Olivia is an athlete. During training this morning, she ran three
laps. It took her 5/6
minute to finish the first lap. The second lap
took her 1/12
more minutes than the first lap. The third lap took her
1/10
less minutes than the second lap. How much time did it take
her to finish the third lap?

The value of line integral of the line segment from (5,4) to, (0,0) is 90.

Given that C is the line segment from (5,4) to (0,0):-

So, our first task is to calculate the line segment

After calculating the line segment, we will be able to calculate the line integral

We know that the equation of line is -

y - y1 = (y1 - y2)/ (x1 - x2) * (x - x1)

So now,

y - 0 = (4 - 0)/ (5 - 0) * (x - 0)

y = 4/5 x

5x - 4y = 0 -----------> (1)

A line integral is used to calculate the area covered by that line

c1 = ∫₀⁴ 5x dx ------> (2)

c2 = ∫₀⁵ -4y dy -----> (3)

c1 = [ 5 x²/2 ]₀⁴ = 5 * ( 4² - 0)/2 = 40

c2= [ -4 y²/2 ]₀⁵ = -4 * ( 5² - 0)/2 = 50

The value of the line integral: c1 + c2 = 40 + 50 = 90

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Answer:

1. ΔCDE≅ΔJEH

2. ΔIHG≅ΔIHD

3. ΔIHJ≅ΔIXT

4. ΔIJT≅ΔJIH

5. ΔEFD≅ΔDKJ

6.ΔGWY≅ΔGHI

The value of the given expression cos(π/2 - sin⁻¹(1/2)) will be equal to 1/2.

The fundamental six functions of trigonometry have a range of numbers as their result and a boundary input value that is the angle of the right triangle.

As per the given information in the question,

cos(π/2 - sin⁻¹(1/2))

Use the formula given below,

cos(π/2 - θ) = sin θ

From the above formula,

sin(sin⁻¹ (1/2))

= 1/2

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Answer:

not a function.  There cannot be mutiple y-values under one x value.  

Step-by-step explanation:

The system of linear equations, y = 2x + 4 ;

2y = x + 6 has a unique solution and it is a consistent system of linear equations.

An ordered pair that satisfies all equations of the system is the solution of the system. A system of linear equations can have one solution, no solution, or an infinite number of solutions. The systems of equations can be classified according to the number of solutions. If a system has at least one i.e unique solution, it is called consistent. We have, the system of equations is

y = 2x + 4 => 2x - y + 4 = 0 --(1)

2y = x + 2 => x - 2y + 6 = 0 --(2)

Comparing the equation (1) with a₁x + b₁y + c₁=0

and equation(2) with a₂x + b₂y + c₂=0

We get, a₁ = 2 , a₂= 1 , b₁ = -1 , c₁= 4 , b₂= -2 , c₂ = 2

Now, compute the ratio of coefficients of variables .

a₁/a₂ = 2/1 , b₁/b₂ = -1/-2 = 1/2 , c₁/c₂= 4/6 = 2/3

=> a1/a2 ≠ b1/b2 ,

here, both lines are intersect at a point and a unique solution exist for pair of linear equations. In such a case , the pair of linear equations is said to be consistent. Thus, system is consistent.

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Complete question:

Is the system of equation is consistent and

independent consistent and dependent or inconsistent?

y = 2x + 4 , 2y = x + 6

the perimeter of the pentagon greater than 26 centimeters is given by

23.51

Given that a pentagon with 5  sides of equal length and 5 interior angles of equal measure is inscribed in a circle

The circle has area of 16 pi sq cm.

Hence radius of circle = 4 cm

The pengagon each side would be a chord of equal length subtending angle 72 at the centre.

visualize the triangle made by one side of pentagon with centre.  This is isosceles with angles 72, 54 and 54

Use sine angle for this triangle.

, where R = radius =4 and s = side of pentagon.

s= 4.702

Perimeter = 5s = 23.5114 cm

Perimeter not greater than 26 cm.

If origin is at the centre then two vertices would be (4,0) (4cos 72, 4sin72),(4cos 144, 4 sin 144) and so on.

Longest diagonal = distance between (4,0) and (4cos 144, 4 sin 144)

= (-3.236, 2.351) and (4,0)

=7.608

Yes greater than 8 cm

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The statement would no longer be true if you did not flip the signs.

Example: 1 < x < 2 multiplied by (-1) equals -2 < x < -1, because you can't have a number that is greater than -1, and less than -2 at the same time.

we need 31/2 pounds mirepoix to make 31/2 gallons of soup.

let we need x% (percent) of mirepoix to make 1 gallon of soup

given we have 1 pound of mirpoix which yeilds 1 gallon soup of soup

so total amount of mirepoix that required in the solution is = [tex]\frac{x}{100} *1 pound[/tex]

so x/100 = 1 gallon / pound

we will use this equation for further calculation

let we need y pounds of mirepoix to make 31/2 gallon of soup  ans we know that x% of mirepoix is required for this solution.

so [tex]\frac{x}{100} * y = 31/2[/tex]

ans in the above equation x/100 =1 gallon / pound

so  1 * y= 31 /2

and hence y = 31/2 pounds

so we need 31/2 pounds of mirepoix to form requied amount of soup.

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Answer: the slope is [tex]\frac{4}{2}[/tex] which can be simplified to just 2.

Step-by-step explanation:

You can use the equation [tex]\frac{y2-y1}{x2-x1}[/tex] to find the slope of a line. In this case, I chose to use the coordinates (-4,0) and (-6,-4), it doesn't matter which you choose as the (x1,y1) and (x2,y2) coordinates. So, [tex]\frac{-4-0}{-6-(-4)}[/tex] becomes [tex]\frac{-4}{-2}[/tex] which is the same as [tex]\frac{4}{2}[/tex], which is equal to 2. you can repeat this with the other points given to check your answer.

The slope of the line passing through the given points is equal to 2 .

The slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate of that line. The slope of a line is the measure of the tangent of the angle made by the line with the x - axis. It is represented by m: m = y₂-y₁ / x₂ - x₁

Given here, are the points P (-10, -12), Q(-8, -8), R(-6, -4),S (-4, 0)

Now the slope of a line is constant for any two points that lie on a line.

therefore, slope of the line that passes through P,Q,R,S  is

m = -8-(-12) /-8-(-10)

    = 2

 or m= 0-(-4) /-4-(-6)

         = 2

clearly the slope is equal to 2 in either case that's because the line passes through all the four points.

Hence,  the slope of the line passing through the given points is equal to 2.

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We need to start by choosing some 10 integers so that we can ensure that when they are divided by 11, at least two of the integers will give the same remainder.

The following is the explanation:

If you divide a number by 11, the answer will be a fraction. There are 11 remainders which might occur, which are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

If for example we choose one number and divide it by 11, there is a chance that the remainder may be any of the 11 (0 reminders 1). Therefore, if we choose 10 numbers, we will have the opportunity to pick 10 unique remainders, ranging from 0 to 10.

In conclusion, if we select one more integer, that is we pick 10 integers, then at least two of them would have the same remainder since there are only 10 remainders.

Because of this, we need to choose 10 numbers such that we can guarantee that at least two of them will provide the same remainder when they are divided by 11.

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Answer:

58.3

Step-by-step explanation:

divide the length value by 2.54

58.2677

Answer:

58,3 inches

Step-by-step explanation:

1 inch = 2.54 cm

[tex]148 \: cm \:*\:\frac{1\:inch}{2.54\: cm} = 58,267716535433070866141732283465\\\\148\: cm=58,3 \:inches[/tex]

Answer:

Domain (interval notation) : [-4,4)

Range (interval notation): [1,4)

Domain (inequality notation): [tex]-4\leq x < 4[/tex]

Range (inequality notation): [tex]1\leq x < 4[/tex]

Step-by-step explanation:

Domain is the x-values of a function

Range is the y values of a function

Answer:

[tex]x=\dfrac{1}{2} \pi + 2\pi n[/tex]

[tex]x=\dfrac{3}{2}\pi +2 \pi n[/tex]

[tex]x=\dfrac{1}{6}\pi+2 \pi n[/tex]

[tex]x=\dfrac{5}{6}\pi+2 \pi n[/tex]

Step-by-step explanation:

Given trigonometric equation:

[tex]\sin x \cos x &= \dfrac{1}{2} \cos x[/tex]

Rearrange the equation so that it equals zero:

[tex]\begin{aligned}\sin x \cos x &= \dfrac{1}{2} \cos x\\2 \sin x \cos x &= \cos x\\2 \sin x \cos x - \cos x &=0\\ \cos x (2 \sin x - 1)&=0\end{aligned}[/tex]

Apply the zero-product property.

Case 1

[tex]\begin{aligned}\cos x &=0\\x&=\cos^{-1}(0)\\x&=\dfrac{1}{2} \pi +2\pi n, \; \dfrac{3}{2}\pi +2 \pi n\end{aligned}[/tex]

Case 2

[tex]\begin{aligned}2\sin x - 1& = 0\\2 \sin x & = 1\\\sin x & = \dfrac{1}{2}\\x&=\sin^{-1}\left(\dfrac{1}{2}\right)\\x & = \dfrac{1}{6} \pi+2 \pi n, \; \dfrac{5}{6} \pi +2 \pi n\end{aligned}[/tex]

Answer: D

Step-by-step explanation:

Answer:D

Step-by-step explanation: A triangle has no diagonals

Answer:

(2x + 1)^2 = 7

Step-by-step explanation:

To write the quadratic equation 4x^2 + 8x - 10 = 0 in vertex form, we need to first complete the square. To do this, we need to add and subtract the same value to the quadratic term and the linear term so that the resulting quadratic has the form (x - h)^2 = k.

In this case, we need to add and subtract the square of half of the coefficient of the linear term, which is 8/2 = 4. This gives us the equation:

4x^2 + 8x + 4 - 4 - 10 = 0

This simplifies to 4(x^2 + 2x + 1) - 14 = 0, which can be rewritten as (2x + 1)^2 - 7 = 0.

To put this in vertex form, we need to rewrite the right side of the equation as a perfect square, so we add 7 to both sides to get (2x + 1)^2 = 7.

Then, we take the square root of both sides to get 2x + 1 = ±√7. We can then solve for x to get x = -1/2 ± √7/2.

Therefore, the equation 4x^2 + 8x - 10 = 0 can be written in vertex form as (2x + 1)^2 = 7.

If it is a line that does go through 0,0 then it is NOT PROPORTIONAL

Answer:

all real numbers

Step-by-step explanation:

the graph continues to the left and to the right because there are arrows

The probability that both coins will land on heads is 50%. In other words, each coin toss is an independent event and each coin has an equal chance of landing on either heads or tails.

This is because the result of the first coin toss does not influence the outcome of the second coin toss, meaning each toss is an independent event with a 50% chance of landing on heads.The probability that both coins will land on heads is 50%. This is because the result of the first coin toss does not influence the outcome of the second coin toss. In other words, each coin toss is an independent event and each coin has an equal chance of landing on either heads or tails. This means that the probability of both coins landing on heads is the same as the probability of either coin landing on heads, which is 50%. Therefore, the probability that both coins will land on heads is 50%.

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Answer:_18

replace _4 instead of x

-5*-4=_20

_20+2=_18

Step-by-step explanation:

The graph of the first five terms can be seen in the image at the end.

We know that we have an arithmetic sequence:

3, -10, -23, -36

The common difference is what we get when we subtract two consecutive terms, we will get:

d = -36 - (-23) = -3

Then the recursive relation is:

a(n) = a(n - 1) - 13

At the moment we know:

a(1) = 3

a(2) = -10

a(3) = -23

a(4) = -36

Then fifth term will be:

a(5) = a(4) - 13 = -36 - 13 = -49

Now to graph it, we use the "n-th" value as the input, then we need to graph the five points (1, 3), (2, -10), (3, -23), (4, -36), (5, -49).

The graph can be seen in the image below:

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Answer: No, Gwen's ratio is 3:5 soup to total, and Bernard's is 1:2 soup to total

Step-by-step explanation:

Bernard donates 30 cans, 15 of which are soup.

15soup/30cans = 1soup/2cans = 1 soup to 2 total cans

Gwen donates 20 cans, 12 of which are soup.

12soup/20cans = 3soup/5cans = 3 soup to 5 total cans

In general, a change in the price of the product causes a movement along the demand curve; and a change in production cost and related factors causes a shift in the supply curve.

The demand curve is a graphical representation of the relationship between the price of a good or service and the quantity demanded for a given period of time. In a typical representation, the price will appear on the left vertical axis of the graph, and the quantity demanded on the horizontal axis.

The supply curve is a graphic representation of the relationship between product price and quantity of product which a seller is willing and able to supply. Product price is measured on the vertical axis of the graph, and the quantity of product supplied on the horizontal axis.

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The actual area of the park is 376068 meters squared. If A scale drawing of a rectangular park had a scale of 1 cm = 110 m.

The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the product of its length and breadth.

Given

A scale drawing of a rectangular park had a scale of 1 cm = 110 m.

Length of rectangle,

7.4  × 110

814m

Breadth of rectangle,

4.2 × 110

462 m

Area of rectangle

length × breadth

814 ×462

376068

The actual area of the park is 376068 meters squared. If A scale drawing of a rectangular park had a scale of 1 cm = 110 m.

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Answer:

15x +147

Step-by-step explanation:

The probability that no letters are repeated is 0.0015, rounded to the nearest thousandth.

The probability that no letters are repeated is calculated using the formula P = n! / (r^n * (n-r)!)

, where n is the total number of letters and r is the number of each letter.

The numbers here are n = 7 and r = 1.

This means the probability of no letters being repeated is 7! / (1^7 * 6!) = 0.0015.

This can be rounded to the nearest thousandth, giving the answer of 0.0015.

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an instance where a region's u.s. land surface has changed subsided due to groundwater withdrawal. The land surface in the Central Valley has subsided by as much as 30 feet in distance some areas due to unsustainable groundwater withdrawals.

The most famous case of land subsidence due to groundwater withdrawal in the United States is the Central Valley of California. The land surface in the Central Valley has subsided by as much as 30 feet distance in some areas due to unsustainable groundwater withdrawals. In addition to land subsidence, the unsustainable withdrawals have caused significant groundwater depletion, surface water contamination, and reduced agricultural productivity.

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Answer:

d = 0

Step-by-step explanation:

We have the equation

7.5d = 2.5d

We divided both sides by factors and get

d = 0

Value of d is 0.

According to question

7.5d=2.5d

Lin divides each side by 2.5d

∴7.5d÷2.5d=2.5d÷2.5d

⇒3=1

which is not possible and Lin is doing wrong

Elena subtract 2.5d from each side

∴7.5d-2.5d=2.5d-2.5d

⇒5d=0

⇒d=0

So Elena is right and the value of d is 0.

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A. Let x be a real number,B. Add x to both sides of the equation, then C. x - x = 0,D. Therefore, x = 0

A. Let x be a real number - This step states that we are selecting a real number for which we will prove that it is equal to 0. This step does not contain an error.

B. Subtract x from both sides of the equation - This step does not contain an error as it is the first step in the process of proving that the real number is equal to 0.

C. x - x = 0 - This step contains an error, as it doesn't provide enough information to prove that the real number is equal to 0.

D. Therefore, x = 0 - This step also contains an error, as it assumes that the proof is correct without providing any evidence.

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Answer: 55%

the percent of the female participants is: [tex]\frac{121}{121+99}.100=\frac{121}{220}.100=55[/tex] (%)

Step-by-step explanation: