Find the measures of the angles of the triangle whose vertices are A=(-2,0), B=(2,2), and C=(2,-2). The measure of ZABC is (Round to the nearest thousandth.)
Answers
To find the measures of the angles of the triangle ABC with vertices A=(-2,0), B=(2,2), and C=(2,-2), we can use the distance formula and the dot product.
First, let's find the lengths of the sides of the triangle:
AB = √[(x₂ - x₁)² + (y₂ - y₁)²]
= √[(2 - (-2))² + (2 - 0)²]
= √[4² + 2²]
= √(16 + 4)
= √20
= 2√5
BC = √[(x₂ - x₁)² + (y₂ - y₁)²]
= √[(2 - 2)² + (-2 - 2)²]
= √[0² + (-4)²]
= √(0 + 16)
= √16
= 4
AC = √[(x₂ - x₁)² + (y₂ - y₁)²]
= √[(2 - (-2))² + (-2 - 0)²]
= √[4² + (-2)²]
= √(16 + 4)
= √20
= 2√5
Now, let's use the dot product to find the measure of angle ZABC (angle at vertex B):
cos(ZABC) = (AB·BC) / (|AB| |BC|)
= (ABx * BCx + ABy * BCy) / (|AB| |BC|)
where ABx, ABy are the components of vector AB, and BCx, BCy are the components of vector BC.
AB·BC = ABx * BCx + ABy * BCy
= (2 - (-2)) * (2 - 2) + (2 - 0) * (-2 - 2)
= 4 * 0 + 2 * (-4)
= -8
|AB| |BC| = (2√5) * 4
= 8√5
cos(ZABC) = (-8) / (8√5)
= -1 / √5
= -√5 / 5
Using the inverse cosine function, we can find the measure of angle ZABC:
ZABC = arccos(-√5 / 5)
≈ 128.189° (rounded to the nearest thousandth)
Therefore, the measure of angle ZABC is approximately 128.189 degrees.
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Related Questions
the length of a puppy on a scale is drawing is 6cm if the scale is 1:9 what is the actual length of the puppy
Answers
Answer:
14cm 54cm 48cm
Step-by-step explanation:
find the answer
Test Practice
9. Kim and her two brothers each use
1 cups of milk
for breakfast. How many fluid ounces of milk do they
use in 4 days?
A 144 fl oz
B 108 fl oz.
C 72 fl oz
D 36 fl oz
Answers
Answer:
Step-by-step explanation:
There are three people who each use 1 cup of milk for breakfast. That's a total of 3 cups, just for breakfast. There is no information given on any other milk consumption, so we have to assume that is all the milk they drink in a day.
Over a 4 day period, that amounts to (4 days)*(3 cups/day) = 12 cups of milk in 4 days.
1 cup of milk is equal to 8 fluid ounces. We can make this into a conversion factor:
(8 fluid oz)/(1 cup)
Since the top is equal to the bottom (8 oz = 1 cup), this numerically is equivalent to 1, which we can multiply by anything.
Let's multiply it times the 12 cups of milk the three consume in 4 days:
(12 cups/4 days)*(8 fluid oz/cup)
Note that the cups cancel and we are left with the unit fluid oz/4 days.
96 fluid oz over 3 days. I don't see that as an option, so please check the numbers.
I need help on this asap
Answers
The solution (2, 2) means that 2 adults and 2 children boarded the raft and the weight of the raft didn't exceed its maximum weight.
The solution (5, 0) means that 5 adults boarded the raft and the weight of the raft exceeded its maximum weight.
How to write the required system of linear inequalities?Based on the information provided above, a system of linear inequalities that represent both the minimum (least) and maximum (most) weight Chase can carry in terms of rafters is given by;
Minimum: 75x + 50y ≥ 150
Maximum: 200x + 100y ≤ 800
where:
x represent the number of adult rafters.y represent the number of rafters for children under age 16.For the first trip wherein, Chase guides 2 adults and 2 children;
75x + 50y ≥ 150
75(2) + 50(2) ≥ 150
150 + 100 ≥ 150
250 ≥ 150 (True).
200x + 100y ≤ 800
200(2) + 100(2) ≤ 800
400 + 200 ≤ 800
600 ≤ 800 (True).
For the second trip wherein, Chase guides 5 adults;
75x + 50y ≥ 150
75(5) + 50(0) ≥ 150
375 + 0 ≥ 150
375 ≥ 150 (True).
200x + 100y ≤ 800
200(5) + 100(0) ≤ 800
1,000 + 0 ≤ 800
1,000 ≤ 800 (False).
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Complete Question:
Chase estimates the weight of each adult as approximate 200 pounds and the weight of each child under age sixteen as approximate 100 pounds. Chase charges adults $75 and children under age sixteen $50 to ride down the river with him. His goal is to earn at least $150 each rafting trip.
To write an inequality to represent the most weight Chase can carry in terms of rafters. Define your variables.
Darryl has a shipping box with dimensions 16 in. By 16 in. By 16 in. He needs a cube whose volume is three times bigger, to hold all his stuff. What will be the new dimensions rounded to the hundredths?
Answers
Answer:
23.08 in
Step-by-step explanation:
Volume of the shipping box = length × width × height
= 16 × 16 × 16
= 4,096 in³
He needs a cube whose volume is three times bigger
New volume of cube = 3 × 4,096 in
= 12,288 in
New volume of cube = 12,288 in³
New dimensions:
Volume of cube = s³
12,288 in³ = s³
s = 3√12,288
s = 23.0759931249 in
To the nearest hundredth = 23.08 in
Find the 81st term of the arithmetic sequence 8,7,6
Answers
Refer to picture
Let S1 be the amount allowing 10% discount on the price of some goods and then adding 10% VAT. Let S2 be the amount adding 10% VAT and then allowing 10% discount. Which of the following is true? (i) S1 > S2 (ii) S1 < S2 (iii) S1 = S2 (iv) Cant be decided
Answers
Using decimal multipliers, the correct statement is given by:
(iii) S1 = S2.
What is a decimal multiplier?Increases of a% or decreases of a% re represented by decimal values, as follows:
The equivalent multiplier for an increase of a% is given by: \(\frac{100 + a}{100}\)The equivalent multiplier for an decrease of a% is given by: \(\frac{100 - a}{100}\)Hence, in the context of this problem:
An increase of 10% is represented by 1.1.A decrease of 10% is represented by 0.9.The options are given as follows:
S1 = 0.9 x 1.1 = 0.99.S2 = 1.1 x 0.9 = 0.99.They are equal, hence option (iii) is correct.
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Consider the polynomial 6x4 + 24x3 − 72x2. What is the greatest common factor (GCF) of the terms of the polynomial?
Answers
Answer:
24x
Step-by-step explanation:
=6x×4+24x×3-72x
=24x+24×3x-72x
=24x+72x-72
=24x
Gasoline is pouring into a vertical cylindrical tank of radius 55 feet. When the depth of the gasoline is 66 feet, the depth is increasing at 0.30.3 ft/sec. How fast is the volume of gasoline changing at that instant
Answers
The volume of gasoline in the cylindrical tank is increasing at 23.56 ft.³/sec when the depth of the gasoline in the tank is 6 feet. Computed using differentiation.
Since the tank is cylindrical in shape, its volume can be written as:
V = πr²d,
where V is its volume, r is the radius, and d is the depth.
The radius is constant, given r = 5ft.
Thus the volume can be shown as:
V = π(5)²d,
or, V = 25πd.
Differentiating this with respect to time, we get:
δV/δt = 25πδd/δt ... (i),
where δV/δt, represents the rate of change of volume with respect to time, and δd/δt represents the rate of change of depth with respect to time.
Now, we are given that when the depth increases at 0.3 ft./sec when the depth of the gasoline is 6 feet.
Thus, we can take δd/δt = 0.3 ft./sec, in (i) to get:
δV/δt = 25πδd/δt = 25π(0.3) ft.³/sec = 23.56 ft.³/sec.
Thus, the volume of gasoline in the cylindrical tank is increasing at 23.56 ft.³/sec when the depth of the gasoline in the tank is 6 feet. Computed using differentiation.
The question written correctly is:
"Gasoline is pouring into a vertical cylindrical tank of radius 5 feet. When the depth of the gasoline is 6 feet, the depth is increasing at 0.3 ft./sec. How fast is the volume of gasoline changing at that instant?"
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Can someone please solve this
Answers
Answer:
20
Step-by-step explanation:
- Combine multiplied terms into a single fraction
- Eliminate redundant parentheses
- Multiply all terms by the same value to eliminate fraction denominators
please answer
4. Suppose that for 3MA Forecast, my Mean Absolute Deviation (MAD) is \( 3.0 \) and my Average Error (AE) is \( -2.0 \). Does my forecast fail the bias test? a. Yes b. No
Answers
The answer is: a. Yes, the forecast fails the bias test.
To determine whether the forecast fails the bias test, we need to compare the Average Error (AE) with zero.
If the AE is significantly different from zero, it indicates the presence of bias in the forecast. If the AE is close to zero, it suggests that the forecast is unbiased.
In this case, the Average Error (AE) is -2.0, which means that, on average, the forecast is 2.0 units lower than the actual values. Since the AE is not zero, we can conclude that there is a bias in the forecast.
Therefore, the answer is:
a. Yes, the forecast fails the bias test.
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solvable problems for which no polynomially bounded algorithms exist are called ____.
Answers
Solvable problems for which no polynomially bounded algorithms exist are called NP-hard problems.
In computer science, the class of problems known as NP (nondeterministic polynomial time) consists of decision problems that can be verified in polynomial time, meaning that the time it takes to verify a solution to the problem grows at most polynomially with the size of the input. NP-hard problems are a subset of NP that are at least as hard as the hardest problems in NP.
An algorithm for an NP-hard problem is considered polynomially bounded if the time it takes to solve the problem grows at most as a polynomial function of the size of the input. This means that for large inputs, the running time of the algorithm does not increase too quickly. NP-hard problems are of particular interest because, although they may not have a polynomial time solution, they can be used to model many real-world problems and can provide insights into the complexity of computational problems.
Examples of NP-hard problems include the traveling salesman problem, the subset sum problem, and the knapsack problem. These problems have been shown to be NP-hard through a process called reduction, in which a problem can be transformed into another problem that is known to be NP-hard. By showing that the original problem can be reduced to an NP-hard problem, it can be concluded that the original problem is also NP-hard.
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can u pls help me with this question
Answers
8x+16 + 7x-9
collect like terms
=15x + 7
Answer
x + 7.
Step-by-step explanation:
The answer is X + 7 because you know, 8x + 13 and if 7x - 9 we're solded. We remove 7x at 8x so at least we have only one x and we remove 9 than 16 so we have 7. That's why the reply is x + 7. Sorry if I wasn't clear, I am not really good at english.
What is the equation of the line?
Answers
(Character limit filler)
Answer:
UNDEFINED!
Step-by-step explanation:
The x-coordinate never changes no matter what the y-coordinate is!
Solve for d. d-8/-2 =12
Answers
solution
d=8
Answer:
-16
Step-by-step explanation:
d - 8 / -2 = 12
d - 8 = 12 * -2
d - 8 = -24
d = -24 + 8
d = -16
Two sides of a triangle are 8 inches and
10 inches in length and the angle θ between
them is increasing at a rate of 1/10 radians
per second.
Find the rate at which the area of the tri-
angle is increasing when θ = π/3.
Answers
When the angle θ of a triangle, with sides measuring 8 inches and 10 inches, is increasing at a rate of 1/10 radians per second, the rate at which the area of the triangle is increasing when θ = π/3 is approximately 6.43 square inches per second.
To find the rate at which the area of the triangle is increasing, we can use the formula for the rate of change of the area with respect to time:
dA/dt = (1/2) * a * b * dθ/dt * sin(θ),
where A is the area of the triangle, a and b are the lengths of the sides, θ is the angle between the sides, and dθ/dt is the rate of change of θ with respect to time.
In this case, a = 8 inches, b = 10 inches, and dθ/dt = 1/10 radians per second. We are interested in finding the rate of change of the area when θ = π/3.
Plugging in these values into the formula, we have:
dA/dt = (1/2) * 8 * 10 * (1/10) * sin(π/3).
Simplifying the expression, we get:
dA/dt = 4 * sin(π/3) = 4 * (√3/2) = 2√3.
Therefore, when θ = π/3, the rate at which the area of the triangle is increasing is approximately 2√3 square inches per second. Evaluating this expression, we find that the rate is approximately 6.43 square inches per second.
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Let f(x)=18/1+3^e-0.1x What is the point of maximum growth rate for the logistic function f(x)? Show all work. Round your answer to the nearest hundredth
Answers
Answer:
(0, 4.5)
Step-by-step explanation:
*The equation can be put into Desmos, to find the point, but the work to prove it is here*
f(x)=c/1+Ae^-Bx
Y=C
C=18 A=3 -B=-0.1
*Replace x with 0 in the equation, so you know 0 is the x value, and it leads you to the y value*
f(0)=18/1+3e^-o.1(0)
= 18/1+3e^0
=18/1+3(1)
=18/1+3
=18/4
=4.5
x=0 y=4.5
Maximum growth rate = (x,y) --> (0, 4.5)
Hope this helps:))!!
Can someone help me out with this question as I’m completely stuck
Answers
Answer:
Step-by-step explanation:
∠BEF = ∠ABE {Alternate interior angle}
∠BEF = 60
∠EQR = ∠ BEF {Corresponding angles}
∠EQR = 60
In ΔEQR
∠QER + ∠EQR + ∠ERQ = 180 {angle sum property}
80 + 60 +x = 180
140 + x = 180
x = 180- 140
x = 40
Picture attached help please!
Answers
The missing lengths in the triangles are h = 3/2√2 and b = 4√3
How to determine the missing lengthsTriangle a and b
From the question, we have the following parameters that can be used in our computation:
A special right triangle
For a right triangle with an angle of 45 degrees
The measure of the leg is
h = Hypotenuse/√2
So, we have
h = 3/√2
Evaluate
h = 3/2√2
For the other triangle, we have
sin(60) = b/6
So, we have
b = 6/sin(60)
Evaluate
b = 4√3
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Mr. Tieu spent $23 on apples, bananas, and oranges. He bought 10 more apples than oranges, and 6 fewer bananas than apples. How many of each kind of fruit did he purchase if one apple costs 70 cents, one apples costs 50 cents, and an orange costs 80 cents each?
Answers
Answer:
apples: 17
oranges: 11
bananas: 7
Step-by-step explanation:
hope this helps!
The zurn family ate at a restaurant that was having 15% discount on that day .Their meal costs 64.75,and they left a 20% tip .What is the total cost of the meal? (Note: the tip applies to the total cost of the meal before the discount was applied)
Answers
The total cost of the meal is 66.045
Given,
The cost of the meal = 64.75
The discount given on that day = 15%
The tip given by Zurn family = 20%
We have to find the total cost of the meal.
First we have to find the total cost including tip before discount is added.
That is,
120% of 64.75
= 64.75 × 120/100
= 6.475 × 12
= 77.7
Here, the total cost including tips before discount is 77.7
Now, we have to deduct the discount.
100 - 15 = 85
That is,
85% of 77.7 will be the total cost of the meal
= 77.7 × 85/100
= 6604.5 / 100
= 66.045
Therefore, the total cost of the meal is 66.045
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Find the 100th term for the sequence: -10, – 15, -20, - 25, ...
,
Answers
Step-by-step explanation:
please mark me as brainlest
Answer:
-505
Step-by-step explanation:
First term is -10, second is -15, third -20, fourth -25, and so on. Here, this is a pattern. Every question having pattern also have a formula to solve it. To solve this question first you need to understand the pattern. In this pattern it is adding -5. First term is -10, so if we add -5 to -10 we will get the second term that is -15, and to get third term add -5 to the result with the previous number that will -15 + -5 = -20. So, now we are confirm that to get the next term we have to add -5 to the previous number. Here, we have to find the hundredth term. So, if we add -5 with the result hundred times it will take time. So, we need to solve this with the help of a formula. The formula according to me is, -5 × term number + (-5). Before finding the term which is not given in the question, we have to try this formula with the terms given in the question to know whether the formula is correct✅ or not❌. So, first we will find the first term using the formula.
= -5 × 1 + (-5)
= -5 + (-5)
= -10
We got the first term and it is correct but, I am finding all terms given in this question using the formula to show that the formula is correct.
Second term using formula
= -5 × 2 + (-5)
= -10 + (-5)
= -15
Third term using formula
= -5 × 3 + (-5)
= -15 + (-5)
= -20
Fourth term using formula
= -5 × 4 + (-5)
= -20 + (-5)
= -25
Now, I think you know how to find 100th term. To find 100th term, multiply -5 with 100 then add -5 to the result.
= -5 × 100 + (-5)
= -500 + (-5)
= -505
If you want to find more terms you can find it using the formula.
If you did not understood my explanation or my answer is incorrect than sorry, you can report my answer. But, if you understood than tell me in comment or please give me a Thanks.
If you think my answer is incorrect, before reporting it you should find the 100th term using long method by only adding -5 till you find the 100th term to check my answer.
Please someone help meeee
Answers
Answer:
2431.01
Step-by-step explanation:
What is the volume of each of the five colors in a 4-inch cubed notepad? Assume each color has the same number of sheets.
. 512 in3
3. 2 in3
64 in3
12. 8 in3
Answers
The volume of each of the five colors in a 4-inch cubed notepad is given as follows:
0.512 in³.
How to obtain the volume of a cube?The volume of a cube of side length a is given by the cube of the side length, as follows:
V(a) = a³.
The side length for this problem is given as follows:
4/5 = 0.8 in.
Hence the volume is given as follows:
V = 0.8³ = 0.512 in³.
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A density graph for all of the possible temperatures from 60 degrees to 160
degrees can be used to find which of the following?
OA. The probability of a temperature from 90 degrees to 180 degrees
OB. The probability of a temperature from 30 degrees to 120 degrees
OC. The probability of a temperature from 30 degrees to 90 degrees
OD. The probability of a temperature from 90 degrees to 120 degrees
Answers
Answer:
The density graph for all possible temperatures from 60 degrees to 160 degrees can be used to find the probability of a temperature falling within a certain range.
Option (A) is incorrect because it includes temperatures that are outside the range of the graph.
Option (B) is incorrect because it includes temperatures that are outside the range of the graph.
Option (C) is incorrect because it includes temperatures that are outside the range of the graph.
Option (D) is the only option that falls within the range of the graph. Therefore, the density graph can be used to find the probability of a temperature from 90 degrees to 120 degrees, which is option (D).
Step-by-step explanation:
If 96 out of 200 pet owners own cats, what fraction and what percentage of
pet owners do not own cats?
Check all that apply.
A. 52%
104
IL B.
200
C. 48%
D. 0.52%
E 96 help ASAP plz
200
Answers
Answer:
A. 52% and B. 104/200
Step-by-step explanation:
To find the answer, we first have to find how many pet owners own cats. As percentages are x/100, when we have x/200 we divide the numerator and denominator by 2 to bring the fraction to 48/100. (96/200 divided by 2 equals 48/100). Now that we have the percentage of pet owners that own cats (48%), we need to find how many do not own cats. To do so, we just subtract 100-48 to get 52. Then, we do the same to the fraction of 96/200. (200-96 = 104). This brings our answers to A. 52% and B. 104/200
The percentage of owners that do not own cat is 52%
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Given here, 96 out of 200 pet owners own cats then the owners who do not own cat are 104
Therefore the number of non cat owners in percentage terms is
= (104/200) ×100
= 52.5%
Hence, the answer is 52.5%
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identify the domain of the graph write your answer in interval notation
Answers
The domain of the given graph is (-4,4]
The elements that make up a function are its domain and range. A function's domain is the set of all potential input values, while its range is the range of possible output values.
"All the values" that are input into a function are referred to as the domain of a function. The collection of all potential inputs for a function is its domain. Think of this box as the f(x) = 2x function. The domain is only the collection of natural numbers when the input values are x = 1,2,3,4,..., and the values that are returned are referred to as the range.
Hence from the graph we get the domain as (-4,4]
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What are the x-intercepts of the graph of f(x) = (2x-1)(2x-5)? Show your work.
Answers
Answer:
Step-by-step explanation:
The x intercepts are obtained by equating the factors to zero.
2x - 1 = 0
2x = 1
x = 1/2
2x - 5 = 0
2x = 5
x = 5/2
x = 2 1/2 or 2.5
The graph of f(x) = (2x -1)*(2x - 5) is given below. The x intercepts are labeled.
It is a function written as f(x)=b^x where bis greater than 0, b is not equal to 1, and x is any real number.
Answers
The function with the following formula is an exponential function with base b:
Given: f(x) = b^x, where b > 0, b ≠ 1 is a real number.
If r is a rational number, we can determine what b means.
An exponential function's domain is all real numbers since b^x may be defined for all real values r.
Now, all you need to know is that any positive number b^x and any real number r can be used to approximate the value of b using this approximation.
B can be any real number greater than 0 in the range.
An exponential function is always positive. And if in addition 0 < b < 1, f is a decreasing function.
Hence, f(x) decreases as x increases.
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Select all the triangles that have an area of 30 square units.
B C 6 6 10 10 10 10 8.66 10 10 D E 10 10 6 DA E *ASAP WILL GIVE BRAINLIEST LOL*
Answers
Answer:
A and C
Step-by-step explanation:
Area of ∆ = ½*base*height
Area of figure A:
base = 6
height = 10
Area = ½*6*10 = 3*10 = 30 square units
Area of figure B:
base = 10
height = 8.66
Area = ½*10*8.66 = 5*8.66 = 43.3 square units
Area of figure C:
base = 10
height = 6
Area = ½*10*6 = 5*6 = 30 square units
Area of figure D:
base = 6
height = 8
Area = ½*6*8 = 3*8 = 24 square units
Area of figure E:
base = 3
height = 10
Area = ½*3*10 = 3*5 = 15 square units
Which of these equations best describes the line of best fit for the data in the scatter plot relating time and distance?
(Answer options in the picture)
Answers
Answer:
D
Step-by-step explanation:
The y-intercept can't be 1.7 it's too low of a number and there can't be no y-intercept in the problem because the line does meet the y-axis