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3 years ago

Solve the equation using inverse operations. Check your solutions. In your final answer, include all of your work.

Mathematics

1 answer:

REY [17]3 years ago

4 0

Answer:

$x=\sqrt{10}$

Step-by-step explanation:

The given equation is :

$5-2x^2=-15$

We need to solve it using inverse operations.

Subtract 5 from both sides of the equation.

$5-2x^2-5=-15-5\\\\-2x^2=-20\\\\2x^2=20\\\\x^2=10\\\\x=\sqrt{10}$

So, the solution of the given equation is $x=\sqrt{10}$ .

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Please help me! I'm spending 50 points on this question and my last two questions never even got answered!

Verdich [7]

Answer:

Step-by-step explanation:

Domain is only affected if certain values can make the result something that either doesn't make sense or is an error. In your situation, it wants you to find the domain of f/g, which is a fraction. The only rule we have for fractions regarding domain is that we simply can't divide by zero, to find the domain for any fraction with variables in the denominator, what I do is take the denominator, set it equal to 0, and solve for x.

So, if we're taking f/g, we have:

$\frac{3x^2 + x^4 + 2}{4x - 3}$

4x - 3 makes up our denominator, the bottom part of the fraction. So

4x - 3 = 0

4x = 3

x = 3/4

So the denominator is equal to zero when x is equal to 3/4. This would produce an error in any calculator because you can't divide by zero. The domain here is all real numbers except for 3/4.

(For future problems, the only thing to look out for is if your numerator, the top part of the fraction, factors into something that cancels with the bottom. In that case, it wouldn't affect domain because you aren't actually dividing by anything. For example:

$\frac{x^2 - 4}{x-2}$

If we factor the top, we see that x^2 - 4 = (x - 2)(x + 2). In this case, we have (x - 2) in both the top and bottom of the fraction, so it cancels out, and from there nothing else is restricting our domain. It would be all real numbers in a case like that.)

8 0

2 years ago

A) What is the median of the given data?

maks197457 [2]

Answer:

The median is 190

Step-by-step explanation:

Answer is quite easy

6 0

3 years ago

The moon has a surface area of approximately 14,650,000 m^2. Estimate its radius to the nearest mile

Elza [17]

$\bf \textit{surface area of a sphere}\\\\ SA=4\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ A=14650000 \end{cases}\implies 14650000=4\pi r^2 \\\\\\ \cfrac{14650000}{4\pi }=r^2\implies \cfrac{3662500}{\pi }=r^2\implies \sqrt{\cfrac{3662500}{\pi }}=r\implies 1079.73\approx r$

7 0

2 years ago

The product of two numbers is 2400 iftheir LCM is 120 find their LCM.... BY STEPS!!.....

aliina [53]

Answer:

60 and 40 or 120 and 20

Step-by-step explanation:

60 x 2=120

40 x 3=120

60 x 40=2400

120 x 1=120

20 x 6=120

120 x 20=2400

You can try a few others, but no others have an lcm of 120

4 0

3 years ago

Find the area of the shaded region

Alex777 [14]

∆BOC is equilateral, since both OC and OB are radii of the circle with length 4 cm. Then the angle subtended by the minor arc BC has measure 60°. (Note that OA is also a radius.) AB is a diameter of the circle, so the arc AB subtends an angle measuring 180°. This means the minor arc AC measures 120°.

Since ∆BOC is equilateral, its area is √3/4 (4 cm)² = 4√3 cm². The area of the sector containing ∆BOC is 60/360 = 1/6 the total area of the circle, or π/6 (4 cm)² = 8π/3 cm². Then the area of the shaded segment adjacent to ∆BOC is (8π/3 - 4√3) cm².

∆AOC is isosceles, with vertex angle measuring 120°, so the other two angles measure (180° - 120°)/2 = 30°. Using trigonometry, we find

$\sin(30^\circ) = \dfrac{h}{4\,\rm cm} \implies h= 2\,\rm cm$

where $h$ is the length of the altitude originating from vertex O, and so

$\left(\dfrac b2\right)^2 + h^2 = (4\,\mathrm{cm})^2 \implies b = 4\sqrt3 \,\rm cm$

where $b$ is the length of the base AC. Hence the area of ∆AOC is 1/2 (2 cm) (4√3 cm) = 4√3 cm². The area of the sector containing ∆AOC is 120/360 = 1/3 of the total area of the circle, or π/3 (4 cm)² = 16π/3 cm². Then the area of the other shaded segment is (16π/3 - 4√3) cm².

So, the total area of the shaded region is

(8π/3 - 4√3) + (16π/3 - 4√3) = (8π - 8√3) cm²

7 0

1 year ago