No, you cannot stop at the step 3x = 126 degrees. The measure of angle JML is approximately 56.67 degrees
What is the measure of angle θ?
A radian is the length of an arc formed by an angle that, when shown as a central angle, equals the length of the circle's radius.
No, you cannot stop at the step 3x = 126 degrees.
To find the measure of angle JML, we need to solve for x and then use that value to find the measure of the angle.
We can start by using the fact that the angles in triangle JLM must add up to 180 degrees. We have:
m∠JLM + m∠JML + m∠LMJ = 180
Substituting the given values, we get:
4x + (2x + 18) + (3x - 12) = 180
Simplifying and combining like terms, we get:
9x + 6 = 180
Subtracting 6 from both sides, we get:
9x = 174
Dividing both sides by 9, we get:
x = 19.33...
Now that we have the value of x, we can use it to find the measure of angle JML. We have:
m∠JML = 2x + 18
Substituting x = 19.33..., we get:
m∠JML = 2(19.33...) + 18 = 56.67...
Therefore, the measure of ∠JML is approximately 56.67 degrees
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a Which equation represents a line that passes through (-2, 4) and has a slope of 2/5?
y = 2/5x +24/5, is the equation which represents a line that passes through (-2, 4) and has a slope of 2/5.
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
The slope intercept form of a line is
y = mx+b
where m is the slope and b is the y intercept
y = 2/5 x +b
Substitute the point (-2,4) into the equation and solve for b
4 = 2/5(-2)+b
4 = -4/5 +b
Add 4/5 to each side
20/5 +4/5 = b
24/5 = b
Hence, y = 2/5x +24/5, is the equation which represents a line that passes through (-2, 4) and has a slope of 2/5.
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a university is conducting research on ways to improve study habits and help students with lower grade point averages. it sends out a questionnaire to undergraduate students asking how they study and what they feel is the most productive way to study. what data collection method is the university using?
As the university is sending out questionnaires, the data collection method the university is using is a survey
The term "survey" describes the method of gathering data on a certain subject generally by employing questionnaires. In order to understand more about a certain topic, a survey is a method of data collection that involves asking a sample of respondents a number of questions. In the given case, the university is using a survey as a tool for gathering data.
Here, the institution is distributing a survey to undergraduate students to learn more about their study habits and what they believe to be the most effective method of studying. In order to efficiently gather data from a large number of participants quickly and effectively, surveys are frequently employed in research investigations.
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rectangle abcd is dilated by a scale factor of 1/4 to form a’b’c’d’. point t is the center of dilation and lies on segment ab as shown
The slope of A'B' is 0 and the length of A'B' is 1/4(5) = 1.25 units.
What is transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
The line AB has the following coordinates.
A = (1, 4)
B = (6, 4)
The distance between AB is given as:
AB = √(6 - 1)² + (4 - 4)²
AB = √(5)²
AB = 5
The slope of AB = 0.
For the dilated rectangle the slope remains the same.
The slope of A'B' is 0 and the length of A'B' is 1/4(5) = 5/4 = 1.25 units.
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The correct question is:
The inn has ten rooms. One-half of the rooms are reserved for Friday. The rest are vacant. Of 12 more rooms are reserved for Friday, what will be the total number of occupied rooms on Friday?
Using, the mathematical inequalities, we can conclude that the total number of occupied rooms on Friday is 10.
Number of rooms in the inn = 10
It is given that One-half of the rooms are reserved for Friday which means 5 rooms were initially reserved on Friday.
Now, 12 more rooms are reserved for Friday.
So, the Initial reservation for Friday = 5
Final reservations for Friday = 5 + 12 = 17
Now, Final reservations for Friday(17) > Total number of rooms in the inn(10).
As the reservation exceeds the capacity of the hotel, 7 reservations will be cancelled and all 10 rooms will be occupied on Friday.
Hence, the total number of occupied rooms on Friday is 10.
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g(n) = -1 +1 n f(n) = - 1 n-1
Find the approximate values of the five number summary for the data set represented by this box plot,
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
The Approximate values of the five number summary are ;
(i) the Minimum is 10 ,
(ii) the First quartile is 30 ,
(iii) the Third Quartile is 80 ,
(iv) the Median is 55 ,
(v) the Maximum is 100 .
The values of the data set are : {10 ,15 ,20 ,25 ,30 ,35 ,40 ,45 ,50 ,55 ,60 ,65 ,70 ,75 ,80 ,85 ,90 ,95 ,100 } ;
The Five number summary consists of the minimum , maximum , first quartile , third quartile and the median .
(i) the Minimum of the data set is = 10 ;
(ii) we split the data set into , 2 halves ;
that means ; {10 ,15 ,20 ,25 ,30 ,35 ,40 ,45 ,50 } and {60 ,65 ,70 ,75 ,80 ,85 ,90 ,95 ,100 } ;
the first quartile lies in the lower half : {10 ,15 ,20 ,25 ,30 ,35 ,40 ,45 ,50 } ;
So , first quartile (Q₁) = 30 ;
(iii) the third quartile (Q₃) lies in the upper half : {60 ,65 ,70 ,75 ,80 ,85 ,90 ,95 ,100 } ;
So , Q₃ = 80 ;
(iv) the total number of terms in the set is = 19 ;
So , the median is = tenth term = 55 ;
(v) the maximum of the data set is = 100 .
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#5
CONNECTING CONCEPTS You use 94 inches of plastic to frame the perimeter of a kite. One side of the kite has a
length of 18 inches. Find the length of each of the three remaining sides in order from least to greatest.
Length: in.,in., in
The length of the tree remaining sides are 18 inches, 29 inches and 29 inches.
What are the lengths of the remaining sides?A kite is an object with four sides. It length of the two adjacent sides are of equal length. No pair of sides in a kite are parallel. The perimeter of a kite is the sum of the length of the four sides of the kite.
Perimeter of a kite = 2( a + b)
94 = 2(18 + b)
94 / 2 = 18 + b
47 = 18 + b
b = 47 - 18
b = 29 inches
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2. Order the following decimals from least to greatest.
0.439
0.394
0.441
0.531
0.342
Answer: 0.342 -> 0.394 -> 0.439 -> 0.441 -> 0.531
Step-by-step explanation:
0.342 -> 0.394 -> 0.439 -> 0.441 -> 0.531
If you convert the decimals into fractions out of a hundred, then it will be easily to keep going from least to greatest or greatest to least and soon you won't need help. Keep trying! :)
A.seqn T5 = 20, T₂² = T₁ T4 Find the order of the 1st term whose value is greater than 106.
The order of the first term whose value is greater than 106 is the smallest integer greater than 1 + [log(0.5)(T₁) - log(0.5)(212)].
How did we get the value?Using the given information, we can find the common ratio of the geometric sequence A.
First, we can use the equation T₂² = T₁ T4 to find T4. Substituting n = 4, we get:
T₂² = T₁ T4
20² = T₁ T4
T4 = 400/T₁
Next, we can use the equation T5 = 20 to find T₁r⁴:
T5 = T₁r⁴
20 = T₁r⁴
We can now substitute T4 in terms of T₁ in the equation above:
20 = T₁r⁴
20 = T₁(400/T₁)r⁴
20 = 400r⁴
r⁴ = 1/20
Therefore, the common ratio r = (1/20)^(1/4) = 0.5.
To find the order of the first term whose value is greater than 106, we can use the formula for the nth term of a geometric sequence:
Tn = T₁r^(n-1)
We want to find the smallest value of n such that Tn > 106. Substituting r = 0.5 and rearranging, we get:
T₁(0.5)^(n-1) > 106
T₁ > 212(0.5)^(1-n)
Since T₁ > 0, we can take the logarithm base 0.5 of both sides:
log(0.5)(T₁) < log(0.5)(212) + (n-1)
Solving for n, we get:
n > 1 + [log(0.5)(T₁) - log(0.5)(212)]
Therefore, the order of the first term whose value is greater than 106 is the smallest integer greater than 1 + [log(0.5)(T₁) - log(0.5)(212)].
Note that the exact value of this order depends on the value of T₁, which was not given in the original problem statement.
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Which expression is NOT equal to 125?
5(5^3/2/5)^2
(5^3/5^4)^-3
5^-2/5^-5
5(5^5/5^3)
There are 342 boys and girls at the canteen. After 51 boys and an equal number of girls as boys returned to their classroom, there were three times the number of boys than girls in the canteen. How many boys were there in the canteen at first?
Let b be the initial number of boys, and let g be the initial number of girls. We know that the total number of students at the canteen is 342, so:
b + g = 342
After 51 boys and an equal number of girls returned to their classroom, there were three times the number of boys than girls in the canteen. This means that the number of girls remaining in the canteen is:
g - 51
And the number of boys remaining in the canteen is:
b - 51
Since there were three times as many boys as girls, we can write:
b - 51 = 3(g - 51)
Now we have two equations and two unknowns. We can solve for one variable in terms of the other in the first equation, and substitute into the second equation:
b + g = 342
g = 342 - b
b - 51 = 3(g - 51)
b - 51 = 3(342 - b - 51)
b - 51 = 3(291 - b)
b - 51 = 873 - 3b
4b = 924
b = 231
So there were 231 boys in the canteen at first. To check our answer, we can substitute into the first equation:
b + g = 342
231 + g = 342
g = 111
Therefore, there were 231 boys and 111 girls in the canteen at first.
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Please read the photo
The average rate of change is 2.The rate of change of the function is its gradient or slope.
How is the average rate determined?To get the average rate of change, divide the change in y-values by the change in x-values.Knowing the average rate of change is necessary to detect changes in observable metrics like average speed or average velocity.
What is the average change rate?It displays the typical rate of change of the function for each unit during that time. It is determined using the slope of the line connecting the ends of the interval in the function graph.
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In the linear equation y=2x+3, if x increases by 4 points, how much will y increase?
In the linear equation y=2x+3, if x increases by 4 points, the y will increase by 8 points.
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation's graph will always be a straight line. A linear equation is expressed using the linear equation formula. There are numerous ways to accomplish this. A linear equation, for instance, can be written in standard form, slope-intercept form, or point-slope form.
According to that,
y=2x+3 is the linear equation.
x will now rise by 4 points.
According to the data given, the calculation is as follows:
x = x + 4
So = 2(x)
= 2(x + 4) + 3
= (2x + 3) + 8
= y + 8
Eight points should be added to the y.
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Please help i’ll give brainliest
Answer: 4.5
Step-by-step explanation:
For some value of b, the expression 3(5x - 1) + b(2x - 7) is a constant. What is the constant?
The expression is constant for b = -7.5, and the constant is 49.5.
What is a mathematical Expression?A mathematical expression is a phrase that contains at least two terms or numbers and one action. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given that, The expression 3(5x - 1) + b(2x - 7) is constant
It means the expression doesn't consist of a variable. So, we need to find the 'b' such that the variable 'x' need to be eliminated.
The co-efficient of the 'x' should be '0'.
3(5x - 1) + b(2x - 7)
= 15x - 3 + 2bx - 7b
= (15 + 2b)x - 3 - 7b
Now, 15 + 2b = 0
2b = -15
b = -7.5
On substituting the value of 'b' in the expression,
= -3 - 7 * (-7.5)
= 52.5 - 3
= 49.5
Therefore, The expression is constant for b = -7.5, and the constant is 49.5
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Henry buys candy that costs $4 per pound. He will spend at most $20 on candy. What are the possible numbers of pounds he will buy?
Use p for the number of pounds Henry will buy
Write your answer as an inequality solved for p.
Answer:
5 pounds
Step-by-step explanation:
$20/$4 = 5 pounds
HOPE IT HELPS!
The blood pressure in millimeters was measured for a large sample of people. The average pressure is 140 mm, and the SD of the measurements is 20 mm. The histogram looks reasonably like a normal curve. Use the normal curve to estimate the following percentages. Choose the answer that is closest to being correct.
a. 10.6%
b. 89.4%
c. 39.4%
d. 78.8%
e. 68.27%
100 is what percent less than 110?
Answer:
9.09%
(⬇Read my notes⬇)
Notes:
Hi there,
I know this answer is going to be incorrect on RSM, but it is the correct answer. Everyone has been saying that it's 9.09%, and I even found that as well. So I don't know why RSM is saying that it's wrong, because it should be correct.
- 201600823
Can any one help with me please
For given geometrical shape, The angles which we need to find are ∠z=115° and y=21.
What are geometric shapes, exactly?
Geometric shapes are mathematical figures that reflect the shape of objects we see in our daily lives. Shapes are geometric shapes that have boundary lines, angles, and surfaces. There are several types of 2d and 3d shapes.
Shapes are also classified according to their regularity or homogeneity. A symmetrical regular form, such as a square or circle, is common. Asymmetry can take on irregular shapes. They're also referred to as organic forms or freeform shapes. A tree, for example, has an irregular or organic shape.
In plane geometry, two-dimensional forms are flat shapes and closed figures such as circles, squares, rectangles, rhombuses, and so on. In solid geometry, the three-dimensional shapes are the cube, cuboid, and sphere.
Now,
In given figure ∠z+65°=180° (Sum of two interior angles)
then ∠z=115°
and ∠z=∠6y-11 (vertically opposite angles)
6y-11=115
6y=126
y=21
Hence,
For given geometrical shape, ∠z=115° and y=21.
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Peter has a total of 22 nickels and dimes. There is a total of $1.80. Which of the following is a possible combination of coins that Peter has?
====================================================
Work Shown:
n = number of nickels
22-n = number of dimes
5n = value of the nickels in cents
10(22-n) = value of the dimes in cents
5n+10(22-n) = total value in cents
5n+10(22-n) = 180
5n+220-10n = 180
-5n+220 = 180
-5n = 180-220
-5n = -40
n = -40/(-5)
n = 8 is the number of nickels
22-n = 22-8 = 14 is the number of dimes
-----------------
Check:
8 nickels = 8*5 = 40 cents
14 dimes = 14*10 = 140 cents
8 nickels + 14 dimes = 40 cents + 140 cents = 180 cents = $1.80
8 nickels + 14 dimes = 22 coins total
The answers are confirmed.
How would you check values for x and y after solving linear equations in x and y?
Answers:
1. substitute the x and y values into the original equations
2. divide the x and y values into the original equations
3. cross-multiply the x and y values by the original equations
4. subtract the x and y values from the original equations
please help
On a coordinate plane, the fountain is at (7, 5), the gardens are at (3, negative 5), the pond is at (negative 1, 7), and concessions are at (negative 7, 0). Your sister texted you, but the text cut off. Her text read, “Meet me at the trails located at (–2,”. Assuming that the trails are not located on the x-axis and given the content of her text, you can conclude that the trails must be located in either .
Answer: B quadrant 2 or quadrant 3
Step-by-step explanation:
In the country of Enigmia the postage charge for sending a letter is calculated according to the
following formula:
20 cents per 50 square centimetres of envelope area plus 32 cents per 40 grams of weight.
All measurements of area and weight are rounded up to the next multiples of 50 square
centimetres and 40 grams before calculation.
Jennifer has a letter weighing 125 grams in a 20 cm by 12 cm rectangular envelope that she
wants to send.
What will the postage charge be for Jennifer's letter?
I
Answer:
$2.12
Step-by-step explanation:
First, let's find the area of Jennifer's envelope: 20 cm x 12 cm = 240 square cm.
Since the area needs to be rounded up to the next multiple of 50 square cm, we will round up 240 square cm to 250 square cm.
Next, let's round up the weight of the letter to the next multiple of 40 grams: 125 grams rounded up to 140 grams.
Now that we have the rounded up values for both weight and area, we can use the formula to find the postage charge:
20 cents per 50 square cm x (250 square cm ÷ 50) = 100 cents
32 cents per 40 grams x (140 grams ÷ 40) = 112 cents
So the total postage charge will be 100 cents + 112 cents = 212 cents = $2.12.
Therefore, the postage charge for Jennifer's letter will be $2.12.
Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ
X-1
2x + 4
6
X
Determine the value of x in the
given diagram
The value of x in the diagram is given as follows:
x = 10.
What are similar triangles?Similar triangles share these two features:
Congruent angles, that is, angles that have the same measure.Proportional side lengths.Considering the similar triangles, the proportional relationship for the side lengths is given as follows:
6/(6 + x) = (x - 1)/(2x + 4).
Applying cross multiplication, the value of x is obtained as follows:
(x - 1)(x + 6) = 6(2x + 4)
x² + 5x - 6 = 12x + 24
x² - 7x - 30 = 0.
Factoring, we obtain the solutions are follows:
(x - 10)(x + 3) = 0.
x - 10 = 0 -> x = 10 -> value of x.x + 3 = 0 -> x = -3 -> extraneous, as a length cannot be negative.More can be learned about similar triangles at brainly.com/question/11920446
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I need some help I'm confused
PLEASE GIVE BRAINLIEST!
thank you and have a good day :)
Answer:
b^5
Step-by-step explanation:
When you are multiplying exponents with the same letter base, you simply just add the exponents.
for example, x^2 * x^3 = x^5
another example, y^6 * y^8 = y^14
An expression equivalent to b^3 * b^2 would be b^5
I hope this helps!
Three times the quantity of a number increased by 4 is -9. Write the equation and solve
The value of the number is -13/3
What are algebraic expressions?Algebraic expressions are defined as expressions that are composed of arithmetic operations such as subtraction, multiplication, division, addition, bracket and parentheses.
These expressions are also made up of variables, terms, coefficients, constants and factors.
From the information given, we have that;
The number = x
3x + 4 = -9
collect like terms
3x = -9 - 4
subtract the like terms
3x = -13
Make 'x' the subject
x = -13/3
Hence, the value is -13/3
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Let f(x) = x^2 − 2x + 1. Find the inverse function of f by identifying an appropriate restriction of its domain.
The inverse of f(x) is restricted to the domain x ≥ 1, since this is when[tex]x^2 − 2x + 1[/tex] is always greater than 0.
To find the inverse function of f(x), we must first determine the domain of f(x). We can do this by finding the values of x where f(x) is greater than or equal to 0.
We can start by setting f(x) to 0 and solving for x:
[tex]x^2 − 2x + 1 = 0[/tex]
[tex]x^2 − 2x + 1 − 1 = 0 − 1[/tex]
[tex]x^2 − 2x = -1[/tex]
(x − 1)(x − 1) = -1
x = 1
Therefore, the inverse of f(x) is restricted to the domain x ≥ 1, since this is when [tex]x^2[/tex] − 2x + 1 is always greater than 0.
The inverse of a function f(x) is a function that "undoes" f(x). In order to find the inverse of a function, the domain of the function must first be identified. This is done by solving f(x) = 0 and determining which values of x make the equation equal to 0.In the case of f(x) =[tex]x^2[/tex] − 2x + 1, the equation is equal to 0 when x = 1. This means that the inverse of f(x) is restricted to the domain x ≥ 1, since this is when [tex]x^2[/tex] − 2x + 1 is always greater than 0.Once the domain of the function is restricted, the inverse function can be found by switching the x and y values, and solving for the new equation. This process can be used to find the inverse of any function, as long as the domain is appropriately restricted.
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Which expression is equivalent to
O
13
√√2
√√√/2
8-3√11 is the expression which is equivalent to √11+√64-2√44.
What is Expression?The combination of variables, numbers and operators is called as expression.
The given expression is √11+√64-2√44
Square root of 11 plus square root of sixty four minus two square root of forty four.
Let us find the equivalent expression of √11+√64-2√44
The expressions in which the expressions look different but have save same value are Equivalent
√11+√64-2√44
√11+8-2√4×11
√11+8-4√11
Combine like terms
8-3√11
Hence, 8-3√11 is the expression which is equivalent to √11+√64-2√44.
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Which expression is equivalent to √11+√64-2√44
A. 8-4√44
B. 5√3-4√11
C. 8-3√11
Use the Pythagorean Theorem to find the distance between points F and C.
A. 2 √3
B. √41
C. 4 √3
D. 3 √5
Please help I’ll give brainliest!!!!!!!!
The solution set of the system of equations is {(2,2), (4,-2)}
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
4x+2y =12------>(1)
Take some random values for x. Find the corresponding y values
Example: when x=0
(1) => 4(0)+2y = 12
=> 0+2y = 12
=> 2y =12
=> y= 12/2 = 6
The point obtained is (x,y) = (0,6)
This way, we get a line when we graph the equation 4x+2y =12.
Similarly, when we graph the equation y= -x² + 4x -2 , we get a parabola
Graph is attached:
In the graph, both graphs intersect at the points (2,2) and (4,-2)
Thus, the solution set of the system of equations is {(2,2), (4,-2)}
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