Pythagorean theorem and its converse
problem 3:
leg:16
leg:x
hypo:27
problem 4:
leg:12.8
leg:5.3
hypo:x
problem 5
18 <--------->
`20
x'
The missing measures, using the Pythagorean Theorem, are given as follows:
3. Leg x = 21.75.
4. Hypotenuse x = 13.85.
What is the Pythagorean Theorem?The Pythagorean Theorem states that length of the hypotenuse squared is equals to the sum of each of the sides of the triangle squared.
For item 3, we have that the leg x is missing, while another leg and the hypotenuse are given, meaning that the relation is of:
x² + 16² = 27²
Hence:
x² = 27² - 16²
[tex]x = \sqrt{27^2 - 16^2}[/tex]
x = 21.75.
For item 4, we are given two legs and want to find the hypotenuse, hence the relation is given as follows:
x² = 12.8² + 5.3²
[tex]x = \sqrt{12.8^2 + 5.3^2}[/tex]
x = 13.85.
As for item 5, there is not enough information to answer, but the procedure should be the same.
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All of Marcy's marbles are blue, red, green, or yellow. One third of her marbles are blue, one fourth of them are red, and six of them are green. What is the smallest number of yellow marbles
After solving, the smallest number of yellow marbles are 4.
In the given question, all of Marcy's marbles are blue, red, green, or yellow.
One third of her marbles are blue, one fourth of them are red, and six of them are green.
We have to find the smallest number of yellow marble.
The 6 green marbles and yellow marbles of the total marbles = 1 - (1/3) - (1/4)
The 6 green marbles and yellow marbles of the total marbles = 5/12
Now, suppose the total number of marbles is x
We know the number of yellow marbles is 5/12 x-6 and a positive integer.
Therefore, 12 must divide x
Trying the smallest multiples of 12 for x.
We see that when x = 12
We get there -1 yellow marbles, which is impossible.
However, when x = 24 here are
= 5/12 x - 6
= 5/12*24 - 6
= 4
So, the yellow marbles are 4 which must be the smallest possible.
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What are the 3 possible solutions when solving a system of equations?
Three possible solutions when solving a system of equation are: one solution, no solution, and infinite solutions.
The 3 possible solutions of a system of equations are:
- Unique or one solution
- Infinite solutions
- No solution
In case of a system of linear equations, we can determine the type of its solution as follows:
- If the slopes are different, then their graphs will intercept in one point. Hence, the system of linear equation will have one solution.
- If the slopes are the same but the equation of the lines are different, the lines are parallel, hence they will not intercept. Therefore, there is no solution.
- If the linear equations are exactly (or can be transformed to exactly) the same equations, the solution is infinite.
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solve for x(best answer brainliest)
24x+15=25x+45
[tex]24x+15=25x+45[/tex]
Subtract 25x from both sides:
[tex]24x+15-25x=25x+45-25x[/tex]
[tex]-x+15=45[/tex]
Subtract 15 from both sides:
[tex]-x+15-15=45-15[/tex]
[tex]-x=30[/tex]
Divide both sides by -1(to remove negative from variable):
[tex]\dfrac{-x}{-1} =\dfrac{30}{-1}[/tex]
[tex]\fbox{x = -30}[/tex]
Answer:
[tex] \sf \: x = - 30[/tex]
Step-by-step explanation:
Now we have to,
→ find the required value of x.
The equation is,
→ 24x + 15 = 25x + 45
Then the value of x will be,
→ 24x + 15 = 25x + 45
→ 24x - 25x = 45 - 15
→ -x = 30
→ [ x = -30 ]
Hence, the value of x is -30.
A jar contains quarters, loonies, and toonies. If four coins are selected from the jar, how many unique coin combinations are there
When selecting four coins from a jar containing quarters, loonies, and toonies, there are a total of 27 unique combinations.
This can be calculated by using the formula for combination, which is nCr.
In this case,
n is the total number of coins in the jar (3) and
r is the number of coins selected (4).
Therefore, 3/(4(3-4)) = 3/0 = 3/1 = 3,
which is the number of possible combinations in the jar for the quarters, loonies, and toonies. When you multiply 3 by 3, you get 9, and when you multiply 9 by 3 again, you get 27.
Therefore, there are 27 unique coin combinations when selecting four coins from the jar.
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solve the inequality and explain how
Answer:
B. (see attached)
Step-by-step explanation:
You want the solution and graph of the inequality |x+3| > 2.
SolutionThe inequality resolves to two inequalities with different domain definitions:
|x +3| > 2
When the argument is negative, (x+3) < 0, this is ...
-(x +3) > 2
-x -3 > 2 . . . . . . eliminate parentheses
x +3 < -2 . . . . . . multiply by -1
x < -5 . . . . . . . . . subtract 3; consistent with the domain definition
When the argument is positive, (x+3) > 0, this is ...
x +3 > 2
x > -1 . . . . . . . . subtract 3
-1 < x . . . . . . . . same thing using the < symbol
These differing solution sets do not overlap, but elements of either set are solutions to the inequality. The appropriate conjunction is "OR":
solution: x < -5 or -1 < x
The graph is attached.
__
Additional comment
We like to use the < or ≤ symbols when expressing the solution to an inequality. That way, the relation of the variable to the boundary value is the same as its relation on a number line. Solution values are left of -5 or right of -1:
x < -5 or -1 < x
It helps provide a check that the graph is properly drawn.
The inequality can be rewritten as ...
|x -(-3)| > 2
which can be interpreted as saying the positive distance from x to -3 is more than 2. This tells you the graph will have two disjoint branches, and the appropriate conjunction is OR.
If the problem were different, and the inequality were ...
|x -(-3)| < 2
it would be telling you the solution values have a distance less than 2 from -3. They will be in one continuous band from -5 to -1, so the appropriate conjunction is AND. The solution in this case is usually written as a compound inequality with no conjunction: -5 < x < -1. (Note the use of < symbols puts the variable value in the middle, between the boundary values, as in graph D.)
On a negatively skewed curve, which is true?
The mean of negatively skewed facts can be less than the median. If the information graphs symmetrically, the distribution has 0 skewness, no matter how lengthy or fat the tails are.
What is a curve ?
Curve can be defined as the path on which it is usually generated by the equation.
In statistics, a negatively skewed (also called left-skewed) distribution is a sort of distribution wherein more values are targeting the right side (tail) of the distribution graph while the left tail of the distribution graph is longer.
negatively skewed distribution refers to the distribution kind where greater values plot at the graph's proper facet, the tail of the distribution is longer on the left aspect, and the suggest is decrease than the median and mode. It is probably 0 or poor due to the data being distributed negatively.
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Examine the graph of the function. The graph of a line that contains points (negative 1, 7), (0, 5), and (2, 1). © 2017 StrongMind. Created using GeoGebra. What is the initial value of the function? Enter your answer as a number, like this: 42
The initial value of the function is equal to 5.
How to determine the initial value of the function?In order to determine the initial value of the function, we would have to find the slope from line graph and then write the required equation based on the data points contained in the table by using the slope-intercept form.
Mathematically, the slope-intercept form of a line is modeled by this mathematical equation:
y = mx + c
Where:
m represents the slope.x and y are the data points.c represents the y-intercept or initial value.Next, we would determine the slope of the data points as follows;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (5 - 7)/(0 + 1)
Slope, m = -2/1
Slope, m = -2.
At point (0, 5), an equation of this line can be calculated in slope-intercept form as follows:
Note: The y-intercept or initial value is equal to 5.
y = mx + c
y = -2x + 5
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Are isosceles triangles always 180?
No, isosceles triangles are not always 180 degrees. The sum of the interior angles of an isosceles triangle is 180 degrees, but the individual angles can be different.
Isosceles triangles do not necessarily have a 180-degree angle. Any triangle with two equal sides is said to be isosceles. Any triangle's internal angles add up to 180 degrees. An isosceles triangle's individual angles can change depending on how long its sides are, though. An isosceles triangle, for instance, might have a third side that is longer or shorter than the other two sides if the first two sides are equal. The size of the inner angles will be impacted by this. As a result, an isosceles triangle need not have angles that are 180 degrees. An isosceles triangle has interior angles that add up to 180 degrees, but the individual angles might vary.
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Kelvin and Lewie each design surveys in order to determine the average number of people who buy food at the mall. Kelvin surveys every other person leaving the food area. Lewie surveys every fifth person leaving the mall main entrance. Which set of survey results is most likely to show biased results for people who buy food at the mall
The set of survey results that is most likely to show biased results for people who buy food at the mall is Lewie's survey.
Lewie's survey samples only every fifth person leaving the mall's main entrance, which means that it only captures a small percentage of the total number of mall visitors. Additionally, by only surveying people leaving the main entrance, Lewie's survey may not capture people who enter and exit the mall through other entrances or exits and may also miss those who don't leave the mall after buying food. As a result, Lewie's survey may not accurately represent the total number of people who buy food at the mall and may lead to biased results.
On the other hand, Kelvin's survey samples every other person leaving the food area. This method captures a larger percentage of the total number of people who buy food at the mall and is more likely to provide a more accurate representation of the total number of people who buy food at the mall.
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Answer:
A. Kelvin’s because he surveyed people leaving an area where food is sold
Step-by-step explanation:
You want to ride your bike down the street to your friend's house, which is 340 meters from your house. The trip takes you 68 seconds from start to finish. How fast are you traveling on your bike?
The speed of the Bike is 5 meters per second
What is speed?Speed is a scalar quantity that describes how fast an object is moving . It is defined as the distance an object travels divided by the time it takes to travel that distance. The units of speed are typically meters per second (m/s) or kilometers per hour (km/h).
To find out how fast you are traveling on your bike, you can use the formula:
Speed = [tex]\frac{Distance}{Time}[/tex]
In this case, the distance is 340 meters and the time is 68 seconds. So, you can plug these values into the formula and get:
Speed = 340 meters / 68 seconds
Speed = [tex]\frac{340 meters}{68 seconds}[/tex] = 5 meters per second
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Seth built a wooden step stool out of two rectangular prisms and two cubes. Before fastening the components together, he stained each component to give it its final color.
To completely stain the bottom rectangular prism, Seth had to cover
square inches of wood. For one of the cubes to be completely stained, he had to cover
square inches of wood. To completely stain the top rectangular prism, he had to cover
square inches of wood.
Once the stool was fastened together, he applied a coat of sealant to all exposed surfaces of the stool, including the bottom, to cover a total of
square inches.
To complete stain the bottom rectangular prism, he needs to cover 624 square inches.
What is surface area?A solid object's surface area is a measurement of the overall space that the object's surface takes up.
Given that:
Bottom rectangular prism:
Length = 22 in
Width = 8 in
Height = 6 in
The surface area of the rectangular prism is:
SA = 2( lh + wh + lw)
SA = 2((22)(6) + (8)(6) + (22)(6))
SA= 624 square inches.
To complete stain the bottom rectangular prism, he needs to cover 624 square inches.
Square:
Side = 4 in
The surface area of the cube is:
[tex]SA = 6a^2[/tex]
[tex]SA = 6 (4)^2\\\\SA= 96[/tex]square inches.
To completely stain two squares, he needs to cover 96 * 2 = 196 square inches.
Top rectangular prism:
Length = 18 in
Width = 5 in
Height = 2 in
The surface area of the rectangular prism is:
SA = 2( lh + wh + lw)
SA = 2((18)(2) + (5)(2) + (18)(5))
SA = 136 square inches
Hence to completely stain top rectangular prism, he needs to cover 136 square inches.
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Alice is playing a game in which she will roll 4 6-sided dice at the same time. She gets 5 points for each die that shows an even result. Let x represent the total number of points awarded on any given toss of the dice. What is the expected value of x? A. 1/2 B. 2 C. 10 D. 15 E. 20
The number of points is simply 5 times this random variable, and E(C*Y) = C*E(Y), where C is a constant and Y is a random variable, according to expected value principles. As a result, E(X) = 5*2 = 10.
What is probability?The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Here,
The number of dice that are showing an even number is a binomial random variable with n = 4, and p = 1/2 (because half the faces on the die are even and half are odd).
The expected value of this random variable is n*p = 4*1/2 = 2.
The number of points is simply 5 times this random variable, and by the rules of expected value, E(C*Y) = C*E(Y), where C is a constant and Y is a random variable. Thus E(X) = 5*2 = 10.
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How do you know if there are 2 real solutions?
For Quadratic equation, It is possible to know if there are 2 real solutions by examining the discriminant that is [tex]b^2-4ac[/tex] of the equation [tex]ax^2+bx+c[/tex].
What do you mean by a solution?In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.
What are ideal and real solutions?In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.
discriminant : [tex]b^2-4ac[/tex]
if [tex]b^2-4ac[/tex] is positive, Both solutions are real.
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Sarah has 3 bags of marbles. Each bag has 16 marbles. If 3/4 of the marbles are blue, what is the total number of blue marbles in the bags?
Answer: 12
Step-by-step explanation: 3/4 divid by 3
=Round each number to five decimal places: a. 23.54 b. 0.916?
Therefore the rounded numbers are 23.54 and 0.9160.
Define rounded numbers.An integer containing one or more "0"s at the end in a certain base is said to be round. In this way, 590 is more rounded than 592 but less rounded than 600. A round number is frequently understood to stand for a value or values close to the nominal value given in both formal and informal language.
What is integer?Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The set of integers is frequently represented in mathematical notation by the boldface Z or blackboard bold mathbb Z.
a. To round 23.54 to five decimal places, we look at the sixth decimal place, which is 4. Since 4 is less than 5, we leave the fifth decimal place as is, and the number rounded to five decimal places is 23.54.
b. To round 0.916 to five decimal places, we look at the sixth decimal place, which is 1. Since 1 is greater than or equal to 5, we increase the fifth decimal place by one, and the number rounded to five decimal places is 0.9160.
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Select the linear function from the following:
Select one:
a.
− 3 / x + y / 7 = 11
b.
− x / 3 + 7 / y = 11
c.
− x / 3 + y / 7 = xy
d.
− x / 3 + y / 7 = 11
The linear function in the option is − x / 3 + y / 7 = 11.
How to know linear function?A linear function is a function that represents a straight line on the coordinate plane.
Linear function can be represented in slope intercept form as follows:
y = mx + b
where
m = slope of the lineb = y-interceptTherefore, let's select the linear function from the options:
− 3 / x + y / 7 = 11
-3x⁻¹ + 1 / 7 y = 11 (Not a linear function)
− x / 3 + 7 / y = 11
- 1 / 3 x + 7y⁻¹ = 11 (Not a linear function)
− x / 3 + y / 7 = xy (Not a linear function)
− x / 3 + y / 7 = 11
- 1 / 3 x + 1 / 7 y = 11 (This is the linear function)
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Choose all of the equations that represent a parabola with the focus (3,9) and the vertex (3, 6).
A. 12y = x² - 6x+81
B. 24y=x²-12x + 72
C. 24y=x² - 6x + 225
D. (x-3)2 24 (-9)
E. (x-3)² = 12 (y – 6)
F. (x-9)² = 24 (y - 3)
(x-3)² = 12 (y – 6) is the equation for a parabola with the vertex (3, 6) and focus (3, 9) in it.
what is parabola ?A parabola is a U-shaped plane curve in which every point is situated at an equal distance from both the focus, a fixed point, and the directrix, a fixed line. The topic of conic sections includes parabola as a key component, and all related parabola topics are discussed. a plane curve produced by a point shifting such that its separation from a fixed point equals its separation from a fixed line: junction of a plane parallel to an element of a right circular cone with the cone. : a bowl-shaped object (such as an antenna or microphone reflector)
given
focus (3,9) and the vertex (3, 6)
general equation of parabola = (x - h)2 = 4a (y - k)
a = |y2 - y1| = | 9 - 6 |
a = 3
so
(x - 3 )[tex]^{2}[/tex] = 4 * 3 ( y - 6 )
= [tex](x-3)^{2} = 12 ( y - 6 )[/tex]
(x-3)² = 12 (y – 6) is the equation for a parabola with the vertex (3, 6) and focus (3, 9) in it.
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a pair of sneakers in on sale as shown the sale price is $51. This is 75% of the original price. what was the original price of the shoes
pls help, explanation required
What does this symbol mean ∈?
A hat symbol (^) is used to represent an estimated value in regression analysis.
We know that in regression analysis, the predicted values are the y-hat values.
Here y is the output variable or dependent variable
A 'hat' symbol (^) is used to denote an estimator.
A ^ symbol is placed over the variable name to denote the estimated value.
In matrix system, a hat matrix is nothing but the projection matrix.
It projects the vector of observations, y, onto the vector of predictions, y^
We know that a vector has magnitude and direction. A ^ symbol is used is represent the direction of unit vector.
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How do you do a simple random sample on a calculator?
Using the calculator there are various methods according to the calculator we used and the approach we follow, Basic answer is to select N and generate random number.
What do you mean by random sampling?Random sampling is a method of selecting a sample from a population in such a way that each member of the population has an equal probability of being selected. This ensures that the sample is representative of the population, and reduces bias in the sampling process. In simple random sampling, a random sample is drawn from a larger population by using random number generators, tables of random numbers, or other methods that ensure that each member of the population has an equal chance of being selected.
What are samples?A sample is a portion or a subset of a population that is selected for the purpose of studying characteristics of the population. The sample is used to make inferences or conclusions about the population from which it was drawn. The sample is usually smaller in size than the population, and it is selected through a process called sampling. The process of sampling is used to select a sample that is representative of the population, meaning that the sample has similar characteristics as the population.
Define the population size (N) and the sample size (n) that you want to obtain.
Use the calculator's random number generator to generate a random number between 1 and N. This will be the first element of your sample.
Repeat step 2 to generate the remaining elements of the sample, making sure that each element is different from the previous ones.
Record the elements of the sample, which are the random numbers that have been generated.
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Simplify algebraic expression
Answer:
1
Step-by-step explanation:
To start, we will substitute 8 in for w. So, we get:
[tex]5 - \frac{32}{8}[/tex]
Then, we simplify our fraction, giving us:
5 - 4
Then, 5 - 4 = 1. So our answer is 1.
Hope this helped!
Answer:
5 - (32/w) = 1
Step-by-step explanation:
Given expression,
→ 5 - (32/w)
Now we have to use,
→ w = 8
Let's solve the expression,
→ 5 - (32/w)
→ 5 - (32/8)
→ 5 - (4)
→ 5 - 4
→ 1 => final value
Therefore, the answer is 1.
Please help me find the shaded area!
Answer:
216
Step-by-step explanation:
first multiply 4by6 to get that area we will call that a
then 12 by 20 to get that area we will call that b
the shaded area is a's area minus B's area
(12*20)-(4*6)
240-24
216
Answer:
216 in²
Step-by-step explanation:
(12)(20) - (4)(6) = 240 - 24 = 216
Select the correct answer. what is the equation of a parabola whose vertex is (0, 5) and whose directrix is x = 2?
a. y2 = 8(x − 5)
b. 8(y − 5) = x2
c. (y − 5)2 = 8x
d. (y − 5)2 = -8x
Check the picture below, so the parabola looks more or less like so, with a vertex at (0 , 5) and a "p" distance of negative 2 units, since it's opening to the left, so
[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{p~is~negative}{op ens~\supset}\qquad \stackrel{p~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=0\\ k=5\\ p=-2 \end{cases}\implies 4(-2)(~~x-0~~) = (~~y-5~~)^2\implies {\Large \begin{array}{llll} -8x=(y-5)^2 \end{array}}[/tex]
A man bought an item for N5000.00 and sold it at a loss of 25%. How much did he sell it? A. N6250.00 B.N4750.00 C.N3750.00
D. N2250.00
Answer: B. 3750
Step-by-step explanation:
We start by converting the percentage 25% to the decimal 0.25.
Next, we multiply the original price by this decimal (5000*0.25=1250)
And Finally, Since it is a loss we subtract the 1250 from the original price.
5000 - 1250 = 3750
Is a 45 45 triangle isosceles?
Yes, a 45 45 triangle is an isosceles triangle, meaning that two of its sides are equal in length.
A 45 45 triangle is a triangle in which two of its angles are 45 degrees. This type of triangle is also known as an isosceles triangle because it has two sides of equal length. To determine whether a triangle is isosceles, we need to measure the lengths of its sides. In a 45 45 triangle, both sides are equal in length as the angles are equal. Therefore, a 45 45 triangle is an isosceles triangle. The triangle also has two acute angles (less than 90 degrees) and one obtuse angle (greater than 90 degrees). This type of triangle is a special type of triangle and is often used in geometry and trigonometry.
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What is the measure of m?
n
m
28
7
m = [? ] V
Give your answer in simplest form.
when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. Check the picture below.
[tex]\cfrac{35}{m}=\cfrac{m}{7}\implies 245=m^2\implies \sqrt{245}=m\implies \sqrt{7^2\cdot 5}=m\implies 7\sqrt{5}=m[/tex]
Squares $ABCD$ and $EFGH$ are equal in area. Vertices $B$, $E$, $C$, and $H$ lie on the same line. Diagonal $AC$ is extended to $J$, the midpoint of $GH$. What is the fraction of the two squares that is shaded
The fraction of the two squares that is shaded exists 5/16 area shaded.
What is the difference between diagonal and vertices?A diagonal is a line segment connecting two opposite corners (vertexes) of a polygon, however it is not an edge (side). In other words, it connects any two non-adjacent polygonal vertices. Therefore, by connecting any two vertices in a polygon directly (i.e., without using a side), we create a diagonal.
A line segment known as a diagonal joins two polygonal vertexes (corners), although it is not an edge (side). To put it another way, it joins any two polygonal vertices that are not adjacent. Therefore, by connecting any two vertices in a polygon directly (i.e., without using a side), we create a diagonal.
The triangle on the bottom exists 1/2 × 1/2 × 1/2 of the original area of the lower square = 1/8 of the lower square
2 square = [1/2 (square) + 1/8 (square) ] / 2 square
= 5/16 area shaded
Therefore, the fraction of the two squares that is shaded exists 5/16 area shaded.
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The fraction of the two squares that is shaded exists 5/16 area shaded.
What is the difference between diagonal and vertices?A diagonal is a line segment that joins two opposed polygonal corners (vertexes), although it is not an edge (side). In other words, it joins any two polygonal vertices that are not neighbouring. As a result, we can make a diagonal by directly joining any two vertices of a polygon (i.e., without utilising a side).
Although it is not an edge, a line segment known as a diagonal connects two polygonal vertexes (corners) (side). In other words, it connects any non-adjacent pair of polygonal vertices. As a result, we can make a diagonal by directly joining any two vertices of a polygon (i.e., without utilising a side).
The triangle on the bottom exists 1/2 × 1/2 × 1/2 of the original area of the lower square = 1/8 of the lower square
2 square = [1/2 (square) + 1/8 (square) ] / 2 square
= 5/16 area shaded
Therefore, the fraction of the two squares that is shaded exists 5/16 area shaded.
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6x - 4y = 8 ; x
Solve for indicated value
Solved equation is, x = 4/3 + 2y/3
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
here we have,
Write equation
6x - 4y = 8
Then,
Solve for x
Add 4y to both sides: 6x = 8 + 4y
Divide both sides by 6: x = 8/6 + 4y/6
Simplify: x = 4/3 + 2y/3
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In the adjoining figure, the area of the rectangular surfaces of the prism is 720 sq. Cm, XX' 20 cm and XY : XZ: YZ = 5:3 : 4, find the length of XY
The length of XY, with the area of the rectangular surface of the prism 720 sq.cm, XX' 20 cm and XY : XZ: YZ = 5:3:4, is 12 cm.
Area of the rectangular surface of the prism = 720 sq. cm
XX' = 20 cm
XY : XZ: YZ = 5:3:4
As we know, area of prism = 3 × area of rectangle
⇒720 = 3 × area of rectangle
⇒area of rectangle = 720/3
⇒XY × XX' = 240
⇒XY × 20 = 240
⇒XY = 240/20
⇒XY = 12 cm
Thus, the length of the XY is 12 cm.
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