Solve the following equations.
$ \frac{z}{z+15}=\frac{4}{9} $.

Academic Mathematics NCERT Class 8

Given:

\( \frac{z}{z+15}=\frac{4}{9} \)

To do:

We have to solve the given equation.

Solution:

$\frac{z}{z+15}=\frac{4}{9}$

$\Rightarrow 9(z)=4 \times(z+15)$ [On cross multiplication]

$\Rightarrow 9z=4z+60$

$\Rightarrow 9z-4z=60$

$\Rightarrow 5z=60$

$\Rightarrow z=\frac{60}{5}$

$\Rightarrow z=12$

The value of $z$ is $12$.

Tutorialspoint

Updated on: 10-Oct-2022

32 Views

Find the following products:\( \frac{-4}{27} x y z\left[\frac{9}{2} x^{2} y z-\frac{3}{4} x y z^{2}\right] \)
Simplify and solve the following linear equations.\( 3(5 z-7)-2(9 z-11)=4(8 z-13)-17 \).
On dividing $^{3}+6 z+4 z^{5} $by $ 2 z-1 $, the quotient obtained is a and the remainder is b.What are the values of a and b?A) $ a=2 z^{4}-z^{3}+z^{2}-\frac{z}{2}+\frac{13}{4} \ and \ b=-\frac{13}{4} $B) $ a=2 z^{4}+z^{3}+z^{2}+\frac{z}{2}+\frac{13}{4} \ and \ b=\frac{13}{4} $C) $ a=2 z^{4}-z^{3}+\frac{z^{2}}{2}+\frac{z}{4}+\frac{23}{8} \ and \ b=-\frac{23}{8} $D) $ a=2 z^{4}+z^{3}+\frac{z^{2}}{2}+\frac{z}{4}+\frac{23}{8} \ and \ b=+\frac{23}{8} $
Solve the following equations.\( \frac{9 x}{7-6 x}=15 \).
Solve:$\frac{2}{5} z\ =\ \frac{3}{8} z\ +\ \frac{7}{20}$
Solve the following:$3(5 z-7)-2(9 z-11)=4(8 z-13)-17$.
Find the following products:\( \frac{-8}{27} x y z\left(\frac{3}{2} x y z^{2}-\frac{9}{4} x y^{2} z^{3}\right) \)
Solve the following equations and check your results.\( 4 z+3=6+2 z \).
Verify the property: $x \times (y \times z) = (x \times y) \times z$ by taking:(i) \( x=\frac{-7}{3}, y=\frac{12}{5}, z=\frac{4}{9} \)(ii) \( x=0, y=\frac{-3}{5}, z=\frac{-9}{4} \)(iii) \( x=\frac{1}{2}, y=\frac{5}{-4}, z=\frac{-7}{5} \)(iv) \( x=\frac{5}{7}, y=\frac{-12}{13}, z=\frac{-7}{18} \)
Solve the following equations.\( 6=z+2 \).
Solve the following equations.\( \frac{x}{3}+1=\frac{7}{15} \).
Solve the following system of equations:$\frac{10}{x+y} +\frac{2}{x-y}=4$$\frac{15}{x+y}-\frac{9}{x-y}=-2$
Solve the following system of equations: $\frac{2}{x}\ +\ \frac{3}{y}\ =\ \frac{9}{xy}$ $\frac{4}{x}\ +\ \frac{9}{y}\ =\ \frac{21}{xy}$
Verify the property: $x \times(y + z) = x \times y + x \times z$ by taking:(i) \( x=\frac{-3}{7}, y=\frac{12}{13}, z=\frac{-5}{6} \)(ii) \( x=\frac{-12}{5}, y=\frac{-15}{4}, z=\frac{8}{3} \)(iii) \( x=\frac{-8}{3}, y=\frac{5}{6}, z=\frac{-13}{12} \)(iv) \( x=\frac{-3}{4}, y=\frac{-5}{2}, z=\frac{7}{6} \)
Find the value of z by transposing method.$\frac{z}{3} = \frac{5}{4}$

Kickstart Your Career

Get certified by completing the course

Get Started

Advertisements