Please help with this.........

[tex]\bf cot(x)cos(x)-cot(x)=0\implies cot(x)[cos(x)-1]=0 \\\\[-0.35em] ~\dotfill\\\\ cot(x)=0\implies \cfrac{cos(x)}{sin(x)}=0\implies cos(x)=0\\\\\\ x=cos^{-1}(0)\implies \boxed{x= \begin{cases} \frac{\pi }{2}\\\\ \frac{3\pi }{2} \end{cases}} \\\\[-0.35em] ~\dotfill\\\\ cos(x)-1=0\implies cos(x)=1\implies x=cos^{-1}(1)\implies \boxed{x=0}[/tex]

Answer:

x = π/2, 3π/2  

Step-by-step explanation:

cot(x)cos(x) - cot(x) = 0

Factor out cot(x)

cot(x)[cos(x) -1] = 0

Solve each part separately

cot(x) = 0                cos(x) - 1 = 0

x = π/2, 3π/2           cos(x) = 1

                                x = 0

There are three possible solutions:

x = 0, π/2, 3π/2

However, the function is undefined for x = 0.

∴ x = π/2, 3π/2

Answer:

15

Step-by-step explanation:

10 + 25= 35 and 35-20 = 15

please give branlest

Answer:

Step-by-step explanation: She Needs To Deposit $35 Dollars To Return To The Orginal Ammount She Started With On Monday.

The vertex, would be the tip of the pyramid. If it was sliced at the vertex, the shape would be a triangle. Since the slice doesn't intersect the vertex, the point of the pyramid would net be included, it would be as if the tip was cut off.

You would then have a trapezoid, because the top would be a straight horizontal line parallel with the bottom line.

Answer:

For Kaisorn: [tex]y=50-2.50x[/tex]

For Thom: [tex]y=40-2x[/tex]

Step-by-step explanation:

Each month, Kaisorn deposits $50.00 onto her public transportation card.

It costs her $2.50 per trip to ride the subway. Means 2.50x

Thom deposits $40.00 on his public transportation card. It costs him $2.00 per trip to ride the subway. Means 2x

Let x represents the number of trips

Let y represents the amount remaining in each account.

Then the system of equations represents their transportation costs are :

For Kaisorn: [tex]y=50-2.50x[/tex]

For Thom: [tex]y=40-2x[/tex]

D

generally,

[tex] \sin( \alpha ) = \cos(90 - \alpha )[/tex]

you can visualize this by drawing a right triangle with acute angles a and 90-a

Answer:

D.  Both a and c are true.

Step-by-step explanation:

a . sin 18 = cos (90 - 18) = cos 72 so a is True.

b. this is not true.

c. sin 72 = cos(90 - 72) = cos 18, so c is true.

Answer:

Step-by-step explanation:

We have a rectangle measuring 25 feet × 9 feet. Remove from the rectangle two regular hexagons with a side length equal to 2 feet.

The formula of an area of a rectangle:

[tex]A_r=lw[/tex]

l - length, w - width.

Substitute l = 25 ft and w = 9 ft:

[tex]A_r=(25)(9)=225\ ft^2[/tex]

The formula of an area of a regular hexagon:

[tex]A_h=6\cdot\dfrac{a^2\sqrt3}{4}[/tex]

a - side

Substitute a = 2 ft:

[tex]A_h=6\cdot\dfrac{2^2\sqrt6}{4}=6\sqrt3\ ft^2[/tex]

The area of the wall:

[tex]A=A_r-2A_h[/tex]

Substitute:

[tex]A=225-2(6\sqrt3)=225-12\sqrt3\approx225-20.785=204.215\ ft^2[/tex]

Paiting the wall costs $1.75 per ft². Calculate:

[tex](\$1.75)(204.215)\approx\$357[/tex]

Answer:

0.78

Step-by-step explanation:

There are 500 students in total. Thus,

The probability that one of the students on the trip is an athlete or a band memeber is

[tex]Pr=\dfrac{325+40+25}{500}=\dfrac{390}{500}=0.78.[/tex]

Answer:

the answer is 0

Step-by-step explanation:

A) multiples of 12 up to 72 ( 72 total cards)

12, 24, 36, 48, 60, 72 = 6 cards.

36 are gold.

Total gold cards and multiple of 12 = 36 + 6 =42

Probability of getting one of them is 42/72, which reduces to 7/12

B) 36 silver cards

Multiples of 9:  9, 18, 27, 36, 45, 54,63 = 7 cards

Silver cards are even and there is 3 even cards that are also multiples of 9, so subtract 3 from 7 to get 4.

Total silver cards and multiples of 9 = 36 + 4 = 40

Probability = 40/72 which reduces to 5/9

Answer:

Step-by-step explanation:

A.

Because there is no overlap between good card and card with a multiple of 12,

P(gold card or a card with a multiple of 12)

= P(gold card) + P(a card with a multiple of 12)

P(gold card)

= no. of gold cards / total no. of cards

= 36 / (36 + 36)

= 36 / 72

= 1/2

P(a card with a multiple of 12)

= no. of cards with multiples of 12 / total no. of cards

= (12, 24, 36, 48, 60, 72) / 72

= 6/72

= 1/12

P(gold card or a card with a multiple of 12)

= 1/2 + 1/12

= 7/12

B. There ARE overlaps between a silver card and a card with a multiple of 9,

P(silver card or a card with a multiple of 9)

= P(silver card) + P(a card with a multiple of 9) - P(silver card AND a multiple of 9)

P(silver card)

= no. of silver cards / total no. of cards

= 36 / (36 + 36)

= 36 / 72

= 1/2

P(a card with a multiple of 9)

= no. of cards with multiples of 9 / total no. of cards

= (9, 18, 27, 36, 45, 54, 63, 72) / 72

= 8/72

= 1/9

P(silver card AND a multiple of 9)

= no. of silver cards AND a multiple of 9 / total no. of cards

= (18, 36, 54, 72) / 72

= 4/72

= 1/18

P(silver card or a card with a multiple of 9)

= 1/2 + 1/9 - 1/18

= 10/18

= 5/9

Answer:

2

Step-by-step explanation:

Let's disect the problem. Three times a particular number plus fourteen equals 20. Let's make an equation, and replace the number with x.

We'll first minus 14 from each side to balance the equation, but with the intention of isolating the variable, x.

We have almost successfully isolated the variable. To isolate the variable, we can divide by three on each side.

First, to simplify the expression 5 + 8(3 + x), distribute the 8 to everything inside the parentheses to get 5 + 24 + 8x. Then, combine the numerical terms to get the answer 29 + 8x.

The expression you are asked to simplify is 5 + 8(3 + x). To do this, you'll need to use the distributive property, which allows you to multiply a number outside a set of parentheses by every term inside the parentheses.

Start with the expression: 5 + 8(3 + x)

Before adding, you'll need to multiply eight by every term inside the parentheses, three, and x:

5 + 8*3 + 8*x

That changes your expression to:

5 + 24 + 8x

Now, you need to combine like terms (add together the numbers that are not attached to variable x):

5 + 24 = 29

So, the simplified version of the expression is:

29 + 8x

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Bryant's score is 55 (given)

Jack's score is twice the score of Bryant, so it's

[tex]55\cdot 2 = 110[/tex]

Brenda's score is 13 less than Jack, so it's

[tex]110-13 = 97[/tex]

Answer:

The volume of a rectangular prism is [tex]28\frac{7}{8}\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the rectangular prism is equal to

[tex]V=BHL[/tex]

Convert the given dimensions to an improper fractions

[tex]B=3\frac{1}{2}\ cm=\frac{3*2+1}{2}=\frac{7}{2}\ cm[/tex]

[tex]H=1\frac{1}{2}\ cm=\frac{1*2+1}{2}=\frac{3}{2}\ cm[/tex]

[tex]L=5\frac{1}{2}\ cm=\frac{5*2+1}{2}=\frac{11}{2}\ cm[/tex]

substitute in the formula

[tex]V=(\frac{7}{2})(\frac{3}{2})(\frac{11}{2})=\frac{231}{8}\ cm^{3}[/tex]

Convert to mixed number

[tex]\frac{231}{8}=\frac{224}{8}+\frac{7}{8}=28\frac{7}{8}\ cm^{3}[/tex]

Answer:

Reflection across x-axis, horizontal stretch by a factor of 10

and vertical translation up 4 units ⇒ answer (c)

Step-by-step explanation:

* The basic function of tanФ is

# y = tanФ

1- If y = -tanФ ⇒ reflect y over the x-axis

2- If y = tan(-Ф) ⇒ reflect y over the y-axis

3- If y = tan(Ф - k) ⇒ shift y right k units

4- If y = tan(Ф + k) ⇒ shift y left k units

5- If y = tanФ + k ⇒ shift y up k units

6- If y = tanФ - k ⇒ shift y down k units

7- If y = k tanФ ⇒ multiply y-values by k

 (k > 1 stretch, 0 < k < 1 compressed vertical)

 The scale factor is k

8- If y = tan(kФ) ⇒ divide x-values by k

 (k > 1 compressed, 0 < k < 1 stretch horizontal)

 The scale factor is 1/k

* Lets solve the problem

∵ y = -tan(1/10)x + 4

* We will use rules number 1 , 5 and 8

∴ Reflect y over the x-axis, shift y up k units and stretch

   horizontal by scale factor is 1/k (0 < k < 1)

∴ Reflection across x-axis, horizontal stretch by a factor of 10

  and vertical translation up 4 units

Answer:

Angles UWV and UWZ are complementary

Step-by-step explanation:

we know that

If the sum of the measures of two angles is equal to 90 degrees, then, the angles are complementary

so

In this problem

[tex]m<UWZ+m<UWV=90\°[/tex]

therefore

Angles UWV and UWZ are complementary

Answer:

9.9 cm

Step-by-step explanation:

We can use the Pythagorean theorem to find the length of CY

a^2 + b^2 = c^2

CY^2 + YZ^2 = CZ^2

YZ = XY  since CZ is the perpendicular bisector

YZ = 5

CZ = 7

CY ^2 + 5^2 = 7^2

CY^2 +25 = 49

Subtract 25 from each side

CY^2 = 49-25

CY^2 = 24

Take the square root of each side

sqrt(CY^2) = sqrt(24)

CY = 4.898979

CY = 4.9 cm

We want the length of WY

WY = WC + CY

WC is a radius which is 5 cm

WY = 5cm + 4.9cm

WY = 9.9 cm

Answer:

We should work backwards we need to find YC+CW to get YW

angle bisector theorem means that ZC and XC are equal

then we can use the Pythagorean theorem to get YC

5^2 + x = 7^2

YC= √13

CW = 7 because they are both the radius of a circle

YW= 7+√13

YW=10.60 (rounded)

Answer:

D

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Edge 2021

The inverse function of f(x) = 7x^9 is found to be f^{-1}(x) = (x/7)^{1/9}. By substituting f(x) into its inverse, we can verify that f^{-1}(f(x)) = x, which shows that the composition is indeed a function. Therefore, the correct answer is option a.

The student has asked to find the inverse function of f(x) = 7x^9 and determine if the composition of the original function and its inverse is a function. The inverse function, denoted as f^{-1}(x), undoes the action of the original function. To find the inverse, we replace f(x) with y, switch the roles of x and y, and then solve for y:

This gives us option a: y = (x/7)^{1/9}. To check if f^{-1}(f(x)) is a function, we substitute f(x) into the inverse, resulting in f^{-1}(7x^9) = (7x^9/7)^{1/9} = x, which is indeed a function. Therefore, f^{-1}(x) is a function, and option a is correct.

Answer:

x = 5

Step-by-step explanation:

For the parallelogram to be a square we use the property

The diagonals of a square are congruent, hence

12x - 23 = 4x + 17 ( subtract 4x from both sides )

8x - 23 = 17 ( add 23 to both sides )

8x = 40 ( divide both sides by 8 )

x = 5

The ratio of muffins to donuts in the bakery is 4:7, calculated by dividing the number of muffins (36) by the number of donuts (63).

To find the ratio of muffins to donuts, we divide the number of muffins by the number of donuts.

Given:

- Number of donuts: 63

- Number of muffins: 36

Ratio of muffins to donuts:

[tex]\[ \text{Ratio} = \frac{\text{Number of muffins}}{\text{Number of donuts}} \][/tex]

[tex]\[ \text{Ratio} = \frac{36}{63} \][/tex]

We can simplify this ratio by finding the greatest common divisor (GCD) of 36 and 63, which is 9.

[tex]\[ \text{Ratio} = \frac{\frac{36}{9}}{\frac{63}{9}} \][/tex]

[tex]\[ \text{Ratio} = \frac{4}{7} \][/tex]

So, the ratio of muffins to donuts is  4:7 .

The ratio of muffins to donuts is [tex]\( \frac{4}{7} \)[/tex].

To find the ratio of muffins to donuts, we divide the number of muffins by the number of donuts:

[tex]\[ \text{Ratio of muffins to donuts} = \frac{\text{Number of muffins}}{\text{Number of donuts}} \][/tex]

Given that the bakery has 63 donuts and 36 muffins, we can substitute these values into the formula:

[tex]\[ \text{Ratio of muffins to donuts} = \frac{36}{63} \][/tex]

Now, we can simplify this fraction:

[tex]\[ \frac{36}{63} = \frac{4 \times 9}{7 \times 9} = \frac{4}{7} \][/tex]

So, the ratio of muffins to donuts is [tex]\( \frac{4}{7} \)[/tex].

Answer:

The value of x = 0.41

Step-by-step explanation:

∵ [tex]6e^{2x}-5e^{x}=6[/tex]

Let [tex]e^{x}=y[/tex]

∴ [tex]e^{2x}=y^{2}[/tex]

∴ 6y² - 5y = 6

∴ 6y² - 5y - 6 = 0 ⇒ factorize

∴ (3y + 2)(2y - 3) = 0

∴ 3y + 2 = 0 ⇒ 3y = -2 ⇒ y = -2/3

∴ 2y - 3 = 0 ⇒ 2y = 3 ⇒ y = 3/2

∵ [tex]y=e^{x}[/tex]

∴ [tex]e^{x}=\frac{-2}{3}[/tex] ⇒ refused

  ([tex]e^{ax}[/tex] never gives -ve values)

∵ [tex]e^{x}=3/2[/tex] ⇒ insert ln in both sides

∵ [tex]lne^{ax}=axlne=ax[/tex] ⇒ ln(e) = 1

∴ [tex]xlne=ln(3/2)[/tex]

∴ x = ln(3/2) = 0.41

Answer:

[tex]8\ games[/tex]

Step-by-step explanation:

Let

x----->number of games won by the football team

we know that

[tex]25\%=25/100=0.25[/tex]

so

[tex]x=0.25(32)=8\ games[/tex]

Answer:

Option b

Step-by-step explanation:

We know that, by definition:

[tex]secx = \frac{1}{cosx}[/tex]

We also know that:

[tex]tanx = \frac{sinx}{cosx}[/tex]

Applying these identities we can simplify the given expression

[tex]\frac{secx}{tanx} = \frac{\frac{1}{cosx}}{\frac{sinx}{cosx}}\\\\\frac{secx}{tanx} = \frac{cosx}{sinxcosx}\\\\\frac{secx}{tanx} = \frac{1}{sinx}[/tex]

We know that, by definition:

[tex]\frac{1}{sinx} = cscx[/tex]

Final answer:

To simplify sec x/tan x, we use trigonometric identities to show that sec x/tan x equals csc x, which is the cosecant of x.

Explanation:

To simplify the expression sec x/tan x, we need to recall the trigonometric identities for secant (sec) and tangent (tan). We know that sec x is equal to 1/cos x and tan x is equal to sin x/cos x. When we divide sec x by tan x, we are essentially dividing 1/cos x by sin x/cos x. This simplifies to:

To summarize, the simplified form of the expression sec x/tan x is csc x.

➷ Find the difference from one peak ( highest point) to the next

In this case, it is 2 pi

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

2 pi

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

1/3 since there are two numbers less than three, and there are 6 possible outcomes, so 2/6 = 1/3.

Answer: -0.6

Step-by-step explanation:

First thing to do is to solve for θ and ϕ from the given information

tan(θ) = 4/3,

θ = tan-¹4/3,

θ = 53.1°

Since tan is positive in quadrant III, θ = 53.1°

Also,

sin(ϕ) = − 10/10 ,

ϕ = sin-¹-1

ϕ = 270°

If ϕ is in the fourth quadrant, that gives 360 - ϕ i.e 360 - 270 = 90°

Substituting the values of θ and ϕ into sin(θ − ϕ), we have;

Sin(53.1 - 90)

= sin (-36.9°)

= -0.6

The given expression sin(θ - ϕ), with tan(θ) = 4/3, θ in Quadrant III, sin(ϕ) = -10/10, and ϕ in Quadrant IV, is evaluated by using trigonometric principles and identities. Upon calculations, sin(θ - ϕ) comes out to be -3/5.

The question is asking us to evaluate the expression sin(θ − ϕ), given that tan(θ) = 4/3, θ is in Quadrant III, sin(ϕ) = -10/10, and ϕ is in Quadrant IV. In trigonometry, tan θ = sin θ/cos θ. We have tan θ = 4/3 and we know that in Quadrant III, tangent is positive but sine and cosine are negative. So, we can make a right triangle where the opposite side is 4 (basing this on the absolute value of the tan θ) and the adjacent side is 3. The hypotenuse then, by using Pythagoras theorem, comes out to be 5. Then sin θ = -4/5 and cos θ = -3/5.

For sin(ϕ), we are given that it equals -1. In Quadrant IV, sine is negative and cosine is positive, so cos ϕ = √(1 - (-1)^2) = 0.

Finally, utilizing the formula sin (a ± ß) = sin a cos ß ± cos a sin ß, we plug in our values to come to the solution sin(θ - ϕ) = (sin θ cos ϕ) - (cos θ sin ϕ) = ((-4/5)*0) - ((-3/5)*-1) = -3/5

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Answer:  (2, 6.5)

Step-by-step explanation:

[tex]Midpoint_{x,y}=\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\\.\qquad \qquad \quad=\bigg(\dfrac{-3+7}{2},\dfrac{4+9}{2}\bigg)\\\\\\.\qquad \qquad \quad=\bigg(\dfrac{4}{2},\dfrac{13}{2}\bigg)\\\\\\.\qquad \qquad \quad=\large\boxed{(2,6.5)}[/tex]

Answer:

x = 25 mm

Step-by-step explanation:

The perimeter of a rectangle is given by

P = 2(l+w) where l is the length and w is the width

We know the perimeter is 60 mm and the width is 5 mm and the length is x

60 = 2(x +5)

Divide each side by 2

60/2 = 2/2(x+5)

30 = x+5

Subtract 5 from each side

30-5 = x+5-5

25 =x

x = 25 mm

[tex]\huge\bold\red{Answer}[/tex]

☑The diagram which is shown above is a rectangle.

✍ Perimeter= 60mm

✍ breadth = 5mm

➡ Perimeter of rectangle = 2(l+b)

✍ 60 = 2(l +5)

✍ 60/2 = l+5

✍ 30 - 5 = l

✍ 25 = l

☑ L = 25mm

❣..hope it helps you..❣