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2 years ago

Select TWO possible values for x in the equation x2=45.

Mathematics

1 answer:

kirill [66]2 years ago

5 0

Answer:

$3 \sqrt 5}$ and $-3 \sqrt 5}$

Step-by-step explanation:

Given

$x^2 = 45$

Required

Determine the values of x

$x^2 = 45$

Take square root of both sides

$\sqrt{x^2} = \±\sqrt{45}$

$x = \±\sqrt{45}$

Expand 45 as 9 * 5

$x = \±\sqrt{9 * 5}$

Split the square root

$x = \±(\sqrt{9} *\sqrt 5}$

$x = \±3 *\sqrt 5}$

$x = \±3 \sqrt 5}$

This can be further split to:

$x = 3 \sqrt 5}$ or $x = -3 \sqrt 5}$

Hence, the possible values of x are

$3 \sqrt 5}$ and $-3 \sqrt 5}$

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Suppose vanilla beans cost $600 per kilogram. Julie bought 9 grams of vanilla beans. Jacques bought 70 grams of vanilla beans.

GenaCL600 [577]

The Correct option is 36.60
Step-by-step explanation:
The key to solving this question lies
around measurement
conversion,specifically converting
grams into its equivalence in
kilograms.
1000 grams equal one kilogram
9 grams=9/1000 kg
9 grams=0.009 kg
70 grams=70/1000 kg 1000 grams equal one kilogram
9 grams=9/1000 kg
9 grams=0.009 kg
70 grams=70/1000 kg
70 grams=0.07 kg
Julie pays=$600*0.009=$5.4
Jacques pays=$600*0.07=$42
Jacques pays $36.60 more ($42-
$5.4) than Julie paid
Option is wrong because that was Jacques pays=$600*0.07=$42
Jacques pays $36.60 more ($42-
$5.4) than Julie paid
Option is wrong because that was
what Julie paid
Option D is wrong because that was
what Jacques paid
Option B is obviously wrong

4 0

2 years ago

7-c<1 ?? HELPPPP!!!MEEEeee

sesenic [268]

Answer:

c>6, since a negative coefficient reverses the sign

Step-by-step explanation:

7-c<1

-c<-6

c>6

5 0

2 years ago

Find sinϴ and cosϴ if tanϴ=1/4 and sinϴ>0

eduard

If you're using the app, try seeing this answer through your browser: brainly.com/question/2787701

_______________

$\mathsf{tan\,\theta=\dfrac{1}{4}\qquad\qquad(sin\,\theta\ \textgreater \ 0)}\\\\\\
\mathsf{\dfrac{sin\,\theta}{cos\,\theta}=\dfrac{1}{4}}\\\\\\
\mathsf{4\,sin\,\theta=cos\,\theta\qquad\quad(i)}$

Square both sides:

$\mathsf{(4\,sin\,\theta)^2=(cos\,\theta)^2}\\\\
\mathsf{4^2\,sin^2\,\theta=cos^2\,\theta}\\\\
\mathsf{16\,sin^2\,\theta=cos^2\,\theta\qquad\qquad(but,~cos^2\,\theta=1-sin^2\,\theta)}\\\\
\mathsf{16\,sin^2\,\theta=1-sin^2\,\theta}$

$\mathsf{16\,sin^2\,\theta+sin^2\,\theta=1}\\\\
\mathsf{17\,sin^2\,\theta=1}\\\\
\mathsf{sin^2\,\theta=\dfrac{1}{17}}\\\\\\
\mathsf{sin\,\theta=\pm\,\sqrt{\dfrac{1}{17}}}\\\\\\
\mathsf{sin\,\theta=\pm\,\dfrac{1}{\sqrt{17}}}$

Since $\mathsf{sin\,\theta}$ is positive, you can discard the negative sign. So,

$\mathsf{sin\,\theta=\dfrac{1}{\sqrt{17}}\qquad\quad\checkmark}$

Substitute this value back into $\mathsf{(i)}$ to find $\mathsf{cos\,\theta:}$

$\mathsf{4\cdot \dfrac{1}{\sqrt{17}}=cos\,\theta}\\\\\\
\mathsf{cos\,\theta=\dfrac{4}{\sqrt{17}}\qquad\quad\checkmark}$

I hope this helps. =)

Tags: <em>trigonometric identity relation trig sine cosine tangent sin cos tan trigonometry precalculus</em>

7 0

2 years ago

Let f(x) = 8x3 − 28x + 61 and g(x) = 2x + 5. Find f of x over g of x.

antoniya [11.8K]

Answer:

$4x^2-10x+11+\frac{6}{2x+5}$