Cot^2 x- 6cotx - 5=0

Answer: 91/288

Step-by-step explanation: To divide mixed numbers, first write the mixed numbers as improper fractions.

We can do this by multiplying the denominator by the whole number and then adding the numerator. Then, we put our new numerator over our old denominator.

So here, we can write 1 and 5/8 as the improper fraction 13/8 and we can write 5 and 1/7 as the improper fraction 36/7.

So here, we have 13/8 ÷ 36/7.

Dividing by a fraction is the same as multiplying by the reciprocal of that fraction.

So here, 13/8 ÷ 36/7 is the same as 13/8 × 7/36.

So now we are simply multiplying fractions and we do this by multiplying across the numerators and multiply across the denominators.

[tex]\frac{13}{8} x \frac{7}{36} = \frac{91}{288}[/tex]

So now we have 91/288 which is in lowest terms.

This means that 1 and 5/8 divided by 5 and 1/7 is 91/288.

Answer:Can You please like this I want to rank up

Step-by-step explanation:

Press the Heart

P.S. Please

The equation of the circle in standard form is: (x + 2)² + (y - 1)² = 1

What is the equation of the circle?

The general form of the equation of a circle is:

(x - h)² + (y - k)² = r²

Where;

(h, K) is the coordinate of the center of the circle.

r is radius.

To find the equation of the circle in standard form, we need to determine the center and radius of the circle.

Since the center of the circle lies on the line y = 3x + 1 and is tangent to the x-axis at (-2,0), we can determine that the center of the circle is (-2,1) and the radius is 1.

Therefore, the equation of the circle in standard form is:

(x + 2)² + (y - 1)² = 1

Answer:

0.04

Step-by-step explanation:

12^(-x) = 5   (taking log on both sides)

log [ 12^(-x)] = log 5

-x log 12 = log 5

-x = log 5 / log 12

x = - (log 5/log12)

x = -0.6477

12^(2x)

= 12^[2(-0.6477)]

= 12 ^ (-1.295)

= 0.04

Step-by-step explanation:

x=10+4=14

14+14=28

the answer is 28 fts

Answer:

Step-by-step explanation:

The image attached shows the context that the problems refered.

Notice that two acute angles from those triangles are congruent, just because their complement are also congruent.

[tex]\angle AOB \cong \angle COD[/tex]

[tex]\angle AOB= \angle COD=90\° - a[/tex]

Remember that the tangent function is defined as

[tex]tan(\theta)=\frac{Opposite \ Leg}{Adjacent \ Leg}[/tex]

Replacing each equiavlence, we have

[tex]tan(90-a)=\frac{6}{4}=\frac{10}{x}[/tex]

Then, we solve for [tex]x[/tex]

[tex]\frac{6}{4} =\frac{10}{x}\\ x=\frac{40}{6}\\ x \approx 6.67 ft[/tex]

Thereofre, the answer is 6.67 feet, approximately.

Answer:

B

Step-by-step explanation:

Answer:

a. no

Step-by-step explanation:

The sequence is arithmetic.  It has a common difference of 14.

7 + 14 = 21

21 + 14 = 35

35 + 14 = 49

A geometric series has a common ratio (multiplication).  For example:

7 × 3 = 21

21 × 3 = 63

63 × 3 = 189

Answer:

I would say you're right, 2 + 2

Step-by-step explanation:

Final answer:

The mathematics optimization problem involves finding the maximum sum of the square of one non-negative number and the cube of the other, with their total being 4. Calculus is applied by taking the derivative of the function representing the sum, setting it to zero to find critical points, and checking the second derivative to ensure a maximum is found. The optimized numbers are x and 4-x, based on the critical point found.

Explanation:

To solve the optimization problem, we need to use calculus to find the maximum value of the sum of the square of one number and the cube of the other, given that the sum of the two numbers is 4. Let's call these numbers x and y, with x + y = 4. We want to maximize S = x^2 + y^3.

Since x + y = 4, we can express y as y = 4 - x. Substituting this into S, we have S = x^2 + (4-x)^3. This becomes a function of one variable.

To find the maximum value, we differentiate S with respect to x, set the derivative equal to zero, and solve for x. We can check the second derivative to ensure it is a maximum. The function S' will have a maximum when the first derivative is zero (S'(x) = 0) and the second derivative is negative (S''(x) < 0).

Therefore, the two non-negative numbers that maximize S are x and 4-x, with x being the value at which S' equals zero with S'' negative.

Answer:

[tex]9 {x}^{2} - 49[/tex]

Step-by-step explanation:

Do FOIL, first outside inside last

3x × 3x = 9x^2

3x × -7 = -21x

7 × 3x = 21x

7 × -7 = -49

[tex]9 {x}^{2} - 21x + 21x - 49 \: midde \: cancels \: each \: other \: out[/tex]

So it would just be 9x^2 - 49

(3x + 7)(3x - 7) =

= 9x² + 21x - 21x - 49

= 9x² - 49

Answer:

39 square feet

Step-by-step explanation:

The outdoor carpet consists of two rectangles.

The area of the rectangle is

[tex]A=\text{Length}\times \text{Width}[/tex]

1st rectangle:

Length = 11 ft

Width = 3 ft

Area [tex]=11\cdot 3=33 \ ft^2[/tex]

2nd rectangle:

Length = 3 ft

Width = 2 ft

Area [tex]=3\cdot 2=6 \ ft^2[/tex]

Total area:

[tex]33+6=39\ ft^2[/tex]

Answer: C) 19%

Step-by-step explanation:250 +200 + 150 + 125 + 50 = 775 total complaints.  150 rude sales clerks out of 775 total complaints equals 150/775 = 0.1935 which is a 19 percent. So 19 percent of the complaints are about rude sales clerks.

Answer: 42 pages

Step-by-step explanation: 6 pages x 7 days= 42 pages

Slope is already given in the question so we only need to solve for the y-intercept.

Slope intercept form: y = mx + b

m = slope

b = y-intercept

-3/5 = -0.6

1 = -0.6(1) + b

1 = -0.6 + b

1 + 0.6 = -0.6 + b + 0.6

1.6 = b

Now, write in slope-intercept form.

y = -3/5x - 1.6

______

Best of Luck,

Wolfyy :)

The first five terms of the sequence are:

6 , 8 , [tex]\frac{32}{3}[/tex] , [tex]\frac{128}{9}[/tex] , [tex]\frac{512}{27}[/tex]

Step-by-step explanation:

The recursive formula of the sequence is

[tex]a_{1}=6[/tex] and [tex]a_{n}=\frac{4}{3}*a_{n-1}[/tex]

To find the first five terms do that:

∵ [tex]a_{1}=6[/tex]

∴ [tex]a_{2}=\frac{4}{3}*6[/tex]

∴ [tex]a_{2}=8[/tex]

∵ [tex]a_{2}=8[/tex]

∴ [tex]a_{3}=\frac{4}{3}*8[/tex]

∴ [tex]a_{3}=\frac{32}{3}[/tex]

∵ [tex]a_{3}=\frac{32}{3}[/tex]

∴ [tex]a_{4}=\frac{4}{3}*\frac{32}{3}[/tex]

∴ [tex]a_{4}=\frac{128}{9}[/tex]

∵ [tex]a_{4}=\frac{128}{9}[/tex]

∴ [tex]a_{5}=\frac{4}{3}*\frac{128}{9}[/tex]

∴ [tex]a_{5}=\frac{512}{27}[/tex]

The first five terms of the sequence are:

6 , 8 , [tex]\frac{32}{3}[/tex] , [tex]\frac{128}{9}[/tex] , [tex]\frac{512}{27}[/tex]

Learn more:

You can learn more about sequences in brainly.com/question/1522572

#LearnwithBrainly

Answer:

The measure of angle F is m∠F=130°

Step-by-step explanation:

step 1

Find the measure of angle E

we know that

An isosceles triangle has two equal sides and two equal interior angles

In this problem

DF=EF ----> given problem

so

Triangle DEF is an isosceles triangle

m∠D=m∠E

we have

m∠D=25°

substitute

m∠E=25°

step 2

Find the measure of angle F

we know that

The sum of the measures of the interior angles in a triangle must be equal to 180 degrees

so

m∠D+m∠E+m∠F=180°

substitute the values

25°+25°+m∠F=180°

50°+m∠F=180°

m∠F=180°-50°

m∠F=130°

Answer:

25

Step-by-step explanation:

0.25/0.01

=25

Answer:

1. f

2.b

3. d

4. a

5. e

6. g

7. c

Step-by-step explanation:

The parent function is [tex]y = 3 (5)^{x}[/tex].

So,  

1. [tex]y = - 3 (5)^{x} + 4[/tex] ≡ f. reflected across x-axis and 4 units up

2. [tex]y = 3 (5)^{x - 4} - 4[/tex] ≡ b. 4 units down and 4 units right.

3. [tex]y = 3 (5)^{x + 4} + 4[/tex] ≡ d. 4 units up and 4 units left.

4. [tex]y = - 3 (5)^{x} - 4[/tex] ≡ a. reflected across x-axis and 4 units down.

5. [tex]y = 3 (5)^{x} - 4[/tex] ≡ e. 4 units down

6. [tex]y = 3 (5)^{x} + 4[/tex] ≡ g. 4 units up.

7. [tex]y = 3 (5)^{x - 4}[/tex] ≡ c. 4 units right. (Answer)

Answer:

Option B [tex]2\frac{2}{3}\ units[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

Triangles ABC and ADE are similar by AA Similarity Theorem

so

[tex]\frac{AB}{AD}=\frac{AC}{AE}[/tex]

substitute the given values

[tex]\frac{3}{3+2}=\frac{4}{AE}[/tex]

Solve for AE

[tex]\frac{3}{5}=\frac{4}{AE}[/tex]

[tex]AE=5(4)/3[/tex]

[tex]AE=\frac{20}{3}\ units[/tex]

Find the length of CE

[tex]AE=AC+CE\\CE=AE-AC[/tex]

substitute the values

[tex]CE=\frac{20}{3}-4[/tex]

[tex]CE=\frac{8}{3}\ units[/tex]

Convert to mixed number

[tex]\frac{8}{3}\ units=\frac{6}{3}+\frac{2}{3}=2\frac{2}{3}\ units[/tex]

Answer:

Step-by-step explanation:

A) 1/7, 3/7, 9/7, 27/7,81/7

Explanation: actually in it we simply multiply the nominator with 3.

B) 24,12,6,3,1.5

Explanation: In this we simply half the value or we can say that divided by 2.

Answer:

The linear equation is 1.25x + 0.5x = y

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Price of ride ticket at country fair = US$ 1.25

Total spent by Tom for rides and admission= US$ 43.75

Number of ride tickets bought by Tom = 25

Price of admission is the same for everyone

Total cost = y

Number of tickets = x

2. Let's find out the cost of the admission:

Total cost of ride tickets + Total cost of admission = Total cost of rides tickets and admission

Replacing with real values:

1.25 * 25 + Cost of admission * 25 = 43.75

31.25 + 25 * Cost of admission = 43.75

25 * Cost of admission = 43.75 - 31.25 (Subtracting 31.25 at both sides)

25 * Cost of admission = 12.50

Cost of admission = 12.50/25 (Dividing by 25 at both sides)

Cost of admission = 0.50

3. Let's write a linear equation to determine the cost for rides tickets and admission:

Total cost of ride tickets + Total cost of admission = Total cost of rides tickets and admission

Total cost = y

Number of tickets = x

1.25x + 0.5x = y

Answer:

117/78

Step-by-step explanation:

(-50-67)/(-12-56)=-117/-78=117/78

Answer:

They are arranged greatest to least

Answer:

From given option ,  the equation of parabola is                                            y = negative x² divided by 12

Step-by-step explanation:

Given as for parabola :

The focus is at (0 , - 3)

The directrix equation is y = 3

Now, equation of parabola parallel to y-axis is

( x - h )² = 4 p ( y - k )

where focus is ( h , k+p )   and  directrix equation is y = k - p

So, from equation

h  = 0     and   k + p = - 3

And y = k - p   i.e k - p = 3

Now solving  ( k + p ) + (  k - p ) = - 3 + 3

or, 2 k = 0  ∴ k = 0

Put the value of k , k + p = - 3

So, 0 + p = - 3    ∴ p = - 3

Now equation of parabola with h = 0  , k = 0  , p = - 3

( x - h )² = 4 p ( y - k )

I.e ( x - 0 )² = 4 × ( - 3 ) ( y - 0 )

Or, x² = - 12 y   is the equation of parabola

Hence  From given option ,  the equation of parabola is                                y = negative x² divided by 12       Answer

Answer:

40 girls 80 boys

Step-by-step explanation:

80/2=40

40+80=120

Answer:

80 girls

Step-by-step explanation:

120/3 = 40.

40 x 2 = 80

Final answer:

The costs for members and nonmembers of a local fitness center will be the same after attending 6 aerobics classes. Members have an initial $12 membership fee plus $2 per class, while nonmembers pay $4 per class.

Explanation:

To find the number of aerobics classes for which the cost for members and nonmembers will be the same, we need to set up an equation that compares the two cost structures. For members, the cost is a $12 membership fee plus $2 per class, which we can express as Cm = 12 + 2n, where Cm is the cost for members and n is the number of classes. For nonmembers, the cost is $4 per class, so we can express that as Cnm = 4n, where Cnm is the cost for nonmembers.To find the number of classes where costs are the same, we set Cm equal to Cnm:

Subtract 2n from both sides: 12 = 2n

Divide both sides by 2: n = 6

Therefore, the costs for members and nonmembers will be the same when they attend 6 aerobics classes.

Answer:

w=4

Step-by-step explanation:

10+15(w-2)=40

distribute the 15

10+15w-30=40

combine like terms

-20 + 15w = 40

15w=60

w=4

Answer:

the answer will be 48

Step-by-step explanation:

The answer 48 because 12 times 3 is 36 and then you add Jose's score and you get 48

Answer:

C) -19w-3

Step-by-step explanation:

(-14w-3)-5w

-14w-3-5w

-19w-3

The area of square flake of gold is [tex]53.29 \times 10^{-8} \mathrm{mm}[/tex]

Given that width of square flake of gold is [tex]7.3 \times 10^{-4}[/tex] millimeter

To find : Area of square flake

Since gold flake is in shape of square, we can use area of square formula

The formula for area of square is given as:

[tex]area = s^2[/tex]

where "s" is the length of one side

[tex]\begin{array}{l}{\text { Area of a square flake }=\left(7.3 \times 10^{-4}\right) \times\left(7.3 \times 10^{-4}\right)} \\\\ {\text { Area of a square flake }=53.29 \times 10^{8}}\end{array}[/tex]

Hence , the calculated area of flake is [tex]53.29 \times 10^{-8} \mathrm{mm}[/tex]

Answer:

Domain:  -∞ < x < +∞

Range : 2 ≤ f(x) < +∞

Step-by-step explanation:

See the graph attached to this question.

The two arrow shows the graph of a function y = f(x).

Now, the value of x varies from +∞ to -∞.

So, the domain of the function is -∞ < x < +∞

Again from the graph the range of the function i.e. values of y varies from 2 to +∞ and including 2.

Therefore, the range of the function is 2 ≤ f(x) < +∞ (Answer)

Answer:

1. The required slope m, for the context is[tex]m = \frac{-25}{3}[/tex]

2. The y-intercept in the context is [tex]P_{2}(d) = y = 100[/tex]

3. The x-intercept of the linear model is [tex]d = x = 12[/tex]

Step-by-step explanation:

Given:

[tex]P_{2}(d) = \frac{-25}{3}\times d + 100[/tex]

Where,

[tex]P_{2}[/tex] is the number of phones.

d is the number of days he has worked that week.

This is a linear model type equation.

Can be represented in the slope intercept form  which is equal to

[tex]y = mx + c[/tex]

Where,

m = Slope of the line.

c = y-intercept.

Now if we compare the given model by slope intercept formula we get

[tex]m = \frac{-25}{3}\\\\c = 100[/tex]

So ,the slope in the context of the problem is [tex]m = \frac{-25}{3}[/tex].

and the y intercept in the context of the problem [tex]P_{2}(d) = c = y = 100[/tex]

For finding x-intercept put y = 0

Here,[tex]P_{2}(d) = 0[/tex]

[tex]\therefore 0 = \frac{-25}{3}\times d + 100\\ \therefore \frac{25}{3}\times d = 100\\\therefore d=\frac{300}{25}\\\therefore d=12[/tex]

So, the x intercept of the linear model is [tex]d = x = 12[/tex]