Krystal throws a rappelling rope at a speed of 10 m/s down a 50 m cliff. When will the rope hit the ground? Use the drop-down to put the correct order to solve for when the rope will hit the ground.

X = 7 & -7/2

First, use the distributive property to simplify the equation:

2 - 5/(x+7) = -7/(x-3)(x+7)

2(x-3)(x+7) - 5(x-3) = -7(x+7)

2x2 + 7x - 6x - 15 = -7x - 49

2x2 -13x - 49 = 0

This equation can be solved by factoring the binomial:

2x2 -13x - 49 = 0

2x(x-7) - 7(x-7) = 0

(2x-7)(x-7) = 0

Therefore, the solution for x is x = 7 and x = -7/2.

Learn more about distributive property

brainly.com/question/5637942

#SPJ11

1:1.618 (the golden ratio).

To construct a golden spiral that involves a golden rectangle with length 4 meters, first draw a 4 meter long line. Divide it into two segments, such that the longer segment has a ratio of 1:1.618 (the golden ratio) to the shorter segment.

Draw a right angle at the end of the shorter segment. This creates a square that has a side length of 4 meters. Draw an arc centered at the intersection of the two line segments with a radius equal to the shorter segment and connect the ends of the arc. This creates a golden rectangle with a length of 4 meters.

Draw a quarter circle at each corner of the golden rectangle and connect the endpoints. This creates a spiral, and it is a golden spiral if the ratio of the lengths of the two line segments is 1:1.618 (the golden ratio).

Learn more about golden spiral

brainly.com/question/29059993

#SPJ11

Rounded to the nearest whole number, the international company has approximately 86,026.2 employees in total.

We must first divide the value by the whole sum, and then multiply the result by 100 to get the percentage.

Let's use algebra to solve the problem.

If 19,700 employees represent 22.9% of the company's total number of employees, we can write:

0.229 = 19,700 / Total number of employees

To find the total number of employees, we can isolate the variable on one side of the equation:

Total number of employees = 19,700 / 0.229

Using a calculator, we get:

Total number of employees = 86,026.2

Rounded to the nearest whole number, the international company has approximately 86,026.2 employees in total.

To know more about percentage visit:

https://brainly.com/question/29306119

#SPJ1

The slope of the linear equation is; 0.5

The y-intercept of the Linear Equation is: 4.75

Yes the equation is proportional

The equation we are given is expressed as;

y = ¹/₂x + 4³/₄

When x = 0,

y = ¹/₂(0) + 4³/₄

y = 4.75

When x = 1,

y = ¹/₂(1) + 4³/₄

y = 5.25

When x = 2,

y = ¹/₂(2) + 4³/₄

y = 5.75

When x = 3,

y = ¹/₂(3) + 4³/₄

y = 6.25

If we go on and on till x = 10, we will see the constant difference in y for every change in x is 0.5

Thus, slope = 0.5

y-intercept = 4.75

Read more about Linear Equation Graph at; https://brainly.com/question/26148595

#SPJ1

Ezra should increase the stage's dimensions by the following factor in order to make the picture half the size of the original blueprint:

50%.

The modified blueprint will have a perimeter that is half that of the original layout.

When the scale factor is multiplied by the coordinates of an image's vertices, the result is a dilatation, which alters the side lengths of a figure.

The scale factor of the dilation is supplied as follows because, for this issue, we want the updated stage's dimensions to be half those of the original stage.

k = 1/2.

Given that both the perimeter and the side lengths have the same unit, 50%, or half of the original stage's perimeter, will be represented by the updated stage's perimeter.

Learn more about dilation here:

https://brainly.com/question/3457976

#SPJ9

Answer:

$0.45

Step-by-step explanation:

Answer:

To find the name of the restaurant, we need to find the intersection point of the two streets.

The equation of Second Street is y = (-4/3)x + 4/3.

The equation of Washington Boulevard is y = (3/7)x - 3/7.

To find the intersection point, we can set the two equations equal to each other:

(-4/3)x + 4/3 = (3/7)x - 3/7

Multiplying both sides by 21 (the least common multiple of 3 and 7) to eliminate fractions, we get:

-28x + 28 = 9x - 9

Bringing all the x terms to one side and all the constants to the other side, we get:

-37x = -37

Dividing both sides by -37, we get:

x = 1

Substituting this value of x into either equation, we can find y:

y = (-4/3)(1) + 4/3 = 0

Therefore, the intersection point of Second Street and Washington Boulevard is (1,0), which means the restaurant is located at that point.

Step-by-step explanation:

Answer:

(-3, -4)

Step-by-step explanation:

Rotating a point that has the coordinates (x,y) 180° about the origin in a clockwise or counterclockwise direction, produces a point that has the coordinates (−x,−y). Ari's error was that she rotated "N" by 90 degrees instead of 180 degrees, as the rule for a 90 degree rotation is (-y, x). Therefore, the correct coordinated for N' can only be (-3,-4)

The measure that is considered an outlier is the data-set is a measure of 29.5.

The interquartile range is calculated as the difference between the third quartile and the first quartile.

The values that are outliers are given as follows:

The quartiles for this problem are given as follows:

Q1 = 17, Q3 = 22.

Hence the IQR is of:

IQR = 22 - 17

IQR = 5.

Meaning that the outliers are given as follows:

More can be learned about interquartile range at brainly.com/question/12323764

#SPJ1

The probability that Ann's score is above 600 is 1 - 0.6628 = 0.3372.

(a) The shape of the sampling distribution of the sample means will be approximately normal. This is because of the Central Limit Theorem, which states that the sampling distribution of the sample means will be approximately normal if the sample size is large enough, regardless of the shape of the population distribution. In this case, the sample size of 35 is large enough for the Central Limit Theorem to apply.

(b) The mean of the sampling distribution of the sample means will be equal to the mean of the population, which is 550. The standard deviation of the sampling distribution of the sample means will be equal to the standard deviation of the population divided by the square root of the sample size, which is 120/√35 ≈ 20.28.

(c) To find the probability that the average score of the 35 selected students is above 600, we need to find the z-score for 600 using the mean and standard deviation of the sampling distribution of the sample means. The z-score is (600 - 550)/20.28 ≈ 2.47. Using a z-table, we can find the probability that the z-score is less than 2.47, which is 0.9932. Therefore, the probability that the average score of the 35 selected students is above 600 is 1 - 0.9932 = 0.0068.

(d) To find the probability that Ann's score is above 600, we need to find the z-score for 600 using the mean and standard deviation of the population. The z-score is (600 - 550)/120 ≈ 0.42. Using a z-table, we can find the probability that the z-score is less than 0.42, which is 0.6628.

Learn more about probability

brainly.com/question/30034780

#SPJ11

The odds against the next car leaving the lot being black = option(A) is correct option.

The odds against getting three tails when you flip three coins = option(B) is the correct option.

What is probability?

The potential of any random event's result is referred to as probability. To determine the likelihood that any event will occur is the definition of this phrase.

There 34 cars out of which 20 are green, 8 are gold and 6 are black.

So, The odds against the next car leaving the lot being black

    = no. of black cars / no. of non black cars

    = 6/28

    =3/14 (A)

If three coins are flipped together,

the total number of outcomes will be = 2³ = 8

no. of outcomes getting three tails = 1

The odds against getting three tails when you flip three coins

= no. of outcomes getting three tails/ no. of outcomes not getting three tails

= 1/7 (option B)

To learn more about Probability, visit the link:

https://brainly.com/question/24756209

#SPJ1

Answer:

60

Step-by-step explanation:

24 + 36 = 60

You can use the Gold Digger for the distributive property! * Factor as if you want to find the Greatest Common Factor.

Answer:

4.2 represents the initial height of the ball.

Step-by-step explanation:

h(x) = -16x² + 24x + 4.2

At x = 0, h(0) = 4.2

4.2 represents the initial height of the ball.

In response to the query, we have that The two graphs are oriented and coordinates  have the same form in common. The moment where the two graphs come together (1, 2).

A coordinate system is a technique used in geometry to precisely locate points or other geometry objects on a manifold, also including Euclidean space, using one or more numbers or coordinates. A point or item on a two-dimensional sphere is located using a pair of numbers known as coordinates. The x and y positions are two numbers that describe a point's location on a 2D plane. a collection of integers that indicate exact locations. Typically, the figure has two numbers. The first number represents the front-to-back distance, while the second column represents the top-to-bottom distance. When there are 12 units below and 5 above, as in (12.5), this is an example.

f(1/x) = 2/(1/x) = 2x, where g(x) =

Hence, g(x) = f(1/x) is equivalent to f(x) = 2x.

The values of x and g(x) are as follows:

x= 1 2 3 4 5\sg(x)= 1/8 1/4 1/2 1 2

f(x) = 2x: (1, 2), (2, 4), (3, 6), (4, 8), (5, 10) (5, 10)

g(x) = f(1/x) = 2x: (1, 2), (1/2, 1), (1/3, 2/3), (1/4, 1/2), (1/5, 2/5)

The appropriate choices are thus:

A reflection of the graph of f(x) about the line y = x is the graph of g(x).

The two graphs are oriented and have the same form in common.

The moment where the two graphs come together (1, 2).

To know more about coordinates  visit:

https://brainly.com/question/27749090

#SPJ1

Answer:

2(−x 2−3)

Simplify the expression

−2x 2−6

Factor the expression

−2(x 2+3)

The solution to the equation is z = 15.

To solve the equation 2(2z-3)=3(z+3), we first need to simplify each side of the equation by distributing the numbers outside of the parentheses to the terms inside the parentheses.

On the left side of the equation, we have 2(2z-3). Distributing the 2 to the terms inside the parentheses gives us:

2(2z) - 2(3) = 4z - 6

On the right side of the equation, we have 3(z+3). Distributing the 3 to the terms inside the parentheses gives us:

3(z) + 3(3) = 3z + 9

Now we can rewrite the equation as:

4z - 6 = 3z + 9

Next, we want to get all of the z terms on one side of the equation and all of the constant terms on the other side. We can do this by subtracting 3z from both sides of the equation and adding 6 to both sides of the equation:

4z - 3z = 9 + 6

Simplifying gives us:

z = 15

To know more about constant terms  click on below link:

https://brainly.com/question/28157327#

#SPJ11

We can use the properties of logarithms to evaluate each expression. The properties of logarithms include:

1) loga (xy) = loga (x) + loga (y)

2) loga (x/z) = loga (x) - loga (z)

3) loga (x^p) = p loga (x)

4) loga (square root x) = (1/2) loga (x)

Using these properties, we can evaluate each expression as follows:

(a) loga (xy) = loga (x) + loga (y) = 3.1 + 5.8 = 8.9

(b) loga (x/z) = loga (x) - loga (z) = 3.1 - 1.1 = 2

(c) loga (y^7) = 7 loga (y) = 7 * 5.8 = 40.6

(d) loga (square root y) = (1/2) loga (y) = (1/2) * 5.8 = 2.9

Therefore, the answers are:

(a) loga (xy) = 8.9

(b) loga (x/z) = 2

(c) loga (y^7) = 40.6

(d) loga (square root y) = 2.9

Know more about properties of logarithms here:

https://brainly.com/question/30226560

#SPJ11

Answer: The y-intercept is 30 and the coefficient is -5

Step-by-step explanation:

In the slope-intercept form (y = mx + b) b stands for your y-intercept, in this case, 30.

The coefficient is the number being multiplied by the variable, or in this case, the slope, or -5.

Answer: Third answer option, [tex]\sqrt{3} *\sqrt{12}[/tex]

Step-by-step explanation:

     Both 3 and 9 are not irrational numbers, so the first option is incorrect.

     The [tex]\sqrt{3}[/tex] is irrational, but 0 is not, so the second option is also incorrect.

     The [tex]\sqrt{3}[/tex] and [tex]\sqrt{12}[/tex] are both irrational. Let us see if they result in a rational number when multiplied together;

                 [tex]\sqrt{3} *\sqrt{12} =\sqrt{3*12} =\sqrt{36} =6[/tex]

      They do, so this answer option is correct.

Dina's older brother has a hot chocolate that is more chocolaty, as his recipe has a higher proportion of cocoa.

The more chocolaty recipe is defined obtain the proportion of cocoa for each recipe.

The proportion of cocoa for each recipe is obtained dividing the amount of cocoa used by the sum of the amounts of cocoa and milk used.

Hence the proportion for Dina's older brother is calculated as follows:

2/(2 + 3) = 2/5 = 0.4 = 40% cocoa.

The proportion for Dina's is obtained as follows:

3/(3 + 5) = 3/8 = 0.375 = 37.5% cocoa.

40 > 37.5, hence Dina's older brother has a hot chocolate that is more chocolaty, as his recipe has a higher proportion of cocoa.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer: I'd say A

Step-by-step explanation:

-1+1=0

a)0.1587 (or 15.87%)

b)0.6827 (or 68.27%)

c)0.0228 (or 2.28%)

1. Using the Normal Distribution formula with a mean (μ) of 64 inches and standard deviation (σ) of 10 inches, the probability of randomly selecting a female college student with a height less than 63 inches is 0.1587 (or 15.87%).

2. Using the Normal Distribution formula with a mean (μ) of 64 inches and standard deviation (σ) of 10 inches, the probability of randomly selecting a female college student with a height between 61 and 69 inches is 0.6827 (or 68.27%).

3. Using the Central Limit Theorem, the probability of finding an average of greater than 65 inches with a sample of 35 female college students is 0.0228 (or 2.28%).

Learn more about Probability

brainly.com/question/29381779

#SPJ11

Answer:

300

Step-by-step explanation:

x(100%-7%)=279

        0.93x=279

                x=300

When a point is reflected across the x-axis, its y-coordinate changes sign while its x-coordinate remains the same.

Therefore, to find the coordinates of the reflected point D, we simply change the sign of the y-coordinate of point D.

Given that the coordinates of point D are (3/4,3), its reflected point D' across the x-axis will have the coordinates (3/4, -3).

Therefore, the reflected point D' is located at the point (3/4, -3).

Coordinates are pairs of numbers used to identify the position of a point in a two-dimensional plane. In a Cartesian coordinate system, the two numbers represent the x-coordinate (the horizontal position) and the y-coordinate (the vertical position) of the point.

For example, the point (3, 5) has an x-coordinate of 3 and a y-coordinate of 5. This means that the point is located 3 units to the right of the origin (the point where the x- and y-axes intersect) and 5 units above the x-axis. Similarly, the point (-2, -1) has an x-coordinate of -2 and a y-coordinate of -1, which means that it is located 2 units to the left of the origin and 1 unit below the x-axis.

To learn more about coordinates visit;

https://brainly.com/question/16634867

#SPJ1

The expression are classified as follows

1. Decay

2. Growth

3. Growth

3.  Decay

4. Growth

5. Decay

6. Decay

Exponential function refers to functions of the form

f(x) = a(b)^x

where

the starting = a

the base = b

the exponents = x

The base is what determines exponential growth or decay

when the base is greater than 1 we have exponential growth

when the base is 0 < x < 1 we have exponential decay

comparing the base of the functions shows that

1. y = 500(0.30)  decay

2. y = 500(1.70) growth

3. y = 0.3(500) growth

3. y=500(0.30) - 6  decay

4.y = 0.3(1.7)¹-2 growth

5. y = 500(0.30)+2 decay

6. y = 500(0.30)-6  decay

Learn more about exponential decay at:

https://brainly.com/question/27822382

#SPJ1

The distance between the two groups after the hikes is approximately 12.04 miles.

A right triangle's connection between its sides is described by the Pythagorean Theorem, a foundational idea in mathematics. It claims that the hypotenuse's square length, which is the side that faces the right angle, equals the sum of the squares of the lengths of the other two sides of any right triangle. The Pythagorean Theorem is frequently used to solve issues involving distance, velocity, and acceleration and has various applications in the disciplines of geometry, trigonometry, and physics.

The distance between the two groups serves as the hypotenuse of a right triangle, which is formed by the two pathways. The following formula can be used to determine the hypotenuse's length:

Distance = √((2+7)² + (5+3)²)

= √(9² + 8²)

= √(81 + 64)

= √(145)

≈ 12.04 miles

Therefore, the distance between the two groups after the hikes is approximately 12.04 miles.

Learn more about Pythagoras Theorem here:

https://brainly.com/question/343682

#SPJ1

Answer:

The math coach has delivered 4 boxes of books, so the number of boxes she still needs to deliver is b. Each box contains 15 books, so the total number of books she still needs to deliver is 15b. She has 495 books to deliver in total. Therefore, we can write the equation:

15b = 495 - 4(15)

Simplifying the right-hand side:

15b = 495 - 60

15b = 435

Dividing both sides by 15:

b = 29

So the math coach still needs to deliver 29 boxes of books.

One cheeseburgers have 550 Cal and on smalls Fries have 320 Cal.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Two cheeseburgers and one small order of fries contain a total of 1420 calories.

Three cheeseburgers and two small orders of fries contain a total of 2290 calories.

let the number of Calories in one cheeseburgers  be x and in one fries be y.

So, the system of Equation is:

2x + y = 1420

3x + 2y= 2290

solving the above two equation

x= 550 and y= 320

So, one cheeseburgers have 550 Cal and on smalls Fries have 320 Cal.

Learn more about equation here:

https://brainly.com/question/29657983

#SPJ1