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3 years ago

Please help, fast! 50 points!

Mathematics

2 answers:

Nat2105 [25]3 years ago

4 0

Answer: e?

Step-by-step explanation:

den301095 [7]3 years ago

3 0

Answer:

Step-by-step explanation:

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Explain how you know if a system of equations has one solution, no solutions, or infinitely many solutions. Write your answers (

Nataliya [291]

Answer:

Written Below.

Step-by-step explanation:

A system of linear equations has one solution when the graphs intersect at a point. A system of linear equations has no solution when the graphs are parallel. A system of linear equations has infinite solutions when the graphs are the exact same line.

(This uses graphing.)

Sidenote: I hope this helps! :)

7 0

3 years ago

Axis of sym: x =

marta [7]

Answer:

<h2>SEE BELOW</h2>

Step-by-step explanation:

<h3>to understand this</h3><h3>you need to know about:</h3>

quadratic function
PEMDAS

<h3>let's solve:</h3>

vertex:(h,k)

therefore

vertex:(-1,4)

axis of symmetry:x=h

therefore

axis of symmetry:x=-1

to find the quadratic equation we need to figure out the vertex form of quadratic equation and then simply it to standard form i.e ax²+bx+c=0

vertex form of quadratic equation:

y=a(x-h)²+k

therefore

y=a(x-(-1))²+4
y=a(x+1)²+4

it's to notice that we don't know what a is

therefore we have to figure it out

the graph crosses y-asix at (0,3) coordinates

so,

3=a(0+1)²+4

simplify parentheses:

$3 = a(1 {)}^{2} + 4$

simplify exponent:

$3 = a + 4$

therefore

$a = - 1$

our vertex form of quadratic equation is

y=-(x+1)²+4

let's simplify it to standard form

simplify square:

$y = - ( {x}^{2} + 2x + 1) + 4$

simplify parentheses:

$y = - {x}^{2} - 2x - 1 + 4$

simplify addition:

$y = - {x}^{2} - 2x + 3$

therefore our answer is D)y=-x²-2x+3

the domain of the function

$x\in \mathbb{R}$

and the range of the function is

$y\leqslant 4$

zeroes of the function:

$- {x}^{2} - 2x + 3 = 0$

$\sf divide \: both \: sides \: by \: - 1$

${x}^{2} + 2x - 3 = 0$

$\implies \: {x}^{2} + 3x - x + 3 = 0$

factor out x and -1 respectively:

$\sf \implies \: x(x + 3) - 1(x + 3 )= 0$

group:

$\implies \: (x - 1)(x + 3) = 0$

therefore

$\begin{cases} x_{1} = 1 \\ x_{2} = - 3\end{cases}$

4 0

3 years ago

ПОЖАЛУЙСТА ПОМОГИТЕ РЕШИТЬ ДАЮ 23 ОЧКА!!!

posledela

(Простите, пожалуйста, мой английский. Русский не мой родной язык. Надеюсь, у вас есть способ перевести это решение. Если нет, возможно, прилагаемое изображение объяснит достаточно.)

Use the shell method. Each shell has a height of 3 - 3/4 <em>y</em> ², radius <em>y</em>, and thickness ∆<em>y</em>, thus contributing an area of 2<em>π</em> <em>y</em> (3 - 3/4 <em>y</em> ²). The total volume of the solid is going to be the sum of infinitely many such shells with 0 ≤ <em>y</em> ≤ 2, thus given by the integral

$\displaystyle 2\pi \int_0^2 y \left(3-\frac34 y^2\right) \,\mathrm dy = 2\pi \left(\frac32 y^2 - \frac3{16} y^4\right)\bigg|_0^2 = 6\pi$

Or use the disk method. (In the attachment, assume the height is very small.) Each disk has a radius of √(4/3 <em>x</em>), thus contributing an area of <em>π</em> (√(4/3 <em>x</em>))² = 4<em>π</em>/3 <em>x</em>. The total volume of the solid is the sum of infinitely many such disks with 0 ≤ <em>x</em> ≤ 3, or by the integral

$\displaystyle \pi \int_0^3 \left(\sqrt{\frac43x}\right)^2 \,\mathrm dx = \frac{2\pi}3 x^2\bigg|_0^3 = 6\pi$

Using either method, the volume is 6<em>π</em> ≈ 18,85. I do not know why your textbook gives a solution of 90,43. Perhaps I've misunderstood what it is you're supposed to calculate? On the other hand, textbooks are known to have typographical errors from time to time...