$4,700 is invested in an account earning 6.2% interest (APR), compounded

Can anyone help me with the answer for number 4

klio [65]

Answer:

b

Step-by-step explanation:

Given K is the midpoint of JL, then

JK = KL ← substitute values

6x = 3x + 3 ( subtract 3x from both sides )

3x = 3 ( divide both sides by 3 )

x = 1

Hence

JK = 6x = 6 × 1 = 6

KL = 3x + 3 = (3 × 1) + 3 = 3 + 3 = 6

JL = 6 + 6 = 12

7 0

3 years ago

Emma put $35,000 in an education

elena-14-01-66 [18.8K]

A = ( 1 +r/n)^nth
or something, use .0585

6 0

4 years ago

Rachel runs 2km to her bus stop, and then rides 4.5 km to school. On average, the bus is 45 km/h faster than Rachel's average ru

Mice21 [21]

Answer:6.042km/h 6km/h approximately

Step-by-step explanation:

First off we have to know the formula relating speed, distance and time which is

Speed = distance/time

Now we are looking for Rachel's running speed

We are to find Rachel's running speed, so let's label is x

We are given that the distance Rachel runs to her bus stop is 2km

We were not given the time she uses to run to the bus stop

So let's label the time Rachel uses to run to her bus stop as y

So from the formula speed = distance/time

We have x = 2/y

Now we are told that the speed the bus uses to get to school is 45km/h faster than her speed used to run

So speed of bus = 45 + x

And the overall time for the whole journey is 25mins, changing this to hours, because the speed details given is in km/h we divide 25 by 60 which will give 0.417

Now if the total time is 0.417 hours, and we labeled the time for Rachel to run to the bus as y, so the time for the time for the bus to get to school will be 0.417 - y

We are also told the bus rides for 4.5km to school

So adding this together to relate the speed, distance and time of the bus with the formula speed = distance/time

We get 45 + x = 4.5/(0.417 - y)

So we have two equations

x = 2/y (1)

45+x = 4.5/(0.417-y) (2)

So putting (1) in (2) we have

45 + (2/y) = 4.5/(0.417-y)

Expanding further

(45y + 2)/y = 4.5(0.417-y)

Cross multiplying

(45y + 2)(0.417 - y) = 4.5y

Opening the brackets

18.765y - 45y2 + 0.834 - 2y = 4.5y

Collecting like terms

-45y2 + 18.765y -2y - 4.5y + 0.834 = 0

-45y2 + 12.265 + 0.834 = 0

Dividing all sides by -45 to make the coefficient of y2 1

y2 - 0.273y - 0.019 = 0

Now we have gotten a quadratic equation, and since it's with decimal numbers we can use either completing the square method of almighty formula

I'm using almighty formula her

For solving

ax2 + bx + c = 0

x = (-b +-root(b2-4ac)/2a

For our own equation, we are finding y

From our our quadratic equation

a = 1, b=-0.273, c = -0.834

you = (-(-0.273)+-root(-0.273-4(1)(-0.019))/2(1)

y = (273+-root(0.151))/2

y = (0.273+0.389)/2 or (0.273-0.389)/2

y = 0.331 or -0.085

So we use the positive answer which is 0.331, because time can't be negative

Then we put y = 0.331 in (1)

x = 2/y

x = 2/0.331

x = 6.042km/h

x = 6km/h approximately

4 0

3 years ago

Write the equation of a line in slope intercept form that is perpendicular to the line y = –4x and passes through the point (2,

Gnesinka [82]

1. If the line that we are searching for is perpendicular to the line y = -4x, this means that the gradient of our line and the gradient of the perpendicular line will multiply to give -1. Thus if we call the gradient of our line m, then:

m*(-4) = -1

-4m = -1

m = 1/4

2. Since we know that m = 1/4 and we have a point (2,6) on our line, we can use the formula y - y1 = m(x - x1) to find the equation of our line, where (x1, y1) is the coordinates of a point on the line. Thus:

y - y1 = m(x - x1)

y - 6 = (1/4)(x - 2)

y - 6 = (1/4)x - 2/4 (Expand (1/4)(x - 2))

y = (1/4)x - 1/2 + 6 (Simplify 2/4 and add 6 to each side)

y = (1/4)x + 11/2 (Evaluate -1/2 + 6)

Slope-intercept form is given by y = mx + c. As our equation is already in this form, there is nothing more to do. Thus, the answer is y = (1/4)x + 11/2

6 0

3 years ago

If you roll a number cube two times, what is the probability of rolling an even on the first roll and a four on the second roll?

Bad White [126]

Answer:

1/12

Step-by-step explanation:

Probability is a ratio derived as the number of possible outcomes divided by the total outcome.

On a number cube, the even sides are 2, 4 and 6. This means that the possible outcome for rolling an even is 3 while the total outcome is 6. Hence the probability of rolling an even P(E)

= 3/6

The probability of rolling a 4 P(4)

= 1/6 (4 appears on one side)

Hence the probability of rolling an even on the first roll and a four on the second roll

P(En4) = 3/6 * 1/6

= 3/36

= 1/12

7 0

3 years ago