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3 years ago

Which graph represents a quadratic function with a vertex at (0,0)

Mathematics

1 answer:

Volgvan3 years ago

6 0

Answer:

the graph of x²

Step-by-step explanation:

The graph of x² has a vertex with coordinates (0,0)

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If , find the value of 2 square root of 17-x = 2x-10, find the value of x/4.

ira [324]

$2 \sqrt{17-x} =2x-10\ \ \ \ \Rightarrow\ \ \ D:(17-x \geq 0\ \ \ and\ \ \ 2x-10 \geq 0)\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x \leq 17\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x \geq 5\\\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ D=\\\\2 \sqrt{17-x} =2(x-5)\ /:2\\\\ \sqrt{17-x} =x-5\ \ \ \Rightarrow\ \ \ (\sqrt{17-x})^2 =(x-5)^2\\\\17-x=x^2-10x+25\\\\$

$x^2-9x+18=0\\\\ x^2-3x-6x+18=0\\\\x(x-3)-6(x-3)=0\\\\(x-3)(x-6)=0\ \ \ \ \Leftrightarrow\ \ \ (x-3=0\ \ \ \ or\ \ \ \ x-6=0)\\\\x=3\ \notin\ D\ \ \ \ \ \ \ \ \ \ \ x=6\ \in\ D\ \ \ \Rightarrow\ \ \ \frac{x}{4} = \frac{6}{4} =1.5\\\\Ans.\ \frac{x}{4} =1.5$

7 0

3 years ago

Which is the equation of a hyperbola centered at the origin with x-intercept +\- 3 and asymptote y=2x

Radda [10]

Answer:

${\dfrac{x^{2}}{9} - \dfrac{y^{2}}{36} = 1}$

Step-by-step explanation:

The hyperbola has x-intercepts, so it has a horizontal transverse axis.

The standard form of the equation of a hyperbola with a horizontal transverse axis is $\dfrac{(x - h)^{2}}{a^{2}} - \dfrac{(y - k)^{2}}{b^{2}} = 1$

The center is at (h,k).

The distance between the vertices is 2a.

The equations of the asymptotes are $y = k \pm \dfrac{b}{a}(x - h)$

1. Calculate h and k. The hyperbola is symmetric about the origin, so

h = 0 and k = 0

2. For 'a': 2a = x₂ - x₁ = 3 - (-3) = 3 + 3 = 6

a = 6/2 = 3

3. For 'b': The equation for the asymptote with the positive slope is

$y = k + \dfrac{b}{a}(x - h) = \dfrac{b}{a}x$

Thus, asymptote has the slope of

$\begin{array}{rcl}m& =& \dfrac{b}{a}\\\\2& =& \dfrac{b}{3}\\\\b& =& \mathbf{6}\end{array}$

4. The equation of the hyperbola is

$\large \boxed{\mathbf{\dfrac{x^{2}}{9} - \dfrac{y^{2}}{36} = 1}}$

The attachment below represents your hyperbola with x-intercepts at ±3 and asymptotes with slope ±2.

7 0

2 years ago

A new roller coaster at an amusement park requires individuals to be at least 4' 8" (56 inches) tall to ride. It is estimated

Maksim231197 [3]

Answer:

a) 34.46% of 10-year-old boys is tall enough to ride this coaster.

b) 78.81% of 10-year-old boys is tall enough to ride this coaster

c) 44.35% of 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part a

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 54, \sigma = 5$

a. What proportion of 10-year-old boys is tall enough to ride the coaster?

This is 1 subtracted by the pvalue of Z when X = 56.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{56 - 54}{5}$

$Z = 0.4$

$Z = 0.4$ has a pvalue of 0.6554

1 - 0.6554 = 0.3446

34.46% of 10-year-old boys is tall enough to ride this coaster.

b. A smaller coaster has a height requirement of 50 inches to ride. What proportion of 10-year-old boys is tall enough to ride this coaster?

This is 1 subtracted by the pvalue of Z when X = 50.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{50 - 54}{5}$

$Z = -0.8$

$Z = -0.8$ has a pvalue of 0.2119

1 - 0.2119 = 0.7881

78.81% of 10-year-old boys is tall enough to ride this coaster.

c. What proportion of 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part a?

Between 50 and 56 inches, which is the pvalue of Z when X = 56 subtracted by the pvalue of Z when X = 50.

From a), when X = 56, Z has a pvalue of 0.6554

From b), when X = 50, Z has a pvalue of 0.2119

0.6554 - 0.2119 = 0.4435

44.35% of 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part a

5 0

2 years ago

Write a slope-intercept form of the equation if it passed the

inna [77]

Answer:

$\sf\longrightarrow \boxed{\pink{\sf 3x + 4y -8=0}}$

Step-by-step explanation:

We need to write the slope intercept form of the equation which passes through (4,-1) and parallel to the line y = -3/4x .

We know that the line parallel to a given line has the same slope . Therefore the slope of the line will be , ( on comparing to Slope Intercept Form ) .

$\sf\longrightarrow Slope =\dfrac{-3}{4}$