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Irina18 [472]
3 years ago
6

Select the correct answer from each drop-down menu.

Mathematics
1 answer:
serious [3.7K]3 years ago
6 0

Answer:

Center: (4,8)

Radius: 2.5

Equation: (x-4)^2+(y-8)^2=6.25

Step-by-step explanation:

It was given that; the endpoints of the longest chord on a circle are (4, 5.5) and (4, 10.5).

Note that the longest chord is the diameter;

The midpoint of the ends of the diameter gives us the center;

Use the midpoint formula;

(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2} )

The center is at; (\frac{4+4)}{2} ,\frac{5.5+10.5}{2}=(4,8)

To find the radius, use the distance formula to find the distance from the center to one of the endpoints.

The distance formula is;

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

r=\sqrt{(4-4)^2+(10.5-8)^2}

r=\sqrt{0^2+(2.5)^2}

r=\sqrt{0^2+(2.5)^2}=2.5

The equation of the circle in standard form is given by;

(x-h)^2+(y-k)^2=r^2

We substitute the center and the radius into the formula to get;

(x-4)^2+(y-8)^2=2.5^2

(x-4)^2+(y-8)^2=6.25

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Solve the equation using the zero-product property (2x-8)(7x+5)=0
Iteru [2.4K]
If xy=0 assume that x and y=0
so
(2x-8)(7x+5)=0
assume
2x-8=0 and 7x+5=0
solve each

2x-8=0
2x=8
x=4

7x+5=0
7x=-5
x=-5/7

so x=-5/7 or 4
7 0
3 years ago
Read 2 more answers
Hi! I need help with this:
arlik [135]
<h3>Answer:  50</h3>

==========================================================

Explanation:

We simply multiply the two values given to us

600*(1/12) = 600/12 = 50

We expect about 50 bulbs to be defective.

Note how if we had 50 bad bulbs, then 50/600 = (1*50)/(12*50) = 1/12 of the batch of 600 bulbs is defective.

5 0
3 years ago
When temperature is zero degree Celsius, the Fahrenheit temperature is 32. When the Celsius temperature is 100, the correspondin
7nadin3 [17]

Answer:

\\ y = 1.8(x) + 32 or \\ y = \frac{9}{5}(x) + 32

or equivalently:

\\ F = 1.8(C) + 32 or \\ F = \frac{9}{5}(C) + 32

Step-by-step explanation:

To express the Fahrenheit temperature <em>as a linear function of the Celsius temperature</em>, F(c), we can proceed as follows.

We can use here <em>the two-point form</em> <em>equation</em> of a line:

\\ y-y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x-x_1) [1]

We are asked to express the <em>Fahrenheit temperature</em> as a function of <em>Celsius temperature</em>, so the independent variable, in this case, is <em>x</em> (Celsius temperature) and the dependent variable is <em>y</em> (Fahrenheit temperature).

When temperature is zero degree Celsius (\\x_1 = 0), the Fahrenheit temperature is 32 (\\y_1 = 32).

When the Celsius temperature is 100 (\\x_2 = 100), the corresponding Fahrenheit temperature is 212 (\\y_2 = 212).

Then, using [1], we have:

\\ y-32 = \frac{212 - 32}{100 - 0}(x-0)

\\ y-32 = \frac{180}{100}(x)

\\ y-32 = 1.8(x).

It could be also be written as:

\\ y-32 = \frac{18}{10}(x) = \\ y-32 = \frac{9}{5}(x), as it commonly appears in books.

Then <em>the Fahrenheit temperature express as a linear function of the Celsius temperature, F(c</em>) is ( solving the equation for <em>y </em>) :

\\ y = 1.8(x) + 32 or \\ y = \frac{9}{5}(x) + 32.

Or equivalently:

\\ F = 1.8(C) + 32 or \\ F = \frac{9}{5}(C) + 32

We can check this using the given values from the question:

For 0 Celsius degrees, the Fahrenheit temperature is:

\\ y = 1.8(0) + 32 = 32 Fahrenheit degrees.

For 100 Celsius degrees, the Fahrenheit temperature is:

\\ y = 1.8(100) + 32 = 180 + 32 = 212 Fahrenheit degrees.

5 0
3 years ago
Kenya has 2 hours to make a 104 mile trip. What rate must she average to make the trip in 2 hours? A) 50 mph B) 51 mph C) 52 mph
sattari [20]
C. 52 mph.
104\2 = 52
8 0
3 years ago
Could a triangle be constructed with side lengths 4 cm, 5 cm and 13 cm? *​
Ratling [72]

Answer:

NO.

Step-by-step explanation:

No because 13 > 4 + 5.

7 0
3 years ago
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