Find the measure of an angle whose supplement is sixteen times its complement. Hint: Supplement and complement of an angle are (180-0) and (90-0) respectively.

The equation 3tan²x = 3tanx solved for all real values of x is [tex]x = n\pi[/tex] or [tex]x = \dfrac{\pi + 4n\pi}{4}[/tex], where n is an integer

Solving the equation for all real values of x.

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

3tan²x = 3tanx

This can be expressed as

3tan²x - 3tanx = 0

Factor out 3tanx

3tanx(tanx - 1) = 0

Expand

3tanx = 0 or tanx - 1 = 0

So, we have

tanx = 0 or tanx = 1

Take the arctan of both sides

x = tan⁻¹(0) or x = tan⁻¹(1)

Evaluate the arctan for all real values of x.

[tex]x = n\pi[/tex] or [tex]x = \dfrac{\pi + 4n\pi}{4}[/tex], where n is an integer

Answer:

120 different ways

Step-by-step explanation:

For the first lunch, Emilce has 5 options to choose,

In the second lunch, now she has only 4 options, as one was already chosen.

Then, in the third lunch, she has 3 options.

In the fourth lunch, she has 2 options.

In the last lunch, she has just 1 option.

So, the number of different ways she can order her lunches in the week is:

5 * 4 * 3 * 2 * 1 = 120

She can order in 120 different ways.

Answer:

7/22

Step-by-step explanation:

Drama or Sports:

85 + 200 - 60

225

330 - 225 = 105

Probability: 105/330

7/22

The weight of the last fish was 3.1 kg. It's found by subtracting the sum of the weights of the first 7 fish from the sum of all weights.

To find the weight of the last fish, we can use the mean weight formula:

[tex]\[\text{Mean weight} = \frac{\text{Sum of all weights}}{\text{Number of fish}}\][/tex]

Given:

- Jeremy caught 8 fish.

- The mean weight of the fish was 4.3125 kg.

- The sum of the weights of the first 7 fish is [tex]\(4.3 + 5.3 + 6.8 + 2.6 + 3.2 + 4.4 + 4.8\).[/tex]

First, let's calculate the sum of the weights of the first 7 fish:

[tex]\[4.3 + 5.3 + 6.8 + 2.6 + 3.2 + 4.4 + 4.8 = 31.4\text{ kg}\][/tex]

Now, let's find the sum of all weights of the 8 fish:

[tex]\[4.3125 \times 8 = 34.5\text{ kg}\][/tex]

To find the weight of the last fish, we subtract the sum of the weights of the first 7 fish from the sum of all weights:

[tex]\[34.5 - 31.4 = 3.1\text{ kg}\][/tex]

So, the weight of the last fish was 3.1 kg.

Answer:

a. 26° C

b. 40m

c. Yes

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  Please have a look at the attached photo.

a. What was the approximate temperature at a depth  of 70 m? At the surface?  

26° C

b. At what depth was the temperature  a little more than 27°C?

40 m

c. Do the points in the scatter plot show a relationship?  Explain your thinking.

Yes, the scatter plot show a relationship between the depth and the temperature of Lake Turkana. It shows a negative correlation between the two variables. The deeper the lake is, the cooler the temperature .

Hope it will find you well.

Answer:

Increases

Step by Step Explanation:

More time on your homework means more time to cheat/figure the answer out.

Answer:

Improved

Step-by-step explanation:

The more you study or do homework, the more you learn, and the better your grade

Answer:

2.57

Step-by-step explanation:

1/4×22/7×3×3=7.07

1/2×9=4.5

7.07-4.5=2.57

Answer:

The mean temperature is 31.

Step-by-step explanation:

The formula for the z-sore is

          x - mean

z = ----------------------

        (std dev)

In this case let's multiply both sides by (std dev), obtaining:

x - mean = z*(std dev).

Solving for (mean), we get

mean = x - z*(std dev)

Substituing 37 for x, 2.4 for z and 2.5 for (std dev), we get:

mean = 37 - (2.4)(2.5) = 31

The mean temperature is 31.

Final answer:

To find the mean temperature with the given z-score and standard deviation, the z-score formula is used. After calculation, the mean temperature in Philadelphia for the first 15 days of February is determined to be 31°.

Explanation:

The question is asking us to find the mean temperature in Philadelphia for the first 15 days in February, given that the daily high temperatures are normally distributed with a standard deviation of 2.5° and that on Valentine's Day (February 14th), the temperature was 37° with a z-score of 2.4. To solve for the mean temperature, we can use the z-score formula:

Z = (X - μ) / σ

Where:
Z is the z-score,
X is the value in the dataset,
μ is the mean, and
σ is the standard deviation.

We know Z = 2.4, X = 37°, and σ = 2.5°. Plugging these values into the z-score formula, we can solve for the mean (μ).

2.4 = (37 - μ) / 2.5

Multiplying both sides by 2.5, we get:

2.4 x  2.5 = 37 - μ
6 = 37 - μ
μ = 37 - 6
μ = 31°

Therefore, the mean temperature in Philadelphia for the first 15 days in February is 31°.

Answer:

Correct answer: a) m = 9 ; b) m = 2 and n = 3

Step-by-step explanation:

Given:

a) m x² - 36  = (3 x + 6) (3 x - 6)  ⇒ m = ?

b) (m x + n y)² = 4 x² + 12 x y + 9 y²  ⇒ m, n = ?

a)  m x² - 36 (3 x + 6) (3 x - 6)  

The right side of the equation is the difference of the square, so we will present the left side in the same way:

(√m x)² - 6² = (3 x + 6) (3 x - 6)

(√m x + 6) (√m x - 6) = (3 x + 6) (3 x - 6)

√m = 3 /²  when we square both sides of the equation we get:

m = 9

b)

(m x + n y)² = 4 x² + 12 x y + 9 y²

The left side of the equation is the complete square of the binomial, so we will present the right side in the same way:

(m x + n y)² = (2 x)² + 2 · 2 x · 3 y + (3 y)² = (2 x + 3 y)²

(m x + n y)² = (2 x + 3 y)²  ⇒

m = 2 and n = 3

God is with you!!!

For part (a), m must be 9 to make the equation true. For part (b), m can be 2 or -2, and n can be 3 or -3 to satisfy the equation.

To find values for m and n to make the statements true, we must compare coefficients or recognize patterns in the given equations.

Part (a)

We have the equation mx^2 - 36 = (3x + 6)(3x - 6). We can expand the right side to get 9x^2 - 36. To make this equation true, we need the coefficient of x^2 on the left to be equal to the coefficient on the right, which is 9. Therefore, m must be 9 for the equation to be true.

Part (b)

We have (mx + ny)^2 = 4x^2 + 12xy + 9y^2. Expanding the left side, we get m^2x^2 + 2mnxy + n^2y^2. To equate it to the right side, we need m^2 = 4 and n^2 = 9. This gives us two possibilities each for m and n: m can be 2 or -2 and n can be 3 or -3.

Answer: The value of a is the number that the​ x-values are multiplied by to get to the corresponding​ y-values. So, a equals 5

We have

y=ax  

so a is clearly the number we multiply by the x values.

Substituting either  points (2,10) and (-2,-10),

10 = a(2)

a = 10/2 = 5

Answer:

36

Step-by-step explanation:

6 9 15 24 ...

The sequence goes like this:

+3, +6, +9, +12, +15 (Adding 3 each time)

For example:

6 + 3 = 9  (First +3)

9 + 6 = 15  (Then +6)

15 + 9 = 24 (Then +9)

24 + 12 = 36

The next term of this quadratic sequence will be 36.

What is Quadratic equation?

An algebraic equation with the second degree of the variable is called an Quadratic equation.

Given that;

The quadratic sequence is,

⇒ 6, 9, 15, 24

Now,

The first term = 6

The second term = 6 + 3 = 9

The third term = 9 + 6 = 15

The fourth term = 15 + 9 = 24

Thus, The pattern of adding are;

3 , 6 , 9, ..

So, For next term we add 12 in fourth term, we get;

The next term = 24 + 12

                      = 36

Thus, The next term of this quadratic sequence will be 36.

Learn more about the quadratic equation visit:

https://brainly.com/question/28038123

#SPJ3

Answer: The length of a rectangle would be 7.5

Step-by-step explanation:

To find the length is [tex]l = \frac{A}{w}[/tex]

-Solve:

[tex]l=\frac{135}{18}[/tex]

-Divide 135 by 18 and you get 7.5

[tex]\frac{135}{18} = 7.5[/tex]

-Result:

[tex]l= 7.5[/tex]

Answer:

According to my calculation, the two possible coordinates of vertex C, is [tex](1,\sqrt{27}) and (1,-\sqrt{27})[/tex].

Answer:

According to my calculation, the two possible coordinates of vertex C, is .

Step-by-step explanation:

9514 1404 393

Answer:

  12

Step-by-step explanation:

The applicable relationship here is ...

  AD² = AB·AC

  AD = √(AB·(AB +BC)) = √(6·(6+18)) = √144

  AD = 12

Answer:

It is actually 7

Step-by-step explanation:

yup :)

Answer:

shed get $1.82 back

Step-by-step explanation:

Answer:

She would get $1.82 back

Step-by-step explanation:

If she bought 3 cartons costing $1.06 each, you would have to multiply $1.06 by 3

$1.06 x 3 = $3.18

Then if she paid with a five dollar bill you have to subtract $3.18 from 5

5 - 3.18 = 1.82

$1.82 is the answer

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:   x > - 1

Step-by-step explanation:

Answer:

x  > -1

Step-by-step explanation:

To solve, we must isolate the variable, x

8+8(x + 4) >32

Distribute the 8

8+ 8*x +8*4

8+8x+ 32 >32

Combine like terms

8+32 +8x  >32

40 + 8x >32

Subtract 40 from both sides

8x  > -8

Divide both sides by 8

x  > -1

Answer:

Included in screenshot

Answer: cc

Step-by-step explanation:

Answer:

670.32

Step-by-step explanation

Final answer:

In a triangle, the sum of all interior angles is always 180 degrees. Given the ratio of the other interior angles, we can find their measures.

Explanation:

In a triangle, the sum of all interior angles is always 180 degrees. Given that one of the interior angles is 40 degrees, let's denote the measures of the other two angles as 3x and 5x. The sum of all three angles is 40 + 3x + 5x = 180. Simplifying this equation, we get 8x + 40 = 180. Subtracting 40 from both sides gives us 8x = 140. Dividing both sides by 8, we find x = 17.5.

Now, we can substitute the value of x back into the expressions for the other two angles. So, the first angle is 3x = 3(17.5) = 52.5 degrees, and the second angle is 5x = 5(17.5) = 87.5 degrees.

Answer:

10

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

( x^3 + x^2) (-4x - 4)

x^2 ( x+1) -4 (x+1)

(x^2 - 4) (x+1)

(x-2) (x+2) (x+1)

X= 2 x=-2 x=-1

Answer:

Yes

Step-by-step explanation:

f(x) = x^3 + x^2 −4x − 4

Factor by grouping  taking x^2 out of the first group and -4 out of the second

0 = x^3 + x^2      −4x − 4

     x^2(x+1)     -4(x+1)

Factor out (x+1)

0=(x+1)(x^2-4)

Now we have the difference of squares

0=(x+1) (x-2)(x+2)

x+1 is a factor

A) Variables:

X = number of weeks she puts money into the account.

Y = total amount in account after x weeks.

B) m would be the amount she puts in per week, b is the starting amount she has in the account

Y = 5x + 40

C) replace x with the x values in the cart and solve for y:

O : y = 40. Coordinates (0,40)

1: Y = 45. (1,45)

2: 50, (2,50)

3: 55, (3,55)

4: 60, (4,60)

D) make the graph using the above points

E) y intercept is when x is 0, which is 40. This was the starting value of how much money was saved.

Answer:

DO you still need help? Considering this was posted a long time ago.

Step-by-step explanation:

Answer:

114

Step-by-step explanation:

find the solution below

Answer:

$0.42

Step-by-step explanation:

Given:

Luisa Díaz drove her vehicle about 7,200 miles last year.

Total fixed cost = $1,058.40

Total variable cost = $1965.60

Question asked:

How much did it cost per mile ?

Solution:

Total cost of driving 7200 miles = Total fixed cost + Total variable cost

                                                     = $1,058.40 + $1965.60

                                                     = $3024

By unitary method:

Cost of driving 7200 miles = $3024

Cost of driving 1 mile = $3024 [tex]\div[/tex] 7200

                                   = $0.42

Thus, cost of driving per mile is $0.42

Answer:

The type of angles of <1 and <5 are corresponding angles

Step-by-step explanation:

Answer:

Step-by-step explanation:

3+1.5*4

3+6

9 inches in total 4 hours from now

Answer:

3 + 1.5(4) = 9

then the second one will be: 3 + 1.5t

Step-by-step explanation:

1.5t is increasing do therefore that is the answer.

Answer:

approximately 462.24

Step-by-step explanation: