Answer:
Step-by-step explanation:
Given the vectors based on the number line as RS = 7y +3, ST = 5y +8, and RT = 83, the equation RS+ST = RT will be used to get the unknown.
Substituting the given equation into the expression we will have;
7y +3+5y +8 = 83
collect like terms'
7y+5y+3+8 = 83
12y + 11 = 83
12y = 83-11
12y = 72
y = 72/12
y = 6
b) Substitute y = 6 into RS and ST
Given RS = 7y+3
RS = 7(6)+3
RS = 42+3
RS = 45
For ST;
ST = 5y+8
ST = 5(6)+8
ST = 30+8
ST = 38
g If a bowling ball with a radius of 12 centimeters rolls down an 18 meter lane, through how many radians does it rotate
Answer:
150 radians
Step-by-step explanation:
Arc length as a function of angle is ...
s = rθ
Then the angle is ...
θ = s/r = (1800 cm)/(12 cm) = 150 . . . radians
Write the equation the line that has a slope of 2 and a y-intercept (0,-9) then graph.
Answer:
The equation is y = 2x - 9
Step-by-step explanation:
To graph, start at 0,-9 and go up twice and right one.
63 1/4 divided by 2 1/5
Answer:
[tex] \boxed{ \bold{ \huge{\boxed{ \sf{28 \frac{3}{4} }}}}}[/tex]
Step-by-step explanation:
[tex] \sf{63 \frac{1}{4} \div 2 \frac{1}{5} }[/tex]
Convert mixed fraction into improper fraction
⇒[tex] \sf{ \frac{63 \times 4 + 1}{ 4} \div \frac{5 \times 2 + 1}{5} }[/tex]
⇒[tex] \sf{ \frac{252 + 1}{4} \div \frac{10 + 1}{5} }[/tex]
⇒[tex] \sf{ \frac{253}{4} \div \frac{11}{5} }[/tex]
We know that division by fraction is the inverse of multiplication. If any number or fraction is divided by a fraction, we multiply the dividend by the reciprocal of the divisor.
⇒[tex] \sf{ \frac{253}{4} \times \frac{5}{11} }[/tex]
Reduce the numbers with Greatest common factor 11
⇒[tex] \sf{ \frac{23}{4} \times \frac{5}{1} }[/tex]
To multiply one fraction by another, multiply the numerators for the numerator and multiply the denominators for its denominator
⇒[tex] \sf{ \frac{23 \times 5}{4 \times 1} }[/tex]
⇒[tex] \sf{ \frac{115}{4} }[/tex]
Convert improper fraction into mixed fraction
⇒[tex] \sf{28 \frac{3}{4} }[/tex]
Hope I helped!
Best regards!
Will mark brainliest, 42 points
24. 1st one
Step-by-step explanation:
the X cancals out the x leaving the z so it is the 1st one
Answer:
24. [tex]-\frac{3}{2} z[/tex]
25. 6
Step-by-step explanation:
For number 24:
To simplify this down, we can break it up into this:
[tex]\frac{3}{-2} \cdot \frac{x}{x} \cdot \frac{z}{1}[/tex]
3 divided by -2 is [tex]-\frac{3}{2}[/tex], x over x is just 1, and z over 1 is z.
So [tex]-\frac{3}{2} z[/tex].
For number 25:
If we know the value of y and z we can just substitute inside the equation.
[tex]\frac{-18}{-3}[/tex]
A negative divided by a negative is the same as a positive over a positive.
[tex]18\div3=6[/tex]
Hope this helped!
What is the reciprocal of?
Answer:
8
Step-by-step explanation:
Just flip it up... it will be 8
Answer:
0.125
When you multiply fractions, multiply numerators to find solution numerator, then multiply denominators to find solution of denominator. Divide your fractions, multiply the first fraction by reciprocal of the second fraction. It can be crossed multiplied.
-6n - 6(- 8 n + 2 simplify
Answer:
42n-12Step-by-step explanation:
[tex]-6n - 6(- 8 n + 2)[/tex]
Use -6 to open the bracket
[tex]-6n+48n-12\\42n - 12\\= 6(7n -2)[/tex]
Find the midpoint of the segment with the following endpoints.
(-9, -5) and (-1, -9)
Answer:
The answer is
[tex]( - 5 \: , \: - 7)[/tex]Step-by-step explanation:
The midpoint M of two endpoints of a given line segment can be found by using the formula
[tex]M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )[/tex]where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-9, -5) and (-1, -9)
The midpoint M is
[tex]M = ( \frac{ - 9 - 1}{2} , \: \frac{ - 5 - 9}{2} ) \\ = ( - \frac{10}{2} , \: - \frac{14}{2} )[/tex]We have the final answer as
[tex]( - 5 \: , \: - 7)[/tex]Hope this helps you
Answer ASAP and I'll make you the brainliest Alberto multiplied a whole number by a fraction. The whole number is greater than 1. The fraction is greater than 0 and less than 1. Which BEST describes the product of the whole number and the fraction? A. equal to the fraction B. equal to the whole number C. less than the whole number D. greater than the whole number
Answer:
C. less than the whole number
Step-by-step explanation:
Think of the product as 1/2(0.5)×3 ; the answer would equal 1.5, half of 3. Any number less than 1, multiplied by a whole number, always comes out with a product less than the whole numbers. i.e. 1/3(0.3)×9 = 3
1/4(0.25)×8 = 2
1/5(0.20)×5 = 1
(Anyone correct me if I'm wrong.)
Answer: C) less than the whole number
Step-by-step explanation: I tried examples and they are less than the whole number. The first choice is also equal to the fraction but that’s not for most cases.
a bread recipe requires 3 cups of flour to make 24 servings
On a coordinate plane, kite W X Y Z is shown. Point W is at (negative 3, 3), point X is at (2, 3), point Y is at (4, negative 4), and point Z is at (negative 3, negative 2). What is the perimeter of kite WXYZ? units units units units
Answer:
[tex]P = 10 + 2\sqrt{53}[/tex] units
Step-by-step explanation:
Given
Shape: Kite WXYZ
W (-3, 3), X (2, 3),
Y (4, -4), Z (-3, -2)
Required
Determine perimeter of the kite
First, we need to determine lengths of sides WX, XY, YZ and ZW using distance formula;
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
For WX:
[tex](x_1, y_1)\ (x_2,y_2) = (-3, 3),\ (2, 3)[/tex]
[tex]WX = \sqrt{(-3 - 2)^2 + (3 - 3)^2}[/tex]
[tex]WX = \sqrt{(-5)^2 + (0)^2}[/tex]
[tex]WX = \sqrt{25}[/tex]
[tex]WX = 5[/tex]
For XY:
[tex](x_1, y_1)\ (x_2,y_2) = (2, 3)\ (4,-4)[/tex]
[tex]XY = \sqrt{(2 - 4)^2 + (3 - (-4))^2}[/tex]
[tex]XY = \sqrt{-2^2 + (3 +4)^2}[/tex]
[tex]XY = \sqrt{-2^2 + 7^2}[/tex]
[tex]XY = \sqrt{4 + 49}[/tex]
[tex]XY = \sqrt{53}[/tex]
For YZ:
[tex](x_1, y_1)\ (x_2,y_2) = (4,-4)\ (-3, -2)[/tex]
[tex]YZ = \sqrt{(4 - (-3))^2 + (-4 - (-2))^2}[/tex]
[tex]YZ = \sqrt{(4 +3)^2 + (-4 +2)^2}[/tex]
[tex]YZ = \sqrt{7^2 + (-2)^2}[/tex]
[tex]YZ = \sqrt{49 + 4}[/tex]
[tex]YZ = \sqrt{53}[/tex]
For ZW:
[tex](x_1, y_1)\ (x_2,y_2) = (-3, -2)\ (-3, 3)[/tex]
[tex]ZW = \sqrt{(-3 - (-3))^2 + (-2 - 3)^2}[/tex]
[tex]ZW = \sqrt{(-3 +3)^2 + (-2 - 3)^2}[/tex]
[tex]ZW = \sqrt{0^2 + (-5)^2}[/tex]
[tex]ZW = \sqrt{0 + 25}[/tex]
[tex]ZW = \sqrt{25}[/tex]
[tex]ZW = 5[/tex]
The Perimeter (P) is as follows:
[tex]P = WX + XY + YZ + ZW[/tex]
[tex]P = 5 + \sqrt{53} + \sqrt{53} + 5[/tex]
[tex]P = 5 + 5 + \sqrt{53} + \sqrt{53}[/tex]
[tex]P = 10 + 2\sqrt{53}[/tex] units
C is the answer.
That is all.
Match the following differential equations with their solutions. The symbols A, B, C in the solutions stand for arbitrary constants. You must get all of the answers correct to receive credit.
1. d^2y/dx^2 + 25y = 0
2. dy/dx = 2xy/x^2 - 5y^2
3. d62y/dx^2 + 16 dy/dx + 64y = 0
4. dy/dx = 10xy
5. dy/dx + 24x^2y = 24 x^2
A. y = Ce^-8x^3 + 1
B. 3yx^2 - 5y^3 = C
C. y = Ae^-8x + Bxe^-8x
D. y = Ae^5x^2
E. y = A cos(5x) + B sin(5x)
Answer:
[tex]1 \rightarrow E, 2\rightarrow B, 3\rightarrow C, 4\rightarrow D, 5\rightarrow A[/tex]
Step-by-step explanation:
1. [tex]\frac{d^2y}{dx^2}+25y=0[/tex]
The characteristic equation for the given differential equation is:
[tex]r^{2} +25=0[/tex]
[tex]\Rightarrow r^2=-25[/tex]
[tex]\Rightarrow r=\pm 5i[/tex]
Since the roots are complex
Now, the general solution is:
[tex]y=A\cos 5x+B\sin 5x[/tex]
2. [tex]\frac{dy}{dx}=\frac {2xy}{x^2}-5y^2[/tex]
[tex]\Rightarrow \frac{dy}{dx}-\frac 2xy=-5y^2[/tex]
Divide both sides by [tex]y^{-1}[/tex]
Let, [tex]v=y^{-1} \Rightarrow \frac{dv}{dx}=-y^{-2}\frac{dy}{dx}[/tex]
[tex]\Rightarrow -\frac{dv}{dx}-\frac 2xv=-5[/tex]
[tex]\Rightarrow \frac{dv}{dx}+\frac 2xv=5[/tex]
Here, [tex]p(x)=\frac 2x\; \text{and}\;\; q(x)=5[/tex]
I.F. [tex]=e^{\int \frac 2xdx}=x^2[/tex]
Now, the general solution is:
[tex]vx^2=\int x^2 5dx=\frac {5x^3}3+c[/tex]
[tex]\Rightarrow \frac {x^2}y-\frac {5x^3}3=c[/tex]
[tex]\Rightarrow 3x^2-5x^3y=Cy[/tex]
3. [tex]\frac{d^2y}{dx^2}+16\frac{dy}{dx}+64y=0[/tex]
The characteristic equation is:
[tex]r^2+16r+64=0[/tex]
[tex]\Rightarrow r^2+8r+8r+64=0[/tex]
[tex]\Rightarrow r(r+8)+8(r+8)=0[/tex]
[tex]\Rightarrow (r+8)(r+8)=0[/tex]
[tex]\Rightarrow r=-8,-8[/tex]
Since the roots are real and repeated.
Now, the general solution is:
[tex]y=Ae^{-8x}+Bxe^{-8x}[/tex]
4. [tex]\frac {dy}{dx}=10xy[/tex]
[tex]\Rightarrow \frac {dy}{y}=10xdx[/tex]
Integrating both sides
[tex]\int\frac {dy}y=\int 10xdx+\log c[/tex]
[tex]\Rightarrow \log y=5x^2+\log c[/tex]
[tex]\Rightarrow y=e^{5x^2}+c[/tex]
5. [tex]\frac {dy}{dx}+24x^2y=24x^2[/tex]
Here, [tex]p(x)=24x^2 \; \text{and}\;\; q(x)=24x^2[/tex]
I.F.[tex]= e^{\int 24x^2dx}=e^{8x^3}[/tex]
Now, the general solution is:
[tex]y.e^{8x^3}=\int 24x^2 e^{8x^3}dx=24\int x^2e^{8x^3}dx[/tex]
Let, [tex]8x^3=t \Rightarrow 24x^2dx=dt\Rightarrow x^2dx=\frac {dt}{24}[/tex]
[tex]\Rightarrow ye^{8x^3}=\int e^tdt[/tex]
[tex]\Rightarrow ye^{8x^3}=e^{8x^3}+c[/tex]
[tex]\Rightarrow y=1+ce^{-8x^3}[/tex]
A woman measures the angle of elevation of a mountaintop as 12.00. After walking 1.00 km closer to the mountain on level ground, she finds the angle to be 14.00. Find the mountain’s height, neglecting the height of the women’s eyes above ground. Hint: Distances from the mountain (x and x-1 km) and the height y are unknown.
Answer:
Step-by-step explanation:
2+2 idk what is the answer and im just confused of what it is
2+2 = 4
Very Simple!▶Add 2 to 2 , you may count it with your fingers.
Additionally Information:(-) This sign means subtraction i.e. you must take out!(×) This sign means multiplication i.e.you must multiply ! (÷) This sign means division i.e. you must divide!This are for beginners ✔
Hope you understandAnswer:
The answer, my man, is 4.
Explanation:
2+2-2*2/2=2
Or... 2 plus 2 minus 2 times 2 divided by 2 equals 2.
A more complex way of doing this is: 2+2=4
Hopefully, this helps! :D
Find the equation of the line through the points (−6,4) and (−5,−10). Enter your answer in slope-intercept form y=mx+b.
Answer:
y = -14x - 80
Step-by-step explanation:
jst did it and i got it right
The equation of the line passing through the points (−6,4) and (−5,−10) is y = -14x - 80.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The line through the points (−6,4) and (−5,−10).
(y + 10) = (-10-4)/(-5+6)[x + 5]
y + 10 = -14(x + 5)
y + 10 = -14x - 70
y = -14x - 80
Thus, the equation of the line passing through the points (−6,4) and (−5,−10) is y = -14x - 80.
Learn more about the straight line here:
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a missle was fired from a submarine from 370 feet below sea level. if the missile reached a height of 8400 feet before exploding, what was the change in the altitiude of the missile?
Answer:
8770 feet
Step-by-step explanation:
Add 370 to 8400:
8400 - 370
= 8770 feet
If 9% of a number equals 30, find 27% of that number.
Answer:
90
Step-by-step explanation:
Answer:
90
Step-by-step explanation:
Rewriting what is given: (0.09)(n)=30
Where n is the unknown number and 0.09 is the numerical form of 9%. Solving for n gives:
n=(30/0.09)=333.333....
27% as a number is 0.27. So 27% of n is:
(0.27)(n)=(0.27)(333.333...)=90
27% of that number is 90.
If g(x) = 2x + 2 and h(x) = 4x2 + 8x + 8, find a function f such that f ∘ g = h. (Think about what operations you would have to perform on the formula for g to end up with the formula for h.)
Answer:
Step-by-step explanation:
Hello,
[tex](\forall x \in \mathbb{R}) (fog)(x)=f(g(x))=f(2x+2)=h(x)=4x^2+8x+8\\\\=(2x+2)^2-2^2+4(2x+2)\\\\=(2x+2)^2+4(2x+2)-4\\\\\text{So, we conclude by.}\\\\\large \boxed{\sf \bf f(x)=x^2+4x-4}[/tex]
If g(x) = 2x + 2 and h(x) = 4x2 + 8x + 8, then function f is 16x²+48x+40
What is a function?A relation is a function if it has only One y-value for each x-value.
The given functions are g(x) = 2x + 2 and h(x) = 4x² + 8x + 8.
fog=h
Now we have to find f(x)
fog=h
f(g(x))=h
f(2x+2)=4x² + 8x + 8.
=4(2x+2)²+8(2x+2)+8
=4(4x²+4+8x)+16x+16+8
=16x²+16+32x+16x+16+8
=16x²+32x+16x+16+16+8
=16x²+48x+40
Hence, function f is 16x²+48x+40
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|4х + 6| — 1 =
- 1 = 3х
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
Answer: 7
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
Absolute value is the distance between that number and zero. To find the absolute value, you basically just take the negative sign away if there is one. So you need to find the absolute value of 4x+6. Since you can't simplify this equation, you just keep it the way it is. The absolute value of 4x+6 is 4x+6.
So now you have 4x + 6 - 1. Since 6 and 1 are both constant variables, you can directly subtract it. 6-1 equals 5. Now you have 4x-5.
Now you have 4x-5 = -1 = 3x. You should isolate the variables as well as "removing" an equal sign. To bring away the -1, you have to add 1. -1 + 1 equals 0, AKA nothing. But you also have to do it with all the other expressions too...
4x - 5 + 1 = 4x-6
3x+1 = 3x+1
Now the equation is 4x-6 = 3x+1
So now you have to get rid of the 6. To do that, add 6 to each side of the equation.
4x-6+6 = 4x
3x+1+6 = 3x+7
Now the equation is 4x = 3x+7
Did you notice that you have to add 1x to 3x to get 4x?
3x+1x = 4x (AKA the left side of the equation)
Also, you added the 7.
So that means 7 is the 1x.
So x equals 7.
━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━
The equation v/2 -21=-15 is solved in several steps below.
For each step, choose the reason that best justifies it.
Step. Reason
* v/2-21=-15
v/2-21+21=-15+21
v/2=6
2·v/2=6·2
v=12
Options!
*Given equation
a. addition property of equality
b. subtraction propertyof equality
c. multiplication property of equality
d. division property of equality
e. simplifying
f. distributive property
Answer:
V/2 - 21 = -15
V/2 - 21 + 21 = -15 + 21
V/2 + 0 = 6
V/2 * 2 = 6 * 2
V = 12
9,058 to the nearest thousand
This is because the given value is closer to 9,000 than it is to 10,000.
The digit in the thousands place is 9. The digit to the right of this is 0, which is not 5 or greater. So we round down to the nearest thousand. So basically everything after the 9 is replaced with 0.
21x - 12y = -15
- 7x + 4y = 5
Answer:
0
Step-by-step explanation:
_7x+4y=5 *(3)
_21x+12y=15
21x_12y=_15
____________
If I am right
I think !that is the answer
-18-3s=15 solve for s. can someone plz help
Answer:
The correct answer is s = -11.
Step-by-step explanation:
To solve this problem, we must move all of the variable terms to one side of the equation and move all of the constant terms to the other side. Let's keep the variable terms on the left and move the constants to the right. Our first step will be to add 18 to both sides of the equation to cancel out the -18 on the left side:
-18 + 18 - 3s = 15 + 18
-3s = 33
Our next and final step will be to divide both sides by -3 to get the variable s completely isolated on the left side of the equation.
-3s/-3 = 33/-3
s = -11
Therefore, the correct answer is s = -11.
Hope this helps!
What's 4+4. I am having a really hard time figuring this out. Hurry quick and I will dramatically mark you as the bran-list
Find c1 and c2 such that M2+c1M+c2I2=0, where I2 is the identity 2×2 matrix and 0 is the zero matrix of appropriate dimension.
The question is missing parts. Here is the complete question.
Let M = [tex]\left[\begin{array}{cc}6&5\\-1&-4\end{array}\right][/tex]. Find [tex]c_{1}[/tex] and [tex]c_{2}[/tex] such that [tex]M^{2}+c_{1}M+c_{2}I_{2}=0[/tex], where [tex]I_{2}[/tex] is the identity 2x2 matrix and 0 is the zero matrix of appropriate dimension.
Answer: [tex]c_{1} = \frac{-16}{10}[/tex]
[tex]c_{2}=\frac{-214}{10}[/tex]
Step-by-step explanation: Identity matrix is a sqaure matrix that has 1's along the main diagonal and 0 everywhere else. So, a 2x2 identity matrix is:
[tex]\left[\begin{array}{cc}1&0\\0&1\end{array}\right][/tex]
[tex]M^{2} = \left[\begin{array}{cc}6&5\\-1&-4\end{array}\right]\left[\begin{array}{cc}6&5\\-1&-4\end{array}\right][/tex]
[tex]M^{2}=\left[\begin{array}{cc}31&10\\-2&15\end{array}\right][/tex]
Solving equation:
[tex]\left[\begin{array}{cc}31&10\\-2&15\end{array}\right]+c_{1}\left[\begin{array}{cc}6&5\\-1&-4\end{array}\right] +c_{2}\left[\begin{array}{cc}1&0\\0&1\end{array}\right] =\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]
Multiplying a matrix and a scalar results in all the terms of the matrix multiplied by the scalar. You can only add matrices of the same dimensions.
So, the equation is:
[tex]\left[\begin{array}{cc}31&10\\-2&15\end{array}\right]+\left[\begin{array}{cc}6c_{1}&5c_{1}\\-1c_{1}&-4c_{1}\end{array}\right] +\left[\begin{array}{cc}c_{2}&0\\0&c_{2}\end{array}\right] =\left[\begin{array}{cc}0&0\\0&0\end{array}\right][/tex]
And the system of equations is:
[tex]6c_{1}+c_{2} = -31\\-4c_{1}+c_{2} = -15[/tex]
There are several methods to solve this system. One of them is to multiply the second equation to -1 and add both equations:
[tex]6c_{1}+c_{2} = -31\\(-1)*-4c_{1}+c_{2} = -15*(-1)[/tex]
[tex]6c_{1}+c_{2} = -31\\4c_{1}-c_{2} = 15[/tex]
[tex]10c_{1} = -16[/tex]
[tex]c_{1} = \frac{-16}{10}[/tex]
With [tex]c_{1}[/tex], substitute in one of the equations and find [tex]c_{2}[/tex]:
[tex]6c_{1}+c_{2}=-31[/tex]
[tex]c_{2}=-31-6(\frac{-16}{10} )[/tex]
[tex]c_{2}=-31+(\frac{96}{10} )[/tex]
[tex]c_{2}=\frac{-310+96}{10}[/tex]
[tex]c_{2}=\frac{-214}{10}[/tex]
For the equation, [tex]c_{1} = \frac{-16}{10}[/tex] and [tex]c_{2}=\frac{-214}{10}[/tex]
points (2,7) ana (5,10).
3. Convert 3x + 5y = 15, from standard form to
slope intercept form.
Answer:
Below.
Step-by-step explanation:
3x + 5y = 15
Subtract 3x from both sides:
5y = -3x + 15
Divide through by 5:
y = -3/5 x + 3 <-----------slope-intercept form
The contingency table below shows the results of a survey of video viewing habits by age. Find the following probabilities or percentages: Probability that viewers is aged 18-34.
Answer:
The answer is ( 0.74 ) or ( 74/100 ).
Amber has been saving quarters and dimes. She opened up the piggy bank and determined that it contained 18 coins worth $2.85. Determine how many dimes and quarters were in the piggy bank.
Corbin is helping his grandfather plant the corn in the field. The field covers an area of 43,200 square feet. The length of the field is triple the width. What are the dimensions?
Answer:
the length is 360 feet and the width is 120 feet.
Step-by-step explanation:
Set up an equation with the area formula, A = lw
The width can be represented by x, and the length can be represented by 3x since it is 3 times the width
43,200 = (3x)(x)
43,200 = 3x²
Solve for x:
14,400 = x²
120 = x
So, the width is 120 feet.
The length is 3 times this, so multiply the width by 3 to find the length
120(3)
= 360
So, the length is 360 feet and the width is 120 feet.
What is the value of the expression? 3 x [(30 - 8) divided by 2 + 2]
Answer:
3×30=90
3×8=24
90-24=66
66÷4=16.5
18. A sum of money was shared among
Okpala, Olu and Bello such that
Okpala had one sixth of the money.
Olu had one quarter of the money
and Bello had the rest. By what
fraction of the money is Bello's share
greater than Okpala's and Olu's
shares put together?
Answer is something I’m not sure of
Bello's share is greater than Okpala's and Olu's shares combined by a fraction of 1/6 of the total sum of money.
Here, we have,
Let's assign variables to represent the shares of Okpala, Olu, and Bello.
Let M be the total sum of money.
Okpala's share = (1/6)M
Olu's share = (1/4)M
Bello's share = M - Okpala's share - Olu's share
To find the fraction of the money by which Bello's share is greater than Okpala's and Olu's shares put together, we need to calculate the difference between Bello's share and the sum of Okpala's and Olu's shares, and then express it as a fraction of the total sum of money M.
Bello's share - (Okpala's share + Olu's share) = (M - Okpala's share - Olu's share) - (Okpala's share + Olu's share)
= M - Okpala's share - Olu's share - Okpala's share - Olu's share
= M - 2(Okpala's share) - 2(Olu's share)
= M - 2[(1/6)M] - 2[(1/4)M]
= M - (1/3)M - (1/2)M
= M - (2/6)M - (3/6)M
= M - (5/6)M
= (1/6)M
Now, let's express this difference as a fraction of the total sum of money M:
Fraction of Bello's share greater than Okpala's and Olu's shares
= [(1/6)M] / M
= (1/6)
Therefore, Bello's share is greater than Okpala's and Olu's shares combined by a fraction of 1/6 of the total sum of money.
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