Final answer:
By using the given lengths of AE and BC, along with the equality of AB, DB, and DC, we can solve for CE to be 14.67cm.
Explanation:
The lengths of AE, BC, AB, DB, and DC are given or can be determined with the information provided. Since AB = DB = DC and BC is given as 10 cm, we can deduce that AB + BC + CE = AE. Given AE is 28cm and BC is 10cm, we can find the length of AB by realizing that AB + AB + AB (which is AB + DB + DC) is the same as BC or 10cm. This makes each section AB, DB, and DC equal to 10cm / 3.
With AB, DB, and DC all being equal to 10cm / 3, and knowing AE is 28cm, we can then calculate the length of CE:
AE = AB + BE (and BE = BC + CE)
28cm = (10cm/3) + (10cm + CE)
To find CE, rearrange the equation:
CE = 28cm - 10cm - (10cm/3)
CE = 28cm - 10cm - 3.33cm
CE = 18cm - 3.33cm
CE = 14.67cm
To solve for the length of CE in a line segment configuration, we calculate CE = AE - BC - DC after determining the lengths of AB, BC, and DC. The solution reveals that CE is 9cm.
Explanation:The student has a geometry problem, which involves calculating the length of segment CE on a line segment AE. We know that AE = 28cm and BC = 10cm, with AB, DB, and DC being equal in lengths.
Since B is between A and C, and D is between B and C, and C is between B and E, we can write the entire length AE as AB + BC + CE. Because AB = DB = DC, we can substitute DB and DC for AB in the sums to get 2(DB) + BC = 28cm.
We are given that BC = 10cm, so we can set up an equation: 2(DB) + 10cm = 28cm. Solving for DB, we find that DB = 9cm. Since DC is equal to DB, DC is also 9cm. CE can be found by subtracting BC and DC from the total length of AE: CE = AE - BC - DC, so CE = 28cm - 10cm - 9cm, resulting in CE = 9cm.
What is the value of the expression?
5/6−(1/8÷3/4)
Enter your answer, as a fraction in simplest form, in the box
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
We are given that an expression
[tex]\frac{5}{6}-(\frac{1}{8}\div\frac{3}{4})[/tex]
We have to find the value of expression.
[tex]\frac{5}{6}-(\frac{1}{8}\div\frac{3}{4})[/tex]
When we change divide into multiply then the term will be reciprocal.
By using this property
[tex]\frac{5}{6}-(\frac{1}{8}\times \frac{4}{3})[/tex]
[tex]\frac{5}{6}-\frac{1}{6}[/tex]
By simplification
[tex]\frac{5-1}{6}[/tex]
By simplification
[tex]\frac{4}{6}[/tex]
By using subtraction property of integers
[tex]\frac{2}{3}[/tex]
Hence, the value of given expression =[tex]\frac{2}{3}[/tex]
Sylvia has 6 1/2 boxes of chocolate to share at a family picnic. if she gives eacah person 1/3 of a box, how many people can receive chocolate
Answer:
The correct Answer is 19
The number of people who will receive the chocolate will be equal to 19.
What is a fraction?In mathematics, a fraction is represented by a specific number that designates a portion of an entire. A fraction is a piece or section of a whole, whereby a can have been any number, a particular value, or an object.
As per the provided data in the question,
Total boxes of chocolate = 13/2
Chocolate received by each person = 1/3 of a box
Then, the number of people who receive the chocolate is,
13/2 ÷ 1/3 = 19.5 or,
A total of 19 people will receive the chocolate.
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solve for n , S = (n - 2)180
Wilma and Betty are playing a number game. Wilma tells Betty, "I'm thinking of a number between 1 and 10. If I take the number and add 4 to it and then multiply that by 3, I get 30." What number is Wilma thinking of?
The function y = [x] is defined as follows: for any input x, the output is the smallest integer that is greater than or equal to x (“rounding up” any non-integer to the next integer).
Draw the graph of y = [x] for -2 ≤ x ≤ 2. Upload a handwritten copy of your graph as your final answer.
Answer:
Step-by-step explanation:
How to find the angle measure of a triangle with x and x+4 and 9x?
In triangle ABC, < A = 38° and < B = < C. Find < B.
m< B =
A.) 26°
B.) 71°
C.) 142°
71 odyssey just had this
A crew of ten workers was hired to complete a job in 8 days. After working for two days, there was a new request to complete this job in two days. How many more workers need to be hired to finish this job in 2 days?
Answer:
29 more workers are needed.
Step-by-step explanation:
Let us assume that the 10 workers, working at their normal rate would finish the job in exactly 8 days.
The rate of working for 1 worker is:
[ 1/10 of the job ] / [ 8 days ] = [ 1 job ] / [ 80 days ]
This is also [ 1/80 of the job ] / [ 1 day ]
In 2 days, the fraction of the job that gets done is:
[tex]2\times \frac{1}{80}=\frac{1}{40}[/tex]
Job left = [tex]1-\frac{1}{40} =\frac{39}{40}[/tex]
Now the rate has to be :
[tex]\frac{\frac{39}{40} }{2} =\frac{39}{80}[/tex]
Now, let w be the additional number of workers needed.
We get:
[tex]\frac{10+w}{80}=\frac{39}{80}[/tex]
Solving for w;
[tex]10+w=39[/tex]
[tex]w=39-10[/tex]
w = 29
Therefore, 29 more workers are needed.
-------------------------------------------------------------------------------------
There can be another approach as well.
Fraction of the job done by 10 workers in 2 days = 1/4
Remaining fraction = 1-1/4 = 3/4
Lets say W workers are needed more.
So, we can say that 3/4 of the work is to be done by 10+W workers.
Hence, it will take a total of 30 workers to complete the job.
Making it additional 20 workers.
A particular shade of purple paint is made of a ratio of 2 pints of red paint to 1 pint of blue paint. List 4 other combinations of red and blue paint that would make the same shade of purple paint
A triangle can have at most ____ right angle(s).
No
1
2
4
Answer:
The answer is 1
A triangle is isosceles. if one angle of the triangle measures 102°, what are the measures of the largest and smallest angles of the triangle?
In an isosceles triangle with one angle measuring 102°, the other two angles are both 39°. The sum of all angles in a triangle is 180°. Therefore, the largest angle is 102° and the smallest are both 39°.
If a triangle is isosceles and one angle measures 102°, we can determine the measures of the other two angles. Since it's an isosceles triangle, two angles are the same. According to the properties of triangles, we know that the sum of all three angles must be 180°. Therefore, we can subtract the known angle from 180° to determine the sum of the remaining two angles.
180° - 102° = 78°
Since the two remaining angles are equal, we divide 78° by 2 to find the measure of each angle.
78° ÷ 2 = 39° each
The measures of the largest and smallest angles in the isosceles triangle are 102° (the largest) and 39° (the smallest).
What is A rational number? square root of 15, square root of 16 square root of 17, square root of 18
Answer:
B. [tex]\sqrt{16}[/tex]
Step-by-step explanation:
We have been given 4 numbers. We are asked to find the rational number from our given choices.
We know that a number is a rational number, when it could be written as a fraction.
Let us check our given choices one by one.
A. [tex]\sqrt{15}[/tex]
[tex]\sqrt{15}=3.8729833462074169[/tex]
Since our given number has non-terminating decimal, therefore, [tex]\sqrt{15}[/tex] is not a rational number.
B. [tex]\sqrt{16}[/tex]
[tex]\sqrt{16}=\sqrt{4^2}=4[/tex]
Since our given number is an integer and we can write it as a fraction [tex]\frac{4}{1}[/tex], therefore, [tex]\sqrt{16}[/tex] is a rational number.
C. [tex]\sqrt{17}[/tex]
[tex]\sqrt{17}=4.1231056256176605[/tex]
Since our given number has non-terminating decimal, therefore, [tex]\sqrt{17}[/tex] is not a rational number.
D. [tex]\sqrt{18}[/tex]
[tex]\sqrt{18}=4.2426406871192851[/tex]
Since our given number has non-terminating decimal, therefore, [tex]\sqrt{18}[/tex] is not a rational number.
It is to be noted that from the options given, the rational number is √16
What is a rational number?A rational number is any number that can be expressed as a fraction, where the numerator and denominator are integers.
Among the given numbers, the √16 is a rational number.
The √16 equals 4, which can be expressed as the fraction 4/1.
The square roots of 15, 17, and 18 are irrational numbers because they cannot be expressed as fractions or terminate or repeat in decimal form.
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NEED ASAP!!!!
In quadrilateral ABCD, diagonals AC and BD bisect one another:
What statement is used to prove that quadrilateral ABCD is a parallelogram?
Angles ABC and BCD are congruent.
Sides AB and BC are congruent.
Triangles BPA and DPC are congruent.
Triangles BCP and CDP are congruent.
Answer:Triangles BPA and DPC are congruent is used to prove that ABCD is a parallelogram.
Explanation:Here, we have given a quadrilateral ABCD in which diagonals AC and BD bisect each other.
If P is a an intersection point of these diagonals
Then we can say that, AP=PC and BP=PD ( by the property of bisecting)
So, In quadrilateral ABCD,
Let us take two triangles, [tex]\triangle BPA[/tex] and [tex]\triangle DPC[/tex].
Here, AP=PC
BP=PD,
[tex]\angle APB=\angle DPC[/tex] ( vertically opposite angles.)
So, By SAS postulate,[tex]\triangle BPA\cong \triangle DPC[/tex]
Thus AB=CD ( CPCT).
Similarly, we can prove, [tex]\triangle APD\cong \triangle BPC[/tex]
Thus, AD=BC (CPCT).
Similarly, we can get the pair of congruent opposite angle for this quadrilateral ABCD.
Therefore, quadrilateral ABCD is a parallelogram.
Note: With help of other options we can not prove quadrilateral ABCD is a parallelogram.
The congruence of triangles BPA and DPC, proven through the Side-Angle-Side postulate or other congruency postulates, can be used to prove that quadrilateral ABCD is a parallelogram when diagonals AC and BD bisect one another.
The statement used to prove that quadrilateral ABCD is a parallelogram when diagonals AC and BD bisect one another is that triangles BPA and DPC are congruent. The congruence of these triangles can be shown through the Side-Angle-Side (SAS) postulate or other congruency postulates depending on a given figure, and this property that diagonals bisect each other is a defining trait of a parallelogram. Therefore, by showing the congruence of triangles BPA and DPC, we can deduce that ABCD is a parallelogram.
Bonita is testing prototype model rocket engines. To be considered a successful launch, the rocket must reach a height of at least 24 ft and must go a horizontal distance of no more than 10 ft. The vertical height must be at least three times as high as the horizontal distance. No rocket should go higher than 33 ft.
The graph shows the feasible region, where x represents the horizontal distance and y represents the vertical distance.
Which ordered pairs meet all the constraints for a successful launch and make sense in context of the situation?
Select each correct answer.
(0, 33)
(4, 36)
(4.8, 30.5)
(9, 26)
(2, 22)
A one compartment vertical file is to be constructed by bending the long side of an 8 in 8 in. by 10 10 in. sheet of plastic along two lines to form a U shape. How tall should the file be to maximize the volume that it can hold?
In order to maximize the volume of the file, it should be 2 inches high. This is calculated using the optimization principle in calculus applied to the volume formula of a rectangular prism.
Explanation:This problem involves optimizing the volume of a vertically filed object, which is a common theme in calculus. The file is being formed from a rectangular sheet of plastic that is 8 inches by 10 inches by bending it to form a U-shape.
The volume of a rectangular prism (which is what the file will essentially be) is given by the formula length x width x height. In this case, the length will always be 10 inches because it's the undisturbed dimension. The 8-inch side will be divided into a height part and a width part once we bend it into a U shape. Since we don't know a priori what the height is yet, let's call it x. This means the width will then be 8 - 2x (since we lose x from each side to form the height).
Our volume function V becomes: V(x) = length x width x height = 10(8-2x)x. To maximize this volume, you want to take the derivative V'(x), set it to 0 and then solve for x. Taking the derivative will give you V'(x) = 10(8-4x), and setting it to 0 and solving gives you x = 2 inches. So, the file should be 2 inches high to maximize the volume it can hold.
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Of all rectangles with a fixed perimeter of p, which one has the maximum area? (give the dimensions in terms of p.)
For a rectangle with a fixed perimeter P, the one with maximum area has dimensions L = P/4 and W = P/4 obtained by optimizing the area expression.
To find the rectangle with the maximum area given a fixed perimeter P, we can use optimization techniques. Let L represent the length and W represent the width of the rectangle. The perimeter is given by P = 2L + 2W, and the area is given by A = LW.
Since P is fixed, we can express one of the variables in terms of the other using the perimeter equation. Solving for L, we get L = (P/2) - W. Substituting this expression into the area equation, we have A = ((P/2) - W)W.
To find the dimensions that maximize A, we take the derivative of A with respect to W, set it equal to zero to find critical points, and check for endpoints (since we are dealing with real-world dimensions).
(dA/dW) = (P/2) - 2W = 0.
Solving for W, we get W = P/4. Substituting this value back, we find L = P/4.
Therefore, the rectangle that maximizes the area for a fixed perimeter P has dimensions L = P/4 and W = P/4.
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The question probable may be:
What are the dimensions of the rectangle with the maximum area given a fixed perimeter P?
Please help with these questions and show all work.
In a flock of black and white sheep, 2 out of 5 sheep are white. If there are 8 more black sheep than white sheep, how many sheep are in the flock?
To find the total number of sheep in the flock where 2 out of 5 are white and there are 8 more black than white sheep, we set up a ratio and solve for the number of white sheep (W), which is 16. We then determine the number of black sheep (B) to be 24, leading to a total of 40 sheep.
Explanation:The subject of the question is mathematics, and it appears to be at the middle school level. The task involves determining the total number of sheep given that 2 out of 5 are white and there are 8 more black sheep than white. Let's define the variables: W for white sheep and B for black sheep. From the statement, we have the ratios W/B = 2/3 because for every 2 white sheep, there are 3 black sheep which are proportionally 5 sheep in total (2+3=5), and we have the relationship B = W + 8 because there are 8 more black than white sheep. Using these equations, we can solve for W and B.
From the ratio W/B = 2/3, we can express B as B = 3/2 * W.Replace B in the second equation with 3/2 * W:Therefore, the total number of sheep in the flock is 40.
"Eventually the things in life that gave you pause mean nothing. Time... becomes your friend." (math 1 help plz)
When using the law of sines, why can the SSA case result in zero, one, or two triangles? Explain.
Answer: If you have SSA, then the third side determines the triangle. If it is too short to intersect the other side, then it does not form a triangle. The third side can also be just the right length to meet the other side, making one triangle. Finally, the third side might be long enough to intersect the other side at two different points, creating two triangles.
i just took the assignment
There are different rules in mathematics. The explanation is that when a person have SSA, the third side is often used to know the type of triangle and also;
When it too short to pass through the other side, it rather then not form a triangle. The third side can be the appropriate length to meet the other side, creating one triangle.
Furthermore, the third side can be able to pass through or intersect the other side at two key areas or points, forming two triangles.
Note that;
When the third side of the triangle is too little to intersect the other side, there is no triangles that is created.When the third side is said to be long enough to meet the other side at a certain point, only one triangle is created.When the third side is able and long enough to pass through the other side at two points, as a result, two triangles are created or made.Can The Law of Sines be used in SSA case?"SSA" is known to be when one knowns two sides and an angle that is said to be not or not part of the angle between the sides.
The Law of Sines is known to be used first to calculate one of the other two angles.
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the simplest form of the square root of 3,025 is
What is the point slope form of the line with slope −3/7 that passes through the point (5, 8)?
Answer:y−8=−[tex]{\frac{3}{7}[/tex](x−5)
Step-by-step explanation:
At the beginning of an experiment, there are 400 grams of contaminants. Each hour, three-fourths of the contaminants are filtered out.
A. Formulate a recursive sequence modeling the number of grams after "n" hours.
B. Use the model to calculate the amount of contaminants after the third hour of the experiment.
The recursive sequence is:[tex]T_n = \frac 14T_{n-1}[/tex] and there are 25 contaminants left after the third hour of the experiment
The recursive sequenceThe initial number of contaminant is 400.
If 3/4 contaminants are filtered out, there are 1/4 contaminants left.
So, the recursive sequence is:
[tex]T_n = \frac 14T_{n-1}[/tex]
Where T1 = 400
The number of contaminants after the third hourThis means that n = 3.
So, we have:
[tex]T_3 = \frac 14 * T_2[/tex]
[tex]T_2 = \frac 14 * T_1[/tex]
Substitute [tex]T_2 = \frac 14 * T_1[/tex] in [tex]T_3 = \frac 14 * T_2[/tex]
[tex]T_3 = \frac 14 * \frac 14 * T_1[/tex]
Substitute 400 for T1
[tex]T_3 = \frac 14 * \frac 14 * 400[/tex]
Evaluate
[tex]T_3 = 25[/tex]
Hence, there are 25 contaminants left after the third hour of the experiment
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Final answer:
A recursive sequence can be formulated to model the number of grams of contaminants after "n" hours. After plugging in the values, the amount of contaminants after the third hour is 168.75 grams.
Explanation:
A. To formulate a recursive sequence modeling the number of grams after "n" hours, we can start with the initial amount of contaminants of 400 grams and then multiply it by three-fourths each hour. This can be represented by the formula: an = (3/4) * an-1. This formula tells us that to find the amount of contaminants after "n" hours, we multiply the amount after the previous hour by three-fourths.
B. To calculate the amount of contaminants after the third hour of the experiment, we can use the recursive formula. Let's plug in the values: a0 = 400 grams, a1 = (3/4) * a0 = (3/4) * 400 = 300 grams, a2 = (3/4) * a1 = (3/4) * 300 = 225 grams, a3 = (3/4) * a2 = (3/4) * 225 = 168.75 grams.
Therefore, the amount of contaminants after the third hour of the experiment is 168.75 grams.
Tours of the art museum are offered every 1/3 hour starting at 10 A.M. The museum closes at 4:00 P.M. How many tours are offered each day?
And
Small juice bottles come in packages of 6. yogurt treats come in packages of 10. paula qanta to have the exact same number of each item. what is the least number of bottles of juice and individual yogurt treats she will have? how many packages of each will she need?
What is a classification for a triangle with angle measures of 20, 80, and 80 degrees,?
Answer:
its a icolaleas
Step-by-step explanation:
What is the measure of ∠DAE? 45° 46° 91° 146°
Answer:
The answer/measure is 45 degress.
Step-by-step explanation:
The measure of ∠DAE is 45°.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
In the given figure let's say angle FAE = x than
x = 180 - 134 = 46 degree
Now by line CAF angle ∠DAE = 180 - ( 89 + 46 ) = 45° hence it will be correct answer.
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Determine the x-intercepts of the function. Check all that apply. (–2, 0) (–1, –2) (0, 0) (1, 0) (2, 0)
it's (0, 0) and (-2, 0) so A & C
Answer: A, C
Step-by-step explanation:
Hope this helps!!
Marisol keeps track of her weekly quiz grades as shown in the table.
a. Complete the table
b. In which class did Marisol have the higher score?
c. Suppose Marisol scored a 96% on an english test. There were 50 questions on the test. How many did Marisol answer correctly?
Test / Number/Score/Total
Correct
____________________
Math/ 68 / /85
Science/ / 90% / 70
Marisol got 80% on her Math quiz by answering 68 out of 85 questions correctly, and 90% on her Science quiz by answering 63 out of 70 questions correctly. She scored higher in Science. For her English test, by scoring 96%, she got 48 out of 50 questions correct.
Explanation:To complete the table and find the number of questions Marisol got correct in Science, we use the percentage score and total number of questions. For the Math test, she got 68 questions correct out of a total of 85 questions. To find the corresponding percentage, we calculate (68/85) * 100%.
For the Science test, we use the given percentage score of 90% and the total of 70 questions to find the number of correct answers. The calculation is (90/100) * 70.
To find out in which class Marisol had the higher score, we compare the calculated percentage scores from the Math and Science classes.
Finally, to determine the number of questions Marisol answered correctly on the English test, where she scored 96% on a 50 question test, we use the calculation (96/100) * 50.
when a graph of a cubic polynomial function rises to the left, it falls to the right true or false
Final answer:
The statement about cubic polynomial functions rising to the left and falling to the right is false; the behavior of a cubic function's graph depends on the sign and magnitude of its coefficients, particularly the leading coefficient.
Explanation:
The statement that a graph of a cubic polynomial function that rises to the left must necessarily fall to the right is false. While this behavior is common for many cubic functions, it's not a definitive rule. Cubic functions are defined by the equation f(x) = [tex]ax^3 + bx^2[/tex] + cx + d, where a, b, c, and d are constants, and a ≠ 0. The sign and magnitude of these constants, especially the leading coefficient 'a', influence the end behavior of the function.
For example, if 'a' is positive, the right end of the cubic function's graph will rise, and depending on the signs and magnitudes of the other coefficients, the left end might also rise or fall. Similarly, if 'a' is negative, the right end will fall, and the left end's behavior can vary. Cubic graphs can also exhibit turning points where the function's direction changes, which is dictated by the local minima and maxima.
Therefore, while many cubic polynomials may display the behavior of rising to the left and falling to the right, others with different coefficients could have a completely different end behavior or shape, such as rising on both ends or falling on both ends. Two-dimensional (x-y) graphing tools and learning about graphing polynomials can provide visual understanding of these concepts.
find the area of a figure whose coordinates are A (-2,2) B (2,2) C (2,-2) D (-2,-2)
12 units.squared
16 units.squared
20 units.squared
24 units.squared