<span>3n-8+2(5n+3)=8n+5+4n first I will do the multiplication
3n-8+10n+6=8n+5+4n Now I will simplify
13n -2 = 12n +5 Now I will add 2 to both sides
13n = 12n + 7 then I subtract 12n from both sides
n = 7</span>
Answer:
c) x=2
Step-by-step explanation:
2.5(6x-4)=10+4(1.5+0.5x)?
=15x-10=10+6+2x
=15x-2x=10+6+10
=13x=26
=13x/13=26/13
=therefore X=2
Answer: approximately <u>188.07</u> feet
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Explanation:
Refer to the diagram below. Note that the 62 degree angle is from the fact that 90-28 = 62.
With the reference angle 62 degrees in mind, we have an unknown opposite side x feet and a known adjacent side 100 feet.
Use the tangent trig ratio to tie the two sides together, and then solve for x.
tan(angle) = opposite/adjacent
tan(62) = x/100
100*tan(62) = x
x = 100*tan(62)
x = 188.072646534633 approximately
x = 188.07 feet approximately
Your calculator needs to be in degree mode. One way to check is to compute something like tan(45) and the result should be 1.
9. y=-1/4x^2+4x-19
group
y=(-1/4x^2+4x)-19
undistribute -1/4
y=-1/4(x^2-16x)-19
take 1/2 of -16 and squer it to get 64 then add neg and pos inside
y=-1/4(x^2-16x+64-64)-19
factorperfect square
y=-1/4((x-8)^2-64)-19
expand
y=-1/4(x-8)^2+16-19
y=-1/4(x-8)^2-3
vertex is (8,-3)
10.
group
y=(1/4x^2-3x)+18
undistribute
y=1/4(x^2-12x)+18
take 1/2 of -12 and square it and add neg and pos isndie
y=1/4(x^2-12x+36-36)+18
factor
y=1/4((x-6)^2-36)+18
expand
y=1/4(x-6)^2-9+18
y=1/4(x-6)^2+9
get to form (x-h)^2=4p(y-k)
minus 9 both sides and times 4
(x-6)^2=4(y-9)
(x-6)^2=4(1)(y-9)
so 1>0 so opens up and focus is 1 above vertex
vertex is (6,9)
so focus i (6,10)
11.
y=(-1/6x^2+7x)-80
y=(-1/6)(x^2-42x)-80
take 1/2 of linear coefient and squer it and add negative and positive inside
-42/2=-21, (-21)^2=441
y=(-1/6)(x^2-42+441-441)-80
factor perfect square the square
y=(-1/6)((x-21)^2-411)-80
expand
y=(-1/6)(x-21)^2+73.5-80
y=(-1/6)(x-21)^2-6.5
add 6.5 to both sid
y+6.5=(-1/6)(x-21)^2
times both sides by -6
-6(y+6.5)=(x-21)^2
(x-21)^2=-6(y+6.5)
(y-21)^2=4(-3/2)(y-(-6.5))
vertex is
-3/2<0 so directix is above
it is -3/2 or 1.5 units above the vertex
up is y so
-6.5+1.5=-5
the directix is y=-5
11.
in form (y-1)^2=4p(x+3)
opens left or right
(y-1)^2=4(4)(x+3)
vertex is (-3,1)
4>0 so opens right
dirextix is to left
it is 4 units to left
(-3,1)
left right is x
4 left of -3 is -4-3=7
x=-7 is da directix
Answer:
292,466,875.95
Step-by-step explanation:
