From the figure
We have the folloing points
\(A(0,0),B(a,c),C(b,-),D(-,-)_{}\)We need to find the missing points
Since the trapezoid is isosceles the side AB = Side CD
Considering coordinates B and C
let the missing point in C be z then
\(\begin{gathered} B=(a,c) \\ C=(b,z) \end{gathered}\)since Points B and C lie on the same y axis then
z = c.
Hence the coordinate C becomes
\(C=(b,c)\)Next we need to find the missing points in D
let the missing x coordinate be x
let the missing y cordinate be y
Therefore
\(D=(x,y)\)From the Graph,
The point Dlie on the x axis hence the coordinate of y is 0
hence y = 0
Therefore point D will become
\(D=(x,0)\)Finally we are to find the value of x
Recall that the trapezoid is isosceles
hence
\(\text{length AB = length CD}\)Applying the formula for distance between two points
The formula is give as
\(\text{Distance =}\sqrt[]{(x_2-x_1)^2-(y_2-y_1)^2}\)For points AB
A=(0,0), B = ( a,c)
Hence
\(\begin{gathered} x_1=0,x_2=a \\ y_1=0,y_2=c \end{gathered}\)Therefore distance AB is
\(\begin{gathered} AB=\sqrt[]{(a-0)^2+(c-0)^2} \\ AB=\sqrt[]{a^2+c^2} \end{gathered}\)For points CD
C = (b,c), D = (x,0)
Hence,
\(\begin{gathered} x_1=b,x_2=x \\ y_1=c,y_2=0 \end{gathered}\)Therefore, distance CD is
\(\begin{gathered} CD=\sqrt[]{(x-b)^2+(0-c)^2} \\ CD=\sqrt[]{(x-b)^2+c^2} \end{gathered}\)Recall distance AB = distance CD
Hence
\(\begin{gathered} AB=CD \\ \sqrt[]{a^2+c^2}=\sqrt[]{(x-b)^2+c^2} \end{gathered}\)Simplifying further
we will get
\(\begin{gathered} a^2+c^2=(x-b)^2+c^2 \\ a^2+c^2-c^2=(x-b)^2 \\ a^2=(x-b)^2 \\ \text{taking square root of both sides} \\ a=x-b \\ x=a+b \end{gathered}\)Therefore,
The coordinate of the point D is
\(D=(a+b,0)\)help!! please! i don’t understand
Answer:
\( 2 \sqrt[3] {60}~mm \)
Step-by-step explanation:
The volume of a cube is the side cubed, so each edge is the cubic root of the volume.
V = 480 mm³
\( s = \sqrt[3] {V} \)
\( s = \sqrt[3] {480~mm^3} \)
\( s = \sqrt[3] {2^3 \times 2^2 \times 3 \times 5~mm^3} \)
\( s = \sqrt[3] {2^3} \times \sqrt[3] {2^2 \times 3 \times 5~mm^3} \)
\( s = 2 \sqrt[3] {60}~mm \)
Identify the correct graph of the system of equations.
3x + y = 12
x + 4y = 4
The sum of three consecutive intergers is 48. Find the integers.
Answer: 15, 16, and 17
Step-by-step explanation: n + n+1 + n+2 = 48. so our numbers should be 15, 16, and 17.
Hope this helps you :)
1. Which one of the following is NOT true about polynomial functions f(x) and g(x) if deg (f) = man * d deg * (g) =n?
A. deg (f + g) = max(m, n)
B. deg (f_{g}) <= m + n
C. If g is a factor of f then deg( f )<= m
D. The deg (f ^ 3) = 3m
The option that is not true about polynomial functions is:
Option D. The deg (f ^ 3) = 3m
How to Interpret the degree of Polynomial functions?For polynomial functions f(x) and g(x), if deg(f) = m * deg(g) = n, then we have the following:
Option A: deg(f + g) = max(m, n)
This is true because we know that the degree of the sum of two polynomials is the maximum of their individual degrees.
Option B: deg(f * g) <= m + n
This is true because we know that the degree of the product of two polynomials is at most the sum of their individual degrees.
Option C: If g is a factor of f, then deg(f) <= m
This is true because If g is a factor of f, it means that f can be divided by g without leaving a remainder. In this case, the degree of f is less than or equal to the degree of g.
D. The deg(f ^ 3) = 3m
This is not true because the degree of the polynomial f raised to the power of 3 is not necessarily equal to 3 times the degree of f. The degree of f^3 will depend on the individual terms and their exponents.
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The surface area of the United States is 3.797 million square miles. The state of Alaska, our largest state in terms of area, occupies 655,400 square miles. Using ratios, determine what percentage of the surface area of the United States is occupied by Alaska, rounded to the nearest whole number.
Alaska occupies 17.22% of the surface area of the United States. Rounding to the nearest whole number, we get 17%. Hence, the answer is:17%
We are given that the surface area of the United States is 3.797 million square miles and the state of Alaska occupies 655,400 square miles. We need to determine what percentage of the surface area of the United States is occupied by Alaska using ratios.To find the percentage, we need to first find the ratio of Alaska's surface area to the surface area of the United States. We can do this by dividing the surface area of Alaska by the surface area of the United States. That is,655,400 / 3,797,000 = 0.1722We can express this ratio as a percentage by multiplying by 100. That is,0.1722 × 100 = 17.22%
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On a test that has a normal distribution, a score of 19 falls one standard deviation below the mean, and a score of 40 falls two standard deviations above the mean. Determine the mean of this test.
Hi there!
We can use the following equation:
\(\large\boxed{z = \frac{x-\mu}{\sigma}}\)
z = amount of standard deviations away a value is from the mean (z-score)
σ = standard deviation
x = value
μ = mean
Plug in the knowns for both and rearrange to solve for the mean:
\(-1 = \frac{19-\mu}{\sigma}\\\\-\sigma = 19 - \mu\\\\ \sigma = -19 + \mu\)
Other given:
\(2 = \frac{40-\mu}{\sigma}\\\\2\sigma = 40- \mu\\\\ \sigma = 20 - \frac{\mu}{2}\)
Set both equal to each other and solve:
\(-19 + \mu = 20 - \frac{\mu}{2}\\\\\frac{3\mu}{2} = 39 \\\\3\mu = 78 \\\\\boxed{\mu = 26 }\)
The box plots display data collected when two teachers asked their classes how many pencils they lose in a school year.
A box plot uses a number line from 5 to 47 with tick marks every one unit. The box extends from 8 to 14 on the number line. A line in the box is at 11. The lines outside the box end at 7 and 45. The graph is titled Mr. Johnson's Class, and the line is labeled Number Of Pencils.
A box plot uses a number line from 0 to 51 with tick marks every one unit. The box extends from 12 to 21 on the number line. A line in the box is at 14.5. The lines outside the box end at 0 and 50. The graph is titled Mr. Simpson's Class, and the line is labeled Number Of Pencils.
Which class lost the most pencils overall based on the data displayed?
Mr. Simpson's class; it has a larger median value 14.5 pencils
Mr. Johnson's class; it has a larger median of 11 pencils
Mr. Simpson's class; it has a narrow spread in the data
Mr. Johnson's class; it has a wide spread in the data
Answer:
A) Mr. Simpson's class; it has a larger median value 14.5 pencils.
Step-by-step explanation:
A box plot is a visual display of the five-number summary:
Minimum value = The value at the end of the left whisker.Lower quartile (Q₁) = The left side of the box.Median (Q₂) = The vertical line inside the box.Upper quartile (Q₃) = The right side of the boxMaximum = The value at the end of the right whisker.From inspection of the box plots (attached), the measures of central tendency (median) and dispersion (range and IQR) are:
Mr Johnson's class:
Median = 11IQR = Q₃ - Q₁ = 14 - 8 = 6Range = max - min = 45 - 7 = 38Mr Simpson's class:
Median = 14.5IQR = Q₃ - Q₁ = 21 - 12 = 9Range = max - min = 50 - 0 = 50In a box plot, the median is a measure of central tendency and tells us the location of the middle value in the dataset. It divides the data into two equal halves, with 50% of the values falling below the median and 50% above it.
The median number of pencils lost in Mr Simpson's class is greater than the median number of pencils lost in Mr Johnson's class. Therefore, Mr. Simpson's class has a larger median value.
The spread of data in a dataset can be measured using both the range and the interquartile range (IQR).
As Mr Simpson's class has a greater IQR and range than Mr Johnson's class, the data in Mr Simpson's class is more spread out than in Mr Johnson's class.
In summary, as Mr Simpson's class has a larger median 14.5 and a wider spread of data, then Mr Simpson's class lost the most pencils overall.
There are 10 males and 18 females in the Data Management class. How many different committees of 5
students can be formed if there must be at least 2 males?
Answer:
There are 10 males and 18 females in the Data Management class. To form a committee of 5 students with at least 2 males, we can use the combination formula. The number of ways to choose k items from a set of n items is given by the formula nCk = n! / (k! * (n-k)!).
The number of ways to choose 2 males and 3 females is (10C2) * (18C3) = 45,360.
The number of ways to choose 3 males and 2 females is (10C3) * (18C2) = 81,680.
Therefore, there are a total of 45,360 + 81,680 = 127,040 different committees of 5 students that can be formed if there must be at least 2 males.
Find the HCF:
3x³ + 15x² and 2x³ - 50x
H.C.F of 3x³+15x² and 2x³-50x is x(x+5)
What is Number system?A number system is defined as a system of writing to express numbers.
The greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.
3x³ + 15x²
Factorize the given expression by taking out 3x²
3x²(x+5)
and the expression 2x³ - 50x
2x(x²-25)
2x(x+5)(x-5)
H.C.F of 3x³+15x² and 2x³-50x is x(x+5)
Hence, H.C.F of 3x³+15x² and 2x³-50x is x(x+5)
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brainly after 12 hours, what would be the difference in the number of signs that each friend has made?
Answer:
4
Step-by-step explanation:
Each day last week, Tex's Taco Truck sold at least 175 tacos. On Tuesday, Tex sold more than 250 tacos even though it was rainy. He is hoping to sell 300 tacos this Tuesday if the weather is good. The median number of tacos sold daily last week was 204, and the interquartile range was 43 tacos. Which is a measure of how much Tex's daily sales varied last week?
50% is a measure of how much Tex's daily sales varied last week
According to given conditions :
The interquartile range (IQR) is a measure of how much the data varies in a given data set. It is defined as the difference between the 75th percentile (Q3) and the 25th percentile (Q1) of the data.
In this case, we know that the interquartile range of Tex's daily taco sales last week was 43 tacos. This means that the middle 50% of his daily sales (between the 25th and 75th percentiles) varied by up to 43 tacos.
The median number of tacos sold daily last week was 204, which tells us that half of the daily sales were above 204 and half were below. We also know that on Tuesday, Tex sold more than 250 tacos, which was higher than his sales on any other day of the week.
Therefore, we can conclude that the range of Tex's daily sales last week was at least 250 - 175 = 75 tacos, and possibly higher. This tells us that there was a significant amount of variability in his daily sales, and that his sales could vary widely from day to day.
In summary, while the interquartile range is a measure of how much Tex's daily sales varied in the middle 50% of his data, the range gives us a sense of the full extent of the variability in his sales.
What is Range ?
Range is a statistical measure that represents the difference between the largest and smallest values in a data set. It is a simple and commonly used measure of the variability or spread of a set of values.
To calculate the range of a data set, you subtract the smallest value from the largest value. For example, if you have a set of data {2, 5, 8, 10, 12}, the range would be 12 - 2 = 10.
The range is a useful measure of variability because it gives an indication of how much the values in a data set differ from each other. However, it is sensitive to outliers, or extreme values that are much larger or smaller than the rest of the values in the data set. Outliers can greatly affect the range, and may make it a less reliable measure of variability.
While the range is a simple and easy-to-calculate measure of variability, there are other measures such as variance, standard deviation, and interquartile range, that are more robust and provide more information about the spread of the data.
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three rectangular prims have the same based area but different heights as the height of these prisms increase the volume increases what is the independent variable in this situation
The independent variable while calculating the volume of a rectangular prisms with equal base area and different height is the height
What is an independent variable?The input values for a specific function are represented by the independent variable (x).
During an experiment, the independent variables are kept under control. The outputs of the function are represented by the dependent variable (y). The quantities being measured are the dependent variables in an experiment.
As regard the problem, the base area is a constant, the volume calculated is the dependent variable while the height iis the independent variable.
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A triangle has two sides of length 3.2 cm and 8.5 cm.
Which value could be the length of the third side of the triangle?
Any value between 5.3 cm and 11.7 cm (exclusive) could be the length of the third side of the triangle which is 6.7cm in the given options.
What is the triangle inequality theorem?The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words, for a triangle with sides a, b, and c, where c is the longest side, the following inequality holds:
a + b > c
This means that the length of any side of a triangle must be less than the sum of the lengths of the other two sides. This theorem is fundamental in geometry and is used in many proofs and applications.
According to the given informationAccording to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, the length of the third side must be greater than the difference between the other two sides and less than their sum.
Let's apply this rule to the given triangle. We have two sides of length 3.2 cm and 8.5 cm.
To be a valid triangle, the length of the third side must satisfy the following inequality:
8.5 cm - 3.2 cm < third side < 8.5 cm + 3.2 cm
5.3 cm < third side < 11.7 cm
Therefore, any value between 5.3 cm and 11.7 cm (exclusive) could be the length of the third side of the triangle. So it's 6.7cm.
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HELP ASAP
When going from smaller to bigger, in the metric system do you divide or multiply?
Answer: When converting a larger unit to a smaller one, you multiply; when you convert a smaller unit to a larger one, you divide.
Step-by-step explanation: im bad at explaining XD
Answer:
Multiply!
Step-by-step explanation:
When going by the metric system you multiply because, dividing would make you go smaller!
Have a great afternoon! :D
Find the equation of the parabola that passes through the points (6, 10), (-2, 18) and (4, 51).
solve for x? please help ive been stuck on this for days.
Since EM is an altitude of triangle EAT, it forms a right angle with AT. So
25x - 10 = 90
Solve for x :
25x = 100
x = 4
10. The local YMCA charges a $79 membership fee and
$42.50 per month. Allison has a coupon that will allow
her to join the club for $298 for 6 months. How much
will Allison save if she uses the coupon?
Answer:
$79
Step-by-step explanation:
Will Give Brainliest Please Help!
Match each theorem with its description.
A. Corresponding Angles Postulate
B. Same-Side Interior Angles Theorem
C. Triangle Midsegment Theorem
D. Alternate Interior Angles Theorem
E. Alternate Exterior Angles Theorem
F. Triangle Sum Theorem
G. Vertical Angles Theorem
H. Isosceles Triangle Theorem
1.
If two angles form a pair of vertical angles, then they are congruent.
2.
The sum of the measures of the interior angles of a triangle is 180°.
3.
If two sides of a triangle are congruent, then the angles opposite those sides are congruent
4.
The midsegment of a triangle is parallel to the third side and its length is one-half the length of the third side.
5.
If two parallel lines are intersected by a transversal, then corresponding angles are congruent.
6.
If two parallel lines are intersected by a transversal, then alternate interior angles are congruent.
7.
If two parallel lines are intersected by a transversal, then the alternate exterior angles are congruent
8.
If two parallel lines are intersected by a transversal, then the same-side interior angles are supplementary.
The given angle theorems and triangle theorems with the description that matches each is shown in the image attached below.
Angle Theorems and Triangle Theorems?Angle theorems are theorems that states the relationship between angle pairs that are formed when two parallel lines are intersected by a transversal line.Triangle theorems, such as midsegment theorem and angle sum theorem, relates specifically to triangles and its measures.Thus, the given angle theorems and triangle theorems with the description that matches each is shown in the image attached below.
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An exterior angle of a regular convex polygon is 40°. What is the number of sides of the polygon?
A. 8
B. 9
C. 10
D.11
Answer:
option B
Step-by-step explanation:
Sum of interior angles of a polygon with n sides:
\(= (n - 2 )\times 180\)
\(Therefore, Each \ interior \ angle = (\frac{n - 2}{n} )\times 180\)
\(Sum \ of \ one \ of \ the \ interior \ angle \ with \ its \ exterior \ angle \ is \ 180^\circ\)
\([ \ because \ straight \ line \ angle = 180^\circ \ ]\)
That is ,
\(Exterior \ angle + Interior \ angle = 180^\circ\\\\40^ \circ + (\frac{n-2}{n}) \times 180 = 180^\circ\\\\40 n + 180n - 360 = 180n\\\\40n = 180n - 180n + 360 \\\\40n = 360 \\\\n = 9\)
OR
Sum of exterior angles of a regular polygon = 360
Given 1 exterior angle of the regular polygon is 40
Therefore ,
\(n \times 40 = 360\\\\n = \frac{360}{40} \\\\n = 9\)
Answer:
9
Step-by-step explanation:
Do the ordered pairs below represent a relation, a function, both a relation and a function, or neither a relation nor a function?
(-4,0) , (2,-6) , (4,-8) , (10,-14) A. Relation only
B. Neither a relation nor a function
C. Function only
D. Both a relation and a function
=======================================================
Explanation:
A relation is any set of (x,y) points usually with some rule tying them together. Though that rule doesn't have to be present. We could simply have a set of points. The set of points we are given is a relation.
A function occurs when we don't repeat the x value. Visually if we had two points stacked on top of each other, then we wouldn't have a function since it fails the vertical line test. A function happens when all x inputs leads to exactly one y output. If we had say { (-4,0), (2,-6), (-4,3) } then this wouldn't be a function since x = -4 repeats itself.
Since none of the x values repeat themselves in our given set, this means we have a function.
Side note: Any function is a relation, but not the other way around.
Consider the figure below. Find the measures of angle CRN and angle GMB
Answer: m<CRN= 107 degrees
m<GMB=148
Step-by-step explanation:
a triangle border has perimeter 24cm and 2 of its sides are 6cm and 8cm.find the cost of painting it at the rate of rupees 9 per cm squarea triangle border has perimeter 24cm and 2 of its sides are 6cm and 8cm.find the cost of painting it at the rate of rupees 9 per cm square
The cost of painting the triangle border at the rate of Rs. 9 per square centimeter is Rs. 216
How to find the cost of painting the triangle border?To find the cost of painting the triangle border, we need to find its area first.
Let's call the length of the third side of the triangle "x". According to the perimeter given in the problem, we have:
Perimeter = sum of all sides of the triangle = 6 cm + 8 cm + x cm = 24 cm
Solving for x, we get:
x = 10 cm
Now, we can use Heron's formula to find the area of the triangle:
s = (6 + 8 + 10)/2 = 12 cm (where "s" is the semi-perimeter of the triangle)
Area = √(s(s-a)(s-b)(s-c)) = √(12(12-6)(12-8)(12-10)) = 24 cm^2
So, the area of the triangle border is 24 square centimeters.
To find the cost of painting the triangle border at the rate of Rs. 9 per square centimeter, we just need to multiply the area by the cost per unit area:
Cost = Area × Cost per unit area = 24 cm^2 * Rs. 9/cm^2 = Rs. 216
Therefore, the cost of painting the triangle border at the rate of Rs. 9 per square centimeter is Rs. 216.
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On your own sheet of paper, use long division to find the quotient of 347 ÷ 4.
What is the remainder?
Answer:
86 Remainder 3
Step-by-step explanation:
What is 347 Divided by 4?
We provide you with the result of the division 347 by 4 straightaway:
347 divided by 4 = 86.75
The result of 347/4 is a terminating decimal with 2 digits to the right of the decimal point.
347 divided by 4 in decimal = 86.75
347 divided by 4 in fraction = 347/4
347 divided by 4 in percentage = 8675%
Note that you may use our state-of-the-art calculator above to obtain the quotient of any two integers or decimals, including 347 and 4, of course. Repetends, if any, are denoted in ().
The conversion is done automatically once the nominator, e.g. 347, and the denominator, e.g. 4, have been inserted. No need to press the button, unless you want to start over.
Give it a try now with a similar division by 4.
What is the Quotient and Remainder of 347 Divided by 4?
Here we provide you with the result of the division with remainder, also known as Euclidean division, including the terms in a nutshell:
The quotient and remainder of 347 divided by 4 = 86 R 3
The quotient (integer division) of 347/4 equals 86; the remainder (“left over”) is 3.
347 is the dividend, and 4 is the divisor.
In the next section of this post you can find the frequently asked questions in the context of three hundred and forty-seven over four, followed by the summary of our information.
Three Hundred And Forty-Seven Divided by Four
You already know what 347 / 4 is, but you may also be interested in learning what other visitors have been searching for when coming to this page. The FAQs include, for example:
What is 347 divided by 4?
How much is 347 divided by 4?
What does 347 divided by 4 equal?
If you have read our article up to this line, then we take it for granted that you can answer these FAQs and similar questions about the ratio of 347 and 4.
347 Divided by 4
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Give the search box a go now, inserting, for instance, three hundred and forty-seven divided by four, or what’s 347 over 4 in decimal, just to name a few potential search terms.
.To sum up, 347/4 = 86.75. The number has 2 decimal places. As division with remainder the result of 347 ÷ 4 = 86 R 3.
Select the number that round to 387.4 when rounded to the nearest tenth.
A. 387.461
B. 387.344
C. 387.309
D. 387.352
E. 387.779
Answer:
D
Step-by-step explanation:
When rounding, the number 5 is rounded up. So the number 387.352 will be rounded up 387.4. Other options are not suitable. Correct answer is "D"
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4. Higher Order Thinking A national TV
news show conducted an online poll to find
the nation's favorite
comedian. The
website showed
the pictures of
5 comedians and
asked visitors of the
site to vote. The news
show inferred that
the comedian with
the most votes was
the funniest comedian
in the nation.
a. Is the inference valid? Explain.
b. How could you improve the poll? Explain.
No, the inference is not valid because it excluded those who were not online and so did not see the poll.
To improve the poll, the news show could have conducted it in a more representative manner by surveying a larger sample of people from a variety of backgrounds
How to improve the poll ?The poll's results may have been influenced by various factors, including but not limited to the order in which the comedians were presented, the demographics of the respondents, and the fact that it was conducted online, possibly excluding those without internet access. Overall, the poll's representative accuracy is questionable.
To enhance the accuracy of the survey, the broadcast could have implemented a more inclusive method by polling a wider range of individuals from diverse backgrounds. An alternate method for conducting the poll would have been by personal or telephonic means, enabling individuals without internet connectivity to participate.
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On the beach boardwalk there are 20 different places to get food 20% of them are ice cream shops how many ice cream Shoppe’s are in the park
Answer:
( 4 )
Step-by-step explanation:
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What happen when you multiply a number by it's reciprocal?
Answer:
When you multiply the number by its reciprocal the numerator of the one becomes the denominator of the other and is equals to 1 .
The question is asked in the attached file,. Kindly someone answer it in the best way.
According to the Empirical Rule, 99.7% of the measures fall within 3 standard deviations of the mean in the normal distribution.
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of approximately 68%.The percentage of scores within two standard deviations of the mean of the distribution is of approximately 95%.The percentage of scores within three standard deviations of the mean off the distribution is of approximately 99.7%.More can be learned about the Empirical Rule at https://brainly.com/question/10093236
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Pupils in a class were asked how they travel to school. The results were recorded in the table below
Car 13 bus 6 train 5 walk 8
If s pupil in the class was picked at random what is the probability that one of them walked to school as a percentage
Answer:
1/3
Step-by-step explanation:
What expression is equal to -8(4y)
Answer:
32y
Step-by-step explanation:
take off the y then do the equation -8×4=32 then put the y back on an theres your answer