Maths homework help!?

Question

I have some calculator questions that i wondered if anyone could tell me how to wrk out.

1. The hypotenuse of a right-angled isoscels triangle is 12cm. what are the lengths of the other 2 sides?

2. Where does the line y=4-xsquared cut the y axis?

3. Calculate the perimeter of a semi-circle of diameter 15cm.

4. Calculate the area of a semi-circle of radius 7cm.

5. Solve
6x + 9y = 21
2x + 7y = 11

Thanks to all thoses who help! <3

Thankyou both DanG and Ol Whit both helped very much! So vote shall choose a winner.

Answer 1

1.

(a and b must be equal)

a^2 + b^2 = c^2
a^2 + b^2 = 144
144/2 = 72
sqrt.72 = 8.49 (3.s.f)

Lengths of two other sides are 8.49 cm

2.

y = 4-x^2
y = -x^2 + 4

Cuts the y axis at +4

3.
(pi) x diameter = perimeter of circle
3.142 x 15 = 47.1 (3.s.f)

Perimeter of circle = 47.1 cm
47.1/ 2 = 23.6 (3.s.f)

Curved perimeter of semi circle = 23.6 cm
23.6+15 = Total Perimeter

Total Perimeter = 38.6 cm (3.s.f)

4.

Area of a circle = (pi)r^2
3.142 x 7^2 = 154 (3.s.f)

Area or semi circle = 154 / 2 = 77.0 (3.s.f)

5.

6x + 9y = 21
6x + 21y = 33 (multiplied all by 3)

(Top - bottom)

-12y = -12
12y = 12
y = 1

(substitute y back in)

6x + 21 = 33
6x = 12
x = 2

y = 1, x = 2

Answer 2

1. Pythagoras: the square of the hypotenuse of a right angled triangle is equal to the sum of the squares of the other two sides.
Isosceles triange: two sides are the same length.
So the square of one of the sides is a half of 12²
Each of the other sides is √72

2. The y axis is x=0
When x=0, 4-x²=4 so the answer is at (0,4)

Had the question been "when does y=4-x² cross the x axis?"
I suspect that this is the more likely question...
That is when y=0, so x²=4, and x=√4 that is x = ±2...

3. The perimeter of a circle is  2πr, so the length of the curved edge of a semicircle will be half that. The length of the straight edge of the semicircle will be 2r.
The total perimeter is 2r + πr = 38.55cm in this case.

4. The area of a circle is πr², so halve this for a semicircle.
The answer is 76.93cm² in this case.

5. If you multiply the second simultaneous equation by 3 (treat both sides of the equality the same), you get:
6x + 21y = 33
If you now take the first equation
6x + 9y = 21
away from this, you get:
12y = 12 so y = 1. Substitute this value back into either of the original equations - you get:
6x + 9 = 21
2x + 7 = 11
looks like x = 2...

The aim with simultaneous equations is to find terms which will cancel, leaving only a single unknown. With the first equation 6x + 9y = 21 it would have been possible to divide all the terms by 3 to get 2x + 3y = 7 and go on from there, but division lke this is not always possible - beeter to learn something which will always work.

Hope this helps more than just the answers!

r = radius
π = pi

Answer 3

1) 4.9 + 4/17 = 4.90 + 0.23 = 5.13 2) 1/2 + 1/2 = 2/2 = 1 3) 4/9 + 1/3 = 4/9 + 3/9 = 7/9 = 0.77 4) 1/2 - 4/17 = 9/34 17/34 - 8/34 = 9/34 9/34 = 9/34 ==> CORRECT 5) 5/6 - 5/17 = 0.83 - 0.29 = 0.54 6) 1/2 - 3/11 = 5.5/11 - 3/11 = 2.5/11 = 0.227 7) 5/7 - 3/13 = 0.71 - 0.23 = 0.48 8) 1/2 x 3/13 = 3/26 (1 x 3) / (2 x 13) = 3/26 3 / 26 = 3/26 ==> CORRECT 9) 1/2 x 4/11 = (1 x 4) / (2 x 11) = 4 / 22 = 2/11 10) 4/7 x 5/19 = (4 x 5) / (7 x 19) = 20 / 45 = 4/9 11) 1/2 x 5/12 = (1 x 5) / (2 x 12) = 5 / 24 12) 5/8 / (5/13) = 1 5/8 5/8 x 13/5 = 1 + 5/8 (5 x 13) / (8 x 5) = 8/8 + 5/8 65 / 40 = 13/8 13 / 8 = 13/8 ==> CORRECT 13) 5/7 / (2/7) = 5/7 x 7/2 = (5 x 7) / (7 x 2) = 35 / 14 14) 2/3 / (1/4) = 2/3 x 4 = 8 / 3 15) 1/2 / (2/9) = 1/2 x 9/2 = 9 / (2 x 2) = 9 / 4 In some cases, when we have a fraction it is better if we write it as a decimal (simply by dividing the numerator with the denominator). But in some cases it's also a better idea to work only with the numerators of the fractions (if they have the same denominator). Also, remember that when dividing fractions you are actually multiplying the fraction by the reciprocal of the other one. Example: 2/9 divided by 5/8 ==> 2/9 / (5/8) divided (/) by 5/8 ==> times (x) 8/5 (reciprocal of 5/8) 2/9 / (5/8) = 2/9 x 8/5 = (2 x 8) / (9 x 5) = 16 / 45 NOTE: If the fraction can be simplified, do it. In this case 16 and 45 can't be simplified but they can be presented as a decimal (16/45 = 0.35). Hope this helped and good luck! :)

Answer 4

1. A right-angled isosceles triange consists of a hypotenuse opposite the 90 degrees, and two sides of equal length. Since a^2 + b^2 = c^2, where c is the length of the hypotenuse, a and b are the lengths of the side, and a = b since it is an isosceles triangle (a^2 + a^2 = c^2). Therefore, since you know c = 12 cm, you can solve for a.

2. A line is defined by the equation y = m*x + b, where m is the slope and b is the y intercept. The same equation applies for a x^2 value. So your equation is y = 4 - x^2, where 4 is the value of b.

3. The perimeter of a circle is also called the "circumference." The equation for the circumference (C) of a circle is: C = 2*pi*r, where pi=3.14 and r is the radius (therefore, 2*r is equal to the diameter of the circle). Since the problem is for a semi-circle (half a circle), the equation is C = pi*r.

4. Area of a circle is: A = pi*r^2. Just like the previous problem, it is a semi-circle (half a circle), therefore the equation is divided by 2.

5.

Equation # 1: 6x +9y = 21
Equation # 2: 2x + 7y = 11

Solve the first problem in terms of x (in other words, leave the x on the left side of the equation and bring everything else over to the right side). You should be left with x = 21/6 + 9y/6.

Now plug this equation for x into the second equation and solve in terms of y (you should start with: 2*(21/6 + 9y/6) + 7y = 11). Now you have a number for y, plug that number into your original equation #1.

Answer 5

1. 144 = 2l^2 where l is the length of the side. Since it is an isosceless triangle, the lenghts of the two sides are equal.

So, l^2 = 72 and l = sqrt.72 = 8.485...cm

2.It cuts it at y = 4 since x = 0 and y = 4 -x^2 = 4

3. Perimeter of a semi-circle of diameter d is pi.d/2

= 3.1416 x 15/2 = 23.562 sq.cm

If it is a closed semi-circle, we add the diameter to it and get 23.562 + 15 = 38.562 cm as the perimeter.

4. Area of a semi-circle of radius r is pi.r^2/2

= 3.1416 X 7 X 7 / 2 = 76.9692 cm^2

5. 6x + 9y = 21
2x + 7y = 11

Let us multiply the second equation with 3. 6x + 21y = 33

We subtract the first equation from the second.

6x + 21y = 33

(-)6x + 9y = 21

We get 12 y = 12 or y = 1

Substituting that value of y in 1st equation,

6x + 9 = 21 or 6x = 12 or x = 2

So, x = 2 and y = 1

Answer 6

Some-one doesn't pay attention in maths class *tut tut*

1. The hypotenuse is side h for example
This method only works in right angled triangles but
side a^2 + b^2 = h^2 (to find h from h^2 find its square root)
side h^2 - b^2 = a^2
side h^2 - a^2= b^2
so
a^2 + b^2 = h^2
h^2 = 144 144/2 =72 square root of 72 is 8.48 to 2 dp



2) I think 4 but I'm not to good on them sorry.


3) The circumference of a circle is 2πr so
2 x π x 15cm = 94.24cm to 2 dp
BUT as its a semi circle you have to divide that amount by 2
so 94.24cm / 2 = 47.12cm to 2 dp
BEWARE this part is the bit people usually miss out. you need to add the diameter on to the distance you already have.
so 47.12cm + 15cm = 62.12


4) Area of a circle = πr^2 so
π x 7cm^2 = π x 49cm = 153.93cm to 2dp
BUT as its a semi circle you have to divide that amount by 2
so 153.93cm / 2 = 76.96 cm2


5) 6x + 9y = 21
2x + 7y = 11
Firstly you need to subtract the x's, y's and amounts.

6x + 9y = 21
-2x -7y -11 (to the line above)

so your left with 4x + 2y = 10

Sorry i couldn't help on the first two to well but the others are correct .

Answer 7

1. An isoscels internal angles are always 90,45,45.
So: Sin45=x/12cm, x=12(sin45), x=8.49 or 8.5cm

2. If y=4, then buy definition it cuts the Y axis in 4. If you graph the ecuation, you'll see that y=4 always and x=all infinite numbers.

3. The formula for the circunference of a circle(perimeter)
= 2(pi)r. Then the radious is 15cm. Its =2(3.141593)(15), divided in two because u want half the perimeter. Its = 47.12cm.

4. The formula for area of a circle =(pi)r^2. Then the radious is 7cm. Its= (3.141593)(7^2), divided in two because it ask for half of the area. its = 76.97cm or 77cm.

5. (a) y = (21-6x)/9; you simplify and goes like this :
y=(7-2x)/3. Now put all the value of Y in the original ecuation: 6x-9[(7-2x)/3]=21 ; solve it and goes like this: x=7/2
(b) y=2x+7y=11; you ssimplify and goes like this:
y=(11-2x)/7. Now put all the value of Y in the original ecuation: 2x+7[(11-2x)/7]=11: you simplify and goes like this:
x=11/2

Answer 8

1) I understand both catets a=b .
Then: 12x12= axa +axa
2axa=144
axa=72
a= square root of 72.( a little moore than 8)

2) y=4-x is zero when x=4. Then it cut the x-axis at that point.

3) 1/2x15x3.14. Use the calculator!

4)first line tells us: x=1/6(21-y)

then 2x1/6(21-y)+7y=11
42/6-2/6y+7y=11
y(7-2/6)=11-7
y(21/3-1/3)=4/5, y=4/5 x 3/20, y= 3/25

x is given in 1.line

Answer 9

1) l^2 + l^2 = 12^2
l^2 = 72
length = l = sqrt(72) = 6 * sqrt(2)


2) It cuts the y-axis when x=0
When x = 0, y = 4
It cuts at (0,4)


3) Perimeter = 15 + 1/2 * pi * 15 = 35.56 cm (approx)


4) Area is semicircle = 1/2 * pi * 7 * 7 = 76.97 cm^2 (approx)


5) 6x + 9x = 21
2x + 3y = 7 --------(1)
2x + 7y = 11 --------(2)

(2) minus (1):
4y = 4
y=1
2x + 3 = 7
x = 2.

Therefore x=2, y=1.

Answer 10

1) let the length of other sides be x
x^2 + x^2 =12^2
2X^2 = 144
:> X =8.485

2)At y-axis x=0
y = 4 - x^2
When x = 0, y = 4
It cuts at (0,4)


3) Perimeter of circle = 2 * pi * r
Perimeter = 2 * 3.14 * 15/2 = 47.1 cm
:>Perimeter of semi circle = 1/2 * 47.1
=23.55

4)Area of circle = pi * r^2
Area is semicircle = 1/2 * pi * 7 * 7 = 76.93 cm^2

5) 6x + 9x = 21
2x + 3y = 7 --------(1)
2x + 7y = 11 --------(2)
-----------------------------------
-4y = - 4
:. y = 1

When y=1
2x + 3(1) = 7
2x = 4
x = 2.