calculation of average speed of a car travelling at 200 km in 2 hours 30 minutes

Option C is correct, the value of x in the triangle is 10.28 units.

The given triangle is right angled triangle.

We know that the sine function is a ratio of opposite side and hypotenuse.

To the angle 40 degrees the opposite side is x.

The hypotenuse is 16.

Sin 40 degrees=x/16

0.6428=x/16

Apply cross multiplication:

x=16×0.6428

x=10.28

Hence, the value of x in the triangle is 10.28 units.

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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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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

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:

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.

Answer:

Step-by-step explanation:

please what grade this if you answer i will help you

Answer:

B). No two lines are parallel

Step-by-step explanation:

In spherical geometry, there are no parallel lines. This is because any two lines on a sphere will eventually intersect.

The correct option is: 5x² - 8x + 10 - 25/(x + 2)

Given that we need to determine, what is the quotient of 5x³+2x2-6x-5 divided by x+2,

Long division can be used to determine the polynomial 5x³+2x2-6x-5 divided by x + 2.

Here is how to accomplish it:

         5x² - 8x + 10

   ____________________

x + 2 | 5x³ + 2x² - 6x - 5

       - (5x³ + 10x²)

       _________________

                  -8x² - 6x

             - (-8x² - 16x)

             _______________

                       10x - 5

                  - (10x + 20)

                  ___________

                          -25

The quotient is 5x² - 8x + 10, and the remainder is -25/(x + 2).

Therefore, the correct option is: 5x² - 8x + 10 - 25/(x + 2)

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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:

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

Answer:

See below for answers and explanations

Step-by-step explanation:

[tex]\displaystyle \lim_{x\rightarrow1^{-}}f(x) = 4-(1)-(1)^2=4-1-1=3-1=2\\\\\lim_{x\rightarrow1^{+}}f(x) = 2(1)-1=2-1=1\\\\\lim_{x\rightarrow1}f(x) = DNE[/tex]

Note that [tex]\displaystyle \lim_{x\rightarrow1^-}f(x)[/tex] represents the left-side limit (so the limit of f(x) as x approaches 1 from the left), and [tex]\displaystyle \lim_{x\rightarrow1^+}f(x)[/tex] represents the right-side limit (so the limit of f(x) as x approaches 1 from the right)

Because [tex]\displaystyle \lim_{x\rightarrow1^-}f(x)\neq\displaystyle \lim_{x\rightarrow1^+}f(x)[/tex], then [tex]\displaystyle \lim_{x\rightarrow1}f(x)=DNE[/tex]

I hope this helped!

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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Answer:

391 cm²

Step-by-step explanation:

area of the parallelogram,

A = base * height

= 23 * 17

= 391 cm²

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]

The domain and the range of the graph are Domain = (-5, -1) U (2, 5] and Range = (-4, 5]

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

The graph

The above graph can be represented as a list of ordered pairs

The rule of a graph is that

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

Domain = (-5, -1) U (2, 5]

Range = (-4, 5]

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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.

Answer:

infinitely many solutions

Step-by-step explanation:

let's compare each equations to equation of a line

which is y=mx+c

first equation

6x - 2y = -4

-2y = -6x -4

divide through by -2

y=3x+2

second equation

3x-y= -2

-y= -3x-2

divide through by -1

y= 3x+2

since the slope and intercept of the first and second equation equal each other then the number of solutions is infinitely many.

note that m is slope and c is intercept.

The statistics that always corresponds to the 75th percentile in a distribution include the following: B. Third Quartile.

In Mathematics and Statistics, IQR is an abbreviation for interquartile range and it can be defined as a measure of the middle 50% of data values when they are ordered from lowest to highest.

Mathematically, interquartile range (IQR) of a data set is the difference between third quartile (Q₃) and the first quartile (Q₁):

IQR = Q₃ - Q₁ = 75th percentile - 25th percentile.

In this context, we can reasonably infer and logically deduce that the 75th percentile in a distribution is always equal to the third quartile.

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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:

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:

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°

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]

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 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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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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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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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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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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Triangle FGH is inscribed in circle O, the length of radius OH is 6, and ma FGH-20. The area of the sector formed by angle FOH, in terms of pi is 6π. Hence, it is neither of the options.

Given that triangle FGH is inscribed in circle O, the length of radius OH is 6, and m∠FGH = 20.

We have to find the area of the sector formed by angle FOH, in terms of pi.

Using the central angle, we know that the measure of ∠FOH is twice that of ∠FGH, which is 40°.

Therefore, the measure of the central angle FOH is 2 * 40 = 80°.

The area of the sector formed by angle FOH, in terms of pi is given by, A = r²θ/2 where A = Area of the sector, r = radius of the circle and θ = central angle in radians.

To calculate the value of A in terms of pi, we have to convert the central angle from degrees to radians.

1 radian = 180°/π radians

Therefore, 80° = 80° * (π/180°) = 4π/9 radians.

Now we can plug in the given values of r and θ to find the area of the sector.

A = (6)² * (4π/9) / 2 = 18π/3 = 6π

Thus, the area of the sector formed by angle FOH, in terms of pi is 6π.

Hence, option 1) 2k is incorrect. Option 2) 3/2 (3) is incorrect. Option 3) 4 is incorrect. Answer: 6π.

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