Applying the Right Triangle Altitude Theorem. Which similarity statement is true?
Answers
The true similarity statement are using Right Triangle Altitude Theorem :
ΔABD similar to ΔBCD
ΔABC similar to ΔADB
ΔABC similar to ΔBDC
Two triangles are said to be similar if the triangles are of the same shape but different size. The angles of the triangle will be equal and the sides are proportional.
By the Right Triangle Altitude Theorem,
If the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then the triangles formed by the division are similar to each other and both are similar to the original triangle.
Using this,
ΔABD similar to ΔBCD
ΔABC similar to ΔADB
ΔABC similar to ΔBDC
Hence the true statements are ΔABD similar to ΔBCD, ΔABC similar to ΔADB, ΔABC similar to ΔBDC.
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The complete question is given below.
Related Questions
Given the values of the linear functions f (x) and g(x) in the tables, where is (f – g)(x) positive?
Answers
The composite function is positive at the interval (-7, ∝)
How to calculate where the composite function is positiveFrom the question, we have the following parameters that can be used in our computation:
The table of values of the function f(x)
Also, we have
The table of values of the function g(x)
The composite function (f - g)(x) is calculated as
(f - g)(x) = f(x) - g(x)
From the table of values, we have the following values
(f - g)(-10) = f(-10) - g(-10) = -3 - 9 = -12 --- negative
(f - g)(-7) = f(-7) - g(-7) = 6 - 6 = 0 --- zero
Also, we have
(f - g)(-4) = f(-4) - g(-4) = 15 - 3 = 12 --- positive
This means that the interval is (-7, ∝)
Hence, the composite function (f - g)(x) is positive at the interval (-7, ∝)
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Consider the line 3x+2y=-1.
Find the equation of the line that is perpendicular to this line and passes through the point (5, 3).
Find the equation of the line that is parallel to this line and passes through the point (5, 3).
Note that the ALEKS graphing calculator may be helpful in checking your answer.
Equation of perpendicular line:
Equation of parallel line:
0
Answers
The given line is in the form Ax + By = C, where A = 3, B = 2, and C = -1. To find the slope of this line, we can rearrange the equation in slope-intercept form (y = mx + b), where m is the slope:
3x + 2y = -1
2y = -3x - 1
y = (-3/2)x - 1/2
The slope of the given line is -3/2. Since a line perpendicular to this line will have a negative reciprocal slope, we can find the perpendicular slope by taking the negative reciprocal of -3/2:
Perpendicular slope = -1 / (-3/2) = 2/3
Now we have the slope of the perpendicular line, and we can use the point-slope form of a line (y - y₁ = m(x - x₁)) to find its equation. Plugging in the values (5, 3) for (x₁, y₁) and 2/3 for m:
y - 3 = (2/3)(x - 5)
Expanding and simplifying:
3y - 9 = 2x - 10
2x - 3y = 1
Therefore, the equation of the line that is perpendicular to 3x + 2y = -1 and passes through the point (5, 3) is 2x - 3y = 1.
To find the equation of a line parallel to the given line and passing through the point (5, 3), we can use the same method. Since parallel lines have the same slope, the slope of the parallel line will also be -3/2.
Using the point-slope form with (5, 3) and -3/2:
y - 3 = (-3/2)(x - 5)
Expanding and simplifying:
2y - 6 = -3x + 15
3x + 2y = 21
Therefore, the equation of the line that is parallel to 3x + 2y = -1 and passes through the point (5, 3) is 3x + 2y = 21.
if i compare 0.10__0.01 what would the answer be?
Answers
The answer will be 0. 10 > 0. 01 . Option B
How to compare the valuesGiven the values as;
0.100.01Turn the values into proper fractions
a. 0. 10 = 10/ 100
Reduce to simpler terms
= 10/ 100
= 1/ 10
b. 0. 01 = 1/ 100
a = 1/ 100
b = 1/ 100
This means that both decimals are not of equal proportion and thus a is greater than (>) b
Thus, the answer will be 0. 10 > 0. 01 . Option B
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i need to determine which functions has the greater rate of change
Answers
We need to compare the rates of change of the functions shown.
The rate of change of a linear function is the change in the y-coordinates divided by the corresponding change in the x-coordinates between two points.
The rate of change for the graphed function can be calculated using points A and B, for example. We obtain:
\(\frac{y_B-y_A}{x_{B-xA}}=\frac{1-0}{0-(-1)}=\frac{1}{1}=1\)Notice that the first two rows of the table represent exactly points A and B: A(-1,0) and B(0,1). Thus, the rate of change will be the same:
\(\frac{1-0}{0-(-1)}=1\)Answer: The rates of change are equal.
which of the following representations show y as a function of x
Answers
The option that is a representation that shows y as a function of x is the graph in option 2. The answer is B.
What is a Function?A function is any relation or table of values which may be represented in a graph that has only one possible y value that is assigned to each x-value.
The first option is not a function because x-value 0 has two corresponding y-values, 4 and 9.
In the third option, we also have two y-values, 5 and -5, that is assigned to one x-value, 0. So, it is not a function.
The graph in option 2 represents y as a function of x, because no two y-values is assigned to the same x-value.
The answer is: B.
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An airplane has a maximum capacity of 118 passengers. The flight attendant has loaded 40 passengers. Which inequality represents the solution set that shows the number of passengers, p, that can still load the plane? A) p ≥ 68 B) p ≤ 68 C) p ≤ 78 D) p ≥ 78
Answers
A certain brand of MP3 player will display how long it will take to play through its entire music library.If the maximum number of songs the MP3 players can hold is 1,000 (and the average song length is 4 minutes), would you want the time displayed in terms of seconds, days, or years worth of music?
Answers
Answer:
I think that days is the most reasonable, sorry if I'm wrong
Step-by-step explanation:
So if you had 1,000 songs and each was 4 minutes, the amount of minutes would be 4*1000 minutes, or 4000 minutes.
4000 minutes = 240000 seconds
4000 minutes = 2.77777... days
4000 minutes = 0.007610350684932... years
Miles has 25 coins in his pocket. Some are nickels and some are dimes. He has a total of $1.65. How many of each type of coin does he have? Let x represent _____________________________ Let y represent _____________________________ System: _____________________ _____________________ Solution: x = ____________ y = ____________
Answers
Answer: 17 nickels, and 8 dimes.
Step-by-step explanation:
So Miles has 25 coins in his pocket, Suppose that x is the number of nickels, and y is the number of dimes, then we have that:
x + y = 25
And we also know that the total value is $1.65
Then we have that:
x*0.05 + y*0.10 = 1.65
Then we have a system of equations:
x + y = 25
x*0.05 + y*0.10 = 1.65
The first step is isolating one of the variables in one of the equations, i will isolate x in the first one.
x = 25 - y
Now we can replace that in the second equation:
(25 - y)*0.05 + y*0.10 = 1.65
Now we solve this for y.
25*0.05 - y*0.05 + y*0.10 = 1.65
1.25 + y*(0.10 - 0.05) = 1.65
y*0.05 = 1.65 - 1.25 = 0.40
y = 0.40/0.05 = 8
So Miles has 8 dimes.
And:
x + y = 25
x + 8 = 25
x = 25 - 8 = 17
And Miles has 17 nickels.
Help! I’ll reward brainest its pretty easy
Answers
1/2 + 1/8 (can’t see properly, is it an 8)
1/8 + 1/8
4/8 + 1/8
=5/8
The table represents a linear function.
X
y
-4
-2
-2
-10
-1
-14
1
-22
2
-26
What is the slope of the function?
O-8
0-4
02
05
Answers
Answer:
-4
Step-by-step explanation:
Consider (-4, -2) and (-2, -10).
Change in x: 2
Change in y: -8
Slope = (change in y)/(change in x) = -4
The slope of the function is -4.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Let us take two points from the table
(-4, -2) and (-2, -10)
Slope = -10+2/-2+4
=-8/2
=-4
Hence, the slope of the function is -4.
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A cylinder has a height equal to its radius.
Find the rate of change of volume V with respect to radius.
Answers
The rate of change of the volume with respect to radius is; 4πr
Rate of change of a cylinder's volumeSince the height of the cylinder is equal to it's radius;
It follows that the volume of the cylinder is given by;
V = 2πr².On this note, the rate of change of the volume with respect to radius is;
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pls help me with this question
Answers
Step-by-step explanation:
1.(12×2+1)/2 - (4×9+1)/4 = 3¼.
2.(5×4+3)/4 - (12×2+5)/12 = 3⅓.
3.(5×7+1)/5 - (10×3+7)/10 = 3½.
4.(3×11+2)/3 - (2×8+1)/2 = 3⅙.
Chen wants to buy a model car and race track with his allowance. He has $30 to spend. The model car costs $8.50, and he will spend the rest of the money on pieces of race track. Each piece of race track costs $2.25.
A. Write an inequality to find the number of race track pieces he can buy.
B. Identify the meaning of your variable.
C. Explain how many pieces of race track he can buy and how much change he will receive from his $30.
Answers
Answer:
All below
Step-by-step explanation:
A. 8.50+2.25x is greater than or equal to $30.00
B. X=number of piece of race track
C. 9
What fraction with a numerator of 2 is equivalent to 48?
Answers
Answer:
\(\frac{2}{\frac{1}{24} }\)
Step-by-step explanation:
2/x = 48
48x = 2
x = (2)/ (1/24)
\(\frac{2}{\frac{1}{24} }\) = 48
When information is being gathered about a group, the entire group of objects, individuals or events is called the....
Answers
Answer:
so hard
Step-by-step explanation:
You have a 10-sided dice with faces numbered 1-10.
Find P(rolling a number less than 2 or greater than 7).
Answers
Answer:
2/5
Step-by-step explanation:
Rolling a number less than two means that you roll a 1.
1/10 is the answer to less than 2
Roll a number greater than 7 means you roll 8 9 or 10 that's 3 out of 10
Answer
1/10 + 3/10 = 4/10 = 2/5
NO LINKS NO FILES. After you add 3 to both sides of the equation 27 = m/6 - 3, what should you do next?
Answers
Answer:
Multiply each side by 6
Step-by-step explanation:
27 = m/6 - 3
Add 3 to each side
27+3 = m/6 - 3+3
30 = m/6
Multiply each side by 6
30*6 = m/6*6
180 = m
Regan won the grand prize at a store giveaway. The grand prize winner is guaranteed to win at least $500 in cash and prizes.
A. List three possible dollar amounts in cash and prizes Regan can win
B. Write an inequality to represent the dollar amounts d in cash and prizes Regan can win.
Answers
An inequality to represent the dollar amounts d in cash and prizes Regan can win is p + d ≥ 500.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given that, Regan won the grand prize at a store giveaway. The grand prize winner is guaranteed to win at least $500 in cash and prizes.
Let d represent the amount of cash in dollars and p represent the amount of prizes.
Since the grand prize winner is guaranteed to win at least $500,
So, p + d ≥ 500
Therefore, an inequality to represent the dollar amounts d in cash and prizes Regan can win is p + d ≥ 500.
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if a(x) = 3x+1 and b(x) = \(square root of x-4\), what is the domain of (boa)(x)
Answers
The domain of (boa)(x) is [1, ∞].
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers (x-values) for which a particular equation or function is defined.
Based on the information provided above, we have the following functions:
a(x) = 3x+1
\(b(x) = \sqrt{x-4}\)
Therefore, the composite function (boa)(x) is given by;
\(b(x) = \sqrt{3x+1 -4}\\\\b(x) = \sqrt{3x-3}\)
By critically observing the graph shown in the image attached below, we can logically deduce the following domain:
Domain = [1, ∞] or {x|x ≥ 1}.
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![if a(x) = 3x+1 and b(x) = [tex]square root of x-4[/tex], what is the domain of (boa)(x)](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/gGe6IRGOQUF4aKHR4HvpxeklJAqlYD78.png)
The record for the most amount of rain in the shortest period of time in the united states was 12 inches in 42 minutes. How much rain fell in 15 minutes?
SHOW YOUR WORK AND HOW YOU GOT THE ANSWER!!!!
Answers
We can say that approximately 4.29 inches of rain fell in 15 minutes.
We can apply a proportion to determine the amount of rain that fell in 15 minutes.
We can calculate the proportion because we know that 12 inches of rain fell in 42 minutes:
x inches in 15 minutes equals 12 inches in 42 minutes.
where x is how much rain fell in 15 minutes.
We can cross-multiply and simplify to find x's value:
42 minutes equals 12 inches times 15 minutes (x inches)
180 = 42x
x = 180 / 42
x = 4.2857...
We may estimate that 4.29 inches of rain, rounded to the nearest hundredth, fell in 15 minutes.
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Please answer this question
Answers
The expression in ascending order is \(e^{log4} < log_326 < log_233 < log_22^6\).
We have,
Using a log and exponent calculator we get,
log 4 = 0.60
So,
\(e^{log 4}\) = \(e^{0.60}\) = 1.82
\(log_233\) = 5.044
\(log_22^6\) = 6
\(log_326\) = 2.97
Now,
Arranging from least to greatest:
\(e^{log4} < log_326 < log_233 < log_22^6\)
Thus,
The expression in ascending order is \(e^{log4} < log_326 < log_233 < log_22^6\).
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The perimeter of an isosceles triangle is 32.7 inches. The length of its base is 9.5 inches. Find the length of each of the other two identical sides.
Answers
Answer:
1.72 inches
Step-by-step explanation:
= P=2s×b
= 32.7=2s×9.5
= 32.7=19s
= 32.7/19=19s/19
= s=1.72
solve for x
(look at photo)
Answers
By definition of proportion, the value of x is,
⇒ x = 80
We have to given that;
In a triangle,
Perpendicular = 60
Now, By Pythagoras theorem we get;
60² = 36² + y²
3600 = 1296 + y²
y² = 3600 - 1296
y² = 2304
y = 48
Hence, By definition of proportion;
⇒ x / 48 = 60 / 36
⇒ x = 80
Thus, By definition of proportion, the value of x is,
⇒ x = 80
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Hi can any one teach me this constant difference
Answers
The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).
How do you find the constant difference in a sequence of numbers?In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.
Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.
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Find the course and ground speed for the following: Track 090°, airspeed 300km/h; wind 060°, 50km/h.
Answers
The course of the airplane relative to true north is 094°, and the ground speed is 344.2 km/h.
What is the ground speed of the plane?The horizontal and vertical component of the airspeed is calculated as follows;
Vx = 300 cos(30) = 259.8 km/h
Vy = 300 x sin(30) = 150 km/h
The horizontal and vertical component of the wind velocity is calculated as follows;
Vx = 50 cos(60) = 25 km/h
Vy = 50 sin(60) = 43.3 km/h
To find the resultant velocity, we can add the x and y components separately:
Vx = 259.8 km/h + 25 km/h = 284.8 km/h
Vy = 150 km/h + 43.3 km/h = 193.3 km/h
The magnitude of the resultant velocity is calculated as;
V = √(284.8² + 193.3²)
V = 344.2 km/h
The direction of the resultant velocity is calculated as;
θ = arc tan (193.3/284.8)
θ = 34.2⁰
The resultant direction to true north is calculated as;
track = 34.2 + 60 = 94.2°
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2/3 es equivalente a 4/5?
Answers
we can conclude that 2/3 is not equal to 4/5.
To determine if 2/3 is equivalent to 4/5, we can compare the fractions by checking if their ratios are equal. The ratio of 2/3 can be written as 2:3, while the ratio of 4/5 can be written as 4:5.
To check if the ratios are equal, we can cross-multiply and see if the products are equal. Cross-multiplying means multiplying the numerator of the first fraction with the denominator of the second fraction, and the numerator of the second fraction with the denominator of the first fraction.
For 2/3 and 4/5, we have:
2 * 5 = 10
3 * 4 = 12
Since 10 is not equal to 12, we can conclude that 2/3 is not equivalent to 4/5.
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HELP PLEASE FAST!! Determine the perimeter of the right triangle shown. Round your final answer to the nearest whole number if necessary.
Answers
Answer:
26
Step-by-step explanation:
One leg measures 7.
One leg measures 8.
a² + b² = c²
7² + 8² = c²
c² = √113 = 10.630 = 11
perimeter = 7 + 8 + 11
perimeter = 26
2. The client wants the four kitchen windows to be framed with a special molding. If the
windows are 22 inches by 24 inches , how many total inches of molding are needed fo
the kitchen windows?
Answers
Answer:
2,112 inches
Step-by-step explanation:
4 kitchen windows
1 window (22 x 24)
4(22 x 24)
multiplying the brackets by 4 for the 4 windows
4(22 x 24) = 2,112
Question
Solve the equation. Check your solutions.
∣3x−45∣=∣12x∣
Answers
Answer:
x could equal -5 or 3
Step-by-step explanation:
3x - 45 = 12x
-45 = 9x
x = -5
3x - 45 = -12x
x = 3
Can you help please on this
Answers
Answer:
5
Step-by-step explanation: