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Liula [17]
3 years ago
12

He sum of two numbers is 47. The greater number is 9 more than the smaller number. Which equation can be used to solve for the s

maller number? (5 points)
x(x + 9) = 47

x + (x + 9) = 47

x(x − 9) = 47

x − (x + 9) = 47
Mathematics
1 answer:
yan [13]3 years ago
7 0
I believe the correct answer from the choices listed above is the first option. The equation that can be used to solve the problem would be x + (x + 9) = 47.

The sum of two numbers is 47. ---> x + y = 47 where x is the smaller number and y is the larger. 

The greater number is 9 more than the smaller number.  -----> y = x + 9 

x + ( x + 9 ) = 47
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What is the equation of the line?
spin [16.1K]

Answer:

y=1/2x+2

Step-by-step explanation:

You want to find the equation for a line that passes through the two points:

(0,2) and (-4,0).

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (0,2), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=0 and y1=2.

Also, let's call the second point you gave, (-4,0), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-4 and y2=0.

Now, just plug the numbers into the formula for m above, like this:

m= 0 - 2-4 - 0 or... m= -2-4 or... m=1/2

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=1/2x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(0,2). When x of the line is 0, y of the line must be 2.

(-4,0). When x of the line is -4, y of the line must be 0.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=1/2x+b. b is what we want, the 1/2 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (0,2) and (-4,0).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(0,2). y=mx+b or 2=1/2 × 0+b, or solving for b: b=2-(1/2)(0). b=2.

(-4,0). y=mx+b or 0=1/2 × -4+b, or solving for b: b=0-(1/2)(-4). b=2.

See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(0,2) and (-4,0)

is

y=1/2x+2

4 0
3 years ago
A kite is stuck in a 36-ft tree. If the angle of elevation from the kite and the ground is 12, find the length of the kite.
yanalaym [24]

Answer:

173.15 ft.  

Step-by-step explanation:

Please find the attachment.

Let L be the length of kite.  

We have been given that a kite is stuck in  36-ft tree. The angle of elevation from the kite and the ground is 12.

We can see from our attachment that kite and tree form a right triangle. height of tree is opposite of angle of elevation and length of kite is hypotenuse.

Since we know that Sine relates the opposite and hypotenuse of a right triangle, so we will use sine to find the length of kite.

sin(12)=\frac{36}{L}    

L=\frac{36}{sin(12)}

L=\frac{36}{0.207911690818}  

L=173.1504364105882792\approx 173.15

Therefore, the length of kite is 173.15 ft.

4 0
2 years ago
Please answer this question only if you know it!
rusak2 [61]

i believe that the answer is b (but it could be c) pls consider what the other person that answers it says

6 0
3 years ago
4(5x - 2) = 72<br> What do I do
Pepsi [2]

Answer:

x = 4

Step-by-step explanation:

4(5x - 2) = 72

Do the distributive property

20x - 8 = 72

Then add 8 to both sides to get 20x alone

20x - 8 = 72

      + 8  + 8

20x = 80

Then divide both sides by 20 to get x

\frac{20x}{20} = \frac{80}{20}

x = 4

6 0
3 years ago
Describe how to find the least common multiple of three numbers
notka56 [123]
Find all the prime factors of the three numbers. pick up the common factors, ONCE, then pick up the non-common factors one by one, multiply the factors, the product is the least common factor.
example: the least common multiple of 6, 8, and 15
6=2*3
8=2*2*2
15=3*5
Note: do not write 8 into 4*2, because 4 is not a prime number. you have to break the number down to prime factors only. 
Notice that 6 and 8 have a common factor 2, so pick up the 2;
 6 and 15 have a common factor of 3, so pick up the 3.
those are the only two shared factors, so 2×3
now pick up whatever is not shared:
the two 2s for 8 and the 5 for 15 is not shared, add 2, 2, and 5 to the multiplication: 2×3×2×2×5=120
120 is the least common multiples of 6,8, and 15

this is basically how it is done. I believe you can explain better in your own words. 

3 0
3 years ago
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