Answer:
Step-by-step explanation:
37.99 * 25%= 9.497 or $9.50 tip
Answer
The line of symmetry x = -4
Step by step explanation
Here we have to use the formula.
The symmetry of a parabola x = -b/2a
Now compare the given equation y = 3x^2 + 24x -1 with the general form y = ax^2 + bx + c and identify the value of "a" and "b"
Here a = 3 and b = 24. Now plug in these values in to the formula to find the line of symmetry.
x = -24/ 2(3)
x = -24/6
x = -4
Therefore, the line of symmetry x = -4.
Thank you.
(tanθ + cotθ)² = sec²θ + csc²θ
<u>Expand left side</u>: tan²θ + 2tanθcotθ + cot²θ
<u>Evaluate middle term</u>: 2tanθcotθ = 
= 2
⇒ tan²θ + 2+ cot²θ
= tan²θ + 1 + 1 + cot²θ
<u>Apply trig identity:</u> tan²θ + 1 = sec²θ
⇒ sec²θ + 1 + cot²θ
<u>Apply trig identity:</u> 1 + cot²θ = csc²θ
⇒ sec²θ + csc²θ
Left side equals Right side so equation is verified
Answer:
Step-by-step explanation:
Eliminate answer 4 immediately, because (4)(3) is not 7.
Look at answer 2: 7x + 3x = 10x, which does not match the middle term 12x in the original polynomial. Eliminate answer 2.
Look at answer 1: 1x + 21x = 22x, which does not match the middle term of the original polynomial. Eliminate answer 1.
All quadratics have solutions. Let's apply the quadratic formula to 3x^2 + 12x + 7: Here a = 3, b = 12 and c = 7, so that the discriminant b²-4ac is
12²-4(3)(7), or 144 - 84, or 60. Being positive, this tells us that the given poly has two real, unequal roots:
-12 ± √60 -12 + 2√15 -12 - 2√15
x = ----------------- = ------------------- and x = --------------------
3 3 3
Normally, if c is a root, then x - c is a factor.
If we try this here, however, the resulting factors do not at all match any of your answer choices.
Don't be offended...but please ensure you have copied this problem down correctly.
If 21 is added to (+ 21) a number (x) the result (=) is 40 less than (- 40) twice the number (2x)
x + 21 = 2x - 40 Add 40 to both sides
x + 61 = 2x Subtract x from both sides
61 = x Switch the sides to make it easier to read
x = 61
