<h2>Answer:</h2>
5x + 7y = 17 ....(1)
x + 4y = 19 .....(2)
<u>From equation 2</u>
x + 4y = 19
x = 19 - 4y
<u>Putting the value of x in Equation (1)</u>
5(19 - 4y) + 7y = 17
95 - 20y + 7y = 17
- 20y + 7y = 17 - 95
-13y = -78
y = 
y = 6
<u>Now, putting the value of y in equation </u><u>(</u><u>2</u><u>)</u>
x + 4y = 19
x + 4(6) = 19
x + 24 = 19
x = 19 - 24
x = -5
<u>Therefore, the value of y is 6 and value of x is -5</u>
Check out the attached image for the answers.
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Statement 2 is blank, but it has the reasoning "Corresponding angles postulate"
Because BD || AE, we know that the corresponding angles are congruent.
One pair of corresponding angles is angle 1 and angle 4. This is because they are on the same side of the transversal AC and they are both above their parallel line counter-part. Similarly, angle 2 and angle 3 are another corresponding pair.
So you'll have "angle1=angle4, angle3=angle2" in the first blank slot
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Reason 3 is blank. The statement is that triangle ACE is similar to triangle BCD. The reason why the are similar is the AA (angle angle) similarity postulate. This says that if you know two pairs of angles are congruent, then the triangles are similar. The two pairs of angles were mentioned back on the previous line (line 2)
So you'll put "Angle-Angle Similarity Postulate" in the second blank.
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Look at the line just above the last line. Here we have
1 + (BA/CB) = 1 + (DE/CD)
If we subtract 1 from both sides, we end up with,
BA/CB = DE/CD
which is what will go in the last blank space
Side Note: The last statement will always be what you want to prove. So you can just look at the very top of the problem where it says "Prove:" under the "Given" part. Then just copy/paste the statement you want to prove, which in this case is BA/CB = DE/CD
The correct answer between all the choices given is the third
choice or letter C.
Exponential functions are related to logarithmic functions in that they are inverse functions. Exponential functions move quickly up towards a [y] infinity, bounded by a vertical asymptote (aka limit), whereas logarithmic functions start quick but then taper out towards an [x] infinity, bounded by a horizontal asymptote (aka limit).
If we use the natural logarithm (ln) as an example, the constant "e" is the base of ln, such that:
ln(x) = y, which is really stating that the base (assumed "e" even though not shown), that:
if we try to solve for y in this form it's nearly impossible, that's why we stick with ln(x) = y
but to find the inverse of the form:
switch the x and y, then solve for y:
So the exponential function is the inverse of the logarithmic one, f(x) = ln x
If one pound of yogurt cost 55 (cents?) then, Two yogurts cost $1.10
Three yogurts cost $1.65
Four yogurts cost $2.20
Five yogurts cost $2.75
Six yogurts cost $3.30
