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3 years ago

What number should be added to both sides of the equation to complete the square? x2 8x = 4

Mathematics

2 answers:

olga55 [171]3 years ago

7 0

Answer:

Step-by-step explanation:

Levart [38]3 years ago

6 0

You would take half of the x term...and square it
so half of 8 is 4....4^2 = 16
u would add 16 to each side

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4. Gloria the grasshopper is working on her hops.

aivan3 [116]

The path that Gloria follows when she jumped is a path of parabola.

The equation of the parabola that describes the path of her jump is $\mathbf{y = -\frac{5}{49}(x - 14)^2 + 20}$

The given parameters are:

$\mathbf{Height = 20}$

$\mathbf{Length = 28}$

Assume she starts from the origin (0,0)

The midpoint would be:

$\mathbf{Mid = \frac 12 \times Length}$

$\mathbf{Mid = \frac 12 \times 28}$

$\mathbf{Mid = 14}$

So, the vertex of the parabola is:

$\mathbf{Vertex = (Mid,Height)}$

Express properly as:

$\mathbf{(h,k) = (14,20)}$

A point on the graph would be:

$\mathbf{(x,y) = (28,0)}$

The equation of a parabola is calculated using:

$\mathbf{y = a(x - h)^2 + k}$

Substitute $\mathbf{(h,k) = (14,20)}$ in $\mathbf{y = a(x - h)^2 + k}$

$\mathbf{y = a(x - 14)^2 + 20}$

Substitute $\mathbf{(x,y) = (28,0)}$ in $\mathbf{y = a(x - 14)^2 + 20}$

$\mathbf{0 = a(28 - 14)^2 + 20}$

$\mathbf{0 = a(14)^2 + 20}$

Collect like terms

$\mathbf{a(14)^2 =- 20}$

Solve for a

$\mathbf{a =- \frac{20}{14^2}}$

$\mathbf{a =- \frac{20}{196}}$

Simplify

$\mathbf{a =- \frac{5}{49}}$

Substitute $\mathbf{a =- \frac{5}{49}}$ in $\mathbf{y = a(x - 14)^2 + 20}$

$\mathbf{y = -\frac{5}{49}(x - 14)^2 + 20}$

Hence, the equation of the parabola that describes the path of her jump is $\mathbf{y = -\frac{5}{49}(x - 14)^2 + 20}$

See attachment for the graph

Read more about equations of parabola at:

brainly.com/question/4074088

7 0

2 years ago

Select all expressions that are equivalent to 64. 2 to the sixth power 2 to the eighth power 4 to the third power 8 squared 16 t

andreyandreev [35.5K]

Answer:

2 to the sixth, 4 to the third, 8 squared

Step-by-step explanation: 2*2*2*2*2*2=64 because you would have 2, 4,8,16,32,64

4*4*4=64 because you would have 4,16,64

8*8=64

3 0

2 years ago

Mary runs 5 miles in 1.25 hours. How many miles does she run in 1 hour? HELP PLSSS

ICE Princess25 [194]

Answer:

She runs 4 miles in one hour

Step-by-step explanation:

5 divided by 1.25=4

7 0

3 years ago

Give the unit rate for the better deal. $156 4 g or $280 7 g

Alexus [3.1K]

Answer:

$156 for 4 g

I did not rally understand how you worded your question so sorry if I got it wrong! <3

Step-by-step explanation:

$156 for 4 g =

$156 / 4 = $39 dollars for 1 g

$280 for 7 g =

$280/7 = $40 dollars for 1 g

8 0

3 years ago

Read 2 more answers

A tv has a listed price of $896.99 before tax. If the sales tax rate is 7.75%, find the total cost of the tv with sales tax incl

nadezda [96]

Answer:69.52

Step-by-step explanation:First set up a proportion which is basically a fraction.To set it up first you must put two fractions together with an equals sign in between both fractions.Then add the whole on the denominator to the left then an x for the one above the whole cause were looking for a part.Then add the percent to the top right which in this case is 7.75 then 100 as the denominator cause it represents a whole.Then when looking for a part multiply Denominator on left which in this case is 896.99 then multiply it by the percent 7.75 which should give you 6951.6725 then divide by 100 which is 69.516725 then round which is 69.52.

7 0

3 years ago