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3 years ago

Factor this polynomial expression.

Mathematics

1 answer:

topjm [15]3 years ago

6 0

The answer is C. I tried factoring the equation itself, and I got the correct answer but I noticed that it isn’t one of the options. Therefore, the options are partly factored but not completely. I decided to just eliminate each of the multiple choice options. I got C after expanding it. Firstly, we need to distribute the 3 to (x-2). This gives us (3x-6)(x-2). After that, we can use the FOIL method. 3x^2 - 6x -6x + 12 is the same as 3x^2 - 12x + 12.

In case you want to see the fully factored polynomial, I won’t explain the steps since you don’t need it here, but it’s 3(x-2)^2. This is equivalent to 3(x-2)(x-2). That’s the same as C.

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Yea shop sells 60 teas in total. 9 of them are caffeinated. What percent is caffeinated

Digiron [165]

Answer:

15% of the teas are caffeinated

Step-by-step explanation:

Use the formula:

part/whole = t/100%

where t will be representing the percent of caffeinated tea.

Plug in the given to the formula shown above:

9/60 = t/100

Solve using cross product

(9 x 100) = (60 x t)

900/60 = 60t/60

15 = t

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2 years ago

Which is the polynomial function of lowest degree with rational real coefficients, a leading coefficient of 3 and roots StartRoo

spayn [35]

Answer:

$f(x)=3x^3-6x^2-15x+30$

$f(x)=3(x-2)(x+\sqrt{5})(x-\sqrt{5})$

Step-by-step explanation:

For a polynomial function of lowest degree with rational real coefficients, each root has multiplicity of 1.

The polynomial has roots $x=\sqrt{5}$ and 2 with a leading coefficient of 3.

By the irrational root theorem of polynomials, $x=-\sqrt{5}$ is also a root of the required polynomial.

By the factor theorem, we can write the polynomial in factored form as:

$f(x)=3(x-2)(x+\sqrt{5})(x-\sqrt{5})$

We expand, applying difference of two squares to obtain

$f(x)=3(x-2)(x^2-5)$

We expand further using the distributive property to get:

$f(x)=3x^3-6x^2-15x+30$

3 0

4 years ago

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Given: FG is an median. What can you conclude?

vredina [299]

Answer:

The last option line DG is congruent to line GE

Step-by-step explanation:

Median: a segment whose endpoints are a vertex of a triangle and the midpoint of the opposite side

So basically G is the midpoint of DE because FG is the median.

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3 years ago

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Step-by-step explanation:

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3 years ago

Does the point (1, StartRoot 7 EndRoot) lie on the circle shown? Explain. Yes, the distance from (–2, 4) to (–2, 0) is 4 units.

Kobotan [32]

Answer:

Yes, the distance from $(-2,0)\ to\ (1,\sqrt{7})\ is\ 4\ units$

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the equation of the circle

we know that

The equation of the circle is equal to

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

where

(h,k) is the center

r is the radius

In this problem we have

$(h,k)=(-2,0)$

and the radius is equal to the distance between the center and the point (-2,4)

$r=4\ units$ ----> look at the graph

substitute in the equation

$(x+2)^{2}+(y)^{2} =4^{2}\\(x+2)^{2}+(y)^{2} =16$

step 2

If the distance between the center and the point is equal to the radius of the circle , then the point lie on the circle

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}\\A(-2,0)\\B(1,\sqrt{7})$

substitute the values

$d=\sqrt{(\sqrt{7}-0)^{2}+(1+2)^{2}}\\d=\sqrt{7+9}\\d=\sqrt16}=4\ units$

therefore

the point lie on the circle

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3 years ago

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