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3 years ago

What is the equation of the following graph?

Mathematics

1 answer:

dangina [55]3 years ago

7 0

There are a couple of different ways you could do this, but I'll show the simpler way. We will use the formula

$y=a(x-h)^2+k$

along with the fact that the vertex has h and k coordinates of 1 and 4 respectively, and that a point on the graph is (3, 5). We could have used any point on the graph where there is a definite integer coordinate pair. We will fill in accordingly and solve for a.

$5=a(3-1)^2+4$ and

5 = 4a + 4. If we subtract 4 from both sides we get that $a=\frac{1}{4}$ . Now we will fill in the formula and expand as needed:

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

$y=\frac{1}{4}(x^2-2x+1)+4$ . If we distribute the 1/4 in and then add the constants the final equation for that graph will be

$y=\frac{1}{4}x^2-\frac{1}{2}x+\frac{17}{4}$

You might be interested in

The volume ( v) of a gas in a container at a constant temperature varies inversely as the pressure (p). If the volume of a gas i

andre [41]

The answer is 12.8 cm³

<span>The volume ( v) of a gas in a container at a constant temperature varies inversely as the pressure (p):
v = k/p
p * v = k (k - constant)

p1v1 = k
p2v2 = k
So, p1v1 = p2v2

v1 = 24 cm</span>³
p1 = 16 lb
v2 = ?
p2 = 30 lb

24 * 16 = x * 30
384 = x * 30
x = 384 / 30
x = 12.8 cm³

3 0

3 years ago

Alguien puede ayudarme en esto

Montano1993 [528]

Lo siento, español no es mi primer lengua, pero trataré ayudar. ¿Qué significa L1, L2, y L3? No recuerdo.
Necesita multiplicar
x-3 • x+2
x-2 • x-1
Pero, obtendrías esto, y no ayudaría
x^2-6 = x^2+2
Es imposible resolver para x con eso.
Creo que la respuesta es e. no existe tal valor para x

7 0

3 years ago

What is the possible number of positive and negative real roots or zeroes in f(x)=x^3+x^2-4

Tanya [424]

This is a third degree polynomial, so we know that the maximum amount of roots will be 3.

We also know that imaginary roots come in pairs, so there is either 0 or 2 imaginary roots.

We can tell the amount of positive / negative roots by applying Descartes' rule of signs.

Let's examine the polynomial: x^3 + x^2 - 4

Note the sign changes.

From left to right, there is one sign change.

We now know there is only one positive real root.

Now, we can replace all values of x with -1 and then simplify. The number of sign changes will tell us the amount of negative roots.

(-1)^3 + (-1)^2 - 4

-1 + 1 - 4

From left to right, there are two sign changes, which tells us there will be 2 or 0 negative roots.

If there are 2, they are not imaginary.

If there are 0, they are imaginary.

<h3>So, our guaranteed root is:</h3><h3>1 positive, real root.</h3><h3>And our possible roots are:</h3><h3>2 negative, real roots.</h3><h3>0 negative, real roots, but 2 imaginary roots.</h3>

3 0

2 years ago

27% of all college students major in STEM (Science, Technology, Engineering, and Math). If 47 college students are randomly sele

scoray [572]

Answer:

0.12995

0.47508

0.0841

0.738

Step-by-step explanation:

Given that:

Percentage of STEM (p) = 27% = 0.27

Sample size (n) = 47

Using Normal approximation :

Mean (m) = n*p = 47 * 0.27 = 12.69

Standard deviation (s) = √(n*p*q)

q = 1 - p = 1 - 0.27 = 0.73

Standard deviation (s) = √(47*0.27*0.73) = 3.04

a. Exactly 13 of them major in STEM.

P(12.5 < x < 13.5)

USing the z formula :

(x - m) / s

(12.5 - 12.69) / 3.04 < x (13.5 - 12.69) / 3.04

-0.0625 < z < 0.2664

Using the z probability calculator:

P(Z < - 0.0625) = 0.47508

P(Z < 0.2664) = 0.60503

0.60503 - 0.47508

= 0.12995

b. At most 12 of them major in STEM.

P(X ≤ 12.5)

Zscore = (x - m) / s

Zscore = (12.5 - 12.69) / 3.04

Zscore = −0.0625

P(Z ≤ - 0.0625) = 0.47508

c. At least 9 of them major in STEM.

P(X ≥ 8.5)

Zscore = (x - m) / s

Zscore = (8.5 - 12.69) / 3.04

Zscore = −1.378

P(Z ≤ - 1.378) = 0.0841

d. Between 8 and 15 (including 8 and 15) of them major in STEM.

(8.5 - 12.69) / 3.04 < x (15.5 - 12.69) / 3.04

-1.378 ≤ z ≤ 0.924

Using the z probability calculator:

P(Z ≤ 0.924) = 0.82226

P(Z ≤ - 1.378) = 0.084102

0.82226 - 0.084102

= 0.738

5 0

2 years ago

PLEASE HELP ASAP<br> what is the square root of 180 in simplest radical form

Artyom0805 [142]

Answer:

6 square foot 5. hope this helps

6 0

2 years ago