On May 8, 2010, a team of kayakers sets a record time for 5h 19 min 17 sec to kayak across the length of Loch Ness, Scotland, UK, a distance of 20.5 mi. When the kayakers were four times as far from the starting point as from the finish, how many miles were traveled?

The single inequality y > |x + 2| is equivalent to:

4. y > x + 2

y < –x – 2

It should be noted that an inequality is simply used to show the relationship between the expressions that aren't equal.

The non-negative value of a real number x, regardless of its sign, is its absolute value or modulus | x |. For instance, 5 has an absolute value of 5, and 5 has a value of 5. One way to think about a number's absolute value is as its distance from zero on the real number line.

It should be noted that based on the information, the inequality is:

y > |x + 2|. This is the positive part of the modulus.

This is the same as y < –x – 2 when the signs are changed. This is the negative part of the modulus.

In conclusion, the correct option is 4.

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The slope of the line is the ratio of the rise to the run, or rise divided by the run.  slope of line is 4/3.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given two points are (3,0) and (0,-4)

y₂=-4, y₁=0, x₁=3, x₂=0

Substitute values in formula

m=-4-0/0-3

m=4/3

Hence slope of line is 4/3.

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Answer:

35ft

Step-by-step explanation:

ignore 11 and 13, you only need the height and one side that corresponds to it. 14*5=70

70/2=35

For the rectangle given, considering its diagonal properties, the value of x=4, while the angle VUR=36°

To answer this question, let us recall the following:

Hence;

the lengths RV and SV are

so, 3x+8=6x-4

6x-3x=8+4 [collecting like terms]

3x=12

when we divide both sides of the equation by 3, we have the value of x=4.

the angles VRS and VRU are complementary

so, 54°+VRU = 90°

VRU = 90°-54°

VRU = 36°

The triangle RUV is an Isosceles

so, angles VRU and VUR are equal, therefore angle VUR = 36°.

We can reduce from our workings that the value of x = 4 and the angle VUR is 36°.

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The operations that would increase the value of a given number include the following:

A. Multiply the number by 10.

D. Divide the number by 0.1.

The operations that would decrease the value of a given number include the following:

B. Multiply the number by 0.1.

C. Divide the number by 10.

Multiplication is a mathematical operation which can be used to increase the value of a given number, especially by multiplying the number by a value that is greater than 1. Similarly, the value of a given number can also be increased by dividing it by a number that is lesser than 1 such as 0.1

Multiplication is a mathematical operation which can be used to decrease the value of a given number, especially by multiplying the number by a value that is lesser than 1. Similarly, the value of a given number can also be decreased by dividing it by a number that is greater than 1 such as 10.

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Answer:

given in picture

Step-by-step explanation:

(-2,10) (-1,7) (0,4) (1,1) (2,-2) (3,-5)

Answer: Draw a line from (2, 2) to (6, 2) for the run.

Draw a line from (6, 2) to (6, 8) for the rise.

The slope of the line is represented by rise/run, so in this case it would be 6/4.

The system of equations has two solutions, these are:

(-0.89, 2.33) and (1.4, 9.2)

Here we have the following system of equations:

y = 3x + 5

y = 4x² + x

We can see that y is already isolated in both equations, so we can write the equation:

3x + 5 = y = 4x² + x

3x + 5 = 4x² + x

now we can solve this for x, this is just a quadratic equation:

3x + 5 - 4x² - x = 0

-4x² + 2x + 5 = 0

Using the quadratic formula, we can see that the two solutions are:

[tex]x = \frac{-2 \pm \sqrt{2^2 - 4*(-4)*5} }{2*-4} \\\\x = \frac{-2 \pm 9.17}{-8}[/tex]

So the solutions are:

x = (-2 +9.17)/-8 = -0.89

x = (-2 - 9.17)/-8 = 1.4

Evaluating the linear equation in these values, we get:

y = 3*(-0.89) +5 = 2.33

y = 3*(1.4) + 5 = 9.2

So the solutions of the system are:

(-0.89, 2.33) and (1.4, 9.2)

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Answer:

C) angle 7

Step-by-step explanation:

all i know is angle 5 and 7 are corresponding angles, the only other practical option could be angle 3 but angle 3 and angle 5 have no correlation with one another

To find the probability that the mean IQ score of people in the sample is less than 98, first we need to convert the value into z-score by using the formula:

Then, when x=98:

By checking in a standard normal table z=-0.1333 has a p-value=0.4471.

Then the probability is 0.4471 that also can be expressed as 44.71%

Solution

We will consider each and every statement and the translate what it mean appropriately

Horizontally translate 4 units left

That means

The option to choose is

Vertically translate 2 units down

That basically mean is to subtract 2

That is

Shrunk vertically by one half

That is

The image below shows what to select

Answer:

g +  18 = 69

Step-by-step explanation:

Translate this sentence into an equation. Goran's score increased by 18 is 69. Use the variable g to represent Goran's score.

g +  18 = 69

solve:

g +  18 = 69

subtract 18 from both sides:

g +  18 - 18 = 69 - 18

g = 51

Answer:

7:8:9=21/2:12:27/2

Step-by-step explanation:

12/8=3/2

3/2*7=21/2

3/2*9=27/2

Pls brainliest

Answer:

see below

Step-by-step explanation:

sum of angles in right triangle is 180

90 + 50 = 140

b = 180 - 140 = 40 deg

find c

cos(50) = 20/ c

c = 20/cos(50) = 31.1

find a

tan(40) = 20/a

a = 20/tan(40) = 23.8

Using the sales tax, the amount of money she still needs is $5.72

A sales tax is a consumption tax imposed by the government on the sale of goods and services.

Jane wants to buy a CD for $12. She has saved $7.

The amount she needs if 6% sales tax is added to the cost can be calculated as follows;

Let's find the sales tax,

sales tax = 6% of 12

sales tax = 6 / 100 × 12

sales tax = 72 / 100

sales tax = $0.72

Therefore,

amount she needs to save = 12 + 0.72 - 7

amount she needs to save = 12.72 - 7

amount she needs to save = $5.72

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xw + 5w - 17 = 0 is the required equation.

Given,

Ali buys 2 comic books a week.

After 5 weeks he has 17 comic books this year.

Solution:

Let w be weeks and c be comic books.

Since Ali buys 2 comic books a week.

1w = 2c

For 5 weeks, he would have,

5w = 10c, if he bought 2books per week.

But he had 17 books,

i.e, he would have collected some books last year.

Let x be the no of unknown weeks last year.

(x + 5)w = 17c

(x+5)w-17c= 0

xw + 5w - 17 = 0 is the required equation.

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Answer:

decreasing: (-∞,3)

increasing: (3,∞)

Step-by-step explanation:

let x be the number of ballpoint boxes and y the number of felt tip boxes

so we get

so we get that the number of felt tip boxes is 6, and therefore the number of ballpoint boxes is 6*3=18

Answer:

a. [tex]y = 21.5x + 376[/tex]

b. [tex]569.5[/tex] or with rounding, [tex]570[/tex].

Step-by-step explanation:

To set up a linear equation in slope-intercept form, we use the formula y=mx+b, where m is slope given by the formula m= [tex]\frac{y_{2}-y_1 }{x_2-x_1}[/tex], and b is the y-intercept (the value of y when x=0). It is given that x is the year, where 2005 is x=0, and y is the number of assistants in thousands, meaning at x=0 (the year 2005), y=376 (376,000 medical assistants). This can be written as the point (0, 376), which is our y-intercept. Using the formula for slope, the slope of this line is found to be [tex]\frac{215}{10}[/tex], or 21.5 ([tex]\frac{591-376}{10-0}[/tex]). This gives us the equation [tex]y = 21.5x + 376[/tex].

For part (b), simply plug in a value for x, then solve for y. The given value is the year 2014, which can be written as x=9 (x=0 is 2005, x=1 is 2006, etc.). This gives us the equation [tex]y=21.5(9)+376[/tex], which gives us y=569.5. However, since this is a real-world problem, you can not have "half" a person, so this rounds up to 570.

The number of DVDs shipped is, 20000 less that the previous year ,

Therefore, the integer -20000 can be used to describe the change.

Answer:

a^3

Step-by-step explanation:

a^5/a^2

When dividing exponents with the same base, we can subtract the exponents

a^ ( 5-2)

a^3

Answer:

a³

Step-by-step explanation:

We know that,

[tex] \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ [/tex]

In the same way, let us solve the given sum.

[tex] \frac{ {a}^{5} }{ {a}^{2} } = {a}^{5 - 2} = {a}^{3} \\ [/tex]

Answer:80100

Step-by-step explanation:

Since "per cent" means parts per hundred, if we can convert the fraction to have 100 as the denominator, we then know that the top number, the numerator, is the percentage. Our percent fraction is 80/100, which means that 80100 as a percentage is 80%.

The difference of population in these two cities are 85900- 3200

= 82,700

Subtract the largest number from the lowest number to determine the difference between two integers. The difference between the two numbers is the product of this sum. As a result, there are 55 between the numbers 45 and 100.

Given: Population of city A= 8.59 x 10^4

and population of city B = 3.2 x 10^3

This can also be written as :

Population of city A= 85,900

and population of city B = 3200

Thus the difference of population in these two cities are 85900- 3200

= 82,700

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Answer:

-100000

Step-by-step explanation:

[tex](-1000)^{5/3} \\ \\ =(\sqrt[3]{-1000})^5 \\ \\ =(-10)^5 \\ \\ =-100000[/tex]

Answer:

22.4%

Step-by-step explanation:

There were twice as many sapodillas as paw paws--take the sapodillas as 2 units and paw paws as 1 unit.

Form an equation.

2u + 1u + 82 = 250

Simplify and solve for 1 unit.

3u = 168

1u = 56

Number of paw paws is 56.

Formula for finding percentage of an object is given as (number of object/total number of items) x 100.

Percentage of paw paws

= (56/250) x 100

= 22.4%

Hello!

To solve for the y-values in the table:

 [tex]\hookrightarrow \text{ Must plug in the corresponding x's value into the equation}[/tex]

             [tex]y = 2(-2) + 3 = -4 + 3 = -1[/tex]

             [tex]y = 2(0) + 3 =3[/tex]

            [tex]y = 2(1) +3=5[/tex]

           [tex]y = 2(3) + 3=6 + 3=9[/tex]

Hope that helps!