, the value of x is approximately 34.02.

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Answer:

please see answers below

Step-by-step explanation:

Volume of sphere = (4/3) X π X r ³

volume of hemisphere = (2/3)X π X r ³

12) volume of hemisphere = (2/3)X π X r ³

= (2/3) X π X (5)³

= (250/3)π

= 261.80 km³ to nearest hundredth

13) 18 foot is the diameter. radius = 1/2 X diameter = 9.

volume of hemisphere = (2/3)X π X r ³

= (2/3) X π X (9) ³

=  1526.81 ft³ to nearest hundredth

The area of smaller triangle is 59 square feet.

The area of the larger triangle is 105 square feet.

And the one side of the larger triangle and the smaller traingle is 16 and 12 feet respectively.

Suppose the height of thesmaller triangle be x feet and the height of the larger triangle be y feet.

Since, the corresponding edges of similar triangles are proportional.

Therefore, y/x=16/12

y=4/3x

Also, the area of larger triangle is 105 square feet.

1/2×4/3x×16=105

The above equation can be written as

1/2×4/3x×4/3×12=105

1/2×x×12=59

Area of smaller triangle  = 59 square feet

Hence, the area of smaller triangle is 59 square feet.

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Answer:

150

Step-by-step explanation:

the formula for this is 2a squared + 4 a h

when we plug everything in we end up getting 2*3 squared + 4*3*11

and when solved it gets toy 150

Answer:

m<A = 66.2°

Step-by-step explanation:

m<A + m<B = 180°

m<B = 113.8°

m<A + 113.8° = 180°

m<A = 180° - 113.8°

m<A = 66.2°

The required angle is 24.5°.

Given is a right triangle with perpendicular side 16 and the base = 35 we need to find an acute angle in it,

To find the acute angle in a right triangle given the lengths of the perpendicular side and the base, you can use the tangent function.

The tangent of an angle is defined as the ratio of the length of the perpendicular side to the length of the base side.

In this case, the perpendicular side is 16 and the base is 35.

Let's denote the acute angle as θ.

Using the tangent function, we can set up the equation:

tan(θ) = perpendicular side / base

tan(θ) = 16 / 35

To find the value of θ, we can take the inverse tangent of both sides:

θ = tan⁻¹(16 / 35)

θ = 24.5°

Hence the required angle is 24.5°.

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The number of degrees the Figure A must be rotated counterclockwise around the origin to line up with Figure B is = 270°

Given data ,

Let the number of degrees the Figure A must be rotated counterclockwise around the origin to line up with Figure B be represented as A

Now , the triangle is represented by the figure A with coordinates as

A ( -2 , 3 )

And , the coordinates of the rotated triangle is A' ( 3 , 2 )

270° clockwise rotation: (x,y) becomes (-y,x)

270° counterclockwise rotation: (x,y) becomes (y,-x)

So , the triangle is rotated 270° counterclockwise rotation

Hence , the rotation is 270° counterclockwise

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