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3 years ago

Solve the simultaneous equations y-2x=6 y+2x=0

1 answer:

5 0

Y-2x=6 => y=6+2x
Y+2x=0
(6+2x) + 2x = 0
6 + 4x = 0
4x= 6
X=6/4
X= 3/2
Y=6+2x
Y=6+2. 3/2
Y= 6 + 3
Y=9
Check: y-2x=6
9-2. 3/2 = 6
9 - 3 = 6

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Online jewelry sales have increased steadily over the last 10 years. In 2003, sales were approximately 2 billion dollars, and in

KiRa [710]

Answer: (i) The unit rate at which online jewelry sales have been increasing is 1.33 billion dollars per year.

(ii) The online jewelry sales in 2019 will be 191.7 billion dollars.

Step-by-step explanation:

In 2003, sales were approximately 2 billion dollars and in 2010, they were approximately 14.8 billion dollars.

(i) If $x$ is the number of years after 2003 and $y$ is the amount of sales....

then the equation will be: $y= ab^x$ , where $a$ is the initial amount and $b$ is the growth rate.

for 2003, $x=0$ and for 2010, $x=7$

So, the two points in form of (x, y) will be: $(0,2)$ and $(7,14.8)$

Now plugging these two points int the above equation....

$2= ab^0\\ \\ a= 2\\ \\ and\\ \\ 14.8=ab^7\\ \\ 14.8=2*b^7\\ \\ b^7=7.4\\ \\b= \sqrt[7]{7.4}=1.3309.... \approx 1.33$

Thus, the online jewelry sales have been increasing at a rate of 1.33 billion dollars per year.

(ii) As we got $a=2$ and $b=1.33$ , so the equation will be now: $y= 2(1.33)^x$

For the year 2019, the value of $x$ will be: (2019-2003) = 16

So plugging $x=16$ into the above equation, we will get.....

$y=2(1.33)^16\\ \\ y=191.7150... \approx 191.7$

(Rounded to the nearest tenth)

Thus, the online jewelry sales in 2019 will be 191.7 billion dollars.

6 0

4 years ago

8 people meet, and each person shakes every other person's hand once. how many handshakes occurred?

Ymorist [56]

There was 28 handshakes

3 0

4 years ago

Read 2 more answers

what is an equation of the line that is parallel to y equals negative 4x - 5 and passes through the point -2, 6

Bond [772]

y = - 4x - 2

the equation of a line in slope-intercept form is

y = mx + c ( m is the slope and c the y-intercept )

y = - 4x - 5 is in this form

with slope m = - 4

• Parallel lines have equal slopes

y = - 4x + c ← is the partial equation

To find c substitute (- 2, 6 ) into the partial equation

6 = 8 + c ⇒ c = 6 - 8 = - 2

y = - 4x - 2 ← equation of parallel line

3 0

3 years ago

Verify that the functions are probability mass functions, and determine the requested probabilities.

Free_Kalibri [48]

Answer:

a) 3/64 = 0.046 (4.6%)

b) 63/64 = 0.9843 (98.43%)

c) 1/64 = 0.015 (1.5%)

d) 1/4 = 0.25 (25%)

Step-by-step explanation:

in order to verify that the f(x) is a probability mass function , then it should comply the requirement that the sum of probabilities over the entire space of x is equal to 1. Then

∑f(x)*Δx = 1

if f(x)=(3/4)(1/4)^x , x = 0, 1, 2, ...

then Δx=1 and

∑f(x) = (3/4)∑(1/4)^x = (3/4)* [ 1/(1-1/4)] = (3/4)*(4/3) = 1

then f represents a probability mass function

a) P(X = 2)= f(x=2) = (3/4)(1/4)^2 = 3/64 = 0.046 (4.6%)

b) P(X ≤ 2) = ∑f(x) = f(x=0)+ f(x=1) + f(x=2) = (3/4) + (3/4)(1/4) + 3/64 = 63/64 = 0.9843 (98.43%)

c) P(X > 2)= 1- P(X ≤ 2) = 1 - 63/64 = 1/64 = 0.015 (1.5%)

d) P(X ≥ 1) = 1 - P(X < 1) = 1 - f(x=0) = 1- 3/4 = 1/4 = 0.25 (25%)

4 0

3 years ago

Simplify without parentheses (4v-3w)^2 Explain.

Lilit [14]

(4v-3w)∧2, Its to the second power so take the exponent 2 and put it on the variables and coefficients so you would have (4∧2)(v∧2)-(3∧2)(w∧2). Then you would do the math and get 16v∧2-9w∧2 than you would add the like terms so you have 25v∧2w∧2.

5 0

3 years ago

Read 2 more answers