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4 years ago

Beth and Amy are trading marbles. Beth has three times more marbles than her sister, Amy.

Mathematics

1 answer:

dusya [7]4 years ago

8 0

Answer:

The answer is c which is 7.

Step-by-step explanation:

3 times so,

21 / 3 = 7

Hopes this helps.

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I needs help with it

Slav-nsk [51]

Answer:

a) initial height = 0 m

b) 8 s

c) vertex = (4, 32)

maximum height = 32 m

Step-by-step explanation:

<u>Given equation</u>:

$h=-2t^2+16t$

where:

h is the height of the arrow about the ground (in metres)
t is the time (in seconds)

The initial height of the arrow will be at the beginning of its journey, so when t = 0

Substitute t = 0 into the equation and solve for h:

$\implies h=-2(0)^2+16(0)$

$\implies h=0$

Therefore, the initial height of the arrow is 0 m.

The arrow will hit the ground when the height is 0 m.

Substitute h = 0 into the given equation:

$\implies -2t^2+16t=0$

Factor out -2t:

$\implies -2t(t-8)=0$

Therefore:

$\implies -2t=0 \implies t=0$

And:

$\implies t-8=0 \implies t=8$

Therefore, the arrow will hit the ground at 8 seconds.

The vertex is the <u>turning point</u> of a parabola - it's minimum or maximum point.

As the leading coefficient for the given equation is <u>negative</u>, the parabola <u>opens downwards</u> and so its <u>vertex</u> is its <u>maximum point</u>.

There are different ways to find the vertex of a parabola. The easiest way to find the x-coordinate is by calculating the midpoint of the x-intercepts.

We have determined that the arrow has a height of 0 m at 0 seconds and 8 seconds. Therefore, t = 0 and t = 8 are the x-intercepts. The midpoint is halfway between zero and 8, so the midpoint is t = 4

To find the y-coordinate, substitute t = 4 into the equation and solve for h:

$\implies h=-2(4)^2+16(4)$

$\implies h=-32+64$

$\implies h=32$

Therefore, the coordinates of the vertex are (4, 32)

The maximum height is the y-coordinate of the vertex.

Therefore, the maximum height is 32 m

6 0

2 years ago

A company is trying to decide which container of coffee to buy for a staff meeting. Which of the following would be the best dea

miv72 [106K]

60 ounces would be the best thing for them to get it the cheapest to get the most

6 0

3 years ago

Simplify this equation please <br> (16a^8/c^12)^1/4

Tcecarenko [31]

Answer:

$\large\boxed{\left(\dfrac{16a^8}{c^{12}}\right)^\frac{1}{4}=\dfrac{2a^2}{c^3}}$

Step-by-step explanation:

$\left(\dfrac{16a^8}{c^{12}}\right)^\frac{1}{4}\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\ \text{and}\ (a^n)^m=a^{nm}\ \text{and}\ (ab)^n=a^nb^n\\\\=\dfrac{(2^4a^8)^\frac{1}{4}}{(c^{12})^\frac{1}{4}}=\dfrac{(2^4)^\frac{1}{4}(a^8)^\frac{1}{4}}{c^{12\cdot\frac{1}{4}}}=\dfrac{2^{4\cdot\frac{1}{4}}\cdot a^{8\cdot\frac{1}{4}}}{c^3}=\dfrac{2^1\cdot a^2}{c^3}=\dfrac{2a^2}{c^3}$

4 0

3 years ago

Read 2 more answers

Use forward or backward substitute to conjecture a closed formula which describes the nth term of the sequence an = an-1 – n, wh

WINSTONCH [101]

The closed formula for <span>an = an-1 – n will be found using the formula for arithmetic sequence given by:
an=a+d(n-1)
where
a=first term
d=common difference
n=number of terms
From the formula given:
a=4
d=n
thus the formula will be:
an=a+n(n-1)
an=4+n(n-1)

</span>

7 0

3 years ago

one of the solutions to x2 − 2x − 15 = 0 is x = −3. what is the other solution? x = −5 x = −1 x = 1 x = 5

Goryan [66]

$x^{2} -2x-15=0$
P(-15)
s(-2)
$x^{2} -5x+3x-15$
=x(x-5)+3(x-5)
=(x+3)(x-5)
x=5

3 0

4 years ago