MATHEMATICS HIGH SCHOOL

Find the values of x:

I don’t understand how to do this please help
Find the values of x: I don’t understand how to - 1

Answers

Answer 1
Answer:

Answer:

x = 8

Step-by-step explanation:

11x - 34 and 7x - 2 are vertical angles and congruent, thus

11x - 34 = 7x - 2 ( subtract 7x from both sides )

4x - 34 = - 2 ( add 34 to both sides )

4x = 32 ( divide both sides by 4 )

x = 8

-----------------------

11x - 34 = 11(8) - 34 = 88 - 34 = 54

18y and 11x - 34 are adjacent angles and supplementary , thus

18y + 54 = 180 ( subtract 54 from both sides )

18y = 126 ( divide both sides by 18 )

y = 7

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Prove that the value of the expression(3^5-3^4)(3^3+3^2) is divisible by 24

Choose a number between 61 and 107 that is a multiple of 3 , 9 and 12

Answers

Let us simply find the least common multiple of 3, 9, and 12.

3 / 3  9  12
3 / 1  3   4
4 / 1  1   4
   /  1  1  1

LCM = 3 * 3 * 4 = 36

Let us multiply 36 by 2 =  36*2 = 72

So 72 is a multiple of 3, 9 and 12 and it is in between 61 and 107.

0.0032 in standard form

Answers

0.0032 = 3.2 x 10^-3
The power is a minus as the decimal point had to move right.
Hope that helps you!

A spherical ballon with a radius r inches has volume V(r)=4/3 pir^3. Find a function that represents the amount of air required to inflate the balloon from a radius inches to a radius of r+1 inches.

Answers

Answer:

The function that represents the amount of air is \Delta V =\cfrac 43 \pi (3r^3+3r+1)

Step-by-step explanation:

The amount of air here represents the difference between V(r) and V(r+1), so we can start working by finding an expression for the volume at r+1, and then subtract the original volume V(r).

Volume of balloon of radius r+1 inches.

We can replace r with r+1 on the formula and we get:

V(r+1)=\cfrac43 \pi (r+1)^3

We can expand (r+1)^3 since we will use it to simplify it later on.

So we will have first

(r+1)^2 = (r+1)(r+1)\n(r+1)^2 =r^2+r+r+1\n(r+1)^2 = r^2+2r+1

We can multiply that result by (r+1) to get (r+1)^3

(r+1)^3= (r+1)^2 (r+1)\n(r+1)^3=(r^2+2r+1)(r+1)\n(r+1)^3= r^3+2r^2+r+r^2+2r+1\n(r+1)^3 =r^3+3r^2+3r+1

Thus the volume equation at r+1 will be

V(r+1)=\cfrac 43 \pi (r^3+3r^2+3r+1)

Finding the amount of air required to inflate from r to r+1

The amount required to inflate is the difference of volumes, so we have

V(r+1)-V(r)=\cfrac 43 \pi (r^3+3r^2+3r+1)  \cfrac 43 \pi r^3

Combinging both into one term by factor \cfrac 43 \pi give us

V(r+1)-V(r)=\cfrac 43 \pi (r^3+3r^2+3r+1-r^3)

Simplifying

V(r+1)-V(r)=\cfrac 43 \pi (3r^2+3r+1)

And that function represents the amount required to inflate the balloon from r  to r+1 inches.

1500 soldiers in a fort have provision for 48 days.After 13 days few soldiers join them and the food lasts 25 days how many soldiers join

Answers

Answer: This is a problem of inverse variation, where the number of days that the food lasts is inversely proportional to the number of soldiers in the fort. We can use the formula:

d = k / s

where d is the number of days, s is the number of soldiers, and k is a constant of proportionality. We can find the value of k by using the initial information:

48 = k / 1500 k = 48 * 1500 k = 72000

Now we can use the information after 13 days to find the new number of soldiers. Let x be the number of soldiers who joined the fort. Then we have:

25 = 72000 / (1500 + x) 25 * (1500 + x) = 72000 37500 + 25x = 72000 25x = 34500 x = 1380

Answer: The number of soldiers who joined the fort after 13 days is 1380.

The line y =3x-5 meet x-axis at the point M. The line 3y+2x=2 meets y-axis at point N. Find the equation of the line joining M and N in the form ax + by + c = 0 where: a,b,c are integers.

Answers

Answer-

The line equation is,

\boxed{\boxed{6x+15y-10=0}}

Solution-

The line y =3x-5 meets x-axis at the point M, i.e M is the x-intercept of this line. At the x-intercept y=0, so

\Rightarrow 0 =3x-5

\Rightarrow 3x=5

\Rightarrow x=(5)/(3)

So, coordinate of M is ((5)/(3),\ 0)

The line 3y+2x=2 meets y-axis at point N, i.e N is the y-intercept of this line. At the y-intercept x=0, so

\Rightarrow 3y+2(0)=2

\Rightarrow 3y=2

\Rightarrow y=(2)/(3)

So, coordinate of N is (0,\ (2)/(3))

The line joining M and N can be found out by applying two point formula of straight line,

\Rightarrow (y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)

\Rightarrow (y-0)/((2)/(3)-0)=(x-(5)/(3))/(0-(5)/(3))

\Rightarrow (y)/((2)/(3))=(x-(5)/(3))/(-(5)/(3))

\Rightarrow -(5)/(3)y=(2)/(3)(x-(5)/(3))

\Rightarrow -5y=2(x-(5)/(3))

\Rightarrow -5y=2x-(10)/(3)

\Rightarrow 2x+5y-(10)/(3)=0

As it is given that all the coefficients are integers, so multiplying with 3

\Rightarrow 6x+15y-10=0

Solution: As given  line y =3x-5 meet x-axis at the point M.

  On x axis y coordinate is zero.

Put y =0 in above equation, we get →x = 5/3

∴ Coordinate of M is (5/3,0).

As, also given , line 3y+2x=2 meets y-axis at point N.

On y axis , x coordinate is zero.

Substituting , x=0 in above equation, gives y =2/3.

Coordinate of point N is (0,2/3).

Equation of line passing through two points (a,b) and (p,q) is given  by

       → (y-b)/(x-a) =(q-b)/(p-a)

Or as X intercept = 5/3, and Y intercept = 2/3

Equation of line in intercept form is →(x)/(a) + (y)/(b) =1, where a and b is X intercept and y intercept respectively.

So, line passing through (5/3,0) and (0,2/3) is given by

→ (x)/((5)/(3))  +  (y)/((2)/(3))=1

 → (3x)/(5) + (3y)/(2) =1  

→ 6 x + 15 y =10 [Taking LCM of 5 and 2 which is 10]

→ 6 x + 15 y -10=0, which is equation of the line joining M and N in the form ax + by + c = 0 where: a,b,c are integers.

each can of paint will cover 450 tiles. Augustin is painting 300 tiles in his bathroom, 675 in his kitchen, and 100 in his hallway. How many cans of paint does he need to buy?

Answers

Answer:

He will need to buy 3 cans.

Step-by-step explanation:

First we need to know how many tiles he will paint.

The total amount of tiles he will paint is 300 + 675 + 100 = 1075 tiles.

We know that a can of paint will cover 450 tiles, therefore, we need to divide the total amount of tiles between the number of tiles covered by can:

1075/450 = 2.38.

He will need 2.38 cans of paint. But he cannot buy this number of cans, therefore he will have to buy 3 cans and will have some paint left.

You have to add all of the tiles that he needs painting.  675+300+100=1075.  Then to figure out how many paint cans you need, divide 1075 by 450.  It equals 2.388... so, you need to round up or else you will be missing some tiles.  The final answer is 3 paint cans.  Hope this helps
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