The shorter leg of a right triangle is 7 inches shorter than the longer leg. The hypotenuse is 17 inches longer than the longer leg. Find the side lengths of the triangle.

Answer:

The equation of the line that is parallel to the given is equal to the expressions below:

[tex]\displaystyle \boxed{ y = -0.75(x - 8) \text{ or } y = -0.75x + 6 }[/tex]

General Formulas and Concepts:
Algebra I

Slope-Intercept Form: y = mx + b

Point-Slope Form: y - y₁ = m(x - x₁)

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyley = - 0.75x \\\text{Point } (8, 0) \\[/tex]

Step 2: Find Equation

Recall that a parallel line has the same slope as the one that is given. Therefore, we can define the slope of our parallel line to be m = -0.75:

We can rewrite this form into slope-intercept form as well by expanding:

[tex]\displaystyle y = -0.75(x - 8) \rightarrow \boxed{ y = -0.75x + 6 }[/tex]

∴ we have found the equation of a line that is parallel to the given information.

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Topic: Algebra I

Answer:

what the guy above said

Step-by-step explanation:

Answer:  The correct option is (A) [tex]x^2+2x-6.[/tex]

Step-by-step explanation:  We are given the following two functions :

[tex]f(x)=2x+1,\\\\g(x)=x^2-7.[/tex]

We are to find the value of [tex](f+g)(x).[/tex]

We know that

for any two functions p(x) and q(x), we have

[tex](p+q)(x)=p(x)+q(x).[/tex]

Therefore, we get

[tex](f+g)(x)\\\\=f(x)+g(x)\\\\=(2x+1)+(x^2-7)\\\\=2x+1+x^2-7\\\\=x^2+2x-6.[/tex]

Thus, option (A) is CORRECT.

Answer:

the Answer is x + y = 8 because 3 + 5= 8

Step-by-step explanation:

Answer:

D Yes, because her calculation should be 70% of 240.

Step-by-step explanation:

D

Answer:

ITS A.) 41

Step-by-step explanation:

Final answer:

The probability that Mike's next free throw attempt will go in the basket is 75%.

Explanation:

To find the probability that Mike's next free throw attempt will go in the basket, we can use the ratio of successful attempts to total attempts. In this case, Mike has made 63 out of 84 attempts. So the probability can be calculated as:

Probability = Number of successful attempts / Total number of attempts

Probability = 63 / 84

Probability = 0.75

Therefore, the probability that Mike's next free throw attempt will go in the basket is 0.75 or 75%.

To find the side length of the square base of a pyramid with the same volume and height as a cone with radius r, one can use the volume formulas V = (1/3)πr²h for a cone and V = (1/3)a²h for a pyramid. Setting them equal and solving for a yields a = r√π, indicating that the pyramid's base side length is the cone's radius times the square root of π.

The student is asking for the relationship between the dimensions of a cone and a pyramid that have the same volume and height. Specifically, if we have a cone with a radius r, and we want to find the side length of a square base of a pyramid that also has the same volume and height as the cone.

The volume of a cone is given by the formula [tex]V = (\frac{1}{3}) \pi r^2h[/tex], where radius of the cone's base is denoted by 'r' and the height is denoted by 'h'. For a pyramid with a square base, the volume formula is [tex]V = (\frac{1}{3} )a^2h[/tex], where a is the side length of the square base and h is again the height.

Given that both volumes are equal, we can set the formulas equal to each other and solve for a: [tex](\frac{1}{3} )\pi r^2h = (\frac{1}{3} )a^2h[/tex]. The heights cancel out, and we can simplify the equation to solve for the side length a: a = r√π. Therefore, the side length of the square base of the pyramid is the radius of the cone's base times the square root of π.

Answer: 12,127.5

Step-by-step explanation:EDGE2021

Sum of the measures of the interior angles of a regular polygon is 180°, using properties of interior and exterior angle and regular polygon.

What is a regular polygon?

A regular polygon is a n-sided polygon in which all sides are of same length and are symmetrically placed about the center.

Properties of interior and exterior angles:

1. The sum of adjacent interior and exterior angle for a polygon is 180°.

2. The sum of exterior angles of a polygon is always equal to 360°.

Here,

Let's consider number of exterior angle=x

given that: each exterior angle measures 120°.

Now, using 2nd property,

         x*120 = 180

         x = 3

So, total number of exterior angles are = 3

Using 1st property,

each interior angle measures = 180 - 120

                                                  = 60°

And total number of interior angle = total number of exterior angle

                                                          = 3

So, the sum of interior angles = 3*60

                                                 = 180° .

Hence, we reached our answer.

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The perimeter of Shelly's property is 152 meter.

Option (B) is correct.

It is required to find the perimeter.

A plane figure with four straight sides and four right angles, especially one with unequal adjacent sides, in contrast to a square. A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees.

Given that:

The  Shelly's property is in the shape of rectangle.

Length of property=41 meter

Breadth of property=35 meter

Perimeter of rectangle=2(Length+ Breadth)

Perimeter of rectangle=2(41+ 35)

Perimeter of rectangle=2*76

Perimeter of rectangle=152 meter

Therefore, the perimeter of Shelly's property is 152 meter.

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Answer:

f(x) = 1/2x^2 – 4x + 5  (the third option)

Step-by-step explanation:

On ed :)

Answer: Total area of the given prism is (104 + 16√13) Square inches.

Step-by-step explanation:

By the given diagram,

In the right triangular prism,

The sides of the base ( right triangle ) are 4 inches and 6 inches,

We have to finds : T.A. ( the total area of the prism )

Thus, the total base area of the prism = 2 ×  ( Area of triangle having base 4 inches and height 6 inches )

= 2× ( 1/2 × 4 × 6 )

= 4 × 6

= 24 square inches,

Let the hypotenuse of the triangles having sides 4 and 6 is x inches, ( shown in the diagram )

Thus, by the given diagram,

[tex]x^2 =4^2+6^2[/tex]

[tex]x^2 = 16 + 36[/tex]

[tex]x^2 = 52[/tex]

[tex]x=2\sqrt{13}[/tex]

Now, the total lateral area of the prism,

= 8×2√13 + 8×4 + 8×6

= 16√13 + 32 + 48

= (16√13 + 80) square inches,

Since, the total area of the given prism (T.A.) = Total base area of the prism(B.A.) + Total lateral area ( L.A.)

= 24 + 16√13 + 80

= (104 + 16√13) Square inches.

We can conclude that, the money recieved by the player will be 2(x + y) and game is a fair game.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is it costs ​$15 to roll a pair of dice and you get paid 2 dollars times the sum of the numbers that appear on the dice.

Assume that you get x and y value on dice 1 and dice 2 respectively. Then the equation representing the money recieved by a individual will be -

2(x + y)

The game will be fair if -

2(x + y) > 15

Now, for the sum of (x + y) = 7, the player will not have any profit. However, from (x + y) = 8, the players will start making profits. So, we can say it is a fair game, if your luck is not bad so far.

Therefore, we can conclude that, the money recieved by the player will be 2(x + y) and game is a fair game.

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The point (0,29) on the graph models the daily high temperature in Santiago, Chile on the hottest day of the year, where '0' represents that hottest day and '29' is the high temperature on that day.

The point (0,29) on the graph represents the weather condition in Santiago, Chile on the hottest day of the year. Here, '0' in the pair represents the day which is essentially the hottest day and '29' is the high temperature on that day. It depicts that on this specific day, the highest temperature was 29. The graph is an example of a time series graph, where the changing patterns or trends are displayed over a certain period of time - in this case, the temperature changes across the days following the hottest day of the year.

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To find the percentage of pizzas that were mushroom pizzas, you must divide the number of mushroom pizzas by the total number of pizzas. To find the total number of pizzas, we must add the number of mushroom and pepperoni pizzas together.

57 + 38 = 95

Next, we can complete our division.

57/95 = 0.6

Finally, we should multiply by 100. This is because to convert a decimal to a percentage, we must move the decimal point two places to the right so that this value is out of 100 total percent.

0.6 * 100 = 60%

Therefore, 60% of the total pizzas are mushroom.

Hope this helps!

The answer is WHOLE NUMBERS.