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4 years ago

7

Solve the system of equations: y=2x-3 y=x2-3

1 answer:

Westkost [7]4 years ago

5 0

Answer: x = 0 or x = 2

Step-by-step explanation:

To solve this, we must note that the two equations speaks of a single function of y. So

y = 2x - 3 = x² - 3

So from.here we can equate the two together and solve for x.

x² - 3 = 2x - 3, biw convert to a quadratic expression

x² - 2x - 3 + 3 = 0

x² - 2x = 0

Now factorize

x( x - 2 ) = 0, so solving for x

x = 0 or x = 2. .I believed getting the 2 won't be a problem

When x - 2 = 0

Then x = 2.

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Find the standard form of the equation of the parabola with a focus at (-2, 0) and a directrix at x = 2.

krok68 [10]

Answer:

$y^2=\frac{1}{8}x$

Step-by-step explanation:

The focus lies on the x axis and the directrix is a vertical line through x = 2. The parabola, by nature, wraps around the focus, or "forms" its shape about the focus. That means that this is a "sideways" parabola, a "y^2" type instead of an "x^2" type. The standard form for this type is

$(x-h)=4p(y-k)^2$

where h and k are the coordinates of the vertex and p is the distance from the vertex to either the focus or the directrix (that distance is the same; we only need to find one). That means that the vertex has to be equidistant from the focus and the directrix. If the focus is at x = -2 y = 0 and the directrix is at x = 2, midway between them is the origin (0, 0). So h = 0 and k = 0. p is the number of units from the vertex to the focus (or directrix). That means that p=2. We fill in our equation now with the info we have:

$(x-0)=4(2)(y-0)^2$

Simplify that a bit:

$x=8y^2$

Solving for y^2:

$y^2=\frac{1}{8}x$

3 0

3 years ago

How to prove that IC is parallel with AB?

Karo-lina-s [1.5K]

There is something wrong with drawing. IC intercepts with AB at A.

7 0

4 years ago

Two sides of a triangle are perpendicular. If the two sides are 8cm and 6cm, calculate correct to the next degree, the smallest

Sati [7]

$\boxed{Given:}$

Length of the perpendicular ( opposite ) = 6 cm.

Length of the base ( adjacent ) = 8 cm.

$\boxed{To\:find:}$

The smallest angle of the triangle.

$\boxed{Solution:}$

$\sf\purple{C.\:37°}$ ✅

$\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}$

In a right-angled triangle, if two sides are given, the measure of the unknown angle can be known.

Since the value of opposite and adjacent sides are given, we use the tangent formula.

tan θ = $\frac{opposite}{adjacent}$

✒ tan θ = $\frac{6 \: cm}{8 \: cm}$

✒ θ = ${tan}^{ - 1}$ (0.75)

✒ θ = 36.9°

✒ θ = 37°

Now let us find the other unknown angle 'x'.

We know that,

Sum of angles of a triangle = 180°

✒ 37° + x + 90° = 180° (90° since it is a right-angled triangle)

✒ x + 127° = 180°

✒ x = 180° - 127°

✒ x = 53°

Therefore, the three angles of the triangle are 37°, 53° and 90°.

Hence, the smallest angle is 37°.

$\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}$

7 0

3 years ago

A card has p meters of lace edging wound on it. Nerys buys n lengths of edging, each x cm long. If Q meters of edging are left o

Diano4ka-milaya [45]

Answer:

Q = P - n(x/100)

Step-by-step explanation:

P is the total number of lace edging, n is the number of times the length x is cut from P, and Q is the remnant of the reduction.

So the number of x length is subtracted from P and must be converted to meters (since it is in centimeters) to get Q. That is;

Q = P - n(x/100)

5 0

3 years ago

What is the slope of this graph ?

aev [14]

Answer:

m=1= slope

Step-by-step explanation:

here u do rise/ run

and the dots there are helping you to make it

you need to join them by doing rise over run

you go 3 to the right from the dot at the bottom and 3 up

which is 3/3 that equals to 1

if this is not right, please tell me

if it right then your welcome

5 0

3 years ago