Answer:
(3h+y)*(3h-y)
Step-by-step explanation:
We are given the following expression:
[tex]\frac{2h+y}{9h^2-y^2}-\frac{4h^2}{3h+y}[/tex]We want to find the LCD for:
9h²-y² and 3h + y.
3h+y is already in it's most simplified way.
9h²-y² , according to the notable product of (a²-b²) = (a-b)*(a+b), can be factored as:
(3h-y)*(3h+y).
The factors of each polynomial is:
3h + y and (3h-y)*(3h+y)
The LCD uses all unique factors(If a factor is present in more than one polynomial, it only appears once).
So the LCD is:
(3h+y)*(3h-y)
Which is option B.
A certain species of deer is to be introduced into a forest, and wildlife experts estimate the population will grow to P(t) = (944)3 t/3, where t represents the number ofyears from the time of introduction.What is the tripling-time for this population of deer?
Ok, so
Here we have the function:
[tex]P(t)=944(3)^{\frac{t}{3}}[/tex]Now we want to find the tripling-time for this population of deer.
If we make t=0, we will find the initial population of deer. This is:
[tex]P(0)=944(3)^{\frac{0}{3}}=944[/tex]Now, we want to find the time "t" such that this population is the triple.
This is:
[tex]\begin{gathered} 944(3)=944(3)^{\frac{t}{3}} \\ 2832=944(3)^{\frac{t}{3}} \\ \frac{2832}{944}=3^{\frac{t}{3}} \\ 3=3^{\frac{t}{3}} \end{gathered}[/tex]We got this exponential equation:
[tex]3=3^{\frac{t}{3}}[/tex]As the base is the same, we could equal the exponents:
[tex]\begin{gathered} 1=\frac{t}{3} \\ t=3 \end{gathered}[/tex]Therefore, tripling-time for this population of deer are 3 years.
classify given equation as rational or irrational:2 root 3 + 3 root 2 - 4 root 3 + 7 root 2
Irrational
Explanation
[tex]2\sqrt{3}+3\sqrt{2}-4\sqrt{3}+7\sqrt{2}[/tex]
Step 1
simplify
[tex]\begin{gathered} 2\sqrt{3}+3\sqrt{2}-4\sqrt{3}+7\sqrt{2} \\ \lparen2-4)\sqrt{3}+\left(3+7\right)\sqrt{2} \\ -2\sqrt{3}+4\sqrt{2} \\ \end{gathered}[/tex]Step 2
the square root of 2 is an irrational number,because there is not number such that
[tex]\sqrt{2}=\frac{a}{b}[/tex]and
The square root of 3 is an irrational number √3 cannot be expressed in the form of p/q
hence
the sum of 2 irrational numbers gives a irrational result,Sum of two irrational numbers is always irrational.
so, the answer is
Irrational
I hope this helps you
after three tests, brandon has a test average of 90. after his fourth test, his average dropped to an 85. what did he score on his fourth test?
Answer:
70
Step-by-step explanation:
Average = Sum/Number of tests
90 = Sum/3 tests
Sum = 270
85 = 270 + test/4 tests
340 = 270 + test
70
help meeeee pleaseeeee!!!
thank you
The values of f(4) , f(0) and f(-5) are 16/7, -12 and -7/11 respectively.
We are given the function:-
f(x) = (x + 12)/(2x - 1)
We have to find the values of f(4) , f(0) and f(-5).
Putting x = 4 in the given function, we can write,
f(4) = (4+12)/(2*4-1) = 16/7
Putting x = 0 in the given function, we can write,
f(0) = (0 + 12)/(2*0 - 1) = 12/(-1) = -12
Putting x = -5 in the given function, we can write,
f(-5) = (-5 + 12)/(2*(-5) - 1) = 7/(-10-1) = 7/(-11) = -7/11
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Show the steps needed to Evaluate (2)^-2
Answer:
[tex]\dfrac{1}{4}[/tex]
Step-by-step explanation:
Given expression:
[tex]2^{-2}[/tex]
[tex]\boxed{\textsf{Exponent rule}: \quad a^{-n}=\dfrac{1}{a^n}}[/tex]
Apply the exponent rule to the given expression:
[tex]\implies 2^{-2}=\dfrac{1}{2^2}[/tex]
Two squared is the same as multiplying 2 by itself, therefore:
[tex]\begin{aligned}\implies 2^{-2}&=\dfrac{1}{2^2}\\\\&=\dfrac{1}{2 \times 2}\\\\&=\dfrac{1}{4}\end{aligned}[/tex]
Solution
[tex]2^{-2}=\dfrac{1}{4}[/tex]
Answer:
1/4
Step-by-step explanation:
Now we have to,
→ find the required value of (2)^-2.
Let's solve the problem,
→ (2)^-2
→ (1/2)² = 1/4
Therefore, the value is 1/4.
Find the slope of the line through the given points . If the slope of the line is undefined state so (13,1) and (1,4)
ANSWER:
A. The slope of the line is -1/4
STEP-BY-STEP EXPLANATION:
Given:
(13,1) and (1,4)
The slope can be calculated using the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]We substitute each value and calculate the slope:
[tex]m=\frac{1-4}{13-1}=\frac{-3}{12}=-\frac{1}{4}[/tex]Therefore, the correct answer would be:
A. The slope of the line is -1/4
A popcorn stand offers buttered or unbuttered popcorn in three sizes: small, medium, and large. What is the P(buttered)
The popcorn we can order is either buttered or unbuttered.
Therefore, the probability of choosing buttered popcorn is 1/2
Use the definition of the derivative to find the derivative of the function with respect to x. Show steps
The derivative of the function f(x) = √x-5 is 1/2√(x-5)
Given f(x) = √x-5
from the formula d/dx (√x) = 1/2√x
hence d/dx √x-5 = 1/2√x-5
or
d/dx √x-5 = 1/2 (x-5)¹/²
The formula for the derivative of root x is d(x)/dx = (1/2) x-1/2 or 1/(2x). The exponential function with x as the variable and base equal to 1/2 is the root x provided by x. Utilizing the Power Rule and the First Principle of Derivatives, we can get the derivative of root x.
Hence we get the value as 1/2 (x-5)¹/²
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Kepler's third law of planetary motion states that the square of the time required for a planet to make one revolution about the sun varies directly as the cube of the average distance of the planet from the sun. If you assume that Jupiter is 5.2 times as far from the sun as is the earth, find the approximate revolution time for Jupiter in years.
Show work pls ;-;
By applying Kepler's third law of planetary motion, the approximate revolution time for Jupiter is equal to 12 years.
What is Kepler's third law?Mathematically, Kepler's third law of planetary motion is given by this mathematical expression:
T² = a³
Where:
T represents the orbital period.a represents the semi-major axis.Note: Earth has 1 astronomical unit (AU) in 1 year of time.
For this direct variation, the value of the constant of proportionality (k) is given by:
T² = ka³
k = T²/a³
k = 1²/1³
k = 1.
When the semi-major axis or the distance of Jupiter from Sun is 5.2, we have;
T² = ka³
T² = 1 × 5.2³
T² = 140.608
T = √140.608
T = 11.858 ≈ 12 years.
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Simplify the expression using order of operation 9/g + 2h + 5, when g = 3 and h = 6
9/g + 2h + 5
When g = 3 and h = 6
First, replace the values of g and h by the ones given:
9/(3) + 2(6) + 5
9/3 + 2(6)+5
Then, divide and multiply:
3+12+5
Finally, add
20
The rotation of the smaller wheel in the figure causes the larger wheel to rotate. Find the radius of the largerwheel in the figure if the smaller wheel rotates 70.0° when the larger wheel rotates 40.0°The radius of the large wheel is approximately ____ cm.
Let's begin by listing out the information given to us:
r (1) = 11.4 cm, θ (1) = 70°, θ (2) = 40°, r(2) = ?
The arc length is the same for the 2 circles
r (1) * θ (1) = r (2) * θ (2)
11.4 * 70° = r (2) * 40°
r (2) = 11.4 * 70 ÷ 40
r (2) = 19.95 cm
Hence, the radius of the larger circle is 19.95 cm
I think of a number.
I add 5 to it and then double the result.
I then subtract 10 from this answer.
I then subtract the original number I thought of.
Using algebra and a pronumeral to represent the number I think of, explain
why I get back to the number I started with.
Answer: [2(x + 5)] - 10 - x = 2x+10-10-x = 2x-x = x
Step-by-step explanation:
I think of a number, represented by the variable/pronumeral x.
I add 5 to it: x + 5
then double the result: 2(x + 5)
I then subtract 10 from this answer: [2(x + 5)] - 10
I then subtract the original number I thought of: [2(x + 5)] - 10 - x
Simplifying the expression will explain why you get the original number.
[2(x + 5)] - 10 - x = 2x+10-10-x = 2x-x = x.
provide evidence that this function is not one to one. explain how your evidence supports that g(x) is not one to one
we have the function
g(x)=(x/3)+2 ---------> interval (-infinite, 1)
g(x)=4x-2 ------> interval [1, infinite)
the given function is not one-to -one function, because don't pass the Horizontal Line Test.
Example
For the horizontal line
y=2
we have the values of
x=0 ---------> g(x)=(x/3)+2
and
x=1 -----------> g(x)=4x-2
that means
two elements in the domain of g(x) correspond to the same element in the range of g(x)
therefore
the function is not one to oneAdding mixed fractions (A)1 1/14 + 3 1/14 =
Explanation:
To add mixed fractions we have to follow these steps:
[tex]1\frac{1}{14}+3\frac{1}{14}=[/tex]1. Add the whole numbers together
[tex]1+3=4[/tex]2. Add the fractions
[tex]\frac{1}{14}+\frac{1}{14}=\frac{2}{14}=\frac{1}{7}[/tex]3. If the sum of the fractions is an improper fraction then we change it to a mixed number and add the whole part to the whole number we got in step 1.
In this case the sum of the fractions results in a proper fraction, so we can skip this step.
Answer:
The result is:
[tex]4\frac{1}{7}[/tex]
-1/2 (2/5y - 2) (1/10y-4)
we multiply the first parenthesis by its coefficient
[tex]\begin{gathered} ((-\frac{1}{2}\times\frac{2}{5}y)+(-\frac{1}{2}\times-2))(\frac{1}{10}y-4) \\ \\ (-\frac{2}{10}y+\frac{2}{2})(\frac{1}{10}y-4) \\ \\ (-\frac{1}{5}y+1)(\frac{1}{10}y-4) \end{gathered}[/tex]now multiply each value and add the solutions
[tex]\begin{gathered} (-\frac{1}{5}y\times\frac{1}{10}y)+(-\frac{1}{5}y\times-4)+(1\times\frac{1}{10}y)+(1\times-4) \\ \\ (-\frac{1}{50}y^2)+(\frac{4}{5}y)+(\frac{1}{10}y)+(-4) \\ \\ -\frac{1}{50}y^2+(\frac{4}{5}y+\frac{1}{10}y)-4 \\ \\ -\frac{1}{50}y^2+\frac{9}{10}y-4 \end{gathered}[/tex]Solve.(3.3 × 10³) (2 × 10²)
Here are the steps in multiplying scientific notations:
1. Multiply the coefficients first.
[tex]3.3\times2=6.6[/tex]2. Multiply the base 10 by adding their exponents.
[tex]10^3\times10^2=10^{3+2}=10^5[/tex]3. Connect the result in steps 1 and 2 by the symbol for multiplication.
[tex]6.6\times10^5[/tex]Hence, the result is 6.6 x 10⁵.
A biologist just discovered a new strain of bacteria that helps defend the human body against the flu virus. To know the dosage that should be given to someone, the doctor must first know if the bacteria can multiply fast enough to combat the virus. To find the rate at which the bacteria multiplies, she puts 10 cells in a petri dish. In an hour, she comes back to find that there are now 12 cells in the dish.
Part 3
An exponential growth function has the general form:
[tex]f(t)=a\cdot(1+r)^t[/tex]where r is the rate of growth, t is the time, and a is a constant. Notice that if calculate f(t) for t = 0, we have (1 + r)º = 1 (any number with exponent 0 equals 1). So, we obtain:
[tex]f(0)=a(1+r)^0=a\cdot1=a[/tex]Thus, the constant a is the initial value of the function.
Now, the rate at which a bacteria grows is exponential. So, the function C(h) is given by:
[tex]C(h)=C(0)\cdot(1+r)^h[/tex]Notice that we represented the time by the letter h instead of t.
Since C(0) = 10 and C(1) = 12, we can replace h by 1 to find:
[tex]\begin{gathered} C(1)=10\cdot(1+r)^1 \\ \\ 12=10+10r \\ \\ 12-10=10r \\ \\ 10r=2 \\ \\ r=0.2 \end{gathered}[/tex]Thus, the number of cells C(h) is given by:
[tex]C(h)=10\cdot(1.2)^h[/tex]Notice that this is valid for C(15) = 154:
[tex]C(15)=10\cdot(1.2)^{15}\cong154.07\cong154_{}[/tex]Part 1
Then, using this formula, we find:
[tex]\begin{gathered} C(2)=10(1.2)^2\cong14 \\ \\ C(3)=10(1.2)^3\cong17.3\cong17 \\ \\ C(4)=10(1.2)^4\cong20.7\cong21 \\ \\ C(5)=10(1.2)^5\cong24.9\cong25 \\ \\ C(6)=10(1.2)^6\cong29.9\cong30 \\ \\ C(7)=10(1.2)^7\cong35.8\cong36 \\ \\ C(8)=10(1.2)^8\cong43 \\ \\ C(9)=10(1.2)^9\cong51.6\cong52 \\ \\ C(10)=10(1.2)^{10}\cong61.9\cong62 \\ \\ C(11)=10(1.2)^{11}\cong74.3\cong74 \\ \\ C(12)=10(1.2)^{12}\cong89.2\cong89 \\ \\ C(13)=10(1.2)^{13}\cong107 \\ \\ C(14)=10(1.2)^{14}\cong128.4\cong128 \end{gathered}[/tex]Part 2
Now, plotting the points, rounded to the nearest whole cell, on the graph, we obtain:
Part 4
Using a calculator, we obtain the following graph of the function C(h):
Comparing the graph to the plot of the data, we see that they match.
Part 5
After a full day, it has passed 24 hours. So, we need to use h = 24 in the function C(h):
[tex]C(24)=10(1.2)^{24}\cong795[/tex]Therefore, the answer is 795 cells.
Count the unit squares, and Ind the surface area of the shape represented byeach net. One cube = 1 ft^2
The surface area of the figure is the sum of the area of the squares. Since they're all equal, is the amount of squares times the area of one square. We have a total of six squares, with a side length equal to 4 units. The area of a square is given by the product of its side length by itself, therefore, the total surface area of this figure is
[tex]6\cdot(4^2)=6(16)=96[/tex]The area of this figure is 96 ft².
Answer: 72 Square Meters sorry super late
Step-by-step explanation:
The number of bottles a machine fills is proportional to the number of minutes the machine operates. The machine
fills 250 bottles every 20 minutes. Create a graph that shows the number of bottles, y, the machine fills in a minutes.
To graph a line, select the line tool. Click on a point on the coordinate plane that lies on the line. Drag your mouse to
another point on the coordinate plane and a line will be drawn through the two points
It is to be noted that the correct graph is graph A. This is because it shows the coordinates (2, 25). See the explanation below.
What is the calculation justifying the above answer?It is information given is the rate of change of the linear relationship between the stated variable variables:
Number of Bottles; andTime.The ratio given is depicted as:
r = [250 bottles]/ [20 mintures]
r = 25/2 bottles per min
By inference, we know that our starting point coordinates (0,0), because zero bottles were filled at zero minutes.
Thus, we must use the point-slope form to arrive at the equation that exhibits or represents the relationship of the linear graph.
The point-slope form is given as:
y-y₁ = m(x-x₁)
Recall that our initial coordinates are (0, 0,) where x₁ = 0 and y₁ = 0. Hence
⇒ y - 0 = 25/2(x-0)
= y = 25x/2
Hence, if x = 2, then y must = 25
Proof: y = 25(2)/2
y = 50/2
y = 25.
Hence, using the principle of linear relationships, the first graph is the right answer, because it shows the points (2,25) which are part of the relation.
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When a projectile is launched at an initial height of H feet above the ground at an angle of theta with the horizontal and initial velocity is Vo feet per second. the path of the projectile...
Given,
The initial height of H feet.
The initial velocity of the object is Vo.
The equation of the path of projectile is,
[tex]y=h+x\text{ tan }\theta-\frac{x^2}{2V_0\cos ^2\theta}_{}\text{ }[/tex]This is the expression of the projectle path.
Hence, the path of the projectile object is y = h + xtan(theta) - x²/2V₀²cos²(theta)
an equation that shows that two ratios are equal is a(n)
An equation that shows that two ratios are equal is referred to as a true proportion.
What is an Equation?This refers to as a mathematical term which is used to show or depict that two expressions are equal and is usually indicated by the sign = .
In the case in which the equation shows that two ratios are equal is referred to as a true proportion and an example is:
10/5 = 4/2 which when expressed will give the same value which is 2 as the value which makes them equal and is thereby the reason why it was chosen as the correct choice.
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This probability distribution shows thetypical grade distribution for a Geometrycourse with 35 students.GradeEnter a decimal rounded to the nearest hundredth.Enter
Explanation:
The total number of students is
[tex]n(S)=35[/tex]Concept:
To figure out the probability that a student earns grade A,B or C
Will be calculated below as
[tex]P(A,BorC)=P(A)+P(B)+P(C)[/tex]The Probability of A is
[tex]P(A)=\frac{n(A)}{n(S)}=\frac{5}{35}[/tex]The probabaility of B is
[tex]P(B)=\frac{n(B)}{n(S)}=\frac{10}{35}[/tex]The probabaility of C is
[tex]P(B)=\frac{n(B)}{n(S)}=\frac{15}{35}[/tex]Hence,
By substituting the values in the concept, we will have
[tex]\begin{gathered} P(A,BorC)=P(A)+P(B)+P(C) \\ P(A,BorC)=\frac{5}{35}+\frac{10}{35}+\frac{15}{35}=\frac{30}{35} \\ P(A,BorC)=0.857 \\ P(A,BorC)\approx0.86(nearest\text{ }hundredth) \end{gathered}[/tex]Hence,
The final answer is
[tex]0.86[/tex]A 12 -inch ruler is closest in length to which one of the following Metric units of measure? 0.030 Kilometers30,000 millimeters30 centimeters30 meters
Inch is one of the units of measuring length.
Converting from inch to meters,
[tex]1inch=0.0254m[/tex]A 12-inch ruler converted to meters will be;
[tex]12\times0.0254=0.3048m[/tex]Converting the meter equivalent of the ruler into the sub-units of meters measurement,
[tex]\begin{gathered} 0.3048m \\ To\text{ kilometer} \\ 1000m=1\operatorname{km} \\ 0.3048m=\frac{0.3048}{1000}=0.0003048\operatorname{km} \\ \\ To\text{ millimeter} \\ 1m=1000\operatorname{mm} \\ 0.3048m=0.3048\times1000=304.8\operatorname{mm} \\ \\ \\ To\text{ centimeters} \\ \text{1m =100cm} \\ 0.3048m\text{ =0.3048}\times100=30.48\operatorname{cm} \\ \\ \\ To\text{ meters } \\ 12\text{ inch = 0.3048m} \end{gathered}[/tex]From the conversions of metric units of length above, the 12-inch ruler measures 30.48cm which is closest to 30cm
Therefore, the ruler is closest to 30 centimeters
CRITICAL THINKING Describe two different sequences of transformations in which the blue figure is the image of the red figi 1 1 2 B I y ET
1) rotation 90° clockwise over the origin and a reflection over the x-axis
2) rotation 90° counter clockwise over the origin and reflection over y-axis
find the value of x for which r parallels s. then find the measures of angles 1 and 2 measure angle 1= 80-2xmeasure angle 2= 93-3xthe value of x for which r parallels s is....measure of angle 1 is.....°measure of angle 2 is.....°
Since the lines r and s are parallel the angles 1 and 2 must be equal
write an equation
[tex]80-2x=93-3x[/tex]solve the equation for x
[tex]\begin{gathered} 80-2x=93-3x \\ -2x+3x=93-80 \\ x=13 \end{gathered}[/tex]the value for x in which r and s are parallel must be 14
measure of angle 1 and 2 must be 54°
A water tank holds 276 gallons but is leaking at a rate of 3 gallons per week. A second water tank holds414 gallons but is leaking at a rate of 5 gallons per week. After how many weeks will the amount of waterin the two tanks be the same?The amount of water in the two tanks will be the same inweeks.
In order to solve the problem we will first create equations to represent the volume of water on the gallons through the weeks. The output of the functions will be the volume of each and the entry will be the number of weeks passed.
For the first one:
[tex]\text{vol(week) = 276 -3}\cdot week[/tex]While on the second one:
[tex]\text{vol(week) = 414 -5}\cdot week[/tex]In order to calculate the number of weeks it'll take until they have the same volume of water we need to find the "week" which would make them equal. So we will equate both expressions and solve for that variable.
[tex]\begin{gathered} 276\text{ - 3}\cdot week\text{ = 414 - 5}\cdot week \\ 5\cdot\text{week - 3}\cdot week\text{ = 414 - 276} \\ 2\cdot\text{week = }138 \\ \text{week = }\frac{138}{2}\text{ = }69 \end{gathered}[/tex]It'll take 69 weeks for the tanks to have the same volume.
Help me please what is the probability of all the letters?
Given:
• Number of male who survived = 338
,• Number if female sho survived = 316
,• Number f children who survived = 57
,• Number of male who died = 1352
,• Number of female who died = 109
,• Number of children who died = 52
,• Total number of people = 2224
Let's solve for the following:
(a). Probability of the passenger that survived:
[tex]P(\text{survived)}=\frac{nu\text{mber who survived}}{total\text{ number if people }}=\frac{711}{2224}=0.320[/tex](b). Probability of the female.
We have:
[tex]P(\text{female)}=\frac{\text{ number of females}}{total\text{ number }}=\frac{425}{2224}=0.191[/tex](c). Probability the passenger was female or a child/
[tex]P(\text{female or child)}=\frac{425}{2224}+\frac{109}{2224}=\frac{425+109}{2224}=0.240[/tex](d). Probability that the passenger is female and survived:
[tex]P(femaleandsurvived)=\frac{316}{2224}=0.142[/tex](e). Probability the passenger is female and a child:
[tex]P(\text{female and child)=}\frac{425}{2224}\times\frac{109}{2224}=0.009[/tex](f). Probability the passenger is male or died.
[tex]P(male\text{ or died) = P(male) + }P(died)-P(male\text{ and died)}[/tex]Thus, we have:
[tex]P(\text{male or died)}=\frac{1690}{2224}+\frac{1513}{2224}-\frac{1352}{2224}=0.832[/tex](g). If a female passenger is selected, what is the probability that she survived.
[tex]P(\text{survived}|\text{female)}=\frac{316}{425}=0.744[/tex](h). If a child is slelected at random, what is the probability the child died.
[tex]P(died|\text{ child)=}\frac{52}{109}=0.477[/tex](i). What is the probability the passenger is survived given that the passenger is male.
[tex]=\frac{338}{1690}=0.2[/tex]ANSWER:
• (a). 0.320
,• (b). 0.191
,• (c). 0.240
,• (d). 0.142
,• (e). 0.009
,• (f). 0.832
,• (g) 0.744
,• (h). 0.477
,• (i) 0.2
A beach ball rolls off a cliff and onto the beach. The height, in feet, of the beach ball can be modeled by the function h(t)=64−16t2, where t represents time, in seconds.What is the average rate of change in the height, in feet per second, during the first 1.25 seconds that the beach ball is in the air?Enter your answer as a number, like this: 42
STEP - BY - STEP EXPLANATION
What to find?
The average rate of change in the height, in feet per second, during the first 1.25 seconds that the beach ball is in the air.
Given:
[tex]h(t)=64-16t^2[/tex]Step 1
Differentiate the heigh with reospect to t.
The rate of change of height is the differentiation of the height.
[tex]\frac{dh(t)}{dt}=-32t[/tex]Step 2
Substitute t= 1.25
[tex]h^{\prime}(t)=-32(1.25)[/tex][tex]=-40ft\text{ /s}[/tex]ANSWER
Average rate = -40 ft / s
pls help. i dont get it
Answer:
hey what don't u get? u didn't show the question
In the diagram, MN is parallel to KL. What is the length of MN? K M 24 cm 6 cm 2 12 cm L O A. 6 cm O B. 18 cm O c. 12 cm D. 8 cm
To solve this question, we shall be using the principle of similar triangles
Firstly, we identify the triamgles
These are JKL and JMN
JKL being the bigger and JMN being the smaller
Mathematically, when two triangles are similar, the ratio of two of their corresponding sides are equal
Thus, we have it that;
[tex]\begin{gathered} \frac{JN}{MN}\text{ = }\frac{JL}{KL} \\ \\ \frac{6}{MN}=\text{ }\frac{18}{24} \\ \\ MN\text{ = }\frac{24\times6}{18} \\ MN\text{ = 8 cm} \end{gathered}[/tex]