Vertex form is basically commplete the square
y=a(x-h)^2+k
y=x^2+14x+4
take 1/2 of 14 and square it, (7^2=49)
add that and its negative to right side
y=x^2+14x+49-49+4
factor perfect squaer
y=(x+7)^2-49+4
y=(x+7)^2-45
answer is A
Yes, you are correct.
From the image, we can see 3 triangles, the large triangle and the two triangles that make the larger triangle.
All 3 of these triangles are similar since they're angle measurements are the same (can be proven by geometry).
We can gather the following information from the given information.
- The largest triangle (the one made up of two triangles) has a hypotenuse of 3+9=12, and a leg length of x. The hypotenuse to leg ratio is 12/x
- The second largest triangle has a hypotenuse length x and leg length 9. The hypotenuse to leg ratio is x/9
We know the hypotenuse to corresponding leg ratio must be equal since these two triangles are similar. Thus, we have the equation:
12/x = x/9
Using the cross product property gives us:
x² = 9 × 12
x² = 108
Taking the square root of both sides gives us:
x = √108
= 6 √3
Thus, your answer is correct. Great job!
Let me know if you need any clarifications, thanks!
His commission is simply: $15,000 x 0.04 = $600
Answer:
$6.25 marked up 25% is $7.81
Step-by-step explanation:
First, you have to find what 25% is of 6.25.
Step 1: Our output value is 25.
Step 2: We represent the unknown value with x.
Step 3: From step 1 above, 25=100%.
Step 4: Similarly, x=6.25%.
Step 5: This results in a pair of simple equations:
25=100%(1)
x=6.25%(2)
Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both
equations have the same unit (%); we have
<u>25 </u> = <u>100</u>
x 6.25
Step 7: Again, the reciprocal of both sides gives
<u> x </u> = <u>6.25</u>
25 100
x= 1.5625
x≈ 1.56
Once you've known what 25% is, you add it to 6.25.
1.56+6.25= 7.81
