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inn [45]
3 years ago
7

Identify the equation of the circle that has its center at (9, 12) and passes through the origin.

Mathematics
1 answer:
katrin [286]3 years ago
4 0

The circle has center at (9, 12) and passes through the origin.

Equation of the circle in center and radius form is given by

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

where r is the radius and center at (h,k)

Now substitute the value of the center we get

(x-9)^2+(y-12)^2=r^2

As it passes through the origin so we can write

(0-9)^2+(0-12)^2=r^2\\ \\ 81+144=r^2\\ \\ 225=r^2\\ \\ r=15\\

Hence the equation of the circle is

(x-9)^2+(y-12)^2=15^2

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Which of the binomials below is a factor of this trinomial? 4x2 + 12x + 9A. 2x-3B. 2x-1C. 2x+1D. 2x+3
katrin [286]

In order to factorate the trinomial, let's first find its roots using the quadratic formula:

\begin{gathered} b^2-4ac=12^2-4\cdot4\cdot9=144-144=0 \\ x_1=x_2=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}=\frac{-12+0}{2\cdot4}=-\frac{12}{8}=-\frac{3}{2} \end{gathered}

Now we can write the trinomial in the form:

a(x-x_1)(x-x_2)

So we have that:

4x2+12x+9=4(x+\frac{3}{2})(x+\frac{3}{2})=(2x+3)(2x+3)

So 2x + 3 is a factor of the trinomial, therefore the answer is D.

8 0
2 years ago
The dimensions of a storage container in the shape of a rectangular prism are 54 in x 32.25 in x 24.5 in. Choose True or False f
AlladinOne [14]

GIVEN

the dimensions ofrectangular prism are

length = 54 in

breadth = 32.25in

height = 24.5 in

formula

volume of the rectangular prism = length×breadth×height

                                                   = 54 ×32.25×24.5

                                                   = 42997.5 in³

first statement is false because the volume of the rectangular prism in two significant digit.

Second statement is false because the volume of the rectangular prism in two significant digit.

FORMULA

surface area of a rectangular prism = 2(wl+hl+hw)

by putting the value of the length , breadth & height

we get

= 2 (54×32.25 + 32.25×24.5 + 24.5×54)

= 7709.25 in²

= 7709.3 in²(approx)

Third statement is true the surface area of the container is rounded  to ones place.

Hence proved

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4 years ago
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3 years ago
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koban [17]
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7 0
3 years ago
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Simplify this expression. If it is already simplified, then write it as it is.<br> 4t^2 + 10t
AleksAgata [21]

Answer:

Already simplified.

Step-by-step explanation:

The only way to simplify an expression is to combine like terms.  Like terms is where the variables are exactly the same.  t^2 is not the same as t.  Thus, cannot combine them, so the expression is already simplified,

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