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4 years ago

I need help with this question. If you find the answer tell me how you got it.

Mathematics

1 answer:

alina1380 [7]4 years ago

6 0

17 3/4 - 2/5x = 4 1/2
-2/5x = 4 1/2 - 17 3/4
-2/5x = 9/2 - 71/4
-2/5x = 18/4 - 71/4
-2/5x = - 53/4
x = (-53/4) / (-2/5)
x = -53/4 * - 5/2
x = 265/8
x = 33 1/8 bottles

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Find the equation of a circle that has a diameter with the endpoints given by the points A(-4,9) and B (- 2, - 3) )

Aleksandr-060686 [28]

The equation of the circle is $(x+3)^{2}+(y-3)^{2}=37$

Explanation:

Given that the endpoints of the circle are A(-4,9) and B(-2,-3)

We need to determine the equation of the circle.

Center:

The center of the circle can be determined using the midpoint formula,

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

Substituting the coordinates A(-4,9) and B(-2,-3), we get,

$Center=(\frac{-4-2}{2},\frac{9-3}{2})$

$Center=(\frac{-6}{2},\frac{6}{2})$

$Center=(-3,3)$

Thus, the center of the circle is (-3,3)

Radius:

The radius of the circle can be determined using the distance formula,

$r=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

Substituting the center (-3,3) and the endpoint (-4,9), we get,

$r=\sqrt{\left(-4+3\right)^{2}+\left(9-3\right)^{2}}$

$r=\sqrt{\left(-1\right)^{2}+\left(6\right)^{2}}$

$r=\sqrt{1+36}$

$r=\sqrt{37}$

Thus, the radius of the circle is $\sqrt{37}$

Equation of the circle:

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

$(x-a)^{2}+(y-b)^{2}=r^{2}$

where (a,b) is the center and r is the radius.

Substituting the values, we have,

$(x+3)^{2}+(y-3)^{2}=(\sqrt{37})^{2}$

$(x+3)^{2}+(y-3)^{2}=37$

Thus, the equation of the circle is $(x+3)^{2}+(y-3)^{2}=37$

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3 years ago

In order for a function to be one-to-one, no two elements of the range may be paired with the same value of the domain AND no tw

kirza4 [7]

A True
The first condition gives that the function is in fact a function and the second condition makes it a one to one

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4 years ago

Luke is building a bike ramp. The ramp is going to be 3 feet tall on the high end and 6 feet long. How long is the base of the r

eimsori [14]

Answer: 5.1961

Step-by-step explanation: I believe you would use the Pythagorean’s theorem, since it’s a problem about a ramp, always draw pictures for word problems. So you would plug your numbers in the formula and solve. 3 squared plus B squared (that’s what we are trying to find so its a variable) equals 6 squared. Then you square and it becomes 9 + b2= 36, subtract 9 on both sides, b2=27, then square root on both sides to get 5.1961. Hopefully that’s right. :)

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4 years ago

Solve by completing the square

erastovalidia [21]

Answer:

Your answers would be:

x = 10 and x = -8

Step-by-step explanation:

Solve for the zeros:

x² - 2x - 78 = 2

Subtract both sides by 2.

x² - 2x - 80 = 0

Use the quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

a = 1

b = -2

c = -80

Plug in and solve:

$x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-80)}}{2(1)}\\\\x=\frac{2\pm\sqrt{(-2)^2-4(1)(-80)}}{2(1)}\\\\x=\frac{2\pm\sqrt{4-4(-80)}}{2(1)}\\\\x=\frac{2\pm\sqrt{4+320}}{2(1)}\\\\x=\frac{2\pm\sqrt{324}}{2(1)}\\\\x=\frac{2\pm18}{2}\\$

Solve for +:

$x=\frac{2+18}{2}\\\\x=\frac{20}{2}\\\\x=10$

Solve for -:

$x=\frac{2-18}{2}\\\\x=\frac{-16}{2}\\\\x=-8$

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3 years ago

What is an example of a quadratic binomial?

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If you asking for a random one then heres a rand om one: Y^3–2 or y^4+7

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3 years ago