In AJKL, JL is extended through point L to point M, m/LJK = (x+9)°,
m/JKL = (x - 2)°, and m/KLM = (5x - 11)°. Find m/LJK.
Answers
For the given triangle JKL, the value of x is 10. An angle is a figure in Plane Geometry formed by two rays or lines that share a common endpoint.
What is meant by angle?When two straight lines or rays intersect at a common endpoint, an angle is formed. An angle's vertex is the common point of contact. Angle is derived from the Latin word angelus, which means "corner." An angle is a figure in Plane Geometry formed by two rays or lines that share a common endpoint. "Angle" comes from the Latin word "angelus," which means "corner." The two rays are known as the sides of an angle, and the common endpoint is known as the vertex.When two lines intersect at a common point, an angle is formed. They are expressed in degrees, which are denoted by the symbol °.Given information:
In ∠J K L,JL is extended through point L to point M.
[tex]$&m \angle J K L=(2 x+14)^{\circ} \\[/tex]
[tex]$&m \angle L J K=(3 x+15)^{\circ} \\[/tex]
[tex]$&m \angle K L M=(7 x+9)^{\circ}[/tex]
See the attached figure.
At point L, the measure of angle JLK will be as,
[tex]$&m \angle J L K=180-m \angle K L M=180-7 x-9 \\[/tex]
[tex]$&=(171-7 x)^{\circ}[/tex]
Now, in triangle JKL, use the angle sum property to find the value of x as,
[tex]$$m \angle J K L+m \angle L J K+m \angle J L K=180[/tex]
[tex]$$$(2 x+14)^{\circ}+(3 x+15)^{\circ}+(171-7 x)^{\circ}=180$[/tex]
-2 x+200=180
2 x=20
x=10
Therefore, the value of x for the given triangle JKL is 10.
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Related Questions
Write an equation in slope-intercept form
to represent the relationship between x
and y shown in the table.
X
Y
-10 -5 0 5
55
20
-15
-50
10
-85
Answers
Answer:
665-09
Step-by-step explanation:
1/x-2 identify the asymptotes
Answers
The vertical asymptote is x=2 and horizontal asymptote is y = 0
What are asymptotes?An asymptote is a straight line that constantly approaches a given curve but does not meet at any infinite distance. In other words, Asymptote is a line that a curve approaches as it moves towards infinity.
There are three types is asymptotes:
Horizontal asymptote , Vertical asymptote and oblique asymptote.
in the expression 1/x-2, the horizontal asymptote is y=0 since the power of x in the numerator is less than that of denominator.
And the vertical asymptote is found by equation the denominator to zero
therefore x-2= 0
x= 2
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Write an equation of the line, in point-slope form, that passes through the two given points.
points: (-2,10), (10 -14)
Answers
The required equation of the line will be y = 2x + 6 which passes through the points (-2,10), (10 -14).
What is the slope of the line?The slope of a line is defined as the gradient of the line.
Given that line passes through the points (-2,10), (10 -14)
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = -2, y₁ = 10
x₂ = 10, y₂ = -14
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute values in the equation, we get
⇒ y - 10 = (-14 - 10)/(10-(-2))[x -(-2)]
⇒ y - 10 = (-24)/(12 )[x +2]
⇒ y - 10 = -2(x +2)
⇒ y = -2x - 4 + 10
⇒ y = -2x + 6
Therefore, the equation of the line would be y = 2x + 6 which passes through the points (-2,10), (10 -14).
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Is y−4=3(x+1) an equation of a line through (-2, 1)? Explain.
Answers
Answer:
Yes
Step-by-step explanation:
(1)-4=3((-2)+1)
-3=3(-1)
-3=-3
The answer is yes because if you substitute x and y for -2 and 1 you can simplify the equation. Then you get the answer -3=-3 which means that the equation is equal.
-4x+3y=2
3x-9y=3
Is (4,1) a solution of the system?
Answers
Answer:
not a solution
Step-by-step explanation:
we can just fill it in on both equations
-4(4)+3(1)=2
-16+3=2
-13=2
It doesn’t work for this equation so it’s not a solution
Hopes this helps please mark brainliest
Answer:
No
Step-by-step explanation:
For (4, 1 ) to be a solution then both equations must be true
substitute x = 4 and y = 1 into both equations
- 4(4) + 3(1) = - 16 + 3 = - 13 ≠ 2
3(4) - 9(1) = 12 - 9 = 3
Since both equations are not true then (4, 1 ) is not a solution of the system.
What value of b will complete the square in the expression below and make the
expression a perfect square trinomial?
x²+bx+144
Enter the perfect square trinomial as a squared binomial.
Answers
At b= 24 will complete the square in the expression x^2 + bx + 144.
What is perfect square trinomial?
A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial satisfying the criterion b^2 = 4ac has the form ax^2 + bx + c, it is said to be a perfect square. The formula for the perfect square trinomial is (ax)^2 + 2abx + b^2 = (ax + b)^2.
Consider the given expression
x^2 + bx + 144
For this type of expression [tex]b = 2\sqrt{c}[/tex] will complete the square.
Here, c = 144
√144 = 12
So, b√c = 2(12) = 24
The expression becomes,
x^2 + 24x + 144 = (x + 12)^2
This is the perfect square.
Hence, b = 24 will complete the square in the expression x^2 + bx + 144.
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HELP MEEE PLEASEEEE
Answers
Answer:
5.8 cm
Step-by-step explanation:
the Pythagorean theorem states that a^2=b^2+c^2, where a is the hypotenuse, and b and c are the legs. Plugging in your values, we get:
4^2 + 4.2^2 = a^2
Simplify: 16 + 17.64=a^2
Simplify again: 33.64 = a^2
Square root both sides: 5.8 = a
The exponential model describes the population, A, of a country in millions, t years after 2003. Use the model A=384. 7e^0. 018t to determine when the population of the country will be 513 million.
The population of the country will be 513 million in __. (Round to the nearest year as needed. )
Answers
The population of the country will be 513 million in 2016 with The exponential model A=384. 7e^0. 018t describes the population, A, of a country in millions, t years after 2003.
What is exponential model?The exponential model represents the degrading failure process using an equation like: where Y = degradation, T = time, and A and B = parameters to be predicted using the regression approach using historical data. Exponentials are frequently utilized when the rate of change of a quantity is proportional to its beginning amount. Y represents exponential decay if the coefficient associated with b and/or d is negative. Y represents exponential growth if the coefficient is positive.
Here,
A = 384. 7e^0. 018t
513=384. 7e^0. 018t
513/384.7= e^0.018t
ln(513/384.7) = 0.018t
ln(513/384.7)/0.018 =t
t=15.9895575229 years
t=16 years
2003+16= 2019
In 2016, the country's population will be 513 million people. The exponential model A=384. 7e^0. 018t explains a country's population, A, in millions, t years after 2003.
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A manager of a fast food chain wants to know how his customers rate their service at the restaurany that day. after randomly picking the 9th customer, he surveys every 5th customer that exits the restaurant. which sampling method? your answer: simple random systematic stratified cluster volunteer
Answers
The sampling method used in this scenario is random Systematic random sampling
Systematic random sampling
Systematic sampling is a form of probability sampling technique in which sample members are chosen from a wider population using a defined, periodic interval but a random beginning point. By dividing the population size by the desired sample size, this interval, also known as the sampling interval, is computed.
If the periodic interval is predetermined and the starting point is random, systematic sampling is still regarded as random even though the sample population has been chosen in advance.
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a journalist for an automotive magazine wants to determine how the weight of a passenger vehicle, in kilograms, is related to its length, in centimeters; the maximum number of passengers; and its safety rating on a 5-point scale. what is the correct format for a multiple regression equation?
Answers
the correct format for a multiple regression equation is
ŷ= [tex]b_{o} + b_{1}x_{1} + b_{2}x_{2} + b_{3}x_{3} + b_{4}x_{4}[/tex]
multiple regression: The relationship between a single dependent or criterion variable and multiple independent or predictor variables is typically explained by multiple regression. The constant term and multiple independent variables with their corresponding coefficients are used to model a dependent variable. The term "multiple regression" refers to the fact that it requires two or more predictor variables.
because, the weight of a passenger vehicle, in kilograms, is related to its length, in centimeters; and the maximum number of passengers.
thus, ŷ=[tex]b_{o} + b_{1}x_{1} + b_{2}x_{2} + b_{3}x_{3} + b_{4}x_{4}[/tex] is the multiple regression equation.
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What is the radius of the circle made by anas brother in the blue car? use 3. 14 and round your answer to the nearest tenth
Answers
The radius of Ana's brother's circle in the blue car is 35 feet.
Define the term radius of the circle?A radius is a line segment that connects the center towards the perimeter of a circle or sphere. The radius length remains constant as from center either to point on the circle or sphere's perimeter.For the given question-
The total distance covered by the Ana's brother in the blue car = 220 feet.
Total distance = circumference of the circle.
circumference of the circle = 2 π r
r = radius of the circle.
π = 3.14
Thus,
220 = 2 x 3.14 x r
r = 220 / (3.14 x 2)
r = 35.03
r = 35 feet.
As a result, the radius of Ana's brother's circle in the blue car is 35 feet.
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The complete question-
The missing data from the question is given in diagram attached.
what does the degree tell you about the zeros of the function of x^3+8x^2+11x-20?
Answers
Answer:
Step-by-step explanation:
the degree of the function , also means how many zeros , or roots, There will be.
Please Help ASAP!!!!!
Answers
Answer:
the forth (7,2).........
If your weekly salary is $1,015.00, how much do you have left each week after you pay for the following? Rent - $443.50 Cable TV -$23.99 Electricity - $45.62 Groceries - $124.87 ?
(need explanation.)
Answers
If you subtract everything from your weekly salary that’s the answer you end up with
HELPPP MEEeeeeeeeeee
Answers
So side NM is congruent to side TR
Explanation- they tell you NMK is =~ to TRP. When they do this, they are telling you
NM =~ TR
Vertices M =~ R
MK =~ RP
So the answer to which side is congruent to TR is NM
I need to know the constant of proportionality for each table and equation. I also need to know what the answer to the question on the bottom is.
Please show your work too. (Important)
Answers
The constant of proportionality for each table are 5, 2/3, 4, 1/5, 3, 2 and 1/2 while that of the equations are 1/8, 1/3 and 3/2
How to determine the constant of proportionality for each table and equation?
The constant of proportionality is the ratio of the y value to the x value i.e.
constant of proportionality(k) = y/x
To find the constant of proportionality for each table, just pick any non-zero corresponding x and y values on the table and find the ratio:
Using constant of proportionality(k) = y/x
1. y/x = 5/1 = 5
2. y/x= 4/6 = 2/3
3. y/x = 2/0.5 = 4
4. y/x= 2/10 = 1/5
5. y/x = 9/3 = 3
6. y/x = 8/4 = 2
7.y/x = 6/12 = 1/2
For the equations, just rewrite the equations in order to make y/x the subject:
8. y =1/8 x
y/x = 1/8
9. 6y = 2x
y/x = 2/6 = 1/3
10. 4y = 6x
y/x = 6/4 = 3/2
Therefore, the constant of proportionality for each table and equation are 5, 2/3, 4, 1/5, 3, 2, 1/2 and 1/8, 1/3, 3/2 respectively
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What is the value of blank and 40.01 is close to 1
Answers
The number that is the numerator of a fraction with denominator of 40.01 and is equals to a coefficient of one is:
40.01.
What is a fraction?A fraction is a numerical representation of the division of the two terms x and y that composed the fraction, as follows:
Fraction = x/y.
The terms are named as follows:
The top term x is the numerator of the fraction.The bottom term y is the denominator of the fraction.Hence the quotient of the division is the numerator divided by the denominator.
In this problem, interpreting the blank variable as x, the fraction that represents the situation is:
x/40.01 = 1.
Applying cross multiplication, the numeric value of the variable x is obtained as follows:
x = 40.01 x 1
x = 40.01.
Missing InformationThe complete problem asks for which number divided by 40.01 is close to 1.
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solve for x and y
picture provided
Answers
The value of x will be 15 and the value of y will be 4.
What is the similarity?If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
Here in the image, we have a triangle having sub-triangles. The value of x is calculated by considering two right-hand triangles.
x / ( x + 5 ) = 18 / ( 18 + 6 )
x / ( x + 5 ) = 18 / 24
24x = 18x + 90
6x = 90
x = 15
The value of y will be calculated by considering the two left-hand triangles.
12 / ( 12 + y) = 15 / 20
240 = 180 + 15y
15y = 60
y = 60 / 15
y = 4
Therefore, the value of x will be 15 and the value of y will be 4.
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Three students ran for class president. lisa got 36 votes for class president. she got six times more votes than lauren. chandler got seven times more than lauren. how many votes did lauren get?
Answers
Lauren got 5 votes in class president election.
Number of votes Lisa got = 36
Let the number of votes of Lauren be x. So, forming the equation between the number of votes of Lisa and Lauren.
36 = x + 6x
Calculating the value of x from mentioned equation
36 = 7x
Rewriting the equation with 7 as denominator
x = 36/7
Performing division on Right Hand Side of the equation
x = 5.14
Rounding off the digits as number of votes will be whole number
x = 5
Based on the mentioned information, Lauren got 5 votes.
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I need help with this graph what is the root or factored form of this? Thank you!
Answers
Answer:
(2.5×20)2=100 then square root of 100;
✓100=10
Hence answer is 10
A football team receives the ball on their
own 10 yard line.
a. They make a gain of 15 yards in the first play. What yard line is the ball on?
b. What represents zero in this situation? Explain.x
Answers
The summation of 10 yards line and 15 yard is 25 yards and the ball represents zero situation when the ball is in net and goals.
Given,
The team receives the ball on their own yards = 10 yards.
that is,
initial position of the ball = 10 yards.
Using summation, (the summation is to add or subtract any two numbers or more terms by doing operation, to get answer).
They make a gain of 15 yards in the first play.
Their final position in 10 yards plus 15 yards
= 10 + 15
=25 yards.
Therefore, the yard line is 25 yards.
The zero situation of the game is when the ball is in net and the player make a goal.
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A pool takes 3,185 gallons to fill. After 2.5 hours the pool is filled with 1,625 gallons how long will it take to fill the whole thing
Answers
[tex]\begin{array}{ccll} hours&gallons\\ \cline{1-2} 2.5 & 1625\\ h& 3185 \end{array} \implies \cfrac{2.5}{h}~~=~~\cfrac{1625}{3185}\implies \cfrac{2.5}{h}=\cfrac{25}{49} \\\\\\ (2.5)(49)=25h\implies \cfrac{(2.5)(49)}{25}=h\implies 4.9=h\qquad \textit{4 hours and 54 minutes}[/tex]
[tex]3\sqrt{6w-288[/tex]
Answers
Use the distributive property to remove the parentheses.
3c³(7c8 +8c+7)
Simplify your answer as much as possible.
Answers
Answer: 21 c^16 + 24c^9+ 21 c^8
Step-by-step explanation: To multiply exponents with the same base, add them.
Answer:
3c^3(7c^8+8c+7)
=(3c^3)(7c^8+8c+7)
=(3c^3)(7c^8)+(3c^3)(8c)+(3c^3)(7)
=21c^11 + 24c^4 + 21c^3
Step-by-step explanation:
Remember.... ^ is for power
can anyone please help with this! it’s so confusing! 100 points to whoever can help me with all of them! and please show how u did it not just answers!! tysm
Answers
Answer:
Step-by-step explanation:
(a is in the file)
B. An add 3 inches to height would affect the surface area more than 3 inches to weight because if the same number was multiplied to 0.13 and 0.08… 0.13 would have the greater outcome.
c. a number more than 10 but less than 11 is 10.5
The height is 50 so plug those two numbers into the equation
10.5=0.08W+(0.13)50-1.03
10.5=0.08W+ 6.5-1.03
10.5=0.08W+5.47
Subtract 5.47 from both sides
5.3=0.08
Divide by 0.08 on both sides
= 62.87lbs in one possibility for the value of W
D. a number between 12 and 13 is 12.5
12.5= 0.08w+ 0.13H-1.03
Subtract 1.03 on both sides
11.47= 0.08w+ 0.13H
Divide 11.47 in 2 so that weight and height can be added up to equal 11.47 in the end
5.73=0.08 5.73=0.13
71.68=W 44.07=H
9. There is so much water in the world, that we normally measure large bodies of water in cubic
miles or cubic kilometers instead of gallons. Cayuga Lake in upstate New York contains an
estimated 9.4 km³. How many cubic miles of water does Cayuga Lake contain?
Answers
Answer:
Step-by-step explanation:
12.5km
i made that up sorry
In the figure below, a pole has two wires attached to it, one on each side, forming two right triangles.
Based on the given information, answer the questions below. Round each answer to the nearest tenth.
Part A: How tall is the pole? Show your work.
Part B: How far from the base of the pole does Wire 2 attach to the ground? Show your work.
Part C: How long is Wire 1? Show your work.
Answers
Part A. tan41 = p/34
p = 29.6 ft
Part B. tan38 = x/29.6
x = 23.1 ft
Part C. 34^2 + 29.6^2 = w^2
2032.16 = w^2
45.1 ft = w
The answers are a) 29.55 ft, b) 23.08 feet and c) 45.05 feet
What are trigonometric ratios?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled.
Given is a figure, of two wires 1 and 2 attached to a pole and ground
Using trigonometric ratios, we have,
a) tan41° = Height of pole/34
Height of pole = tan41°x34
Height of pole = 29.55 ft
b) tan38° = (distance of wire 2 from the base of pole)/29.55
Distance of wire 2 from the base of pole = tan38°x29.55 = 23.08 feet
c) cos41° = 34/length of wire 1
Length of wire 1 = 34/cos41°
Length of wire 1 = 45.05 feet
Hence, The answers are a) 29.55 ft, b) 23.08 feet and c) 45.05 feet
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Kelly has 97 apples, Jason has 72. How may proportional relationships are there?
Answers
There are 6984 inverse proportional relationships and the direct proportional relationships are 97/72.
Given that:
Kelly has 97 apples, and Jason has 72.
The relationship between two variables, X and Y, is directly proportional if it can be expressed in terms of Y/X = k or Y = Xk.
Y/X = k
Substitute the given X and Y values and solve for k.
Suppose, Y = 97, X = 72
then k = 97/72
Distinguish a proportional relationship from other relations, including an inverse relationship (XY = k or Y = k/X).
An inverse proportional relationship is one in which two quantities vary inversely with respect to each other. We say that the variable Y changes inversely with X if
Y = k/X
Substitute the given X and Y values and solve for k.
Suppose, Y = 97, X = 72
then k = 97 x 72
=> k = 6984
Hence, there are 6984 inverse proportional relationships and direct proportional relationships are 97/72 between Kelly which has 97 apples, and Jason which has 72.
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f(-10) = 4, ƒ(8) = -5
Answers
Answer: f(x)=-.5x-1
Step-by-step explanation:
I believe this is the answer you are looking for. Because if you plug in -10 for x and it gives you 4. Do the same with 8 and you get -5
Hope this helps :)
Determine the slope of the graph of x2 = ln(xy) at the point (1, e).
Answers
The slope of the given graph x^2 = ln (xy) at the point (1, e) is e
We have been given a graph x^2 = ln (xy) and a point (1, e)
Differentiate the given graph on both sides
d/dx x^2 = d/dx (ln (xy))
⇒ 2x = 1/xy × d/dx (xy)
⇒ 2x × xy = x.dy/dx + y.dx/dx
⇒ 2x^2y = x.dy/dx + y
⇒ 2x^2y = x.dy/dx + y
⇒ 2x^2y - y = x.dy/dx
⇒ (2x^2y - y)/x = dy/dx … (1)
The slope at the point (1, e)
m = dy/dx at x = 1, y = e
Substitute the values in Equation (1)
⇒ m = (2(1)^2 (e) - e)/1
⇒ m = (2e - e)/1
⇒ m = e/1
⇒ m = e
Hence, the slope of the given graph is e.
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