Answers
..Given an isosceles trapezoid
The following are the properties of an isosceles trapezoid
The legs are congruent by definition (From the diagram, the legs are JM and KL)
The lower base angles are congruent. The lower base angles are
\(m\angle M\cong m\angle L\)The upper base angles are congruent. The upper base angles are
\(m\angle J\cong m\angle K\)Any lower base angle is supplementary to any upper base angle. This means that
\(\begin{gathered} m\angle J+m\angle M=180^0 \\ m\angle K+m\angle L=180^0 \end{gathered}\)\(\begin{gathered} \text{If} \\ m\angle K=61^0 \\ \text{Therefore} \\ m\angle J\cong m\angle K=61^0 \\ m\angle J=61^0 \end{gathered}\)Also,
\(\begin{gathered} m\angle L+m\angle K=180^0 \\ m\angle L+61^0=180^0 \\ m\angle L=180^0-61^0 \\ m\angle L=119^0 \end{gathered}\)\(\begin{gathered} m\angle L\cong m\angle M,m\angle L=119^0 \\ Therefore\colon \\ m\angle M=119^0 \end{gathered}\)Hence
m∠J = 61⁰
m∠L = 119⁰
m∠M = 119⁰
Related Questions
A solid figure is separated into 2 rectangular prisms. The volume of rectangular prism A is 75 cubic yards. Rectangular prism
B has a length of 7 yards and a width of 3 yards. The total volume of the solid figure is 180 cubic yards. What is the height of
rectangular prism B?
Answers
The height of rectangular prism B is 5 yards.
Let's first find the volume of rectangular prism B:
The volume of the solid figure = Volume of prism A + Volume of prism B
180 = 75 + length × width × height of prism B
105 = length × width × height of prism B
We know that the length of prism B is 7 yards and the width is 3 yards,
Substitute those values:
105 = 7 × 3 × height of prism B
105 = 21 × height of prism B
height of prism B = 105/21
height of prism B = 5
Therefore, the height of rectangular prism B is 5 yards.
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What are the angles of △ABC with side lengths a=12, b=21, and c=14?
Round each angle to the nearest tenth of a degree and use that rounded value to find the remaining angles.
Answers
Answer: the answer is A=33∘, B=107.5∘, and C=39.5∘ is correct or c
Step-by-step explanation:
To find the angles of triangle ABC with side lengths a=12, b=21, and c=14, we can use the Law of Cosines and then apply the Law of Sines to find the remaining angles. Let's denote the angles as A, B, and C respectively.
According to the Law of Cosines:
c^2 = a^2 + b^2 - 2ab * cos(C)
Plugging in the given side lengths:
14^2 = 12^2 + 21^2 - 2 * 12 * 21 * cos(C)
196 = 144 + 441 - 504 * cos(C)
504 * cos(C) = 389
cos(C) = 389 / 504
C = arccos(389 / 504)
Using a calculator to find the approximate value of C, we get C ≈ 43.5°.
A cone with a radius of 4 inches and a slant height of 10 inches is shown.
What is the surface area of the cone, in square inches?
62.8
125.7
150.8
O 175.9
4 in.
10 in.
Answers
Answer:
167.6190 approximately 167.62 inches
Step-by-step explanation:
formula for surface area of a cone is 1/3πr×r×slant height. How this helps.
A store is having a sale on almonds and jelly beans. For 4 pounds of almonds and 8 pounds of jelly beans, the total cost is $25. For 2 pounds of almonds and 3
pounds of jelly beans, the total cost is $10. Find the cost for each pound of almonds and each pound of jelly beans.
Answers
let x = number of pounds of jelly beans
y = number of pounds of almonds .
then , 4x + 8y =33
2x + 3y = 13
multiply the second equation by -2 to get the system :
4x + 8y =33
-4x - 6y = -26
adding the equations ,we get 2y=7. so y=3.5
substitute for y in either of the given equations : 2x + 3 (3.5) =13
+ 10.5=13
2x =2.5
x=1.25
answer : A pound of jelly beans costs $1.25 and a pound of almonds costs $3.50.
Solve Logaritmic equation
log16x=3/2
Answers
To solve for x in the equation log(16x) = 3/2, we need to use the definition of logarithms, which states that log base b of a is equal to c if and only if b raised to the power of c equals a.
In this case, we have:
log(16x) = 3/2
Rewriting this in exponential form, we get:
10^(3/2) = 16x
We can simplify 10^(3/2) as follows:
10^(3/2) = 10^(1/2) * 10^1 * 10^(1/2) = (sqrt(10))^2 * 10^(1/2) = 10 * sqrt(10)
Therefore, we have:
16x = 10 * sqrt(10)
Dividing both sides by 16, we get:
x = (10 * sqrt(10)) / 16
Simplifying this expression, we get:
x = (5 * sqrt(10)) / 8
So the solution to the equation log(16x) = 3/2 is x = (5 * sqrt(10)) / 8.
Find the solution for a 2x2 matrix A:
[4 4
0 1] to the nth power = [ ]
Answers
Answer:
Step-by-step explanation:
Answer:
A^n = [4^n 4^n
0 1]
Step-by-step explanation:
To find the solution for the 2x2 matrix A:
[4 4
0 1] to the nth power = [ ]
We can use matrix multiplication to raise A to the nth power. Let's start with n = 1:
A^1 = [4 4
0 1]
Now, let's solve for A^2 by multiplying A^1 by A:
A^2 = A x A^1
= [4 4 [4 4
0 1] 0 1]
= [16 16
0 1]
Next, let's solve for A^3:
A^3 = A x A^2
= [4 4 [16 16
0 1] 0 1]
= [64 64
0 1]
We can see a pattern emerging:
A^1 = [4 4
0 1]
A^2 = [16 16
0 1]
A^3 = [64 64
0 1]
We can generalize this pattern as follows:
A^n = [4^n 4^n
0 1]
Therefore, the solution for the 2x2 matrix A raised to the nth power is:
A^n = [4^n 4^n
0 1]
Triangle ABC lies in the xy-plane such that its circumcenter is the origin, its centroid is (-1,13), and the midpoint of side BC has coordinates (9,18). Find the maximum possible value of the product of the coordinates of the point B.
Answers
The circumradius of a triangle, whose circumcenter is its origin, is the distance between each of its vertices and its origin. As a result, the circumradius of triangle ABC represents the greatest possible distance between the origin and any of the points A, B, or C.
Since the centroid is at (-1,13), the circumradius is the distance between the origin and the centroid.
\(\sqrt{(-1)^2 + 13^2} = 13\sqrt{2}\)
Since (9,18) is the midpoint of side BC, point B's coordinates are (9,18) + t(a,b) for some real values a and b. The distance between point A and point B is therefore
\(\sqrt{(9+ta)^2 + (18+tb)^2}\)
it must be equal to
\(13\sqrt{2}\)
Expanding, we get:
\(
(9+ta)^2 + (18+tb)^2 = 338\)
\(81 + 18ta + t^2a^2 + 324 + 36tb + t^2b^2 = 338\)
\(t^2a^2 + t^2b^2 + 18ta + 36tb = 0\)
We want to maximize the product of the coordinates of point B, which is
\(
(9 + ta)(18 + tb) = 162 + 9ta + 18tb + t^2ab\)
Therefore, we want to maximize
\(t^2ab\)
By the above, the coefficient of in the expansion of
\((t^2a^2 + t^2b^2 + 18ta + 36tb)^2\)
it follows that we maximized
\(t^2ab\)
when we minimized
\(t^2a^2 + t^2b^2 + 18ta + 36tb\)
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You and your family go camping.
Your campsite is square. The area
of your campsite is 900 square
feet. What is the perimeter of the
campsite?
Answers
Answer:
The campsite would be 65 m by 65 m. 65 x 65 = 4,225. Another way to put it (and the way to figure it out) is that the square root of 4,225 is 65.
Step-by-step explanation:
Find l-65|.
\( | - 65| \)
Answers
Answer:
65
Step-by-step explanation:
l-65|
Take the non- negative value of what is inside the parentheses
65
What is equivalent to (7/4)(1/2)
Answers
Answer:
Answer is b(7/8)
Step-by-step explanation:
7/4×1/2=7/8
The solution is Option B.
The value of the equation is A = 7/8
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first number be p
The value of p = ( 7/4 )
Let the second number be q
The value of q = 1/2
A = p x q
Substituting the values in the equation , we get
A = ( 7/4 ) x ( 1/2 )
On simplifying the equation , we get
A = ( 7/8 )
Therefore , the value of A is 7/8
Hence , the equation is A = 7/8
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PLS HELP The histogram displays donations in dollars to a charity. A histogram titled Donations to Charity In Dollars with the x-axis labeled Donations. The x-axis has intervals of 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Number of Donations and starts at 0 with tick marks every one unit up to 5. There is a shaded bar above 10 to 19 that stops at 4, above 20 to 29 that stops at 3, above 30 to 39 that stops at 1, and above 50 to 59 that stops at 1. There is no shaded bar for 40 to 49. Which statement best describes the spread and distribution of the data?
The data is almost symmetric, with a maximum range of 49. This might happen if the charity suggested donation minimum of $35 and donors followed that.
The data is skewed, with a maximum range of 49. This might happen if the donations were only allowed in cash and many donors did not have much cash on them.
The data is bimodal, with a maximum range of 49. This might mean that the most popular amounts to donate were between 10 and 19 and 51 and 59 dollars.
The data is symmetric, with a maximum range of 59. This might happen if everyone donated a percent of their salaries.
Answers
Based on the given histogram, the data is skewed with a maximum range of 49.
This is because the frequency bars are not evenly distributed across the x-axis intervals, indicating that the data is not symmetric. The lack of a shaded bar for the 40 to 49 interval also suggests that there were fewer donations in that range compared to the other intervals.
One possible explanation for this skewness could be that the charity had suggested donation levels, with a minimum of $10, resulting in a large number of donations in the 10 to 19 interval. Additionally, the shaded bar stopping at 1 for the 30 to 39 and 50 to 59 intervals suggests that there were fewer donations in those ranges. This could be due to a variety of reasons, such as donors being more likely to give in the suggested $10 increments, or the charity's fundraising efforts being more effective at attracting donors in certain age or income brackets.
Overall, the histogram does not suggest a bimodal distribution, as there is not a clear separation between two distinct modes. The maximum range of 49 also indicates that there were no extreme outliers or large donations that would skew the data towards a higher range. Therefore, it is likely that the data represents a typical distribution of donations to a charity, with most donors giving smaller amounts and fewer donors giving larger amounts.
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Giving BRAINLIEST for correct awnser! Factor the expression below.
36a^2-25b^2
Which of the following binomials is a factor of the expression?
A. 4a +25b
B. 4a +5b
C. 6a + 5b
D. 6a + 25b
Answers
Answer:
C. 6a + 5b
Step-by-step explanation:
36a^2-25b^2
Rewriting as
(6a)^2 - (5b)^2
We know this is the difference of squares
(x^2 -y^2) = (x-y)(x+y)
(6a - 5b) (6a+5b)
Answer:
C. 6a + 5b
Step-by-step explanation:
36 is a perfect square, meaning it has two factors that are identical, being 6. 25 is also a perfect square, with its factors being 5, however, in this case, 25 is negative, so we need to have a positive 5 and a negative 5. This gives us:
(6a + 5b) (6a - 5b)
But, the answer choices only have (6a + 5b), so choice, "C," is the answer.
What is 1/5%of 116?
A.0.245
B. 0.0232
C.0.232
D.0.0245
Answers
Answer:
C. 0.232
Step-by-step explanation:
1/5% = 1/500
1/500 x 116 = 0.232
Evaluate the expression for the given variable values. (p+g) P-29 if p = 4 and q = 8-13-122024
Answers
We have the expression:
\(\frac{(p+q)^2}{p-2q}\)We have to evaluate it for p = 4 and q = 8.
To do that, we replace the variables p and q with the given values and calculate:
\(\begin{gathered} f(p,q)=_{}\frac{(p+q)^2}{p-2q} \\ f(4,8)=\frac{(4+8)^2}{4-2\cdot8} \\ f(4,8)=\frac{12^2}{4-16} \\ f(4,8)=\frac{144}{-12} \\ f(4,8)=-12 \end{gathered}\)Answer: The value of the expression when p = 4 and q = 8 is -12 [Second option]
PLEASE HELP
x + 2/3 = 9/10
Answers
Answer:
The answer is x= 7/30
Use Pythagoras' theorem to calculate the length of FG. Give your answer in centimetres (cm) to 1 d.p. 8 cm H 13 cm G
Answers
The length of FG is approximately 15.3 cm.
To calculate the length of FG using Pythagoras' theorem, we need to find the length of the hypotenuse (FG) of a right triangle. Let's denote the length of FG as x.
According to Pythagoras' theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, we have:
\(FG^2 = GH^2 + FH^2\)
Given that GH = 8 cm and FH = 13 cm, we can substitute these values into the equation:
\(x^2 = 8^2 + 13^2\)
\(x^2 = 64 + 169\)
\(x^2\) = 233
To find x, we take the square root of both sides:
x = √233 ≈ 15.26 cm (rounded to 1 decimal place)
Therefore, the length of FG is approximately 15.3 cm.
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geometry dilation and translation
Answers
Dilation is the process of enlarging or contracting a figure. Dilations are transformations that result in an enlargement or a decrease.
What are dilation and translation?Dilations are transformations that result in an enlargement or a decrease. Congruence transformations called translations are movements of an object without altering its size or shape. Tracking the location of the object is often done using a coordinate plane.When we translate a figure, we move it in any direction. Flipping a figure over a line is what we mean by reflection. Rotation is the process of turning a figure a specific number of times around a point. Dilation is the process of enlarging or contracting a figure.To learn more about Dilation refer to:
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Olga is using spherical beads to create a border on a picture frame. Each bead has a diameter of 1.5 millimeters. Find the volume of each bead. Round to the nearest tenth.
Answers
The Volume of each bead is approximately 1.767 mm^3 when rounded to the nearest tenth.
The volume of each bead, the volume of a sphere using its diameter. The formula for the volume of a sphere is given by:
V = (4/3) * π * r^3
where V is the volume and r is the radius of the sphere.
Given that the diameter of each bead is 1.5 millimeters, we can calculate the radius as half of the diameter:
r = 1.5 mm / 2 = 0.75 mm
Now, we can substitute the value of the radius into the volume formula:
V = (4/3) * π * (0.75 mm)^3
Using the value of π ≈ 3.14 and performing the calculations:
V ≈ (4/3) * 3.14 * (0.75 mm)^3
V ≈ (4/3) * 3.14 * 0.421875 mm^3
V ≈ 1.767 mm^3 (rounded to the nearest tenth)
the volume of each bead is approximately 1.767 mm^3 when rounded to the nearest tenth.
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(a) From Latoya's results, compute the experimental probability of rolling a 1 or 6.
(b)Assuming that the cube is fair, compute the theoretical probability of rolling a 1 or 6.
(c)Assuming that the cube is fair, choose the statement below that is true.
A. The experimental and theoretical probabilities must always be equal.
B. As the number of rolls increases, we expect the experimental and theoretical probabilities to
become closer, though they might not be equal.
C. As the number of rolls increases, we expect the experimental and theoretical probabilities to
become farther apart.
Answers
(a) To compute the experimental probability of rolling a 1 or 6 from Latoya's results, we need to determine the number of times a 1 or 6 was rolled and divide it by the total number of rolls Latoya made.
Let's assume that Latoya rolled the dice 100 times and obtained 20 1's and 10 6's. The total number of successful outcomes (rolling a 1 or 6) is 20 + 10 = 30.
Therefore, the experimental probability of rolling a 1 or 6 is 30/100 = 0.3 or 30%.
(b) Assuming the cube is fair, the theoretical probability of rolling a 1 or 6 can be determined by considering the favorable outcomes (rolling a 1 or 6) divided by the total possible outcomes (rolling any number from 1 to 6).
Since there are two favorable outcomes (1 and 6) out of six possible outcomes (1, 2, 3, 4, 5, 6), the theoretical probability is 2/6 = 1/3 or approximately 0.3333.
(c) The correct statement is B. As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal. This is due to the law of large numbers, which states that as more trials are conducted, the experimental probability tends to converge towards the theoretical probability. However, it is not necessary for them to be exactly equal. Random variations can cause some discrepancy, but with a larger number of rolls, the experimental probability should approach the theoretical probability more closely.
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Math please help I don’t understand at all
Answers
Answer:
the x and y axis arent clear enough to tell their coordinations can you take the picture again but it has to be clear
Roughly what percentage of water on Earth is accessible by humans for drinking 50% 90% 1% 20%
Answers
IF ANYONE KNOWS THIS PLS HELP ASAP
Answers
Answer:good luck
Step-by-step explanation:
The parent absolute value function is reflected across the x-axis and translated right 2 units. Which function is represented by the graph?
–|x – 2|
–|x + 2|
|–x| – 2
|–x| + 2
Answers
The function represented by the graph with the given transformations is |–x| + 2.
The function represented by the given transformations is |–x| + 2.
Let's analyze the transformations step by step:
Reflection across the x-axis:
Reflecting the parent absolute value function across the x-axis changes the sign of the function. The positive slopes become negative, and the negative slopes become positive. This transformation is denoted by a negative sign in front of the function.
Translation right 2 units:
Translating the function right 2 units shifts the entire graph horizontally to the right. This transformation is denoted by subtracting the value being translated from the input of the function.
Combining these transformations, the function |–x| + 2 results. The negative sign reflects the function across the x-axis, and the subtraction of 2 units translates it right. The absolute value is applied to the negated x, ensuring that the function always returns a positive value.
Thus, the function represented by the graph with the given transformations is |–x| + 2.
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Answer: -lx-2l
Step-by-step explanation:
Please help and thank you!
x=[?]
![Please help and thank you!x=[?]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/2HIhSmBQXYLSXFJqzRAp5YdQzXmE0SFv.jpeg)
Answers
Answer:
10 = x
Step-by-step explanation:
I believe <B = <E.
<B = 50 = <E = 5x
50 = 5x
10 = x
The slope is 60. It represents the rate at which the amount of water changes each hour.
True
False
Answers
Answer:
True
Step-by-step explanation:
Slope:
The slope of an equation represents how the y value changes as the x values changes, defined as: \(\frac{\text{change in y}}{\text{change in x}}\), so the slope of 60 can be represented as: \(\frac{60}{1}\), which tells us the amount of water (y-axis) increases by 60 units each hour (x-axis), or in other words, the rate at which the amount of water changes each hour.
I need help asap please!!!
Answers
The values of the angles given are: 0,90,180,240,270,360,420,480,540,600,630,660,720 and
What is sine of angles?he sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle. It is defined as the length of the opposite side divided by the length of the hypotenuse
The given angles are: 0,30,45,90,120,135,180,210,225,240,270,300,315,330,360
2∅ 2*∅ = 0, 90,180,240,270,360,420,480,540,600,630,660,720
sin 2∅ = sin0 = 0; Sin90=1; sin180=0; sin240= -0.8660; sin270 = -1;
Each angle is multiplied by sine sine360 =1; sin420 = 0.8660; sin480= 0.9848; sin540=1; sin600=-0.8660; sin630=-1; sin660=0.8660; sin720= 0.9397
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Mona had 32 math problems for homework. She completed 3/4 of them before dinner and the remaining 1/4 after dinner. How many problems did she complete before dinner?
Answers
Answer: 24 problems done before dinner
Step-by-step explanation:
Take the 32 total math problems and divide it by 3/4 (the amount of problems done before dinner) getting you 24 problems done before dinner
Math Question.........
Answers
Answer:
x=129
Step-by-step explanation:
triangles are 180 degrees
180-35-94=51
now 180-51
129
M = I1+I₂ 31 +32 2 Now let's substitute in our given values. (-2 , 2) = ((-5 Find 2 and y2 We will now set up two equations to solve for our two unknowns of x2 and y₂. (-5 X2 (-5+₂) -5+22), (7+)) 2 - +₂)/2 = We will first want to multiply by 2 on both sides and will get −5+₂= -4 Adding 5 to both sides we get = 7 This is the coordinate of point B. Now we will set up the equation to solve for y2 +y2)/2 =
Answers
The coordinates of point B are (-3, 17).
The given equation is M = I₁ + I₂ = 31 + 32.
Now let's substitute in our given values:
(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)
We will now set up two equations to solve for our two unknowns, x₂ and y₂:
Equation 1: (-5 + x₂) / 2 = -4
Multiply both sides by 2:
-5 + x₂ = -8
Add 5 to both sides:
x₂ = -3
This gives us the x-coordinate of point B.
Equation 2: (-5 + 2 + y₂) / 2 = 7
Simplify:
(-3 + y₂) / 2 = 7
Multiply both sides by 2:
-3 + y₂ = 14
Add 3 to both sides:
y₂ = 17
This gives us the y-coordinate of point B.
Therefore, the coordinates of point B are (-3, 17).
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a temperature of 0 degrees Celsius:
a temperature of 8.5 degrees Celsius above zero:
a temperature of 7 degrees Celsius below zero:
100 points
Answers
Answer:
mark on the 0, on the 7, and half way past 8
hope this helps, pls give brainliest
Step-by-step explanation: