MATHEMATICS HIGH SCHOOL

Which of the following represents the graph of f(x) = 2(x-3)?

Answers

Answer 1
Answer:

Answer:

i can't do Graphs well but i am sure this will help

graph of the function f(x) = 2(x-3)f(x)=2(x−3) would generally look like:

The function f(x) = 2(x-3)f(x)=2(x−3) is a linear function in the form of y = mx + by=mx+b, where mm is the slope and bb is the y-intercept.

In this case, the slope mm is 2, which means that for every 1 unit increase in xx, yy will increase by 2 units. The fact that the slope is positive indicates that the graph will slant upwards from left to right.

The term (x-3)(x−3) represents a horizontal shift of the graph. When x = 3x=3, f(x) = 0f(x)=0, which means the graph crosses the y-axis at the point (3, 0).

Putting it all together, you can draw a line that passes through the point (3, 0) and slopes upward at an angle of approximately 45 degrees. The line will get steeper as it moves to the right. This graph represents the linear function f(x) = 2(x-3)f(x)=2(x−3).

Remember, you can use graphing tools or calculators to visualize and draw this function accurately.

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Which set of integers is included in (-1,3]?(1) {0,1,2,3} (3) {-1,0,1,2,3,4}
(2) {-1,0,1,2} (4) {-2,-1,0,1,2,3}

Answers

Hello,

N={0,1,2,3,4,5,...}

(-1,3]={0,1,2,3}⊂N

Answer (1) no negative whole numbers.

Divide £56 in a ratio of 4:3

Answers

÷you need to find how many parts there are ;    4 + 3 = 7

you then need to divide the number by the parts ; £56  ÷  7   =  £8

1 part = £8

4:3, 4 parts : 3 parts.   

   4  x  £8   =  £32

   3  x   £8  =  £24

                                            4:3     =     £32:£24

to check your answer ;

add both parts of your final answer , £32 + £24  =   £56
4+3=7
 56/7 = 8 
4 x 8 is 32 
3 x 8 is 24 
The answer is  £32 and £24.
Hope this helps you!! =')

The piggy bank contains 16 dimes, 8 nickels, and 12 quarters. This morning you removed 3 dimes and 5 nickels.Which expression correctly shows the amount remaining in the piggy bank?

Answers

16•0.10= 1.60$
8•0.05= 0.40¢
12•0.25= 3.00$

1.60$+0.40¢+3.00$= 5.00$

3•0.10= 0.30¢
5•0.05= 0.25¢

0.30¢+0.25¢= 0.55¢

5.00$-0.55¢= 4.45$

4.45$ is left in the piggy bank.

The price of apples went from $0.30 per lb to $0.90 per lb in three years. Find the rate of change of the price of apples.

Answers

Answer:

Hence, the rate of change of the price of apples is:

                             $ 0.20 per year.

Step-by-step explanation:

Let P denote the price of apples.

It is given that the initial price of apples is: $ 0.30 per lb.

i.e. P(0)=$ 0.30 per lb.

Also, the price of the apples after three years is:  $ 0.90 per lb.

i.e.  P(3)=$ 0.90 per lb.

Hence, the rate of the change of the price of apples is calculated by:

Rate\ of\ change=(P(3)-P(0))/(3-0)

Now on putting the value in the formula we obtain:

Rate\ of\ change=(0.90-0.30)/(3-0)\n\n\nRate\ of\ change=(0.60)/(3)\n\n\nRate\ of\ change=0.20

                          The rate of change is:

                             $ 0.20 per year.
90c-30c=60cent change

60cents/3years=20cents/year

It changed 20cents a year

If the common difference in an arithmetic sequence is 4, and the 20th term is 36, what is the first term?

Answers

The sum of an arithmetic sequence can be found using the formula S = n/2(a + l) where S equals sum, n equals # terms, a equals the first term and l equals last term we know enough of these to find the missing pieces S = -15n = 20a = 4 -15 = 20/2 (4 + l)  now we only have one unknown -15 = 10 (4 + l)-15 = 40 + 10l-55 = 10l l = -5.5   so the last term is -5.5 now we can use anothe formula to find the common difference l = a + (n-1) d    so the last term equals the first term (a) plus # terms -1 times (d) the common difference -5.5 = 4 + (20-1) d -9.5 = 19 d d = -.5   so your common difference is -.5

There is a proportional relationship between the volume of a sample of helium in liters and the mass of that sample in grams. if the mass of a sample is 5 grams, its volume is 28 liters. (5, 28) is shown on the graph below. what is the constant of proportionality in this relationship, in this situation, what is the meaning of the number you found in question 1?(explain in the short answer) Add at least three more points to the graph above, and label with their coordinates.(Show your work)
Write an equation that shows the relationship between the mass of a sample of helium and its volume. Use m for mass and v for volume.(Please answer in v = form)

Answers

Answer:

  • v = 5.6m

Step-by-step explanation:

Proportional relationship equation:

  • y = kx, where k- constant of proportionality

Use the given point to work out the value of k:

  • 28 = 5k
  • k = 28/5
  • k = 5.6

In our case the equation is:

  • v = 5.6m, where v- volume, m- mass

Answer:

Step-by-step explanation:

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