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JulijaS [17]
3 years ago
10

NEED HELP ASAP!

Mathematics
1 answer:
Brrunno [24]3 years ago
8 0
complette the square to get vertex form or y=a(x-h)^2+k
(h,k) is vertex
1. group x terms, so for y=ax^2+bx+c, do y=(ax^2+bx)+c <span> <span> </span> 2, factor out the leading coefinet (constant in front of the x^2 term), basicallly factor out a </span><span> <span> </span> 3. take 1/2 of the linear coefient (number in front of the x), and square it ,then add negative and positive of it inside parnthases </span><span> <span> </span> 4. complete the squre and expand </span>


so
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)
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Joanie bought a total of 56 presents to put in 7 gift bags.She put 3 pencils and an equal number of stickers in each bag.How man
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Answer:

5 stickers were put in each bag.

Step-by-step explanation:

There is a total of 56 presents and 7 gift bags. If she puts three pencils in each bag, 7 times 3 is 21. 56 presents minus 21 pencils is 35 presents left. 35 divided by 7 is 5, so there are 5 stickers in each bag.

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2 years ago
What is the value of the discriminant, b2 − 4ac, for the quadratic equation 0 = x2 − 4x + 5, and what does it mean about the num
Aleksandr-060686 [28]
So discriminant gives us 3 possibilites connected with result of the equation b^2-4ac. If it is bigger than zero, there are 2 solutions, if answer is exactly 0, then there is one answer and if the number is lower than 0, there are no solutions.

Discriminant of your quadratic equation is (-4)^2-4*1*5=16-20=-4, so there are no solutions.
3 0
2 years ago
Read 2 more answers
After writing part of his novel, Thomas is now writing 16 pages per week. After 4 weeks, he has written 85 pages. Assume the rel
d1i1m1o1n [39]

The initial value is 21 and rate of change is 16 pages per week

<em><u>Solution:</u></em>

Given that After writing part of his novel, Thomas is now writing 16 pages per week

After 4 weeks, he has written 85 pages.

Given that assume the relationship to be linear

Linear relationships can be expressed either in a graphical format or as a mathematical equation of the form y = mx + c

y = mx + c

where "y" is the number of pages written after 4 weeks

x = 4 weeks and m = 16 pages

Therefore,

85 = 16(4) + c

85 = 64 + c

c = 85 - 64

c = 21

Therefore, initial value is 21 and rate of change is 16 pages per week

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3 years ago
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2 years ago
Show that y=cos(t)y=cos(t) is a solution to (dydt)2=1−y2(dydt)2=1−y2. Enter your answers below in terms of the independent varia
GrogVix [38]

Answer:

(\frac{dy}{dt})^2=sin^2t

Step-by-step explanation:

y=cost

DE :(\frac{dy}{dt})^2=1-y^2

If y is a solution of given DE then it satisfied the DE.

Differentiate w.r.t t

\frac{dy}{dt}=-sint

Using the formula

\frac{d(cosx)}{dx}=-sinx

LHS:(\frac{dy}{dt})^2=(-sint)^2=sin^2t

RHS

1-y^2=1-cos^2t=sin^2t

By using the formula

sin^2t=1-cos^2t

LHS=RHs

Hence, y is a solution of given DE

(\frac{dy}{dt})^2=sin^2t

7 0
3 years ago
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