Answers
Answer:
x=12
Step-by-step explanation:
Given that there is only one expression given in each triangle, if we only use the information in a single triangle, there is no way to set up an equation that we could solve to find the expression. (For this situation, at best we could use the triangle sum theorem to say that the three angles in one triangle added to 180°, but since we don't know the other two angles, that's 3 unknowns with only 1 equation... that's not solvable)
The only way to solve this problem is to make a relationship of some sort between the two triangles.
Proving a relationship between triangles - option 1
You may have a theorem about the Third angles of two triangles... "Given two arbitrary triangles, [tex]\triangle ABC[/tex] and [tex]\triangle D E F[/tex], if [tex]\angle A \cong \angle D[/tex] and [tex]\angle B \cong \angle E[/tex], then [tex]\angle C \cong \angle F[/tex] "
If you have this, then the third angles are congruent.
In a more general situation of a similar problem (one in which you don't know two of the angles to begin with), it might be easier to prove triangle congruence, or triangle similarity.
Other Relationships between triangles
There are two main relationships between triangles: similarity and congruence.
Most people learn about congruence first.
In the situation for this problem, the two triangles happen to be congruent (we'll prove it shortly), which implies that all corresponding angles between shapes are congruent (and all corresponding sides between shapes are congruent).
For the purpose of solving for things related to angles, proving that the two triangles are similar is enough to know that angles between triangles are congruent (sides wouldn't necessarily be equal, but would be proportional, and since we're not solving for anything related to side lengths, proving that the triangles are similar would be enough).
Proving a relationship between triangles - option 2 - congruence
Notice that the triangle on top has two angles with markings (a single mark, and a double mark), and one side with a marking (a single tick). These three pieces are in a configuration of ASA (the side is between the two angles).
Looking at the bottom triangle, it also has angles and sides with corresponding markings, and they are also in an ASA configuration.
Thus, by ASA congruence, these triangles are congruent triangles.
Knowing the triangles are congruent (even though we only used 3 parts), the rest of the corresponding parts (including the third angles) are also congruent.
Proving a relationship between triangles - option 3 - Similarity
For similarity, the process is similar to proving congruence, however the theorems we have for proving similarity are different.
SSS, SAS, or AA similarity.
Since the triangles in our problem do have two angles that are congruent, by AA similarity, the triangles are "similar".
Knowing the triangles are similar (even though we only used 2 parts), the last set of corresponding angles are also congruent.
Building our equation
Since the third angle of each triangle is congruent, by definition of congruent angles, the measures of each of those two angles are equal, and so we can build an equation knowing that the two expressions are equal to each other:
[tex]3x-7=2x+5[/tex]
Solving for x
From there, we need some algebraic properties equality to solve for x.
Subtract 2x from both sides...
[tex](3x-7)-2x=(2x+5)-2x\\x-7=5[/tex]
add 7 to both sides...
[tex](x-7)+7=(5)+7\\x=12[/tex]
Extension
Knowing the value for x, we could solve for the measure of the angles, if that had been requested. Simply substitute 12 back into the expressions for the angle measure (the results should be the same for both angles, since they were congruent angles)
[tex]3(12)-7\\36-7\\29[/tex] [tex]2(12)+5\\24+5\\29[/tex]
So, if we had been asked, the measure of the angle is 29°
Related Questions
Determine the area of a sector with√20 radius meters, and central angle 30°.
I will mark brainliest!
Answer Options:
20πm²
5π/3m²
30πm²
π/3²
Answers
Answer: [tex]\frac{5\pi}{3}[/tex]
Step-by-step explanation:
[tex]A=(\sqrt{20})^{2}(\pi)\left(\frac{30}{360} \right)=\boxed{\frac{5\pi}{3}}[/tex]
What is the solution of
x²-1
2
x2 +5X+4
<0?
Answers
Answer:
Step-by-step explanation:
2 more than product of a number and 9 is 8. variable w
Answers
Answer:
w (number) = 2/3
Step-by-step explanation:
Variable w means use the letter w as the unknown number :
This is the equation made from the question :
2+(9w) = 8
Let's subtract 2 from both sides :
9w = 6
Divide both sides by 9 :
w = 6/9
Simplify fraction :
w = 2/3
Hope this helped and have a good day
Which is the graph of f(c)=1/4(4)^x?
Answers
Answer: The graph shown
Step-by-step explanation:
Another graph of the function is attached in this answer.
what are the coordinates of this point help plssssssssssssssss
Answers
Answer:
(-2, -4)
Step-by-step explanation:
Use the (x,y) thing:
x = -2
y = -4
therefore, (-2, -4)
(a) Solve the following formula for b.
1
A = Zab
6
(b) Evaluate b when A= 18 and a = 5
1
(a) The formula A = ab solved for b is b =
6
(b) Evaluate b when A= 18 and a =
5
b = (Type an integer or a simplified fraction.)
Answers
Answer:
J Trump has to be a great day of school and I have a great
Step-by-step explanation:
you thank you thank you thank you thank you thank you thank you thank you thank you thank you thank you for your loss of school and I have a great day of school ii
Find the time diffrence.
If u click there will be pic (very easy im just lazy lol)
Answers
Step-by-step explanation:
2 hours and 45 minutes.
8:45am + 2 hours = 10:45am
10:45am + 45 minutes = 11:30 am
Equations Of Parabolas (Conics) Unscramble
Answers
The match is shown in the picture for the function of a parabola and the graph of a parabola.
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
As we know the standard form of the parabola is:
y = a(x - h)² + k
If a > 0 (parabola opens upwards)
If a < 0 (parabola opens downwards)
or
x = a(y - h)² + k
If a > 0 (parabola opens right side)
If a < 0 (parabola opens left side)
Here (h, k) is the vertex of the parabola and a is the leading term.
Thus, the match is shown in the picture for the function of a parabola and the graph of a parabola.
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if 300 equals 9 and 500 equals 16 what is the pattern? and what will 7 and 18 equal?
Answers
Step-by-step explanation:
hope you can understand
manual spent 4.56 on a sandwich and 2.98 on a drink How much did he spend in all? If he paid with a 10$ bill how much change did he get
Answers
Manual paid with a $10 bill and he got $2.46 as a change.
What is subtraction?Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign, −.
Money spent on sandwich=$4.56 and money spent on drink=$2.98.
We need to find out how much did he spend in all.
That is, the total money spent=4.56+2.98=$7.54
He paid with a $10 bill, he gets change as 10-7.54=$2.46
Hence, he paid with a $10 bill and he got $2.46 as a change.
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any solutions will each system of linear equations have? Match the systems with the correct number of
Solutions
Answers
Based on the information given, the correct options will be
y = x + 6 and 3x - 3y = -18 .... Infinitely many solutions.
y = -2x + 5 and 2x + y = -7 .... No solution.
y = -4x + 11 and -6x + y = 11 ... One solution.
Solving equations
y = -4x + 11 ....... equation i
-6x + y = 11 ...... equation ii
Put equation i into ii.
-6x + y = 11
-6x + (-4x + 11) = 11
-6x - 4x + 11 = 11
-6x - 4x = 11 - 11
-10x = 0
x = 0
Therefore, x = 0 and y = 11. This gives a solution for each variable.
y = -2x + 5 ..... i
2x + y = -7 ..... ii
Put equation I into ii
2x + y = -7
2x + (-2x + 5) = -7
2x - 2x = -7 - 5
0 = -12
This indicates no solution.
y = x + 6 ..... i
3x - 3y = -18 ..... ii
Put equation I into ii
3x - 3y = -18
3x - 3(x + 6) = -18
3x - 3x - 18 = -18
3x - 3x = - 18 + 18
0 = 0
This implies that there are infinitely many solutions.
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URGENT 30 points I need help
Answers
Answer:
- 112 + 100 n
Step-by-step explanation:
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1 )d
~~~~~~~
[tex]a_{1}[/tex] = - 12
d = 100
[tex]a_{n}[/tex] = - 12 + 100( n - 1 )
[tex]a_{n}[/tex] = - 12 + 100n - 100
[tex]a_{n}[/tex] = - 112 + 100 n
(x-8)^2 i need step by step please like eveyone gets x2 -16x +64 i dont get
how
Answers
Answer:
x²-16x+64
use formula =a²-2ab+b²x²-2.x.8+8² (for knowledge 2 × 8 = 16)x²-16x+64Answer:
(x -8)² = x² -16x +64
Step-by-step explanation:
A lot of math is about pattern recognition. For many of the patterns you are asked to recognize, it is helpful to be very familiar with basic math facts: addition facts, multiplication facts, and the squares and cubes of small integers.
All of algebra is based on a few properties of arithmetic and equality. One that is important here is the distributive property.
__
expanding a product of binomialsOne of the patterns that is used with quadratics is the square of a binomial.
(a - b)² = a² -2ab +b²
This is the result of applying the distributive property several times.
First of all, the exponent indicates repeated multiplication:
(a -b)² = (a -b)×(a -b)
The distributive property tells you each term outside parentheses multiplies each term inside:
= a×(a -b) -b×(a -b)
= a·a -a·b -b·a +b·b . . . . . and again
Now, we collect terms, recognizing that ab=ba.
= a² -2(a·b) +b² . . . . . . . using exponents for repeated multiplication
So, the pattern for the square of a binomial is ...
(a -b)² = a² -2ab +b²
__
using the patternFor your specific case, ...
a = xb = 8(x -8)² = x² -2(x)(8) +8² . . . . . . using the above pattern
(x -8)² = x² -16x +64
_____
Additional comment
If you want to do this without using the pattern, just make use of the distributive property:
[tex](x-8)^2=(x-8)(x-8)\\\\=x(x -8) -8(x-8)\\\\=x^2-8x-(8x-64)\\\\=x^2-8x-8x+64\\\\\boxed{(x-8)^2=x^2-16x+64}}[/tex]
__
While the distributive property is the fundamental property involved, some find it helpful to remember a mnemonic that gets you to the same result for the product of binomials: FOIL. The letters refer to First, Outer, Inner, Last, and they remind you of the terms that make up the expansion of the product:
(x -8)(x -8) -- First: x·x = x²(x -8)(x -8) -- Outer: x·(-8) = -8x(x -8)(x -8) -- Inner: (-8)·x = -8x(x -8)(x -8) -- Last: (-8)(-8) = 64Then the product is ...
(x -8)² = x² -8x -8x +64 = x² -16x +64
__
Of course, the distributive property is involved in what we call "collecting terms."
-8x -8x = (-8-8)x = -16x
The variable is factored out using the distributive property, then the coefficients are added to simplify the expression in parentheses.
The weight of corn chips dispensed into a 24-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 25 ounces and a standard deviation of 0.8 ounce. What proportion of the 24-ounce bags contain more than the advertised 24 ounces of chips?
Answers
The percentage of 24-ounce bags containing more than the advertised 24 ounces of chips will be -1.25.
What is the z score?The z-score is a numerical assessment of a value's connection to the mean of a set of values, expressed in terms of standards from the mean, that is used in statistics.
Given data;
Mean,μ = 25
Standard deviation,σ=0.8
The Z score is found as;
[tex]\rm Z = \frac{x-\mu}{ \sigma } \\\\ Z = \frac{24-25}{0.8} \\\\ Z= -1.25[/tex]
The P-value for the obtained z score is .2113.
Hence the percentage of 24-ounce bags containing more than the advertised 24 ounces of chips will be -1.25.
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The volume of a tree stump can be modeled by considering it as a right cylinder. Jin measures its radius as 11 in and its volume as 13685 cubic inches. Find the height of the stump in inches. Round your answer to the nearest tenth if necessary.
Answers
If the radius of tree stump is 11 inches and volume is 13685 cubic inches then the height will be equal to 36 inches.
Given Radius of tree stump is 11 inches and volume is 13685 cubic inches.
We know that the volume of cylinder will be equal to π[tex]r^{2} h[/tex].
Volume which is given as 13685 cubic inches.
13685=π[tex]r^{2}h[/tex]
π=22/7
13685=π[tex](11)^{2}[/tex]h
h=13685*7/22*121
h=95795/2662
h=35.98
if we round it to nearest tenth then the value of h be 36 inches.
Hence if radius is 11 inches, volume is 13685 cubic inches then the height of tree stump will be 36 inches.
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Answer:36
Step-by-step explanation:
Find the inverse of the function.
y = -3x - 9
Write your answer in the form ax + b. Simplify any fractions.
y =
Answers
Answer: [tex]y=-\frac{1}{3} x-3[/tex]
Step-by-step explanation:
To find the inverse of a function you must first swap the places of x and y
[tex]x=-3y-9[/tex]
Now solve for y
Step 1: Flip the equation.
[tex]-3y-9=x[/tex]
Step 2: Add 9 to both sides.
[tex]-3y-9+9=x+9\\-3y=x+9[/tex]
Step 3: Divide both sides by -3.
[tex]\frac{-3y}{-3} =\frac{x}{-3} +\frac{9}{-3} \\y=-\frac{1}{3} x-3[/tex]
-750 DEGREE TO RADIAN
Answers
2pi = 360 degree
If we divide 360 by 2
Pi = 180 degrees
To find 1 radian in degree
180/pi
Cause
Pi = 180 degree
/pi /pi
1 radian = 189/ pi
Classify this triangle. (image down below)
(Acute scalene triangle. (Obtuse isosceles triangle. (Right isosceles triangle (Right scalene triangle?
Answers
Answer: Right iscoleces triangle
Step-by-step explanation: The square on the left bottom side means it is a right angle. The lines means that a side is congruent to the other side. By definition, iscoleces triangles have two congruent sides, so this must be it.
Answer:
right isosceles
Step-by-step explanation:
the right angle and the two sides that are equal make the triangle a right isosceles
The value of the expression 2x2/x+(100-15x) when x=5 is
Answers
Answer:
27
Step-by-step explanation:
Each serving of a cereal is 80 calories.which expression can be used to find the number of calories In 3 servings
Answers
Answer:
[tex]80\times3[/tex]
Step-by-step explanation:
Based on the given conditions, formulate: [tex]80\times3[/tex]
Calculate the product or quotient: 240
get the result: 240
Answer: 240
To find this answer, we had to use the expression 80 * 3, therefore making it the answer.
Answer:
240
Step-by-step explanation:
80*3=240
so u multiply the equation
3
cky has a board that is 2 feet long. She needs to cut the board into 11 pieces of equal length. How long
ould each piece be?
0.223 feet
0.25 feet
0.5 feet
0.75 feet
ase select the best answer from the choices provided
A
В
C
D
Answers
Answer:
0.223 is the answers for the question but I got this answer 0.181
Step-by-step explanation:
please mark me as brainlest
IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Find the probability, rounded to four decimal digits, that the person has an IQ greater than 120. Below is a sketch of the normal curve showing the area to be determined
Answers
The probability that the person has an IQ greater than 120 is 0.2524 of 25.24%
What is probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given:
IQ is normally distributed with a mean of 100 and a standard deviation of 15.
probability that the person has an IQ greater than 120,
P(x >120)
= P(Z > 120-100/ 15)
= P(Z > 0.667)
P(x >120) = 1- P(Z < 0.667)
= 1-0.7476
= 0.2524
= 25.24%
Hence, the probability is 0.2524.
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What is the solution to this system of equations?
Negative 3 x + 5 y = negative 2. 3 x + 7 y = 26.
(4, 2)
(2, 3 and one-third)
no solution
infinitely many solution
Answers
The solution to the system of equation is (-4 , 2) , Option A is the right answer.
What are System Of equation ?A set of equation whose factors are common are called system of equations.
It is given in the question
3x +5y = -2
3x +7y = 2
On solving this we get
-2y = -4
y = 2
On substitution in any equation
x = -4
Therefore solution to the system of equation is (-4 , 2) , Option A is the right answer.
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Answer:
A.
Step-by-step explanation:
took tha quiz
Which is the equation of the line with slope 0 passing through the point (-3, -1)?
Answers
Find the x- and y-intercepts of the parabola y=x2+10x+4
Answers
Answer:
x-intercepts: -5 +/-[tex]\sqrt{21}[/tex]. y-intercept: 4
Step-by-step explanation:
For x-intercepts use the quadratic equation
[tex]x= (-b +/-\sqrt{b^2-4ac} )/2a[/tex]
Fill in your values:
[tex]x= (-10 +/-\sqrt{100-16} )/2[/tex]
And solve
[tex]x=-5 +/- \sqrt{21}[/tex]
For y-intercepts set x=0 and solve. In this case, setting x= 0 gives you y=4.
Which statement is true about this equation Y=-3x2+4x+-11
Answers
Answer:
For plato users, the answer would be letter C.
Step-by-step explanation:
A.
It represents neither a relation nor a function.
B.
It represents a relation only.
C.
It represents both a relation and a function.
D.
It represents a function only.
This equation represents both a relation and a function.
Took the test, hope this helps!
Step-by-step explanation:
I'm a kid. and I'm starting 4th grade so I lied to the computer, Anyhoo. Can anyone PLS help me comvert 6/7.
Answers
6/7 converted to a decimal is 0.8571
Conversion to decimalsFrom the question, we are to convert the given fraction to a decimal
The given fraction is
6/7
6/7 = 0.8571
Thus,
6/7 expressed as a decimal is 0.8571
Hence, 6/7 converted to a decimal is 0.8571
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4. Use the formula for the area of a circle to derive the formula for the area of a sector.
Answers
The area of a circle to derive the formula for the area of a sector will be (θ/2π) x (area of the circle).
What is the area of the sector?Let r be the radius of the circle. Then the area of the circle will be
Area = πr²
Let r is the radius of the sector and θ be the angle subtends by the sector at the center. Then the area of the sector of the circle will be
Area = (θ/2π) πr²
Area = (θ/2π) x (area of the circle)
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5
14
6
3
1
2
Two friends, Andrew and Liz, are playing a game using this spinner. If the
spinner lands on region 2 or 3, Andrew wins. If it lands on region 4, Liz wins. If
it lands on any other region, neither wins. Is this a fair game?
A. Yes. Each friend has a
probability of winning.
B. Yes. Each friend has a
probability of winning.
C. No. Andrew has a probability of winning and Liz has a
probability of winning.
D. No. Andrew has a probability of winning and Liz has a
probability of winning.
Answers
The question is incomplete. Below you will find the missing figure.
Two friends, Andrew and Liz, are playing a game using this spinner. If the
spinner lands on region 2 or 3, Andrew wins. If it lands on region 4, Liz wins. If it lands on any other region, neither wins. Is this a fair game?
A. Yes. Each friend has a 1/4 probability of winning.
B. Yes. Each friend has a 1/6 probability of winning.
C. No. Andrew has a probability of 1/4 winning and Liz has a probability of 1/6 winning.
D. No. Andrew has a probability of 1/3 winning and Liz has a probability of 1/4 winning.
The correct option is Option A: Yes. Each friend has 1/4 probability of winning.
Probability is the possibility of an event to happen which is the ratio of no. favorable outcomes and no. of total outcomes.
P = no. of favorable outcome/ total no. of outcome
Here given in the question,
If the spinner touches region 2 or 3, Andrew wins
If the spinner touches region 4, Liz wins.
This is fair play because both have the same size of region for winning.
If we cut the circle into 8 pieces,
as region 1 is the sum of 2 sub-parts of the circle,
possibility of spinner touching region 1= 2/8= 1/4
possibility of spinner touching the small region = 1/8
So the possibility of the spinner touching the region 2or 3= 1/8+1/8= 2/8= 1/4
Hence the possibility of Andrew wins= possibility of the spinner touching region 1= 1/4
possibility of Liz wins= possibility of the spinner touching the region 2 or 3= 1/4
Therefore the correct option is Option A: Yes. Each friend has 1/4 probability of winning.
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Renate launched an object vertically from a point that is 58.9 meters above ground level with an initial velocity of 21.6 meters per second. This situation can be represented by the equation h=−4.9t2+21.6t+58.9, where h is the height of the object in meters and t
is the time in seconds after the object is launched.
What is the maximum height of the object?
Answers
The maximum height of the object is 82.7034 from the ground
What is Velocity ?Velocity is the measure of movement of an object with respect to time.
It is measured in m/sec
h = -4.9t²+21.6t +58.9
dh/dt = -9.8t +21.6
At maximum height , velocity = 0
therefore
-9.8t +21.6 = 0
9.8t = 21.6
t = 2.204 sec
h = -4.9 (2.204)²+ 21.6 * 2.204 +58.9
h = -23.803 +47.606 +58.9
h = 82.7034 from the ground
h = 23.80 from the point it is launched.
The maximum height of the object is 82.7034 from the ground
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