Katherine wants to prove that the measures of the interior angles of a triangle have a sum of 180. She draws a triangle and extends one of the sides through a vertex. She then draws a line through this vertex that is parallel to the opposite side
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Answer:
As we know, if we add up the interior and exterior angles of one corner of a triangle, we always get 180. the exterior angle in question is equal to the sum of the other two angles in the triangle
Related Questions
P!ease determine the value of the missing angle using the inverse trig function!
Answers
Using a trigonometric relation we will see that the measure of angle x is 40°.
How to find the value of the missing angle?Here we can see a right triangle where one of the angles is x, the hypotenuse is 14 units long, and the opposite cathetus to the known angle is 9 units long.
Here we can use the trigonometric relation:
sin(x) = (opposite cathetus)/hypotenuse
Then we can write:
sin(x) = 9/14
Using the inverse sine function we will get:
Asin(sin(x)) = Asin(9/14)
x = Asin(9/14)
x = 40°
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What is an equation of the line that passes through the points (6, -7) and (-6, 3))? Put your answer in fully reduced form.
Answers
Answer:
The equation of the line is y = \(-\frac{5}{6}\) x - 2
Step-by-step explanation:
The form of the linear function is y = m x + b, where
m is the slopeb is the y-interceptThe rule of the slope is m =\(\frac{y2-y1}{x2-x1}\) , where
(x1, y1) and (x2, y2) are two points on the line∵ The line passes through points (6, -7) and (-6, 3)
∴ x1 = 6 and y1 = -7
∴ x2 = -6 and y2 = 3
→ Substitute them in the rule of the slope above to find it
∵ m = \(\frac{3--7}{-6-6}\) = \(\frac{3+7}{-12}\) = \(\frac{10}{-12}\) = \(\frac{5}{-6}\)
∴ m = \(-\frac{5}{6}\)
→ Substitute it in the form of the equation above
∴ y = \(-\frac{5}{6}\) x + b
→ Substitute x and y in the equation by x1 and y1
∵ x1 = 6 and y1 = -7
∴ -7 = \(-\frac{5}{6}\) (6) + b
∴ -7 = -5 + b
→ Add 5 to both sides
∵ -7 + 5 = -5 + 5 + b
∴ -2 = b
→ Substitute the value of b in the equation
∴ y = \(-\frac{5}{6}\) x + -2
∴ y = \(-\frac{5}{6}\) x - 2
∴ The equation of the line is y = \(-\frac{5}{6}\) x - 2
100 points if someone gets it right
A rectangluar prism has volume of 2,691 centimeters, length 13 centimeters, and height 23 centimeters. Find its width, in centimeters
Answers
Answer:
The width is 9 cm
Step-by-step explanation:
Since the formula for the volume of a rectangular prism is,
Volume = (Height)(Length)(Width)
So,
Width = (Volume)/((Height)(Length))
Now, Volume = 2691, Height = 23, Length = 13, so, we get for the width,
Width = (2691)/((23)(13))
Width = 117/13
Width = 9
So the width is 9 cm
Answer:
9 cm
Step-by-step explanation:
Let's use the formula for the volume of a rectangular prism:
Volume = length * width * height
We know that the volume is 2,691 centimeters, the length is 13 centimeters, and the height is 23 centimeters.
We can plug these values into the formula to find the width:
2,691 = 13 * width * 23
2691=299*width
width=2691/299
width = 9 centimeters
Therefore, the width of the rectangular prism is 9 centimeters.
What is the value of
103x10-5x1010
———————-
106
A. 102
B. 108
C. 1012
D. 1014
E. 1025
Answers
Answer:
Please let me know if my calculations were incorrect. I am very sorry but unfortunately, your answer will be negative and not a whole number. None of the answers fit. It is either that I made a mistake or there is something wrong with the question.
Step-by-step explanation:
\(\frac{103*10-5*1010}{106} \\\frac{1030-5050}{106} \\\frac{-4020}{106} \\\\\frac{-2010}{53}\)
HELP PLEASEEE. WILL GIVE 15 POINTS
Answers
Answer:
PQ=17.088
Step-by-step explanation:
If M is the midpoint of PQ, then PM is half the length of PQ. So we cna find our answer by first finding PM.
Imagine a right angle triangle with PM as its hypotenuse. Since P(x,y)=(5,-15), and M(x,y)=(13,-18), we know that the length of the vertical side of this triangle is the difference between P and M's y (vertical) coordinates, and the length of the horizontal side of this triangle is the difference between P and M's x (horizontal) coordinates. This means the vertical side is equal to -15-(-18)=3 and the horizontal side is equal to 13-5=8. Since we know the lengths of the other two sides and PM is the hypotenuse, we can use pythagorus to find the length of PM:
PM = \(\sqrt{3^{2} +8^{2} } =\sqrt{9 +64 }=\sqrt{73} =\)8.544
Since PM is half PQ, PQ=2(8.544)=17.088
please help asap!!!! i’ll mark brainlist if correct
Answers
Answer: 972
Step-by-step explanation:
Which phrase describes the algebraic expression 5t- 2?
A.) the product of 5 and 2 more than a number
B.) the quotient of 5 and 2
C.)5 times the difference of a number and 2
D.) 2 less than 5 times a number
Answers
Answer:
it is option D
2 less than 5 times a number
hope it helps
In circle B below, diameter RT, radius BE, and chord RE are drawn.
If m2TRE = 15° and BE = 9, then the area of sector EBR is
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The area of sector EBR in the given diagram attached below is: 33.75π units².
What is the Area of a Sector?Area = θ/360º × πr²
Given the following:
m∠TRE = 15° BE = 9Measure of arc TE = 2(m∠TRE) = 2(15) [inscribed angle theorem]
Measure of arc TE = 30°
Arc RE = 180 - arc TE = 180 - 30 [semicircle]
Arc RE = 150°
m∠EBR = Arc RE = 150°
Area of sector EBR = m∠EBR/360 × π(BE²)
Area of sector EBR = 150/360 × π(9²)
Area of sector EBR = 33.75π units²
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a-If given that we were tasked to evaluate the model, between MAPE and R2 which of these parameters do we use?
b-If given that model A has a higher MAPE than model B but model B has a higher R2 than model A, then how do we choose among the two?
c-Between the MAPE , MAD and MSD, which of these parameters shall we use for accuracy measures and why?
Answers
a. When evaluating a model, we use R2 as a parameter for performance assessment.
b. If model A has a higher MAPE but model B has a higher R2, we choose the model with the higher R2 for better overall performance.
c. For accuracy measures, we typically use MAPE (Mean Absolute Percentage Error) due to its interpretability and ability to capture relative errors.
When evaluating a model's performance, it is crucial to choose the appropriate parameters to assess its accuracy and reliability. In the case of MAPE (Mean Absolute Percentage Error) and R2 (Coefficient of Determination), the choice between them depends on the specific evaluation goals.
The R2 parameter is commonly used for evaluating models because it measures the proportion of the dependent variable's variance that can be explained by the independent variables. R2 provides insights into how well the model fits the data and captures the relationship between the input features and the target variable. Therefore, R2 is a suitable parameter to use when evaluating a model.
When comparing two models, if model A has a higher MAPE but model B has a higher R2, it is advisable to choose the model with the higher R2 value. This is because R2 indicates the proportion of variance explained, suggesting that model B performs better in capturing the underlying patterns and predicting the target variable.
Although model A may have a lower relative error (MAPE), it is crucial to prioritize the model's ability to explain and predict the target variable accurately.
Among MAPE, MAD (Mean Absolute Deviation), and MSD (Mean Squared Deviation), MAPE is commonly preferred as a parameter for accuracy measures. MAPE calculates the average percentage difference between the predicted and actual values, making it interpretable and easily understandable.
It captures relative errors and enables comparisons across different scales and datasets. MAD and MSD, on the other hand, measure absolute and squared errors, respectively, but they do not account for the relative magnitude of the errors. Hence, MAPE is a more suitable parameter for accuracy measures.
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a frog is at the bottom of a 25 foot well. each day he climbs up 3 feet, and each night he slips down 2 feet. how many days will it take him to reach the top of the well?
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( BRAINLIEST AND THANKS! )
Which of the following table of ordered pairs represents an exponential decay function?
X Y
--------
1 2
2 4
3 6
4 8
5 10
X Y
--------
1 2
2 4
3 8
4 16
5 32
X Y
--------
1 -2
2 -4
3 -6
4 -8
5 -10
X Y
--------
1 0.50
2 0.25
3 0.13
4 0.06
5 0.03
Answers
Answer:
Step-by-step explanation:
X Y
--------
1 0.50
2 0.25
3 0.13
4 0.06
5 0.03
Answer:56
Step-by-step explanation:
The only reason I’m not here today was my fault I didn’t
The graph shows total cost of a whitewater rafting trip and the corresponding number of passengers on the trip. Find ƒ(8), and explain what it represents.
Answers
Answer:f(n)=259
Step-by-step explanation:
F(n)=75+25(n-1)
F(n)= 75+25(7)
F(n)=75+175
F(n)=250
−4x−y=24minus, 4, x, minus, y, equals, 24Complete the missing value in the solution to the equation.
Answers
Answer:
there is no solution to the problem but after calculating and searching a possible answer is
x = -6
y = 0
Step-by-step explanation:
Help me Please I will give brainliest! (please dont answer if you dont know)
Answers
Answer:
16.5 feet or
about 17 feet long.
Step-by-step explanation:
A = bh
Squares have equal side lengths all around so with there being 4 sides, you will take 66 and divide by 4.
66 ÷ 4 = 16.5
So it is about 17 feet
At this point this one decides my grade
The circumference of a circle is 8π centimeters. What is the area of the circle in terms of π?
Answers
Answer:
A = 16π cm²
Step-by-step explanation:
We require to find the radius r
Given circumference C = 8π , then
2πr = 8π ( divide both sides by 2π )
r = 4 , then
A = πr² = π × 4² = 16π cm²
Answer:
A = 16π cm²
Step-by-step explanation:
took the test
A runner is training for a half marathon. On Wednesday, she ran 6 miles in 50 minutes. On Thursday, she ran 4 miles in 32 minutes. Assume she ran at a constant rate each day. On which day did she run faster? By how much faster did she run?
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The day she runs faster is Wednesday.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
On Wednesday:
She ran 6 miles in 50 minutes.
Unit rate:
= 6/50
= 0.12 miles per minute _____(1)
On Thursday:
She ran 4 miles in 32 minutes.
Unit rate:
= 4/32
= 0.125 miles per minute _______(2)
From (1) and (2),
0.12 > 0.125
Thus,
On Wednesday she runs faster.
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Kenny and Tara are both members of a population, and a simple random sample is being conducted. If the chance of Kenny being selected is 1/29, what is the chance of Tara being selected?
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Given:
a.) The chance of Kenny being selected is 1/29.
From the given, we can say that the total population is 29.
Since it's been given that Kenny and Tara are both memb
Let f(x) = ax + b and g(x) = cx^2 + dx, where a, b, c, and d are constants. Compute f ◦ g and g ◦ f. Determine for which constants a, b, c, and d it is true that f ◦ g = g ◦ f. (Hint: Note that polynomials dnx n + dn−1x n−1 + · · · + d1x + d0 and enx n + en−1x n−1 + · · · + e1x + e0 are equal as functions if and only if dn = en, dn−1 = en−1, . . . , d1 = e1, d0 = e0.)
Answers
f(x) = x + b and g(x) =\(cx^2\) are the only functions that satisfy \(f \circ g = g \circ f\) for all constants b and c.
How to compute \(f \circ g\)?To compute composition of function \(f \circ g\), we substitute g(x) into f(x) and simplify:
f(g(x)) = a(\(cx^2\) + dx) + b
= \(acx^2\)+ adx + b
To compute \(g \circ f\), we substitute f(x) into g(x) and simplify:
\(g(f(x)) = c(ax + b)^2 + d(ax + b)\)
\(= c(a^2x^2 + 2abx + b^2) + dax + db\)
\(= ca^2x^2 + (2abc + da)x + cb^2 + db\)
To find conditions under which \(f \circ g = g \circ f\), we equate the expressions for\(f \circ g\) and \(g \circ f\) and simplify:
\(acx^2 + adx + b = ca^2x^2 + (2abc + da)x + cb^2 + db\)
This is true for all x if and only if the coefficients of each power of x on both sides of the equation are equal. That is:
\(ac = ca^2, ad = 2abc + da, b = cb^2 + db\)
Solving for a, b, c, and d, we get:
a = 0 or 1, b = 0, c = 0 or 1, d = 0
Therefore, f(x) = x + b and g(x) =\(cx^2\) are the only functions that satisfy \(f \circ g = g \circ f\) for all constants b and c.
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A computer costs $600. You pay $150 and will pay the rest in 6 equal installments. How much will each payment be?
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Four more than a number is less than or equal twice that number
Answers
Answer:
x+4≤2x
Step-by-step explanation:
How is the graph of y = negative RootIndex 3 StartRoot x minus 4 EndRoot transformed to produce the graph of y = negative RootIndex 3 StartRoot 2 x minus 4 EndRoot?
Answers
Answer:
Multiply by ∛2 and translate the graph to left by 4 units.
Step-by-step explanation:
The initial function given is:
y = -∛(x - 4)
The transformed function is:
y = -∛(2x - 4)
Consider the initial function.
y = -∛(x - 4)
(Represented by Black line in the graph)
Multiply the function by ∛2. The function becomes:
y = -∛(x - 4) × ∛2
y = -∛(2)(x-4)
y = -∛(2x-8)
(Represented by Red line in the graph represents this function)
Translate the graph 4 units to the left by adding 4 to the x component:
y = -∛(2x-8+4)
y= -∛(2x - 4)
(Represented by Blue line in the graph)
Answer:
c on ed
Step-by-step explanation:
i j did it
(a) can the graph of y = f(x) intersect a vertical asymptote? yes or no
Answers
Answer: no
Step-by-step explanation: So, the function's graph cannot intersect the vertical asymptote because in order for it to do so, the graph should contain a point on the asymptote.
Yes, it is possible for the graph of y = f(x) to intersect a vertical asymptote, and It depends on the specific behavior and properties of the function f(x).
Given that,
The graph of a function is,
y = f (x)
Now, it is possible for the graph of y = f(x) to intersect a vertical asymptote.
While vertical asymptotes typically represent values of x where the function approaches infinity or negative infinity, there may be cases where the graph intersects the asymptote as it approaches or crosses it.
Hence, It depends on the specific behavior and properties of the function f(x).
So, The given statement is true.
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⚠️‼️ HELP PLEASE WILL GIVE POINTS
Answers
Answer:
48°
Step-by-step explanation:
Angles on a straight line sum to 180°Therefore \((7x-92)+(6x+12)=180\)Combine like terms\(13x-80=180\)Add 80 to both sides\(13x=260\)Divide both sides by 13\(x=20\)Insert this into 7x - 927 * 20 - 92 = 140 - 92 = 48- Todd uses 21 white tiles and some black tiles to make a mosaic. The mosaic has a total area of 144 square centimeters. Each tile has an area of 3 square centimeters. How many black tiles did Todd use? Explain.
(Help me please)
Answers
Answer:
48
Step-by-step explanation:
21 white tiles = 63 cm2
total number is 144
144-63 = 81
81/3 = 27
so 27 black tiles
21+27 = 48 total.
The answer is 27 tiles !
21 white tiles × 3 = the total area it takes up!
21 × 3 = 63
144 - 63 = 81
81 is the area left!
Divide by 3 to find how many black tiles are needed!
81÷ 3 = 27
Hope I Helped !
Jeremy can buy two tacos at 75 cents each and a medium drink for $1.00—or a "value meal" with three tacos and a medium drink for $3. For him, the marginal cost of the third taco would be?
A. 0
B. $0.75
C. $1.00
D. $0.50
Answers
Answer: To determine the marginal cost of the third taco for Jeremy, we need to compare the cost of buying it individually to the cost of buying it as part of the value meal.
Buying two tacos individually:
Cost of two tacos: 2 tacos * $0.75/taco = $1.50Buying the value meal with three tacos:
Cost of the value meal: $3.00To calculate the marginal cost, we subtract the cost of buying the value meal from the cost of buying two tacos individually:
Marginal cost = Cost of buying two tacos individually - Cost of the value mealMarginal cost = $1.50 - $3.00Marginal cost = -$1.50
The negative value indicates that buying the value meal is more cost-effective than buying the third taco individually. Therefore, the marginal cost of the third taco for Jeremy would be $0 (option A).
Evaluate cos 150° without using a calculator.Ο Α.√32B. 2O C. -1/2OD. -32
Answers
Note that:
\(\begin{gathered} cos(A+B)=cosAcosB-sinAsinB \\ cos(150^0)=cos(90+60) \end{gathered}\)Applying the addition formula given above to cos 150:
\(\begin{gathered} cos(150)=cos(90)cos(60)-sin(90)sin(60) \\ \\ cos(150)=0(\frac{1}{2})-1(\frac{\sqrt{3}}{2}) \\ \\ cos(150)=0-\frac{\sqrt{3}}{2} \\ \\ cos \end{gathered}\)Answer this question for me please
Answers
Answer:
-8
Step-by-step explanation:
Answer:
4th one is the right answer.
| x | -2 | 1 | 2 | 3 |
| y | -6 | 3| 6 | 9 |
Step-by-step explanation:
The x and y relationship is in the form y=kx and the graph starts from the origin.
Therefore the graph represents a proportional relationship which holds a equation y=x/3, where k=1/3.
Ava and her children went into a restaurant and will buy hotdogs and tacos. She must buy no less than 8 hotdogs and tacos altogether. Write an inequality that would represent the possible values for the number of hotdogs purchased, hh, and the number of tacos purchased, t.t.
Answers
Answer:
h + t ≥ 8
Step-by-step explanation:
h is for hotdogs and t is for tacos and they must buy no less than 8 (buy 8 or more than 8 altogether)
x + 6=13 show the steps
Answers
suppose both decks of cards are first shuffled together and then dealt out to the four players. what is the probability that you get a pair of kings of hearts?
Answers
Therefore, the probability of getting a pair of kings of hearts is (1/5356) divided by the total number of possible outcomes ((104!)/(26!)^4).
To determine the probability of getting a pair of kings of hearts when both decks of cards are shuffled together and dealt to four players, we need to calculate the favorable outcomes and the total number of possible outcomes.
Favorable outcomes: There are two kings of hearts in a standard deck, so we need to calculate the probability of receiving one of them as the first card and the other as the second card.
The probability of receiving the first king of hearts is 2/104 (2 kings of hearts out of 104 total cards).
After receiving the first king of hearts, the probability of receiving the second king of hearts is 1/103 (1 king of hearts out of the remaining 103 cards).
Therefore, the probability of getting a pair of kings of hearts is (2/104) * (1/103) = 1/5356.
Total number of possible outcomes: The total number of ways to deal 104 cards to four players is (104!)/(26!)^4, which represents the number of possible outcomes for distributing the cards.
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