Answer:
x = 45°
Step-by-step explanation:
Since a triangle has a total of 180°, we can make an equation and add all 3 of these angles together:
30° + (2x +10)°+ 50° = 180°
30° + 10° + 50° + 2x = 180°
90° + 2x = 180°
2x = 180° - 90°
2x = 90° / : 2
x = 45°
I WILL MARK BRAINLIST IF CORRECT !!
Explain why opening a parachute can slow a skydiver down to a safe landing speed. You can add drawings to aid your explanation
Answer:
There is no air resistance acting in the upwards direction, and there is a resultant force acting downwards. ... There is no resultant force and the skydiver reaches terminal velocity. When the parachute opens, the air resistance increases. The skydiver slows down until a new, lower terminal velocity is reached.
Step-by-step explanation:
find the area if each figure. round the nearest hundredth where neccessary.
Answer:
351.48cm²
Step-by-step explanation:
Heron’s Formula
Find half the perimeter (30+30+26)/2=43
It’s the square root of each side subtracted from 43, multiplied together, times 43.
√(43-30)*(43-30)*(43-26)*43=√13*13*17*43=√=123539=351.481cm²
Area of triangle is, 351. 39 cm²
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
We have to given that;
All the sides of triangles are,
⇒ 30 cm, 30 cm, and 26 cm
We know that;
⇒ Area of triangle = √ s (s - a) (s - b) (s - c)
Where, 's' is the semi perimeter of the triangle, and a, b and c are three sides of triangle.
Here, Sides are,
⇒ a = 30
⇒ b = 30
⇒ c = 26
Hence, We get;
⇒ s = (a + b + c) / 2
⇒ s = (30 + 30 + 26) / 2
⇒ s = 86 / 2
⇒ s = 43 cm
So, The area of triangle is,
⇒ Area of triangle = √ s (s - a) (s - b) (s - c)
⇒ Area of triangle = √ 43 (43 - 30) (43 - 30) (43 - 26)
⇒ Area of triangle = √ 43 × 13 × 13 × 17
⇒ Area of triangle = 13 √ 731
⇒ Area of triangle = 13 × 27.03
⇒ Area of triangle = 351. 39 cm²
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The box plots show the average speeds, in miles per hour, for the race cars in two different races. average speeds of cars in race a 2 box plots. the number line goes from 120 to 170. for race a, the whiskers range from 120 to 170, and the box ranges from 143 to 165. a line divides the box at 153. for race b, the whiskers range from 125 to 165, and the box ranges from 140 to 150. a line divides the box at 145. average speeds of cars in race b which correctly describes the consistency of the speeds of the cars in the two races? the speeds in race a are likely to be near 170 mph and the speeds in race b are likely to be near to 165 mph. the speeds in race a are likely to be near 153 mph and the speeds in race b are likely to be near to 145 mph. the speeds in race a are likely to be near 120 mph and the speeds in race b are likely to be near to 125 mph. the speeds in race a are likely to be near 145 mph and the speeds in race b are likely to be near to 153 mph.
"The speeds in race a are likely to be near 145 mph and the speeds in race b are likely to be near to 153 mph" correctly describes the consistency of the speeds of the cars in the two races.
Based on the given information, the box plot for race A has a larger range of speeds (from 120 to 170 mph) compared to the range of speeds in race B (from 125 to 165 mph). The box plot for race A also has a larger interquartile range (from 143 to 165 mph) compared to the interquartile range in race B (from 140 to 150 mph). However, the median speed in race A (153 mph) is lower than the median speed in race B (145 mph).
Therefore, it is not accurate to say that the speeds in race A are likely to be near 170 mph and the speeds in race B are likely to be near 165 mph. Likewise, it is not accurate to say that the speeds in race A are likely to be near 120 mph and the speeds in race B are likely to be near 125 mph.
The correct answer is that the speeds in race A are likely to be near 145 mph and the speeds in race B are likely to be near 153 mph. This is because the medians of the two box plots are relatively close to each other, and the box plot for race B has a smaller range and interquartile range, indicating greater consistency in the speeds of the cars in that race compared to race A.
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A ________ exploit is an attack program that is created before patches are available from the vendor.
A zero-day exploit is an attack program that is created before patches or fixes are available from the software vendor.
It refers to a vulnerability or weakness in software that is unknown to the vendor or the general public. This means that the exploit takes advantage of a security flaw that has not yet been discovered or addressed by the software developer.
The term "zero-day" signifies that developers have had zero days to fix or patch the vulnerability. Zero-day exploits are particularly dangerous because they can be deployed by hackers to target systems before any defensive measures are in place, making them highly effective and difficult to defend against.
Therefore, a "zero-day" exploit is an attack program that is created before patches or fixes are available from the software vendor.
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Please help me answer this for a test im having trouble
Answer:
x + 1
y = 9
Step-by-step explanation:
In order to solve this question we need to represent "y "in terms of "x" in the first equation, and the plug in the "y" value in the first equation into the second one. Luckily for us in the first equation it already shows what "y" is equal to in terms of "x" (based on the first equation y = -x + 10). Now we just need to plug in the value that we got instead of "y" in the second equation, and so we get....
y = 7x + 2
(plug in the y value and get the following ….)
-x + 10 = 7x + 2
(now just solve the following equation)
-x + 10 + x = 7x + 2 + x
10 = 8x + 2
10 - 2 = 8x + 2 - 2
8 = 8x
8/8 = 8x/8
1 = x
Now that we know the value of "x", all we need to do now is substitute the value of "x" into any of the equations and we will get the value of "y". So we do the following.....
y = 7x + 2
y = 7(1) + 2
y = 7 + 2
y = 9
* if my savings of $x grows 10% each year how much money would i have in 1 year
I WILL MARK BRAINLIEST
Answer:
10/100*$x
Step-by-step explanation:
You will multiply the $x by 10%
Describe the shape of the distribution.
A. It is symmetric.
B. It is uniform.
C. It is bimodal.
D. It is skewed.
Simplify the expression below.
Use the up-carrot (^) for the exponent.
r6
_
r2
\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{r^6}{r^2}\implies r^6\cdot r^{-2}\implies r^{6-2}\implies r^4\)
At the beginning of the year, John had $40 in savings and saved an additional $13 each week thereafter. Isaac started the year with $80 and saved $9 every week. Let 'J' represent the amount of money John has saved tt weeks after the beginning of the year and let 'I' represent the amount of money Isaac has saved tt weeks after the beginning of the year. Write an equation for each situation, in terms of t, and determine the number of weeks after the beginning of the year until John and Isaac have the same amount of money saved.
Answer:
10 weeks
Step-by-step explanation:
Let’s replace ‘t’ with numbers going up starting from 0 on both sides of the equation. Repeat until you get to 10 and you see that both are equal at $170 has been saved after 10 weeks.
John’s equation: 40 (y intercept) + 13t (saved per week)
Issac’s: 80 (y intercept) + 9t (amount saved per week)
The y-intercept represents the amount of money already saved up.
which is the best measure of center for third period, and why? interquartile range, because there is 1 outlier that affects the center standard deviation, because there are no outliers that affect the center mean, because there are no outliers that affect the center median, because there is 1 outlier that affects the center
Mean, because there are no outliers that affect the center
third period: 3,2,3,1,3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2
Sorted values : 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4
The mean = ΣX / n
n = sample size, n = 15
Mean = 34 / 15 = 2.666
The median = 1/2(n+1)th term.
1/2(16)th term = 8th term.
The 8th term = 2
The best measure of centre is the mean because the values for the second period has no outliers that might have affected the centre of the distribution.
Both interquartile range and standard deviation are measures of spread and not measures of centre.
complete question
A survey was taken of students in math classes to find out how many hours per day students spend
on social media. The survey results for the first., second-, and third-period classes are as follows:
First period: 2,4,3,1,0, 2, 1, 3, 1,4,9,2,4,3,0
Second period: 3,2,3,1,3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2
Third period: 4,5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1, 0, 2, 1,3
Which is the best measure of center for second period and why? (5 points)
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What is meant by the term ‘net
realisable value’? Is this the same as fair value? If not, why
not?
Net realizable value (NRV) is a term used in accounting to represent the estimated selling price of an asset minus the estimated costs of completing and disposing of the asset.
It is a conservative estimate of the asset's value and takes into account any anticipated costs or losses. NRV is not the same as fair value because fair value represents the price at which an asset could be exchanged between knowledgeable and willing parties in an arm's length transaction.
Net realizable value (NRV) is a concept used in accounting to determine the value of assets, particularly inventory or accounts receivable. It represents the estimated amount of cash the company expects to receive from the sale of an asset after deducting any direct costs associated with its sale.
These costs may include selling expenses, distribution costs, or any other costs incurred to make the asset ready for sale. NRV is a conservative estimate that reflects the expected realizable value of an asset in the current market conditions.
On the other hand, fair value represents the price at which an asset could be exchanged between knowledgeable and willing parties in an arm's length transaction.
Fair value considers market conditions, supply and demand factors, and other relevant information to determine the value of an asset. It does not take into account any specific costs associated with selling or disposing of the asset.
While net realizable value and fair value may share some similarities in terms of estimating the value of assets, they are not the same. NRV focuses on the estimated proceeds after deducting direct costs, while fair value considers the value in a hypothetical transaction between knowledgeable parties.
Therefore, the two concepts can provide different values for the same asset depending on the specific circumstances and considerations involved in their calculation.
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find the curvature of the curve → r ( t ) = ⟨ 2 t , 4 t 4 , − 4 t 2 ⟩ at the point t = 2 . give your answer to 2 decimal places.
The curvature at the point t = 2 is 1.4769
How to find the curvature?We want to find the curvature of the curve:
r(t) = (2t, 4t⁴, -4t²) at the point t = 2.
To find the curvature of a curve at a specific point, we need to follow these steps:
Calculate the first derivative of the curve, which gives the tangent vector.Calculate the second derivative of the curve, which gives the principal normal vector.Compute the cross product of the tangent vector and the principal normal vector to obtain the binormal vector.Find the magnitude of the second derivative vector to determine the curvature at the given point.Let's calculate the curvature of the curve r(t) = (2t, 4t⁴, -4t²) at t = 2.
Step 1: Calculate the tangent vector (T)
Differentiating each component of the curve with respect to t:
r'(t) = (2, 16t³, -8t)
Substituting t = 2:
r'(2) = (2, 16(2)³, -8(2))
= (2, 128, -16)
So, the tangent vector (T) at t = 2 is T = (2, 128, -16).
Step 2: Calculate the principal normal vector (N)
Differentiating the tangent vector with respect to t:
T'(t) = (0, 48t², -8)
Substituting t = 2:
T'(2) = (0, 48(2)², -8)
= (0, 192, -8)
So, the principal normal vector (N) at t = 2 is N = (0, 192, -8).
Step 3: Calculate the binormal vector (B)
To find the binormal vector, we take the cross product of the tangent vector and the principal normal vector:
B = T x N
B = (2, 128, -16) x (0, 192, -8)
B = (128(-8), -16(0) - (2)(-8), (2)(192) - (128)(0))
= (-1024, 16, 384)
So, the binormal vector (B) at t = 2 is B = (-1024, 16, 384).
Step 4: Calculate the curvature (κ)
The curvature (κ) is given by the formula:
κ = |T'| / |r'|
To find |T'|, we calculate the magnitude of the second derivative vector:
|T'| = |(0, 192, -8)| = √(0² + 192² + (-8)²) = √(36864) = 192
To find |r'|, we calculate the magnitude of the first derivative vector:
|r'| = |(2, 128, -16)| = √(2² + 128² + (-16)²) = √(16900) = 130
Finally, we can compute the curvature (κ) at t = 2:
κ = |T'| / |r'| = 192 / 130 = 1.4769
Therefore, the curvature of the curve r(t) = (2t, 4t⁴, -4t²) at t = 2 is approximately 1.4769.
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i need help figuring out if these are a Function or Not a Function (if someone can also leave an explanation cause I rly don't understand any of this)
Brenda won 59 lollipops playing hoops at
the county fair. At school she gave two to
every student in her math class. She only
has 1 remaining. How many students are
in her class?
Write an equation for the proportional relationship. Can you compare these two tables?
Answer:
Y=1.88x
Step-by-step explanation:
x1=2 x2=3, y1=3.76 y2=5.64
(2, 3.76) (3, 5.64)
m(slope) =5.64-3.76/3-2
m=1.88
y-3.76=1.88(x-2)
y-3.76=1.88x-3.76
Y=1.88x
An ocicat eats $\frac 35$ of a pound of food daily. How many ocicats can a $19\frac 12$-pound bag of food feed for one week? Explain your solution.
Answer:
\(4\dfrac{9}{14}$ ocicats\)
Step-by-step explanation:
One ocicat eats \(\dfrac35\) of a pound of food daily.
In a week, one ocicat eats: \(\dfrac35 \times 7 =4\dfrac15 $ pounds\)
Therefore, the number of ocicat that can eat \(19\dfrac 12\) pound of food feed
\(=19\dfrac 12 \div 4\dfrac15 \\\\=\dfrac{39}{2} \div \dfrac{21}{5}\\=\dfrac{39}{2} \times \dfrac{5}{21}\\=\dfrac{39 \times 5}{2 \times 21}\\=\dfrac{195}{42}\\=4\dfrac{9}{14}$ ocicats\)
We have determined the number of ocicats that the food will last for a week. However, since ocicats cannot be fractional, the food will feed 4 ocicats with some leftovers,
Answer:
4
Step-by-step explanation:
First calculate how many pounds an ocicat can eat in one week. You get an answer of 21/5 because 3/5x7=21/5. Next, divide 19 1/2 and 3/5. You will get an answer rounded to 4.
HELP PLEASE! URGENT!
Which polynomial represents the sum below?
2x^6 + 8x^2 - x + 1
+
3x^6 + 5x^5 + 1
Answer:
\( \boxed{B. \: 5 {x}^{6} + 5 {x}^{5} + 8 {x}^{2} - x + 2} \)
Step-by-step explanation:
\( = > (2 {x}^{6} + 8 {x}^{2} - x + 1) + (3 {x}^{6} + 5 {x}^{5} + 1) \\ \\ = > 2 {x}^{6} + 8 {x}^{2} - x + 1 + 3 {x}^{6} + 5 {x}^{5} + 1 \\ \\ = > 2 {x}^{6} + 3 {x}^{6} + 5 {x}^{5} + 8 {x}^{2} - x + 1 + 1 \\ \\ = > 5 {x}^{6} + 5 {x}^{5} + 8 {x}^{2} - x + 2\)
The polynomial representing the sum is \(5x^6 + 5x^5 + 8x^2 - x + 2\) (Option B).
The polynomial that represents the sum of the two polynomials is:
\((2x^6 + 8x^2 - x + 1) + (3x^6 + 5x^5 + 1)\)
Combining like terms, we can simplify the expression:
\(2x^6 + 3x^6 + 8x^2 + 5x^5 - x + 1 + 1\)
Now, combining the like terms further:
\(5x^6 + 5x^5 + 8x^2 - x + 2\)
Therefore, the polynomial that represents the sum is:
\(5x^6 + 5x^5 + 8x^2 - x + 2\) (Option B).
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What is the scale factor of a drawing if the scale is 1 inch equals 4 feet
Answer:
the scale factor of a drawing=1:4
Question 3
Select all that are rational
Claire has 6 large envelopes and 11 small envelopes. What is the ratio of large envelopes to the total number of envelopes?
Since Claire has 6 large envelopes and 11 tiny envelopes, the ratio of big envelopes to all envelopes is 6/17.
what is unitary method ?A problem-solving technique known as the unitary approach involves expressing a relationship between two or more variables as a unit rate or a unitary fraction. According to the definition of "unitary," which is "relating to a unit," this technique expresses the relationship between the variables in terms of a single unit, which can be used to determine the value of one of the variables if the value of the other variable is known. For instance, we can use the unitary technique to determine the cost of 1 pencil if the cost of 10 pencils is $2.
given
Claire has the following amount of envelopes in total:
6 + 11 = 17
The following formula can be used to describe the proportion of large envelopes to all envelopes:
oversized envelopes and all envelopes
When we change the numbers, we obtain:
6 / 17
The proportion of big envelopes to all envelopes is shown here. By dividing the numerator and denominator by their largest common factor, in this case 1, it can be made simpler. As a result, the percentage is as follows:
6/17
Since Claire has 6 large envelopes and 11 tiny envelopes, the ratio of big envelopes to all envelopes is 6/17.
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5. Writing to Explain Explain how you
can find a common denominator for
3/5 and 5/8.
Answer:
The common denominator for 3/5 and 5/8 is 40.
Step-by-step explanation:
You can obtain the denominators by simply multiplying both the numerator and the denominator by the same amount.
Or you could see what values each of the denominators have in common for example, 5 times 8 is 40 and 8 times 5 is 40.
Question 2 of 10
f(x)=√x-8. Find f(x) and its domain.
A. f¹(x) = x² +8; xz -8
B. f¹(x) = (x+8)²; xz0
O c. f¹(x) = x² +8; x²0
O D. f¹(x) = (x + 8)²; x² -8
Answer:
C. f¹(x) = x² + 8; x ≥ 8
Explanation:
The given function is f(x) = √(x - 8), which can be rewritten as f(x) = (x - 8)^(1/2).
To find the inverse function, we need to solve for x:
y = (x - 8)^(1/2)
y^2 = x - 8
x = y^2 + 8
Therefore, f¹(x) = x² + 8.
The domain of f(x) is all the values of x that make the expression inside the square root non-negative, that is, x - 8 ≥ 0. Solving for x, we get x ≥ 8. Therefore, the domain of f(x) is x ≥ 8.
Step-by-step explanation:
B. f¹(x) = (x+8)²; xz0
hope the answer is correct
en una tienda de ropa, la semana pasada, 3 pantalones y 2 abrigos costaban 245€. Esta semana estos artículos tienen un descuento del 20% y 5% respectivamente. Si ahora un pantalón y un abrigo cuestan 100,75€, ¿qué costaba cada artículo antes de la rebaja?
Solving a system of equations we can see that each pair of pants costs €82.94 and each coat costs €26.37
How to find the original cost?
Let's define the variables:
x = cost of a pant
y = cost of a coat.
First, we know that:
3x + 2y = 245
And then there are discounts of 20% and 5%, and the cost of one of each is 100.75, then:
0.8x + 0.95y = 100.75
Then we have a system of equations:
3x + 2y = 245
0.8x + 0.95y = 100.75
We can isolate x on the second equation to get:
x = (100.75 - 0.96y)/0.8
x = 125.9 - 1.2y
Replace that in the other equation:
3*(125.9 - 1.2y) + 2y = 245
Solving for y:
3*125.9 - 3*1.2y + 2y = 245
y*(2 - 3*1.2) = 245 - 3*125.9
y = (245 - 3*125.9)/(2 - 3*1.2)
y = 82.94
Then the value of x is:
x = 125.9 - 1.2*82.94
x = 26.37
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Will give Brainliest, A car wash has a weekly ad in the local newspaper that is 2 inches wide and 4 inches high and costs $36.75 per week. The cost of each ad is based on its area. If the owner of the car wash decides to double the width and height of the ad, how much will the new ad cost?
Answer:
4+2+$36.75= $42.75
Step-by-step explanation:
4+2+36.75
6+36.75
42.75
Alternative Form
171/4,42 3/4
Answer:
4+2+$36.75=$42.75.
Step-by-step explanation:
6+36.75=42.75
Acme Widgets had an order to process 250 widgets. The first unit required 200 minutes to assemble. Before starting, the company estimated the amount of time it would require to assemble all 250 widgets if they learned at an 85% rate. After assembling all 250 widgets, Acme realized they had learned at an 80% rate. How much time less than their estimate did Acme take? You should be able to compute the answer within plus or minus 2 hours. Group of answer choices A. 296.1 hours B. 126.6 hours C. 140.3 hours D. 91.2 hours E. 155.8 hours
The estimated time was 140.3 hours, but Acme took 91.2 hours less than the estimate.
1. The estimated time to assemble all 250 widgets, at an 85% rate, is given by:
250 x 200 / 0.85
= 294,117.65 minutes.
2. The actual time taken to assemble all 250 widgets, at an 80% rate, is given by:
250 x 200 / 0.80
= 312,500 minutes.
3. The difference between the estimated time and actual time is given by:
312,500 - 294,117.65
= 18,382.35 minutes.
4. The time in hours is given by: 18,382.35 / 60
= 306.37 hours.
= 306.37 - 166.07 = 140.3 hours
numeric calculations = 18,382.35 minutes / 60 minutes/hour = 306.37 hours - 294,117.65 minutes / 60 minutes/hour = 166.07 hours = 306.37 - 166.07 = 140.3 hours
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Rewrite the equation in slope-intercept form: 5x + 9y = 30
Answer:
y = (-5/9)x + 30/9
Step-by-step explanation:
To rewrite the equation 5x + 9y = 30 in slope-intercept form, we need to isolate y on one side of the equation.
5x + 9y = 30
Subtract 5x from both sides of the equation to isolate 9y:
5x - 5x + 9y = -5x + 30
9y = -5x + 30
Divide both sides of the equation by 9 to solve for y:
9y/9 = (-5x + 30)/9
y = (-5/9)x + 30/9
Help someoneeeeeeeeeee
Answer:
Step-by-step explanation:
17²-8²=9²
9²=18
√18=9
_________
\( \: \)
b² = c² - a²
b² = 17² - 8²
b² = 289 - 64
b² = 225
b = √225
b = 15
A student government organization is interested in estimating the proportion of students who favor a mandatory "pass-fail" grading policy for elective courses. A list of names and addresses of the 645 students enrolled during the current quarter is available from the registrar's office. Using three-digit random numbers in row 10 of table 7. 1 and moving across the row from left to right, identify the first 10 students who would be selected using simple random sampling. The three-digit random numbers begin with 816, 283, and 610
Simple random sampling is a statistical method in which every member of the population has an equal chance of being chosen as a subject for the survey. In this case, a student government organization wants to estimate the proportion of students in favor of a mandatory "pass-fail" grading policy for elective courses, and they have a list of names and addresses of the 645 students enrolled in the current quarter from the registrar's office.
They can use simple random sampling to select a sample of students to participate in the survey. The first 10 students who would be selected using simple random sampling using three-digit random numbers in row 10 of table 7.1 and moving across the row from left to right are as follows:816283610752991768275354233410 The procedure for selecting a simple random sample of size n from a population of N subjects is as follows: Assign a unique identification number to every member of the population Obtain a list of identification numbers of the population. Use a random number generator to select n random numbers from 1 to N, without replacement, to identify the members of the sample. Identify the members of the sample using the randomly selected identification numbers. Simple random sampling is the most straightforward sampling method, and it produces samples that are unbiased and representative of the population. It is important to note that the size of the sample chosen should be large enough to make accurate inferences about the population.For such more question on organization
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Picture below has question/answer choices!!
The statements that is true about the similarity of the two triangles the option D
D. ΔMNO and ΔJKL are not similar triangles
What are similar triangles?Similar triangles are triangles which have proportional corresponding sides
The parameters in the question are;
The length of segment MN = 20
Length of segment NO = 12
Length of segment OM = 25
Measure of angle ∠O = 56°
Length of segment LJ =- 15
Length of segment JK = 12
Length of segment KL = 9
Measure of angle ∠L = 56°
Two triangles are similar if the ratio of two sides on one triangle are proportional to two sides of another triangle, and the included angle between the two sides are congruent
The included angle between sides ON and MO on triangle MNO is congruent to the included angle between segment LK and JL in triangle JKL
However, the ratio of the sides LK to ON and JL to MO are;
9/12 ≠ 15/25
Therefore, the triangles are not similar
The correct option is option D
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Please help 60 points for a rapid answer-In the figure below which of the following is true in circle E?
Answer:
all 3 options are true : A, B, C
Step-by-step explanation:
warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.
they say that A and C are correct.
but I am going to show you that if A and C are correct, then also B must be correct.
therefore, my given answer above is the actual correct answer (no matter what the test systems say).
originally the information about the alignment of the point F in relation to point E was missing.
therefore, I considered both options :
1. F is on the same vertical line as E.
2. F is not on the same vertical line as E.
because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :
the vertical line of EF is like a mirror between the left and the right half of the picture.
A is mirrored across the vertical line resulting in B. and vice versa.
the same for C and D.
this leads to the effect that all 3 given congruence relationships are true.
if we consider assumption 2, none of the 3 answer options could be true.
but if the assumptions are true, then all 3 options have to be true.
now, for the "why" :
remember what congruence means :
both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.
for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.
so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.
therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.
but do you notice something ?
both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.
now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.
therefore, AC must be equal to BD.
and that means that AC is congruent to BD.
because lines have no other congruent criteria - only the lengths must be identical.