Evaluate the function g(t)=23t, when t = 30.

If 3x + 5y = 2 and 2x - 4y = 20, what is 5x - y?

gavmur [86]

Answer:

= 298/11

Step-by-step explanation:

3x + 5y = 2 | ×2 |

2x - 4y = 20 | ×3 |

6x + 10y = 4

6x - 12y = 60

____________--

22y = -56

y = -56/22

y = -28/11

3x + 5y = 2 | ×4 |

2x - 4y = 20 | ×5 |

12x + 20y = 8

10x - 20y = 100

_____________+

22x = 108

x = 108/22

x = 54/11

5x - y

= 5(54/11) - (-28/11)

= 270/11 + 28/11

= 298/11

8 0

3 years ago

The ground temperature at sea level is 60 degrees F. For every 100-foot increase in elevation, the temperature rises 1/10 of one

N76 [4]

<h3>Answer: B. 62 degrees fahrenheit</h3>

====================================================

Explanation:

x = elevation in feet

y = temperature in fahrenheit

The temperature goes up 1/10 = 0.1 degrees for every 100-foot increase of elevation. So the slope is 0.1/100 = 0.001, which tells us how fast the temperature is increasing. In other words, the temperature goes up 0.001 degrees each time the elevation goes up by 1 foot.

The ground temperature is 60 degrees, which is our starting temperature. It's the value of y when x = 0. Therefore, 60 is the y intercept.

We have a slope of m = 0.001 and a y intercept of b = 60. The equation y = mx+b becomes y = 0.1x+60

Now plug in x = 2000 to find the temperature at this elevation

y = 0.001x+60

y = 0.001*2000+60

y = 2+60

y = 62

7 0

3 years ago

Read 2 more answers

Can someone please do number 12 and 14 for me ?

KengaRu [80]

12. Yes, because the diagonals of a parallelogram bisect each other.
14. Yes, a parallelogram has opposite sides that are equal.

Hope this helps =)

3 0

3 years ago

The price of products may increase due to inflation and decrease due to depreciation. Marco is studying the change in the price

likoan [24]

Answer:

A) 3%

B) Product A

Step-by-step explanation:

Exponential Function

General form of an exponential function: $y=ab^x$

where:

a is the initial value (y-intercept)
b is the base (growth/decay factor) in decimal form
x is the independent variable
y is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Part A

Product A

Assuming the function for Product A is exponential:

$f(x) = 0.69(1.03)^x$

The base (b) is 1.03. As b > 1 then it is an increasing function.

To calculate the percentage increase/decrease, subtract 1 from the base:

⇒ 1.03 - 1 = 0.03 = 3%

Therefore, product A is increasing by 3% each year.

Part B

$\sf percentage\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100$

To calculate the percentage change in Product B, use the percentage change formula with two consecutive values of f(t) from the given table:

$\implies \sf percentage\:change=\dfrac{10201-10100}{10100}\times 100=1\%$

Check using different two consecutive values of f(t):

$\implies \sf percentage\:change=\dfrac{10303.01-10201}{10201}\times 100=1\%$

Therefore, as 3% > 1%, Product A recorded a greater percentage change in price over the previous year.

Although the question has not asked, we can use the given information to easily create an exponential function for Product B.

Given:

a = 10,100
b = 1.01
n = t - 1 (as the initial value is for t = 1 not t = 0)

$\implies f(t) = 10100(1.01)^{t-1}$

To check this, substitute the values of t for 1 through 4 into the found function:

$\implies f(1) = 10100(1.01)^{1-1}=10100$

$\implies f(2) = 10100(1.01)^{2-1}=10201$

$\implies f(3) = 10100(1.01)^{3-1}=10303.01$

$\implies f(4) = 10100(1.01)^{4-1}=10406.04$

As these values match the values in the given table, this confirms that the found function for Product B is correct and that Product B increases by 1% per year.

4 0

2 years ago

(12)2what does it equal

julia-pushkina [17]

12 × 2 = 24

anything to ask please pm me

7 0

2 years ago