99pts WILL GIVE BRAINLIEST Use the diagram and given information to answer the questions and prove the statement. Given: X Z
Prove: [see image] Re-draw the diagram of the overlapping triangles so that the two triangles are separated.
What additional information would be necessary to prove that the two triangles, XBY and ZAY, are congruent?
What congruency theorem would be applied?
Prove using a list/flow chart proof.
Answers
Statements [Reasons]
1. Angle X is congruent to Angle Z [Given]
2. Line XY is congruent to Line YZ [Given]
3. Angle Y is congruent to Angle Y [Congruence is reflexive]
4. Triangle XBY is congruent to Triangle ZAY [ASA]
ANSWER: The ASA (Angle Side Angle) Congruency Theorem could be applied.
Related Questions
In the graph below, find the coordinate of the image point, P(3, 0). O is the origin and O,90 is a rotation of 90 degrees about the origin. Rx and Ry are reflections around the x- and y-axes.
Rx O,90: (3,0)
(0, 3)
(-3, 0)
(0, -3)
Answers
Answer:
Thus, (3,0) Rx O,90° changes to (0,-3)
Step-by-step explanation:
O is the origin and O,90 is a rotation of 90 degrees about the origin. Rx and Ry are reflections around the x- and y-axes.Given: Rx O,90: (3,0)
To determine:
Point P (3,0) rotation about origin (0,0) of 90°
and then Reflection about x-axis.
Rotation of P(x,y) about origin of 90°
P(x,y) changes to P'(y,x)
Therefore, P(3,0) changes to P'(0,3)
Now we take reflection about x-axis
R(x,y) changes to R'(x,-y)
Therefore, P'(0,3) changes to P''(0,-3)
Please see the attachment for both rule.
Thus, (3,0) Rx O,90° changes to (0,-3)
Marie decides to work all summer rather than going on vacation. She will be able to earn money and learn new skills but will not be able to spend much time with her friends. What is the opportunity cost in this scenario?
Answers
The opportunity cost in this scenario is the value of the best alternative that Marie gives up by choosing to work all summer rather than going on vacation.
Explanation:The opportunity cost in this scenario is the value of the best alternative that Marie gives up by choosing to work all summer rather than going on vacation. In this case, the opportunity cost could be the time she could have spent with her friends. By deciding to work, Marie forgoes the opportunity to socialize and spend quality time with her friends.
Opportunity cost is an important concept in economics that highlights the trade-offs we face when making choices. It helps us understand the value of the options we give up when we choose one alternative over another. In Marie's case, the opportunity cost of earning money and learning new skills is the limited time she can spend with her friends.
show or describe two different ways to complete the comparison using < , > ,or =: 0.26 () 0.4
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Reason: 0.26 is less than 0.4 which also can be written as 0.40.
The "mouth" points to the bigger number.
Two number cubes are rolled. What is the probability that the sum of the numbers rolled is either 3 or 9?
A.1/6
B.1/13
C.1/18
D.1/162
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[tex] |\Omega|=6^2=36\\
|A|=\underbrace{2}_{\text{the sum is 3}}+\underbrace{4}_{\text{the sum is 9}}=6\\\\
P(A)=\dfrac{6}{36}=\dfrac{1}{6}\approx17\% [/tex]
How can you quickly determine the number of roots a polynomial will have by looking at the equation?
(This is not a math problem simply a question)
Answers
Although that is only for second grade ecuations
The number of roots a polynomial will have can be determined by its degree, assuming that we are considering all possible roots including complex roots and counting each root according to its multiplicity.
For example, a linear polynomial (degree 1) such as [tex]\( ax + b = 0 \)[/tex] will have exactly one root. A quadratic polynomial (degree 2) like [tex]\( ax^2 + bx + c = 0 \)[/tex] will have two roots, which could be real or complex. Similarly, a cubic polynomial (degree 3) will have three roots, and so on.
If the coefficients of the polynomial are real numbers, then any complex roots will occur in conjugate pairs. This means that a real polynomial of odd degree will always have at least one real root.
To summarize, the number of roots of a polynomial equation is equal to the degree of the polynomial, provided that:
1. We include all real and complex roots.
2. We count each root according to its multiplicity (the number of times it is repeated).
3. The polynomial is non-constant (degree greater than 0).
Plot the data for the functions f(x) and g(x) on a grid
Answers
The first thing you have to do is study the graph. The two functions are
f(x) = 4^x That's the curved graph. (in red)
g(x) = x + 4. That's the straight line. (in blue)
You know that the first one is not a linear relationship because the x values go from integer values -2 to 2 (including 0). The y values are a bit different. They go from 1/16 to 16 with those integer values. So you could try y = 4^(-x). It doesn't work, but you could try it. It gives the table numbers for y in the reverse order that the table you are given goes. For x you get -2 -1 0 1 2 and for y you would get 16 4 1 1/4 1/16.
You could try y = (1/4)^x
For this try, you would get x = -2 -1 0 1 2 and for y = 16 4 0 1/4 and 1/16
but that doesn't work either.
You could try until you get y = 4^x which does work.
g(x) is a lot easier to deal with. It looks better behaved. as x goes up, so does y. You will find that the y values obey y = x + 4. You could try other lines, but that one works. Many times it's just a guess
A rocket is launched from atop a 55-foot cliff with an initial velocity of 138 ft/s. a. Substitute the values into the vertical motion formula h = −16t2 + vt + c. Let h = 0. b. Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second.
Answers
Substituting the values into the equation, we have:
0 = -16t² + 138t + 55
The quadratic formula is:
[tex]t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Inserting our information we have:
[tex]t=\frac{-138\pm \sqrt{138^2-4(-16)(55)}}{2(-16)} \\ \\=\frac{-138\pm \sqrt{19044--3520}}{-32} \\ \\=\frac{-138\pm \sqrt{19044+3520}}{-32} \\ \\=\frac{-138\pm \sqrt{22564}}{-32} \\ \\=\frac{-138\pm 150}{-32}=\frac{-138+150}{-32}\text{ or } \frac{-138-150}{-32} \\ \\=\frac{12}{-32}\text { or } \frac{288}{32}=-0.375 \text{ or } 9[/tex]
the domain for f(x) is all real numbers greater than or equal to ___ ?
Answers
5√(x+2) = x is greater than or equal to -2
So the domain is greater than or equal to -2
Answer:
The domain of f(x) is all real numbers greater than or equal to -2
Step-by-step explanation:
We have been given that
[tex]f(x)=2(x)^2+5\sqrt{x+2}[/tex]
Domain is the set of x values for which the function is defined.
The given function is the combination of a square and square root function.
Square function is defined for all real values. Whereas, the square root function is defined for only positive values.
Therefore, the function is defined when
[tex]x + 2\geq0[/tex]
Subtract 2 to both sides
[tex]x\geq-2[/tex]
Hence, the domain of f(x) is all real numbers greater than or equal to -2
Tanya wants to find the height of the tree. She walks away from the base of the tree so the tip of her shadow coincides with the tip of the tree's shadow at point C. BE is two and a half times EC. Tanya is 5 feet, 3 inches tall. How tall is the tree in feet?
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TRIANGLE ABC
The height of the tree is the segment AB. The shadow of the tree is BC.
TRIANGLE DEC
Tanya's height is 5 feet 3 inches (since there are 12 inches in one foot that is (5)(12)+3 = 63 inches).
Tanya's shadow is EC
Since both triangles are right triangles (the both have a right angle) and they share the angle at C, they are similar triangles. That means that their corresponding angles are congruent and their corresponding sides are in proportion.
We can set up the following proportion:
(tree height / tree shadow) = (Tanya's height / Tanya's shadow)
BE is 2.5 times EC. This means that BE is (2.5)(EC). It also means that BC = 2.5EC + EC = 3.5EC
The shadow of the tree is 3.5 times Tanya's shadow. That means that the height of the tree must be 3.5 times Tanya's height.
The height of the tree is (3.5)(63) = 220.5 inches. If we divide this by 12 we get 18.375 which means 18 feet and some inches. (18)(12)=216 and the tree is 220.5. That means the tree is 18 feet and 4.5 inches.
The height of the tree is 7.35 feet.
To find the height of the tree, we need to use similar triangles. Here’s the detailed process:
Understand the problem and convert units: Tanya is 5 feet, 3 inches tall. Convert her height to feet.
- 3 inches is 0.25 feet.
- So, Tanya’s height is [tex]\( 5 + 0.25 = 5.25 \)[/tex] feet.
According to diagram
- A tree T with height h.
- Tanya is standing at a point B, with her shadow extending to point E.
- The tree’s shadow extends to point C.
- The tip of Tanya’s shadow coincides with the tip of the tree’s shadow at point C.
- Let E be the point where Tanya’s shadow ends.
- Let EC = x.
- [tex]\( BE = 2.5 \times EC = 2.5x \)[/tex].
Using similar triangles:
[tex]\[ \frac{\text{Tanya's height}}{\text{Length of Tanya's shadow}} = \frac{\text{Tree's height}}{\text{Length of tree's shadow}} \][/tex]
[tex]\[ \frac{5.25}{2.5x} = \frac{h}{3.5x} \][/tex]
Simplify the ratio:
[tex]\[ \frac{5.25}{2.5} = \frac{h}{3.5} \][/tex]
Cross-multiply and solve for h:
[tex]\[ 5.25 \times 3.5 = 2.5 \times h \][/tex]
Calculate [tex]\( 5.25 \times 3.5 \):[/tex]
[tex]\[ 5.25 \times 3.5 = 18.375 \][/tex]
Now, divide by 2.5 to find h:
[tex]\[ h = \frac{18.375}{2.5} = 7.35 \][/tex]
The complete question is
Tanya wants to find the height of the tree. She walks away from the base of the tree so the tip of her shadow coincides with the tip of the tree's shadow at point C. BE is two and a half times EC. Tanya is 5 feet, 3 inches tall. How tall is the tree in feet?
f √6 is the geometric mean between 6 and another number, then the number is
Answers
What you have here is a geometric series beginning with x ⇒ √6 ⇒ 6
x = √6 / 6 It is the smallest number in the series.
Each number is multiplied by √6 to get to the next number in the series.
√6/6 <<<< answer
HELLO!!! ^-^
The answer is 1.
If √6 is the geometric mean between 6 and another number, then the number is 1.
(I had the same question and got it right using this answer so yeah) ^-^
Have an amazing day!!! ^-^
Historical Fact:
Back in the older days, the word awful was a word used to praise someone! That is because aw in awful comes from the origin awe which is used when someone is in awe of you!!! For example: You are AWESOME!!!
What is the discount and sale price of a $300 item that has been discounted 10%?
(PLEASE EXPLAIN)
Answers
300 x 0.10 = 30
discount = $30
sale price = 300 - 30 = $270
How would the expression x^2-4 be rewritten using Difference of Squares?
A) (x+2)^2
B) (x-4)^2
C) (x+4)(x-4)
D) (x+2)(x-2)
Answers
The answer is D) (x+2)(x-2)
To remember how to factor a difference of perfect squares, the terms, for lack of better words, are divided in half.
Example:
x²: (x+ )(x- )
4: ( +2)( -2)
Do you see what each term "does" to the answer?
(x+2)(x-2)
I really hope this helps!
Best wishes :)
d.........................
a doctor is using a treadmill to assess the strength of a patients heart. he sets the 48 inch long treadmill at an incline of 10 degrees. how high is the treadmill raised
Answers
x = 48* .1736
x = 8.3335
rounds to 8.3"
sin 1o^0 = h/48
h = 48 sin 10^0
so; h = 8.3 inches; or
8.3 in.
say you have a triangle:
outside = 48
outside = h
inside = 10^0
In this exercise we have to use the knowledge of sine to be able to calculate the triangle values, in this way we can say that:
[tex]h= 8.3[/tex]
So from the values initially given we can describe that the calculation for this triangle will be:
[tex]x / 48 = sin(10)\\ x = 48* .1736\\ x = 8.3335\\ sin 10^0 = h/48\\ h = 48 sin 10^0\\ h = 8.3 inches[/tex]
See more about triangles at brainly.com/question/25813512
An apple farm yields an average of 31 bushels of apples per tree when 17 trees are planted on an acre of ground. each time 1 more tree is planted per acre, the yield decreases by 1 bushel (bu) per tree as a result of crowding. how many trees should be planted on an acre in order to get the highest yield?
Answers
To maximize the apple yield from an acre, the optimal number of apple trees to plant is 24 trees.
Explanation:In this problem, we need to maximize the yield of apples from an acre of an apple farm. The yield of apples from an acre is given by the product of the number of trees and the number of bushels per tree. The number of bushels of apples per tree decreases by 1 bushel every time an additional tree is added due to crowding. In mathematical terms, this can be expressed as the equation Y = N * (31 - (N - 17)), where Y is the total yield, and N is the number of trees per acre.
To find the maximum yield, we differentiate this equation with respect to N and set the derivative equal to zero. This gives us N = 24. Therefore, the optimal number of trees to plant per acre in order to maximize apple yield is 24 trees.
Learn more about Maximizing Yield here:https://brainly.com/question/32287841
#SPJ12
To maximize the yield of apples per acre, plant 24 trees. This balances the number of trees and the yield per tree due to crowding.
To find the number of trees that should be planted per acre to get the highest yield, we need to model the yield per acre as a function of the number of trees planted and then find the maximum value of this function.
1. Define the variables:
- Let ( n ) be the number of trees planted per acre.
- The yield per tree decreases by 1 bushel for each additional tree planted, starting from 31 bushels per tree when there are 17 trees planted.
2. Model the yield per tree:
- If ( n = 17 ), the yield per tree is 31 bushels.
- For each additional tree, the yield decreases by 1 bushel, so the yield per tree can be expressed as ( 31 - (n - 17) ).
Simplifying this, we get:
Yield per tree = 31 - n + 17 = 48 - n
3. Model the total yield per acre:
- The total yield ( Y ) per acre is the number of trees ( n ) times the yield per tree.
Y = n × (48 - n)
4. Formulate the quadratic function:
Y = 48n - [tex]n^2[/tex]
5. Find the maximum yield:
- This is a quadratic function of the form [tex]\( Y = -n^2 + 48n \)[/tex], which is a downward-opening parabola. The maximum value of \( Y \) occurs at the vertex of the parabola.
- The vertex of a quadratic function [tex]\( ax^2 + bx + c \)[/tex] occurs at [tex]\( x = -\frac{b}{2a} \)[/tex] . In our case, ( a = -1 ) and ( b = 48 ).
[tex]\[ n = -\frac{48}{2(-1)} = \frac{48}{2} = 24 \][/tex]
So, to get the highest yield, 24 trees should be planted per acre.
Find the slope intercept form for the equation of the line which passes through the point ( -2,15 )and has a slope of -1
Answers
The answer is:
y = -x + 13
Work/explanation:
First, we will write the equation in the form of [tex]\sf{y-y_1=m(x-x_1)}[/tex], which is point slope.
Plug in the data
[tex]\large\begin{gathered}\sf{y-15=-1(x-(-2)}\\\sf{y-15=-1(x+2)}\\\sf{y-15=-1x-2}\\\sf{y-15=-x-2}\\\sf{y=-x-2+15}\\\sf{y=-x+13}\end{gathered}[/tex]
Hence, the slope intercept is y = -x + 13.
What perfect squares divide into 337? I only need two!
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[tex]337 \cdot 337 = 113569[/tex]
A second perfect square that divides into 337 is
[tex]337 \cdot 337 \cdot 2 \cdot 2 = 674\cdot 674 = 454276
[/tex]
How are experimental and theoretical probability alike?
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A hiker is lost in the woods. A search team has created a coordinate grid to represent the woods. Each unit on the grid is one square mile. The hiker was last seen at (4, -9) and could have walked 10 miles in any direction since then. Which equation represents the area the hiker could be in?
A) (x - 4)2 + (y + 9)2 = 102
B) (x + 4)2 + (y - 9)2 = 102
C) (x + 4)2 + (y + 9)2 = 1002
D) (x - 4)2 + (y - 9)2 = 1002
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.. (x -h)^2 +(y -k)^2 = r^2
Selection A is appropriate.
_____
It would be helpful if you would use appropriate math symbols. 102 is very different from 10^2. (Copying and pasting does not work--editing is needed.)
Jessica is designing a large, circular garden for a neighborhood park. A part of the garden will be occupied by a fountain. If the diameter of the garden is 82 meters and the measure of the angle formed by the fountain is 126°, what will be the approximate length of the garden cover by the fountain?
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S = R * theta
Where
S: length of the garden covered by the fountain.
R: Garden radio
theta: angle formed by the source.
Substituting values we have:
S = (82/2) * ((126) * (pi / 180))
S = 90.16 m
Answer:
The approximate length of the garden cover by the fountain will be:
S = 90.16 m
1. Find the cosecant of angle A.
2. Find the secant of angle A.
3. Find the cotangent of angle A.
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Water flowing at the rate of 15km/hr through a pipe of diameter 14cm into a cuboidal pond which is 50m long and 44m wide. In which time will the level of water in the pond rise 21cm?
Answers
We must calculate the volume of water in one hour.
V=15000*PI*0.07²=230,9070600... m^3/h.
Volume of the pond=50*44*.21=462 m^3
Time=462 m^3/ 230.907... m^3/h=2,0008... h≈2 h
Dad just had a birthday. Before this birthday, dividing Dad’s age by 2 left a remainder of 1. How do you know that’s Dad’s new age is not a prime number?
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He's now had a birthday. The way to show this is 2n + 1 for his age before his birthday. He has a birthday so his age is 2n + 1 + 1 = 2n + 2 which is an even number and therefore not prime.
Dad's age after his birthday is not a prime number because before his birthday his age was odd, and adding 1 to it made it even. All even numbers greater than 2 are not prime as they are divisible by 2. The new age's prime factors summed with 1 is also divisible by 3, confirming its non-primality.
Before Dad's birthday, dividing his age by 2 left a remainder of 1, which means his age was an odd number. When an odd number has 1 added to it (as occurs on a birthday), it becomes an even number. Since all even numbers except 2 are not prime because they are divisible by 2, we can conclude that Dad's new age cannot be a prime number.
Prime numbers are those that are only divisible by 1 and themselves, and the smallest even prime is 2. Therefore, if Dad's age increased by 1 and became an even number greater than 2, it cannot be prime due to the divisibility rule.
Considering the character of ages having the sum of their prime factors (including one) divisible by 3, and using the modulus operator, we can affirm that the age after the birthday (which is even) conforms to this pattern, hence, verifying its non-primality.
1 question pleasee i need this asap!! thank you :D
Answers
________________________________________________________
Explanation:
________________________________________________________
Given the following equation:
________________________________________________________
" x² + 3x – 54 = 0 " ; Solve for "x" ;
_____________________________________________________
Check if the part of the equation on the "left-hand side" can be "factored":
" x² + 3x – 54 " ;
→ We see the " + 3x " and the " – 54 "
Factors of " -54 " that add up to " +3" ;
Let us try: " -9, 6" ; → " -9 + 6 = -3 " ; → " -3 ≠ +3 ;
Let us try: " 9, -6" ; → " 9 + (-6) = 9 – 6 = 3 " ; YES!
→ {that is: " +9 , -6 "} ;
So, we can rewrite the entire equation:
→ " (x + 9)(x – 6) = 0 " ;
→ " x = -9 " ; or, " x = 6 " ; which is:
→ Answer choice: [A]: " x = 6 " or " x = - 9 " .
______________________________________________________
If a fair coin is tossed 5 times what is the probability of getting 3 heads in a row
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PLEASE HELP ASAP!!!1
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Each CD costs $11. Therefore the total cost of the CDs is 11 × the amount of CDs, which is represented by y. Hence, the total cost if the cassettes is 11y.
You can at maximum spend $ 39 .
So the cost will always be smaller than or equal to $39. Hence, the inequality will be:
[tex]5x + 11y \leqslant 39[/tex]
TIME SENSITIVE
The range of [tex]y= \frac{4}{5} sinx[/tex] for [tex] \pi \leq x \leq \frac{3 \pi }{2} [/tex] is _____.
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-4/5 <= (4/5)sinx <= 0
How many 1/2 cup servings are in the 7/8 cups of peanut butter
Answers
[tex] \frac{ \frac{7}{8} } { \frac{1}{2} } [/tex]
To solve it invert the 1/2 and multiply.
[tex] \frac{7 * 2}{8 * 1} [/tex]
Which gives you 14 /8 whis is 1 3/4 cups.
Multiply. −5m(−2m6+4m4+m−9) Express the answer in standard form. Enter your answer in the box.
Answers
10m^6-20m^4-5m^-9
im sorry if its not right, just know if its wrong i sacrificed 3 points off my unit test. lol
The new number, 550, is 200 more than the original number. What is the approximate percent change?a The percent change is 33%. b The percent change is 55%. c The percent change is 150%. d The percent change is 175%
Answers
The approximate percent change is:
55%
Step-by-step explanation:It is given that:
The new number, 550, is 200 more than the original number.
Let the original number be: x
That means:
550=200+x
x=550-200
x=350
Now, the percent change is calculated as:
[(New number-Original number)/original number]×100
= [tex]\dfrac{550-350}{350}\times 100\\\\=\dfrac{200}{350}\times 100\\\\=57.14\%[/tex]
which is approximately equal to :
55%
Which of the following best describes the solutions to the inequality shown below?
4c + 5 < 4c + 3
A. All real numbers
B. c < 1/2
C. c > 1/4
D. No solution