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1 year ago

Find a polynomial function of degree 3 such that f(10)=17 and the zeros of f are 0, 5 and 8

Mathematics

1 answer:

fomenos1 year ago

3 0

Step-by-step explanation:

Since f(0) = f(5) = f(8) = 0, we have f(x) = Ax(x - 5)(x - 8), where A is a real constant.

We know that f(10) = 17.

=> A(10)(10 - 5)(10 - 8) = 17

=> A(10)(5)(2) = 17

=> 100A = 17, A = 0.17.

Hence the answer is f(x) = 0.17x(x - 5)(x - 8).

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The rational numbers whose absolute value is 11 by 13 are

ruslelena [56]

The rational numbers who absolute value is 11 by 13 are recurring decimal fraction.

Step-by-step explanation:

The rational numbers are included in the real numbers. On the other hand, they include the integers, natural numbers. In mathematics, a rational number is any number that can be expressed as the fraction p/q of two integers, a numerator p and a non-zero denominator q.

Absolute value means non-negative number with the same magnitude as a given number. In mathematics, the absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign.

Rational numbers consists of fractions which are of rational form following recurring and terminating fraction rules.

11 / 13 is a recurring fraction as it's rounded value is 0.846......

6 0

2 years ago

Your model locomotive is 16 inches long. It is an exact model of a locomotive that is 40 feet long. A window on the locomotive i

Ierofanga [76]

1 feet is 12 inches so 40 feets is 480 inches
Real locomotive is 480/16=30 times wider then the model
And then a window on the real locomotive is 30 times wider then the model.

7 0

2 years ago

Given that Ray E B bisects ∠CEA, which statements must be true? Select three options. m∠CEA = 90° m∠CEF = m∠CEA + m∠BEF m∠CEB =

FromTheMoon [43]

Answer:

Here is the question attached with.

$m\angle CEA =90 \ (deg)$

$m\angle BEF=135\ (deg)$

$\angle CEF$ is a straight line.

$\angle AEF$ is a right angled triangle.

Options $1,4,5,6$ are correct answers.

Step-by-step explanation:

⇒As $\ ray\ AE$ is ⊥ $FEC$ so it will forms right angled triangle then $m\angle CEA =90\ (deg)$ .

⇒Measure of $\angle BEF =135\ (deg)$ as $\angle BEF =\angle AEB +\angle AEF = (45+90)=135\ (deg)$ as $\angle AEB$ is the bisector of $\angle AEC$ ,meaning that $\angle AEB$ is half of $\angle AEC$ so $\angle AEB = 45\ (deg)$ .

⇒ $\angle CEF$ is a straight line as the angles measure over it is $180\ (deg)$ .

⇒Measure of $\angle AEF = 90\ (deg)$ from linear pair concept.

As $\angle CEA + \angle AEF = 180\ (deg)$ ,plugging the values of $m\angle CEA =90\ (deg)$ we have $\angle AEF = 90\ (deg)$ .

The other two options are false as:

$m\angle CEF=m\angle CEA + m\angle BEF = (90+135)=225$

it is exceeding $180\ (deg)$ whereas $\angle CEF$ is a

straight line.

And $m\angle CEB=2(m\angle CEA)$ is not true.

As $\angle CEA = 90\ (deg)$ and $\angle CEB=45\ (deg)$

So we have total $4$ answers.

The correct options are $1,4,5,6$ .

5 0

2 years ago

Read 2 more answers

A shower has a flow rate of 2.3 gallons per minute. If a person takes an average of 6 showers per week and the average length of

shusha [124]

Answer:

161,460 gallons are used in a year.

Step-by-step explanation:

1 shower- 2.3×15=34.5

Number of minutes spent in the shower in a week- 15×6=90

Gallons used per week- 34.5×90=3,105

There is 52 weeks in a year.

52×3,105=<u>161,460</u>

8 0

2 years ago

Read 2 more answers

The list shows the area in square feet of each apartment available for rent in a building. 565, 961, 867, 517, 627, 714, 517, 72

gladu [14]

STEP 1:
put numbers in order from lowest to highest
517, 517, 565, 627, 714, 728, 867, 961

STEP 2:
find the difference between the lowest and highest numbers

961 - 517= 444 ft^2 range

ANSWER: The range of the areas is 444 ft^2.

Hope this helps! :)

8 0

2 years ago

Read 2 more answers