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steposvetlana [31]
2 years ago
15

Which values are the solutions to the polynomial equation? 0 = x2 – 18x + 65

Mathematics
2 answers:
Darina [25.2K]2 years ago
7 0

Answer:

x = 13, 5

Step-by-step explanation:

x² - 18x + 65 = 0

step 1: multiply (1) and (65) together

step 2: find two negative numbers to add together to equal -18 but multiply together to equal 65.

step 3: since there isn't a number in front of x² you could:

(x - 13) (x - 5)

x - 13 = 0           x - 5 = 0

   +13  +13            +5   +5

x = 13                      x = 5

or

(x² - 13x) (-5x + 65)

x(x - 13) -5 (x - 13)

(x - 13) (x - 5)

x - 13 = 0      x - 5 = 0

  +13   +13       +5   +5

x = 13, 5

I hope this helps!

leva [86]2 years ago
5 0

Answer:

If the question is 2x^{2} -18x+65 then the answer is no real solution. If the question is 2x - 18x + 65 than the answer is -16x+65

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Calculate the sample mean and sample variance for the following frequency distribution of heart rates for a sample of American a
spin [16.1K]

Answer:

Mean = 68.9

s^2 =18.1 --- Variance

Step-by-step explanation:

Given

\begin{array}{cccccc}{Class} & {51-58} & {59-66} & {67-74} & {75-82} & {83-90} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}

Solving (a): Calculate the mean.

The given data is a grouped data. So, first we calculate the class midpoint (x)

For 51 - 58.

x = \frac{1}{2}(51+58) = \frac{1}{2}(109) = 54.5

For 59 - 66

x = \frac{1}{2}(59+66) = \frac{1}{2}(125) = 62.5

For 67 - 74

x = \frac{1}{2}(67+74) = \frac{1}{2}(141) = 70.5

For 75 - 82

x = \frac{1}{2}(75+82) = \frac{1}{2}(157) = 78.5

For 83 - 90

x = \frac{1}{2}(83+90) = \frac{1}{2}(173) = 86.5

So, the table becomes:

\begin{array}{cccccc}{x} & {54.5} & {62.5} & {70.5} & {78.5} & {86.5} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}

The mean is then calculated as:

Mean = \frac{\sum fx}{\sum f}

Mean = \frac{54.5*4+62.5*3+70.5*11+78.5*13+86.5*4}{6+3+11+13+4}

Mean = \frac{2547.5}{37}

Mean = 68.9 -- approximated

Solving (b): The sample variance:

This is calculated as:

s^2 =\frac{\sum (x - \overline x)^2}{\sum f - 1}

So, we have:

s^2 =\frac{(54.5-68.9)^2+(62.5-68.9)^2+(70.5-68.9)^2+(78.5-68.9)^2+(86.5-68.9)^2}{37 - 1}

s^2 =\frac{652.8}{36}

s^2 =18.1 -- approximated

5 0
2 years ago
What is the value of the expression: 2 - (3x + 5y) if x = -3 and y = 4?
WARRIOR [948]
<h3>Hello there today we will solve your problem</h3>

here is our equation,

2-(3x+5y),

Now we will plug in our numbers

__________________

  1. {\boxed{x=-3}}
  2. {\boxed{y=4}

__________________

2-(3\cdot-3+5\cdot4)

simplify it and we get

2-(-9+20)

2-11

-9

7 0
2 years ago
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A triangle has a base length of 12 inches and a height of 14 inches. From that
Paladinen [302]
A= bh(1/2)
a=12(14)(1/2)
a= 168(1/2)
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3 years ago
Alan used 9 as an estimate for 3 7/10 + 5 4/10. He added and got 9 1/10 for the actual sum. Is his answer reasonable?
Len [333]

Answer:Yes, he is answer is reasonable

Step-by-step explanation:

First, you plus 3 7/10 with 5 4/8.

Then , when you get 8 11/10 you do add mixed number.

Finally, you get the answer that is 9 1/10

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3 years ago
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OLEGan [10]

Answer:

160 mL of fruit juice and 400 mL of sparkling water

Step-by-step explanation:

According to the statement we have that the ratio between fruit juice and sparkling water is 2/5.

Therefore, we could also say that:

200/500

with it could be done with 200 mL of fruit juice and 500 mL of sparkling water, so for 400 mL, how much would it be:

400 * 200/500 = 160

Therefore, the largest amount of the drink can be made with 160 mL of fruit juice and 400 mL of sparkling water.

5 0
3 years ago
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