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2 years ago

Plz Help A. Yes B. No c. Maybe D. Can4 be determined

Mathematics

2 answers:

Tju [1.3M]2 years ago

8 0

<h3>Answer: A) Yes</h3>

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Explanation:

Convert each mixed number to decimal form

$2 \frac{1}{2} = 2 + \frac{1}{2} = 2 + 0.5 = 2.5\\\\3 \frac{1}{4} = 3 + \frac{1}{4} = 3 + 0.25 = 3.25\\\\5 \frac{1}{8} = 5 + \frac{1}{8} = 5 + 0.125 = 5.125\\\\$

We have the three potential sides of a = 2.5, b = 3.25 and c = 5.125

For a triangle to be possible with these side lengths, the following three inequalities must all be true

a+b > c
a+c > b
b+c > a

Which is due to the triangle inequality theorem.

In other words, we should be able to add any two sides to get a result larger than the third side.

a+b = 2.5+3.25 = 5.75 is larger than c = 5.125, so a+b > c is true.
a+c = 2.5+5.125 = 7.625 is larger than b = 3.25, so a+c > b is true.
b+c = 3.25+5.125 = 8.375 is larger than a = 2.5, so b+c > a is true.

All three inequalities mentioned are true when (a,b,c) = (2.5, 3.25, 5.125)

Therefore, <u>a triangle is possible</u> with these side lengths.

mixer [17]2 years ago

6 0

This answer is C i did this once

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Step-by-step explanation:

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3 years ago

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BARSIC [14]

Answer:

The rate of change is -5

The initial value is 25

Step-by-step explanation:

Since, this is a linear relation

so, we can select any two points and find equation of line

points are (1,20) and (3,10)

so,

$x_1=1,y_1=20$

$x_2=3,y_2=10$

now, we can find slope

$m=\frac{y_2-y_1}{x_2-x_1}$

now, we can plug values

$m=\frac{10-20}{3-1}$

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$y-y_1=m(x-x_1)$

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$y-20=-5(x-1)$

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$y=-5x+25$

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3 years ago

Provide an expression that is equivalent to 5(3-2) ?

VMariaS [17]

Answer:

Step-by-step explanation:

distribute the negative

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15-10

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3 years ago

Statuary Hall is an elliptical room in the United States Capitol in Washington, D.C. The room is also called the Whispering Gall

dalvyx [7]

Answer: a) $\frac{x^{2} }{2352.25 }$ + $\frac{y^{2} }{529}$ = 1

b) The distance of two foci is 85.4 feet

c) Area = 3502.67 square feet

Step-by-step explanation: a) An ellipse has the equation in the form of:

$\frac{x^{2} }{a^{2} }$ + $\frac{y^{2} }{b^{2} }$ = 1, where a is the horizontal axis and b is the vertical axis.

For the Statuary Hall, a = $\frac{97}{2}$ = 48.5 and b = $\frac{46}{2}$ = 23, so the equation will be

$\frac{x^{2} }{2352.25 }$ + $\frac{y^{2} }{529}$ = 1.

b) To determine the distance of the foci, we have to calculate 2c, where c is the distance between one focus and the center of the ellipse. To find c, as a, b and c create a triangle with a as hypotenuse:

$a^{2}$ = $b^{2} + c^{2}$

$c^{2} = a^{2} - b^{2}$

c = $\sqrt{48.5^{2} - 23^{2} }$

c = 42.7

The distance is 2c, so 2·42.7 = 85.4 feet.

The two foci are 85.4 feet apart.

c)The area of an ellipse is given by:

A = a.b.π

A = 48.5 · 23 · 3.14

A = 3502.67 ft²

The area of the floor room is 3502.67ft².

3 0

3 years ago

.The conversion of square feet to square yards can be represented by direct variation. Three square yards are equivalent to 27 s

Citrus2011 [14]

Answer:

The constant of variation is 1/9

The equation representing the direct variation is y/x= 1/9

Step-by-step explanation:

In direct variation, y/x=k denotes the equation, with k being the constant of variation. Here, y is the number of square yards and x is the number of square feet. Therefore, as we know that 27 square feet = 3 square yards, we can write one point (x₁, y₁) as (27 square feet, 3 square yards). Plugging x₁ and y₁ into our equation, we get

y/x = k

3 / 27 = k

(3/27) / (3/3) = 1/9* = k

Therefore, the constant of variation is 1/9

Next, as stated previously, y/x = k represents the equation of direct variation. Therefore, y / x = 1/9 as our equation

* because 3 is a factor of both 3 and 27, we can divide both the numerator and denominator by 3 to keep the fraction the same but also simplify it. One way to find the greatest common factor is to list the factors of each number and see the highest number that is a factor of both

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2 years ago