If line KM bisects angle JKL, angle JKL = 92 degrees, and angle MKL = (5x+1) degrees, find the value of
Answers
The value of the variable x is found to be x = 9.
What is termed as angle bisector?In geometry, an angle bisector is a line that divides an angle into two equal angles. A bisector is something that divides a shape or thing into two equal portions. An angle bisector is a ray that divides an angle into two equal components of the same measurement.A bisected angle divides the two sides in equals.
JKM = LKM
As, both are equal.
Then, each of these angles are 1/2 the angle JKL.
1/2 JKL = MKL
1/2 ×( 92) = 5x + 1
Further simplifying;
46 = 5x+1
Subtract 1 from each side
46-1 = 5x
45 = 5x
Divide each side by 5
45/5 = 5x/5
x = 9
Thus, the value of the unknown variable is found to be x = 9 units.
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Related Questions
Suppose a vector y is orthogonal to vectors u and v. show that y is orthogonal to the vector u v.
Answers
Using Dot product
Two vectors x and y are said to be orthogonal if their dot product is zero
⇒ x.y = 0
This is because orthogonal vectors are make an angle of 90° with each other and therefore θ becomes 90°
Dot product is given by :
x.y = x*y*cosθ = xycos90°
∵cos90° is zero , x.y=0 for orthogonal vectors.
Let u,v,y be vectors in R
y is orthogonal to u and v
⇒ y.u = 0 and y.v=0
Now, we have to prove that y is orthogonal to (u+v)
The dot product of these vectors is given by:
y.(u+v) = y.u + y.v (Dot product is distributive) = 0 + 0 = 0
∵The dot product is zero , vector y and (u+v) are orthogonal
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Givien h(x) = -x- 5, find h(-6)
Answers
Answer:
h(-6) = 1
Step-by-step explanation:
Hello!
Substitute -6 for x in the equation.
Evaluateh(x) = -x - 5h(-6) = -(-6) - 5h(-6) = 6 - 5h(-6) = 1h(-6) is 1.
Please Help!!
Complete the conjecture based on the pattern you observe in the examples below
1) Conjecture: The sum of any two odd numbers is…
1+1=2
1+5=6
7+9=16
9+11=20
13+21=34
101+103=204
2) Conjecture: The product of any two odd numbers is…
1*1=1
1*5=6
7*9=16
9*11=20
13*21=34
101*103=204
3) Conjecture: The product of a number (x-1) and the number (x+1) is always equal to…
3*5=4^2-1
4*6=5^2-1
5*7=6^2-1
7*9=8^2-1
8*10=9^2-1
Answers
Answer:
Hello,
Step-by-step explanation:
1) Conjecture: The sum of any two odd numbers is even
(2a+1)+(2b+1)=2a+2b+2=2(a+b+1) is even
2) Conjecture: The product of any two odd numbers is ODD
(2a+1)*(2b+1)=4ab+2b+2a+1=2(2ab+a+b)+1 is ODD
1*1=1
1*5=5
7*9=63
9*11=99
13*21=273
3) Conjecture: The product of a number (x-1) and the number (x+1) is always equal to the difference of the square of x between 1
(x-1)(x+1)=x²-x+x-1=x²-1
Help I need some help due tomorrow
Answers
Answer:
Angle 1: 141 degrees
Angle 2: 39 degrees
Angle 3: 141 degrees
Step-by-step explanation:
Angle 2 and Angle 4 are equal since they are vertical angles. This means that Angle 2 is equal to 39 degrees.
Angle 1 and Angle 4 add up to 180 degrees. We call these supplementary angles. This means that Angle 1 is equal to 180-39=141 degrees.
Angle 1 and Angle 3 are vertical angles, so Angle 3 is also equal to 141 degrees.
SOLVE ALL OF THESE AND NUMBER THEM ON WHAT QUESTION THE ANSWER IS FOR
Answers
The midpoint of AB is M (0, -4). If the coordinates of A are (2, -1), what are the
coordinates of B?
Answers
Answer: B(-2,-7)
Step-by-step explanation:
[tex]\displaystyle\\M(x_M,y_M)=(\frac{x_A+x_B}{2},\frac{y_A+y_B}{2}) \\\\x_A=2\ \ \ \ x_M=0\ \ \ \ y_A=-1\ \ \ \ y_M=-4\\\\x_M=\frac{x_A+x_B}{2} \\\\Multiply\ both\ parts\ of \ the \ equation\ by\ 2:\\2x_M=x_A+x_B\\\\\Rightarrow\ x_B=2x_M-x_A\\\Rightarrow \ x_B=2(0)-2\\\Rightarrow\ x_B=0-2\\\Rightarrow\ x_B=-2\\Similarly,\\y_B=2y_M-y_A\\y_B=2(-4)-(-1)1\\y_B=-8+1\\y_B=-7\\Thus,\\B(-2,-7)[/tex]
Bombonica s-a gândit la un număr, i-a adăugat 74, rezultatul obţinut l-a mărit de 10 ori, iar din
noul rezultat a luat de 7 ori câte 86 şi a obţinut 318, număr care reprezenta numărul zilelor de când
fusese răpit împăratul. La ce număr s-a gândit?
Answers
[tex]x + 74 \cdot 10 - (7 \cdot 86) = 318[/tex]
[tex]x+74\cdot \:10-7\cdot \:86=318[/tex]
[tex]x+740-7\cdot \:86=318[/tex]
[tex]x+740-602=318[/tex]
[tex]x+138=318[/tex]
[tex]x = 318 - 138 = 80[/tex]
Imparatul s-a gandit la numarul 80.
Find the sum of (8.6 x 106) and (3.7 x 105). Write the final answer in scientific notation.
8.97 x 105
8.97 x 106
1.23 x 1010
12.3 x 1011
Answers
Answer:
8.97 x [tex]10^{6}[/tex]
Step-by-step explanation:
To add in scientific notation, the exponents need to be the same for the bases of 10. You can either make them both to the exponent of 6 or 5. It does not matter. I made them both to the power of 5
(8.6 x [tex]10^{6}[/tex]) + (3.7 x [tex]10^{5}[/tex])
(86 x [tex]10^{5}[/tex]) + (3.7x[tex]10^{5}[/tex])
(86 x 3.7) x [tex]10^{5}[/tex]
89.7 x[tex]10^{5}[/tex] Rewrite in scientific notation
8.97 x [tex]10^{6}[/tex]
Will give brainliest.
Answers
Answer:
Option 3
Step-by-step explanation:
First tke lcm i.e. 6 then multiply the dinominator to make six.
Multiply tje above no. With the same digit the sub. The numerators
Answer:
c) 7/6
Step-by-step explanation:
The difference will be,
→ (5/3) - (1/2)
→ (10/6) - (3/6)
→ (10 - 3)/6
→ 7/6
So, the answer is 7/6.
Find the linear function represented by the graph.
The slope of the line is
.
The y-intercept of the line is at
.
What linear function is represented by the graph?
Answers
Step-by-step explanation:
photo please ......................
Answer:
Step-by-step explanation:
need to see the graph
=. What does the expression (x+3)(9) represent? Why?
Answers
I hope this helps!! :)
i don’t understand this i already tried but got 1.25 bad i’m pretty sure it’s wrong
Answers
Answer:
Smallest integer=14
Step-by-step explanation:
(x+x+2+x+4+x+6)/4=17
(4x+12)/4=17
4x+12=68
4x=68-12
4x=56
x=56/4
x=14
numbers are: 14, 16, 18, 20
find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continuesm8, 0, 8, 0,
Answers
The formula for the general term and of the sequence is ±8.
What do we mean by sequence?A sequence in mathematics is an enumerated collection of objects in which repetitions are permitted and order is important. It, like a set, has members (also called elements, or terms). The length of the sequence is defined as the number of elements (which could be infinite). Unlike a set, the same elements can appear multiple times in a sequence at different positions, and the order does matter. Formally, a sequence can be defined as a function from natural numbers (the sequence's positions) to the elements at each position. The concept of a sequence can be expanded to include an indexed family, which is defined as a function from an index set that may or may not is numbered to another set of elements.To find the formula for the given sequence:
Given sequence: 8, 0, 8, 0, So, the formula cen be ±8.+8 to get the terms of odd numbers and -8 to get the terms of even numbers.Therefore, the formula for the general term and of the sequence is ±8.
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How do I simplify this?
Answers
1- 3/4 = 0.25 which is equivalent to 1/4
the problem now looks like 7/4 / 1/4
you cancel out both 4
this problem simplified looks like 7/1
which is equivalent to 7 if you divide
HELP! (3x4)+ 52 MARKING BRAINLY!
Answers
Answer:
64
Step-by-step explanation:
[tex]3 \times 4\\= 12\\= 12 + 52\\= 64[/tex]
Answer:
64
Step-by-step explanation:
first 3 x 4 = 12
12+52=64
(c) Solve the equation 7x³ +28x² = 0
Answers
Answer:
x = - 4 , x = 0
Step-by-step explanation:
7x³ + 28x² = 0 ← factor out 7x² from each term on the left side
7x²(x + 4) = 0
equate each factor to zero and solve for x
7x² = 0 ⇒ x² = 0 ⇒ x = 0
x + 4 = 0 ⇒ x = - 4
Pigeonhole suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior. is the following statement true or false:
Answers
Suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior: FALSE
What is a sophomore?A sophomore in the United States is a student in their second year at an educational institution, usually a secondary school or a college or university, but also other types of post-secondary educational institutions. A sophomore in high school is equivalent to a tenth-grade or Class-10 student.In sports, a sophomore is a professional athlete in their second season.As in the description, it is given that a sophomore in high school is equivalent to a tenth-grade or Class-10 student.
So, the above-given statement becomes false as it says that every student is a sophomore but the class has juniors and seniors.
Therefore, the statement "suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior" is FALSE.
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The complete question is given below:
Suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior. Is the following statement true or false:
"The course must have at least five sophomores, or at least 20 juniors, or at least 10 seniors."
Write an equation representing the fact that the product of two consecutive odd integers is 255. use x to represent the smaller integer.
Answers
The first odd number = 15
The second is then = 17
The Consecutive numbers are:Consecutive numbers are those that appear consecutively after one another in the range of smallest to largest. An illustration would be the sequence of numbers 1, 2, 3, 4, 5, and so on.
Where can I find consecutive numbers?Let x be the first of the following numbers to represent it algebraically. Following that, the numbers x + 1, x + 2, and x + 3 would be arranged in order. You must make sure that your first selection is an even number if the question requires consecutive even numbers.
According to the given information:We can employ the expression "2n," where n is any integer, to ensure that the result is even. By using the expression "2n + 1," we can ensure an odd number.
"2n + 3" will be the following odd number:
(2n + 1)(2n + 3) is the component of the odd integers, and it equals 255:
(2n + 1)(2n + 3) = 255
4n2 + 8n + 3 = 255
4n2 + 8n - 252 = 0
n2 + 2n - 63 = 0
(n + 9)(n -7) = 0
n = -9 and n = 7
We can disregard n = -9 because we are informed that the figures must be positive.
If n = 7,
The first odd number = 2(7) + 1 = 15
The second is then 17
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I understand that the question you are looking for is:
The product of 2 positive, consecutive odd numbers is 255 .
Part A: Write a quadratic equation in standard form to represent this problem
Part B: What are the 2 numbers?
Part C: Show your work for Part B.
If f (x) = 3x - 1 and g (x) = x² + 1, find the following.
a) g(-4) + f(-2) =
b) f(1) - g(0) =
Will give brainliest and 5 star rating. Thank you. :)
Answers
The value of the functions are:
a. g(-4) + f(-2) = 24
b.. f(1) - g(0) = 1
What is a function?A function can be defined as an expression showing the relationship between two variables.
Given the functions;
f (x) = 3x - 1 g (x) = x² + 1g(-4); substitute the value of x as - 4 in g(x)
g(-4) = (-4)² + 1
g(-4) = 16 + 1
g(-4) = 17
f(-2); substitute the value of x as - 2 in f(x)
f(-2) = 3(-2) - 1
f(-2 = -7
a. g(-4) + f(-2) = 17 -(-7)
g(-4) + f(-2) = = 24
f(1) = 3(1) - 1
f(1) = 2
g(0) = (0)² + 1
g(0) = 1
b. f(1) - g(0) = 2 - 1
f(1) - g(0) = 1
Thus, the value of g(-4) + f(-2) and f(1) - g(0) are 24 and 1 respectively.
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Which exponential function bests models the graph below?
A.
B.
C.
D.
D.
Answers
Which number is greater,
23
×
10
3
or
11
×
10
4
? How do you know? Show your work and explain your steps.
Answers
Answer:
Answer: 11x10^4 is greater. Step-by-step explanation: 23x10^3 = 23x10x10x10 = 23000. 11x10^4 = 11x10x10x10x10 = 110000. 110000 is greater than 23000.
Step-by-step explanation:
cos
A startup sports public relations company is looking to grow. They currently represent 2 clients and plan on representing 3 additional clients each year. The following graph can be used to help determine the number of clients, y, the company will have after x years.
ased on the context, what is the range of the function?
[0, ∞)
[2, ∞)
[−7, 7]
ℝ
Answers
Based on the context, the range of this function is given by: C. [−7, 7]
What is a range?A range can be defined as the set of all real numbers that connects with the elements of a domain. This ultimately implies that, a range refers to the set of all possible output numerical values, which are shown on the y-axis of a graph.
How to identify the range of this graph?The vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph of function f(x) shown, we can infer and logically deduce the following:
Range = [−7, 7]
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. Use Structure is the product the same
when multiplying 22 x (-5) and multiplying
(-5) x 22? Explain.
Answers
Answer:
Yes.
Step-by-step explanation:
Let's say a=22 and b=-5
According to the Commutative Property of Multiplication, a*b=b*a. Hence, 22*(-5)=(-5)*22.
22*(-5)=
-(22*5)=-110
(-5)*22=
-(5*22)=-110
-110=-110 √
-(16 - 5x) simplified
Answers
Answer:
5x-16
Step-by-step explanation:
-(16 - 5x)
Use distributive property to open parenthesis.
-(16 - 5x)=
=(-1*16)+(-1*-5x)=
=(-16)+(5x)=
=5x-16
Finding x.
5x-16=0
5x=16
x=3.2
Hope this helps!
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(-1)^{3}]^{6} find the value of
Answers
The value of Exponent [tex](-1^{3}) ^{6}[/tex] is 1
Exponent:
A number's exponent indicates how many times we multiply a number by itself. For example, [tex]3^{4}[/tex] indicates that we have multiplied 3 four times. The expanded form is 3×3×3×3. An exponent is also known as a number's power. It can be an integer, a fraction, a negative number, or decimals.
Law of Power of a Power: [tex](x^{a}) ^{b}[/tex]=[tex]x^{ab}[/tex] {Here a,b can be an integer, a fraction, a negative number, or decimals}
Given question is [tex](-1^{3}) ^{6}[/tex]
⇒[tex](-1^{3}) ^{6}[/tex]=[tex](-1)^{6.3}[/tex]{ using Law of Power of a Power}
⇒[tex](-1)^{18}[/tex]=1 { -1 raised any even number= positive one}
Therefore,The value of Exponent [tex](-1^{3}) ^{6}[/tex] is 1
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Marcus owes Abdullah
$10. He also owes
$5 to Mariyah. Which
integer represents
Marcus' finances?
A. -15
B. -5
C. 5
D. 15
Answers
-$10 + -$5 = -$15
He owes the money meaning he has to give his money away
Question 2(Multiple Choice Worth 1 points)
(01.01 LC)
Evaluate the expression 5(7-4)2 = 3 + 11.
03
14
026
33
Answers
26 is the right answer .
Given expression 5(7 - 4)² ÷ 3 + 11.
BODMAS rule is an acronym that is used to remember the order of operations to be followed while solving expressions in mathematics. It stands for B - Brackets, O - Order of powers or roots, D - Division, M - Multiplication, A - Addition, and S - Subtraction. It means that expressions having multiple operators need to be simplified from left to right in this order only. First, we solve brackets, then powers or roots, then division or multiplication (whichever comes first from the left side of the expression), and then finally, subtraction or addition, whichever comes on the left side.
Using the BODMAS rule, we solve bracket first,
5(3)² ÷ 3 + 11
45 ÷ 3 + 11
= 15 + 11
= 26
after evaluate the expression we get 26 as answer.
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misha is the 50th best as well as the 50th worst student in her grade. how many students are in misha's grade?
Answers
There are 99 students in Misha's grade.
What do we mean by Venn diagrams?A Venn diagram is a popular diagram style that shows the logical relationship between sets. It was popularized in the 1880s by John Venn (1834-1923). The diagrams are used in probability, logic, statistics, linguistics, and computer science to teach elementary set theory and to illustrate simple set relationships. To represent sets, a Venn diagram employs simple closed curves drawn on a plane. These curves are frequently circles or ellipses.So,
We'll make a Venn diagram (consider the diagram given below).Misha is common in both groups.According to the diagram, 49 + 49 + 1 = 99.Therefore, there are 99 students in Misha's grade.
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what is a mediannnn please help
Answers
Answer:
The middle number in a set of numbers.
Step-by-step explanation:
For example, if I have a set of numbers like 5,6,3,7,9
3 would be the median because it is in the middle.
I hope I helped!!
what is the fraction form of 10.0833333... repeating
Answers
What is 10.0833333 as a fraction?
To write 10.0833333 as a fraction you have to write 10.0833333 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
10.0833333 = 10.0833333/1 = 100.833333/10 = 1008.33333/100 = 10083.3333/1000 = 100833.333/10000 = 1008333.33/100000 = 10083333.3/1000000 = 100833333/10000000
And finally we have:
10.0833333 as a fraction equals 100833333/10000000