Answers
Triangle based on the side lengths 7. 15 and 21 is Obtuse triangle.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
The sides of triangle are 7, 15 and 21.
Let the largest angle be θ.
cosθ=7²+15²-21²/2×7×15
=-167/210
Since arc cos(-167/210)=142.68 degrees.
θ=142.68 degrees.
Which means θ>90 degrees.
So its a obtuse triangle.
7+15=22>21
21-7=14<15
So those angles can make a obtuse triangle.
Hence, triangle based on the side lengths 7. 15 and 21 is Obtuse triangle.
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Related Questions
Can any one explain this question worth points! plz explain if you can
Answers
Answer:
x = 31
Step-by-step explanation:
The given angles are supplementary and their sum is 180 degrees
5x - 16 + x + 10 = 180 add like terms
6x - 6 = 180 add 6 to both sides
6x = 186 divide both sides by 6
x = 31
The figure below shows a quadrilateral ABCD. Sides AB and DC are congruent and parallel:
(image)
Which statement best describes a flaw in the student's proof?
Angle DBC and angle BDA form a pair of vertical angles, not a pair of alternate interior angles, which are congruent.
Triangles ABD and CDB are congruent by the SAS postulate instead of the SSS postulate.
Triangles ABD and BCD are congruent by the AAS postulate instead of the SSS postulate.
Angle DBC and angle BDA form a pair of corresponding angles, not a pair of alternate interior angles, which are congruent.
Answers
The statement that best describes a flaw in the students' proof is;
Option D; Angle DBC and angle BDA form a pair of corresponding angles, not a pair of alternate interior angles, which are congruent.
From the given image, we can see that;
AB ≅ DC
Let us analyze each given option;
A) ∠DBC and ∠BDA are in the same triangle ΔBDC. Now, they can't be a pair of vertical angles because vertical angles are a pair of opposite angles formed when two lines intersect but this is not the case here.
They are also not alternate interior angles because alternate angles are formed when a transverse line intersects two coplanar lines and again that is not the case here.
B) In ΔABD and ΔBDC, we see that;
AB = DC. Also, by theorem of alternate interior angles, we can tell that;
∠ABD = ∠BDC
Similarly, ∠BDA = ∠DBC from alternate interior angles.
Thus, there is one corresponding side and two non-included angles which means the triangles are congruent by AAS Congruency postulate.
C) As seen in B above, this statement is correct because the triangles are congruent by AAS postulate.
D) Corresponding angles lie on the same side of the transversal. In this case, ∠BDA and ∠DBC lie on opposite sides and are even congruent by alternate interior angles.
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The first equation in the following system gives a company's income, in dollars, for selling x baseball caps. The second equation gives the cost of making x baseball caps. Y = 8x y = -0. 01 x2 4x 3,200 The solution of the system is (400, 3,200). How would you interpret this solution?.
Answers
The solution of the equation can be determined by substituting the points in the equation and solving it.
The solution of the given equation would be interpreted by solving the equation for the value of x and y.
The solution of the equation is (400, 3200) and it can be determined by using substitution method.
Given that,The first equation in the following system gives a company's income, in dollars, for selling x baseball caps.
The second equation gives the cost of making x baseball caps.
[tex]\rm y = 8x\\\\ y = -0.01 x^2 + 4x + 3200[/tex]
The solution of the system is (400, 3,200).
We have to determine,How would you interpret this solution?
According to the question,The first equation in the following system gives a company's income, in dollars, for selling x baseball caps.
The second equation gives the cost of making x baseball caps.
[tex]\rm y = 8x\\\\ y = -0.01 x^2 + 4x + 3200[/tex]
On solving both the equation,Substitute y = 8x in the equation 2,
[tex]\rm y = -0.01 x^2 + 4x + 3200\\\\ 8x = -0.01 x^2 + 4x + 3200\\\\0.01x^2+8x-4x-3200=0\\\\0.01x (x+800) -4(x+800)=0\\\\(x+800)\ (0.01x-4)\\\\When \ \ x +800=0, \ x = -800\\\\And\ \ 0.01x-4 = 0, \ \ x = \dfrac{4}{0.01} \ \ x =400[/tex]
The value of x is not -800 because the cost can not be negative.
Then the value of x is 400.
Substitute the value of x in equation 1,
[tex]\rm y = 8x\\\\y = 8(400)\\\\y = 3200[/tex]
Hence, The solution of the equation is (400, 3200).
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solve this
x2 + 14 x + 33 = 0
Answers
Answer:
-11, -3.
Step-by-step explanation:
x^2 + 14x + 33 =0
To factor this we need 2 numbers whose product is 33 and whose sum is 14 .
These are 3 and 11, so:
(x + 3)(x + 11) = 0
x = 11, -3.
Please help me with this question
Answers
Answer:
F
Step-by-step explanation:
Answer:
F
Step-by-step explanation:
You only need to read as far as ...
y ≤
to choose the correct graph. The values in the solution will be less than or equal to those on the boundary line. That means the graph will be shaded below the line, and the line will be solid (because it is part of the solution).
The graph with a solid line and shading below is graph F.
if 6 24 36 are in proportion,find the second proportional.
Answers
9
Step-by-step explanation:
let 2nd proportion be x
6:x=24:36
6÷x=24÷36
x=6×36÷24
x=9
How i can answer this question
Answers
Answer:
A
Step-by-step explanation:
They both equal 2(x+y+1)
Help me out plesseee!!
Answers
Step-by-step explanation:
the rate of change is officially
(f(x2) - f(x1)) / (x2 - x1)
but for a line function (as we have here) this is totally easy : it is the slope of the line.
and that means it is the factor of x.
in our case this is -3/2.
because the slope of a line is the ratio "y coordinate change / x coordinate change". and that is exactly corresponding to the general rate of change definition above.
Answer: (f(x2) - f(x1)) / (x2 - x1)
because the slope of a line is the ratio "y coordinate change / x coordinate change".
Step-by-step explanation: HOPE IT HELPS YOU .THANKS .
Can someone plz help Me?
Answers
the answer to your question is C. 6^4
Answer:C? sorry if im wrong
Step-by-step explanation:
25.4 as mixed number
Answers
Answer:
6.25
Step-by-step explanation:
I believe you were trying to put a fraction in but accidentally pressed the period.
25/4
6 1/4
6.25
Answer:
25 2/5
Step-by-step explanation:
Hope it's right and it helps.
What is the solution to this inequality?
−15x>75
x<−5
x>−5
x≥−5
x≤−5
Answers
Answer:
x < -5 (the first option)
Step-by-step explanation:
I hope this helps!
The solution of the inequality will be;
⇒ x < - 5
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ - 15x > 75
Now,
Since, The inequality is,
⇒ - 15x > 75
Hence, The solution of the inequality is,
⇒ - 15x > 75
⇒ - x > 75/15
⇒ - x > 5
⇒ x < - 5
Thus, The solution of the inequality is,
⇒ x < - 5
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How do I solve for x?
Answers
16 - 36 = -20
X = -20
Here, the opposite angles of the triangle are equal. If 2 opp. angles in a triangle are equal, then the opposite sides will be equal as well.
So,
16 = x + 36
16 - 36 = x
-20 = x
______
Hope it helps ⚜
What the vertex of y=4(x-3)^2+3
Answers
Answer:
(3,3)
Step-by-step explanation:
we rewrite in vertex form and use this form to find the vertex (h,k)
Calculate the volume of the cylinder:
10 cm
6 cm
Answers
Answer:
60
Step-by-step explanation:
10 ×6
that is the simple answer to your question
hey guys can you help me with this question? 20 points :)
Answers
Answer:
About 7 units
Step-by-step explanation:
About 7 units would be correct. 1 + 6 is 7
however 6 isn’t an option so the next closet thing is 7
HOPE THIS HELPED :3
Answer pretty sure that’s 7
Step-by-step explanation:
who was often called the father of modern mathematics because he created analytic geometry and the cartesian coordinate system?
Answers
René Descartes was the person who created analytic geometry and the Cartesian coordinate system
what is the following product 3 sqrt 4 times sqrt 3
Answers
Answer:
c on edge YW
Step-by-step explanation:
The value of ∛4 × √3 is 2.75 or [tex]\sqrt[6]{432}[/tex].
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given;
Expression,
product 3 sqrt 4 times sqrt 3.
In numerator form:
As per the given expression,
∛4 × √3
Simplifying,
∛4 × √3
= [tex]4^{1/3}[/tex] x [tex]3^{1/2}[/tex]
= [tex]4^{2/6}[/tex] x [tex]3^{3/6}[/tex]
= [tex]\sqrt[6]{16 + 27}[/tex]
= [tex]\sqrt[6]{432}[/tex]
= 2.749
= 2.75
Therefore, the product is 2.75 or [tex]\sqrt[6]{432}[/tex].
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The quadratic function f(x)= x^2-14x+53 is equal to zero when x=a+ or - bi
What is the value of a?
What is the value of b?
Answers
Answer:
A= 3x B= 6/8
Step-by-step explanation:
The value of a is 7, and the value of b is 2√(2) for the given quadratic function f(x) = x² - 14x + 53.
What is a quadratic function?The quadratic function is defined as a function containing the highest power of a variable is two.
The quadratic function f(x) = x² - 14x + 53 is equal to zero when x = a + bi or x = a - bi. This means that the roots of the quadratic equation are a + bi and a - bi.
The roots of a quadratic equation can be found using the quadratic formula:
x = (-b +/- √(b² - 4ac)) / (2a)
In this case, a = 1, b = -14, and c = 53. Substituting these values into the quadratic formula, we get:
x = (-(-14) +/- √((-14)² - 4153)) / (2*1)
x = (14 +/- √(196 - 212)) / 2
x = (14 +/- √(-16)) / 2
Since the square root of a negative number is an imaginary number, the roots of the quadratic equation are a + bi and a - bi, where a = 14/2 = 7 and b = √(-16)/2 = 2√(2).
Therefore, the value of a is 7, and the value of b is 2√(2).
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HELP!! Select the values for the domain and range of the functions graphed below.
Answers
Answer:
Graph 1
Domain = -8 =< x =< 10
Range = -9 =< f(x) =< 9
Graph 2
Domain = -1 =< x =< 5
Range = -1 =< f(x) =< 2
Explaination:
Domain means the inputed x values on the x-axis, so to make things simpler and to not write every individual x values. We write it with <, >, and =<. (you can see it as the 'width' of a graph).
Range means the output y values on the y-axis. It's like the 'height' of a graph. And also, to make things simpler and to not write every individual y values. We write it with <, >, and =< with f(x) too because f(x) = y.
In Damien's classroom, the ratio
of boys to girls is 4:5. If there
are 12 boys, how many students
are there in all in Damien's
classroom
Answers
Answer:
The answer would be 27 students
Step-by-step explanation:
4=boys
5=girls
4 x 3 = 12
5 x 13 = 15
12+ 15 = 27
If 5 20 times 2 Superscript 2 minus 3 x Baseline = 10 times 2 Superscript negative 2 x Baseline 5, what is the value of x? â€"3 â€"2 2 3.
Answers
The value of x is 3.
Given that,
If [tex]5 + 20 \times 2^{2-3x}[/tex],
And Baseline = [tex]10 \times 2^{-2x}+5[/tex]
We have to find,
The value of x?
According to the question,
To determine the value of x in the equation following all the steps given below.
Equation; [tex]\rm 5 + 20 \times 2^{2-3x} = 10 \times 2^{-2x}+5[/tex]
Step1; Subtract 5 from both sides,[tex]\rm5- 5 + 20 \times 2^{2-3x} = 10 \times 2^{-2x}+5-5\\\\\rm 20 \times 2^{2-3x} = 10 \times 2^{-2x}[/tex]
Step2; Divided by 10 on both sides,[tex]\rm 20 \times 2^{2-3x} = 10 \times 2^{-2x}\\\\\dfrac{ 20 \times 2^{2-3x} }{10}= \dfrac{10 \times 2^{-2x}}{10}\\\\\rm 2 \times 2^{2-3x} = 2^{-2x}[/tex]
Step3; Rewrite the term into their power form and add the powers,[tex]\rm 2 \times 2^{2-3x} = 2^{-2x}\\\\2^1 \times 2^{2-3x} = 2^{-2x}\\\\2^{2-3x+1} = 2^{-2x}\\\\[/tex]
Step4; The base is the same on both sides, we equate exponents,[tex]\rm 2-3x+1 = -2x\\\\-3x+2x = -1-2\\\\-x = -3\\\\x=3[/tex]
Hence, The required value of x is 3.
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Adam is planning a pool party to celebrate the last day of school. He wants to give out beach towels to his guests as party favors. Adam ordered 14 beach towels from Sunshine Party Supply. Since this was a bulk order, Sunshine Party Supply reduced the price of each towel by $3.25. Adam paid $105 in all. How much does Sunshine Party Supply normally charge for a beach towel?
Answers
Answer:
10.75
Step-by-step explanation:
first step is to find how much adam paid for each towel
so, the equation used will be x/y=c
where x is total cost, y is number of products bought, and c equals individual cost (with discount)
we end up with 105/14= 7.5$ per towel.
and to close out, we add the given discount of 3.25 to the discounted price of 7.5
which brings the usual price per towel to 10.25
Answer:
Step-by-step explanation:
which statement is true?
Answers
Answer:
The slope of function A is less than the slope of function B
Explanation:
The slope for function B is 1/2, which is greaterthan 1/5, the slope of function A.
Answer:
the slope on Function A is less than Function B
Step-by-step explanation:
By doing rise over run we can get 1/2 on Function B and the Y intercept is 5 so the equation is y=1/2x+5
Dante’s chocolate bar is 36% cocoa. If the weight of the chocolate bar is 73 grams, how many grams of cocoa does it contain round your answer to the nearest tenth?
Answers
Answer:
26.3 grams
Step-by-step explanation:
36% = 36/100 = 0.36
73 * 0.36 = 26.28 grams ≈ 26.3 grams
Answer:
i think 26.3 grams
Step-by-step explanation:
0.36×73 = 26.28
When rounded to the nearest tenth, 26.28 should be equal to 26.3
So Dante's the chocolate bar contains 26.3 grams of cocoa.
1.0835 rounded to the nearest tenth
Answers
Answer:
1.1
Step-by-step explanation:
Answer:
1.1
Step-by-step explanation:
1 Name the shapes that are being described. a I have three sides that are all the same length. I have three equal angles. Thave three lines of symmetry and rotational symmetry of order 5. b I have four sides. Thave one line of symmetry and rotational symmetry of order 1. Two of my angles are equal. I have two pairs of equal length sides' C I have six sides. All my sides are the same length. I have six lines of symmetry and rotational symmetry of order
Answers
Answer:
a. Equilateral triangle
b. Quadrilaterals
c. Hexagon
Step-by-step explanation:
Write the name of a polynomial (using the degree) with the sequence of the
outputs: (5,2,-1,-4, ...}*
Type ONE word
Answers
Answer:
pentagon
Step-by-step explanation:
5 degree angle
How to solve 8.9 times 6
Answers
Answer:
53.4
Step-by-step explanation:
8.9 × 6 = 53.4
Hope it help !
PLEASE HELP
Classify each sequence as arithmetic, geometric or neither:
1.) -1/16, 1/4, -1, 4, -16, …
2.) -5, 10, -15, 20, -25, …
3.) 65, 52, 36, 26, 13, …
[] Neither
[] Arithmetic
[] Geometric
Answers
Answer:
1. ARITHMETIC
2. NEITHER
3. GOEMETRIC
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x+y=3
workout the value of 2x-2y
Answers
Answer:
-2
Step-by-step explanation:
x= 1
y= 2
2 times x(1)=2
2 times y(2)=4
2-4= -2