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2 years ago

9. Simplify 1-3 - 81.

Mathematics

2 answers:

vekshin12 years ago

5 0

Answer:

-83

Step-by-step explanation:

just olya [345]2 years ago

3 0

Answer:

-83

Step-by-step explanation:

(1-3)-81

-2-81=-83

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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:

$\mathbf{Height = 20}$

$\mathbf{Length = 28}$

<em>Assume she starts from the origin (0,0)</em>

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

he books in a private library are classified as fiction and nonfiction. There are 400 books in the library. There are 40 more fi

vfiekz [6]

First, you have to set a system of equations to determine the number of fiction and of nonfiction books.Call f the number of fiction books and n the number of nonfiction books. Then 400 = f + n. And f = n + 40 => n = f - 40 => 400 = f + f - 40 => 400 - 40 = 2f => f = 360 / 2 = 180. Now to find the probability of picking two fiction books, take into account the the Audrey will pick from 180 fiction books out of 400, and Ryan will pick from 179 fiction books out of 399, so the probability will be<span> (180/ 400) * (179/399) = 0.20 (rounded to two decimals). Answer: 0.20</span>

3 0

2 years ago

How many baby's does it take to paint a wall

mestny [16]

Answer:

12 I think?

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Train a is traveling at 30 mph faster than train b. If train a travels 350 miles in the same amount of time that train b travels

GalinKa [24]

Answer:

20 mph

Step-by-step explanation:

Let speed of Train a = Va mph

Let speed of Train b = Vb mph

Va = Vb + 30

Let time taken for Train a = Ta

Let time taken for Train b = Tb

time taken = distance travelled/speed

Ta = 350/Va = 350/(Vb+30)

Tb = 140/Vb

But they both travel in the same amount of time.

So, Ta = Tb

$\frac{350}{v_{b} + 30}=\frac{140}{v_{b}}$

Cross multiply

$350v_{b} = 140(v_{b} + 30)\\\\350v_{b} = 140v_{b} + 4200\\\\350v_{b} -140v_{b} = 4200\\\\210v_{b} = 4200$

Divide both sides by 210

$\frac{210v_{b} }{210} \frac{4200}{210} \\\\v_{b} = 20 mph$

4 0

2 years ago

Are all equilateral triangles acute?

Anvisha [2.4K]

Answer:

Yes, all equilateral triangles are acute.

Step-by-step explanation:

yea

hope this helps :)))

8 0

2 years ago