What is the area of the triangle below?

Max has $2,000 he would like to invest in an account that pays simple interest. Max would like to earn a total of $650 in intere

Goryan [66]

Answer: 6.5%

Step-by-step explanation:

Formula for simple interest : I = Prt , where P= principal , r= rate of interest t= time

As per given , P = $2000 , I=$ 650, t= 5 years

Substitute all theses values in the formula , we get

$650=2000\times r\times5\\\\\Rightarrow\ r=\dfrac{650}{2000\times5}\\\\\Rightarrow\ \dfrac{65}{1000}\\\\\Rightarrow\ r=0.065 =0.065\times100\%=6.5\%$

Hence, the required annual interest = 6.5%

7 0

3 years ago

Solve using Substitution y = 6x - 11 -2x - 3y = -7

vladimir2022 [97]

Answer:

(2, 1)

Step-by-step explanation:

To solve by substitution, we solve one equation for one of its variables and then substitute the solved value for that variable into the other equation. Because this system of equations already has one solved for the variable, this makes our job much easier. We only need to implement the solved value for y into the other equation and solve for x.

y = 6x - 11

-2x - 3(6x - 11) = -7 Distribute.

-2x - 18x + 33 = -7 Combine like terms.

-20x + 33 = -7 Subtract 33 from both sides of the equation.

-20x = -40 Divide by -20 on both sides of the equation.

x = 2

Then, with this value, we will place it into the equation that was already solved for y in order to get a definite value for y.

y = 6(2) - 11

y = 12 - 11

y = 1

Using this information, the coordinate pair for this equation (the point of intersection between the two lines) is (2, 1).

4 0

3 years ago

Unit 3 parallel and perpendicular lines Homework 3 proving lines are parallel

IrinaK [193]

Step-by-step explanation:

Since, lines l and m are parallel and a transverse is intersecting these lines.

5). (9x + 2)° = 119° [Alternate intrior angles]

9x = 117 ⇒ x = 13

6). (12x - 8)° + 104° = 180°

12x = 180 - 96

x = ⇒ x = 7

7). (5x + 7) = (8x - 71) [Alternate exterior angles]

8x - 5x = 71 + 7

3x = 78

x = 26

8). (4x - 7) = (7x - 61) [Corresponding angles]

7x - 4x = -7 + 61

3x = 54

x = 18

9). (9x + 25) = (13x - 19) [Corresponding angles]

13x - 9x = 25 + 19

4x = 44

(13x - 19)° + (17y + 5)° = 180°[Linear pair of angles are supplementary]

(13×11) - 19 + 17y + 5 = 180

129 + 17y = 180

17y = 180 - 129

y = 3

10). (3x - 29) + (8y + 17) = 180 [linear pair of angles are supplementary]

3x + 8y = 180 + 12

3x + 8y = 192 -----(1)

(8y + 17) = (6x - 7) [Alternate exterior angles]

6x - 8y = 24

3x - 4y = 12 -----(2)

Equation (1) - equation (2)

(3x + 8y) - (3x - 4y) = 192 - 12

12y = 180

y = 15

From equation (1),

3x + 8(15) = 192

3x + 120 = 192

x = 24

11). (3x + 49)° = (7x - 23)° [Corresponding angles]

7x - 3x = 49 + 23

4x = 72 ⇒ x = 18

(11y - 1)° = (3x)° [Corresponding angles]

11y = 3×18 + 1

11y = 55 ⇒ y = 5

12). (5x - 38)° = (3x - 4)° [Corresponding angles]

5x - 3x = 38 - 4

2x = 34

x = 17

(7y - 20)° + (5x - 38)° + 90° = 180°

[Sum of interior angles of a triangle = 180°]

5x + 7y = 148

5×17 + 7y = 148

85 + 7y = 148

7y = 148 - 85

y =

5 0

3 years ago

What is the anwser for 8/x=5/9

olganol [36]

Answer:

x= 72/5

Step-by-step explanation:

Cross multiply

8/x=5/9

(8) * (9) = 5 * x (* equals multiply)

72=5x

Then Flip the equation

5x=72

Last, Divide both sides by 5

5x/5=72/5

and that’s it uwu✌️

6 0

3 years ago

Niklas takes a dose of 25 micrograms of a certain supplement each day. The supplement has a half life of 4 hours, meaning that 1

MrRa [10]

Answer:

The amount of the supplement in Niklas' body immediately after the 12th dose is 4.30 micrograms.

Step-by-step explanation:

Half life is the time required for an element to decay into half of its initial size. The supplement has a half life of 4 hours means that it decay to half of its size every 4 hours. Therefore there are 6 stages of division in a day.

i.e $\frac{1}{2}$ × $\frac{1}{2}$ × $\frac{1}{2}$ × $\frac{1}{2}$ × $\frac{1}{2}$ × $\frac{1}{2}$ = $\frac{1}{64}$

The amount of the supplement in Niklas' body after the first dose (first day) can be determined by;

= $\frac{1}{64}$ × 25

= 0.390625 micrograms

He used the supplement daily for 12 days (12th dose), but the amount of the supplement in his body immediately after the 12th dose would be;

amount in his body per day × number of period for complete decay

= 0.390625 × 11

= 4.296875

The amount of the supplement in Niklas' body immediately after the 12th dose is 4.30 micrograms. This is because immediately after the 12th dose, the supplement has not reach its half life.

3 0

3 years ago