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schepotkina [342]
3 years ago
11

6(a)If the gradient of the straight line

Mathematics
1 answer:
tensa zangetsu [6.8K]3 years ago
5 0

Answer:

(i) k =1

(ii) y-intercept is 7

Step-by-step explanation:

<u>Given line:</u>

  • ky = kx + x + 7

<u>Divide all terms by k to get slope-intercept form of the line</u>

  • y = (1 + 1/k)x + 7/k

<u>Since the gradient (slope) of the line is 2:</u>

  • 1 + 1/k = 2
  • 1/k = 1
  • k = 1

<u>The equation is now:</u>

  • y = 2x + 7

<u>y - intercept is found when x = 0</u>

  • x = 0 ⇒
  • y = 2*0 + 7
  • y = 7

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A fitness club has two options, one for members and one for nonmembers. Members pay a one-time registration fee of $12 plus $8 p
Liula [17]

Answer:

See below.

Step-by-step explanation:

Let's look at the cost for members (C1) first.  Let x be the number of visits.

C1(x) = 12 + 8x

For non-members (C2), we can do the same.

C2(x) = 10x

You can graph these two equations.

x        C1         C2

0       12          0

1        20        10

2       28        20

3       36        30

4       44        40

5       52        50

6       60        60

7       68        70

Let's make the two equations equal, to find out where the benefit is the same.

12 + 8x = 10x

2x = 12

x = 6

Up to 5 visits, the non-member cost is better.  At 6 visits, there's the same price.  For more than 6 visits, the member cost is better.

7 0
3 years ago
Simplify the expression 6(2x+1)+3(6x+2)
ExtremeBDS [4]

Answer:

30x+12

Step-by-step explanation:

distribute 6 into (2x+1) and 3 into (6x+2) basically multiply

12x+6+18x+6

combine like terms

12x+18x=30x

6+6=18

hope this helps

7 0
3 years ago
Read 2 more answers
-6x+4y=10<br> X-5y=-21<br> Please solve !
galina1969 [7]
X-5y=-21
x=-21+5y

-6(-21+5y)+4y=10
126+-30y+4y=10
126+-26y=10
-26y=-116
y=4.4615
x=1.3076
5 0
3 years ago
Need help with this question
velikii [3]
All you have to do is plug in the given x values. your first equations would read:

f(-3) = 2^(-3)
f(-2) = 2^(-2)
f(-1) = 2^(-1)

these can be solved by moving decimal points or entering them into a calculator. regardless of the method, your answers are:

f(-3) = 0.002
f(-2) = 0.02
f(-1) = 0.2

so just repeat that process to fill in the rest of your table. to graph it, you'll use them as normal (x, y) points:

(-3, 0.002)
(-2, 0.02)
(-1, 0.2)

the graph might be a little difficult, working with such small values, but precision isn't totally important--0.002 will be super close to 0, 0.02 will be slightly further, 0.2 will be slightly further. the smaller values don't matter as much graphically and you'll recognize the graph of a growing exponential as you graph more of the table.
7 0
3 years ago
A test has 19 questions worth a total 100 points. There are ten-point questions and four-point questions. How many questions of
kramer
X + y = 19

10x + 4y = 100

This is a systems of equations. 

Isolate x from the first equation:
x = 19 - y

Now, plug it into the second:

10(19 - y) + 4y = 100
190 - 10y + 4y = 100
-6y + 190 = 100
-6y = -90
y = 15

Plug y in and solve for x:
10x + 4(15) = 100
10x + 60 = 100
10x = 40
x = 4

There are four 10-point questions and fifteen 4-point questions.
3 0
3 years ago
Read 2 more answers
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