A boy bought an article for £9. He spent £4
repairing it and sold it for £18. Calculate the gain
percent on his total costs. (to nearest %)
Help

Answer:

[tex]2y^2-7y+6=0[/tex]

Step-by-step explanation:

We are given that [tex]\alpha[/tex] and [tex]\beta[/tex] are the zeroes of the polynomial [tex]6y^2-7y+2[/tex]

[tex]y^2-\frac{7}{6}y+\frac{1}{3}[/tex]

We have to find a quadratic polynomial whose zeroes are [tex]1/\alpha[/tex] and [tex]1/\beta[/tex].

General quadratic equation

[tex]x^2-(sum\;of\;zeroes)x+ product\;of\;zeroes[/tex]

We get

[tex]\alpha+\beta=\frac{7}{6}[/tex]

[tex]\alpha \beta=\frac{1}{3}[/tex]

[tex]\frac{1}{\alpha}+\frac{1}{\beta}=\frac{\alpha+\beta}{\alpha \beta}[/tex]

[tex]\frac{1}{\alpha}+\frac{1}{\beta}=\frac{7/6}{1/3}[/tex]

[tex]\frac{1}{\alpha}+\frac{1}{\beta}=\frac{7}{6}\times 3=7/2[/tex]

[tex]\frac{1}{\alpha}\times \frac{1}{\beta}=\frac{1}{\alpha \beta}[/tex]

[tex]\frac{1}{\alpha}\times \frac{1}{\beta}=\frac{1}{1/3}=3[/tex]

Substitute the values

[tex]y^2-(7/2)y+3=0[/tex]

[tex]2y^2-7y+6=0[/tex]

Hence, the quadratic polynomial whose zeroes are [tex]1/\alpha[/tex] and [tex]1/\beta[/tex] is given by

[tex]2y^2-7y+6=0[/tex]

Answer:

Side IJ would be 15

Step-by-step explanation:

Since Triangle HIJ is dilated by a scale factor of 5, that means Triangle H'I'J' would have side measurements that are 5 times as much as Triangle HIJ.

They give you that side I'J' is 75

so you divide 75 by 5 and you'll end up with 15

Answer:

11.26 m

Step-by-step explanation:

The height of the tree is about 11.25 meters.

When the respective sides are proportional and the corresponding angles are congruent, two triangles are said to be similar.

Given that, the height of the person is 1.55 meters, the length of the tree's shadow is 38.15 meters, and the distance between the person and the tree is 32.9 meters.

Let the height of the tree be x.

Note that the scenario makes two similar triangles.

Since the ratio of the side lengths of similar triangles is proportional, it follows:

(38.15 - 32.9)/1.55 = 38.15/x

5.25/1.55 = 38.15/x

3.39 = 38.15/x

x = 38.15/3.39

x = 11.25

Hence, the height of the tree is about 11.25 meters.

Learn more about similar triangles: https://brainly.com/question/25882965

#SPJ2

Answer:

6 mps to the nearest mps.

Step-by-step explanation

The rocket that carried the Curiosity Rover to Mars traveled at a speed of 21,000 miles per hour. What is this speed to the nearest mile per second?

1 hr = 3600 sec

Since an hour is 3600 seconds (i.e., 60 x 60), you simply need to divide that number by 3600

→ 21000 mph = 21000 ÷ 3600 mps = 5 5/6 mps →

ANSWER : 6 mps to the nearest mps.

Answer:

Believe the other person

Step-by-step explanation:

I got a 100%, and also got this question.

Answer:

10 plants

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

He planted 10 this year because last year he planted 12, and 1/3 of that is 4. He planted 6 more than that this year, so 4+6=10.

Answer:

Step-by-step explanation:

recall that the inside angles of a triangle add up to 180°

and also that the angle 115° is the other part of a 180° total

180=115+y

180-115 =65

then the inside angle at Y  is 65°

add the three inside (interior of the triangle) angles up

180= 65 + (4k+5) + (6k+10)

180 = 65 + 10k + 15

180 = 80 + 10k

100  = 10k

10 = k

see how I did that?  

Answer:

Hello there ,

The answer to this equation would be:

A=.50j+9

Step-by-step explanation:

this answer should be correct because he started with 9,

and he is selling each cup (j) for 0.50

Let me show you an example:

Ok lets say he sold 10 (j) cups:

you would replace the (j) with the 10

A=0.50(10)+6

A=5+6

A=11 and he would have $11

but that just an example so the real answer to your question is:

A=.50j+9

Hope this help. If correct please give brainliest.

Thank you,

Have a good day !!!!!

Answer:

(f + g)(x) = 5x - 3

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= 2x + 4 + 3x - 7 ← collect like terms

= 5x - 3

Answer:

5x - 3

Step-by-step explanation:

(f + g)(x) = f(x) + g(x)

= 2x + 4 + ( 3x - 7 )

= 5x - 3

Answer:

D) 15

Step-by-step explanation:

This is an arithmatic progression.

The formula for the sum of arithmatic progression is

[tex]s = \frac{n}{2} (2a + (n - 1)d)[/tex]

where d is the common difference between successive terms and a is the first term. By applying this formula,

[tex]120 = \frac{n}{2} (2(1) + (n - 1)(1)) \\ 120 = \frac{n}{2} (1 + n) \\ n(1 + n) = 240 \\ n {}^{2} + n - 240 = 0 \\ (n - 15)(n + 16) = 0 \\ n = 15 \: or \: n = - 16(reject)[/tex]

Answer:

I dont think i dont know this but its 10?

Answer:

50.8°

Step-by-step explanation:

In ∆ IJK :-

Answer:

17253.52

Step-by-step explanation:

100-9.5=90.5

19064.67*0.905=17253.52

Answer:

4 cans of paint

Step-by-step explanation:

Take the area of the wall and divide by the area that the can of pain will cover

10.37 / 3.1

3.34516129 cans

We need to round up to make sure we buy enough cans of paint

4 cans of paint

We can take area as,

Area = A

The required formula is,

→ A of wall ÷ A that paint's can will cover

Then find the no. of cans of paint that are needed to paint the wall.

Now use the formula,

→ A of wall ÷ A that paint's can will cover

→ 10.37 ÷ 3.1

→ 3.34516129032

→ 4 cans (by nearest value)

Hence, we need 4 cans to paint the wall.

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

Explanation:

x = original amount of caster oil (in quarts)

Since 15% remains, this means you used 85% of the original amount x.

Note how 15% + 85% = 100%

So,

85% of x = 34 quarts

0.85x = 34

x = 34/0.85

x = 40

You started with 40 quarts of oil.

15% of that remains, meaning 0.15*40 = 6 quarts of oil are left over.

-----------

We could also solve like this

(amount used)/(amount total) = (percent)/(100)

34/x = 85/100

34*100 = x*85

3400 = 85x

85x = 3400

x = 3400/85

x = 40

So we end up with the same x value as before, and we follow the same set of steps at the end of the first section to end up with the answer of 6 quarts.

Answer:

D. 30°

Step-by-step explanation:

By exterior angle theorem:

x° + 70° = 100°

x° = 100° - 70°

x° = 30°

x = 30

The top right quadrant is quadrant 1.

The top left quadrant is quadrant 2.

The bottom left quadrant is quadrant 3.

The bottom right quadrant is quadrant 4.

Therefore, point D is in the fourth quadrant.

Answer:

A, 12 times the square root of 3

Step-by-step explanation:

24 sqaured plus 12 squared=432

square root of 432=20.9

12 times the sqaure root of 3=20.9

Answer:

I'm pretty sure the answers are options D , E and F .

Step-by-step explanation:

So here's how I did it , I got the original expression , solved it and the answer I found is -6.5. So then I solved all the others and D , E and F gave me -6.5.

Hope this helps lol

You didn't include the right triangle but this is all I could find.

x = 1

H = sqrt(15)

Answer:

7.1

Step-by-step explanation:

We used SOHCAHTOA because it's a right angle triangle

So because we have an angle with an adjacent of 6.3 and hypotenuse of x

We will use

Cos=adjacent /hypotenuse

Answer:

You need to convert all the units to one unit

Answer:

10.

Step-by-step explanation:

Answer:

The number is 10.

Step-by-step explanation:

x/5 = 2

Multiply both sides by 5.

5 * x/5 = 5 * 2

x = 10

Answer: The number is 10.

Answer:

2/5

Step-by-step explanation:

18x+12x=-4+16

30x=12

x=2/5

Answer:

18x-16=-12x-4

18x+12x=-4+16

30x=12

x=12/30

x=2/5

Answer:

8 more players

Step-by-step explanation:

There are already 4 players including Jeff, so in order to have more players, they need from 1-8 more players.

Have a good day!!!!

Answer:

The number of instruments assembled in 7.5 hours are 450 n/t.

Step-by-step explanation:

The number of instruments assembled in t minutes = n

the number of instruments assembled in 1 minute = n / t

Total time = 7.5 hours = 7.5 x 60 = 450 minutes

So, the number of instruments assembled in 450 minutes are

[tex]\frac{n}{t}\times 450\\\\\frac{450 n}{t}[/tex]  

Answer:

2\sqrt2

Step-by-step explanation:

a=5-2√6 ...(1)

[tex]\frac{1}{a}=\frac{1}{5-2 \sqrt{6} } \times\frac{5+2\sqrt{6} }{5+2\sqrt{6} } =\frac{5+2\sqrt{6}}{(5-2\sqrt{6})(5+2\sqrt{6})} =\frac{5+2\sqrt{6}}{5 ^2-(2\sqrt{6})^2} =\frac{5+2\sqrt{6}}{25-24} =5+2\sqrt{6}\\a+\frac{1}{a}=5-2\sqrt{6}+5+2\sqrt{6}=10[/tex]

[tex](\sqrt{a}-\frac{1}{\sqrt{a}})^2=(\sqrt{a})^2+(\frac{1}{\sqrt{a}})^2-2 \times \sqrt{a} \times \frac{1}{\sqrt{a}}=a+\frac{1}{a}-2=10-2=8\\\sqrt{a}-\frac{1}{\sqrt{a}}=\sqrt{8}=2\sqrt{2}[/tex]