Give two sets of potential sides for a triangle. One set of side lengths should be able to be used for a right triangle and the other set of side lengths should not be able to form a right triangle.
Suppose you’re making a triangle where you know the measures of two angles and the length of the side between those two angles. Write to angle measures and the length of the side between them for your triangle. You can use any measurements you want as long as they could really be used to form a triangle.
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Set one: 5, 12, 13
Set two: 4, 9, 12
Notice that the first triangle satisfies Pythagorean theorem:
5^2 + 12^2 = 13^2
25 + 144 = 169
169 = 169, so it is a right triangle.
The second triangle does not follow Pythagorean theorem so it is not a right triangle.
Problem 2:
angle 1: 30°
angle 2: 60°
length of the side between the two angles: 25
Notice that the other sides are determined.
When you draw a segment with length 25, and then add two lines, one from each end of the given segment, one of the lines with angle 30° and the other one with angle 60°, the two lines will intersect each other forming a triangle.
The tirangle given is unique and you can check wheter it is rigth or not.
Related Questions
Multiply: (−8x − 15)(−12x2 + 12x + 3)
A) 96x3 + 84x2 − 156x − 45
B) 96x3 + 84x2 − 204x − 45
C) 96x3 + 276x2 − 204x − 45
D) 96x3 − 84x2 − 156x − 45
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if you want the steps you can leave a comment...
stewart draws a triangle , and each side is 2 1/6 inches long. Judith draws a square , each side is 1 5/8 inches long . which figure has the greater perimeter, the triangle or the square?
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Upon calculating, it is found that both Stewart's triangle and Judith's square have the same perimeter of 6 1/2 inches. This shows that despite different shapes, their perimeters can be equal if the lengths of their sides are chosen accordingly.
Explanation:The question is about comparing the perimeters of a triangle drawn by Stewart and a square drawn by Judith. Stewart's triangle has each side measuring 2 1/6 inches long, which when converted to improper fraction becomes 13/6 inches. For the triangle, the perimeter is calculated by multiplying the length of one side by three (since a triangle has three sides). The perimeter of Stewart's triangle is 13/6 * 3 = 39/6 = 6 1/2 inches.
Judith's square has each side measuring 1 5/8 inches long, which is equivalent to 13/8 inches. For the square, the perimeter is the length of one side times four (because a square has four equal sides). Thus, the perimeter of Judith's square is 13/8 * 4 = 52/8 = 6 1/2 inches.
Therefore, both the triangle and the square have the same perimeter of 6 1/2 inches.
Last year, at the Great American Pie Festival, over 16,000 slices of pie was eaten. If each piece of pie is 1/8 of and entire pie, how many pies were eaten at the festival?
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Answer:
2,000 pies!
Step-by-step explanation:
Find 9*4 1/3 mentally using the distributive property
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117/4
Hope this was helpful :)
What the area of this polygon is
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Jamal wants to build a square pen for his dog that has an area of 144 ft². What is the length of each side of the pen?
A: 12ft
B: 15ft
C: 36ft
D: 72ft
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PLEASE HELP!! Show simple working out
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.. (4*6 +10*10 +15*6 +20*9)/(6 +10 +6 +9) = 394/31 ≈ 12.7
Oki I have a few but I’m giving a lot of points I just didn’t feel like doing them separate.
Anne wants to draw two adjacent angles on a straight line. She wants one angle to be 24 degrees more than the other angle. Select two correct choices.
A. The measure of the smaller angle is 33 degrees.
B. The measure of the smaller angle is 78 degrees
C. The measure of the larger angle is 57 degrees.
D. The measure of the larger angle is 102 degrees.
A triangle has a side 4.23 meters in length, a 63.2 degree angle, and a 75.9 degree angle. Which of the following statements about the triangle is true. Select all that apply.
A. The triangle is an obtuse triangle.
B. The triangle cannot be equilateral.
C. The triangle must have a third angle measuring 40.9 degrees.
D. The triangle should be isosceles
3. Mika used the proportion y-3 over x equals one third. (Y-3/x= 1/3). When deriving the equation on a line with similar triangles. Which of the statements are correct. Select two that apply.
A. It has a slope of negative one third. (-1/3)
B. It has a slope of one third. (1/3)
C. It has a slope of 3.
D. It has a y intercept of 3.
E. It has a y intercept of one third. (1/3)
F. It has a y intercept of 3.
This is a parallelogram shaped sliding door. It has four sides. (P,Q) (P,S) (S,R) (Q,R) and (Q,P)
More simply... Q is on the top right corner of the parallelogram, R is on the bottom right corner of the parallelogram, S is at the bottom left corner, and P is at the top left corner.
Which two of the statements are true if the door moves two feet to the right.
A. Side PQ would be parallel to SR, and angle R would measure 56 degrees.
B. Side PS would be parallel to side QR and angle S would measure 124 degrees.
C. Side PQ would be parallel to side PS and angle P would measure 56 degrees.
D. Side QR would be parallel to side SR and angle Q would equal to 62 degrees.
Last one!!
A parallelogram has the verifies (-4,2) (-3,5) (2,-2) (3,5)
The parallelogram was rotated 270 degrees counterclockwise about the origin. Which 3 would be the vertex of the origin.
A. (-3,5)
B. (-2,-2)
C. (-2,4)
D. (2,4)
E. (3,-5)
F. ( I’m rlly sry but I forgot this one)
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180-63.2-75.9=40.9°. This means C is correct.
This also means that B is correct; if a triangle is equilateral, all angles must be congruent as well, which these are not.
Cross multiplying the proportion we have:
x*1 = 3(y-3)
1x = 3y - 9
Solving for y, we first cancel the 9 by adding:
1x+9 = 3y
Now we cancel the 3 by dividing:
1x/3 + 9/3 = 3y/3
1/3x + 3 = y
In this format, we can see that the slope (m) is 1/3 and the y-intercept (b) is 3.
Going by the directions for the points P, Q, R, and S, PQ would be parallel to SR and PS would be parallel to QR. These sides are not parallel to any other sides of this figure.
For the last problem, the vertices given do not form a parallelogram. There is only 1 pair of parallel sides using these points.
The correct option is (A) (-3,5). The answer covers the relationship between angles in quadrilaterals, properties of triangles, and concepts related to similar triangles and equations.
Angles in quadrilaterals:
In the first scenario, if one angle is 24 degrees more than the other on a straight line, the correct choices are A. The measure of the smaller angle is 33 degrees and D. The measure of the larger angle is 102 degrees.
Triangles:
For the triangle with sides 4.23 meters, the correct statements are A. The triangle is an obtuse triangle and D. The triangle should be isosceles.
Similar Triangles and Equations:
When using the proportion y-3/x=1/3, the correct statements are A. It has a slope of -1/3 and E. It has a y-intercept of 1/3.
consider the following system with a solution (1,3) equation 1 of the system 2x+y=5 equation 2 of the system x-2y=-5 prove that replacing the first equation with the sum of the equation and a multiple of the other produces a system with the same solution
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To prove that replacing the first equation with the sum of the equation and a multiple of the other produces a system with the same solution, we will first calculate the solution to the original system. Then we will calculate the solution to the modified system of equations and check if the solution is the same.
Explanation:To prove that replacing the first equation with the sum of the equation and a multiple of the other produces a system with the same solution, we will first calculate the solution to the original system of equations (1,3). Then we will calculate the solution to the modified system of equations in which the first equation is replaced with the sum of the two equations. If the solution to the modified system is also (1,3), then we have shown that the modified system has the same solution.
Original system:
Equation 1: 2x + y = 5
Equation 2: x - 2y = -5
Substitute x = 1 and y = 3 into the original equations to check if it is a solution:
Equation 1: 2(1) + 3 = 5 => 2 + 3 = 5 => 5 = 5 (true)
Equation 2: 1 - 2(3) = -5 => 1 - 6 = -5 => -5 = -5 (true)
Hence, (1,3) is a solution to the original system of equations.
To create the modified system, we will sum equation 1 and a multiple of equation 2:
New equation 1: (2x + y) + k(x - 2y) = 5 + k(-5), where k is a constant
Expanding and simplifying the equation:
(2 + k)x + (1 - 2k)y = 5 - 5k
Let's substitute x = 1 and y = 3 into the modified equation to check if (1,3) is a solution:
(2 + k)(1) + (1 - 2k)(3) = 5 - 5k
2 + k + 3 - 6k = 5 - 5k
3 - 5k = 5 - 5k
3 = 5 (false)
Therefore, the modified system does not have the same solution as the original system, disproving the statement.
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Somebody Really Help On These Questions 5 and 6!!!!!!!!!!!!!!!
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6 + 6 = 12
n is the same thing on both sides of the equation
6 + 6 - n = 12 - n
You are taking an equal amount off both sides so the left and right sides are both equal still. Try it. Let n = 0.5
6 + 6 - 0.5 = 12 - 0.5
6 + 5.5 = 11.5
11.5 =? 11.5
They are both equal. In algebra a letter in an equation like this one can't change values if that letter is on opposite sides of the equation.
Six
9.5 y + 600 < 900
9.5 y = 300
y < 300 / 9.5
y < 31.57
If there's no sales tax where he lives, he can take 31 students. If it is possible to take 0.57 of a student then he can take 32 (but of course it isn't possible).
using the graph above, explain the meaning of the following coordinate pairs and decide if it belongs to jazmine or kiara
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What is the area of the triangle in this coordinate plane
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If 2/3 of N is 4, then 1/2 of N is
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3(2/3)N = (4)3
2N = 12
N = 6
1/2N = 6/2 = 3
Why is subtracting an expression similar to distributing -1? Explain.
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2x - 1(x - 3). This helps us see the distributive property applies here:
2x - 1x - 1(-3)
2x - 1x - -3
2x - 1x + 3
1x + 3 = x + 3
Subtracting an expression is akin to distributing -1 to each term within the expression. This is because subtraction can be viewed as adding the negation of the expression, which involves multiplying each term by -1. So, each term within the expression gets negated when subtracting.
When you subtract an expression, you can think of it as distributing a negative sign (-1) to each term within the expression. Here's a step-by-step explanation:
Start with the expression you want to subtract from, let's call it A.
When you subtract another expression, let's call it B, from A, you're essentially adding the negation of B to A.
The negation of B is obtained by multiplying each term of B by -1.
Distributing -1 to each term of B results in subtracting each term of B individually from A.
This process aligns with the distributive property, making subtracting an expression akin to distributing -1 to each term within the expression.
What is the answer for 3÷3134
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I don't know for sure
n complete two or more sentences, determine the appropriate model for the given data and explain how you made your decision. (1,0), (2,1.5), (5,2.5), (8,3)
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For this case, the function has a logarithmic behavior, therefore, we choose a linear logarithmic trend.
The function that best suits the problem is:
y = 1.4004ln (x) + 0.2158
The value of R ^ 2 indicates the accuracy of the function
R² = 0.9691
For R ^ 2 = 1 the function is completely accurate.
We note that in that case R² = 0.9691, the function chosen has a good approximation.
Mr. Watkins earns $35 an hour at his new job. During a typical month, he works a total of 160 hours. Mrs. Watkins is a homemaker. After meeting the estimated monthly expenses, how much money will the family have left to spend on other items?
A) $1150
B) $1322
C) $1445
D) $1500
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[tex](35 \times 160) - 4278[/tex]
[tex]5600 - 4278[/tex]
[tex]1322[/tex]
The teacher bought new crayons for her class. She bought 7 packs of 9 crayons. She already has 17 crayons in her classroom. She wants to divide the crayons evenly between her 10 students. How many crayons will each student receive? Use c as the variable. Write an equation and solve the problem.
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Jerry started doing sit-ups every day. The first day he did 15 sit-ups. Every day after that he did 4 more sit-ups than he had done the previous day. Today Jerry did 65 sit-ups. Write an equation that could be solved to find the number of days Jerry has been doing sit-ups, not counting the first day. Let n represent the number of days.
Thanks
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The first day Jerry did 15 sit-ups:
a0 = 15
The 2nd day he did 4 more sit-ups then the previous:
a1 = a0 + 4
The 3rd day he did 4 more sit-ups then the previous:
a2 = a1 + 4
a2 = a0 + 4 + 4
a2 = a0 + 4*4
the (n+1)-th day he did:
an = a0 + 4n
Today Jerry did 65 sit-ups means we have: an = 65 and we need to find n
a0 + 4n = 65
15 + 4n = 65
Now to solve
subtract 15 from both sides
4n = 50
divide both sides by 4
n = 12.5
But I think this is counting the first day
Not counting the first day would be
4n = 65
n = 16.25
I guess that's the answer :)
this figure is 1/4 of a circle what is the best approximation for the perimeter of the figure use 3.14 to approximate pi
A) 3.1
B) 6.3
C) 7.1
D) 12. 3
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Answer: Option 'C' is correct.
Step-by-step explanation:
Since we know that
The figure is known as "Quadrant" in which angle is 90° .
As we know that "Length of an arc":
[tex]Length=\frac{\theta}{360\textdegree}\times 2\times 3.14\times r\\\\Length=\frac{90\textdegree}{360\textdegree}\times 2\times 3.14\times 2\\\\Length=\frac{1}{4}\times 12.56\\\\Length=3.14[/tex]
Perimeter of the figure is given by
[tex]3.14+2+2=7.1[/tex]
Hence, Option 'C' is correct.
Answer:
c
Step-by-step explanation:
i took the test 4 days ago
What is the slant height for the given pyramid to the nearest whole unit?
Pyramid base = 10 cm Height = 12 cm
A. 7 cm
B. 11 cm
C. 13 cm
D. 16 cm
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To find it, what we should do is use the Pythagorean theorem.
We have then:
d = ROOT ((10/2) ^ 2 + (12) ^ 2)
d = ROOT (25 + 144)
d = ROOT (169)
d = 13 cm
Answer:
C. 13 cm
Answer:
13 cm
Step-by-step explanation:
Done the test.
There are three numbers that are their own cube roots. What are the numbers?
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Final answer:
The three numbers that are their own cube roots are 0, 1, and 8.
Explanation:
The three numbers that are their own cube roots are 0, 1, and 8.
A cube root of a number is a value that, when raised to the power of 3, gives the original number. For example, the cube root of 8 is 2 because 2³ = 8. Similarly, the cube root of 0 is 0 and the cube root of 1 is 1.
So, the numbers that are their own cube roots are 0, 1, and 8.
50 POINTS!!! SHOW YOUR WORK AND ANSWER CORRECTLY OR ELSE A MODERATOR WILL HANDLE YOU! Let f (x) = −x^2 − 5x + 36. What is the value of f(-3)? Show your work. Best answer gets brainliest.
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Your question states:
Let f (x) = −x^2 − 5x + 36. What is the value of f(-3)?
Your answer would be:
42
Your explanation:
3^2-5(-3)+36
9-15+36
6+36
[tex]f(x) = -x^2-5x+36\qquad \qquad f(-3)=? \\ \\ \\f(-3) = -(-3)^2-5(-3)+36\\ \\f(-3) = -(9)-5(-3)+36\\ \\f(-3) = -9+15+36 \\ \\ \boxed{f(-3) = 42} [/tex]
The square of a positive number decreased by twice the number is 48. Find the number
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8^2-16=48
Write a algebraic expression for the quotient of 300 and sum of b and 24
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The algebraic expressions for the quotient of 300 and sum of b and 24 would be; 300/(b + 24).
What is an expression?Expression is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given that a is the quotient of 300 and sum of b and 24
We have a dividend and a divisor in a division problem.
The first piece (300) is the dividend, the numerator if we are writing it in fraction form or the first number when using the standard division sign.
The divisor is the sum of b + 24 which means we need to find the answer before dividing by it.
Then place a parentheses around it.
300/(b + 24).
This is an expression, there should be NO equals sign.
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If 20% is 3.5, what is 100%?
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3.5 ÷ 0.2 = 17.5 ← answer
Multiply 3.5 by 5.
5 * 3.5 = 17.5
Solve for P=b+2a+2c for b
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b + 2a + 2c = p or unknown answer,
b plus 2 times a plus 2 times c equals p the unknown answer
From there you use the strategy of guess and check to get your answer.
Helpppp please anyone. I don't understand
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The equation of A=25w Gives the area A (In square feet) of a rectangular dance floor with a width of W feet
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Water from a leaking faucet is dripping into a cylindrical cup. The height of water in inches, y, after x hours is graphed belowThe water level increases by 1 inch each hour.
A The water level increases by 1 inch each hour.
B The water level increases by 2 inches each hour.
C The water level increases by a factor of 1/2each hour.
D The water level increases by a factor of 2 each hour.