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3 years ago

Estimate the value of 9.9 squared 2 x 1.79

Mathematics

1 answer:

Mekhanik [1.2K]3 years ago

5 0

Answer: 180

Step-by-step explanation: 9.9 squared by 1.79 is 180

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Joan joined her school's band. She bought a viola for $72.21, and a song book

Kryger [21]

Hello :D

To do this you need to add the cost of the violin and the song book.

$72.21 + $7.25 = $79.46

$100 - $79.46 = $20.54

The answer is $20.54. I hope this helps :)

7 0

3 years ago

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Could someone help me rnnn?

GuDViN [60]

Answer:

vertex = (0, -4)

equation of the parabola: $y=3x^2-4$

Step-by-step explanation:

Given:

y-intercept of parabola: -4
parabola passes through points: (-2, 8) and (1, -1)

Vertex form of a parabola: $y=a(x-h)^2+k$

(where (h, k) is the vertex and $a$ is some constant)

Substitute point (0, -4) into the equation:

$\begin{aligned}\textsf{At}\:(0,-4) \implies a(0-h)^2+k &=-4\\ah^2+k &=-4\end{aligned}$

Substitute point (-2, 8) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(-2,8) \implies a(-2-h)^2+k &=8\\a(4+4h+h^2)+k &=8\\4a+4ah+ah^2+k &=8\\\implies 4a+4ah-4&=8\\4a(1+h)&=12\\a(1+h)&=3\end{aligned}$

Substitute point (1, -1) and $ah^2+k=-4$ into the equation:

$\begin{aligned}\textsf{At}\:(1.-1) \implies a(1-h)^2+k &=-1\\a(1-2h+h^2)+k &=-1\\a-2ah+ah^2+k &=-1\\\implies a-2ah-4&=-1\\a(1-2h)&=3\end{aligned}$

Equate to find h:

$\begin{aligned}\implies a(1+h) &=a(1-2h)\\1+h &=1-2h\\3h &=0\\h &=0\end{aligned}$

Substitute found value of h into one of the equations to find a:

$\begin{aligned}\implies a(1+0) &=3\\a &=3\end{aligned}$

Substitute found values of h and a to find k:

$\begin{aligned}\implies ah^2+k&=-4\\(3)(0)^2+k &=-4\\k &=-4\end{aligned}$

Therefore, the equation of the parabola in vertex form is:

$\implies y=3(x-0)^2-4=3x^2-4$

So the vertex of the parabola is (0, -4)

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3 years ago

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2/3x- 1/5 is greater than 1

Natasha_Volkova [10]

Answer:

Step-by-step explanation:

$\dfrac{2}{3}x-\dfrac{1}{5}>1\qquad\text{multiply both sides by 15}\\\\15\!\!\!\!\!\diagup^5\cdot\dfrac{2}{3\!\!\!\!\diagup_1}x-15\!\!\!\!\!\diagup^3\cdot\dfrac{1}{5\!\!\!\!\diagup_1}>15\cdot1\\\\(5)(2x)-3>15\qquad\text{add 3 to both sides}\\\\10x>18\qquad\text{divide both sides by 10}\\\\\boxed{x>1.8}$