a) The fraction of all the meal combinations which have at least one vegan option is 1/8.
b) There are 168 different three-course meal combinations available.
What is a fraction?A fraction is a way of representing a part or a ratio of a whole, using a numerator and a denominator separated by a slash ("/") or a horizontal line. The numerator represents the number of parts being considered, and the denominator represents the total number of equal parts that make up the whole.
According to the given information:
a) To work out the fraction of all the meal combinations which have at least one vegan option, we need to count the total number of meal combinations with at least one vegan option, and then divide it by the total number of meal combinations.
The vegan options in the table are:
Mozzarella salad (V)
Cheese pizza (V)
Aubergine curry (V)
There are a total of 4 salads (including the vegan salads) and 6 mains (including the vegan mains). So the total number of meal combinations without any restriction is 4 x 6 = 24.
Now, we can calculate the total number of meal combinations without any vegan option, which is 24 - 3 = 21 (since 3 options are vegan).
So, the fraction of all the meal combinations which have at least one vegan option is (total meal combinations - meal combinations without any vegan option) divided by total meal combinations:
= (24 - 21) / 24
= 3 / 24
= 1 / 8
Therefore, the fraction of all the meal combinations which have at least one vegan option is 1/8.
b) If diners also choose one of 7 dessert options, we can simply multiply the total number of meal combinations (24) by the number of dessert options (7) to get the total number of three-course meal combinations available:
24 x 7 = 168
So, there are 168 different three-course meal combinations available.
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PLEASWWW HELP ITS VERY MUCH APPRECIATED!!
Well, a diameter is double the radius. The radius is given in the image.
So, 2+2 = 4
In this diagram, AT = 2x + 3, CT = 3x - 1, BT = x + 5,
DT = 4x + 1, and mLATD = 41x + 8. If x = 2,
which segment is the perpendicular bisector of the other? Explain your reasoning.
Answer:
CT is the perpendicular bisector of AB
Step-by-step explanation:
calculate the segments using x = 2
AT = 2x + 3 = 2(2) + 3 = 4 + 3 = 7
BT = x + 5 = 2 + 5 = 7
thus AT = BT
CT = 3x - 1 = 3(2) - 1 = 6 - 1 = 5
DT = 4x + 1 = 4(2) + 1 = 8 + 1 = 9
thus CT ≠ DT
∠ ATD = 41x + 8 = 41(2) + 8 = 82 + 8 = 90°
Thus CT is the perpendicular bisector of AB
What is the power of the hypothesis test, using the decision rule given above, if the population mean amount of mercury is 11.5 micrograms per ounce? Give your answer to 4 decimal places.
The true population mean amount of mercury is actually 12 micrograms per ounce (which is a difference of 0.5 from the null hypothesis value of 11.5), then the test has a 76.29% chance of correctly rejecting the null hypothesis and concluding that the mean amount of mercury is different from 11.5 micrograms per ounce.
In hypothesis testing, the power of a test refers to the probability of correctly rejecting a false null hypothesis.
To calculate the power of a test, we need to know the significance level of the test, the sample size, the effect size, and the variance of the population.
Additionally, we need to know the specific hypothesis being tested, as the decision rule and power calculation depend on the null and alternative hypotheses.
A hypothesis test for the population mean amount of mercury in a certain type of fish.
Test whether the mean amount of mercury is different from 11.5 micrograms per ounce, using a two-tailed test at a significance level of 0.05.
If the sample size is 100, the effect size is 0.5, and the population variance is 4, then the power of the test is approximately 0.7629.
This means that if the true population mean amount of mercury is actually 12 micrograms per ounce (which is a difference of 0.5 from the null hypothesis value of 11.5), then the test has a 76.29% chance of correctly rejecting the null hypothesis and concluding that the mean amount of mercury is different from 11.5 micrograms per ounce.
The hypothesis test, it is impossible to calculate the power.
It is essential to know the specific hypothesis being tested, as well as the details of the test, such as the sample size, effect size, and variance.
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A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the number of cookies the college will need?
The college will have about 480 students who prefer cookies.
The college will have about 640 students who prefer cookies.
The college will have about 1,280 students who prefer cookies.
The college will have about 1,440 students who prefer cookies.
The best prediction is that the college will have about 480 students who prefer cookies.
To solve this problem
According to the table, 27 out of 225 students prefer cookies. To find the prediction for the number of cookies the college will need, we can set up a proportion:
27/225 = x/4000
Where x is the predicted number of students who prefer cookies.
Solving for x, we get:
x = (27/225) * 4000
x ≈ 480
Therefore, the best prediction is that the college will have about 480 students who prefer cookies.
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Find the direction angle of w=8j.
Round your answer to the nearest tenth of a degree
the direction angle of w=8j is 90.0 degrees. The direction angle of a complex number is the angle between the positive real axis and the vector representing the complex number in the complex plane.
what is direction angle ?
The direction angle, also known as the argument or phase angle, of a complex number is the angle between the positive real axis and the vector representing the complex number in the complex plane.
In the given question,
The direction angle of a complex number is the angle between the positive real axis and the vector representing the complex number in the complex plane.
In this case, the complex number is w=8j, which has an imaginary part of 8 and a real part of 0. Therefore, the vector representing w points directly upwards in the complex plane, and the angle between this vector and the positive real axis is 90 degrees.
Rounding this to the nearest tenth of a degree gives 90.0 degrees.
So the direction angle of w=8j is 90.0 degrees.
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you are given a 100-meter-long rope, and you need to measure a length of 10 meters without any measuring devices. you can only fold or manipulate the rope, but you cannot cut or mark it. how can you measure 10 meters accurately?
To measure a length of 10 meters without any measuring devices from 100 meters rope is fold the rope ten times and 10th fold of 100 m rope is equals to 10 m.
Total Length of rope = 100 meters
We need to measure a length of 10 meters without using any measuring devices. The ways that we can use to measure the required length includes only fold or manipulate the rope, but you cannot cut or mark it. Now, we use the division arithmetic operation to measure the length. The factors of 100 is written as 100 = 2×2× 5×5 = 10× 10
If we divide 100 by 10 then results 10 as quotient and 0 as remainder. So, the rope with length 100 meters is divided into 10 parts of 10 meters length of rope. But we cannot cut the rope, so folds the rope ten times ( i.e, first half -half then again half into half-half). Therefore, the last fold is measure of length 10 meters.
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research conducted a few years ago showed that 12% of uw-platteville students had traveled outside the us. uw-platteville has recently implemented a new study abroad program and results of a new survey show that out of the 100 randomly sampled students 35 have traveled abroad. to know if the proportion of students at uw-platteville who have traveled abroad has increased after the implementation of the study abroad program, what is the appropriate null and alternative hypothesis?
The null hypothesis is that the proportion of students who have traveled abroad is still 12%, while the alternative hypothesis is that the proportion has increased and is now greater than 12%.
The appropriate null hypothesis is that the proportion of students at UW-Platteville who have traveled abroad remains the same as before the implementation of the study abroad program. The alternative hypothesis is that the proportion of students who have traveled abroad has increased after the implementation of the program.
Mathematically:
H0: p = 0.12
Ha: p > 0.12
where p is the true proportion of students at UW-Platteville who have traveled abroad.
To test this hypothesis, we can use a one-tailed z-test for proportions. Using the given sample information, we can calculate the test statistic as:
z = (0.35 - 0.12) / sqrt((0.12 * 0.88) / 100) = 3.87
where 0.88 is the complement of 0.12, and sqrt denotes the square root. The critical value for a one-tailed test at the 0.05 level of significance is 1.645.
Since the test statistic (3.87) is greater than the critical value (1.645), we reject the null hypothesis and conclude that there is sufficient evidence at the 0.05 level to support the claim that the proportion of students who have traveled abroad has increased after the implementation of the study abroad program.
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the length of a rectangle is 3 feet less than 4 times the width. if the perimeter is 84 feet, find the length and the width of the rectangle.
length: 33, width: 9
write it out as 4x-3(2) + 2x. simplify that and you gey 84= 10x-6. add the 6 over and you get x=9, this is your width. know you just do 4(9) - 3 to find length, which equals 33
I'm confused I need to solve for "C" but I can't figure this out
Answer:
c = 56°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
120° is an exterior angle of the triangle , then
c + 64° = 120° ( subtract 64° from both sides )
c = 56°
If c is the number that satisfies the conclusion of the Mean Value Theorem for f(x)= x^3 - 2x^2 on the interval 0â¤xâ¤2, then c=a) 0b) 1/2c) 1d) 4/3
This means that c must be 1/2, since it is the only value in the interval (0,2) where f'(c) = -1/2, which satisfies the equation given by the Mean Value Theorem.
To apply the Mean Value Theorem, we need to check if f(x) is continuous on [0,2] and differentiable on (0,2).
[tex]f(x) = x^3 - 2x^2[/tex] is a polynomial function, so it is continuous and differentiable everywhere.
Now, we can use the Mean Value Theorem, which states that there exists a number c in (0,2) such that:
[tex]f'(c) = (f(2) - f(0))/(2-0)[/tex]
First, let's find f'(x):
[tex]f'(x) = 3x^2 - 4x[/tex]
Now, we can solve for c:
f'(c) = 3c^2 - 4c
f(2) = 2^3 - 2(2^2) = -4
f(0) = 0^3 - 2(0^2) = 0
(f(2) - f(0))/(2-0) = -4/2 = -2
So, we need to solve the equation 3c^2 - 4c = -2 for c.
Rearranging, we get:
3c^2 - 4c + 2 = 0
Using the quadratic formula, we get:
c = (4 ± sqrt(16 - 24))/6
c = (4 ± 2i)/6
Since the interval is [0,2], we only need to consider real solutions.
[tex]f'(c) = 3c^2 - 4c\\f(2) = 2^3 - 2(2^2) = -4\\f(0) = 0^3 - 2(0^2) = 0\\(f(2) - f(0))/(2-0) = -4/2 = -2\\[/tex]
Therefore, c = 4/3 is not a valid solution.
To choose between the remaining options, we can test if f'(c) is positive or negative.
For c = 0, f'(0) = 0 - 0 = 0.
For [tex]c = 1/2, f'(1/2) = 3(1/2)^2 - 4(1/2) = -1/2.[/tex]
For[tex]c = 1, f'(1) = 3(1)^2 - 4(1) = -1.[/tex]
Therefore, f'(c) is negative on the interval [0,1/2] and positive on the interval [1/2,2].
This means that c must be 1/2, since it is the only value in the interval (0,2) where f'(c) = -1/2, which satisfies the equation given by the Mean Value Theorem.
Therefore, the answer is (b) 1/2.
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Checks: $152.54 and $147.46: cash: 54 one-dollar bills, 12 five-dollar bills, and 6 ten -dollar bills; less $20.00 as cash received.
If cash is 54 one-dollar bills, 12 five-dollar bills, and 6 ten -dollar bills, the total deposit is $454.00.
To find the total deposit, we need to add up the amounts from the checks and cash, and then subtract the cash received.
First, let's add up the amounts from the checks:
$152.54 + $147.46 = $300.00
Next, let's add up the amounts from the cash:
54 one-dollar bills = $54.00
12 five-dollar bills = $60.00
6 ten-dollar bills = $60.00
Total cash = $174.00
Finally, we need to subtract the cash received:
$174.00 - $20.00 = $154.00
Therefore, the total deposit is $300.00 + $154.00 = $454.00.
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Complete question is:
Find the total deposit if you have: Checks: $152.54 and $147.46: cash: 54 one-dollar bills, 12 five-dollar bills, and 6 ten -dollar bills; less $20.00 as cash received.
What is one subtracted by 3/7
Answer:
4/7
Step-by-step explanation:
1-3/7
7/7 -3/7
4/7
Minimum Target Heart Rates by Age
Which function best models the data
in the table?
Age x
(year)
Minimum Target
Heart Rate y
(beats/min)
114
o y=-0. 6x +132
* v - 3420
U
=
30
35
111
y=(x-30 +114
- 19,30x
40
108
45
105
102
RETRY
50
Q00000ODODD
5 of 10
The function best models the data in the table is y=-0.6x+132 (option a).
The table shows the minimum target heart rates by age, which implies that as a person ages, their heart rate should be maintained within a certain range during exercise to achieve optimal cardiovascular benefits. In order to determine the target heart rate for a given age, we need a mathematical function that can accurately model the data in the table.
This is a linear function, which means that it assumes a constant rate of change in the target heart rate as age increases.
However, the data in the table shows that the target heart rate decreases gradually with age. Therefore, this function does accurately model the data and is a suitable option.
Hence (a) is the right one.
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Complete Question:
Age x (year) Minimum Target Heart Rates by Age
30 114
35 111
40 108
45 105
50 102
Which function best models the data in the table?
a) y=-0.6x+132
b) y=(x-30)²+114
c) y= 19/30x
the population of a town is 1,800 and is decreasing at a rate of 3.8% per year what will their population be after 6 years
Step-by-step explanation:
DECREASING 3.8% means 96.2 % is left each year ( .962 in decimal)
1800 (.962) ^6 =~ 1427 population
Answer:
1389.6
explamation
1500 of 3.8% is 68.4
68.4*6=410.4
1800-410.4=139.6
determine if the following is a supervised or unsupervised model. a local restaurant sends a 20% off coupon to its email subscribers. based on past data, what area around the restaurant contains the customers that spend the most when using the coupon?
The model of local restaurant which sends a 20% off coupon to its email subscribers, based on past data is an example of supervised model.
Supervised model is defined by its use of labeled datasets to train algorithms based on classification of data or predict outcomes accurately. While the accuracy of supervised learning models is more than unsupervised learning models. Supervised, as we are using past data. Classification, as we are trying to classify the customers into categories to study which ones will use the coupons. We have a local restaurant which send
a 20% off on a coupon to its email subscribers. It is based on past data. Using the above definition the predicted model for the provide example is supervised model.
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A packet of chips cost $9.99 if the price decreases by 12% what will the new price be
If the price of the packet of chips decreases by 12%, the new price will be:
New price = $9.99 - (12/100) x $9.99
New price = $9.99 - $1.199
New price = $8.791
Therefore, the new price of the packet of chips will be $8.791.
Help would be much appreciated
The statement that is not necessarily correct is ΔTRS ≅ ΔVUW. So, correct option is D.
The given information states that two triangles are congruent based on the corresponding parts, RS ≅ UV, RT ≅ UW and ∠R ≅ ∠U.
To determine which statement is not necessarily correct, we need to use the congruence criteria that are sufficient to prove the congruence of triangles. These criteria are:
SSS (Side-Side-Side): If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
SAS (Side-Angle-Side): If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
ASA (Angle-Side-Angle): If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
AAS (Angle-Angle-Side): If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.
Using the given information, we can apply the SAS criterion to show that ΔRST ≅ ΔUVW. This is because we know that RS ≅ UV, RT ≅ UW, and ∠R ≅ ∠U. Therefore, the statement (a) ΔRST ≅ ΔUVW is correct.
Now, we can use the SAS criterion again to show that ΔSTR ≅ ΔVWU. This is because we know that RS ≅ UV, RT ≅ UW, and ∠R ≅ ∠U. Therefore, the statement (b) ΔSTR ≅ ΔVWU is also correct.
We can also use the SAS criterion to show that ΔTRS ≅ ΔVWU. This is because we know that RS ≅ UV, RT ≅ UW, and ∠R ≅ ∠U. Therefore, the statement (c) ΔTRS ≅ ΔVWU is correct.
However, we cannot use any of the above criteria to show that ΔTRS ≅ ΔVUW. This is because we do not know that TU ≅ VW. Therefore, the statement (d) ΔTRS ≅ ΔVUW is not necessarily correct.
So, correct option is D.
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what is the missing number. Good points
Answer:
Which number is missing?
40 38 35 31 26 20 13 5
Pattern: ( -2, -3, -4, etc)
40 - 2 = 38
38 - 3 = 35
35 - 4 = 31
31 - 5 = 26
26 - 6 = 20
20 - 7 = 13
13 - 8 = 5
Step-by-step explanation:
You're welcome.
Determine the solutions to the equation x^2 = 4x + 41.
Answer:
The solutions to the equation x^2 = 4x + 41 are x = 2 + 2sqrt(11) and x = 2 - 2sqrt(11).
Step-by-step explanation:
To solve the equation x^2 = 4x + 41, we can first rearrange it as x^2 - 4x - 41 = 0.
Next, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = -4, and c = -41.
Substituting these values into the formula, we get:
x = (4 ± sqrt((-4)^2 - 4(1)(-41))) / 2(1)
Simplifying:
x = (4 ± sqrt(176)) / 2
x = (4 ± 4sqrt(11)) / 2
x = 2 ± 2sqrt(11)
Therefore, the solutions to the equation x^2 = 4x + 41 are x = 2 + 2sqrt(11) and x = 2 - 2sqrt(11).
1. Calculate the area of the following parallelogram:
28 in²
26 in²
40 in²
30 in
The area of the parallelogram shown in the figure is 30 in². Option D is correct.
The area of the parallelogram is given by the following formula,
Area = base * height,
From the figure we have base = 10 in and height = 3 in
So area can be given as,
Area = 10 * 3
Area = 30 in²
Thus, the area of the parallelogram shown in the figure is 30 in².
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please answer correctly
The line plot displays the cost of used books in dollars.
A horizontal line starting at 1 with tick marks every one unit up to 9. The line is labeled Cost in Dollars, and the graph is titled Cost of Used Books. There is one dot above 2, 4, 8, and 9.There are two dots above 6 and 7. There are three dots above 3.
Which measure of center is most appropriate to represent the data in the graph, and why?
The mean is the best measure of center because there are no outliers present.
The mean is the best measure of center because there are outliers present.
The median is the best measure of center because there are no outliers present.
The median is the best measure of center because there are outliers present.
The correct statement regarding the best measure of center for the data-set in this problem is given as follows:
The mean is the best measure of center because there are no outliers present.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.
The dot plot shows the number of times that each observation appears, hence the data-set is given as follows:
2, 3, 3, 3, 4, 6, 6, 7, 7, 8, 9.
We can see that the data-set is clustered, meaning that there are no outliers, hence the mean can be used instead of the median.
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Answer step by step due tmrw
The interior angles measure 160° and the exterior measure 200°
How to find the angles?The sum of the interior angles of a polygon of n sides is:
(n - 2)*180
here n = 18
(18 - 2)*180 = 2880
divide that by the number of sides
2880/18 = 160°
That is the measure of each interior angle, and the exteriors are such that the sum is 360, then:
a + 160 = 360
a = 360 - 160 = 200
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1. Suppose that angle AOC, a central angle of a circle, and angle ABC, an inscribed angle of the same circle, intercept the same arc. Circle the correct word(s) in the sentence. The measure of angle AOC is [half | equal to | double] the measure of angle ABC.
Answer:
The measure of angle AOC is double the measure of angle ABC.
Step-by-step explanation:
You want to know the relationship between central angle AOC in circle O and inscribed angle ABC subtending the same arc AC.
Inscribed angleThe measure of an inscribed angle is half the measure of the arc it intercepts. The measure of a central angle is exactly equal to the measure of the arc it intercepts. (That's how the arc measure is determined.)
Hence, the measure of angle AOC is double the measure of angle ABC.
__
Additional comment
Inscribed : central = 1 : 2
Central : inscribed = 2 : 1
You need to be a little careful of the wording of the relationship. Which is double and which is half can be confused when it's written in words. On a diagram, the angle with its vertex in the center will obviously be larger than the one with its vertex on the circle.
9. A solid iron rectangular block of dimensions 3.5 meters, 2.4 meters, and 2 meters is cast into a hollow cylindrical pipe of internal radius 27 centimeters and thickness 4 centimeters. Find the length of the pipe.
Therefore, The length of the hollow cylindrical pipe is approximately 55.48 meters.
To solve this problem, we will first find the volume of the solid iron rectangular block and then use it to find the length of the hollow cylindrical pipe. Here are the steps:
1. Find the volume of the rectangular block:
Volume = Length × Width × Height
Volume = 3.5m × 2.4m × 2m = 16.8 m³
2. Convert the internal radius and thickness to meters:
Internal radius = 27 cm = 0.27 m
Thickness = 4 cm = 0.04 m
3. Calculate the external radius of the pipe:
External radius = Internal radius + Thickness
External radius = 0.27m + 0.04m = 0.31m
4. Let L be the length of the pipe. We can write the volume of the hollow pipe as:
Volume = π × (External radius² - Internal radius²) × Length
16.8 m³ = π × (0.31² - 0.27²) × L
5. Solve for L:
L = 16.8 m³ / [π × (0.31² - 0.27²)]
L ≈ 55.48 meters
Therefore, The length of the hollow cylindrical pipe is approximately 55.48 meters.
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7x-y=2. -21x-3y=5 por metodo de reduccion
The solution to the system of equations is:
x = -1/42
y = -11/6
What you understand by variables?In mathematics, a variable is a symbol that represents a value that can vary or change. It is often represented by a letter, such as x, y, or z. Variables are used to write algebraic expressions and equations that can be solved to find unknown quantities. The value of a variable can be determined by solving an equation that involves the variable, or by assigning a specific value to the variable. In algebra,
To solve this system of equations by the method of elimination, we need to eliminate one of the variables by adding the two equations together. We can do this by multiplying the first equation by 3, which will make the y terms cancel out when we add the equations:
7x - y = 2 (multiply by 3)
-21x - 3y = 5
21x - 3y = 6 (first equation multiplied by 3)
-21x - 3y = 5
Now we can add the two equations together:
(21x - 3y) + (-21x - 3y) = 6 + 5
0x - 6y = 11
Simplifying, we get:
-6y = 11
Dividing both sides by -6, we get:
y = -11/6
Now that we have solved for y, we can substitute this value back into either equation to solve for x. Let's use the first equation:
7x - y = 2
7x - (-11/6) = 2
Multiplying both sides by 6 to eliminate the fraction, we get:
42x + 11 = 12
Subtracting 11 from both sides, we get:
42x = -1
Dividing both sides by 42, we get:
x = -1/42
Therefore, the solution to the system of equations is:
x = -1/42
y = -11/6
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The ratio of girl to boys in mr Day class is 3 to 5 . If there is 15 boys in mr Day class how many more boyz are there then girls
Answer:
If there are 15 boys in Mr. Day’s class and the girl to boy ratio is 3 to 5, then there are 9 girls in Mr. Day’s class. To find out how many more boys there are than girls, you can subtract the number of girls from the number of boys:
15 boys - 9 girls = 6 more boys than girls.
Step-by-step explanation:
!!CAN SOMEONE CHECK IF IM CORRECT PLEASEEE!!
The amount that the Jones family would pay in the 18th month would be $1,233.45
How to find the amount ?Prior to determining the required payment for the 18th month, it is paramount to calculate the collective minimum payments by the Jones family during the course of seventeen months.
First, find the amount that had been paid in total by the Jones in 17 months to be :
= Monthly payment x minimum monthly payment
= 17 x 25
= $ 425
The balance after 17 months is :
= $ 1 , 658. 45 - $ 425
= $ 1, 233. 45
The remaining balance of $ 1, 233. 45 would have to be paid in the 18th month.
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Which angle is supplemental to angle 6?
Select one:
a.
Angle 8
b.
Angle 2
c.
Angle 7
d.
Angle 3
Supplementary angles are angles that add up to 180°. Angle 6 is a right angle, so it's worth 90°. This means that the other angle(s) have to be 90° as well.
As you can see, the other angle with 90° is angle 3, thus, making it the correct answer.
Kylie brought 5 pears to soccer practice to share with her teammates. She cuts each pear into thirds. How many slices of pears does she have to share with her teammates? Which equations can you use to solve the problem? Select two equations. A. 5 × 3 = 15 B. 1 5 × 1 3 = 1 15 C. 1 5 × 3 = 3 5 D. 5 ÷ 1 3 = 15 E. 1 3 ÷ 5 = 1 15 answer quick please
Answer:
Eqation a and 15
Step-by-step explanation:
because 5 pears all cut into thirds is 15 slices 5 times 3 is 15
solve for x
khan academy solve similar triangles advanced
Value of side CD = x=3
What is similarity of two triangle ?When two triangles are are referred to as similar figures when they share the same shape but different in size.
given that CB and ED are perpendicular to AD,
in triangle ABC and ADE
∠A=∠A (common angle )
∠B=∠D (both are 90 degree)
ΔABC≈ ΔADE by angle-angle similarity .
and we know that when two triangle are similar then their corresponding sides are with in the same ratio or proportional.
so ,here we proved that triangle ABC and ADE are similar,
then ,
[tex]\frac{BC}{ED}=\frac{AB}{AD}[/tex]
[tex]\frac{x}{5}=\frac{9}{9+6}[/tex]
[tex]\frac{x}{5} =\frac{9}{15}\\ X=3[/tex]
x=3
from above result ,value of side CB =x=3
know more about similarity visit :
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