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3 years ago

The square of a number is increased by 27 and the result is 148. Find all possible solutions for the number.

Mathematics

2 answers:

professor190 [17]3 years ago

8 0

Answer:

121

Step-by-step explanation:

Alex_Xolod [135]3 years ago

3 0

One if the solutions is 11

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How to find the vertex calculus 2What is the vertex, focus and directrix of x^2 = 6y

son4ous [18]

Solution:

Given:

$x^2=6y$

Part A:

The vertex of an up-down facing parabola of the form;

$\begin{gathered} y=ax^2+bx+c \\ is \\ x_v=-\frac{b}{2a} \end{gathered}$

Rewriting the equation given;

$\begin{gathered} 6y=x^2 \\ y=\frac{1}{6}x^2 \\ \\ \text{Hence,} \\ a=\frac{1}{6} \\ b=0 \\ c=0 \\ \\ \text{Hence,} \\ x_v=-\frac{b}{2a} \\ x_v=-\frac{0}{2(\frac{1}{6})} \\ x_v=0 \\ \\ _{} \\ \text{Substituting the value of x into y,} \\ y=\frac{1}{6}x^2 \\ y_v=\frac{1}{6}(0^2) \\ y_v=0 \\ \\ \text{Hence, the vertex is;} \\ (x_v,y_v)=(h,k)=(0,0) \end{gathered}$

Therefore, the vertex is (0,0)

Part B:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

$\begin{gathered} x^2=6y \\ 6y=x^2 \\ 4(\frac{3}{2})(y-k)=(x-h)^2 \\ \text{putting (h,k)=(0,0)} \\ 4(\frac{3}{2})(y-0)=(x-0)^2 \\ Comparing\text{to the standard form;} \\ p=\frac{3}{2} \end{gathered}$

Since the parabola is symmetric around the y-axis, the focus is a distance p from the center (0,0)

Hence,

$\begin{gathered} Focus\text{ is;} \\ (0,0+p) \\ =(0,0+\frac{3}{2}) \\ =(0,\frac{3}{2}) \end{gathered}$

Therefore, the focus is;

$(0,\frac{3}{2})$

Part C:

A parabola is the locus of points such that the distance to a point (the focus) equals the distance to a line (directrix)

Using the standard equation of a parabola;

$\begin{gathered} 4p(y-k)=(x-h)^2 \\ \\ \text{Where;} \\ (h,k)\text{ is the vertex} \\ |p|\text{ is the focal length} \end{gathered}$

Rewriting the equation in standard form,

Since the parabola is symmetric around the y-axis, the directrix is a line parallel to the x-axis at a distance p from the center (0,0).

Hence,

$\begin{gathered} Directrix\text{ is;} \\ y=0-p \\ y=0-\frac{3}{2} \\ y=-\frac{3}{2} \end{gathered}$

Therefore, the directrix is;

$y=-\frac{3}{2}$

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1 year ago

How do you solve 4•(4y/3-2) + 3y = 17

Hunter-Best [27]

Us photo math , it show u even the steps of how was it solve

6 0

3 years ago

2.8*10⁶=?<br>solve the equation, please

garri49 [273]

Answer:

2800000

Step-by-step explanation:

10^6 means 1000000

2.8 x 1000000 = 2800000

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3 years ago

Rewrite the expression in the form 2".<br> E

Vlad [161]

Answer:

z^ {8/5}

Step-by-step explanation:

$(z^{\frac{-4}{3})^{\frac{-6}{5} } \\We\ know\ that\ a^{(b)^c} = a^{bc}\\\\Hence, \\\\{z^{\frac{-4}{3})^{\frac{-6}{5}}\\}={z^{\frac{-4}{3}*\frac{-6}{5}\\}\\=z^{\frac{24}{15}}\\=z^\frac{8}{5}$

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3 years ago

Quadrilateral ABCD is inscribed in a circle<br> What is the measure of angle A?

Katen [24]

Answer:

Quadrilateral ABCD is inscribed in a circle, then

A + C = 180

=> 2x + 9 + 3x + 1 = 180

=> 5x = 170

=> x = 34

=> A = 2 x 34 + 9 = 77 deg

Hope this helps!

4 0

3 years ago

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