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MatroZZZ [7]
3 years ago
11

Determine the equation of each of the following parabolas

Mathematics
1 answer:
nata0808 [166]3 years ago
4 0

Try this solution with a short explanation:

a) y=ax²+5; ⇒ substitution (4;0): 16a+5=0; ⇒ a= -5/16.

Answer: <u>y= -5/16 x²+5</u>;

b)<u> y=x²</u>;

c) y=ax(x+7); ⇒ substitution (4;4): 4a(4+7)=4; ⇒a=1/11.

Answer: <u>y= 1/11 x²+ 7/11 x</u>;

d) y=a(x-1)(x-3); ⇒substitution (0;3): (-1)*(-3)*a=3; ⇒a=1.

Answer: <u>y=x²-4x+3</u>;

e) y=a(x-1)(x+3); ⇒ substitution (-1;5): (-2)*2*a=5; ⇒ a= -5/4.

Answer: <u>y= -5/4 x² -5/2 x +15/4</u>;

f) y=ax²+bx+c; ⇒ substitution (2;2): 4a+2b+6=2 or 2a+b= -2 (the I-st equation of the system);

the x-coordinate of the vertex: -b/2a=2; ⇒ b= -4a (the II-d equation of the system);

\left \{ {{2a+b=-2} \atop {b=-4a}} \right. \ => \ \left \{ {{a=1} \atop {b=-4}} \right.

Answer: <u>y=x²-4x+6.</u>

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In ΔFGH, what is the measure of &lt; H?
kogti [31]
X + x - 1 + 43 = 180.  Solve for x.  2x +42 = 180 and 2x = 138.  Therefore, x = 69.  If x = 69, then angle H is 68 and angle G is 69.  68 + 69 + 43 = 180.

3 0
3 years ago
Kanye and jay wanted to see who could run faster in a minute.They both started in the same spot and ran in different directions.
Lena [83]

Answer:

Kanye run faster.

Step-by-step explanation:

Given that,

Time = 1 min = 60 sec

Suppose, we find the speed of kanye and Jay.

According to number line,

Kanye covers the -160m distance and Jay covers the 140 m distance.

Negative sign shows the opposite direction.

We need to calculate the speed of Kanye

Using formula of speed

v=\dfrac{d}{t}

Where, v = speed

d = distance

t = time

Put the value into the formula

v=\dfrac{160}{60}

v=2.66\ m/s

We need to calculate the speed of Kanye

Using formula of speed

v=\dfrac{d}{t}

Put the value into the formula

v=\dfrac{140}{60}

v=2.33\ m/s

The speed of kanye is more than jay.

Hence, Kanye run faster.

6 0
3 years ago
What is the factorization of the trinomial below -x^2 + 2x + 48
OlgaM077 [116]

For this case we must factor the following expression:

-x ^ 2 + 2x + 48

We take the sign "-" as a common factor of the expression, taking into account that:

- * - = +\\- (x ^ 2-2x-48)

To factor, we must find two numbers that, when multiplied, result in -48 and when added, result in -2. These numbers are -8 and +6.

-8 + 6 = -2\\(-8) * (+ 6) = - 48

Then, we factor the expression within the parenthesis as:

- ((x-8) (x + 6))

Answer:

- (x-8) (x + 6)

4 0
3 years ago
25 points! Please help me!
fgiga [73]

When x = 5. Plug in 5 for x

f(5) = -5(5) - 4

Remember to follow PEMDAS. First, multiply -5 with 5

-5 x 5 = -25

Next, subtract 4

f(5) = -25 - 4

f(5) = -29

B. f(5) = −29 is your answer

hope this helps

8 0
3 years ago
Read 2 more answers
What is the distance in the standard (x, y) coordinate<br> plane between the points (2,3) and (5,5)?
Naddik [55]
<h3>The distance between the points (2,3) and (5,5) is 3.6 units</h3>

<em><u>Solution:</u></em>

<em><u>Distance between two points is given by:</u></em>

d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}

We have to find the distance in the standard (x, y) coordinate  plane between the points (2,3) and (5,5)

From given,

(x_1, y_1) = (2, 3)\\\\(x_2, y_2) = (5, 5)

Substituting the values we get,

d = \sqrt{(5-2)^2 + (5-3)^2}\\\\Simplify\\\\d = \sqrt{3^2 + 2^2}\\\\d = \sqrt{9+4}\\\\d = \sqrt{13}\\\\In\ decimal\ form\\\\d = 3.605 \approx 3.6

Thus distance between the points (2,3) and (5,5) is 3.6 units

3 0
3 years ago
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