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2 years ago

What are the solutions for x when y is equal to 0 in the following quadratic

Mathematics

1 answer:

navik [9.2K]2 years ago

6 0

Answer:

The correct answer option is E) No solution.

Step-by-step explanation:

We are given the following quadratic equation which we are to solve for x when the value of y is 0:

$y = x ^2+ 6x +12$

$x ^2+ 6x +12=0$

Using the quadratic formula since there are no factors:

$x=\frac{-b \pm \sqrt{b^2-4ac }}{2a}$

Substituting the values in the formula to get:

$x=\frac{-6 \pm \sqrt{6^2-4(1)(12) }}{2(1)}$

$x=-3+\sqrt{3}i$ or $x=-3-\sqrt{3}i$

There are no real number solutions to this quadratic equation.

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Find the slope of the line that goes through (0, 2) and (4, −2).

zmey [24]

M = (y2 - y1) / (x2 - x1)

m = (-2 - 2) / (4 - 0)

m = -4 / 4

m = -1

The slope of the line that goes through (0, 2) and (4, -2) is -1.

5 0

3 years ago

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(NEED ASAP) 15 POINTS

yulyashka [42]

Answer:

1 and 2 go in the 2nd area and 3 gos to the 1st and 4th gos to the last one

Step-by-step explanation:

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6 0

3 years ago

6x - 2(x + 2) > 2 - 3(x+3) Solve the inequality plz help

Mumz [18]

Answer:

x > -3/7

Step-by-step explanation:

6x - 2(x + 2) > 2 - 3(x + 3)

Distribute the two and three inside the parenthesis.

6x - 2x - 4 > 2 - 3x - 9

Combine like terms.

4x - 4 > -3x - 7

Add 4 to both sides.

4x > -3x - 3

Add 3x to both sides.

7x > -3

Divide both sides by 7.

x > -3/7

7 0

3 years ago

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A quality analyst of a tennis racquet manufacturing plant investigates if the length of a junior's tennis racquet conforms to th

Burka [1]

Answer:

Confidence interval : $21.506$ to $24.493$

Step-by-step explanation:

A quality analyst selects twenty racquets and obtains the following lengths:

21, 25, 23, 22, 24, 21, 25, 21, 23, 26, 21, 24, 22, 24, 23, 21, 21, 26, 23, 24

So, sample size = n =20

Now we are supposed to find Construct a 99.9% confidence interval for the mean length of all the junior's tennis racquets manufactured at this plant.

Since n < 30

So we will use t-distribution

Confidence level = 99.9%

Significance level = α = 0.001

Now calculate the sample mean

X=21, 25, 23, 22, 24, 21, 25, 21, 23, 26, 21, 24, 22, 24, 23, 21, 21, 26, 23, 24

Sample mean = $\bar{x}=\frac{\sum x}{n}$

Sample mean = $\bar{x}=\frac{21+25+23+22+24+21+25+21+23+ 26+ 21+24+22+ 24+23+21+ 21+ 26+23+ 24}{20}$

Sample mean = $\bar{x}=23$

Sample standard deviation = $\sqrt{\frac{\sum(x-\bar{x})^2}{n-1}}$

Sample standard deviation = $\sqrt{\frac{(21-23)^2+(25-23)^2+(23-23)^2+(22-23)^2+(24-23)^2+(21-23)^2+(25-23)^2+(21-23)^2+(23-23)^2+(26-23)^2+(21-23)^2+(24-23)^2+(22-23)^2+(24-23)^2+(23-23)^2+(21-23)^2+(21-23)^2+(26-23)^2+(23-23)^2+(24-23)^2}{20-1}}$

Sample standard deviation= s = $1.72$

Degree of freedom = n-1 = 20-1 -19

Critical value of t using the t-distribution table $t_{\frac{\alpha}{2}$ = 3.883

Formula of confidence interval : $\bar{x} \pm t_{\frac{\alpha}{2}} \times \frac{s}{\sqrt{n}}$

Substitute the values in the formula

Confidence interval : $23 \pm 1.73 \times \frac{1.72}{\sqrt{20}}$

Confidence interval : $23 -3.883 \times \frac{1.72}{\sqrt{20}}$ to $23 + 3.883 \times \frac{1.72}{\sqrt{20}}$

Confidence interval : $21.506$ to $24.493$

Hence Confidence interval : $21.506$ to $24.493$

3 0

3 years ago

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On a cruise ship, 400 passengers are adults and 350 are children. What percent of passengers are adults?

kkurt [141]

Step-by-step explanation:

percentage of adults= number of adults over total number of persons times 100;

400/400+350*100

400/750*100

40/75*100

8/15*100

8/3*20

160/3

=53.3%

3 0

2 years ago