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dsp73
3 years ago
5

Write a system of equations and solve using elimination. Ricardo has two bills. The two bills together are $21. One bill is wort

h $19 more than the other. What are the two bills?
Mathematics
1 answer:
djyliett [7]3 years ago
5 0

Answer:

The worth of one bill is $20 and the worth of the other bill is $1

Step-by-step explanation:

Let

x----> the worth of one bill

y ---> the worth of the other bill

I assume x > y

we know that

x+y=21 ----> equation A

x=y+19 ---> equation B

Solve the system by elimination

Multiply equation B by -1 both sides

-x=-y-19 ----> equation C

Adds equation A and equation C

x+y=21

-x=-y-19

------------

y=21-y-19

2y=2

y=1

Find the value of x

x=y+19 -----> x=1+19=20

therefore

The worth of one bill is $20 and the worth of the other bill is $1

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If his heartbeat has increased by 8 beats per minute after 20 minutes of working out how much will his heartbeat have increased
-BARSIC- [3]

Answer:

12 beats per minute after 30minutes

Step-by-step explanation:

Since we are told by how much his heartrate increased in 20 minutes, we can simply calculate how much it increased in 10 minutes and add that amount to the current heart rate to know how much his heartrate increased after 30 minutes of working out. Since 10minutes would be half of the 20minutes we simply divide the beats per minute by 2.

8 / 2 = 4 beats per minute after 10 minutes

Now we simply add this to the beats per minute at the 20minute mark to calculate the beats per minute at 30minutes

8 + 4 = 12 beats per minute after 30minutes

3 0
3 years ago
Complete the solution table from left to right for the quadratic function. (I did not select an answer, that was a mistake) Than
Karo-lina-s [1.5K]

Answer: OPTION D

Step-by-step explanation:

To complete the table, you need to substitute the values of "x" given in the table into the quadratic equation y=x^{2}-x-6 to obtain the corresponding value of "y".

Then:

When x=-5 :

y=(-5)^{2}-(-5)-6

y=24

When x=-3 :

y=(-3)^{2}-(-3)-6

y=6

When x=-1 :

y=(-1)^{2}-(-1)-6

y=-4

When x=2 :

y=(2)^{2}-(2)-6

y=-4

8 0
4 years ago
lauren is the youngest of four sisters. the average of their ages(all different whole numbers) is 9 years. what is the oldest th
Elina [12.6K]

The max of Lauren's age --> the minimum of the others' ages, 1, 2 & 3

4*avg = 4*9 = 36

36 - (1+2+3) = 30

Lauren is 30 yrs of age, or younger.

3 0
3 years ago
A rectangle with an area of 4/7 meters squared is dilated by a factor of 7. What is the area of the dilated rectangle?
nikklg [1K]

Answer:

49

Step-by-step explanation:

Every time you multiply both sides of a rectangle by a number x, its area if multiplied by x^{2}.

In our example:

Area of a rectangle = width . length

width = 4

length   = 7

A_{1} = 4 . 7 = 28

When you multiply both sides by 7:

width = 4 . 7 = 28

length = 7 . 7 = 49

A_{2}  = 28 . 49

A_{2}  = 1372

A_{2}  / A_{1} = 1372 / 28 = 49 = (7)^{2}

Both sides multiplied by 7 => Area multiplied by 7^{2}

Got it?

;-)

7 0
3 years ago
Use the laplace transform to solve the initial value problem: y''+y=1, y(0)=2 and y'(0)=0
Evgesh-ka [11]

Answer:

y(s) = sin t + 2 cost

Step-by-step explanation:

given,

     y''  + y = 1,                       y(0) = 2  and  y'(0) = 0

applying Laplace transformation both side

s²y(s) - s y(o)- y'(0) + y(s) = L{1}

s²y(s) - 2 s + y(s)  = L{1}

y(s)(s² + 1 ) =  L{1}  + 2 s

y(s)= L^{-1}(\dfrac{L(1)}{s^2 + 1})+2L^{-1}(\dfrac{s}{s^2+1})

     y(s) = sin t + 2 cost

hence, the required solution of Laplace will be

     y(s) = sin t + 2 cost

5 0
3 years ago
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