Solve 5x 2 - 7x + 2 = 0 by completing the square. What is the constant added on to form the perfect square trinomial?

Solution:

Independent Events:

Consider an experiment of Rolling a die, then getting an even number and multiple of 3.

Total favorable outcome = {1,2,3,4,5,6}=6

A=Even number = {2,4,6}

B=Multiple of 3 = {3,6}

A ∩ B={6}

P(A)=[tex]\frac{3}{6}=\frac{1}{2}[/tex], P(B)= [tex]\frac{2}{6}=\frac{1}{3}[/tex]

P(A ∩ B)=[tex]\frac{1}{6}[/tex]

So, P(A)× P( B)=[tex]\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}[/tex]=P(A ∩ B)

Hence two events A and B are independent.

Option (c). the outcome of one event does NOT determine the outcome of the other event

Answer:

C on edge or the outcome of one event does NOT determine the outcome of the other event

Step-by-step explanation:

Answer:

Sunglasses

Step-by-step explanation:

Answer:

4 ÷ 5

Step-by-step explanation: becuz i said so

Answer:

y = (4 -3x)/5

Step-by-step explanation:

Find the terms containing y. If they are all on one side of the equation (it is), then identify the terms not containing y. Subtract those. Then, divide by the coefficient of y.

3x +5y = 4

5y = 4 - 3x . . . . . non-y term subtracted

y = (4 -3x)/5 . . . . divide by the coefficient of y

_____

If you like, you can rearrange this to slope-intercept form:

... y = -3/5x +4/5

Answer:

She's right the answer is a horizontal stretch.

Answer:

0.05

Step-by-step explanation:

Given :

Hair Color Boys Girls

Black          4                 5

Blonde          4                  6

Brown          10                 8

Red                  2                   1

Solution :

Since ware required to find the probability that a student is a boy with red hair.

Total no. of boys with red hair = 2

Total no. of students = 4+4+10+2+5+6+8+1=40

Thus the probability  that a student is a boy with red hair = [tex]\frac{\text{No. of boys with red hair }}{\text{total no. of students }}[/tex]

⇒[tex]\frac{2}{40}[/tex]

⇒[tex]\frac{1}{20}[/tex]

⇒[tex]0.05[/tex]

Hence the probability that a student is a boy with red hair is 0.05

Answer:

6:40

Step-by-step explanation:

Answer: A(s) = [tex]\frac{s\sqrt{144-s^{2} } }{2}[/tex] ; 10) c) 14ft

Step-by-step explanation:  Area of a triangle is: A = [tex]\frac{b.h}{2}[/tex]

where:

b is base of a triangle

h is height of a triangle

For this right triangle, it is known one side, s, and hypotenuse, 12. To determine the other side, we use Pythagoras Theorem:

hypotenuse² = side² + side²

[tex]12^{2} = s^{2} + x^{2}[/tex]

[tex]x^{2} = 12^{2} - s^{2}[/tex]

[tex]x^{2} = 144 - s^{2}[/tex]

x = [tex]\sqrt{144 - s^{2} }[/tex]

To determine the Area of the right triangle as function of s:

A = [tex]\frac{b.h}{2}[/tex]

A = [tex]\frac{1}{2}[/tex](s.x)

A = [tex]\frac{1}{2}[/tex] . (s.[tex]\sqrt{144 - s^{2} }[/tex])

Therefore, the area of the right triangle is:

A = [tex]\frac{1}{2}[/tex] . (s.[tex]\sqrt{144 - s^{2} }[/tex])

The ladder and the wall form a right triangle. The height of it is 13 ft, the base is 5ft and the hypotenuse is the length of the ladder. So, to find the minimum length, use Pythagoras Theorem:

hypotenuse² = side² + side²

h² = 13² + 5²

h² = 169 + 25

h = [tex]\sqrt{194}[/tex]

h = 14

The minimum length the ladder has to have to reach the top is 14 ft.

The equation of the line with a slope of -3/5 and a y-intercept of 7/10 is y = (-3/5)x + (7/10).

To write an equation of a line with a given slope (m) and y-intercept (0,b), we use the slope-intercept form of a linear equation which is y = mx + b. In this case, the slope is -3/5 and the y-intercept is 7/10.

Substituting these values into the slope-intercept formula, the equation of the line is y = (-3/5)x + (7/10).

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The area of sector GPH is [tex]\(\frac{1}{4}\pi r^2\).[/tex]

To find the area of sector GPH, we use the formula for the area of a sector of a circle, which is given by [tex]\(\frac{\theta}{360^\circ} \times \pi r^2\)[/tex], where [tex]\(\theta\)[/tex] is the central angle of the sector in degrees, and [tex]\(r\)[/tex] is the radius of the circle.

Given that the central angle of sector GPH is [tex]\(90^\circ\) (or \(\frac{\pi}{2}\)[/tex] radians, since[tex]\(180^\circ\) is \(\pi\) radians)[/tex], and the radius [tex]\(r\)[/tex] is unspecified, we can express the area of the sector in terms of [tex]\(r\).[/tex]

 Using the formula for the area of a sector:

[tex]\[ \text{Area of sector GPH} = \frac{\theta}{360^\circ} \times \pi r^2 \][/tex]

Substituting [tex]\(\theta = 90^\circ\):[/tex]

[tex]\[ \text{Area of sector GPH} = \frac{90^\circ}{360^\circ} \times \pi r^2 \][/tex]

Simplifying the fraction:

[tex]\[ \text{Area of sector GPH} = \frac{1}{4} \times \pi r^2 \][/tex]

 So, the area of sector GPH is [tex]\(\frac{1}{4}\pi r^2\)[/tex], which is one-fourth of the area of the entire circle. This makes sense because the sector represents a quarter of the circle's area due to its [tex]\(90^\circ\)[/tex] central angle.

No, the null hypothesis will be, there is no difference between the mean scores of campus 1 and campus 2.

Therefore, the null hypothesis would be:

H₀: µ₁ - µ₂ = 0

where µ₁ is the population mean score of campus 1 and µ₂ is the population mean score of campus 2.

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Now, We test this null hypothesis against the alternative hypothesis that the mean score on campus 1 is higher than on campus 2:

Hₐ: µ₁ > µ₂

Hence, if there is sufficient evidence to reject the null hypothesis and conclude that there is a significant difference between the mean scores of campus 1 and campus 2.

Thus, No, the null hypothesis will be, there is no difference between the mean scores of campus 1 and campus 2.

Therefore, the null hypothesis would be:

H₀: µ₁ - µ₂ = 0

where µ₁ is the population mean score of campus 1 and µ₂ is the population mean score of campus 2.

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Answer:

9

Step-by-step explanation:

Answer with explanation:

Pottery is on a Kiln.

Unit of temperature can be Kelvin(°K) or Degree Celsius(°C) or Fahrenheit(°F).

Unit of time is second, minute and hour.

Rate of change of temperature of the pottery over time can be written as

     [tex]1.=\frac{\text{Degree Celsius}}{\text{Second}}\\\\2.=\frac{\text{Degree Celsius}}{\text{Minute}}[/tex]

Internationally , Kelvin is used as S.I unit of Temperature.

So,Yanin can use

  [tex]1.=\frac{\text{Kelvin}}{\text{Second}}\\\\2.=\frac{\text{Kelvin}}{\text{Minute}}[/tex]

 as Rate of change of temperature of the pottery over time.

The statement which is true about the dilation is:

                        [tex]\dfrac{3}{2}=\dfrac{6}{4}[/tex]    

We know that the dilation transformation changes the size of the original figure but the shape is preserved.

The dilation transformation either reduces the size of the original figure i.e. the scale factor is less than 1 or enlarges the size of the original figure i.e. the scale factor is greater than 1.

The ratio of the corresponding sides of the two figure are equal.

i.e.

                 [tex]\dfrac{3}{2}=\dfrac{6}{4}[/tex]

Kaelyn has 14 coins made of dimes and nickels valued at $1.20. By setting up a system of equations and solving for the number of nickels, we determine that she has 4 nickels.

The student is asking a mathematical question involving coin values and combinations. When working with combinations of coins, we typically use a system of equations or algebraic expressions. Kaelyn has 14 coins consisting of dimes and nickels with a total value of $1.20. To systematize, let's let D be the number of dimes and N be the number of nickels. The following equations represent the relationships between the coins:

Multiply the second equation by 100 to deal with whole numbers:

From the first equation, we can express D as:

Substitute this into the second equation:

So, Kaelyn has 4 nickels and the rest are dimes.

Answer:

a,b and c.

Step-by-step explanation:

We have to find the the functions that are their own inverses.

a.t(p)=p

Then the inverse function of given function is

[tex]p=t^{-1}(p)[/tex]

Therefore, the given function is inverse function of itself.

Hence, option a is true.

b.y(j)=[tex]-\frac{1}{j}

Let y(j)=y then we get

[tex]y=-\frac{1}{j}[/tex]

[tex]j=-\frac{1}{y}[/tex]

[tex]j=-\frac{1}{y(j)}[/tex]

[tex]j=-\frac{1}{\frac{-1}{j}}[/tex]

[tex]j=j[/tex]

Hence, the function is inverse of itself.Therefore, option b is true.

c.[tex]w(y)=-\frac{2}{y}[/tex]

Suppose that w(y)=w

Then [tex]w=-\frac{2}{y}[/tex]

[tex]y=-\frac{2}{w}[/tex]

[tex]w(y)=-\frac{2}{-\frac{2}{w}}[/tex]

[tex]w(y)=w[/tex]

[tex]w(y)=-\frac{2}{y}[/tex]

Hence, the function is inverse function of itself.Therefore, option c is true.

d.[tex]d(p)=\frac{1}{x^2}[/tex]

Let d(p)=d

If we replace [tex]\frac{1}{x^2}by p then we get

[tex]d=\frac{1}{x^2}[/tex]

[tex]x^2=\frac{1}{d}[/tex]

[tex]x=\sqrt{\frac{1}{d}}[/tex]

[tex]x=\sqrt{\frac{1}{d(p)}[/tex]

Hence, the function is not self inverse function.Therefore, option d is false.

Answer:

The answer is the third option/choice.