Yu-Xi draws a triangle with two angles measuring 79 degrees and 23 degrees.What is the measure, in degrees, of the third angle?
Answers
180-102=78
the third angle is 78 degrees
Answer:
The Triangle Drawn by ,Yu-Xi,has measure of two angles ,79° and 23°.
All the Basic Learners who knows Math ,that,sum of Measures of three Interior angles of Triangle is 180°.
→79°+23°+Third Angle =180°
→102°+Third Angle =180°
→Third Angle =180° -102°
Third Angle =78°
Related Questions
The hypotenuse of a right triangle is 50 and the short leg is 30, find the projection of the leg onto the hypotenuse
Answers
CB/CA = CD/CB
30/50 = projection/30
projection = 30^2/50
projection = 18
Easy Geometry! Easy Geometry! Easy Geometry!
Answers
b. Linear Pair
c. Definition of supplementary
d. Substitution; Combine like terms
e. Division Property of Equality
f. Definition of Right Angle
g. Definition of Perpendicular
=========================================
Further Explanations:
b. A linear pair is simply a result of cutting a straight angle into two pieces. They are adjacent and supplementary (add to 180 degrees)
c. If two angles are supplementary then they add to 180. This is simply a definition to memorize.
d. The "m < 2" is replaced with "m < 1" through the substitution property. This is possible because of statement (a) on the first line of the proof. The teacher has also combined like terms. Technically this step would require its own line.
e. Think of this as 2x = 180 solving to x = 90. The step done here is dividing both sides by 2, which uses the division property of equality. Alternatively you can use the multiplication property of equality to multiply both sides by 1/2 = 0.5
f. If an angle is 90 degrees, then by definition it is considered a right angle. This is another thing you memorize.
g. Also to be memorized is the fact that if two segments form a right angle, then they are considered perpendicular segments. The upside down T symbol means "perpendicular to"
Answer:
b) Linear Pair
c) Definition of supplementary
d) Substitution; Combine like terms
e) Division Property of Equality
f) Definition of Right Angle
g) Definition of Perpendicular
Solve for x in the equation x2+20x+100=36
Answers
[tex] x = - 64 \div 22 = -2.909091[/tex]
But if x2 was supposed to be x^2 then the answer is:
[tex]x = - 4.-16[/tex]
Answer:
x = -4 and x = -16.
Step-by-step explanation:
We have the equation,
[tex]x^{2}+20x+100=36[/tex]
i.e. [tex]x^{2}+20x+64=0[/tex]
As the solution of a quadratic equation [tex]ax^{2}+bx+c=0[/tex] is given by [tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex].
On comparing, a = 1, b = 20, c = 64.
So, the solution is,
[tex]x=\frac{-20\pm \sqrt{(20)^{2}-4\times 1\times 64}}{2a\times 1}[/tex].
i.e. [tex]x=\frac{-20\pm \sqrt{400-256}}{2}[/tex].
i.e. [tex]x=\frac{-20\pm \sqrt{144}}{2}[/tex].
i.e. [tex]x=\frac{-20\pm 12}{2}[/tex].
i.e. [tex]x=\frac{-20+12}{2}[/tex] and [tex]x=\frac{-20-12}{2}[/tex].
i.e. [tex]x=\frac{-8}{2}[/tex] and [tex]x=\frac{-32}{2}[/tex].
i.e. x = -4 and x = -16
Thus, the solution of the given equation is x = -4 and x = -16.
If the length of a rectangle is decreased by 4 cm and the width is increased by 5 cm, the result will be a square, the area of which will be 40 cm2 greater than the area of the rectangle. Find the area of the rectangle.
Answers
(x +4)*(x -5) +40 = x^2
x^2 -x -20 +40 = x^2
20 = x
The rectangle is 15 cm by 24 cm, and its area is 360 cm^2.
what is the change of entropy for a heat engine using 500.0j at 20.0c
Answers
hope it helps :D!!
The formula to find change in entropy is given by :
[tex] Change in entropy = \frac{Q}{T} [/tex]
where Q is change in heat and T is temperature.
We are given Q = 500 joule and T = 20 degree C
Plugging these values in the formula,
[tex] Change in entropy = \frac{500}{20} [/tex]
We get change in entropy = 25 J/Celsius.
which statement about sqrt x-5 minus sqrt x=5 true?
-3 is a true solution
-3 is a extraneous solution
9 is a true solution
9 is a extraneous solution
Answers
Answer:
9 is an extraneous solution.
Step-by-step explanation:
Extraneous solution is a solution that when plugged into the equation do not hold true.
Here we are given an algebraic equation in terms of single variable x as:
[tex]\sqrt{x-5}-\sqrt{x}=5-----(1)[/tex]
Now, we will solve this equation to obtain the solution as:
on squaring both side of the equation we obtain:
[tex](\sqrt{x-5}-\sqrt{x})^2=5^2[/tex]
[tex]x-5+x-2\sqrt{x-5}\sqrt{x}=25\\\\2x-5-2\sqrt{x-5}\sqrt{x}=25\\\\2x-30=2\sqrt{x-5}\sqrt{x}\\\\on\ dividing\ both\ side\ by\ 2\ we\ obtain:\\\\x-15=\sqrt{x-5}\sqrt{x}[/tex]
Again on squaring both side of the equation we obtain:
[tex]x^2+225-30x=(x-5)x\\\\\x^2+225-30x=x^2-5x\\\\225=-5x+30x\\\\225=25x\\\\x=9[/tex]
Now when we plug x=9 back to the original equation i.e. equation (1) we get:
[tex]\sqrt{9-5}-\sqrt{9}=5\\\\\sqrt{4}-\sqrt{9}=5\\\\2-3=5\\\\-1=5[/tex]
Hence, the equation does not hold true.
Hence, 9 is a extraneous solution
Your team gets an ice sculpture in the shape of a basketball. It has a radius of 12 inches. What is the volume of the ice? Use 3.14 for pi. Round your answer to the nearest hundredth.
Answers
The equation would be 4/3 * 3.14 * 12^3.
4/3 * 3.14 * 1728
4/3 * 5425.92
7234.56
Is the system of equations is consistent, consistent and coincident, or inconsistent?
y=−3x+12y=−6x+2
Select the correct answer from the drop-down menu.
Answers
Coincident is one line on the graph
Consistent is two parallel lines
Answer:
The given system of equations is inconsistent.
Step-by-step explanation:
We have been given a system of equations and we are asked to find whether our given system of equation is consistent, consistent and coincident, or inconsistent.
[tex]y=-3x+12...(1)[/tex]
[tex]y=-6x+2...(2)[/tex]
Since we know that a system of equations is inconsistent if it has no solution. Parallel lines are inconsistent because they do not intersect.
Consistent system of equations can have one or infinitely many solution. As if two lines are same then they will have infinitely many solution. If lines intersect at only one point, then they will have only one solution.
Now let us check slope of given lines.
Upon dividing equation (2) by 2 we will get,
[tex]y=-3x+1...(2)[/tex]
We can see that both lines have slope of negative 3. Since y-intercept of both equations are different, so they will not intersect at any point.
Since our given equations represent parallel lines, therefore, our given system of equations is inconsistent.
Simplify (3x − 5) − (5x + 1).
−2x + 6
−2x − 6
2x − 6
2x + 6
can you please work this out for me?
thank you verymuch.
Answers
we have been asked to simplify
[tex] (3x-5)-(5x + 1) [/tex]
To Simplify this, we will first open the parenthesis, as below
[tex] (3x-5)-(5x + 1)=3x-5-5x-1\\
\\
\text{take the like terms together and simplify we get}\\
\\
(3x-5)-(5x + 1)=3x-5x-5-1\\
\\
(3x-5)-(5x + 1)=-2x-6\\
\\
[/tex]
Hence the simplified expression is -2x-6
Answer:
-2x-6
Step-by-step explanation:
which figures can be precisely defined by using only undefined terms? check all that apply
1) angle
2) arc
3) circle
4) line segment
5) parallel lines
Answers
Organize the following expressions from greatest to least by number of terms: x + 2xyz 9x2yz 18x2 + 5ab − 6y 4x3 + 3x2 − x − 4
Answers
Answer:
The answer is the option C
IV, III,I,II
Step-by-step explanation:
helppppppppppppppppppppppppppppp
Answers
We have then:
2 (16x ^ 3y) ^ (1/3) + 4 (54x ^ 6y ^ 5) ^ (1/3)
We then have to use properties of exponents:
4 ((2 ^ (1/3) xy ^ (1/3)) + 12 ((2 ^ (1/3)) x ^ 2y ^ (5/3))
4 ((2 ^ (1/3) xy ^ (1/3)) + 12 ((2 ^ (1/3)) x ^ 2 * y * y ^ (2/3))
We rewrite:
4x ((2y) ^ (1/3)) + 12 * x ^ 2 * y ((2y ^ 2) ^ (1/3))
Answer:
4x ((2y) ^ (1/3)) + 12 * x ^ 2 * y ((2y ^ 2) ^ (1/3))
option 1
Parts of Complex Numbers
z=4.1i+85
Re(z)=_____
Im(z)=_____
Answers
where a is the real number of z (Re z) while b is the imaginary part of z (im z)
Therefore in this case; z=4.1 i +85, therefore
Re(z) =85
Im(z) = 4.1
The equation y=4.75x+20 gives the cost y of towing a car if the car is towed x miles.
According to to the model, what is the best estimate of the cost for towing a car 22 miles.
A. $24.75
B $46.25
C $104.50
D $124.50
Answers
Answer: $124.50
Step-by-step explanation:
We are given that the equation y=4.75x+20 gives the cost y of towing a car if the car is towed x miles.
To find the best estimate of the cost for towing a car 22 miles., we substitute x= 22 in the above equation, we get
Cost of towing a car 22 miles=[tex]y=4.75(22)+20=[/tex]
[tex]\rightarrow\ y=104.50+20=124.50[/tex]
Therefore, the best estimate of the cost for towing a car 22 miles = $124.50
The rectangle is the image after a dilation with the center of dilation at the origin of rectangle ABCD. The pre-image of A' point A, has coordinates of (–4, 3.2). What is the scale factor of the dilation and what are the coordinates of point C?
Answers
Answer:
The scale factor is 2.5 and the coordinates of point C are (–2.4, –0.8).
Step-by-step explanation:
Amir's checking account charges a $9.75 monthly service fee and a $0.12 per-check fee. If Amir writes 15 checks per month, should he switch to a checking account that charges an $11.50 monthly service fee and no per-check fee
Answers
[tex]0.12(15) = 1.80 [/tex]
[tex]1.80 + 9.75 = 11.55[/tex]
Yes Amir should switch because it's a nickel less
Is it possible to toss a coin 20 times and have it land heads-up 20 times? Is this likely to happen? explain.
Answers
factor the GCF: 15a+25b
Answers
The factored form of the expression 15a + 25b with respect to the Greatest Common Factor (GCF) is 5 (3a + 5b). The GCF of 15 and 25 is 5.
Explanation:To factor the Greatest Common Factor (GCF) from 15a + 25b, we first have to identify the GCF. The GCF of 15 and 25 is 5. Hence, we divide each term in the expression by this GCF.
We get: 5 (3a + 5b). So, the expression 15a + 25b factored by the GCF is 5 (3a + 5b).
Learn more about Factoring here:https://brainly.com/question/33624529
#SPJ11
Please help out with this question! Thanks :)
Answers
If 11 is among the choices, that is the answer I'd choose.
What is 59.69 in expanded form
Answers
50 +9 + 0.6+ 0.09
Expanded Factors Form:
5 × 10 +9 × 1 +6 × 0.1+9 × 0.01
Expanded Exponential Form:
5 × 101+9 × 100+6 × 10-1+9 × 10-2
Word Form:
fifty-nine and sixty-nine hundredths
Triangle FGH is similar to JKM.
If f = 14.4 cm, g = 16.56 cm, h = 25.92 cm, and k = 9.2 cm, what is the measure of m?
A. 5.104 cm
B. 14.4 cm
C. 10.58 cm
D. 8 cm
Answers
so we can find the scale that FHG was dilated by.
[tex]16.56 \div 9.2 = 1.8[/tex]
so the sides of the triangle KMJ were multiplied by 1.8.
to find m :
[tex]25.92 \div 1.8 = 14.4[/tex]
m=14.4
hope this helps
PLEASE HELP I NEED THE ANSWER TO THIS ASAP. YOU JUST NEED TO MATCH EACH THING ON THE LEFT TO ITS CORRECT ANSWER ON THE RIGHT.
Match the following items.
Complete the proof for Theorem 3-13. (if you dont know what this theorem is i added a picture that explains it so you can help)
Answers
But I'll give it a try:
1) l // m ___ Given
2) <1 = <3 ___ if parallel lines, then corresponding angles (<s) are equal
3) <2 = <3 ___ Vertical <s are equal
4) <1 = <2 ___ Substitution
The complete proof of the theorem in chronological order is;
GivenIf lines are ∥, corresponding angles are equal.Vertical angles are equalSubstitutionHow to complete a proof?The proof that when a transversal cut two parallel lines, alternate angles are equal.
1.
Statement: l ∥ m
Reason: Given
2.
Statement: m ∠ 1 = m ∠ 3
Reason: If lines are ∥, corresponding angles are equal.
3.
Statement: m ∠ 2 = m ∠ 3
Reason: Vertical angles are equal
4.
Statement: m ∠ 1 = m ∠ 2
Reason: Substitution
Therefore, alternate exterior angles are equal when a transversal cut two parallel lines,
Read more on vertical angles:
https://brainly.com/question/1673457
#SPJ3
Hellllllllłllllllllllllllllllllllllllllllllllpp
Answers
The circumference (C) of a swimming pool is 47 feet. Which formula can you use to find the radius (r) if you know that C = 2πr ?
Answers
2. you get r = c/2π
Answer:
r=C/2*pie
Step-by-step explanation:
I got it correct on TTM
Find the midpoint of the line segment whose endpoints are (7,5) and (7,11)
Answers
How many times would a coin have to show heads in 50 tosses to have an experimental probability of 20% more than the theoretical probability of getting heads? 10 25 35 45
Answers
A 4040 inch wire is to be cut. one piece is to be bent into the shape of a square, whereas the other piece is to be bent into the shape of a rectangle whose length is twice the width. find the width of the rectangle that will minimize the total area. what is the width of the rectangle that will minimize the total area?
Answers
perimeters: 40 = 4s + 2(r + 2r) = 4s + 6r → s = (1/4)(40 - 6r) = 10 - 1.5r areas: A = s² + 2r² = (10 - 1.5r)² + 2r² = 100 - 30r + 4.25r²
Then dA/dr = 0 = 9.5r - 30 r = 30/9.5 = 3.16 in ← width of rectangle (length is twice the width) d²A/dr² = 9.5 > 0, so it is a minimum.
With $3500 each, Martin and Edward opened separate accounts. Each account offered 4.5% interest over 10 years. At the end of 10 years, Edward earned more than Martin. Why? A. Edward invested for a different amount of time than Martin. B. Edward had a different interest rate than Martin. C. Edward earned compound interest, and Martin earned simple interest. D. Edward e
Soomeone helpppp meeee
Answers
The interest earned from above cash under simple interest will be:
S.I=(PRT)/100
S.I=3500*4.5/100*10=$1575
the total amount after 10 years will therefore be:
1575+3500
=$5075
The same amount if it was compounded annually, the amount after 10 years will be:
FV=P(1+r/100)^n
FV=3500(1+3.5/100)^10
FV=4,937.10
we therefore conclude that the answer is:
Edward must have earned simple interest while Martin earned compound interest.
HELP PLEASE HELP HELP
Answers
The answer is D
Raul used the steps shown below to solve the equation. In which step did Raul make a mistake?
5x-3(2x+7)=2x+9
Step 1: 5x-6x-21=2x+9
Step 2: -11x-21=2x+9
Step 3: -12x=30
Step 4: x=-30/12
A. Step 1
B. Step 2
C. Step 3
D. Step 4
Answers
5x-3(2x+7)=2x+9
This is the equation and Raul had to solve it for x
So he started with simplifying the parenthesis first
To simplify the parenthesis -3 gets multiplied with 2x and 7 , to get rid of parenthesis
So it came out to be
5x-3(2x+7)=2x+9
STEP-1
5x-6x -21 = 2x+9 , So the STEP-1 is correct,
After this in Step -2 , he has combined the like terms on left side, the like terms are 5x and -6x , 5x-6x should combine to -x , because 5-6 = -1
So
STEP-2
-x -21 = 2x+9 , So STEP -2 is INCORRECT
So he made a mistake in STEP-2
After that subtract 2x from both sides
-3x -21 = 9
add 21 to both sides
-3x = 30
divide both sides by -3
x=-10
Hence Option B is correct , he made a mistake in STEP -2