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2 years ago

What is the equation of a circle with center -4, 7 and radius 6

Mathematics

1 answer:

Kitty [74]2 years ago

4 0

Answer:

$( x + 4 )^2 + ( y - 7 )^2 = 36$

Step-by-step explanation:

Use the circle equation, $( x - h )^2 + ( y - k )^2 = r^2$

Plug in the center and radius:

$( x + 4 )^2 + ( y - 7 )^2 = 6^2$

Simplify:

$( x + 4 )^2 + ( y - 7 )^2 = 36$

So, the equation is $( x + 4 )^2 + ( y - 7 )^2 = 36$

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Is the square root of 16.45 a rational number or irrational number?

trapecia [35]

Answer:

Irrational

Step-by-step explanation:

The square root of 16.45 would be a number that will never end, making it irrational.

3 0

3 years ago

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How do you find the greatest common denominator, when comparing two numbers? Explain your thought process, in the example I prov

maksim [4K]

Answer:

20 is the greatest common denominator. You can find this by listing the factors of each number. The highest number that can fit into both individual numbers is the common denominator. Since 40 is just 20 doubled, and 20 is just 20 once, it fits into both numbers and is also the highest number that can fit.

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2 years ago

Write a quadratic equation given the roots -1/3 and 5, show your work

Travka [436]

$\boxed{(x - a)(x - b) = 0}$

The equation above is the intercept form. Both a-term and b-term are the roots of equation.

$x = - \frac{1}{3} \\ x = 5$

These are the roots of equation. Therefore we substitute a = - 1/3 and b = 5 in the equation.

$(x + \frac{1}{3} )(x - 5) = 0$

Here we can convert the expression x+1/3 to this.

$x + \frac{1}{3} = 0 \\ 3x + 1 = 0$

Rewrite the equation.

$(3x + 1)(x - 5) = 0$

Simplify by multiplying both expressions.

$3 {x}^{2} - 15x + x - 5 = 0 \\ 3 {x}^{2} - 14x - 5 = 0$

Answer Check

Substitute the given roots in the equation.

$3 {(5)}^{2} - 14(5) - 5 = 0 \\ 75 - 70 - 5 = 0 \\ 75 - 75 = 0 \\ 0 = 0$

$3( - \frac{1}{3} )^{2} - 14( - \frac{1}{3}) - 5 = 0 \\ 3( \frac{1}{9} ) + \frac{14}{3} - 5 = 0 \\ \frac{1}{3} + \frac{14}{3} - \frac{15}{3} = 0 \\ \frac{15}{3} - \frac{15}{3} = 0 \\ 0 = 0$

The equation is true for both roots.

Answer

$\large \boxed {3 {x}^{2} - 14x - 5 = 0}$

8 0

2 years ago

10 = 7 - m* It says solve & check solution. Can someone help asap

Stels [109]

Answer:

see explanation

Step-by-step explanation:

Given

10 = 7 - m ( subtract 3 from both sides )

3 = - m ( multiply both sides by - 1 )

- 3 = m , or

m = - 3

As a check

Substitute m = - 3 into the right side of the equation and if equal to the left side then it is the solution

7 - m = 7 - (- 3) = 7 + 3 = 10 = left side

Thus m = - 3 is the solution to the equation

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3 years ago

Solve for x: one over four (4x + 15) = 24 (5 points)

skelet666 [1.2K]

The answer is eighty one over four

4 0

3 years ago