The surveyor can find AB if he finds CD as CD = AB.
What actually means by a triangle's congruency?Two triangles are said to be congruent if their three corresponding sides are equal and their three corresponding angles are equal in size.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are readjusted, they will coincide.Two triangles are congruent if they satisfy all five congruence conditions.They are side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).So,
First, connect B and D and make a square ACDB with BC as a diagonal.
In triangle ACB and DCB:So, ACB ≅ DCB under SAS condition.
Therefore, the surveyor can find AB if he finds CD as CD = AB.
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Use the given conditions to write an equation for the line in point-slope form and general form.
Passing through (7,−9) and perpendicular to the line whose equation is
The equation of the line in point-slope form is
The equation of the line in general form is
The equation of the line in point-slope form is y = -1/3 x + 20/3 and 3y + x = 20
Equation of a lineThe equation of line perpendicular to another line in point slope form is expressed as;
y-y₁ = -1/m(x-x₁)
Given the equation of a line x -3y - 8 = 0
x - 3y = 8
-3y = -x + 8
y = 1/3x - 8/3
Slope m = 1/3
Substitute the point (-7, 9) and slope 1/3 into the equation
y-9 = -1/3(x-(-7))
y-9 = -1/3(x+7)
3(y-9) = -(x+7)
3y-27 = -x -7
3y = -x + 20
y = -1/3 x + 20/3
Write in general form.
3y = -x + 20
3y + x = 20
Hence the equation of the line in point-slope form is y = -1/3 x + 20/3 and 3y + x = 20
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Pls help I'll mark brainliest and it's 20 points, very important!
Melanie wants to rent a bike on her vacation for less than $50. At Mike's Bike Shop, she can rent a bike for $8 per hour plus a $6 flat fee. Any portion of an hour is charged as a full hour.
The inequality that represents this situation is 8h+6<50, where h represents the number of hours Melanie rents the bike.
What does the solution for the inequality mean in relation to the situation
The solution h<5.5 means that Melanie can rent the bike for no more than 5.5 hours.
he solution h<7 means that Melanie can rent the bike for no more than 7 hours.
The solution h<5.5 means that Melanie can rent the bike for no more than 5 hours.
Answer:
The solution h < 5.5 means that Melanie can rent the bike for no more than 5.5 hours.
Hope this helps :)
Explanation and Check part below.
Step-by-step explanation:
1. Isolate the variable by doing the inverse operation which is in this case subtracting 6 on bothsides of the equation.
8h + 6 < 50
- 6 - 6
8h < 44
2. Dive both sides of the equation by 8.
8h < 44
--- ----- <--------- fraction bar, divide
8 8
h < 5.5
rewrite (1)/(6)x^(3)y+(5)/(6)xy^(2) using a common factor.
The equivalent expression of the given expression is (x^3y + 5xy^2)/6
How to rewrite the expression?The expression is given as:
(1)/(6)x^(3)y+(5)/(6)xy^(2)
Rewrite properly as
1/6x^3y + 5/6xy^2
Take the LCM
So, we have
(x^3y + 5xy^2)/6
Hence, the equivalent expression of the given expression is (x^3y + 5xy^2)/6
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Find the number of possible outcomes for following situation.
Perry chooses from 6 colors and 2 seat designs for his new mountain bike.
The number of possible outcomes is 12.
What do we mean by permutation and combination?A permutation is an act of arranging objects or numbers in a particular order. Combinations are a method of selecting objects or numbers from a collection or group of objects in such a way that the order of the objects is irrelevant. For example, we consist of four letters: P, Q, R, and S. Every possible arrangement is a combination. However, the combinations of P, Q, R, and S are permutations.To find the possible outcomes:
Given: 6 colors and 2 seat designs.
Therefore, the number of possible outcomes is 12.
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Can someone help me with this I don't understand this. :(
Answer:
See the attached photos for help!
Step-by-step explanation:
I also recommend looking up desmos graphing calculator to actually see the graphs!
If you need more in depth assistance on this, feel free to let me know :]
There are 63 books on the bookshelf. There
are 9 books on each shelf. How many
shelves are there?
Answer:
there are 7 shelves. 9 x 7=63
Answer:
the answer is 7 shelves
Step-by-step explanation:
63÷9=7
7. Sound travels through air at 330 meters per second. How long will it take a bat's cry to reach its prey and echo back if the prey is 1 meter away? Round to the nearest thousandth of a second. (please show how you got the answer)
It will take 0.006 seconds for bat's cry to reach its prey and echo back.
What is Sound?Sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid.
Given is the speed of sound which is 330 m/s. The prey is 1 meter away from the bat.
The time it takes a bat's cry to reach its prey and echo back can be calculated using the formula -
time = distance / speed
The distance covered by the sound as it reaches the prey and echo back is equal to 2 x 1 = 2 meters.
Speed of sound → 330 m/s.
So, the time taken will be -
t = 3/330
t = 0.006 s
Therefore, it will take 0.006 seconds for bat's cry to reach its prey and echo back.
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The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending c
Rewrite 99 + (88 +77) using the Associative Law of Addition.
O (99 +88) + 77
O (88+77) +99
O (99+77) +88
O 99 + (77 +88)
Step-by-step explanation:
The answer is 99+(77+88)
Find the value of x to the nearest tenth. 1086/π = x
x = 345.54545454 is the value of x to the nearest tenth. 1086/π = x
What is π ?
The circumference to diameter ratio of any circle is known as pi, and it is represented by the Greek letter p, or. No matter how big the circle is, this ratio will always be equal to pi. The value of pi in decimal notation is around 3.14.Why is pi so important?
It is a number that is just a little bit larger than three and represents the ratio of a circle's circumference to its diameter. We can better comprehend our cosmos thanks to the constant. A new idea for measuring angles and a new unit of measurement were both inspired by the definition of.1086/π = x
Put value of π = 22/7
1086/22/7 = x
x = 49.363636 × 7
x = 345.54545454
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Write a function rule for the direct variation in the table.
The function rule for the direct variation in the table is [tex]y = 24/x[/tex] , indirect variation ; x = 2.4.
What is direct variation?Direct variation is the change in one quantity as a result of the change in another. This suggests that if one quantity rises or falls, the other must rise or fall correspondingly as well.
The formula y = kx is used to answer direct variation questions. If finding the proportionality constant is necessary, the answer is obtained by dividing y by x.
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Brian spent 14 minutes washing the dishes. That was 35% of the total number of minutes he spent doing chores.
How many minutes did Brian spend doing chores?
Answer: I got my answer by dividing 14 by 35, then multiplying by 100.
Answer: 250 minutes.
Step-by-step explanation: You make a fraction.
Actual time / Percentage
Then you multiply that by 100.
need help solving ToT
Answer:
Again the answer is D
Step-by-step explanation:
Which expressions are simplified? Pls help!!
Answer:
Only A
Step-by-step explanation:
[tex]b) \: \frac{1}{ {n}^{ - 5} } = {n}^{5} \\ \\ c) \: {n}^{6} \times {n}^{ - 8} = {n}^{ - 2} \\ \\ d) \: {n}^{7} \times {n}^{8} = {n}^{15} \\ \\ e) \: \frac{1}{ {n}^{3} } = {n}^{ - 3} [/tex]
The radius, diameter, or circumference of a circle is given. Find the missing measure to the nearest hundredth.
d = 8 1/2in., r=?, C=?
The missing measure to the nearest hundredth is r = 2.25 in, C = 14.13 in.
What is circumference of circle?A circle's outside boundary is called the circumference and can be measured, or calculated, by using
Circumference = 2πr
where r is the radius of circle.
Now it is given that,
Diameter of circle, d = 8 1/2 in = 9/2 in
So, radius of circle, r = d/2 = 9/4 in
⇒ r = 2.25 in
Therefore,
∵ Circumference of circle, C = 2πr
∴ Circumference of circle, C = 2π*9/4
⇒ Circumference of circle, C = 14.130 in
Thus, the missing measure to the nearest hundredth is r = 2.25 in, C = 14.13 in.
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Solve and graph 3|2x+2|-2x=x+3
Answer: x= -1
Step-by-step explanation:
[tex]3\left|2x+2\right|-2x=x+3\\[/tex]
Next, we find Positive and Negative Intervals!
[tex]x < -1,\:\:x\ge \:-1[/tex]
Then Last we Solve The inequality for each interval.
No Solution or x= -1
2x_____=2x10^=______ please help!!!!!!!!!!!!
We have the expression to be written as 2 × 10 = 2 x 10^ 1 = 20
What is index form?
The index form of a number can be defined as that number written as an exponential expression.
It is also said to be a single number that is raised to another number.
Given the expression;
2x _____ = 2 x 10^ 1 = ______
It is important to note that a number raised to the power 1 is that same number, so we have;
2 × 10
2 x 10^1 = 2 × 10
2 × 10 = 20
Thus, we have the expression to be written as 2 × 10 = 2 x 10^ 1 = 20
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Which set of ordered pairs (x,y)(x,y) could represent a linear function?{A}= A= {(-6, 6),(-3, 2),(0, -1),,\,(3, -5} {(−6,6),(−3,2),(0,−1),(3,−5)} {B}= B={(-9, 5),(-1, 3),(, 2),(7, 1) {(−9,5),(−1,3),(3,2),(7,1)} {C}= C= {(-9, -3),(-3, 0),(2, 3),(8, 6) {(−9,−3),(−3,0),(2,3),(8,6)} {D}= D= {(-4, -5),(0, -2),(5, 1) (9, 4)} {(−4,−5),(0,−2),(5,1),(9,4)}
From the given linear functions, the ordered pairs that represents a function is A= {(-6, 6),(-3, 2),(0, -1) (3, 5})
Linear functionsA set of ordered equation represents a linear function if the domain of the coordinates are not repeated.
For instance, the ordered pairs that is a function are the coordinates that do not have any repeated x-coordinates.
From the given linear functions, the ordered pairs that represents a function is A= {(-6, 6),(-3, 2),(0, -1) (3, 5})
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OCPS Dashboard
Storyline Online W Race Now - 100% F
Jose has 13 1/4 cups of raspberries. He uses 7/8 cup of raspberries to make a smoothie. Jose uses the
remaining raspberries to make pancakes. If it takes 1 3/8 cups to make one pancake, how many pancakes can he make?
the number of pancakes that can be made using the remaining raspberries are 9 pancakes.
We are given that:
Total raspberries = 13 1/4 cups
Total raspberries = 53 / 4 cups
Now, he used 7 / 8 cups to make a smoothie.
So, Raspberries left = 53 / 4 - 7 / 8
Left = 99 / 8 cups
Now, for making 1 pancake Raspberries required = 1 3/8 sups
= 11 / 8 cups
So, the number of pancakes will be calculated by using division:
Number = 99 / 8 ÷ 11 / 8
Number = 99 / 11
Number = 9 pancakes
Therefore, we get that, the number of pancakes that can be made using the remaining raspberries are 9 pancakes.
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The directly proportional dependence is given by the formula y=3/8x
For the formula y = 3/8x , as x increases or decreases, the value of y increases or decrease by 3/8 times of x.
We have the following statement -
'The directly proportional dependence is given by the formula y = 3/8x '.
We have to analyze this statement.
What is the meaning of direct proportionality between variables ?Directly proportional means as the value of one variable increases, the value of another variable increases at the same rate.
According to the question, we have -
y = 3/8x
Here - y is directly proportional to x. This means that as x increases or decreases, the value of y increases or decrease by 3/8 times of x.
The graph of this equation is a straight line passing through origin. Therefore - Direct proportionality is represented by a straight line graphically.
Hence, for the equation y = 3/8x , as x increases or decreases, the value of y increases or decrease by 3/8 times of x.
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find the value of z.
Answer:
z = 14.4
Step-by-step explanation:
RX is an angle bisector and divide the opposite side that are proportional to the other 2 sides , that is
[tex]\frac{SX}{XT}[/tex] = [tex]\frac{RS}{RT}[/tex] ( substitute values )
[tex]\frac{5}{6}[/tex] = [tex]\frac{12}{z}[/tex] ( cross- multiply )
5z = 72 ( divide both sides by 5 )
z = 14.4
Find the greatest common factor of 24, 40 and 60.
Answer:
GCF of numbers 24, 40, 60 is 4
GCF(24, 40, 60) = 4
(x+4) {2}+(y-6) {2} = 48 what is the radius
By interpreting the equation of the circle in standard form, we conclude that the circle (x + 4)² + (y - 6)² = 48 has a radius of approximately 6.928 units.
What is the radius of the equation of the circle?
In this question we find the equation of a circle in standard form, whose expression is described and explained below:
(x - h)² + (y - k)² = r²
Where:
(h, k) - Coordinates of the center of the circle.r - Radius of the circleAccording to the equation given in the statement, we find a circle with a center at (- 4, 6) and a radius of 6.928 units.
By interpreting the equation of the circle in standard form, we conclude that the circle (x + 4)² + (y - 6)² = 48 has a radius of approximately 6.928 units.
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please help. The question is attached. Do only C,D,E,F,G
Main Answer:
c. The value of x = 5 and y = 5.
d. The value of x = 1and y = 2.
e. The value of x = 10 and y = 2.
f. The value of x = 2 and y = 1.
g. The value of x=2 and y = 4.
Explanation for all parts:
A linear equation is an algebraic equation of the form y=mx+b involving a constant and a linear term.A square root of a number is a value that when multiplied by itself gives the number.Elimination method is a technique for solving a system of linear equation by eliminating the same variables.c. Given: 3y = x + 10
[tex]x^{2} +y^{2}=100[/tex]
To find: Solve the simultaneous equations.
[tex]x^{2} +y^{2}=100[/tex]
On taking square root from both sides of the equations, we get,
x + y = 10
3y = x + 10
x = 3y - 10
x - 3y = -10
By elimination method,
x - 3y = -10
x + y = 10
-----------------
-4y = -20
y = 5
On substituting the value of y = 5 in the equation x + y = 10 , we get,
x + y =10
x + 5 = 10
x = 5
Therefore, the required value of x = 5 and y = 5.
d. Given: y = 3x - 1
8[tex]x^{2}[/tex] - 2xy = 4
To find: Solve the simultaneous equations.
By substitution method,
We will substitute the value of y in equation 8[tex]x^{2}[/tex] - 2xy = 4 to get,
8[tex]x^{2}[/tex] - 2x(3x-1) = 4
8[tex]x^{2}[/tex] - 6[tex]x^{2}[/tex] +2x = 4
2[tex]x^{2}[/tex] + 2x = 4
By dividing the equation by 2 on both sides, we get,
[tex]x^{2}[/tex] + x = 2
[tex]x^{2}[/tex] + x - 2 = 0
[tex]x^{2}[/tex] + 2x - x - 2 = 0
x(x+2) -1(x+2) = 0
(x+2)(x-1) = 0
x+2 = 0 or x - 1= 0
x = -2 or x = 1
We will not consider the negative values of x.
So, x = 1.
y= 3x - 1
y = 3 × 1- 1
y = 3 - 1
y = 2
The value of x = 1and y = 2..
e. Given: x - 2y = 6
[tex]x^{2}[/tex] - 4xy = 20
To find: Solve the simultaneous equations
x - 2y = 6
x= 6 + 2y
By substitution method,
We will substitute the value of x= 6 + 2y in the equation
[tex]x^{2}[/tex] - 4xy = 20 to get,
[tex](6+2y)^{2}[/tex] - 4(6+2y)y = 20
36 + 4[tex]y^{2}[/tex] +24y - 24y - 8[tex]y^{2}[/tex] = 20
-4[tex]y^{2}[/tex] = 20 - 36
-4[tex]y^{2}[/tex] = -16
By dividing the equation by -4 on both sides, we get,
[tex]y^{2}[/tex] = 4
y = 2
So, x = 6 +2y
x = 6 + 2×2
x = 6+4
x=10
Therefore, the value of x = 10and y = 2.
f. Given: 4x - 3y = 5
[tex]x^{2} +3xy = 10[/tex]
To find: Solve the simultaneous equations.
4x - 3y = 5
4x= 5 + 3y
x = [tex]\frac{5+3y}{4}[/tex]
By substitution method,
We will substitute the value of x = [tex]\frac{5+3y}{4}[/tex] in the equation
[tex]x^{2} +3xy = 10[/tex] to get,
[tex](\frac{5+3y}{4} )^{2}[/tex] + 3[tex](\frac{5+3y}{4} )[/tex]y =10
[tex]\frac{25+9y^{2}+30y }{16}+ \frac{15y+9y^{2} }{4}[/tex] = 10
[tex]\frac{25+9y^{2}+30y+60y+36y^{2} }{16}[/tex]=10
25 + 45[tex]y^{2}[/tex] + 90y=160
By dividing the equation by 5 on both sides, we get,
5 + 9[tex]y^{2}[/tex] +18y= 32
[tex]9y^{2}[/tex] +18y - 27 = 0
By dividing the equation by 3 into both sides, we get,
[tex]y^{2}[/tex] +2y - 3 = 0
[tex]y^{2}[/tex] +3y -y - 3 = 0
y(y+3) - 1(y+3) = 0
(y+3)(y-1) = 0
y =-3 or y =1
We will not consider the negative values of x.
So, y=1.
x= [tex]\frac{5+3y}{4}[/tex]
x = [tex]\frac{5+3(1)}{4}[/tex]
x= [tex]\frac{5+3}{4}[/tex]
x= [tex]\frac{8}{4}[/tex]
x = 2
Therefore, the value of x=2 and y= 1.
g. Given: 2x+ y= 8
xy= 8
To find: Solve the simultaneous equations.
According to the equation,
2x+ y= 8
y = 8 - 2x
By substitution method,
We will substitute the value of y = 8 - 2x in the equation xy = 8 to get,
x(8-2x) = 8
8x - 2[tex]x^{2}[/tex] = 8
8x - 8 = 2[tex]x^{2}[/tex]
2[tex]x^{2}[/tex] - 8x + 8 = 0
2[tex]x^{2}[/tex] - 4x - 4x + 8 =0
2x(x - 2) - 4(x - 2) = 0
(x - 2)(2x - 4) = 0
x = 2 or 2x = 4
x= 2 or x =2
So, y = 8 - 2x
y = 8 - 2(2)
y = 8 - 4
y = 4
Therefore, the value of x = 2 and y= 4.
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Question below, please answer if you know :)
The final coordinates of the triangle are A''(x, y) = (3, 2), B''(x, y) = (- 1, 4) and C''(x, y) = (2, 0), respectively.
What are the coordinates of the vertices of the image derived from transformation rules?
In this question we know the coordinates of the three vertices of the triangle, whose image must be generated by combining reflection across y-axis and translation, two kinds of rigid transformations, whose formulas are summarized below:
Reflection across y-axis
P'(x, y) = P(x, y) + (- 2 · p, 0) (1)
Translation
P'(x, y) = P(x, y) + T(x, y) (2)
Where:
P(x, y) - Original pointP'(x, y) - Resulting pointT(x, y) - Translation vectorp - x-Coordinate of the original point.If we know that A(x, y) = (1, - 3), B(x, y) = (5, - 1) and C(x, y) = (2, - 5), then the final coordinates are:
Reflection across y-axis
A'(x, y) = (1, - 3) + (- 2, 0)
A'(x, y) = (- 1, - 3)
B'(x, y) = (5, - 1) + (- 10, 0)
B'(x, y) = (- 5, - 1)
C'(x, y) = (2, - 5) + (- 4, 0)
C'(x, y) = (- 2, - 5)
Translation
A''(x, y) = (- 1, - 3) + (4, 5)
A''(x, y) = (3, 2)
B''(x, y) = (- 5, - 1) + (4, 5)
B''(x, y) = (- 1, 4)
C''(x, y) = (- 2, - 5) + (4, 5)
C''(x, y) = (2, 0)
The final coordinates of the triangle are A''(x, y) = (3, 2), B''(x, y) = (- 1, 4) and C''(x, y) = (2, 0), respectively.
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whats 8 3/4 as a decimal
Answer:8.75
Step-by-step explanation:
3/4=0.75
0.75+8=8.75
11) Each of Jeff's family, of four, buys a new phone. The total cost is $25 above or below $1200. Write
an equation that models the cost x, in dollars, of a single phone.
The equation that models the cost x in dollars of a single phone is given by 293.75 ≤ x ≤ 306.25.
What are inequalities ?
When two values are compared , an inequality represents whether one is greater than, less than, or not equal to the other.
It is given that total cost of phone is $25 above or below $1200.
This is a case of inequality.
Let's assume the cost of one phone is $x.
So cost of 4 phones will be given by 4x.
and this will be equal to total cost which is given as $25 above or below $1200.
So , the inequality is given by ;
1200 - 25 ≤ 4x ≤ 1200 + 25
1175 ≤ 4x ≤ 1225
If we divide by 4 through this inequality then ;
(1175/4) ≤ (4x/ 4) ≤ (1225/ 4)
or
293.75 ≤ x ≤ 306.25
The cost of one phone will lie between $293.75 and $306.25.
Therefore , the equation that models the cost x in dollars of a single phone is given by 293.75 ≤ x ≤ 306.25.
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The length of a pool is 5 more than the width. The perimeter is 96. Whats is the are of the pool.
Answer:
569,75
Step-by-step explanation:
Write an equation of each line in point-slope form.
(-4,2) and (-3,5)
The equation of the line in point-slope form, which passes through the pair of points located at (-4 , 2) and (-3 , 5), is y - 2 = 3(x + 4).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Getting the slope of the two points: (-4 , 2) and (-3 , 5).
m = (y2 - y1)/(x2 - x1)
m = (5 - 2)/(-3 - -4)
m = 3
Using the point slope form, plug in the values of the slope and Point A to set up the equation.
(y - y1) = m(x - x1)
where m = 3 and (x1 , y1) = (-4 , 2)
(y - 2) = 3(x - -4)
y - 2 = 3(x + 4)
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The half-life of nickel-63 is 92 years. The amount of nickel-63 in a sample is .670 g. How much nickel-63
would be left after 460 years?
[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &\stackrel{grams}{0.67}\\ t=\textit{elapsed time}\dotfill &\stackrel{years}{460}\\ h=\textit{half-life}\dotfill &\stackrel{years}{92} \end{cases} \\\\\\ A=0.67\left( \frac{1}{2} \right)^{\frac{460}{92}}\implies A=0.67\left( \frac{1}{2} \right)^5\implies A\approx 0.021~grams[/tex]
Solve each equation. Check the solution. 3/b+2 = 6/b-1
The solution of the given equation 3/b+2 = 6/b-1 is found to be (y = -5).
What is termed as cross multiplication?The numerator of the 1st fraction is multiplied by denominator of the 2nd fraction, and the numerator of the 2nd fraction is multiplied by denominator of the 1st fraction in cross-multiplication.
During cross multiplication, denominators are removed.It is used to compare fraction sizes and solve proportional as well as percentage problems.In proportion problems, it is common to have an absent value or variable.After having removed the denominators using cross multiplication, mathematics skills are used to solve for the missing variable once more.Proportion and percentage problems have been solved in the same way.Now, for the given equation in the question;
3/b+2 = 6/b-1
Cross multiplying the terms;
3(b - 1) = 6(b + 2)
Opening the brackets;
3b - 3 = 6b + 12
Bring the variables and constants on the different sides.
6b - 3b = -3 - 12
3b = -15
b = -5
Therefore, the solution of the stated equation 3/b+2 = 6/b-1 is found to be (b = -5).
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