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soldier1979 [14.2K]
3 years ago
7

Write a quadratic function in standard form whose graph passes through (4,0) and (6,0)

Mathematics
1 answer:
Diano4ka-milaya [45]3 years ago
8 0

Answer:

f(x) = x² - 10x + 24

Step-by-step explanation:

The quadratic function has a graph that passes through the points (4,0) and (6,0).

Therefore, the graph has two x-intercepts at x = 4 and x = 6 and those are the roots of the equation.

So, (x - 4) and (x - 6) are two factors of the quadratic equation.

Then we can write the equation as  

f(x) = (x - 4)(x - 6)

⇒ f(x) = x² - 4x - 6x + 24

⇒ f(x) = x² - 10x + 24

Hence, this is the required quadratic function in standard form. (Answer)

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In a sample of 234 individuals over the age of 25, chosen at random from the state of Oregon, 48 did not have a high school dipl
Anna71 [15]

Answer:

The upper bound of a 95% confidence interval for the proportion of individuals over the age of 25 in Oregon who do not have a high school diploma is of 0.2568.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

95% confidence level

So \alpha = 0.05, z is the value of Z that has a p-value of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

In a sample of 234 individuals over the age of 25, chosen at random from the state of Oregon, 48 did not have a high school diploma.

This means that n = 234, \pi = \frac{48}{234} = 0.2051

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2051 + 1.96\sqrt{\frac{0.2051*0.7949}{234}} = 0.2568

The upper bound of a 95% confidence interval for the proportion of individuals over the age of 25 in Oregon who do not have a high school diploma is of 0.2568.

6 0
3 years ago
What would the answer be?
gizmo_the_mogwai [7]

At 55 miles per hour, he travels 55 miles in every hour. So, in 2 hours he goes 55 x 2 miles, or 110 miles.

In the same way: at 70 miles per hour he goes 70 miles in every hour, and he only travels for an hour, so he goes 70 miles.

Going 50 mph (miles per hour) for 2 hours, he travels 50 x 2 miles or 100 miles.

Add these numbers up: 110+70+100 = 280.

5 0
3 years ago
A tree casts a 242 centimeters shadow. A person next to the tree casts a 89 centimeter shadow. If the person is 181 centimeters
defon

Answer:

150 centimeters

5 0
3 years ago
Read 2 more answers
Find the minimum and maximum possible areas of a rectangle measuring 2 km by 5 km.Find the minimum and maximum possible areas of
jeka57 [31]

<u>Answer:</u>

Minimum possible area = 6.75 km^2

Maximum possible area = 13.75 km^2

<u>Step-by-step explanation:</u>

This question relates to significant figures so assuming that each of the given values is rounded off to the nearest kilometer.

So we can find the minimum and maximum possible areas of the rectangle.

Minimum possible area of rectangle = 1.5 × 4.5 = 6.75 square kilometers

Maximum possible area of rectangle = 2.5 × 5.5 = 13.75 square kilometers

7 0
3 years ago
The y-value is two more than three times the x-value
Nimfa-mama [501]
The strategy for these is to look at what these problems are telling you.

It says the y-value, so you know that this is a y = equation.

y = what? 

y = 2 more than. 4 is two more than 2, right? So saying it's more than is another way of saying "y is 2 + blah blah."

So y = 2 + what? Three times the x-value. What does that mean? 3*X = 3X.

Thus we arrive at the final answer, y = 3x + 2
8 0
3 years ago
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