evaluate the following trigonometric expression

20 meters equal to 65.6168 feet by unit conversion.

What is unit conversion?

Using the given information about unit conversion, that,

1 foot = 0.305 meters

1 meter= (1/0.305) feet

20 meters = (1/0.305)*20 = 65.6168 feet

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Dividing both into this (15 x 32) below.

15=10+5

32=30+2 and both of the equations will give you the result of 4 partial products.

10x30=300

5x30=150

10x2=20

 5x2=10

Answer:

E.200.5ft²

Step-by-step explanation:

To find the area of the composite figure we simply split it into two regular shapes, a half circle and a square, we then find the area of the two shapes individually and add them together.

Area of square = s² where s = side length

It appears the given side length is 12 so s = 12

Which means area = 12² = 144ft²

For semi circle

Area = 1/2(πr² ), where r is the radius

The side length of the square is shared with the diameter of the semi circle meaning that the diameter of the semi circle is 12

To convert to radius from diameter we simply divide by 2 so r = 12/2 = 6

We have area = 1/2(πr² ) and r = 6

So area = 1/2(π6²)

==> evaluate exponent

Area = 1/2(36π)

==> take one half of 36

Area = 18π

==> multiply 18 and π

Area = about 56.5

Finally we add the two areas together

Total area = 56.5 + 144 = 200.5ft²

Each coordinate was multiplied by 2 instead of divided by 2

the correct coordinates are

preimage                                image

A (2, 5)   → (2 * 1/2, 5 * 1/2) →   A' (1, 2.5)

B (2, 0)  → (2 * 1/2, 0 * 1/2) →    B' (1, 0)  

C (4, 0)  → (4 * 1/2, 0 * 1/2) →    C' (2, 0)

Dilation is a method of transformation that magnify or shrink the preimage depending on the scale factor

The transformation rule for dilation is as follows

(x, y) for a scale factor of r → (rx, ry)

following similar procedure for the given problem we solve with scale factor of 1/2

preimage                                 image

A (2, 5)   → (2 * 1/2, 5 * 1/2) →   A' (1, 2.5)

B (2, 0)  → (2 * 1/2, 0 * 1/2) →    B' (1, 0)  

C (4, 0)  → (4 * 1/2, 0 * 1/2) →    C' (2, 0)

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(2x+1)(x-3)

y(x-3) .... let y = 2x+1

y*x+y(-3) .... distribute

xy - 3y

x( y ) - 3( y )

x( 2x+1 ) - 3( 2x+1) ... replace y with 2x+1

2x^2 + x - 6x - 3 ..... distribute

2x^2 - 5x - 3

Answer is choice A

Answer:

No.

Step-by-step explanation:

Explanation below.

Answer:

$185.19

Step-by-step explanation:

The square of  x² + 16x + 63 = 0 is given by (x + 8)² = 127.

Given that,
x² + 16x + 63 = 0
To complete the square of above given equation.

Power is the degree of values that are mentioned at the superscript of the value.

Here,
x² + 16x + 63 = 0
Dividing the coefficient of x by 2, and adding and subtracting the square of the quotient.
x² + 16x + 64 - 64 - 63 = 0
(x + 8)² = 127

Thus, the square of  x² + 16x + 63 = 0 is given by (x + 8)² = 127.

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Yes , the arithmetic sequence ( written as sequences of the form (a , a+k , a+2k , a+3k for some constants a and k ) is a subspace of V .

To determine whether subsets of V in the arithmetic sequences are subspaces of V, we check if they satisfy the three conditions for a subset to be a subspace:

(i) The subset must contain the zero vector.

(ii) The subset must be closed under vector addition.

(iii) The subset must be closed under scalar multiplication.

Let S be a subset of V consisting of arithmetic sequences.

Now we check the three conditions :

(i) We find an arithmetic sequence in S that has all its terms equal to zero. The only arithmetic sequence that satisfies this is the sequence (0, 0, 0, 0, ...), which is in S.

So , the subset "S" contains zero vector.

(ii) Next we need to show that if u and v are two arithmetic sequences in S, then their sum "u + v" is also an arithmetic sequence in S.

Let U = (a, a+k, a+2k, a+3k, ...) and V = (b, b+l, b+2l, b+3l, ...) be two arithmetic sequences in S.

Then, their sum is ⇒ u+v = (a+b, a+k+b+l, a+2k+b+2l, a+3k+b+3l, ...).

This is also an arithmetic sequence,

So , subset "S" is closed under vector addition.

(iii) Next , we show that if U is an arithmetic sequence in S and C is a scalar, then CU is also an arithmetic sequence in S.

Let U = (a, a+k, a+2k, a+3k, ...) be an arithmetic sequence in S, and let c be a scalar.

we get , CU = (ca, ca+ck, ca+2ck, ca+3ck, ...) is also an arithmetic sequence,

So , subset "S" is closed under scalar multiplication.

we see that , S satisfies all three conditions, it is a subspace of V.

Therefore, any subset of V consisting of arithmetic sequences is a subspace of V.

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The given question is incomplete , the complete question is

Let V be the space of all infinite sequences of real numbers , Which of the subsets of V in The arithmetic sequences [i.e. sequences of the form (a , a+k , a+2k , a+3k for some constants a and k] are subspaces of V ?

Answer:

b i think brainlest me plz

Step-by-step explanation:

The exact values of the remaining trigonometric functions of θ are:

sin(θ) = √(1/64)

cos(θ) = -8

tan(θ) = -8√(1/64)

csc(θ) = 1

cot(θ) = -√(1/64) / 8

Given that sec(θ) = -8 and sin(θ) > 0, we can find the exact values of the remaining trigonometric functions using the Pythagorean identity:

sec^2(θ) = 1/sin^2(θ)

Substituting the value of sec(θ), we have:

(-8)^2 = 1/sin^2(θ)

64 = 1/sin^2(θ)

sin^2(θ) = 1/64

sin(θ) = ±√(1/64)

Since sin(θ) > 0, we take the positive square root:

sin(θ) = √(1/64)

Next, we use the reciprocal identity for cosecant:

csc(θ) = 1/sin(θ)

Substituting the value of sin(θ), we have:

csc(θ) = 1/√(1/64) = 8√(1/64) = 8/√(64) = 8/8 = 1

Next, we use the reciprocal identity for cotangent:

cot(θ) = 1/tan(θ)

We can find the value of tan(θ) using the definition:

tan(θ) = sin(θ) / cos(θ)

Substituting the values of sin(θ) and cos(θ), we have:

tan(θ) = √(1/64) / (-8) = -√(1/64) / 8

Finally, we use the reciprocal identity for a tangent:

tan(θ) = 1/cot(θ)

Substituting the value of cot(θ), we have:

tan(θ) = -8√(1/64)

Therefore, the exact values of the remaining trigonometric functions of θ are:

sin(θ) = √(1/64)

cos(θ) = -8

tan(θ) = -8√(1/64)

csc(θ) = 1

cot(θ) = -√(1/64) / 8

The complete question is:-

Find the exact value of each of the remaining trigonometric functions of

θ. Rationalize denominators when applicable.

secθ=−8, given that sinθ>0

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a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:

\(x' = Ax\)

where x is a vector and A is a square matrix.

b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.

If all eigenvalues have negative real parts, the system is stable.

If at least one eigenvalue has a zero real part, the system is neutrally stable.

If at least one eigenvalue has a positive real part, the system is unstable.

c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation

\(det(A - \lambda I) = 0\),

where λ is the eigenvalue and I is the identity matrix.

By solving this equation, we obtain the eigenvalues.

Substituting each eigenvalue into the equation

\((A - \lambda I)v = 0\),

where v is the eigenvector, we can solve for the eigenvectors.

d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:

\(A = PDP^{(-1)}\)

where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.

To show that this relationship is valid, we can compute \(PDP^{(-1)}\) and verify that it equals A.

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Answer:

210

Step-by-step explanation:

you have to multiple 15 by 14

Answer:

DO NOT MULTIPLY 15x14! THAT IS WRONG

Step-by-step explanation:

To find the area of a triangle the formula is 1/2 x b x h
If 15 and 14 is the base and height just do half of 15 x 14
so 15 x 14= 210/ divided by 2= 105  


Formula for area of a circle= 1/2*b*h

Answer:

10b/y^2

Step-by-step explanation:

Hope this helps! :)

The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

Answer:

What must be true

Step-by-step explanation:

Answer:

1.875 %

Step-by-step explanation:

Divide the sample size by the population then multiply by 100:

percent = (75 ÷ 4000) x 100 = 1.875 %

Answer:     = (the third option)

Step-by-step explanation

Answer:

the answer is this sign <!

Step-by-step explanation:

Answer:

  (a)  twenty-eight ninths, square root of nineteen, cube root of eighty-eight

Step-by-step explanation:

When ordering a list of numbers by hand, it is convenient to convert them to the same form. Decimal equivalents are easily found using a calculator.

The attachment shows the ordering, least to greatest, to be ...

  \(\dfrac{28}{9}.\ \sqrt{19},\ \sqrt[3]{88}\)

__

Additional comment

We know that √19 > √16 = 4, and ∛88 > ∛64 = 4, so the fraction 28/9 will be the smallest. That leaves us to compare √19 and ∛88, both of which are near the same value between 4 and 5.

One way to do the comparison is to convert these to values that need to have the same root:

  √19 = 19^(1/2) = 19^(3/6) = sixthroot(19³)

  ∛88 = 88^(1/3) = 88^(2/6) = sixthroot(88²)

The roots will have the same ordering as 19³ and 88².

Of course, these values can be found easily using a calculator, as can the original roots. By hand, we might compute them as ...

  19³ = (20 -1)³ = 20³ -3(20²) +3(20) -1 = 8000 -1200 +60 -1 = 6859

  88² = (90 -2)² = 90² -2(2)(90) +2² = 8100 -360 +4 = 7744

Then the ordering is ...

  28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Answer:

the ordering is

28/9 < 19³ < 88²   ⇒   28/9 < √19 < ∛88

Step-by-step explanation:

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

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Answer:

87.5%

Step-by-step explanation:

The area of the entire rectangle is 8 by 6,

8x6=48 so the area is 48 units^2.

The area of the triangle is A=1/2bh

A=1/2(2)(6)

A=1(6)

A=6 units^2

6/48=0.125

0.125=12.5%

You need to find the percent it will not land in the triangle, so subtract 12.5 from 100.

100-12.5=87.5

There is an 87.5% chance it will not land in the triangle

The amount of cups of lemonade sold by Abbie is 6 x 8 = a.

Hence, option A is correct.

Use the concept of multiplication defined as:

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that,

Number of lemonade cups sold by Lust = 8

Number of lemonade cups sold by Abbie =  6 times of lust

Let 'a' represents the number of cups sold by Abbie,

Therefore,

6 x 8 = a

Hence,

The correct expression is 6 x 8 = a which is option A.

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The complete question is:

Luct sold 8 cups of lemonade Abbie sold 6 times as many cups of lemonade. Which equation helps us find how many cups Abbie sold if the number of cups sold by Abbie is 'a'.

A. 6x8 = a

B. 8xa = 6

C. 6xa = 8

Answer:

square root of 64 is 8

Step-by-step explanation:

8^2=64

Answer:

lol  bro i hope these help u out

Step-by-step explanation:

good job me

A. P(6, then 1) = 1/90

B. P(even, then 5) = 1/18

C. P(8, then odd) = 1/18

D. P(3, then prime) = 2/45

E. P(prime, composite) = 4/15

F. P(even, then 3, then 5) = 1/144

Given:

Total number of cards: 10

A. P(6, then 1):

P(6, then 1) = 1/10 x 1/9

= 1/90

B. P(even, then 5):

Number of favorable outcomes: 5 x 1 = 5

P(even, then 5) = 5/10 x 1/9

= 1/18

C. P(8, then odd):

Number of favorable outcomes: 1 x 5 = 5

P(8, then odd) = 1/10 x 5/9

= 1/18

D. P(3, then prime):

Number of favorable outcomes: 1 x 4 = 4

P(3, then prime) = 1/10 x 4/9

= 2/45

E. P(prime, composite):

Number of favorable outcomes: 4 x 6 = 24

P(prime, composite) = 4/10 x 6/9

= 4/15

F. P(even, then 3, then 5):

Number of favorable outcomes: 5 x 1 x 1 = 5

P(even, then 3, then 5) = 5/10 x 1/9 x 1/8

= 1/144

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Answer:

1 cm and 18 cm

2 cm and 9 cm

3 cm and 6 cm

Step-by-step explanation:

We need to find the factors of 18
which are; 1,18; 2,9; 3,6
So therefore we'd pick:
1 cm and 18 cm

2 cm and 9 cm

3 cm and 6 cm

We are required to find the unit rate, that is, miles per hour

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A) The maximum of the periodic function is 1.

B) The minimum of the periodic function is - 3.

C) The equation of the midline of this periodic function is (1 - 3)/2 = - 1.

D) The amplitude of the periodic function is (1 + 3)/2 = 2.

E) the period of the periodic function is 2π/3.

F) We know frequency = 2π/period = 2π/2π/3 = 2π×(3/2π) = 3.

G) The amplitude of the periodic function is 2sin3((πx - π/6)) - 1.

A period is the amount of time between two waves, whereas a periodic function is one whose values recur at regular intervals or periods.

A function f will be periodic with period x, so if we have

f (a + x) = f (a), For every a > 0.

A) The periodic function's maximum value is 1.

B) The periodic function's minimum value is -3.

C) This periodic function's midline's equation is (1 - 3)/2 = - 1.

D) The periodic function's amplitude is (1 + 3)/2 = 2.

E) The periodic function's period is 2π/3.

F) We already know that frequency = 2π/period

= 2π/2π/3 = 2π×(3/2π) = 3.

G) The periodic function is  2sin3((πx - π/6)) - 1.

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