The hypotenuse of a right triangle is 8 centimeters long. One of the legs of the triangle is 7 centimeters. What is the length of the triangle's other leg?

The value of the 3 in the ten thousands place is 30,000, while the value of the 3 in the thousands place is 3,000. The value of a digit in a place depends on its position in the number.

The value of the 3 in the ten thousands place in 33,294 is 30,000. The value of the 3 in the thousands place is 3,000. The value of a digit in a place depends on its position in the number. In this case, the 3 in the ten thousands place is ten times greater than the 3 in the thousands place.

The value of x should be equal to and greater than -12.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

twice a number x is at most -24.

So, the mathematical expression is

2x ≥ -24

Now, divide both side by 2

2x / 2 ≥ -24 /2

x ≥ -12

So, the value of x should be equal to and greater than -12.

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The length of the third side of the triangle will be 2.65 units.

Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle C, then we have:

a² + b² – 2ab cos(C) = c²

A triangle has two sides of length 2 and 3 and that the angle between these two sides is π/3.

Then the length of the third side of the triangle will be

c² = 2² + 3² – 2 x 2 x 3 x cos(π/3)

c² = 4 + 9 – 12 x (1/2)

c² = 13 – 6

c² = 7

c = √7

c = 2.65 units

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To find the initial velocity, we rearrange the given velocity equation to solve for the initial velocity, then substitute the given values. The initial velocity is found to be 127 ft/s.

The given formula for velocity is v = v0 - 32t, where 'v' is the velocity at a certain time 't', and 'v0' is the initial velocity. In this case, we're given that v is 31 ft/s after 3 seconds. To find the initial velocity 'v0', you need to rearrange the equation to solve for 'v0'. This gives:

v0 = v + 32t

Substituting the given values into the rearranged equation gives:

v0 = 31ft/s + 32(3s)

This simplifies to:

v0 = 31ft/s + 96ft/s = 127ft/s

So the initial velocity of the object is 127 ft/s.

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Answer:

214.45 feet.    

Step-by-step explanation:

Please find the attachment.

Let x be the length of building's shadow.

We have been given that the sun is 25 degrees above the horizon. The length of the building is 100 feet tall.

We can see from our attachment that the length of the building is opposite side and the length of the shadow is adjacent side for the angle of 25 degrees.

Since tangent relates the opposite side of right triangle with adjacent side, so we can set an equation to find the length of building's shadow as:

[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]

[tex]\text{tan}(25^{\circ})=\frac{100}{x}[/tex]      

[tex]x=\frac{100}{\text{tan}(25^{\circ})}[/tex]

[tex]x=\frac{100}{0.466307658155}[/tex]

[tex]x=214.45069\approx 214.45[/tex]

Therefore, the length of shadow cast by the building is 214.45 feet.

When finding the number of blue balls in the scenario described, the equation will have x + x + x + 1 = 9, where x represents the number of blue balls.

An equation created to find the number of blue balls will have:

Let x be the number of blue balls.

The equation will be x + x + x + 1 = 9.

Solving the equation, we get x = 2.67.

We want to find how far is the jogger from his house after he runs a total of 8 miles, we will see that the distance is equal to 7 miles.

So we need to define a coordinate axis, the point (0, 0) will be the jogger's house (where he/she starts). North is the positive y-axis and East is the positive x-axis.

Then the jogger starts at (0, 0).

Then he ran 3 miles due East, so the new position is:

(0, 0) + (3mi, 0) = (3mi, 0)

Then he ran 5 miles at 30° East of North (or 60° North of East).

The components are:

Then the new position is:

(3mi, 0) + (2.5mi, 4.33 mi) = (5.5mi, 4.33 mi)

The distance to the jogger's house is just the magnitude of that final vector, which is:

||  (5.5mi, 4.33 mi) || =  √( (5.5mi)^2 + (4.33mi)^2) = 7mi

So the jogger is at 7 miles from his/her house.

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The jogger is approximately 5.83 miles away from his house at a heading of 51.83° northeast after running 8 miles.

To find how far the jogger is from his house after running 8 miles, we need to calculate the resultant displacement. The jogger ran 3 miles due east, so his displacement in the east direction is 3 miles. Then, he ran 5 miles at a heading of 30° east of north (or 30° NE). We can split this displacement into the north and east components. The east component can be calculated as 5 miles * cos(30°) = 5 miles * 0.866 = 4.33 miles. The north component can be calculated as 5 miles * sin(30°) = 5 miles * 0.5 = 2.5 miles.

To calculate the resultant displacement, we can use the Pythagorean theorem. The east and north components form a right triangle, with the resultant displacement as the hypotenuse. The magnitude of the resultant displacement can be found as √(3^2 + 4.33^2 + 2.5^2) = √(9 + 18.7489 + 6.25) = √33.9989 = 5.83 miles. The direction of the resultant displacement can be found using trigonometry. tan(θ) = opposite/adjacent = (2.5 miles + 3 miles)/(4.33 miles) = 5.5/4.33. Taking the arctan of both sides, θ = arctan(5.5/4.33) = 51.83°. Therefore, the jogger is approximately 5.83 miles away from his house at a heading of 51.83° northeast.

Final answer:

The farmer needs to buy 320 linear feet of fence to enclose the rectangular area behind his barn.

Explanation:

Let's represent the width of the rectangle as x. Since the length is three times the width, we can represent the length as 3x. The perimeter of a rectangle is calculated by adding up all four sides, so we have the equation:

2(x + 3x) = 320

Simplifying, we get:

2(4x) = 320

8x = 320

x = 40

So the width of the rectangle is 40 feet, and the length is 3 times that, which is 120 feet. The perimeter is calculated by adding up all four sides: 40 + 120 + 40 + 120 = 320 feet. Therefore, the farmer needs to buy 320 linear feet of fence.

Tis the actual answer :)

A rectangle becomes a square when all of its sides are congruent, which is the defining characteristic that differentiates it from a rectangle. While rectangles do share other attributes such as parallel sides, right angles, and convex angles, these do not specifically define a square.

A rectangle becomes a square when all of its sides are congruent. This by definition means that all four sides of the shape are of equal length. While rectangles do have parallel sides and right angles, these characteristics alone do not suffice to differentiate a square from a rectangle, as rectangles also have these attributes. In the case of convex angles, both squares and rectangles have angles that are convex, so this also cannot be used to distinguish a square from a rectangle.

To specifically address the options provided:

Therefore, the most accurate answer is (c) when its sides are congruent.

40 percent of a fraction increase if its numerator is decreased by 30% and its denominator is decreased by 50%.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, numerator is decreased by 30% and its denominator is decreased by 50%.

Let x/y be the original fraction.

Then, the new fraction is (x-30% of x)/(y-50% of y)

= 0.7x/0.5y

Now, difference = 0.7x/0.5y-x/y

= 0.7x/0.5y - 0.5x/0.5y

= 0.2x/0.5y

Percentage increase = 0.2x/0.5y ÷ x/y

= 0.2/0.5 ×100

= 40%

Therefore, 40 percent of a fraction increase if its numerator is decreased by 30% and its denominator is decreased by 50%.

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Answer $ 168

as per the question,

money earned for working 5 hours = 70

money earned for working 1 hour = 70/5= 14

money earned for working 12 hours = 12 * 14

money earned for working 12 hours = $168

Answer:

0.9987

Step-by-step explanation:

Given that X, The distribution of the baggage weights for passengers using a particular airline has a mean of 19.4 lbs and a standard deviation of 5.3 lbs.

For a sample of size 100, we have

n=100

Hence std deviation of sample = [tex]\frac{SD}{\sqrt{n} } =0.53[/tex]

To find the probability that X>2100/100 lbs

=P(X<21[tex]\frac{21-19.4}{0.53} =3.019[/tex]) =P(Z<3.019)

=0.5+0.4987

0.9987

Answer:

Numbers are -2 and 1.

Step-by-step explanation:

Let x be the second number,

⇒ First number = 4 less than twice a second number

= 2 × Second number - 4

= 2x - 4

Thus, the product of first and second number is,

[tex]f(x) = x(2x-4)[/tex]

[tex]\implies f(x) = 2x^2 - 4x[/tex]

Differentiating with respect to x,

[tex]f'(x) = 4x -4[/tex]

Again differentiating with respect to x,

[tex]f''(x) = 4[/tex]

Now, for maximum or minimum,

[tex]f'(x)=0[/tex]

[tex]\implies 4x - 4 = 0\implies 4x = 4\implies x = 1[/tex]

Since, for x = 1, f''(x) = Positive,

Therefore, the function f(x) is minimum for x = 1,

⇒ The product is smallest for x = 1,

Hence, the second number = x = 1,

And, first number = 2x - 4 = 2 - 4 = -2

The percentage of the children in the class who is a girl and wears glasses is 8%.

Given that:

Total students in the class = 100%

Percentage of students in the class who are girls = 40%

Percentage of girls who wear glasses = 20%

It is required to find the percentage of students in the class who are girls wearing glasses.

This can be found as:

P = 40% × 20%

  = 0.4 × 0.2

  = 0.08

Now 0.08 in terms of percentage is 0.08 × 100 = 8%.

Hence the percentage of girls who wear glasses is 8%.

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Answer: A. Yes.

Step-by-step explanation:

To find out if the function represented in the graph has an inverse function, you must apply the Horizontal Line Test, which is used to know if a function is a One-to-one function.

A one-to-one function is that  function where each x value has an unique y value.

Therefore, if in the Horizontal Line Test, the horizonal  intersects the graph of the function at only and only one point, then the function has an inverse function.

As you can see in the graph attached, the horizontal lines intersect the function at only one point, therefore, you can conclude that it is a One-to-one function and it has an inverse function.

TRUE. The graph represents a function that has an inverse function because it passes the horizontal line test.

The graph represents a function that has an inverse function if and only if each horizontal line crosses the graph at most once. This is known as the horizontal line test. If a function passes the horizontal line test, then it has an inverse function. If it fails the horizontal line test, then it does not have an inverse function.

In this case, we can see that the graph passes the horizontal line test because each horizontal line intersects the graph at most once. Therefore, the graph represents a function that has an inverse function.

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