Please help me with this question

A total of $27,000 is invested, part of it at 12% and the rest at 13%. The total interest after one year is $3385. How much was

Sveta_85 [38]

The amount invested in each rate are $14500 and $12500 respectively;

Let the amount invested in each be P1 and P2

Let the individual interest be I1 and I2 respectively;

I1 = P1R1T/100

I2 = P2R2T/100

If a total of $27,000 is invested, then;

P1 + P2 = 27000 ........... 1

If the total interest after one year is $3385, then;

I1 + I2 = 3385

$\frac{P_1(12)(1)}{100} + \frac{P_2(13)(1)}{100} = 3385\\0.12P_1+0.13P2=3385\\12P_1 + 13P_2=338500 ........................... 2$

Solving equations 1 and 2 simultaneously;

P1 + P2 = 27000 ........... 1 * 12

12P1 + 13P2 = 338500 ........... 2 * 1

________________________________

12P1 + 12P12 = 324000

12P1 + 13P2 = 338500 ...

Subtract both equations

12P2 - 13 P2 = 324000 - 338500

-P2 = -14500

P2 = 14500

Recall that P1 + P2 = 27000

P1 = 27000 - P2

P1 = 27000 - 14500

P1 = 12500

Hence the amount invested in each rate are $14500 and $12500 respectively;

Learn more here: brainly.com/question/19088526

7 0

3 years ago

Simplify. 7/8+(−2/3) over 5/6 Enter your answer, in the simplest form, in the boxes.

igor_vitrenko [27]

Answer:

1/4

Step-by-step explanation:

7 0

3 years ago

I'll fan

Nezavi [6.7K]

Remark: the x-intercepts are clearly (0, 0) and (20, 0), not (0, 0), (0, 20).

having the 2 x intercepts and the vertex we can draw the graph, check picture 1 attached.

Moreover, we can also determine the quadratic function as follows.

The quadratic function with roots a and b, is given by the equation:

f(x)=c(x-a)(x-b).

[ since f(a)=0, f(b)=0, f(x) must have one factor (x-a) and one (x-b)]

The x coordinates of the x intercepts are the roots of the function so with the roots given:

f(x)=c(x-0)(x-20)=cx(x-20), the vertex is at (10, 15) so

15=f(10)=c*10*(10-20)=c*10*(-10)=-100c
c=-15/100=-3/20

the quadratic function (expressed in factorized form) is

f(x)=-3/20x(x-20)

part A: the x intercept 0 is the point where the ball was hit, the x intercept 20 is the point where the ball fell back to the ground, 20 feet away from the kicker.

the function is increasing in the interval x∈(0, 10) and decreasing in x∈(10, 20)
this means that the height is increasing in the interval (0, 10) and decreasing as x goes through the interval (10,20)
the distance from the kicker is increasing during the whole interval (0, 20)

Part B: at x=15, f(x)=f(15)=-3/20*15(15-20)= $\frac{-3}{20}*15*(-5)= \frac{-3}{4}*3*(-5)= \frac{45}{4}$

at x=12, f(x)=f(12)=-3/20*12(12-20)= $\frac{-3}{20}*12*(-8)= \frac{-3}{5}*3*(-8)= \frac{72}{5}$

the average rate of change is the ratio of the differences in y to the differences in x : $\frac{y_1_5-y_1_2}{x_1_5-x_1_2}= \frac{\frac{45}{4}-\frac{72}{5}}{15-12}= -1.05$

so the average rate of change is -1.05. The minus, tells us that the height is decreasing in the following way: for 1 feet in distance, we are loosing 1.05 feet in height.

6 0

3 years ago

Read 2 more answers

The high school baseball team won the championship this season. The total runs scored for each of their 15 game are listed below

Keith_Richards [23]

Answer:

what data

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

BEST ANSWER GETS BRAINLIEST!!!!!!!!

Ad libitum [116K]

Answer:

(x + 6, y + 0), 180° rotation, reflection over the x‐axis

Step-by-step explanation:

The answer can be found out simply , a trapezoid has its horizontal sides usually parallel meanwhile the vertical sides are not parallel.

The horizontal parallel sides are on the x-axis.

Reflection over y- axis would leave the trapezoid in a vertical position such that the trapezoid ABCD won't be carried on the transformed trapezoid as shown in figure.

So option 1 and 2 are removed.

Now, a 90 degree rotation would leave the trapezoid in a vertical position again so its not suitable again.

In,The final option (x + 6, y + 0), 180° rotation, reflection over the x‐axis, x+6 would allow the parallel sides to increase in value hence the trapezoid would increase in size,

180 degree rotation would leave the trapezoid in an opposite position and reflection over x-axis would bring it below the Original trapezoid. Hence, transformed trapezoid A`B`C`D` would carry original trapezoid ABCD onto itself

8 0

3 years ago