Which shows the correct way to evaluate 10 × 4 – (5 – 3) + 2? 10 × 4 – (5 – 3) + 2 10 × 4 – (2 + 2) 10 × 4 – 4 10 × 0 0 10 × 4 – (5 – 3) + 2 10 × 4 – (2 + 2) 10 × 4 – 4 40 – 4 36 10 × 4 – (5 – 3) + 2 10 × 4 – 2 + 2 10 × 2 + 2 20 + 2 22 10 × 4 – (5 – 3) + 2 10 × 4 – 2 + 2 40 – 2 + 2 38 + 2 40

Answer:

Land on round 4 times; land on square 4 times

Step-by-step explanation:

Answer:

The correct option is 4.

Step-by-step explanation:

In the graph orange region represents the ways Janelle can win the beanbag toss game.

From the given graph it is clear that the related line passes through the points (2,5) and (10,0).

If a line passes through two points, then the equation of line is

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

The equation of related line is

[tex]y-5=\frac{0-5}{10-2}(x-2)[/tex]

[tex]y-5=-\frac{5}{8}(x-2)[/tex]

Add 5 on both the sides.

[tex]y-5+5=-\frac{5}{8}(x)+\frac{5}{4}+5[/tex]

[tex]y=-\frac{5}{8}(x)+\frac{25}{4}[/tex]

The shaded region is above the line, so the sign of inequality is ≥.

The required inequality is

[tex]y\geq -\frac{5}{8}(x)+\frac{25}{4}[/tex]

Check the each point whether it satisfy the inequality of not.

In option (1), the given point is (7,1).

[tex]1\geq -\frac{5}{8}(7)+\frac{25}{4}[/tex]

[tex]1\geq 1.875[/tex]

This statement is false.

In option (2), the given point is (6,2).

[tex]2\geq -\frac{5}{8}(6)+\frac{25}{4}[/tex]

[tex]2\geq 2.5[/tex]

This statement is false.

In option (3), the given point is (5,3).

[tex]3\geq -\frac{5}{8}(5)+\frac{25}{4}[/tex]

[tex]3\geq 3.125[/tex]

This statement is false.

In option (4), the given point is (4,4).

[tex]4\geq -\frac{5}{8}(4)+\frac{25}{4}[/tex]

[tex]3\geq 3.75[/tex]

This statement is true. It means the point (4,4) describes a way Janelle can win the game. Therefore the correct option is 4.

Answer:

The correct answer option is P (S∩LC) = 0.16.

Step-by-step explanation:

It is known that the probability if someone is a smoker is P(S)=0.29 and the probability that someone has lung cancer, given that they are also smoker is P(LC|S)=0.552.

So using the above information, we are to find the probability hat a random person is a smoker and has lung cancer P(S∩LC).

P (LC|S) = P (S∩LC) / P (S)

Substituting the given values to get:

0.552 = P(S∩LC) / 0.29

P (S∩LC) = 0.552 × 0.29 = 0.16

Answer:

[tex] R = 28.07^\circ [/tex]

Step-by-step explanation:

Since you have the lengths of all the sides, you can use sine, cosine, or tangent to find the answer. Let's use the tangent ratio.

For angle R, PQ is the opposite leg, and QR is the adjacent leg.

[tex] \tan R = \dfrac{opp}{adj} [/tex]

[tex] \tan R = \dfrac{8}{15} [/tex]

[tex] R = \tan^{-1} \dfrac{8}{15} [/tex]

[tex] R = 28.07^\circ [/tex]

Answer:

were are the answer selection

Step-by-step explanation:

add payment history and total debt it gibes you 65%

Answer:

The answer is circle; 2(x')² + 2(y')² - 5x' - (5√3)y' - 6 = 0 ⇒ answer (b)

Step-by-step explanation:

* At first lets talk about the general form of the conic equation

- Ax² + Bxy + Cy²  + Dx + Ey + F = 0

∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.

∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.

∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.

* Now we will study our equation:

* x² - 5x + y² = 3

∵ A = 1 , B = 0 , C = 1

∴ B² - 4AC = (0) - 4(1)(1) = -4 < 0

∵ B² - 4AC < 0

∴  it will be either a circle or an ellipse

* Lets use this note to chose the correct figure

- If A and C are equal and nonzero and have the same sign,

 then the graph is a circle.

- If A and C are nonzero, have the same sign, and are not equal

 to each other, then the graph is an ellipse.

∵ A = 1 an d C = 1

∴ The graph is a circle.

* To find its center of the circle lets use

∵ h = -D/2A and k = -E/2A

∵ A = 1 and D = -5 , E = 0

∴ h = -(-5)/2(1) = 2.5 and k = 0

∴ The center of the circle is (2.5 , 0)

* Now lets talk about the equation of the circle and angle Ф

∵ Ф = π/3

- That means the graph of the circle will transformed by angle = π/3

- The point (x , y) will be (x' , y'), where

* x = x'cos(π/3) - y'sin(π/3) , y = x'sin(π/3) + y'cos(π/3)

∵ cos(π/3) = 1/2 and sin(π/3) = √3/2

∴ [tex]y=\frac{\sqrt{3}}{2}x'+\frac{1}{2}y'=(\frac{\sqrt{3}x'+y'}{2})[/tex]

∴ [tex]x=\frac{1}{2}x'-\frac{\sqrt{3}}{2}y'=(\frac{x'-\sqrt{3}y'}{2})[/tex]

* Lets substitute x and y in the equation x² - 5x + y² = 3

∵ [tex](\frac{x'-\sqrt{3}y'}{2})^{2}-5(\frac{x'-\sqrt{3}y'}{2})+(\frac{\sqrt{3}x'-y'}{2})^{2}=3[/tex]

* Lets use the foil method

∴ [tex]\frac{(x'^{2} -2\sqrt{3}x'y'+3y')}{4}-\frac{(5x'-5\sqrt{3}y')}{2}+\frac{(\sqrt{3}x'+2\sqrt{3}x'y'+y'^{2})}{4}[/tex]=3

* Make L.C.M

∴ [tex]\frac{(x'^{2}-2\sqrt{3}x'y'+3y'^{2})}{4}-\frac{(10x'-10\sqrt{3}y')}{4}+\frac{(3x'^{2}+2\sqrt{3}x'y'+y'^{2})}{4} =3[/tex]

* Open the brackets ∴[tex]\frac{x'^{2}-2\sqrt{3}x'y'+3y'^{2}-10x'+10\sqrt{3}y'+3x'^{2}+2\sqrt{3}x'y'+y'^{2}}{4}=3[/tex]

* Collect the like terms

∴ [tex]\frac{4x'^{2}+4y'^{2}-10x'+10\sqrt{3}y'}{4}=3[/tex]

* Multiply both sides by 4

∴ 4(x')² + 4(y')² - 10x' + (10√3)y' = 12

* Divide both sides by 2

∴ 2(x')² + 2(y')² - 5x' + (5√3)y' = 6

∵ h = -D/2A and k = E/2A

∵ A = 2 and D = -5 , E = 5√3

∴ h = -(-5)/2(2) = 5/4 =1.25

∵ k = (5√3)/2(2) = (5√3)/4 = 1.25√3

∴ The center of the circle is (1.25 , 1.25√3)

∵ The center of the first circle is (2.5 , 0)

∵ The center of the second circle is (1.25 , 1.25√3)

∴ The circle translated Left and up

* 2(x')² + 2(y')² - 5x' - (5√3)y' - 6 = 0

∴ The answer is circle; 2(x')² + 2(y')² - 5x' - (5√3)y' - 6 = 0

* Look to the graph

- the purple circle for the equation x² - 5x + y² = 3

- the black circle for the equation (x')² + (y')² - 5x' - 5√3y' - 6 = 0

Answer:

B

Step-by-step explanation:

edge

Answer:

3x=$20

Step-by-step explanation:

well first you divide    3x/3=$20/3                      

3 can go into 20 6 times that                                                                                                          would 18 and then u would have a remainder of 2 dollars and 3 cant go into 2 so it would be .67 so x=6.67

Answer:

Part A) Option B. [tex]-4n^{3}+24n^{2}-12n[/tex]

Part B) Option A. [tex]4n^{4}-24n^{3}+12n^{2}[/tex]

Step-by-step explanation:

Part A) we have

[tex](n^{2}-6n+3)(-4n)[/tex]

the product is equal to

[tex]=(n^{2})(-4n)-6n(-4n)+3(-4n)\\=-4n^{3}+24n^{2}-12n[/tex]

Part B) When this product is multiplied by -n, the result is

we have

[tex](-4n^{3}+24n^{2}-12n)(-n)[/tex]

[tex]=(-4n^{3})(-n)+24n^{2}(-n)-12n(-n)\\=4n^{4}-24n^{3}+12n^{2}[/tex]

Answer:

line B.)

Step-by-step explanation:

2x+5y=10

5y=-2x+20

(5y/5) (2x+10/5)

y= (-2/5)x +2

Answer:

Step-by-step explanation:

Let x be the amount of colored pencils she buys, and let y be the number of jelly beans that she buys. We have the following inequalities..

4x + 2y ≤ 20     (the cost times the amount has to be less than or equal to 20)

4x + 2y > 8       (she spends more than $8)

We can rewrite the inequality like this...

8 < 4x + 2y ≤ 20

Now reduce since all coefficients are even, they can be divided by 2

4 < 2x + y ≤ 10

We want values of x and y that can satisfy the situation.  

There are many points,

If x = 1, then you can have y =3 to 8

If x = 2,  then you can have y = 1 to 6  

If x = 3, then you can have y = 1 to 4

If x = 4, then you can have y = 1 or 2

x = 5,  the y = o

Final answer:

To find the possible number of pounds of jelly beans Cindy could purchase, we set up a compound inequality considering the $4 spent on colored pencils and the $2 per pound cost of jelly beans. Solving the inequality 4 < 4 + 2x < 20 gives us the range 0 < x < 8, meaning Cindy could have bought more than 0 pounds but less than 8 pounds of jelly beans.

Explanation:

To solve the problem involving Cindy's shopping at the store, let's create a compound inequality with the following conditions: she has $20 to spend, she has already spent $4 on colored pencils, and the jelly beans cost $2 per pound. Cindy wants to spend more than $8 in total at the store, which includes the cost of the pencils and the jelly beans.

Let's define x as the number of pounds of jelly beans that Cindy can purchase. The cost of the jelly beans is $2 per pound, so the total cost for the jelly beans is $2x.

Since she spent $4 on pencils, adding the cost of the jelly beans needs to be more than $4 (to exceed the $8 total spending) but less than $20 (to stay within her budget). Hence, the compound inequality will be:

4 < 4 + 2x < 20

Now let's solve for x:

First, subtract 4 from all parts of the inequality:

0 < 2x < 16

Next, divide all parts by 2:

0 < x < 8

The solution tells us that Cindy could have purchased more than 0 but less than 8 pounds of jelly beans.

Answer:

Choice D is correct

Step-by-step explanation:

The eccentricity of the conic section is 1, implying we are looking at a parabola. Parabolas are the only conic sections with an eccentricity of 1.

Next, the directrix of this parabola is located at x = 4. This implies that the parabola opens towards the left and thus the denominator of its polar equation contains a positive cosine function.

Finally, the value of k in the numerator is simply the product of the eccentricity and the absolute value of the directrix;

k = 1*4 = 4

This polar equation is given by alternative D

[tex] ln( \sqrt{ex {y}^{2} {z}^{5} } ) \\ = ln{(ex {y}^{2} {z}^{5} ) }^{ \frac{1}{2} } \\ = \frac{1}{2} ln(ex {y}^{2} {z}^{5} ) \\ = \frac{1}{2} ln(e) + \frac{1}{2} ln(x {y}^{2} {z}^{5} ) \\ = \frac{1}{2} + \frac{1}{2} ln(x {y}^{2} {z}^{5} ) [/tex]

Answer:

Answer A  B and D

Step-by-step explanation:

This one requires and eagle eye. You have to be a bit careful with it.

The one you checked (D) is correct. There are a couple more and one is really tricky.

The first one is actually correct.

So is the second one, which I'll show first. Only C is incorrect.

======

B]

ln(e^(1/2) + ln(x^(1/2)) + ln(y^(2/2) + ln(z^(5/2))

1/2 + ln(x^(1/2)) + ln(y) + (5/2) ln(z)

1/2 + 1/2 ln(x) + ln(y) + 5/2 ln(z)

A]

(1/2) * Ln(ex*z) + ln(yz^2)

(1/2)ln(e) + (1/2)ln(x) + (1/2)ln(z) + ln(y) + lnz^2

ln(e) = 1;   ln(z^2) = 2 ln(z)

1/2 + 1/2 ln(x) + 1/2 ln(z) + ln(y) + 2ln(z)

1/2 ln(z) + 2ln(z) = 5/2 ln(z)

So put all this together

1/2 + 1/2 ln(x) + 5/2 ln(z) + ln(y) which is Exactly like B

Final answer:

To find the inverse function of a given function, interchange x and F(x) and solve for x. The steps involve replacing F(x) with y, interchanging x and y, and then solving for y.

Explanation:

To find the inverse function of F(x) = (8 - 2x)², we need to switch the roles of x and F(x) and solve for x. Step by step:

Replace F(x) with y: y = (8 - 2x)²

Interchange x and y: x = (8 - 2y)²

Solve the resulting equation for y: y = 4 - √(x) / 2

The function F(x) = (8 - 2x)² does not have an inverse function because it's not one-to-one. Instead, for all x, the inverse is a constant function [tex]\( F^{-1}(x) = 4 \)[/tex].

To find the inverse function of F(x) = (8 - 2x)², we need to switch the roles of x and y and then solve for y. So, let's start by writing y instead of F(x):

y = (8 - 2x)²

Now, our goal is to solve this equation for x. First, we'll expand the expression:

y = (8 - 2x)(8 - 2x)

y = 64 - 16x - 16x + 4x²

y = 4x² - 32x + 64

Now, to find the inverse, we switch x and y and solve for y :

x = 4y² - 32y + 64

This is a quadratic equation in terms of y, so we need to solve it. To do that, we can use the quadratic formula:

[tex]\[ y = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]

where a = 4, b = -32, and c = 64. Plugging in these values:

[tex]\[ y = \frac{{32 \pm \sqrt{{(-32)^2 - 4(4)(64)}}}}{{2(4)}} \][/tex]

[tex]\[ y = \frac{{32 \pm \sqrt{{1024 - 1024}}}}{{8}} \][/tex]

[tex]\[ y = \frac{{32 \pm \sqrt{0}}}{{8}} \][/tex]

[tex]\[ y = \frac{{32 \pm 0}}{{8}} \][/tex]

[tex]\[ y = \frac{{32}}{{8}} \][/tex]

y = 4

So, the inverse function of F(x) is [tex]\( F^{-1}(x) = 4 \)[/tex].

This result suggests that the function F(x) is not one-to-one, meaning it doesn't have an inverse that's a function. Instead, it suggests that for every value of x, the function F(x) produces the same output, which is 4. Therefore, F(x) doesn't have a unique inverse function.

Why this is so easy

Ok so, 75/5=15

15*7 =105 so the answer is 105 pages

multiply 2x+y = 3 by 2

4x + 2y = 6

x - 2y = -1

add terms (be careful about signs!)

5x + 0 = 2

Answer:

5x=5

Step-by-step explanation:

Answer:First one is D

Step-by-step explanation:

The graph passses through the pints neccessary for it to decrease by 300

Answer:

The answer is (b) moved right 3 units and moved down 3 units

Step-by-step explanation:

∵ f(x) = 4^x ⇒ red in the graph

∵ f(x) = 4^(x-3) - 3 ⇒ blue in the graph

∵ x  becomes x - 3 ⇒ means:

 The graph moved right 3 units

∵ f(x) = 4^x becomes 4^(x-3) - 3 ⇒ means:

  The graph moved down 3 units

∴ The answer is (b)

The graph of f(x) = 4ˣ - 3  is shifted down 3 units compared to the graph of f(x) = 4ˣ

An exponential function is in the form:

y = abˣ

Where y,x are variables, a is the initial value of y and b is the multiplication factor.

The graph of f(x) = 4ˣ - 3 and f(x) = 4ˣ is attached.

The graph of f(x) = 4ˣ - 3  is shifted down 3 units compared to the graph of f(x) = 4ˣ

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Answer:

The contribution is $ [tex]16.92\\[/tex] per biweekly payment

Step-by-step explanation:

Salary received in each of the [tex]26 \\[/tex] pay is

[tex]\frac{2}{100} * \frac{22000}{26} \\= 16.92\\[/tex]

Final answer:

To take full advantage of your company's retirement match, contribute at least $16.92 from each bi-weekly paycheck to your retirement account, which is 2% of your annual salary divided by 26 pay periods.

Explanation:

To determine how much you should contribute to the retirement account each pay period to take full advantage of the company match, you need to calculate 2% of your annual salary and then divide that number by the number of pay periods in a year. Here's the step-by-step calculation:

To fully utilize the company's matching program, you should contribute at least $16.92 from each bi-weekly paycheck to your retirement account.

Answer:

{0.16807, 0.36015, 0.3087, 0.1323, 0.02835, 0.00243}

Step-by-step explanation:

The expansion of (p+q)^n for n = 5 is ...

(p+q)^5 = p^5 +5·p^4·q +10·p^3·q^2 +10·p^2·q^3 +5·p·q^4 +q^5

When the probability p=0.3 and q = 1-p = 0.7 the terms of this series correspond to the probabilities of 5, 4, 3, 2, 1, and 0 favorable outcomes out of 5 trials.

For example, p^5 = 0.3^5 = 0.00243 is the probability of 5 favorable outcomes in 5 trials where the probability of each favorable outcome is 0.3.

___

The attachment shows the calculation of these numbers using a graphing calculator. It lists them in reverse order of the expansion of (p+q)^5 shown above, so that they are the probabilities of 0–5 favorable outcomes in the order 0–5.

The largest volume that the box can have is 2.25 ft^3, and it's obtained when x = 0.5 ft. This came from a mathematical analysis of the volume function V(x) = 4x^3 - 12x^2 + 9x.

Given that a square is cut from each corner of the cardboard to form an open box, we can come up with the following: The width of the base, represented by y, would be equal to the initial width of the cardboard (3 ft) minus two times the sides of the squares being cut out (2x), so y = 3 - 2x. Part c: will be the Volume of the box which is given by V = x * y^2, substituting for y from the relation obtained above we get. Part d: V = x * (3 - 2x)^2. Part e: is just the simplification of the equation obtained in part d: V(x) = 4x^3 - 12x^2 + 9x. Part f: To find the maximum volume, we need to find the critical points of the V(x) function, these are obtained by setting the derivative of the function equal to zero, solving for x will give x = 0.5 and x =1.5 but since x > 1.5 would give a negative y, the maximum volume is obtained at x = 0.5, substituting this x into the V(x) equation gives V = 2.25 ft^3.

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By using elimination to subtract the second equation from the first, we solve for x and then substitute x back into one of the original equations to solve for y, finding the solution as the ordered pair (1, -1).

To solve the system using elimination, we look at the given equations:

1) 5x + 4y = 1
2) -3x + 4y = -7

The goal is to eliminate one variable to solve for the other. In this case, we can subtract the second equation from the first one since they both have the same coefficient for y, which will eliminate the y variable.

Now that we have found x, we can substitute x into one of the original equations to find y:

5(1) + 4y = 1

The solution to the system is (1, -1), which is an ordered pair representing the x and y values that satisfy both equations.

Answer:

89

Step-by-step explanation:

86+78+80+99+99+92+86 = 620

620/7 = 88.57142857

And since you requested the nearest whole number the 88 turns into an 89 due to the fact that the tenth place is a 5 (or greater).

Answer:

Step-by-step explanation:

Answer is G

Graph [G] will be the correct graph representing the  lifeguard’s weekly earnings in dollars for working [h] hours over 40.

The general equation of a straight line is -

y = mx + c

Where -

[m] is the slope of the line.

[c] is the y - intercept.

Given is A lifeguard earns $320 per week for working 40 hours plus $12 per hour worked over 40 hours. A lifeguard can work a maximum of 60 hours per week.

For over 40 hours of work, the graph on the y - axis will start from the point (0, 320). Of the two possible graphs, we have to find the find whose slope will be 12 since, the lifeguard receives $12 per hour.

Slope of graph [F] = (400 - 320)/(10 - 0) = 80/10 = 8

Now, slope of graph [G] = (500 - 320)/(15 - 0) = 180/15 = 12

Graph [G] is the correct choice.

Therefore, Graph [G] will be the correct graph representing the  lifeguard’s weekly earnings in dollars for working [h] hours over 40.

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Answer:

x = 13.9

Step-by-step explanation:

With respect to the angle shown, we have the hypotenuse (the side opposite the 90 degree angle) and we have the adjacent side (which is the side labeled x). thus we can use the ratio "cosine" to solve this.

The ratio of cosine is defined as:

[tex]Cos\theta=\frac{Adjacent}{Hypotenuse}[/tex]

Where adjacent and hypotenuse are the respective sides and [tex]\theta[/tex] is the angle

Thus, we can now write:

[tex]Cos\theta=\frac{Adjacent}{Hypotenuse}\\Cos(35)=\frac{x}{17}\\Cos(35)*17=x\\x=13.9[/tex]

The first answer choice is right, x = 13.9

The value of X to the nearest tenth in the triangle is 13.9.  

We have the neighboring side, which is the side with the letter x, and the hypotenuse, which is the side across from the 90-degree angle, with regard to the angle displayed.

Therefore, the ratio "cosine" can be used to solve this.

The definition of the cosine ratio is:  [tex]Cos \theta[/tex] = Adjacent side / hypotenuse.

where the angle and the corresponding sides are called the hypotenuse and adjacent.

So that we may write now:

[tex]Cos(35)= \frac{x}{17}[/tex]

[tex]Cos(35) \times 17 = x[/tex]

Therefore 13.9 = x  .

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Final answer:

To find the length (c) of a rectangle when the perimeter is 30 inches, we use the formula c = (P - 2w) / 2, with P representing the perimeter and w the width.

Explanation:

The perimeter of a rectangle is given by the formula P = 2l + 2w, where P is the perimeter, l is the length, and w is the width. Given that the perimeter (P) is 30 inches, and we are looking to find the formula that shows the length of side c assuming c represents either the length or the width of the rectangle. Let's say c represents the length for this context. Therefore, the formula rearranges to c = (P - 2w) / 2. We use this formula when we know the perimeter and the width (w), and we want to find the length (c).

y=×^2+23

Answer letter B

×=y-23

Since he has four cuts for each pizza, jason has 8 pizzas

Answer:

The exact form of [tex]\tan(\frac{7\pi}{8})[/tex] is [tex]-\sqrt{2}+1[/tex]

Step-by-step explanation:

We need to find the exact value of [tex]\tan(\frac{7\pi}{8})[/tex] using half angle identity.

Since, [tex]\frac{7\pi}{8}[/tex]  is not an angle where the values of the six trigonometric functions are known, try using half-angle identities.

[tex]\frac{7\pi}{8}[/tex]  is not an exact angle.

First, rewrite the angle as the product of [tex]\frac{1}{2}[/tex] and an angle where the values of the six trigonometric functions are known. In this case,

[tex]\frac{7\pi}{8}[/tex] can be written as ;

[tex](\frac{1}{2})\frac{7\pi}{4}[/tex]

Use the half-angle identity for tangent to simplify the expression. The formula states that [tex] \tan \frac{\theta}{2}=\frac{\sin \theta}{1+ \cos \theta}[/tex]

[tex]=\frac{\sin(\frac{7\pi}{4})}{1+ \cos (\frac{7\pi}{4})}[/tex]

Simplify the numerator.

[tex]=\frac{\frac{-\sqrt{2}}{2}}{1+ \cos (\frac{7\pi}{4})}[/tex]

Simplify the denominator.

[tex]=\frac{\frac{-\sqrt{2}}{2}}{\frac{2+\sqrt{2}}{2}}[/tex]

Multiply the numerator by the reciprocal of the denominator.

[tex]\frac{-\sqrt{2}}{2}\times \frac{2}{2+\sqrt{2}}[/tex]

cancel the common factor of 2.

[tex]\frac{-\sqrt{2}}{1}\times \frac{1}{2+\sqrt{2}}[/tex]

Simplify,

[tex]\frac{-\sqrt{2}(2-\sqrt{2})}{2}[/tex]

[tex]\frac{-(2\sqrt{2}-\sqrt{2}\sqrt{2})}{2}[/tex]

[tex]\frac{-(2\sqrt{2}-2)}{2}[/tex]

simplify terms,

[tex]-\sqrt{2}+1[/tex]

Therefore, the exact form of [tex]\tan(\frac{7\pi}{8})[/tex] is [tex]-\sqrt{2}+1[/tex]

The exact value of [tex]\( \tan\left(\frac{7\pi}{8}\right) \)[/tex] is [tex]\( \frac{2 - \sqrt{2}}{\sqrt{2}} \)[/tex].

To find the exact value of [tex]\( \tan\left(\frac{7\pi}{8}\right) \)[/tex] using the half-angle identity, we proceed as follows:

1. Identify the appropriate half-angle identity:

  The tangent half-angle identity is given by:

  [tex]\[ \tan\left(\frac{\theta}{2}\right) = \frac{1 - \cos(\theta)}{\sin(\theta)} \][/tex]

2. Apply the identity for [tex]\( \theta = \frac{7\pi}{4} \)[/tex] :

  First, determine [tex]\( \theta = \frac{7\pi}{4} \)[/tex] , then find [tex]\( \frac{\theta}{2} \)[/tex].

3. Calculate [tex]\( \cos\left(\frac{7\pi}{4}\right) \)[/tex] and [tex]\( \sin\left(\frac{7\pi}{4}\right) \)[/tex]:

  [tex]\[ \cos\left(\frac{7\pi}{4}\right) = \cos\left(\frac{2\pi + \frac{\pi}{4}}{2}\right) = \cos\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} \][/tex]

  [tex]\[ \sin\left(\frac{7\pi}{4}\right) = \sin\left(\frac{2\pi + \frac{\pi}{4}}{2}\right) = \sin\left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2} \][/tex]

4. Apply the half-angle identity:

  [tex]\[ \tan\left(\frac{7\pi}{8}\right) = \frac{1 - \cos\left(\frac{7\pi}{4}\right)}{\sin\left(\frac{7\pi}{4}\right)} = \frac{1 - \frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} \][/tex]

5. Simplify:

  [tex]\[ \tan\left(\frac{7\pi}{8}\right) = \frac{2 - \sqrt{2}}{\sqrt{2}} \][/tex]

Therefore, [tex]\( \tan\left(\frac{7\pi}{8}\right) = \frac{2 - \sqrt{2}}{\sqrt{2}} \)[/tex].

Using the half-angle identity for tangent, we substituted [tex]\( \theta = \frac{7\pi}{4} \)[/tex] and calculated [tex]\( \cos\left(\frac{7\pi}{4}\right) \)[/tex] and [tex]\( \sin\left(\frac{7\pi}{4}\right) \)[/tex] to find [tex]\( \tan\left(\frac{7\pi}{8}\right) \)[/tex] in exact form.

Answer:

3.7  liters

Step-by-step explanation:

The required amount of water in each bottle is 0.5 gallon.

Given that,
2.5 gallons of water are poured into 5 equally sized bottles, how much water is in each bottle is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Total volume = 2.5 gallon,
Number of bottle = 5,
Gallon per bottle = 2.5 / 5 = 0.5 gallon per bottle

Thus, the required amount of water in each bottle is 0.5 gallons.

Learn more about simplification here:

https://brainly.com/question/12501526

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Answer:

-1/2

Step-by-step explanation:

Rise in X / Rise in Y

1 / 2 = 1/2

The answer to ur question is slope =-1/2