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ivann1987 [24]
2 years ago
13

Can someone please help me solve this problem

Mathematics
1 answer:
MrMuchimi2 years ago
7 0

Step-by-step explanation:

Step 1:  After adding 875 to both sides of the original equation, you get

x^2+10x+\text{ ----- }=875

Step 2: <em>b</em> is the coefficient of the <em>x</em> term, so <em>b</em> = 10.  Divide in half (always half for completing the square!).

\frac{10}{2}=5

Square that result to get 25.  That's <em>c</em>, the amount to add to both sides of the equation.

Step 3:  Adding <em>c</em> to both sides produces

x^2+10x+25=875+25

Step 4: The result of Step 3 is x^2+10x+25=900, and the left side factors as a perfect square.

(x+5)^2=900

Step 5: After taking square roots of both sides, you get

x+5=\pm 30  which represents "two equations in one."

Separate them.

x+5=30 \text{ or } x+5 =-30\\x=25 \text{ or } x=-35

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Marcy determined that her father's age is the quotient of her age and 5, increased by 10. If x represents Marcy's age, write an
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Do you think there are any ordered pairs that are solutions to BOTH y = x + 5 and y = –2x – 1? Explain.
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Can someone please teach me how to do this? You can please do like 2 questions and please explain exactly how you got the answer
spayn [35]

All of these questions require one thing: trigonometric functions.

There are 3 main trigonometric functions, which can only be used on right triangles: sine, cosine, and tangent.

Sine = opposite / hypotenuse

Cosine = adjacent / hypotenuse

Tangent = opposite / adjacent

When trying to figure out what function to use, we always start by looking from the angle. Take problem a, for example. Looking from angle E, of which the value is not given, we have the side opposite and the side adjacent. Therefore, we should use the tangent function.

---The hypotenuse is always the longest side of the triangle. It is never considered the opposite or adjacent side.

Let's set up our function with the given information from problem a.

tan(x) = 9.7 / 5.2

---The tangent of an unknown angle is equal to the quotient of the opposite side and the adjacent side.

Now, solving for the value of x will require a calculator. We'll need to use what's called an inverse trigonometric function. Most calculators have these directly above the regular trigonometric functions, and the inverse functions are accessed using a "second" key.

---Ensure that your calculator is in degrees, not radians!

x = tan^-1(9.7 / 5.2)

x = 61.805 = 62 degrees

Next, let's take a look at problem b. This time, we're solving for a side length instead of an angle. But, we're still going to start by looking from our angle.


Looking from the 38 degree angle, we are given the adjacent side and an unknown hypotenuse. Therefore, we should use the cosine function.

cosine(38) = 53.1 / r

---The cosine of a 38 degree angle is equal to the quotient of 53.1 and an unknown hypotenuse, r.

Use your algebra skills to isolate the variable r.

r * cosine(38) = 53.1

r = 53.1 / cosine(38)

---From here, all you need to do is plug this into your calculator. Since we are solving for a side length (and given an angle), we are just using the regular trigonometric function buttons on the calculator.

r = 67.385 = 67.4 units

Hope this helps!

4 0
1 year ago
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