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solmaris [256]
3 years ago
6

Find the value of a if the line joining the points (3a,4) and (a,-3) has a gradient of 1

Mathematics
1 answer:
Otrada [13]3 years ago
6 0

Recall that the slope or gradient of a line segment through two points is the ratio of the change in the <em>y</em> coordinate to the change in the <em>x</em> coordinate.

If the gradient is 1, then

1 = (-3 - 4) / (<em>a</em> - 3<em>a</em>)

Solve for <em>a</em> :

1 = -7 / (-2<em>a</em>)

1 = 7/(2<em>a</em>)

2<em>a</em> = 7

<em>a</em> = 7/2

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Answer:

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Step-by-step explanation:

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5 0
3 years ago
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2x+8y=5<br> 24x-4y=-15<br> the solution to the system is ( , ) ( , )
kicyunya [14]

[-½, ¾]; use either "Substitution" or "Elimination" to do this, and you'll see that this answer is correct.

3 0
3 years ago
25. John hired a plumber who charges a flat fee of $75 plus $55 per hour. The total charge
mestny [16]

Answer: 55x + 75 = 350; 5 hours

Step-by-step explanation:

What we know:

- A flat fee is $75

- John charges $55 an hour

- The total charge is $350

We need to write an equation to find how many hours John works.

<em>x </em>will represent hours worked.

55x + 75 = 350

We now need to solve for x.

Subtract 75 from both sides.

55x + 75 - 75 = 350 - 75

Simplify.

55x = 275

Divide 55 from both sides.

55x/55 = 275/55

Simplify.

x = 5

John worked 5 hours.

To check our work, we just plug in our x value!

55(5) + 75

275 + 75 = 350

3 0
3 years ago
You need to strengthen a 19% alcohol solution with pure alcohol solution to obtain 40% solution. How much pure alcohol should yo
Alex73 [517]
Let x be the number of mm of pure alcohol to be added:

I will add the mm to express the volume in mm
100mm.(19%) + (100%).x mL = (100 mL+x mL).(40%).
Now right again without the %
100.(0.19) + x.(1) = (100+x).(0.4)

19 + x = = 40 + 04x
x - 0.4x = 40 - 19
0.6 x = 21
x = 21/0.6  and x = 35 mL. This te quantity of pure alcohol should to be added to get a solution at 40%.



8 0
3 years ago
Ashley charges $6 for a bracelet and 12$ for a necklace. She earned $168. Use b for bracelets and n for necklaces, and write an
yarga [219]

Answer:

Step-by-step explanation:

let the number of bracelet be b

Let the number of necklace be n

If Ashley charges $6 for a bracelet , the total amount charged for b bracelets will be 6b

If she charge $12 for a necklace, the total amount for n necklace will be 12n

If she earned $168 in total, then:

6b + 12n = 168

Divide through by 6

b + 2n = 28

Hence the equation for this situation is b + 2n = 28

Next is to solve for b:

Make b the subject of the formula:

b + 2n = 28

subtract 2n from both sides

b + 2n - 2n = 28 - 2n

b = 28 -2n

Hence the function for b will  be b = 28-2n

8 0
3 years ago
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