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3 years ago

Given the system

Mathematics

1 answer:

Irina-Kira [14]3 years ago

6 0

we have

y > -2 x + y < 4

using a graph tool

see the attached figure

The shaded area is the solution of the system

<u>Part 1) </u>Name an ordered pair that is a solution to this system and explain how you know that this is a solution point

Let

A ( -40,20)

The point A is solution of the system because the point lie on the shaded area

<u>Check</u>

If the point A is solution of the system must satisfy both system inequalities

point A

x=-40

y=20

substitute

y > -2-------> 20 > -2-------> is ok

x + y < 4----> -40+20 < 4-----> -20 < 4-----> is ok

therefore

<u>the answer Part 1) is</u>

The point A is a solution of the system

Part 2) Name an ordered pair that is not a solution to the system and explain how you know that it is not a solution

Let

B(20,20)

The point B is not solution of the system because the point not lie on the shaded area

<u>Check</u>

If the point B is not solution of the system must not satisfy both system inequalities

point B

x=20

y=20

substitute

y > -2 -------> 20 > -2-------> is ok

x + y < 4---->20+20 < 4-----> 40 < 4------> is not ok

therefore

<u>the answer part 2) is</u>

The point B is not a solution to the system

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What are 2 equivalent expressions that are equal to 10m-40

yuradex [85]

It's simple, there is a ton
Multiply all the numbers by 2: 20m - 80
or Divide all the numbers by 2: 5m- 20
or Multiply all the numbers by 3: 30m - 120

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2 years ago

Read 2 more answers

I need help I don't really understand this

pantera1 [17]

The perimeters of both are equal.
The side of the square is 12.
Therefore, its area equals to : 12² = 144

The rectangle base is 19.
Because it has the same perimeter as the square's, so rectangle perimeter is : 19 + 19 + side + side = 12 + 12 + 12 + 12
= 38 + 2side = 48
= 2side = 48 - 38
= side of rectangle = 5
Therefore, its area is 19 x 5 = 95

If you subtract it from the area of the square, you will get : 144 - 95 = 49.
So the answer is : the area of the square is 49 units largee than the area of the square (C)

8 0

2 years ago

Jenny studied the characteristics of two species of bacteria. The number of bacteria of species A, A(t), after t hours is repres

fredd [130]

Answer: D . $N(t) = 3 + (0.25t)^3 - 8(1.06)^t$

Step-by-step explanation:

Given : Jenny studied the characteristics of two species of bacteria. The number of bacteria of species A, A(t), after t hours is represented by the function,

$A(t) = 5 + (0.25t)^3$

The number of bacteria of species B, B(t), after t hours is represented by the function, $B(t) = 2 + 8(1.06)^t$

Then, the difference in the number of bacteria, N(t), of both the species after t hours will be :-

$N(t)=A(t)-B(t)\\\\=5 + (0.25t)^3-(2 + 8(1.06)^t)\\\\=5 + (0.25t)^3-2-8(1.06)^t\\\\=5-2 +(0.25t)^3-8(1.06)^t\\\\=3+(0.25t)^3-8(1.06)^t$

Hence, the correct answer should be : D . $N(t) = 3 + (0.25t)^3 - 8(1.06)^t$

7 0

3 years ago

You want to buy a car, and a local bank will lend you $30,000. The loan would be fully amortized over 6 years (72 months), and t

Georgia [21]

Answer:

<h2>- 56,667cents</h2><h2>- 6.17%</h2>

Step-by-step explanation:

Before we can determine the monthly loan paymnet, we must first calculate the total amount paid at the end of 6years.

Amount = Principal + Interest

Given Principal = $30,000

Interest = Principal * rate * time/100

Interest = $30,000*6*6/100

Interest = $10,800

Amount = $30,000+ $10,800

Amount = $40,800

If amount paid after 6years is $40,800, my monthly loan payment = $40,800/72 ≈ $566.67 to nearest dollar.

since $1 - 100cents

$566.67 = 100 * 566.67

$567 = 56,667cents

Monthly loan payment to nearest cent will be 56,667cents

EFF = (1 + r /n)^n - 1

r is the rate and n is the number of period per year which is 12months

%EFF = EAR = (1 + 0.06 /12)^ 12 - 1

%EFF = 1.005^12

%EFF = 1.061678 - 1

%EFF = 0.061678

%EFF = 6.17% to 2dp

6 0

3 years ago

Maria invests $6,154 in a savings account with a fixed interest rate of 8% compounded continuously. What will the account balanc

Vitek1552 [10]

Answer:

$13,695.98

Step-by-step explanation:

We can use the continuous compound interest formula to solve:

$A = Pe^{rt}$

<em>P = principal amount</em>

<em>r = interest rate (decimal)</em>

<em>t = time (years)</em>

<em />

First, lets change 8% into a decimal:

8% -> $\frac{8}{100}$ -> 0.08

Now, lets plug in the values:

$A=6,154e^{0.08(10)}$

$A=13,695.98$

The account balance after 10 years will be $13,695.98

3 0

3 years ago