The flight path of a plane is a straight line from city J J to city K K. The roads from city J J to city K K take the long way around, traveling 9.4 9.4 miles south and then 15.1 15.1 miles east. How many degrees east of south is the plane's flight path, to the nearest tenth? M ∠ J ≈ ? M∠J≈

Answer:

The equation is not true.

Step-by-step explanation:

Starting with the left side,

sin²(θ) - cos²(θ) = 1 - cos²(θ) - cos²(θ) = 1 - 2cos²(θ)

The right side,

2 sin²(θ) - 1 = 2(sin²(θ) - 0.5)

Thus, in general, sin²(θ) - cos²(θ) ≠ 2 sin²(θ) -1.

Answer:

x = −2

Step-by-step explanation:

4x + 1 = x − 5

Subtract 1 from both sides

4x + 1 − 1 = x − 5 − 1

Simplify

4x = x − 6

Subtract x from both sides

4x −x = x − 6 − x

Simplify

3x = −6

Divide both sides by 3

\({\frac{3x}{3}\)=\(\frac{-6}{3}\)

Simplify

x = −2

The monthly mortgage payment for a $100,000 loan with a 5% annual interest rate and a 30-year fully amortizing term is approximately $536.82.

To calculate the monthly mortgage payment, we can use the formula for calculating the fixed monthly payment for a fully amortizing loan. The formula is: M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly mortgage payment

P = Principal balance

r = Monthly interest rate (annual interest rate divided by 12 and converted to a decimal)

n = Total number of monthly payments (loan term multiplied by 12)

Plugging in the given values into the formula:

P = $100,000

r = 0.05/12 (5% annual interest rate divided by 12 months)

n = 30 years * 12 (loan term converted to months)

M = 100,000 * (0.004166667 * (1 + 0.004166667)^(3012)) / ((1 + 0.004166667)^(3012) - 1)

M ≈ $536.82

Therefore, the monthly mortgage payment for a $100,000 loan with a 5% annual interest rate and a 30-year fully amortizing term is approximately $536.82.

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Answer:

  98

Step-by-step explanation:

As a function of the number of days (d), Evan makes ...

  evan = 10 +8(d -1) = 8d +2

Similarly, the number Dorinda makes is ...

  dorinda = 8d

The total they make in d days is ...

  evan +dorinda = (8d +2) +(8d) = 16d +2

In 6 days, they make 16·6 +2 = 96 +2 = 98 . . . bracelets

They will make 98 bracelets in 6 days.

_____

Evan makes 50; Dorinda makes 48.

The approximate length of ab is 12.2 feet

A right triangle's hypotenuse (the side that faces the right angle) has a square length that, according to the Pythagorean theorem, is equal to the sum of the squares of the other two sides' lengths.

It can be written as c2 = a2 + b2 where c is the hypotenuse's length and a and b are the other two sides' lengths. Pythagoras, a Greek mathematician, is credited with discovering the theorem, which bears his name.

The Pythagorean theorem, which asserts that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side, can be used to estimate the length of AB (the hypotenuse).

The distances along the room's 11-foot and 13-foot sides serve as the two shorter sides in this situation, while AB serves as the hypotenuse. AB is around the following length:

√(11^2 + 13^2 + 10^2) = √(146) = 12.2 feet

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V = 8, because it can’t be simplified any further.

Answer: (j-1)(7j-3)

Step-by-step explanation:

Answer:

Final result :

(j - 1) • (7j - 3)

Step-by-step explanation:

Step by Step Solution

STEP1:

Equation at the end of step 1

(7j2 - 10j) + 3

STEP2:

Trying to factor by splitting the middle term

2.1 Factoring 7j2-10j+3

The first term is, 7j2 its coefficient is 7 .

The middle term is, -10j its coefficient is -10 .

The last term, "the constant", is +3

Step-1 : Multiply the coefficient of the first term by the constant 7 • 3 = 21

Step-2 : Find two factors of 21 whose sum equals the coefficient of the middle term, which is -10 .

-21 + -1 = -22

-7 + -3 = -10 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -7 and -3

7j2 - 7j - 3j - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

7j • (j-1)

Add up the last 2 terms, pulling out common factors :

3 • (j-1)

Step-5 : Add up the four terms of step 4 :

(7j-3) • (j-1)

Which is the desired factorization

Final result :

(j - 1) • (7j - 3)

On solving the linear equations - 9x - 3y = -21 and 9x + 9y = -9 the value of x is x = 4 and y is y = -5.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The linear equations are -

- 9x - 3y = -21 .... (1)

9x + 9y = -9 .... (2)

Add the equations (1) and (2) -

- 9x - 3y + 9x + 9y = -21 - 9

6y = -30

y = -5

Substitute the value of y in equation (1) -

- 9x - 3(-5) = -21

- 9x + 15 = -21

- 9x = -36

-x = -4

x = 4

Therefore, the values of x and y is 4 and -5.

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Answer:

40 apps in a minute!

The decision rule for rejecting the null hypothesis is:

If the calculated t-value is greater than 1.708, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

To determine the decision rule for rejecting the null hypothesis, we need to perform a hypothesis test based on the given information. Let's set up the null and alternative hypotheses:

Null Hypothesis (H0): The mean pressure of the valve is 5.8 pounds/square inch.

Alternative Hypothesis (H1): The mean pressure of the valve is greater than 5.8 pounds/square inch (the valve performs above specifications).

We'll conduct a one-sample t-test since we have the sample mean, sample standard deviation, and sample size.

Given:

Sample mean (\(x^-\)) = 6.1 pounds/square inch

Sample standard deviation (s) = 0.9

Sample size (n) = 26

Level of significance (α) = 0.05 (corresponds to a 5% significance level)

To determine the decision rule, we need to find the critical t-value or the critical region for rejection. Since the alternative hypothesis is one-tailed (the mean pressure is expected to be greater than 5.8), we'll find the critical t-value for the upper tail.

Using the t-distribution table or a t-distribution calculator with (n-1) degrees of freedom (df = 26 - 1 = 25) and the significance level α = 0.05, we find the critical t-value.

The critical t-value at a 5% significance level for the upper tail is approximately 1.708.

Therefore, the decision rule for rejecting the null hypothesis is:

If the calculated t-value is greater than 1.708, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

In summary, the decision rule for rejecting the null hypothesis is: Reject H0 if the calculated t-value is greater than 1.708.

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Answer:

20 more girls

Step-by-step explanation:

so if 2/5 of the pupils are boys that means 3/5 of the pupils are girls

and 3/5 = 30

to find out how many boys there are we need to find 1/5

1/5 = 10

so theres 10 boys and 30 girls

30-10 = 20

The dimension of the null space of B is 7. The dimension of the row space of B is 5. the dimension of the column space of B is 5.

(a) The dimension of the null space of B

The dimension of the null space of matrix B is given by

nullity (B) = number of columns of B – rank of B= 12 – 5= 7

Therefore, the dimension of the null space of B is 7.

(b) The dimension of the row space of B

The row space of matrix B is the span of the set of rows of matrix B. Since the rank of matrix B is 5, then we know that there are 5 rows of matrix B that are linearly independent and span the row space of matrix B. So, the dimension of the row space of B is 5.

(c) The dimension of the column space of B

The dimension of the column space of matrix B is given by rank (B). Therefore, the dimension of the column space of B is 5.

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Answer:

  59.7 mL

Step-by-step explanation:

You want to know the amount of acid if 341 milliliters of a solution of acid and water is 17.5% acid.

The relation between base, percentage, and amount is ...

  amount = percentage × base

In this relation, the percentage can be used directly on many calculators and spreadsheets. On others, it needs to be converted to a number or fraction before the multiplication can be done.

It can be useful to think of the % symbol as equivalent to "/100". Then we have ...

  amount = 17.5/100 × 341 mL = 59.675 mL

There are about 59.7 mL of acid in the solution.

The value of the equation x² - x + 3 is 37/9.

We have,

We can start by multiplying both sides of the equation by x:

2x - 3/x = x + 1

2x - 3 = x^2 + x

Rearranging and simplifying, we get:

x^2 - x + 3 = (2x - 3) + x^2

x^2 - x + 3 = x^2 + 2x - 3

-x + 3 = 2x - 3

5 = 3x

x = 5/3

Now we can substitute x into the equation x^2 - x + 3:

x^2 - x + 3 = (5/3)^2 - 5/3 + 3

x^2 - x + 3 = 25/9 - 15/9 + 27/9

x^2 - x + 3 = 37/9

Therefore,

The value of x² - x + 3 is 37/9.

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The percent of the regular price is 81.5%.

From the information, the shirt that normally costs $40 is on sale for 32.60.

The percent of the regular price that the sale price is will be gotten thus:

= Sale price / Regular price × 100

= 32.60 / 40 × 100

= 81.5%

The percentage is 81.5%.

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Answer:

11=h

11 hours of work

Step-by-step explanation:

350=30h+20

subtract 20 from each side

330=30h

divide by 30 to each side

11=h

Hello! :)

x+12=20

Move all numbers to the right, using the opposite operation:

x=20-12

x=8

Therefore, x=8

Hope it helps. Enjoy your day! :)

Do ask me if you have any question.

~An excited gal

\(MagicalNature\) here to help

To solve this question, we need to find the formula for the nth term of the geometric sequence. The formula is:

Where:

a_n is the nth term of the sequence

a_1 is the first term of the sequence

r is the common ratio

In this case:

a_1 8

r = 2/3

The answer is:

256/243

Answer:

14

Step-by-step explanation:

 ✩brainliest appreciated✩

Answer: 14 is the common factor

Step-by-step explanation:

Answer:

6 seconds

Step-by-step explanation:

The computation of the number of second would be

In the case when the ball would hit the ground, the ball height would be zero

So the following equation would be

\(0 = -(x -2)^2 + 16\\\\(x -2)^2 = 16\\\\x - 2 = \sqrt{16}\\\\x -2 = 4\\\\x = 6\)

So the number of seconds is 6

The ordered pair that is the solution of the given system of inequalities is (2, -2)

A relationship between two expressions or values that are not equal to each other is called inequality.

Given is a system of inequalities, y < -x and 2x+y > 2, we need to determine solution set of the given system of inequalities,

The inequalities are,

y < -x....(i)

2x+y > 2

y < 2-2x...(ii)

To find the ordered pair, put y = -x in equation Eq(ii) and replace < by =

-x = 2 - 2x

x = 2

y = -2

Therefore, the ordered pair, is (2, -2) {look at the graph attached}

Hence, the ordered pair that is the solution of the given system of inequalities is (2, -2)

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a) The unit vector from P towards Q is u⃗ = (8/17, 15/17).

b)  A vector of length 51 pointing in the same direction as u⃗ is v⃗ = (24, 45).

a) To find the unit vector from point P=(1,2) towards Q=(9,17), we need to first find the displacement vector from P to Q, which is given by:

Q - P = (9-1, 17-2) = (8, 15)

Next, we normalize this vector by dividing it by its magnitude:

||Q - P|| = sqrt(8^2 + 15^2) = 17

u⃗ = (Q - P)/||Q - P|| = (8/17, 15/17)

Therefore, the unit vector from P towards Q is u⃗ = (8/17, 15/17).

b) To find a vector of length 51 pointing in the same direction as u⃗, we simply multiply u⃗ by 51:

v⃗ = 51u⃗ = (8/17 * 51, 15/17 * 51) = (24, 45)

Therefore, a vector of length 51 pointing in the same direction as u⃗ is v⃗ = (24, 45).

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Answer:

the answer is b because I know I just did that

Answer:

y= -24

Step-by-step explanation:

since the slope is 7 the value of y should decrease as the value of x decreases. and since you went back 3 on the x, you should go down 21 on the y resulting in -3-21 which is -24

We have to calculate how many T-shirts the hay to sell in order to raise $720, including the $60 dollars they already saved.

They earn $12 for every T-shirt, so the amount of money raised is 12x, being x the number of T-shirts.

Then, 12x has to be at least equal to 720-60=660:

Then, if we divide both sides by 12, we get the number of T-shirts they have to sell:

They have to sell at least 55 T-shirts.

Answer:

1. Congruent(SAS)

2. Congruent(AAS)

3. Congruent(HL)

4. Not congruent

5. Congruent(SSS)

6. Congruent(AAS)

Answer:

y = -5x - 4

Step-by-step explanation:

-20x - 4y = 16

-4y = 20x + 16

4y = -20x - 16

y = -5x - 4

Answer:

124

Step-by-step explanation: