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Solve for the value of x
1.) Given: $9x-81=0$ Adding 81 to both sides, we have $9x-81+81=0+81\Rightarrow9x=81$. Dividing both sides by the coefficient of $x$, which is 9, we have $\dfrac{9x}{9}=\dfrac{81}{9}\Rightarrow x=9$. Therefore, $x=9$. 2.)Â Given: $5x+2=27$ Subtracting 2 from both sides, we have $5x+2-2=27-2\RiRead more
1.) Given:
Adding 81 to both sides, we have
.
Dividing both sides by the coefficient of
, which is 9, we have 
.
Therefore,
.
2.)Â Given:
Subtracting 2 from both sides, we have
.
Dividing both sides by the coefficient of
, which is 5, we have 
.
Therefore,
.
c.) Given:
Using foil/distributive law to expand, we have
.
Subtracting
from both sides gives 
.
Subtracting 10 from both sides gives
.
Dividing both sides by 2 gives
.
Therefore,
.
See lessHow we can convert degree measures to radians?
To convert an angle from degree to radians (in terms of ), we use the formula . Given $122^o 37'$, we first convert 37' to decimals by dividing it by 60. So, $37'=(\dfrac{37'}{60'})^o=0.6167^o$. Thus, $122^o 37'=122.6167^o$. Therefore, $122.6167^o\equiv\dfrac{122.6167^o\times\pi}{180^o}=0.6812\pi\apRead more
To convert an angle from degree to radians (in terms ofÂ
), we use the formula 
.
Given
, we first convert 37′ to decimals by dividing it by 60. So, 
. Thus, 
.
Therefore,
radians.
See lessThe first term of an arithmetic sequence is -4 and its common difference is 5.
The nth term of an arithmetic sequence is given by $T_n=a+(n-1)d$, where $a$ is the first term and $d$ is the common difference. Given: $a=-4$, $d=5$. The 9th term is given by $T_9=-4+(9-1)\times5=-4+8(5)=-4+40=36$. The sum of the first n terms of an arithmetic sequence is given by $S_n=\dfraRead more
The nth term of an arithmetic sequence is given by
, where 
is the first term and 
is the common difference.
Given:
, 
.
The 9th term is given by
.
The sum of the first n terms of an arithmetic sequence is given by
.
The sum of the first 12 terms is given by
.
See lessanswer correctly
Here, 'x' is a binary operation defined by a x b = 2a - 3b + ab. Thus, 3 x 5 = 2(3) - 3(5) + (3)(5) = 6 - 15 + 15 = 6, and 5 x 3 = 2(5) - 3(3) + (5)(3) = 10 - 9 + 15 = 16. Therefore, 3 x 5 + 5 x 3 = 6 + 16 = 22.
Here, ‘x’ is a binary operation defined by a x b = 2a – 3b + ab.
Thus, 3 x 5 = 2(3) – 3(5) + (3)(5) = 6 – 15 + 15 = 6,
and 5 x 3 = 2(5) – 3(3) + (5)(3) = 10 – 9 + 15 = 16.
Therefore, 3 x 5 + 5 x 3 = 6 + 16 = 22.
See lessA number is thrice another number. The sum of their reciprocals is 4. Find The numbers.
Let the first number be $x$, then the other number is $3x$ and their reciprocals are $\dfrac{1}{x}$ and $\dfrac{1}{3x}$. Thus, $\dfrac{1}{x}+\dfrac{1}{3x}=4$. Multiplying through by the Least Common Denominator (LCD), which is $3x$, we have $3x\left(\dfrac{1}{x}+\dfrac{1}{3x}\right)=3x(4)$ $\RightarRead more
Let the first number be
, then the other number is 
and their reciprocals are 
and 
.
Thus,
.
Multiplying through by the Least Common Denominator (LCD), which is
, we have 
Thus, the first number is
and the other number is 
.
Therefore, the numbers are
and 1.
See lessQuestion of the Day (28/03/2021)
First, let us represent the information in a ven diagram for better understanding. Since we have three languages, we will have three intersecting circles. Let the circle labeled F, S, and C represent the people that enrolled in French, Spanish, and Chinese. Also, let $x$ represent the number of peopRead more
First, let us represent the information in a ven diagram for better understanding.
Since we have three languages, we will have three intersecting circles. Let the circle labeled F, S, and C represent the people that enrolled in French, Spanish, and Chinese. Also, let
represent the number of people that enrolled for the three languages, then:
The number of people that registered for French and Spanish only is given by
.
The number of people that registered for French and Chinese only is given by
.
And the number of people that registered for Chinese and Spanish only is given by
.
The information is represented in the attached Venn diagram.
Since a total of 70 people enrolled, the sum of all the parts of the Venn diagram will give us 70.
Thus,
Therefore, 31 people enrolled in the three languages.
See lesswhat is crammer rule?
Cramer's rule is a method of solving a system of linear equations using determinants of matrices.
Cramer’s rule is a method of solving a system of linear equations using determinants of matrices.
See lessWrite the equation of a line if the gradient is
and the y-intercept is 
The equation of a line is given by $y=mx+c$; where $m$ is the slope or gradient, and $c$ is the y-intercept. Given: $m=6$ and $c=-\dfrac{1}{3}$ Therefore, the required equation is $y=6x-\dfrac{1}{3}$.
The equation of a line is given by
; where 
is the slope or gradient, and 
is the y-intercept.
Given:
and 
Therefore, the required equation is
.
See less