Short Tasks: Creating Equations 1 1.
If V -
12R
(r+R)
make R the subject of the equation.
2a.
Jane, Maria, and Ben each have a collection of marbles. Jane has 15
more marbles than Ben, and Maria has 2 times as many marbles as
Ben. All together they have 95 marbles. Find how many marbles
Maria has.
2b.
Dave sold 40 tickets for a concert. He sold x tickets at $2 each and y
tickets at $3 each. He collected $88.
Write down two equations connecting x and y.
Solve these two equations to find how many of each kind of ticket he
sold.
2c.
A rectangle has length (x + 5)cm and width (x-2)cm. Its area is 60
cm?
Write a quadratic equation, and solve it to find the length and width of
this rectangle.

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)

the image is given below

since the options are not given so we draw it from the equation

the given equation is

y = (x-1) (x+4)

y = y² + 3x - 4

the above equation is a quadratic equation which will have two roots. if we draw the graph for it, it will look like this