Acandle burned at a steady rate. after 32 minutes, the candle was 11.2 inches tall. eighteen minutes later, it was 10.75 inches tall. use an equation in point-slope form to determine the height of the candle after 3 hours. round the answer to the tenth place if necessary.

Let
x = time, minutes
y = length, inches

When x = 32 min, y = 11.2 in
When x = 32+18 = 50, y = 10.75 in
Assume that a linear relatioship exists between x and y.

In table form, the given data is
x, min:   32       50
y, in:     11.2   10.75

The slope is
m = (10.75 - 11.2)/(50 - 32) = -0.025

In point-slope form, the required equation is


When x = 3 hours = 180 minutes, obtain
y - 10.75 = -0.025*(180 - 50) = -3.25
y = -3.25 + 10.75 = 7.5 in

7.5 inches

21

Sofia cuts a piece in the shape of a kite for an art project  

top two sides measure 20 cm each  

bottom two sides measure 13 cm each.  

One diagonal, EG, measures 24 cm

Find out the length of the other diagonal, DF.

explanation-

DE = EF = 20cm

DG = GF = 13cm

EG = 24cm

DF = ?

In kite shape

One diagonal is the perpendicular bisector of the other diagonal.

i.e EG is the perpendicular bisector of DF

i.e EG is divided into two equal parts

thus EA = AG = 12cm

in Δ EAF

By applying the pythagorus theorem

we have

EF² = FA²+ EA²

20² = 12² + FA²

400 -144 = FA²

256 =FA²

16cm = FA

Now in Δ DAG

DG² = AG² + DA²

13² = 12 ²+ DA²

169 -144 = DA²

25 = DA²

5cm = DA

Step-by-step explanation: