CE is an angle bisector of angle ACB.
If m angle ACE = 2x - 15 and m angle ECB = x +5,
determine the value of x.
Answers
Answer:
x = 20
Step-by-step explanation:
[tex] \because \overrightarrow {CE}[/tex] is an angle bisector of[tex] \angle ACB. [/tex]
[tex]\therefore m \angle ACE = m \angle ECB\\ 2x - 15 = x + 5 \\ 2x - x = 15 + 5 \\ \huge \orange{ x = 20}[/tex]
The value of x from the angle bisector is: x = 20
How to find the value of the angle bisector?Angle bisector theorem is a theorem in geometry that states that an angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle. An angle bisector is a ray that divides a given angle into two angles of equal measures.
Thus, we can say that:
∠ECB = ∠ACE
Thus:
x + 5 = 2x - 15
2x - x = 15 + 5
x = 20
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Related Questions
Which of the following sets are subspaces of R3 ?
A. {(x,y,z)|3x+8y-5z=2}
B. {(x,y,z)|-4x-9y+7z=0}
C. {(x,y,z)|x
D. {(-4,y,z)|y,z arbitrary numbers}
E. {(x,0,0)|x arbitrary number}
F. {(-2x,-3x,-8x)|x arbitrary number}
Answers
Answer:
The following are the solution to the given points:
Step-by-step explanation:
for point A:
[tex]\to A={(x,y,z)|3x+8y-5z=2} \\\\\to for(x_1, y_1, z_1),(x_2, y_2, z_2) \varepsilon A\\\\ a(x_1, y_1, z_1)+b(x_2, y_2, z_2) = (ax_1+bx_2,ay_1+by_2,az_1+bz_2)[/tex]
[tex]=3(aX_l +bX_2) + 8(ay_1 + by_2) — 5(az_1+bz_2)\\\\=a(3X_l+8y_1- 5z_1)+b (3X_2+8y_2—5z_2)\\\\=2(a+b)[/tex]
The set A is not part of the subspace [tex]R^3[/tex]
for point B:
[tex]\to B={(x,y,z)|-4x-9y+7z=0}\\\\\to for(x_1,y_1,z_1),(x_2, y_2, z_2) \varepsilon B \\\\\to a(x_1, y_1, z_1)+b(x_2, y_2, z_2) = (ax_1+bx_2,ay_1+by_2,az_1+bz_2)[/tex]
[tex]=-4(aX_l +bX_2) -9(ay_1 + by_2) +7(az_1+bz_2)\\\\=a(-4X_l-9y_1+7z_1)+b (-4X_2-9y_2+7z_2)\\\\=0[/tex]
[tex]\to a(x_1,y_1,z_1)+b(x_2, y_2, z_2) \varepsilon B[/tex]
The set B is part of the subspace [tex]R^3[/tex]
for point C: [tex]\to C={(x,y,z)|x<y<z}[/tex]
In this, the scalar multiplication can't behold
[tex]\to for (-2,-1,2) \varepsilon C[/tex]
[tex]\to -1(-2,-1,2)= (2,1,-1)[/tex] ∉ C
this inequality is not hold
The set C is not a part of the subspace [tex]R^3[/tex]
for point D:
[tex]\to D={(-4,y,z)|\ y,\ z \ arbitrary \ numbers)[/tex]
The scalar multiplication s is not to hold
[tex]\to for (-4, 1,2)\varepsilon D\\\\\to -1(-4,1,2) = (4,-1,-2)[/tex] ∉ D
this is an inequality, which is not hold
The set D is not part of the subspace [tex]R^3[/tex]
For point E:
[tex]\to E= {(x,0,0)}|x \ is \ arbitrary) \\\\\to for (x_1,0 ,0) ,(x_{2},0 ,0) \varepsilon E \\\\\to a(x_1,0,0) +b(x_{2},0,0)= (ax_1+bx_2,0,0)\\[/tex]
The [tex]x_1, x_2[/tex] is the arbitrary, in which [tex]ax_1+bx_2[/tex]is arbitrary
[tex]\to a(x_1,0,0)+b(x_2,0,0) \varepsilon E[/tex]
The set E is the part of the subspace [tex]R^3[/tex]
For point F:
[tex]\to F= {(-2x,-3x,-8x)}|x \ is \ arbitrary) \\\\\to for (-2x_1,-3x_1,-8x_1),(-2x_2,-3x_2,-8x_2)\varepsilon F \\\\\to a(-2x_1,-3x_1,-8x_1) +b(-2x_1,-3x_1,-8x_1)= (-2(ax_1+bx_2),-3(ax_1+bx_2),-8(ax_1+bx_2))[/tex]
The [tex]x_1, x_2[/tex] arbitrary so, they have [tex]ax_1+bx_2[/tex] as the arbitrary [tex]\to a(-2x_1,-3x_1,-8x_1)+b(-2x_2,-3x_2,-8x_2) \varepsilon F[/tex]
The set F is the subspace of [tex]R^3[/tex]
An open box is constructed of 3500 cm2 of cardboard. The box is a cuboid, with height h cm and square base of side x cm. What is the value of x which maximises the volume of the box? Give your answer in cm correct to 3 significant figures.
Answers
Answer:
this is confusing and my head hurts
Step-by-step explanation:
The coordinates of three of the vertices of parallelogram ABCD are A(2, 0), B(4, 3), C(3, 1). How many possibilities are there for the position of the fourth vertex? What are coordinates of the fourth vertex?
Answers
Answer:
probability is one for the position of the fourth vertex
it's co ordinates will be (2,2)
A truck can be rented from Company A for $110 a day plus $0.40 per mile. Company B charges $80 a day plus $0.60 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same. PLZ HELP
Answers
Answer: i am also looking for the answer so far i’ve gotten x=200 but it told me it was wrong feel free to try it i guess
Lila works 40 hours a week and earns $9 an hour . Her baby stays with a sitter during the hours Lila works . Lila pays the sitter $5 an hour . After paying the sitter , how much of her paycheck does Lila have left
Answers
Answer: $160
Step-by-step explanation: If she works 40 hours a week, than that is $360 a week, if she pays the sitter $5 a week, then that means she pays the sitter $200 a week. Subtract and you get $160.
The square of a number is that number ___________________________________. The square of an integer is a _________________________.
The square of negative 12 is written as _______________. The opposite of the square of 12 is written as ______________.
2 • 2 = 4. Another number that can be multiplied by itself to equal 4 is _______.
2. Fill in the blanks with square root or principal square root.
A ___________________________________ is a number that produces a given number when it is multiplied by itself.
The ___________________________________ is the positive square root of a number and is shown using the radical symbol, √.
3. Complete the table to describe perfect cubes.
Definition A number multiplied by itself _______ times.
Examples 13 = 1 • 1 • 1 = _____
23 = _____ • _____ • _____ = 8
_____3 = 4 • 4 • 4 = _____
4. Answer the questions about cube roots.
What is a cube root?
Use the radical symbol to represent the cube root of 8.
What is the cube root of –8?
Main idea: Solving equations by taking the square root
5. Complete the steps to show how to solve x2 = 36.
6. Answer the questions about Ally's web page icons as you work through the problem in the study.
Each icon contains 1024 pixels arranged in rows. What does p represent in the equation p2 = 1024?
What is the first step in solving p2 = 1024?
Why doesn't the solution p = –32 make sense for this problem?
Main idea: Solving equations by taking the cube root
7. Solving an equation in the form x3 = p is similar to solving equations with squared terms. Complete the table to show the differences.
x2 = p x3 = p
To solve: Take the square root.
Number of solutions and their sign(s): Two solutions. One is positive and one is negative.
Example:
8. Answer the questions about Tanisha's baking supply container as you work through the problem in the study.
The volume of the salt container is 125 cm3. What does x represent in the equation x3 = 125?
What is the first step in solving x3 = 125?
Is x = –5 a solution to the equation? Why or why not?
Key Terms
Use this table to write definitions for the key terms from this activity in your own words. If you're confident you know a term, put a check mark next to it and move on.
Key Term Definition
cube
cube root
integer
inverse operations
perfect square
principal square root
square
square root
I
Answers
Did you just copy and paste your assignment??
If yes, please do not do such a thing and give it in a question by question basis, sorry but I can't type such a big one. Suggestion!!
The triangle below is an equilateral triangle. What is the perimeter of the triangle?
Answers
Answer:
[tex]5.4x+15[/tex] inches
Step-by-step explanation:
This is an equilateral triangle.
Therefore, all sides are equal to each other. This means that we don't need to go through the whole hassle of adding up all the sides together. We can just take the easiest side and multiply it by 3 (as the perimeter of an equilateral triangle is [tex]3s[/tex], s being the side length.)
In my opinion, the side [tex]1.8x+5[/tex] is the easiest to work with.
Let's multiply this by 3.
[tex]3(1.8x+5)[/tex]
We can apply the distributive property - multiply all terms inside the parentheses by 3.
[tex]1.8\cdot 3 = 5.4\\5\cdot3 = 15\\\\5.4x+15[/tex]
Hope this helped!
The drama club spent $8.50 per person on food for a cast party. The total cost of the flood was $229.50. How many people were at the cast party?
Answers
Answer:
229.50 ÷ 8.50= 27 people
Can someone explain aswell
Answers
Answer:
24 ft²
Step-by-step explanation:
find the length of the base of each triangle through a² + b² = c², c being hypotenuse.
after finding the length of each individual base, use A= 1/2bh (multiply base and height and then divide by 2) to calculate area of each triangle. then add and round. hope this helps
Consider a situation that you might need to use your understanding of probability to make an informed decision.
Answers
NEED HELP NOW!!!! find the measure of the angle BXE using the figure below
Answers
Answer:
bxe is a triangle
Step-by-step explanation:
Help me ASAP plsssssssssssssssssssssssssssss
Answers
Answer:
B
Step-by-step explanation:
Answer: B. Recycling
Step-by-step explanation: Recycling is turning something like newspapers and making them into new products.
Mark Brainliest if you want!
A car rental agency advertised renting a car for $26.95 per day and $0.24 per mile. If Kevin rents this car for 3 days, how many whole miles can he drive on a $250 budget?
miles (Round down to the nearest whole mile.)
Answers
Answer: 26.95 * 3 = 80.85
250/0.24 = 60
Point C divides AB into two segments with lengths that form which ratio?
А с B
HH
15 20 25 3035
AHH
Answers
Answer:2:3
Step-by-step explanation:
pls help me pls pls
Answers
7x = 2x + 20
5x = 20
X =4
Hope it helped
Thank You
The cost (y) to rent a car is $45 per day plus 22 cents per mile. Which is the constant value in this situation?
A)
0.22x
B)
45
х
D)
у
Answers
Answer: is b andrea
Step-by-step explanation: i just took the same test
Answer:
Thy answer is B my queen
Step-by-step explanation:
Please help!!!!!!!!!!!!!
Answers
Answer:
r=8
Step-by-step explanation:
r*4=32
32/4=8
Therefore, r=8
Answer:
r = 8
Step-by-step explanation:
Ok don't worry. This question is not as hard as it should be.
It states it's a balanced equation. So that means 32 is equal to the other side.
there are 4 r's on the other side
32=4r
Divide 4 on both sides so the variable is independent
32/4=4r/4
8=r
Hope this helps!
Please see picture
What type(s) of symmetry does this figure have?
A. Both rotational and reflectional
B. This figure is not symmetrical.
C. Rotational
D. Reflectional
Answers
ANSWER = MY ETERNAL LOVE determine an equation of the line which is the perpendicular bisector of the segment whose endpoints are (-5,3) and (7,2). make sure to show all work.
Answers
Answer:
Perpendicular Bisector Equation: y = 12x - 9.500
Step-by-step explanation:
Let find out the midpoint for given coordinates as follows:
[(-5+7)/2, (3 +2)/2]
= (2/2, 5/2)
= (1,5/2)
The midpoint coordinates are (1,5/2) means (x1 , y2)
2. Find the slop of line for given coordinates as follows:
(2-3)/(7-(-5)
= -1/12
3. Find the negative reciprocal as follows
-1/12
= 12 (m)
4. Now find the perpendicular bisector equation as follows:
y – y1 = m ( x – x1)
y – 3 = 12 (x – (-5)
y = 12x - 9.5
The required equation of the line is x + 12y = 41 which is the perpendicular bisector of the segment whose endpoints are (-5,3) and (7,2).
What is a perpendicular bisector?A perpendicular bisector is defined as a line that divides an angle into two equal angles.
The perpendicular bisector of the segment whose endpoints are (-5,3) and (7,2).
We have to determine the equation of the line
Let x₁ = -5, y₁ = 3 and x₂ = 7, y₂ = 2
The required of equation line is:
y - y₁ = (y₂ - y₁ )/( x₂ - x₁ )( x - x₁ )
Substitute the values in the formula to get the line,
y - 3 = (2 - 3)/(7 - (-5))(x - (-5))
y - 3 = (-1/12)(x+5)
12y - 36 = -x -5
x + 12y = 41
Thus, the required equation of the line is x + 12y = 41.
To learn more about the equations click here:
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8. John is in a club that collects annual dues. In the first year that he was a member, he paid $20 in club dues. However, the club dues increase by $2 each year. Identify the function that describes the relationship between the number of years that John has been a member of the club and the dues he pays that year.
options:
A. f(n) = 20 + 2(n – 2)
B. f(n) = 20 + 2(n + 1)
C. f(n) = 20 + 2(n – 1)
D. f(n) = 20 + 2n
Answers
Answer: C) f(n) = 20 + 2(n - 1)
Step-by-step explanation:
The explicit formula is: [tex]a_n=a_1+d(n-1)[/tex] where
[tex]a_1[/tex] is the first termd is the difference between consecutive termsGiven: In the first year he paid $20 --> [tex]a_1[/tex] = 20
Dues increase $2 each year --> d = 2
[tex]a_n[/tex] = 20 + 2(n - 1)
Answer:
C f(n) = 20 + 2(n – 1)
Step-by-step explanation:
got it right on test
Marty drew a model of the school library. The total area of the floor is 132 square
centimeters. What is the area of the shaded part of the model shown below?
10 centimeters
6 centimeters
Answers
Answer:
Step-by-step explanatio11n:
116
This year omar watched 80 movies. He thought that 54 of them were very good. of the movies he watched, what percentage did he rate as very good
Answers
Answer:
percentage flim rated very good = 54/80*100%
= 67.5%
Step-by-step explanation:
Approximtely how many 27cubic volume cabinets will a container98,000cbic volume hold?
Answers
Answer: 3630
Step-by-step explanation:
Given that:
Volume of container = 98,000 cubic volume
Volume of cabinet = 27 cubic volume
The number of cabinets which the container will. Hold equals:
Volume of container / volume of cabinet
= 98000 cubic volume / 27 cubic volume
= 3629.6296
The container will hold approximately 3630 27 cubic volume of cabinet.
Need help -5(1+2k)-8(-4+5k)
Answers
Answer:
27 - 50k
Simplify
1. Distribute
-5 ( 1 + 2k ) - 8 ( -4 + 5k )
-5 - 10k - 8 ( -4 + 5k )
2. Distribute
-5 - 10k - 8 ( -4 + 5k )
-5 - 10k + 32 - 40k
3. Add the numbers
-5 - 10k + 32 - 40k
27 - 10k - 40k
4. Add the same term to both sides of the equation
27 - 10k - 40k
27 - 50k
Select all the statements that are true.
Answers
Answer:
Sqrt(7) is irrational because 7 is not a perfect square.
7.1234... is irrational because it is a nonterminating nonrepeating decimal.
Step-by-step explanation:
A rational number is a number that can be expressed in terms of fractions which result in terminating decimals, repeating decimals, or integer values.
An irrational number is a number that cannot be expressed in terms of fractions resulting in nonrepreating nonterminating decimals.
All options other than the two selected do not make sense. Pi is irrational because it is a nonrepeating nonterminating decimal.
Cheers.
Given that the 3rd term in an arithmetic sequence is -2 and the 7th term is -10, tell me what the 1st term in the sequence is. Explain how you know.
Answers
Answer:
2
Step-by-step explanation:
a₃ = -2
a₇ = -10
The nth term of an arithmetic sequence is:
a = a₁ + d (n − 1)
Therefore:
-2 = a₁ + d (3 − 1) = a₁ + 2d
-10 = a₁ + d (7 − 1) = a₁ + 6d
Subtract the equations:
8 = -4d
d = -2
Plug into either equation to find the first term.
-2 = a₁ + 2(-2)
a₁ = 2
Russell runs 910 mile in 5 minutes. At this rate, how many miles can he run in one minute?
Answers
Russell would run 182 miles for 1 minute.
Brighton Company launched a new gaming console. They sold 200 consoles prior to the launch.
The number of consoles sold each day after the launch is shown by the graph below.
Answers
Answer: in the domain of this situation, there is no asymptote.
Step-by-step explanation:
Asymptote would be on the left where x is negative but this function only shows all positive values of X
The value of k is -0.25. The graph shows that the actual number of consoles sold is slightly higher than the predicted number of consoles sold.
The graph shows that the number of consoles sold each day after the launch of the Brighton Company gaming console follows an exponential decay pattern. This means that the number of consoles sold each day is decreasing at a rate that is proportional to the number of consoles that have already been sold.
The equation that can be used to model this exponential decay pattern is:
N = A * [tex]e^{-kt[/tex]
where:
N is the number of consoles sold on day t
A is the initial number of consoles sold (200 consoles)
k is a constant that determines the rate of decay
e is the base of the natural logarithm
We can use the data from the graph to estimate the value of k. The first day after the launch, 180 consoles were sold. This means that on day 1, N = 180. The initial number of consoles sold, A, is known to be 200 consoles. Therefore, we can write the following equation:
180 = 200 * [tex]e^{-kt[/tex]
Solving for k, we get:
k = -ln(1.8) / 1
≈ -0.25
The value of k is approximately -0.25. This means that the number of consoles sold each day is decreasing at a rate of 25%.
We can use the equation to predict the number of consoles sold on future days. For example, on day 2, we would predict that 150 consoles would be sold. On day 3, we would predict that 120 consoles would be sold.
The graph shows that the actual number of consoles sold is slightly higher than the predicted number of consoles sold. This is because the exponential decay pattern is not perfect. There are other factors that can affect the number of consoles sold, such as the availability of the console and the price of the console.
To learn more about graph here:
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is 3 by 3=9 rational or inrational and why
Answers
Answer:
KCC off KCC off off egg LLC
Answer:
rational
Step-by-step explanation:
3by3=3/3
= 1
1 is not eq. to 9
and 3/3 is 1
and 1 is rational no.
There are 128 ounces in a gallon. There are 4 quarts in a gallon. How many ounces are in a quart
Answers
32 ounces.
128/4 = 32
1 quart = 128/4= 32ounces