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Ad libitum [116K]
3 years ago
6

10. The Johnson family purchased a new television that had a 62 inch diagonal. The height of the television was 30 inches. Appro

ximately how wide is the new television? show work​
Mathematics
1 answer:
lana66690 [7]3 years ago
7 0

Answer:

Width = 54.3 inches

Step-by-step explanation:

We solve this question using the Pythagoras Theorem

Width² + Height² = Diagonal²

From the above question

Width= ??

Height = 30 inches

Diagonal = 62 inches

Width² + 30² = 62²

Width² = 62² - 30²

Width = √62² - 30²

Width =✓2944

Width = 54.258639865 inches

Approximately

Width = 54.3 inches

Hence, the new television was 54.3 inches wide.

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The polynomial $f(x)$ has degree 3. If $f(-1) = 15$, $f(0)= 0$, $f(1) = -5$, and $f(2) = 12$, then what are the $x$-intercepts o
Alex_Xolod [135]

Your calculator's cubic regression function can tell you the equation is

... f(x) = 2x³ + 5x² -12x = x(x +4)(2x-3)

The x-intercepts are -4, 0, +1.5.

_____

If you want to solve this "by hand", you can first of all recognize that since there is an x-intercept at 0, the cubic will only have three coefficients. That is, you can write the equation as

... f(x) = ax³ + bx² + cx

Substituting the given points (except (0, 0)) gives three linear equations in a, b, c.

... -a +b -c = 15 . . . . . for x=-1

... a + b + c = -5 . . . . for x=1

... 8a +4b +2c = 12 . . for x=2

adding the first two equations gives 2b=10, or b=5. Now, you can reduce the system to

... a + c = -10

... 4a +c = -4

Subtracting the first of these equations from the second gives 3a=6, or a=2. That tells you c=-12 (from a+c=10).

Then your equation is

... f(x) = x(2x² +5x -12)

Factoring by any of the usual techniques, or graphing, or using the quadratic formula will tell you the zeros (x-intercepts) are as above.

_____

Since the input values are sequential, you can also develop the function from differences of the output values. Those are 15, 0, -5, 12. First differences are -15, -5, +17. Second differences are +10, +22. The third difference is 12. Using the first of these differences in appropriate places in the interpolating polynomial formula, we have

... f(x) = 15 + (x+1)(-15 + (x)/2·(10 + (x-1)/3·(12))) = 2x³ +5x² -12x . . . . as above

4 0
3 years ago
The most common ages of children that use the library are
Nady [450]

Answer:

12-17

Step-by-step explanation:

this is right. trust (:

7 0
2 years ago
he life of light bulbs is distributed normally. The variance of the lifetime is 625 and the mean lifetime of a bulb is 540 hours
almond37 [142]

Using the normal distribution, it is found that there is a 0.877 = 87.7% probability of a bulb lasting for at most 569 hours.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

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

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

\mu = 540, \sigma = \sqrt{625} = 25

The probability of a bulb lasting for at most 569 hours is the <u>p-value of Z when X = 569</u>, hence:

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

Z = \frac{569 - 540}{25}

Z = 1.16

Z = 1.16 has a p-value of 0.877.

0.877 = 87.7% probability of a bulb lasting for at most 569 hours.

More can be learned about the normal distribution at brainly.com/question/24663213

#SPJ1

8 0
2 years ago
Match each root with its meaning.
IRISSAK [1]
Port is to carry
Voc is to voice or call
Tract is to pull
Vac is to empty
Struct is to build or form
7 0
3 years ago
What is 787.526 rounded to the nearest tenths A; 787.6 B; 787.0 C; 787.5
sasho [114]

Answer:

I believe it's <em>C</em>

Step-by-step explanation:

4 or less let it rest 5 or more go next door I think is how it goes lol

forgot to explain: 6 is more than 5 so we add one to the next place. that makes 2 + 1 which is 3 and 3 is less than 4 so we don't add to the next place.

7 0
3 years ago
Read 2 more answers
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