Prove the identity
1. cot²x= csc²x-1

2. sin x tan x= sec x - cos x

Answer:

(1/2)^2= 0.25 thank you

Answer:

∠E = 150°

Step-by-step explanation:

All sides of the convex pentagon ABCDE are of equal length, and ∠A = ∠B = 90°. What is the degree measure of ∠E?

Solution:

A pentagon is a polygon with five sides and five angles. For a regular polygon, all the sides are equal and each angle is 108°.

Since ∠A and ∠B are right angles, and AE = BC = AB = CE. Therefore ABCE is a square. This means ∠AEC = 90°

Also triangle CDE is equilateral because all sides of the triangle are equal, hence ∠DEC = 60°.

Therefore ∠E = ∠AEC + ∠DEC = 90° + 60°

∠E = 150°

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\rm{YOUR\ EQUATION: \dfrac{x}{2}}[/tex]

[tex]\large\text{If x = 16, then substitute it where the x-value is in the given equation}[/tex]

[tex]\rm{NEW\ EQUATION: \dfrac{16}{2}}[/tex]

[tex]\rm{\dfrac{\bold{16}}{{2}}[/tex]

[tex]\rm{= \underline{\bf 8}}[/tex]

[tex]\large\text{Because, 8}\times\large\text{2 gives you 16}[/tex]

[tex]\boxed{\boxed{\large\text{Answer: \huge \bf Option A. 8}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

So sin in math means:

In a right angled triangle, the sine of an angle is: The length of the side opposite the angle divided by the length of the hypotenuse. The abbreviation is sin.

Con in math means:

In a right angled triangle, the cosine of an angle is: The length of the adjacent side divided by the length of the hypotenuse. The abbreviation is cos. cos(θ) = adjacent / hypotenuse.

in this case it has to be a sin. So its either A, or B.

ii think a tho

Answer:

(a)

Step-by-step explanation:

Sin (37) = x/10.3

using trigonometric identity (Sin θ = AC/AB)

The correct answer is n - 7 = 30

Answer:

it's 19 degrees because it's a 90 degree angle

Answer:

19 degrees

Step-by-step explanation:

90-71=is 19 because it is a 90 degree angle.

Answer:

x = 9

Step-by-step explanation:

When two chords intersect inside a circle, the product of the lengths of the segments of one chord equals the product of the lenfgths of the segments of the other chrod.

That means that

2x = 3 × 6

2x = 18

x = 9

Answer:

Step-by-step explanation:

for missing angle of triangle ABC

let the missing angle be y

31+111+x=180(sum of interior angle of a triangle is 180 degree)

142+y=180

y=180-142

y=38 degree

x=y(being alternate angles)

x=38 degree

Answer:

(1, -2)

Step-by-step explanation:

The dilation that has a center of (0, 0) means that you would multiply each number in your coordinate point by your given scale factor.

For your given point (2, -4) with a scale factor of 0.5:

2 times 0.5 = 1

-4 times 0.5 = -2

Therefore your new point will be (1, -2).

Answer:

k = 24·√2

Step-by-step explanation:

Given that the angles of the triangle are 45° by 45 by 90°, we have;

The given right triangle = An isosceles right triangle by two angles being equal

The given angle of the right triangle = 90°

The given leg of the right triangle = 24

For an isosceles right triangle, both legs are equal, therefore;

The length of the other leg of the right triangle = 24

By Pythagoras theorem, the measure of the side opposite the 90° side, 'k', is given as follows;

k² = (One leg length)² + (The other leg length)²

∴ k² = 24² + 24² = 1152

k = √1152 = 24·√2 ≈ 33.94.

20 / 52 = 5 / 13

Probability(P) is the likelihood of occurrence of an event. It is given by;

P = total number of favourable outcomes ÷ total number of possible outcomes

In a pack of playing cards, there are 52 cards altogether.

Therefore, the total number of possible outcomes = 52

To get the probability that a card drawn at random is neither a face nor a black card, the following should be noted.

i. There are 12 face cards in the pack. These are the kings (4 cards), queens(4 cards) and the jacks (4 cards).

Therefore, number of cards that are not face cards = 52 - 12 = 40

ii. Black cards are half of the total number of cards = 26.

These black cards contain half of the kings, queens and jacks cards = 6 which are already included in the face cards. Therefore, the remaining black cards will be 26 - 6 = 20

Neither a face card nor a black card = 40 - 20 = 20 [number of favourable outcomes]

The probability of getting neither a face card nor a black card is

=> total number of favourable outcomes ÷ total number of possible outcomes

=> 20 / 52 = 5 / 13

Answer:

d

Step-by-step explanation:

Answer:

8. hope this helps

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

Answer:

you need all answers????

Answer:

∠1 = ∠5 (corresponding angle)

⇒∠5 = 50 deg

∠5+∠6=180 deg   (total sum is 180)

50+∠6=180

∠6=180-50

∠6=130

Step-by-step explanation:

∠5=86 (corresponding angle)

∠5=(4x+38) (vertically opp angle)

86=4x+38

4x=86-38

4x=48

x=12

Answer:

angle 1+angle 6=180(being exterior alternate angle)

50+angle 6=180

angle 6=180-50

angle 6=130

for value of x

angle 5=86 degree(being corresponding angle)

angle 5=angle 4x-38

86=4x-38

86+38=4x

124/4=x

31=x

relationship between angle 2 and 6 is they are corresponding angles

angle 1=63+61

angle 1=124 degree

5 no .second option is correct

6 no a=75 degree

last question answer =34 degree

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

When you are raising a power to a power, you can multiply them:

[tex](49^3)^{\frac{1}{6}}=49^{3*\frac{1}{6}}[/tex] = [tex]49^{\frac{3}{6}}[/tex] = [tex]49^{\frac{1}{2}}[/tex]

When raising a number to the power of 1/2, you are basically finding the square root of the number:

[tex]49^{\frac{1}{2}}[/tex] = [tex]\sqrt{49}[/tex] = 7

Answer:

can't answer without the picture because you need the route to know how far.

Answer:

2x²−13x+21

Step-by-step explanation:

Answer: x+4/x-4

Step-by-step explanation:

Answer:

90°

Step-by-step explanation:

m arc AC = 90°

_____________

The measure of the arc length AC is 90 degrees.

The arc length of a circle is the distance between two points on the curve of the circle.

We have,

The arc length and the angles with the center on a circle are equal.

So,

Arc length AC makes a 90-degree angle with the center of the circle.

Now,

Arc AC = 90 degrees.

Thus,

The measure of the arc length AC is 90 degrees.

Learn more about arc lengths here:

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Answer:

-44.35

Step-by-step explanation:

1/4 = 0.25 (as 0.25 * 4 = 1)

-25 1/4 = -25.25

-25.25 - 19.1 = -44.35

The value is -44.35.

The process of replacing a mathematical expression with one that is equivalent, simpler, and typically shorter. Examples of simplification include simplifying algebraic expressions in computer algebra, simplifying Boolean expressions in logic optimization, and simplifying fractions by using conjunction elimination in logic inference to produce a formula that is simpler but typically not equivalent to the original.

Given [tex]-25\frac{1}{4}[/tex] - 19.1

[tex]-25\frac{1}{4}[/tex] can be written as -(25 + 1/4)

1/4 multiply and divide by 25

we get 25/100

to convert fraction into decimal make the base multiple of 10 and put decimal ahead the no. of digits

20/100 = 0.25

equation is -25.25 - 19.1 = -44.35

Hence the value is -44.35.

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Answer:

79 degrees

Step-by-step explanation:

79 degrees is parallel to a. The line below is the same as the line above, since they are parallels, beaning d and b also are both 79 degrees

Answer:

[tex]79^{\circ}[/tex]

Step-by-step explanation:

From vertical angles, [tex]m\angle a=79^{\circ}[/tex]

From corresponding angles, [tex]m\angle b=m\angle a[/tex]

Therefore, we have [tex]m\angle b=m\angle a=\boxed{79^{\circ}}[/tex]

5 )

x^2 = 5^2 + 5^2

x^2 = 2 × 5^2

x = √( 2 × 5^2 )

x = 5√2 cm

_____________

6 )

x^2 = 30^2 + 40^2

x^2 = 900 + 1600

x^2 = 2500

x = √2500

x = 50 yards

Answer:

Spirometer measurement is the most appropriate instrument to use

Step-by-step explanation:

Answer:

1.anlyatical engine

2.difference engine

Answer:

Inventions of Charles Babbage :

Answer:

1,317,840

17×17=289×16=4,624×19=87,856×15=1,317,840

The answer is not listed in the options. The credit score points are 170.

To determine the answer, we need to find the interest rate and monthly payment associated with Stanley's credit score of 544.

Since Stanley's credit score is not listed in the table, we need to estimate the interest rate and monthly payment based on the information provided. Generally, the lower the credit score, the higher the interest rate and monthly payment.

Let's assume that Stanley's interest rate would be 10% and his monthly payment would be $1,000 based on his credit score of 544.

Using the table, we can see that for a $150,000 mortgage with a 10% interest rate, the monthly payment would be $1,316.

Now, we need to determine how much Stanley can afford to pay per year in mortgage payments, which is $12,000. We can divide $12,000 by the monthly payment of $1,316 to get the number of payments he can make in a year: $12,000 ÷ $1,316 = 9.12 payments.

Since there are 12 months in a year, Stanley can only make 9 payments per year. Therefore, he can only afford a mortgage with 9 payments of $1,316, which is $11,844 per year.

To afford a $150,000 mortgage, Stanley would need to lower his interest rate or increase his monthly payment. Since he cannot afford a higher monthly payment, he would need to improve his credit score to lower his interest rate.

Looking at the table, we can see that the interest rate associated with a credit score of 675-699 is 6.25%, which would result in a monthly payment of $924. To afford a $150,000 mortgage with a monthly payment of $924, Stanley would need to improve his credit score by 544 - 675 + 1 = 170 points.

Therefore, the answer is not listed in the options.

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Answer:

D

Step-by-step explanation:

Ratio of oranges to tangerines : 5/3

Oranges in box : 20

Tangerines in box : x

Oranges/Tangerine ratio = Oranges/Tangerine in box

5/3 = 20/X

Answer:

Angles of depression and elevation

The term angle of elevation denotes the angle from the horizontal upward to an object. The term angle of depression denotes the angle from the horizontal downward to an object. ... An observer's line of sight would be below the horizontal.

Step-by-step explanation:

I hope it's help u

Answer:

So the dimensions are 11 1/2 yds × 15 3/4 { 11 whole number 1 by 2 yards multiplied by 15 whole number 3 by 4}

Step-by-step explanation:

Here multiplicative property will be used .

a*1/a= 1

1* a/1= a   ( reciprocal)

23/147 yd × 3/14 will be multiplied with the reciprocal of the factor 2/147 to

get the original number.

23/147 yd*147/2 × 3/14*147/2

23/2 yds  × 441/28

11 1/2 yds × 15 3/4

So the dimensions are 11 1/2 yds × 15 3/4  11 whole number 1 by 2  multiplied by 15 whole number 3 by 4.