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vlada-n [284]
3 years ago
12

Which equation can be used to solve for m, the greater integer? m(m – 3) = 108 m(m + 3) = 108 (m + 3)(m – 3) = 108 (m – 12)(m –

9) = 108
Mathematics
1 answer:
nata0808 [166]3 years ago
5 0

Answer:

m(m-3)=108

Step-by-step explanation:

Complete question below:

Two positive integers are 3 units apart on a number line. Their product is 108.

Which equation can be used to solve for m, the greater integer?

m(m – 3) = 108

m(m + 3) = 108

(m + 3)(m – 3) = 108

(m – 12)(m – 9) = 108

Solution

On the number line,

Let

m= larger integer

The integers are 3 numbers apart on the number line, so

m-3=smaller integer

The product (×) of the larger and smaller integers=108

(m)*(m-3)=108

m(m-3)=108

Therefore, the equation that can be used to solve for m, the larger integer is:

 m(m – 3) = 108 

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Answer: the future value is $1748.4

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We would apply the formula for determining compound interest which is expressed as

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r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

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t = 3 years

Therefore,.

A = 1550(1 + 0.04/365)^365 × 3

A = 1550(1+0.00011)^1095

A = 1550(1.00011)^1095

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A 95-foot wire attached from the top of a cell phone tower makes a 62 degree angle with the ground. Joey is standing 150 feet be
a_sh-v [17]

Answer:

23.32 degrees

Step-by-step explanation:

We set up a large right triangle that has 2 triangles within it.  The large triangle is a right triangle.  The height of it is the height of the tower, the base angle is 62, the hypotenuse is 95, and the base measure is y.  The other triangle has the same height which is the height of the tower, the angle is what we are looking for, and the base measure is 150 feet beyond y, so its measure is y + 150.  We have enough information to find the height of the tower, so let's do that first.  Going back to the first smaller triangle.  

sin62=\frac{x}{95} so the height of the tower is 83.88 feet.  Now we need to solve for y.  Using that same triangle and the tangent ratio, we find that tan62=\frac{83.88}{y}.  Now let's do the same thing for the other triangle with the unknown angle.

tan\beta =\frac{83.88}{y+150}

Solve both of these for y.  The first one solved for y:

y=\frac{83.88}{tan62}

The second one solved for y will simplify to:

y=\frac{83.88-150tan\beta }{tan\beta }

Now that these are both solved for y, and y = y, we can set them equal to each other by the transitive property of equality:

\frac{83.88-150tan\beta }{tan\beta }=\frac{83.88}{tan62}

Cross multiply to get this big long messy looking thing:

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Distribute through the parenthesis to get

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Get the unknown angles on the same side so it can be factored out:

83.88tan62=83.88tan\beta +[(tan62)(150tan\beta )]

And then factoring it out gives you:

83.88tan62=tan\beta(83.88+150tan62)

Divide to get

tan\beta =\frac{83.88tan62}{83.88+150tan62}

Do this on your calculator in degree mode to give you an angle measure of 23.32°.  I know this is really hard to follow without being able to draw the pics for you like I do in my classroom, but hopefully you can follow my description and draw your own triangles and follow from that!

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