Answers
The triangle which could be drawn as per the given description is only option b. isosceles triangle with measure 20° and 80°.
An acute triangle with sides measuring 7, 4, and 2
In an acute triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side .
According to the Pythagorean Theorem.
Here, 7² is greater than (4² + 2²).
So this is not possible.
An isosceles triangle with angles measuring 20° and 80°
In an isosceles triangle, two angles are equal, so if two angle measures 20° and 80°,
Then the third angle measures is
180° - 20° - 80°= 80°
Two angles are congruent implies two sides are congruent.
It is possible to form isosceles triangle.
An obtuse triangle with sides measuring 5, 10, and 15
In an obtuse triangle, the longest side is opposite the largest angle.
Sum of squares of two shorter sides is less than square of longest side according to Pythagorean Theorem.
However, 15²is greater than (5²+ 10²),
so this is not possible.
A scalene triangle with angles measuring 110° and 35°
The sum of the angles of any triangle is 180°,
so the third angle must measure
180° - 110° - 35° = 35°.
Two angles are congruent so it is isosceles triangle.
It is not possible to form scalene triangle.
Therefore, the triangle possible to draw as per the given condition is only option b. isosceles triangle with measure 20° and 80°.
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Related Questions
Convert the rectangular coordinates (5,−5√3) to polar form. Let r>0 and 0≤θ<2π.
Enter your answer by filling in the boxes. Enter coordinates as simplifed fractions or radicals in simplest form.
( , )
Answers
Answer:
(10, 5π/3)
Step-by-step explanation:
To convert rectangular coordinates (5, -5√3) to polar form, we can use the following formulas:
r = √(x^2 + y^2)
θ = arctan(y/x)
Substituting the given values, we get:
r = √(5^2 + (-5√3)^2) = √(25 + 75) = √100 = 10
θ = arctan((-5√3)/5) = arctan(-√3) = -π/3
Note that the value of θ is in the fourth quadrant, which corresponds to a negative angle. However, we need to express the angle θ in the range 0 ≤ θ < 2π. To do this, we can add 2π to the angle if it is negative:
θ = -π/3 + 2π = (5π/3)
Therefore, the rectangular coordinates (5, -5√3) in polar form are (10, 5π/3).
Alina wants to make keepsake boxes for her two best friends. She doesn't have a lot of money, so she wants to make each box described so that it holds as much as possible with a limited amount of material.
For Jen, Alina wants to make a box with a square base whose sides and base are made of wood and whose top is made of metal. The wood she wants to use costs 5 cents per square inch, while the material for the metal top costs 12 cents per square inch. What is the largest possible box (in terms of volume measured in cubic inches) that Alina can make for Jen if she only has $30.00 to spend on materials? (Round your answer to three decimal places.)
Answers
Answer:
So Alina can make a box with dimensions 8.445 inches by 8.445 inches by 8.445 inches (with a metal top) that will hold approximately 606.526 cubic inches.
Step-by-step explanation:
Let's assume that the length of one side of the square base of the box is "x". Then the height of the box is also "x" to maximize the volume.
The surface area of the box (excluding the top) is given by:
2(x^2) + 4(x^2) = 6(x^2)
The surface area of the metal top is:
x^2
The total surface area of the box is the sum of the surface area of the box and the surface area of the metal top:
6(x^2) + x^2 = 7(x^2)
The cost of the wood for the box is:
5 cents per square inch * 6(x^2) = 30x^2 cents
The cost of the metal for the top is:
12 cents per square inch * x^2 = 12x^2 cents
The total cost of the box is:
30x^2 + 12x^2 = 42x^2 cents
We want to find the maximum volume of the box that can be made with $30, which is 3000 cents. Therefore, we can set up the equation:
42x^2 = 3000
Solving for x, we get:
x^2 = 71.429
x ≈ 8.445
Therefore, the maximum volume of the box is:
V = x^2 * x = (8.445)^3 ≈ 606.526 cubic inches.
So Alina can make a box with dimensions 8.445 inches by 8.445 inches by 8.445 inches (with a metal top) that will hold approximately 606.526 cubic inches.
Polygon ABCD is drawn with vertices at A(1, 5), B(1, 0), C(−1, −1), D(−4, 2). Determine the image vertices of A′ if the preimage is rotated 270° counterclockwise.
A′(−1, −5)
A′(−1, 5)
A′(−5, 1)
A′(5, −1
Answers
Answer:
(d) A'(5, -1)
Step-by-step explanation:
You want the coordinates of A(1, 5) after it has been rotated 270° CCW about the origin.
RotationThe transformation for rotation 270° CCW is the same as that for rotation 90° CW:
(x, y) ⇒ (y, -x)
For the given point, this is ...
A(1, 5) ⇒ A'(5, -1)
The image of A is A'(5, -1), choice D.
a⃗ =⟨4, −3⟩ and b⃗ =⟨−1,−2⟩.
Represent a⃗ +b⃗ by using the head to tail method.
Use the Vector tool to draw the vectors, complete the head to tail method, and draw a⃗ +b⃗ . Do not draw any unnecessary vectors.
To use the Vector tool, select the initial point and then the terminal point.
Answers
The vector addition of vector a = < 4, - 3 > and b = < - 1, - 2 > is given by,
a + b = < 3, -5 >
The graph of the vector sum is given below.
The addition of vectors suggests the addition of the corresponding components of the involving vectors.
Given the vectors are:
a = < 4, - 3 >
b = < - 1, - 2 >
So doing vector addition we get,
a + b = < 4, - 3 > + < - 1, - 2 > = < (4 + (-1)), (-3+(-2)) > = < (4 - 1), (-3 -2) > = < 3, -5>
Head to tail method is a method to draw vector addition, where the initial point of a vector involved in vector addition is started from tail point of another vector involved in vector addition.
Using vector tool we draw the vector addition of given vectors 'a' and 'b' we get,
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Answer: Look at the image below
Step-by-step explanation: I took the test.
Step 1: Select Vector
Step 2: Click on (0, 0), then click on (4, -3); (for every point your going to have to click on where you start then where you want to go.)
Step 3: Click on (4, -3), then (3, -5). Why?: ((4 - 1), (-3 - 2)) = (3, -5)
Step 4: To complete the problem and thus completing the "head to tail" method, you need to click on the origin (0,0) and finally click on (3, -5)
Your answer should now look like mine, now go get that A.
in the diagram at the right, the length of a square is (3x+7) units. The dimensions of the cut-out rectangle are x by (2x+5) units. Which choice expresses the area of the shaded regions, in square units?
Answers
[tex] {(3x + 7)}^{2} - ((2x + 5) \times x) [/tex]
[tex] = 7 {x}^{2} - 5x + 49[/tex]
Use a net to find the surface area of the prism.
A. 426 m2
B. 213 m2
C. 306 m2
D. 336 m2
Answers
The surface area of the rectangular prism in this problem is given as follows:
A. 426 m².
What is the surface area of a rectangular prism?The surface area of a rectangular prism of height h, width w and length l is given by:
S = 2(hw + lw + lh).
This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas. -> net method.
By the net method, the prism is divided as follows:
Two rectangles of dimensions 5 m and 12 m.Two rectangles of dimensions 5 m and 9 m.Two rectangles of dimensions 12 m and 9 m.Hence the surface area of the prism is given as follows:
S = 2(5 x 12 + 5 x 9 + 12 x 9)
S = 426 m².
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hey guys, im b-o-r-e-d in class... what should i do?
Answers
Answer:
Do whatever you want, but paying attention would really help you.
Step-by-step explanation:
If you find yourself bored in class, consider the following options to make the most of your time and stay engaged:
1. Actively participate: Ask questions, contribute to discussions, and try to engage with the material. Active participation can make the class more interesting and help you retain the information better.
2. Take notes: Focus on taking detailed notes, even if you think you understand the material. This will help you stay engaged and make it easier to review the content later.
3. Find connections: Try to relate the class material to your interests or real-world applications. This can make the content more engaging and relevant.
4. Set learning goals: Set specific learning objectives for each class, and try to achieve them during the session. This can help you stay focused and motivated.
5. Practice active listening: Pay attention to the teacher and try to understand the main points they are making. This can help you stay focused and better comprehend the material.
6. Break down the material: Divide the content into smaller chunks and focus on understanding each part. This can make the material more manageable and engaging.
7. Speak with your teacher: If you're consistently bored in class, consider discussing your concerns with your teacher. They may be able to offer suggestions or modify their teaching approach to better suit your learning style.
Remember, it's essential to stay engaged in class to maximize your learning experience and make the most of your education.
Answer:
watch RUN BTS EPISODE simple
1. Lana completed 22 of the puzzles in
her puzzle book. There are 10 puzzles
remaining. What percent of the puzzle
has she completed?
Answers
Answer:
Lana has completed 22 out of 32 puzzles in her book. To find the percentage of the puzzle she has completed, divide the number of puzzles she has completed by the total number of puzzles in the book and multiply by 100.
22/32 x 100 = 68.75%
Lana has completed 68.75% of the puzzles in her book.
Answer:
Lana has completed 68.75% of the puzzles in her puzzle book.
Step-by-step explanation:
Lana has completed a total of 22 puzzles and there are 10 puzzles remaining, so the total number of puzzles in the book is:22 + 10 = 32To find the percentage of puzzles Lana has completed, we can use the following formula:percentage = (completed puzzles / total puzzles) x 100%Substituting the values, we get:percentage = (22 / 32) x 100%
percentage = 0.6875 x 100%
percentage = 68.75%Therefore, Lana has completed 68.75% of the puzzles in her puzzle book.
what is the surface area of a sphere with a radius of 12 centimeters
A) 302cm^2
B) 452cm^2
C) 576cm^2
D) 1810cm^2
Answers
The surface area of the sphere is 1810 cm²
What is a sphere?A sphere is a three-dimensional object that is round in shape. Examples of object with spherical shape is a ball, an egg e.t.c.
The area occupied by a three-dimensional object by its outer surface is called the surface area.
The surface area of sphere is expressed as;
A = 4πr². where r is the radius.
A = 4 × 3.14 × 12²
A = 1809.7 cm²
approximately to the nearest whole number
A = 1810 cm²
Therefore the surface area of the sphere to the nearest whole number is 1810 cm².
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A mountain climber is at an elevation of 10,000 feet. If she descends 2,000 feet a day, which equation would be used to show how many days it will take to reach sea level (0 feet)?
-10,000 ÷ (-2,000)
-10,000 ÷ 2,000
10,000 ÷ 2,000
10,000 ÷ (-2,000)
Answers
Answer: The correct equation to use is, C. 10,000 ÷ 2,000
Which simplifies to: 5
Therefore, it will take 5 days for the mountain climber to descend from an elevation of 10,000 feet to sea level, assuming they descends at a constant rate of 2,000 feet per day.
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Which best demonstrates the way consumers and producers influence each other in the free-market system? O assembly line Circular-flow model downward spiral O flow chart
Answers
Answer:
The best choice is:
Circular-flow model
The circular-flow model demonstrates how consumer demand and production supply influence each other in a market economy. Some key points:
• Consumers demand goods and services by spending money (aggregate demand). This drives production.
• Producers supply goods and services to meet demand (aggregate supply). But supply depends on and influences demand.
• There is a continuous flow and feedback loop between consumers, producers, and the money/resources flowing between them.
The circular-flow model highlights this interconnectedness and interdependence. It shows how consumer spending drives production, which in turn enables more consumer spending, and so on. Changes in demand, supply, spending or consumption ripple through the economy.
The other choices do not accurately represent this relationship:
• Assembly line - Focuses on supply-side production process, not the demand-supply feedback loop.
• Downward spiral - Implies a negative, self-defeating cycle rather than the mutually supporting feedback in the circular-flow model.
• Flow chart - Too generic. A flow chart could represent any process, not specifically the demand-supply relationship.
So in summary, the circular-flow model is the best choice as it demonstrates the way consumer demand and producer supply interact with and influence each other in a free market system. The circular flow of money, resources, supply and demand relies on this interconnection.
Does this help explain the circular-flow model and why it is the best choice? Let me know if you have any other questions!
Step-by-step explanation:
IN CASE YOU ARE LOOKING FOR THE ANSWER
In 2010, the population of Houston, Texas, was 2,099,451 and the population density was 3501 people per square mile.
What was Houston's land area in 2010?
Enter your answer as a decimal in the box. Round your answer to the nearest tenth.
Answers
Answer: 599.7 square miles
Step-by-step explanation: Divide 2,099,451 by 3501 and then round to the nearest tenth.
The fucntion F is defined by f(x) =12/x +1/2. Find each value of th e fucnction. F(3)
Answers
The function f(x) = 12/x + 1/2 is given. To find f(3), we substitute x=3 in the function expression and simplify: f(3) = 12/3 + 1/2 = 4 + 0.5 = 4.5. Therefore, the value of the function f at x=3 is 4.5.
To find f(3) for the function f(x) = 12/x + 1/2. Start with the given function f(x) = 12/x + 1/2. Replace x with 3: f(3) = 12/3 + 1/2. Simplify the first term: 12/3 = 4
Add the two terms: f(3) = 4 + 1/2
Convert the mixed number to an improper fraction: 4 + 1/2 = 8/2 + 1/2 = 9/2
Simplify the fraction: 9/2 = 4 1/2
So, f(3) = 4 1/2 or 9/2, depending on the desired form of the answer.
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Which expression is equivalent to 3w-4-w-93w−4−w−9?
A 2w-13
b 4w - 13
c 2w + 5
d -w - 13
Answers
Answer: A
Step-by-step explanation:
To simplify 3w-4-w-9, we need to combine the like terms (terms that have the same variable and exponent).
3w - w = 2w
-4 - (-9) = -4 + 9 = 5
So,
3w - 4 - w - 9 = 2w - 13
Therefore, the expression 3w-4-w-9 is equivalent to 2w-13, which is option A.
What's this answer?
2 5/6 • -3 2/4 =
Answers
Answer:
-9 11/12
Step-by-step explanation:
You want the product of 2 5/6 and -3 2/4.
ProductThe product of mixed numbers is often most easily computed by rewriting them to improper fractions.
(2 5/6)(-3 2/4) = (17/6)(-7/2) = -(17·7)/(6·2) = -119/12
= -(108/12 +11/12)
= -9 11/12
__
Additional comment
Your calculator can probably help you with this.
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Help! I dont know the answe and Ive been stuck for a minute..
Dm on ig: 1.rockkyy I have more questions!
Answers
Answer:
a³ = -357911/5832.
Step-by-step explanation:
We can use the given equation to find the value of n, and then use it to find the value of a³.
a¹ = 13 and a = ⁿ⁻¹ - 4
Substituting the value of a in terms of n in the first equation, we get:
ⁿ⁻¹ - 4 = 13
ⁿ⁻¹ = 13 + 4
ⁿ⁻¹ = 17
ⁿ = 18
Now, substituting the value of n in the equation a = ⁿ⁻¹ - 4, we get:
a = 18⁻¹ - 4
a = 1/18 - 4
a = -71/18
Finally, to find a³, we can cube the value of a:
a³ = (-71/18)³
a³ = -357911/5832
Therefore, a³ = -357911/5832.
CAN SOMEONE HELP WITH THIS QUESTION?
Answers
The number of cars that pass through the intersection between 6 am and 10 am is 4800.
To find the number of cars that pass through the intersection between 6 am and 10 am, we need to integrate the traffic flow rate function r(t) over the interval [0,4].
Integrating r(t) with respect to t, we get:
∫(400+ 600t - 150t²)dt = 400t + 300t² - 50t³ + C
where C is the constant of integration.
Evaluating this expression between t=0 and t=4 (since we are interested in the interval between 6 am and 10 am), we get:
(400(4) + 300(4)² - 50(4)³) - (400(0) + 300(0)² - 50(0)³) = 4800 cars
In summary, we can find the number of cars that pass through an intersection between two specific times by integrating the traffic flow rate function over that interval.
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Find the multiplicative inverse of
[tex] \frac{ - 4}{9} + ( \frac{2}{5} + \frac{3}{8} )[/tex]
Answers
Multiplicative inverse of given expression is 9/5.
The given expression,
-4/9 + (2/5 + 3/5)
Simplify it,
⇒ -4/9 + (2+3)/5
⇒ -4/9 + 5/5
⇒ -4/9 + 1
⇒ (-4 + 9)/9
⇒ 5/9
So its multiplicative inverse = 1/(5/9) = 9/5
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SOS need help on this math project with all the work
Answers
To perform this and any other construction in math, you need to use the right tools which include a compass, your drawing board or paper, and a clear understanding of the instruction.
How to construct the shapes and anglesA key to getting the shape and angles of any construction includes knowing what is required of you and implementing these in your construction. In the second slide, you are told to use the segment tool to create segment AB. This tool will be a scale and the measurement will be that of a line AB.
Next, identify the radius of the circle. This is the point from the center of the circle to any line on the circle. Understanding the instructions is key to bisecting the segment and completing the other activities.
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4. Malaki has a 'no interest-free period' credit card that charges 16.5% p.a. interest. On 9 January he purchases a phone costing K395.00. His January statement is dated 28 January and the phone is the only item on it.
a. How much interest is charged on the January credit card statement?
b. Malaki pays K100.00 off the amount owed on 28 January and makes no more purchases or payments before the next credit card statement arrives on 28 February. How much will this statement show that Malaki owes?
Answers
Answer:
K5.60.
Step-by-step explanation:
ing Angles
If m/DBC = 47°, then
m
A
B
47°
D
Enter
D
Answers
Answer:
<ABC + <CBD =180⁰
<ABC =180⁰ - <CBD
<ABC =180⁰ - 47⁰
<ABC =133⁰
12 cm
He
4 cm 3 cm 5 cm
3 cm 5 cm
4 cm
4 cm
3 cm
What is the surface area of the solid?
A. 81 square centimeters
B. 192 square centimeters
C. 156 square centimeters
OD. 168 square centimeters
12 cm
Answers
Answer:
2(1/2)(3)(4) + 12(3) + 12(4) + 12(5)
= 12 + 36 + 48 + 60 = 156 cm^2
C is the correct answer.
Given that a/b=3/4 and b/c=5/6 find a:b:c Give you answer in its simplest form
Answers
Answer:
LCM of 4 and 5 is 20.
a/b = 3/4 = 15/20
b/c = 5/6 = 20/24
a:b:c = 15:20:24
1/3 divided by 2/9 simplified?
Answers
Answer:3/2
Step-by-step explanation:
1/3 ÷ 2/9=
1/3 ×9/2=3/2
Answer:
3/2 u can also do 1 1/2 their equivalent fractions
Step-by-step explanation:
sorry about the handwriting :) not the best
5/3X + 1/3X= 2 2/3+ 8/3X
Answers
The solution of the given equation 5X/3 + X/3 = 2 (2/3) + 8X/3 is, X = - 4.
The equation is a mathematical statement involving mathematical variable, numerical values, mathematical operation with a equal sign.
The given equation is,
(5/3)*X + (1/3)*X = 2 (2/3) + (8/3)*X
Solving the equation we get,
5X/3 + X/3 = (2*3 + 2)/3 + 8X/3
5X/3 + X/3 - 8X/3 = (6 + 2)/3
(5X + X - 8X)/3 = 8/3
- 2X/3 = 8/3
- 2X = 8
X = 8/(-2)
X = - 4
Hence the solution is, X = - 4.
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A circular racetrack has a circumference of one mile. What is the diameter of the racetrack in feet?
Answers
The diameter of the racetrack in feet is 1,681.53 feet.
How to calculate the circumference of a circle?In Mathematics and Geometry, the circumference of a circle can be determined by using the following mathematical equations:
C = πD or C = 2πr
Where:
C represents the circumference of a circle.D represents the diameter of a circle.r represents the radius of a circle.Conversion factor;
1 mile = 5280 feet
By substituting the given parameters into the formula for the circumference of a circle, we have the following;
5280 = 3.14 × D
Diameter, D = 5280/3.14
Diameter, D = 1,681.53 feet.
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Which of the following questions about a particular animal could NOT be answered using only the data collected for the tracking collars?
Answers
The question about a particular animal that could NOT be answered using only the data collected from the tracking collars would be do the movement patterns of the animal vary according to the weather? That is option C.
What are tracking collars?A tracking collars is a neck device that usually has a GPS device attached to it which is used by biologists to track the movement of animals that are under study.
The functions of the tracking collars include the following:
It allows them to note how many miles the animal can travel in a given time.It allows them to note the pattern of movement of the animals.It allows them to note the location preferred by the animal to travel.Learn more about tracking here:
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Complete question:
Biologists often attach tracking collars to wild animals. For each animal, the following geolocation data is collected at frequent intervals.
The time
The date
The location of the animal
Which of the following questions about a particular animal could NOT be answered using only the data collected from the tracking collars?
A. Approximately how many miles did the animal travel in one week?
B. Does the animal travel in groups with other tracked animals?
C. Do the movement patterns of the animal vary according to the weather?
D. In what geographic locations does the animal typically travel?
C. Do the movement patterns of the animal vary according to the weather?
1. The possible missing terms to make x²_____+100 a perfect square trinomial are
a. 4x and 25x.
b. -10x and 10x.
c. -20x and 20x.
d. -4x and -25x.
Answers
Answer:
c. -20x and 20x
Step-by-step explanation:
x² is the square of x.
100 is the square of 10 and of -10.
The middle term of (a + b)² is 2ab.
For b = 10:
2ab = 20x
for b = -10:
2ab = -20x
Answer: c. -20x and 20x
Fred brought a shirt and a wallet for a total of 34.26 before tax. The price of the wallet was $15 less than the price of the shirt. What was the price of the shirt?
Answers
Answer:
The price of the shirt is $24.63.
Step-by-step explanation:
Let's assume the price of the shirt is x. Then the price of the wallet will be x - 15. We know that the total cost before tax is 34.26, so we can set up the equation:
x + (x - 15) = 34.26
Simplifying, we get:
2x - 15 = 34.26
Adding 15 on both sides:
2x = 49.26
Dividing by 2:
x = 24.63
Therefore, the price of the shirt is $24.63.
A poll showed that 53.2% of Americans say they believe that statistics teachers know the true meaning of life. What is the probability of randomly selecting someone who does not believe that statistics teachers know the true meaning of life. Round to 3 decimal places.
Answers
The probability that a statistics teachers do not know the true meaning of life is 46.8%
What is the probability of someone who does not believeFrom the question, we have the following parameters that can be used in our computation:
53.2% of Americans say they believe that statistics teachers know the true meaning of life.
This means that
P(Believe) = 53.2%
For the required probability, we have
P(Not believe) = 1 - P(Believe)
So, we have
P(Not believe) = 1 - 53.2%
Evaluate
P(Not believe) = 46.8%
Hence, the probability that a statistics teachers do not know the true meaning of life is 46.8%
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