Stella's friends got her a skydiving lesson forher birthday. Her helicopter took off from theskydiving center, ascending in an angle of37°, and traveled a distance of 2.1kilometers before she fell in a straight lineperpendicular to the ground.How far from the skydiving center did Stellaland?

Answer:

b=–2

Step-by-step explanation:

we've got:

(3+bx)⁵===> b⁵x⁵+15b⁴x⁴+90b³x³+720b²x²+405bx+243

and we've also got the coefficient of x³ as –720

90b³=–720===> b³=–8===> b=–2

Starting with the given equation: 2 sin x cos x = cos x

By dividing both sides by cos x, we may simplify: 2 sin x = 1

Dividing both sides by 2:

sin x = 1/2

The values of x that fulfil sin x = 1/2 must now be found, and they are:

x = π/6 + 2πn or x = 5π/6 + 2πn, where n is any integer.

Therefore, the general solution is:

x = π/6 + 2πn or

x = 5π/6 + 2πn, where n is any integer.

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The area of the border is 105.53 feet².

We have,

The swimming pool is a combination of two shapes.

Rectangle:

Length = 60 feet

Width = 30 feet

Area = 60 x 30 = 1800 feet²

Semicircle:

Diameter = 30 feet

Radius = 15 feet

Area = π/2 r² = 1/2 x 3.14 x 15 x 15 = 353.25 feet².

Now,

The area of the swimming pool.

= 1800 + 353.25

= 2153.25 feet²

Now,

Without the border.

Area of the swimming pool.

= rectangle area + semicircle area

= 60 x (30 - 1) + 1/2 x π x (15 - 1)²
= 60 x 29 + 1/2 x 3.14 x 14 x 14

= 1740 + 307.72

= 2047.72 feet²

Now,

The area of the border.

= 2153.25 - 2047.72

= 105.53 feet²

Thus,

The area of the border is 105.53 feet².

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Answer:

(-2, 4)

Step by step explanation:

-2 is the x coordinate and 4 is the y coordinate

(x, y) = (-2, 4)

There is your answer

The amount of sinking fund payment is $2028.06.

So, the correct answer is option A.

The fee a customer pays to a lender for borrowing cash over time, expressed as a percentage of the loan amount. The interest rate is the amount charged by the lender to the borrower above and beyond the principal amount. In terms of the receiver, a person who deposits money in any bank or financial institution obtains additional income due to the time value of money, which is referred to as depositor interest.

The basic interest formula is as follows: P x R x T = Interest. P denotes the principal sum.

Given, Amount=35000

Time=4 years

Interest rate=4% compounded quarterly

i=4/4%

i=1%

35000=(1+(1/100))ⁿ

35000=(101/100)ⁿ

35000=x(1-(101/100)¹⁶)/((1-(1/100)))

x=2028.0609

Therefore, The amount is $2028.06

So, option A is correct

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Subtract 48-19=29 Correct me if I'm wrong.

That means it's 29 cups.

Answer:

29 cups

Step-by-step explanation:

step 1: since the liquid in the photo is shown to go up to between 18 and 20, it has to be 19 cups.

step 2: so she had 48 cups, right? and she used 19. so we have to subtract 19 from 48.

step 3: 48-19 = 29. she has 29 cups left..

i hope this helps!

Answer:

x=9b

Step-by-step explanation:

The value of x for the expression will be equal to 9 / b.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is bx − 4=5, the value of x will be calculated as,

bx − 4=5

bx = 5 + 4

bx = 9

x = 9 / b

Therefore, the value of x for the expression will be equal to 9 / b.

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Answer:

Given:

Area of the sector (A) = 104π/9 square inches

Central angle (θ) = 65 degrees

The formula for the area of a sector of a circle is:

A = (θ/360) * π * r^2

We can rearrange this formula to solve for the radius (r):

r^2 = (A * 360) / (θ * π)

Plugging in the given values:

r^2 = (104π/9 * 360) / (65 * π)

r^2 = (104 * 40) / 9

r^2 = 4160 / 9

r^2 ≈ 462.22

Taking the square root of both sides:

r ≈ √462.22

r ≈ 21.49

Therefore, the radius of the circle is approximately 21.49 inches.

Answer: 8 inches

Step-by-step explanation:

Answer: yes true or false

Step-by-step explanation: 7 true, 8 true, and 9 false

Answer:

i7x+×52=/67, hope this helps!!!!

Answer:

-1.25

Step-by-step explanation:

\(\boxed{slope = \frac{y1 - y2}{x1 - x2} }\)

☆ (x₁, y₁) is the 1st coordinate and (x₂, y₂) is the 2nd coordinate

Slope of line

\( = \frac{6 - ( - 4)}{1 - 9} \\ = \frac{6 + 4}{ - 8} \\ = - \frac{10}{8} \\ = - \frac{5}{4} \\ = - 1.25\)

The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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The area of the new rug in factored form is 2(9x + 19x) square units

Given:

Area of blue rug = 8(x + 1)

Area of red rug = 10 (x+3)

Total area = blue + red

= 8(x + 1) + 10 (x+3)

= 8x + 8 + 10x + 30

= 8x + 10x + 8 + 30

= 18x + 38

= 2(9x + 19x)

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Answer:

(4, 11 ) ; (- 4, 27 )

Step-by-step explanation:

Given

f(x) = x² - 2x + 3 → (1)

f(x) = - 2x + 19 → (2)

Substitute f(x) = x² - 2x + 3 into (2)

x² - 2x + 3 = - 2x + 19 ( add 2x to both sides )

x² + 3 = 19 ( subtract 3 from both sides )

x² = 16 ( take square root of both sides )

x = ± \(\sqrt{16}\) = ± 4

Substitute these values into (2) for corresponding values of y

x = 4 : y = - 2(4) + 19 = - 8 + 19 = 11 ⇒ (4, 11 )

x = - 4 : y = - 2(- 4) + 19 = 8 + 19 = 27 ⇒ (- 4, 27 )

To find out how many flowers will be in each centerpiece, we can divide the total number of flowers by the number of centerpieces:

Total number of flowers: 1,064

Number of centerpieces: 28

Number of flowers in each centerpiece = Total number of flowers / Number of centerpieces

Number of flowers in each centerpiece = 1,064 / 28 = 38

Therefore, there will be 38 flowers in each centerpiece.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer: 38

Step-by-step explanation:

The question is asking you to divided.

1064 divided by 28 = 38

So there will be 38 flowers in each centerpiece

(x + 12)° + (5x)° = 90°

m∠1 = 25° and m∠2 = 65°

We know that the little box represents 90 degrees. We will write an equation using this information.

      (x + 12)° + (5x)° = 90°

Next, we will solve by isolating the x variable with inverse operations and combing like terms.

      (x + 12)° + (5x)° = 90°

      x° + 5x° = 78°

      6x° = 78°

      x = 13°

Lastly, we will find the value of each angle by substituting.

       m∠1 = (x + 12)° = ((13) + 12)° = 25°

       m∠2 = (5x)° = (5(13))° = 65°

The transformation in this problem is a translation combined with a reflection, hence yes, it is a rigid motion, as the side lengths of the transformed figure are equal to the side lengths of the original figure.

Examples of transformations are given as follows:

The dilation is the only transformation that is not a rigid motion, as it changes the side lengths of the figure.

The transformation for this problem has the rule defined as follows:

(x,y) -> (x + 2, -y).

The transformations are defined as follows:

Neither transformation is a dilation, hence it is a rigid motion.

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We know that

• The penny is located at the bottom, 8 feet deep.

The water level is zero, which means the initial position of the penny is represents by the integer -8.

However, after Andy brings it up to the surface, the penny is at 0 water level.

Answer:

The length of the third side is approximately ≈ 14.79 inches

Step-by-step explanation:

A piece of wire is bent into the shape of a triangle. Two sides have lengths of 16 inches and 23 inches. The angle between these two sides is 40°. What is the length of the third side to the nearest hundredth of an inch?

Use the law of cosines to find the length of the missing side.

Let C be the third side.

A = 18

B = 23

Angle C = 40^∘

c^2  =  a^2  +  b^2 - 2ab  cos C

c =  √a^2 + b^2 - 2ab cos C

c =  √18^2 + 23 ^2 - 2 (18) (23) cos 40^∘

c = √583 - 828 cos40^∘

≈ 14.79

Thus, The length of the third side is approximately  14.79 inches.

Hope this helps!

Answer:

2b + 3 = 15

b = 6

Step-by-step explanation:

The equation y - 5 = (4/3)(x - 6) can be written in point-intercept form as y = (4/3)x - 3, where the slope is 4/3 and the y-intercept is -3.

The point-slope form of a line is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. The point-slope form of a line can be converted to the slope-intercept form of a line, y = mx + b, where b is the y-intercept.

The equation y - 5 = (4/3)(x - 6) can be rearranged into the point-slope form of a line by isolating the y-term and simplifying: y - 5 = (4/3)(x - 6)y - 5 = (4/3)x - 8y = (4/3)x - 3

Now, we have the point-slope form of the line with slope 4/3 and y-intercept -3.

To convert this to the slope-intercept form of a line, we simply rearrange the equation to solve for y:y = (4/3)x - 3 This is the slope-intercept form of the line, where the slope is 4/3 and the y-intercept is -3.

Thus, the equation y - 5 = (4/3)(x - 6) can be written in point-intercept form as y = (4/3)x - 3, where the slope is 4/3 and the y-intercept is -3.

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The quotient of  10⁻⁴/10² is 10⁻⁶

Quotient is the result obtained by dividing one quantity by another. It represents the value that is obtained after division.

For example, if you divide 20 by 2, the quotient is 10 because 20 divided by 2 equals 10.

Division law states that:

10ᵃ / 10ᵇ = 10ᵃ⁻ᵇ

In this case have:

10⁻⁴/10² = 10⁻⁴⁻²   (Division law)

10⁻⁴/10² = 10⁻⁶

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Answer:

12/12 or 1

Step-by-step explanation:

Tina baked 12 peanut butter cookies, and it is said that 12 of them had chocolate chips. So, we can make a fraction, being 12/12

Depositing money into savings account each month will increase the amount of interest she is earning on her savings account.

What is interest on savings account?

A bank or other financial institution will offer a depositor interest on a savings account as compensation for keeping their money on deposit. In a sense, a bank borrows money from its depositors by using the money placed to make loans to other clients. The bank reciprocally gives the depositor interest on the amount in their savings account.

Savings accounts offer interest based on the balance.

Money deposited into a savings account each month will increase the account's total balance, which will result in a greater interest rate. This is a strategy to increase the interest you are collecting on your savings.

The other options are not viable because opening a checking account with the money from the savings account and making monthly withdrawals from the savings account will result in a decreased balance and interest rate.

Additionally, switching to a savings account with a lower interest rate is not a wise move because, with a lower interest rate, you will get less money overall.

Hence, depositing money into savings account each month will increase the amount of interest she is earning on her savings account.

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Question: Your sister is looking for a way to increase the amount of interest she is earning on her savings account. What should she do?

A. Deposit money into her savings account each month

B. Use the money from her savings account to open a checking account instead

C. Switch to a savings account with a lower interest rate

D. Make monthly withdrawals from her savings account

The bank reconciliation shows an adjusted bank balance of Br.5,301.42 and an adjusted ledger balance of Br.4,173.83.

To prepare the bank reconciliation and journal entry for ABC Company based on the given information, we need to compare the transactions recorded in ABC's ledger with the transactions shown in the bank statement. Here's the bank reconciliation:

1. Bank Statement Balance:

Cash on deposit at July 31: Br.4,964.47

2. Adjusted Bank Balance:

Bank Statement Balance: Br.4,964.47

3. Deposit not on the statement: + Br.410.90

(Adjusted Bank Balance: Br.5,375.37)

Erroneously charged check: + Br.79

(Adjusted Bank Balance: Br.5,454.37)

Outstanding checks:

Check 801: - Br.100.00

Check 888: - Br.10.25

Check 890: - Br.294.50

Check 891: - Br.205.00

(Adjusted Bank Balance: Br.4,844.62)

4. Incorrectly charged check: + Br.90

(Adjusted Bank Balance: Br.4,934.62)

5. Collection of interest-bearing note: + Br.500

(Adjusted Bank Balance: Br.5,434.62)

6. Interest earned: + Br.24.75

(Adjusted Bank Balance: Br.5,459.37)

7. Incorrectly recorded check: - Br.90

(Adjusted Bank Balance: Br.5,369.37)

8. Collection fee: - Br.5.00

(Adjusted Bank Balance: Br.5,364.37)

9. NSF check: - Br.50.25

(Adjusted Bank Balance: Br.5,314.12)

10. Service charge: - Br.12.70

(Adjusted Bank Balance: Br.5,301.42)

Adjusted Ledger Balance:

Bank Balance in ABC's Ledger: Br.4,173.83

Reconciled Bank Balance: Br.5,301.42

Reconciled Ledger Balance: Br.4,173.83

Journal Entry:

To record the bank reconciliation, we make the following journal entry:

Debit: Cash (Ledger Balance adjustment) - Br.5,301.42

Credit: Cash (Bank Statement Balance adjustment) - Br.4,964.47

Credit: Miscellaneous Income/Expense - Br.336.95 (the difference between the two balances)

This journal entry ensures that the ledger balance matches the reconciled bank balance by adjusting for the discrepancies identified during the reconciliation process.

The journal entry reflects the necessary adjustments to reconcile the two balances, with a debit to Cash (Ledger Balance adjustment), a credit to Cash (Bank Statement Balance adjustment), and a credit to Miscellaneous Income/Expense to account for the difference.

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Answer:

5.15%

Step-by-step explanation:

Difference between estimated throw and actual throw

= estimated - actual

= 22.52 - 21.36

= 1.16 m

As a fraction of estimated throw:
1.16/22.52

As a percentage:
1.16/22.52  x 100 =  5.15%

The expression which shows how many grams of raisins are in the bowl will be

(0.01x) * 150 + (0.01y) * 250

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The expression which shows how many grams of raisins are in the bowl will be:

= (x% × 150) + (y% × 250)

= (0.01x) * 150 + (0.01y) * 250

This equation represents the total grams of raisins in the bowl by multiplying the weight of the Oreana's bag by the percentage of raisins in it, and adding that to the product of the weight of Brandon's bag and the percentage of raisins in it. The "0.01" is used to convert the percentages from x and y to decimal form.

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