For seven days, she has learnt: 15 . 7 = 105 (new words)

\(-\dfrac{5}{6}< \dfrac{x}{21}< -\dfrac{5}{7}\Leftrightarrow\dfrac{-35}{42}< \dfrac{2x}{42}< \dfrac{-30}{42}\)

\(\Rightarrow-35< 2x< -30\)

\(\Rightarrow-17.5< x< 15\Rightarrow x=16\)

a) \(\Delta ABC\left(AB=AC\right)\)

AM is the median of ABC 

So, AM is also the the height of ABC.

=> \(AM\perp BC\)

b) ​ ​​ ​​ ​\(\Delta ABC\left(AB=AC\right)\)

AM is the median and the height of ABC

=> ABC is a equilateral triangle.

=> BC = 34 cm 

=> BM = MC = CB/2 = 34/2 = 17 cm (AM is the median)

b) \(\Delta AMC\left(\widehat{M}=90^o\right)\)

Pythagora's theorem:

\(AM^2+MC^2=AC^2\)

\(AM^2+17^2=34^2\)

\(AM^2=34^2-17^2=867\left(cm\right)\)

\(AM=\sqrt{867}cm\)

The intersection of sements a and c is B because they go through point "B"

The first, we beat the blue ghost, it dies. The red one is scared and become blue so we beat and it dies. So two ghost are dead.

My English is bad. So if I have wrong words/ grammar, I will sorry :(( 

There are 2 ghosts not ghost. 

Change: \(30\%=\dfrac{3}{10}\)

Linda kept: \(1-\left(\dfrac{1}{5}+\dfrac{3}{10}\right)=\dfrac{1}{2}\) of the 100 dollars as cash.

Nick will need: \(1\dfrac{3}{4}+3\dfrac{3}{4}=\dfrac{11}{2}=5.5\) (cups of flour)

After Sunday night, fraction of book left is:

\(1-\dfrac{3}{4}=\dfrac{1}{4}\) (book)

So fraction of book she read on Monday afternoon is:

\(\dfrac{1}{4}-\dfrac{1}{5}=\dfrac{1}{20}\) (book)

On Monday afternoon, she read:

\(\dfrac{1}{20}-\left(\dfrac{1}{20}.\dfrac{1}{4}\right)=\dfrac{3}{80}\) (book)

She spent : 18.03 + 19.94 = 37.97 (dollars)