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3 years ago

Determine if (-3, 4) is a solution to the following system of equations:

Mathematics

1 answer:

ValentinkaMS [17]3 years ago

7 0

Answer:

(-3,4) does not work with the equations

Step-by-step explanation:

3(-3)+2(4)=-1

-9+8=-1

-2(-3)-3(4)=-5

6-12=-6

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The temperature, H, in degrees Celsius, of a cup of coffee placed on the kitchen counter is given by H = f(t), where t is in min

Deffense [45]

Answer:

f'(t) is negative

The unit is degC/min

At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.

Step-by-step explanation:

From the question we are told we are told that

The equation for the temperature of a cup of coffee place on a counter is

$H= f(t)$

Here t is the time in minutes the coffee was put on the counter

Generally f(t)' is the derivative of f(t) at it represents the change of the temperature of the cup of coffee with respect to time

Generally for the coffee placed on the counter after a couple of minutes the temperature will decrease hence f(t)' is negative

Generally the unit of the temperature is in degrees Celsius while that of time is in minutes

So the change in temperature with time f(35)' will be in degrees Celsius/minutes (i.e degC/min)

From the question we are told that

$|f(35)'| = 1.5$

i.e the rate of change of temperature after 35 minutes is 1.5

and

$|f(35)| = 68$

i.e the temperature of the cup of coffee after 35 minutes is 67 degC

Now after another t= 30 seconds = $\frac{30}{60}= 0.5 \ minutes$ the rate of change of the temperature of the cup of coffee is

$R = |f(35)'| * t$

=> $R = 1.5 * 0.5$

=> $R = 0.75$

At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.

5 0

3 years ago

The touchdown to fumble ratio for Bobby Boucher was 9:2 If Bobby ran for 18 touchdowns,

Vika [28.1K]

Answer: He had 14 more touchdowns than he did fumbles.

Step-by-step explanation:

Step 1. Ok, so we need to see how many times 9 will divide into 18.

18/9=2.

Step 2. So now that we know that 9 goes into 18 two times and we know he has two fumbles for every 9 touchdowns we can multiply 2 by 2 to find out how man fumbles he had.

2*2=4

Step 3. Now to find out how many more touchdowns than fumbles he had we need to subtract his fumbles from his touchdowns.

18-4= 14. So, now we know he had 14 more touchdowns than he did fumbles.

Hope this helps!

4 0

3 years ago

Joe is building a post for his mailbox. To find the correct dimensions, he needs to expand this expression: (x-3) (x-9) (x-4) Se

kolbaska11 [484]

Answer:

$(x-3)(x-9)(x-4)=x^3-16x^2+75x-108$

Step-by-step explanation:

Given:

The expression to expand is given as:

$(x-3)(x-9)(x-4)$

Let us expand the first two binomials of the given expression using FOIL method.

The FOIL method states that:

$(a + b)(c + d) = ac + ad + bc + bd$

$(x-3)(x-9)=(x\times x)+(x\times -9)+(-3\times x)+(-3\times -9)\\\\(x-3)(x-9)=x^2-9x-3x+27=x^2-12x+27$

Now, let us multiply the result with the remaining binomial. Multiplying each term of the trinomial with each term of the binomial, we get:

$(x^2-12x+27)(x-4)\\\\= (x^2\times x)+ (x^2\times -4)+(-12x\times x)+(-12x\times -4)+(27\times x)+(27\times -4)\\\\=x^3-4x^2-12x^2+48x+27x-108\\\\=x^3-16x^2+75x-108...........(\because-12x^2-4x^2=-16x^2,48x+27x=75x)$

Therefore, the equivalent expression after expanding is given as:

$(x-3)(x-9)(x-4)=x^3-16x^2+75x-108$

3 0

2 years ago

7/5+(-5/12) in commutative property (addition)

lorasvet [3.4K]

Answer:

0.93

Step-by-step explanation:

7 0

3 years ago

What is the probability of rolling two dice, and having a total of 8 dots showing? Express your answer as a percent

Solnce55 [7]

Answer:

Step-by-step explanation:

8 0

3 years ago