The measure of ∠Z is 165 degrees to the nearest degree.
In a triangle, the measure of each angle is equal to the sum of the measures of the other two angles subtracted from 180 degrees. This is known as the Triangle Sum Theorem.
Given that x = 5.2 inches, y = 9.8 inches, and z = 7.1 inches in triangle XYZ, we can use the theorem to find the measure of angle Z.
∠Z = 180 - (x+y)
∠Z = 180 - (5.2+9.8)
∠Z = 180 - 15
∠Z = 165
So the measure of ∠Z is 165 degrees to the nearest degree.
Therefore, The measure of ∠Z is 165 degrees to the nearest degree.
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Write a ratio of the following in three ways.
Write your answers on the blanks.
1) 6 Weeks to 12 days_____
2) 10 decimeters to 10 centimeters_______
3) 4 days to 36 hours___
4) 4 months to 8 weeks___
5) 30 seconds to 6 minutes__
6) 24 girls to 16 boys___
7) 12 mangoes to 36 fruits__
8) 2. Years to 36 months__
9) 45 points to 9 games__
10) 468 students for 9 classrooms___
Ratios express the relationship between two or more quantities, they can be expressed in different forms such as 6:12, 42:12 and 3:1, 10:10, 100:10, and 10:1, 24:36 and 2:3.
1. 6 Weeks to 12 days:
6:12 (using the same unit of measurement, weeks)42:12 (converting weeks to days, 6 weeks x 7 days/week = 42 days)3:1 (simplifying the ratio to its simplest form)2. 10 decimeters to 10 centimetres:
10:10 (using the same unit of measurement, decimeters)100:10 (converting decimeters to centimeters, 10 decimeters x 10 centimeters/decimeter = 100 centimeters)10:1 (simplifying the ratio to its simplest form)3. 4 days to 36 hours:
4:36 (using the same unit of measurement, days)24:36 (converting days to hours, 4 days x 24 hours/day = 96 hours)2:3 (simplifying the ratio to its simplest form)4. 4 months to 8 weeks:
4:8 (using the same unit of measurement, months)16:8 (converting months to weeks, 4 months x 4 weeks/month = 16 weeks)2:1 (simplifying the ratio to its simplest form)5. 30 seconds to 6 minutes:
30:6 (using the same unit of measurement, seconds)180:6 (converting seconds to minutes, 30 seconds x 6 minutes/60 seconds = 0.5 minutes)30:1 (simplifying the ratio to its simplest form)6. 24 girls to 16 boys:
24:16 (using the same unit of measurement, girls and boys)3:2 (simplifying the ratio to its simplest form)7. 12 mangoes to 36 fruits:
12:36 (using the same unit of measurement, mangoes and fruits)1:3 (simplifying the ratio to its simplest form)8. 2 years to 36 months:
2:36 (using the same unit of measurement, years and months)6:36 (converting years to months, 2 years x 12 months/year = 24 months)1:6 (simplifying the ratio to its simplest form)9. 45 points to 9 games:
45:9 (using the same unit of measurement, points and games)5:1 (simplifying the ratio to its simplest form)10. 468 students for 9 classrooms:
468:9 (using the same unit of measurement, students and classrooms)52:1 (simplifying the ratio to its simplest form)To learn more about the ratio, visit:
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The length of the base of an isosceles triangle is x. The length of a leg is 5x -2. The perimeter of the triangle is 106. Find x. X =
Answer:
x = 10
Step-by-step explanation:
the legs of an isosceles triangle are congruent.
the perimeter is the sum of the 3 sides of the triangle
sum the 3 sides and equate to 106
x + 5x - 2 + 5x - 2 = 106
11x - 4 = 106 ( add 4 to both sides )
11x = 110 ( divide both sides by 11 )
x = 10
2 diagonals of a regular nonagon (a 9-sided polygon) are chosen. What is the probability that their intersection lies inside the nonagon
The probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
What is the probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event.
In this problem, the event of interest is the intersection of the two diagonals lying inside the nonagon. A nonagon is a 9-sided polygon, so there are 9 total corners, each of which can be one end of a diagonal. Therefore, there are 9 choose 2 = 36 total ways to choose two diagonals.
To find the number of favorable outcomes, we need to find the number of ways to choose two diagonals such that their intersection is inside the nonagon. To do this, we can notice that the diagonals that have an intersection inside the nonagon are the diagonals that connect non-adjacent corners of the nonagon. There are 8 non-adjacent corners, so there are 8 choose 2 = 28 ways to choose two non-adjacent corners.
So the probability of the intersection of the two diagonals lying inside the nonagon is:
P(intersection inside nonagon) = favorable outcomes / total outcomes = 28/36 = 2/3
Hence, the probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
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The probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
What is the probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event.
In this problem, the event of interest is the intersection of the two diagonals lying inside the nonagon. A nonagon is a 9-sided polygon, so there are 9 total corners, each of which can be one end of a diagonal. Therefore, there are 9 choose 2 = 36 total ways to choose two diagonals.
To find the number of favorable outcomes, we need to find the number of ways to choose two diagonals such that their intersection is inside the nonagon. To do this, we can notice that the diagonals that have an intersection inside the nonagon are the diagonals that connect non-adjacent corners of the nonagon. There are 8 non-adjacent corners, so there are 8 choose 2 = 28 ways to choose two non-adjacent corners.
So the probability of the intersection of the two diagonals lying inside the nonagon is:
P(intersection inside nonagon) = favorable outcomes / total outcomes = 28/36 = 2/3
Hence, the probability of the intersection of the two diagonals chosen lying inside the nonagon is 2/3.
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Sonji has $5.25 in nickels and dimes.The coin value can be modeled by the equation , where d represents the number of dimes and n represents the number of nickels. If Sonji has 21 dimes, how many nickels does she have
The number of nickels that Sonji has as per the given equation is 63.
What is the value of N mean?In mathematical operations, “n” is a variable, and it is often found in equations for accounting, physics and arithmetic sequences. A variable is a letter or symbol that stands for a number and is used in mathematical expressions and equations. In an arithmetic sequence, which is a list of numbers that follow a pattern, “n” is a variable representing the number of the term to find.For instance, if students want to find the value of the seventh term, “n” would be 7. In physics, an equation for standing waves uses “n” as an integer symbolizing the harmonic number or number of antinodes. The equation evaluates the length of the string in terms of its wavelength. In accounting, “n” is used in the equation for compound interest. It represents the number of compounding in 1 year.We are given the information that Sonji has 21 dimes (which means that d=21). We can use the equation to find the number of nickels n.
0.10d + 0.05n = 5.25
0.10(21) + 0.05n = 5.25
2.10 + 0.05n = 5.25
0.05n = 3.15
n = 3.15 / 0.05
n = 315 / 5
n = 63
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What if Aya and Sakura could only afford a monthly payment of $1800?
What would be the maximum mortgage amount they could afford to borrow from the bank, if all the other conditions were the same?
What is the total amount that would be paid to the lender over 25 years?
a) The maximum mortgage amount they could afford to borrow from the bank, if all the other conditions were the same = $369,181.93.
b) The total amount that would be paid to the lender over 25 years = $540000
To find the maximum mortgage amount they could afford to borrow if they could only pay $1800.
Here, future value = 0
number of periods = 25 years
= 25 × 12 months per year
= 300
payment amount = -1800 dollars
interest rate = 4.25% per year
= 0.3542% per month
the maximum mortgage amount they could afford = $369,181.93.
And the total payments would be equal to 300 × 1800 = 540000
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The complete question is:
Aya and Harumi would like to buy a house and their dream house costs $500,000. They have $50,000 saved up for a down payment but would still need to take out a mortgage loan for the remaining $450,000 and they're not sure whether they could afford the monthly loan payments. The bank has offered them an interest rate of 4.25%, compounded monthly.
What if Aya and Harumi could only afford a monthly payment of $2,000?
What would be the maximum mortgage amount they could afford to borrow from the bank if all the other conditions were the same?
What is the total amount that would be paid to the lender over 25 years?
The table shows the number of students going on a field trip one chaperone is needed for every 12 students
Answer:
I'm not sure what equation is needed here. Could you share the table?
Either way, you can take the number of students there are and multiply that to the number of chaperones needed per group of 12- basically see how many groups of 12 you can fit in the overall group of students
What is the degree of 3x³?
Answer:
3x³ is a polynomial of degree
The degree of the polynomial 3x³ is 3
You use a technical support company for your computer. The company bills you at a rate of $10 per month and $35 per hour for phone support.
a. Identify the fixed cost (the constant).
b. Identify the independent variable (x).
c. Identify the dependent variable (y).
d. Write an equation that describes the situation above.
e. If you were billed $97.50 for last month, how many hours of phone support did you need? Show all work.
Answer:fixed cost=10
Independent variable=months paid
Dependent=hours on support
month=x,h=hour,10x+35h=total cost
97.50=10+35h
87.50=35h
h=2.5 hours
Step-by-step explanation:
showed work
how does the value of A determine the range for f(x) = a|x|
HELP PLEASE ASAP
Answer:
It will either invert the graph or stretch/compress the horizontal
Step-by-step explanation:
When a is negative It will invert the graph, and reflect it over the x-axis
By plugging in a=1 you get a normal absolute value function of x ( a V on the graph)
If a>1 then your graph will compress
If a<1 then your graph will stretch
How do you find the third side of an isosceles triangle when given the angle?
The third side of the isosceles triangle is equal to the square root of 2 multiplied by the hypotenuse, multiplied by the sine of the opposite angle.
Given an isosceles triangle with an angle and two equal sides, we can use the Pythagorean Theorem to calculate the missing side.
The Pythagorean Theorem states that the sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse. Therefore, we can use this formula to calculate the missing side of the triangle.
First, let's call the two equal sides of the triangle 'a', and the angle opposite to them 'A'.
We can then use the Pythagorean Theorem to calculate the missing side, 'c', which is the third side of the triangle.
[tex]c^2 = a^2 + a^2\\c^2 = 2a^2\\c = sqrt(2a^2)[/tex]
To calculate 'c', we can first calculate 'a' by using the formula:
a = c * sin(A)
Then we plug 'a' into the equation for 'c':
c = sqrt(2*(c * sin(A))^2)
c = sqrt(2)*c*sin(A)
Therefore, the third side of the isosceles triangle is equal to the square root of 2 multiplied by the hypotenuse, multiplied by the sine of the opposite angle.
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When two rotations are performed on a single figure, does the order of the rotations sometimes, always, or never affect the location of the final image? Explain.
When two rotations are performed on a single figure, the order of the rotations never affect the location of the final image.
What is the rotation?In mathematics, rotation is defined as that of the circular movement of an object around with a center, an axis, or a fixed point. Since rotations are rigid transformations, the size, length, shape, and angle measurements of the figure are maintained.
Precession, nutation, and intrinsic rotation are the names of these rotations. The rotation of the earth on its axis is one of the greatest instances of rotation in nature.
There are broad guidelines for rotations of 90, 180, and 270 degrees around the origin that are both clockwise and anticlockwise. Counterclockwise. X and Y are rotated by 90 degrees that means (x , y) ----> (-y , x); Rotation of 180 degrees: (x, y) —- (-x , -y); Rotation of 270 degrees: (x, y) —- (y , -x).
Here two times rotation means 180 degrees that means no change in the final image.
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The function
h
defined by
h(t) = (49 + 4. 9t)(10 – t)
models the height, in meters, of an object
t
seconds after it is dropped from a helicopter.
1. Find or approximate the time when the object hits the ground. Explain or show your
reasoning
2. From what height is the object dropped? Explain or show your reasoning.
Answer:
55555555546776546567
What is the value of 3 in tan?
The value of tan 3° is 0.0524.
tangent is the trigonometric ratio.
we can find out the value of tangent by taking perpendicular of the triangle divided by base of the triangle.
tan Q = perpendicular of the triangle /base of the triangle.
sine theta divided by cos theta gives the value of tan theta.
tan Q = sin Q/ cos Q.
some formula of the tan Q are as follows,
1- tan Q = sin Q/cos Q
2- tan Q= 1 /cot Q
3-tan^2 Q =sec^2 Q -1
4- tan(90 - Q)=cot Q
5- tan (Q+π) = tan Q
6- tan (π-Q) = -tan Q
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Find the vertices and foci of the hyperbola with equation quantity x plus 4 squared divided by 9 minus the quantity of y plus 3 squared divided by 16
Vertices are at (-7, 5) and (-1, 5) and foci are at (-9, 5) and (1, 5) of the hyperbola with equation quantity x plus 4 squared divided by 9 minus the quantity of y plus 3 squared divided by 16.
As per the given data the given equation is:
[tex]\\$$\frac{ (x+4)^2}{9} - \frac{(y-5)^2 }{16}=1$$[/tex]
The standard form for the equation of a hyperbola with center (h, k) is [tex]\frac{(x-h)^{2} }{a^{2} } - \frac{(y-k)^2}{b^{2} } =1[/tex]
Your hyperbola opens left/right, because it is of form x - y.
Comparing terms, we find that
h = -4, k = 5, a = 3, y = 4
In the general equation, the coordinates of the vertices are at [tex]$(h \pm a, k)$[/tex].
Thus, the vertices of your hyperbola are at (-7,5) and (-1,5).
The foci are at a distance c from the center, with coordinates [tex]$(\mathrm{h} \pm \mathrm{c}, \mathrm{k})$[/tex], where [tex]$c^2=a^2+b^2$[/tex]
[tex]c^2=9+16=25$[/tex], so c = 5.
The coordinates of the foci are (-9, 5) and (-1, 5).
The Figure below shows the graph of the hyperbola with its vertices and foci.(attached at the end of solution)
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I’m doing math homework and is about functions they said f(x)= x-3 and g(x)= √x-2
After I set them up I have this
am I supposed to just add the numbers or is there something else to do?
√ (x-3)-2
Answer: It looks like you are trying to find the value of the function h(x) = √ (x-3) - 2.
To find the value of this function for a given value of x, you need to substitute the value of x into the function definition and simplify the expression.
For example, if you want to find the value of h(x) for x = 5, you would substitute 5 for x in the function definition and simplify the expression to get:
h(5) = √(5-3) - 2
= √2 - 2
= 1.4 - 2
= -0.6
Therefore, the value of h(x) for x = 5 is -0.6.
You can follow this same process to find the value of h(x) for any other value of x. Just be sure to substitute the correct value of x into the function definition and simplify the expression to find the final result.
Step-by-step explanation:
Answer:
g[f(x)]
Step-by-step explanation:
Given functions:
[tex]f(x)=x-3[/tex]
[tex]g(x)=\sqrt{x}-2[/tex]
Composite functions are when the output of one function is used as the input of another.
Therefore, to create √(x-3)-2, substitute the function f(x) in place of the x in function g(x):
[tex]\begin{aligned}\implies g[f(x)]&=\sqrt{f(x)}-2\\&=\sqrt{x-3}-2\end{aligned}[/tex]
How many terms are there in the expression 7x2 5x?
There are 3 terms in expression 7[tex]x^{2}[/tex]-5x+5.
Monomials, binomials, trinomials, and polynomials are all examples of algebraic expressions in mathematics. Algebraic expressions are those that are modeled utilizing unknowable constants, coefficients, and variables. A variable can have any value because it is not fixed, unlike a constant, which has a definite value. Monomials, binomials, trinomials, and polynomials are examples of algebraic expressions that are created by combining variables and constants using arithmetic operations. Terms are the components of algebraic expressions that are separated by addition or subtraction. The type of expression—monomial, binomial, trinomial, or polynomial—depends on the number of terms.
An algebraic expression with three terms is called a trinomial.
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7. A triangle has sides with lengths 7, 24, and 25. (Lesson 4-5)
a. Verify this is a Pythagorean triple.
b. Approximate the acute angles in this triangle.
A triangle has sides of 7, 24, and 25 cm. The length of the hypotenuse is equal to 25 cm if the triangle is a right triangle.
What are the angles of a 7/ 24/ 25 triangle?The triangle's sides are 7 cm, 24 cm, and 25 cm, as is obvious.
49, 576, and 625 are the results of squaring the lengths of the side of the.
49 + 576 = 625\s(7)2 + (24)2 = (25)2
As a result, the aforementioned equation satisfies Pythagoras's theorem. As a result, it is a right-angled triangle.
the hypotenuse is 25 cm long.
Angles of 16.26 degrees and 73.74 degrees are suitable.
Yes, since 72+242=252 (sum of squares on smaller two sides equals square on largest side).
The triangle's sides are 7 cm, 24 cm, and 25 cm, as is obvious. 49, 576, and 625 are the results of squaring the lengths of the side of the. As a result, the aforementioned equation satisfies Pythagoras's theorem. As a result, it is a right-angled triangle.
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What are the intervals of 5?
The set of numbers x such that 0 ≤ x ≤ 5 is an interval containing 0, 5, and all numbers between 0 and 5.
Interval notation is a way of representing intervals on the number line. That is, how to write a subset of the real number line. Intervals include numbers between two specific numbers.
In mathematics, a (real) interval is a set of real numbers containing all real numbers between any two numbers in the set. For example, the set of numbers x such that 0 ≤ x ≤ 1 is an interval containing 0, 1, and all numbers in between. Other examples of intervals are the set of numbers with 0 < x < 1, the set of all real numbers, the set of non-negative real numbers, the set of positive real numbers, the empty set, and any Singleton (a set of one element).
Real intervals play an important role in integral theory. This is because real intervals are the simplest set whose "length" (or "scale" or "magnitude") is easy to define. The notion of measure can be extended to more complex sets of real numbers, leading to the Boral measure and finally the Lebesgue measure.
Intervals are central to interval arithmetic, a general numerical technique that automatically provides guaranteed bounds for any mathematical expression, even in the presence of uncertainties, mathematical approximations, and arithmetic rounding.
Complete Question:
What is the interval of 0,5 ?
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Can someone help me!!!!!!
The y - intercept of the graph, given the formula of 2 y - 5x = 16, is y - intercept : ( 0, 8)
How to find the y - intercept ?To find the y - intercept, use the slope - intercept form of the equation of a line which is:
y = mx + b
m = slope
b = y - intercept
So first rewrite the formula given to look like the slope - intercept :
2 y - 5x = 16
2 y = 5x + 16
( 2 y = 5x + 16 ) / 2
y = 5/ 2 x + 8
The y- intercept is therefore 8. As a point on the graph, this is ( 0, 8 )
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In store the ratio of blue shirts to red shirts is 2:5. If there is 100 red shirts in the store, how many blue shirts are there?
The ratio of blue shirts to red shirts is 2:5, so for every five red shirts, there are two blue shirts.
What is ratio?Ratio is a mathematical term used to compare two different values. It is a way of expressing one quantity in relation to another. Ratios can be written as fractions, decimals, or percentages. Ratios are used in many different areas, such as finance, economics, science, and engineering. Ratios are also used to compare the size, speed, or cost of different items. Ratios can be used to compare parts of a whole, or to compare different items within a group.
Since there are 100 red shirts in the store, there are 40 blue shirts in the store (100 / 5 x 2 = 40).
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Using the graph below with the following point find the length of the two diagonals to determine if TUVW is a rectangle or not T(-5,0) U(7,3) V(9,-6) W(-3,-9)
The lengths of each diagonal are given as follows:
[tex]TV = \sqrt{232}[/tex][tex]WU = \sqrt{244}[/tex]As the lengths are different, the polygon TUVW is not a rectangle.
How to obtain the diagonals?The diagonal length is obtained using the formula for the distance between two points, presented as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
In which [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of each point.
The first diagonal is TV, and the length is given as follows:
[tex]TV = \sqrt{(9 - (-5))^2 + (6 - 0)^2} = \sqrt{232}[/tex]
The second diagonal is WU, and the distance is given as follows:
[tex]WU = \sqrt{(-3 - 7)^2 + (-9 - 3)^2} = \sqrt{244}[/tex]
A rectangle has diagonals of equal length, hence the polygon for this problem is not a rectangle.
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solvve for z: (1st answer or nice and detailed answer brainliest)
1/2z+5=57
[tex]\dfrac{1}{2} z+5=57[/tex]
Subtract 5 from both sides:
[tex]\dfrac{1}{2} z+5-5=57-5[/tex]
[tex]\dfrac{1}{2} z=52[/tex]
Multiply both sides by 2:
[tex]2\times(\dfrac{1}{2} z)=2\times(52)[/tex]
[tex]\fbox{z = 104}[/tex]
Answer:
z=104
Step-by-step explanation:
1/2z=57-5
1/2z=52
1/2z*2=52*2
1z=104
1/1z=104/1
z=104
The domain of y = √√√x-5-1 is
DONE
3 of 8
P
10
1000
098
7
6
5
4
3
12
y
2
19
Ð
6
8x
The function domain is X≥5 Or in interval notation [5, ∞)
What is Domain definition?The domain of a function is the set of input or argument values for which the function is real and definedThe domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limitedIn mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by {\displaystyle \operatorname {dom} } or {\displaystyle \operatorname {dom} f}, where f is the functionFind non-negative values for radicals x≥5solve x-5≥0:x≥5 function domain is X≥5 Or in interval notation [5, ∞)To learn more about Domain definition refers to:
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A line passes through the points (-2,8) and (5,-20)
The linear equation that passes through these two points is:
y = -4x
How to find the equation for the line?A general linear equation can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know that the line passes through two known points (x₁, y₁) and (x₂, y₂), then we can write the slope as:
a = (y₂ - y₁)/(x₂ - x₁)
Here we know the two points (-2, 8) and (5, -20), so the slope is:
a = (-20 - 8)/(5 + 2) = -28/7 = -4
So the line is:
y = -4*x + b
To find the value of b, we can replace the values of the point (-2, 8), so we will get:
8 = -4*(-2) + b
Now we can solve this for b.
8 = -4*(-2) + b
8 = 4*2 + b
8 = 8 + b
8 - 8 = b
0 = b
Then the linear equation is:
y = -4*x
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Angle J and Angle M are base angles of isosceles trapezoid JKLM. If angle j= 23x+5, and angle m = 13x+15 , find measure k .
The angle K for the Isosceles trapezoid is a supplementary angle to the angle J and the measure of angle K = 152°
What is an Isosceles trapezoidThis is a trapezoid in which the base angles are equal and therefore the left and right side lengths are also equal. The opposite angles are supplementary which implies they sum up to 180°.
angle J and angle M are base angles for the Isosceles trapezoid and are equal, so:
23x + 5 = 13x + 15
23x - 13x = 15 - 5 {collect like terms}
10x = 10 {divide through by 10}
x = 1
angle J = 23(1) + 5 = 28°
Angle K and angle J are supplementary so:
K = 180 - 28
K = 152°
Therefore, the measure of the angle K for the Isosceles trapezoid JKLM is equal to 152°
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The stem and leaf plot shows the number of days of snowfall at a winter sports resort for each of the past 171717 years.
The stem represents the tens place and the leaves represent the unit place of each data point, allowing for easy visualization of the distribution of the data.
A stem-and-leaf plot is a type of graph used to display the distribution of a set of data. It is a way to show the frequency of different values in a dataset. In this case, it is showing the number of days of snowfall at a winter sports resort for each of the past 171717 years.
Continuous and discrete data distributions are the two main forms found in statistics. Continuous data is information having a wide range of possible values. When measuring this kind of information, such weight or temperature, a scale is frequently used. A histogram is another tool for representing continuous data.
The complete question will be :
The stem and leaf plot shows the number of days of snowfall at a winter sports resort for each of the past years. represents a year with days of snowfall. Here is the five-number summary for these data Five-number summary According to the - IQR rule for outliers, how many high outliers are there in the data set?
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Answer:
0
Step-by-step explanation:
the survey is a research method in which: group of answer choices individuals are carefully observed in their natural environments. a representative, random sample of individuals are questioned regarding their attitudes or behaviors. an individual is studied in great depth. an investigator determines the extent to which two variables influence each other.
The correct answer is A representative, random sample of individuals are questioned regarding their attitudes or behaviours. (Option B)
A) "Individuals are carefully observed in their natural environments" is a description of participant observation, which is a type of qualitative research method. In this method, researchers observe and interact with individuals in their natural environments in order to understand their behaviours and attitudes in context. This method is often used in fields such as anthropology, sociology, and psychology.
B) "A representative, random sample of individuals are questioned regarding their attitudes or behaviours" describes a survey, which is a quantitative research method. Surveys are used to gather information from a representative sample of individuals in order to make inferences about a larger population. Surveys can be conducted in various ways, such as through phone calls, mail or online and can be used to study the attitudes, behaviours, and characteristics of a population.
C) "An individual is studied in great depth" is a description of a case study, which is a qualitative research method. In this method, a researcher closely examines an individual or a small group of individuals in order to gain a detailed understanding of their experiences, behaviours, and attitudes. Case studies are often used in fields such as psychology, sociology, and anthropology.
D) "An investigator determines the extent to which two variables influence each other" is a description of a correlation study, which is a quantitative research method. In this method, the researcher examines the relationship between two or more variables. The researcher measures the values of the variables for a sample of individuals, and then uses statistical methods to determine the degree of association between the variables, and if there is a causal relationship or not.
Thus, The correct answer is A representative, random sample of individuals are questioned regarding their attitudes or behaviours. (Option B)
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What is the numerical coefficient of the term − 6xy?
The numerical coefficient of xy in the given expression 6xy is 6.
In mathematical terms, a coefficient is a numerical value that is multiplied by a variable in an algebraic expression. The coefficient is the number that appears in front of the variable.
For example, in the expression 3x, the coefficient is 3. In the expression 2[tex]y^2[/tex], the coefficient is 2. In the expression -5[tex]z^3[/tex], the coefficient is -5.
In the case of a constant term in an expression, the coefficient is the constant term itself.
For example, in the expression 3x + 4, the coefficient of x is 3 and the coefficient of the constant term 4 is 4.
Here, in the expression 6xy, the numerical coefficient of xy is 6.
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3y+2=2y-5x into y=mx+b form
3y + 2 = 2y - 5x
3y - 2y = -5x -2
y = -5x - 2
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Corresponding angle pairs - (1,5) , (2,6) , (3,7) and (4,8)