The lengths of three sides of a triangle are in the ratio 3: 5:

Find the equation of the axis of symmetry of the following parabola algebraically.

mr Goodwill [35]

Answer:

the equation of the axis of symmetry is $x=8$

Step-by-step explanation:

Recall that the equation of the axis of symmetry for a parabola with vertical branches like this one, is an equation of a vertical line that passes through the very vertex of the parabola and divides it into its two symmetric branches. Such vertical line would have therefore an expression of the form: $x=constant$ , being that constant the very x-coordinate of the vertex.

So we use for that the fact that the x position of the vertex of a parabola of the general form: $y=ax^2+bx+c$ , is given by:

$x_{vertex}=\frac{-b}{2\,a}$

which in our case becomes:

$x_{vertex}=\frac{-b}{2\,a} \\x_{vertex}=\frac{48}{2\,(3)} \\x_{vertex}=\frac{48}{6} \\x_{vertex}=8$

Then, the equation of the axis of symmetry for this parabola is:

$x=8$

4 0

3 years ago

Vern sold his 1964 Ford Mustang for $55,000 and wants to invest the money to earn him 3.6% interest per year. He will put some o

noname [10]

Answer: He should invest $44000 in fund A and $11000 in fund B.

Step-by-step explanation:

Let x represent the amount which he invested in fund A.

Let y represent the amount which he invested in fund B.

Vern sold his 1964 Ford Mustang for $55,000 and wants to invest the money to earn him 3.6% interest per year. He will put some of the money into Fund A that earns 2% per year and the rest in Fund B that earns 10% per year.. This means that

x + y = 55000

The formula for determining simple interest is expressed as

I = PRT/100

Considering fund A,

P = $x

T = 1 year

R = 2℅

I = (x × 2 × 1)/100 = 0.02x

Considering fund B,

P = $y

T = 1 year

R = 10℅

I = (y × 10 × 1)/100 = 0.1y

The interest that he wants to earn on the total amount in a year is 3.6%. The interest would be

I = (55000 × 3.6 × 1)/100 = 1980

Therefore,

0.02x + 0.1y = 1980 - - - - - - - - - -1

Substituting x = 55000 - y into equation 1, it becomes

0.02(55000 - y) + 0.1y = 1980

1100 - 0.02y + 0.1y = 1980

- 0.02y + 0.1y = 1980 - 1100

0.08y = 880

y = 880/0.08

y = 11000

x = 55000 - y = 55000 - 11000

x = 44000

4 0

3 years ago

Ross chose a card at random from a deck of 52 cards. Ross replaced the card and then chose a second card. What is the probabilit

DaniilM [7]

Answer:

$\frac{1}{208}$

Step-by-step explanation:

We have been given that Ross chose a card at random from a deck of 52 cards. Ross replaced the card and then chose a second card.

Let us find probability of getting a club.

$\text{ Probability of getting a club}=\frac{13}{52} =\frac{1}{4}$

Now let us find probability of getting the ace of spades.

$\text{ Probability of getting ace of spades}=\frac{1}{52}$

Now let us multiply these to find probability of getting a club and ace of spades.

$\text{ Probability of getting a club and then ace of spades}=\frac{1}{4}*\frac{1}{52}=\frac{1}{208}$

Therefore, probability of getting a club and then the ace of spades $\frac{1}{208}$ .

8 0

3 years ago

How do you calculate the common difference?

SCORPION-xisa [38]

Answer:

<h3> second term minus first term </h3>

Step-by-step explanation:

Difference is a result of subtracting (not dividing!)

To calculate difference between two terms we have to subtract the previous from the next:

$d=a_2-a_1=a_3-a_2=a_4-a_3=...=a_n-a_{n-1}$

7 0

2 years ago

A binomial experiment consists of 14 trials. The probability of success on trial 7 is 0.84. What is the probability of failure o

r-ruslan [8.4K]

Answer:

The probability of failure of trial 11 is $q = 0.16$

Step-by-step explanation:

Generally one the attributes of a binomial experiment is that the probability of success and failure is constant every trial so given from the question that the probability of success is 0.84 for trial 7 , then the probability of failure of trial 7 will be evaluated as

$q = 1 - 0.84$

=> $q = 0.16$

And from the attribute stated above the probability of failure of trial 11 is $q = 0.16$

6 0

2 years ago