4.
One endpoint of a segment has the coordinates (1,-2). The coordinates of the midpoint
are (5,-5). What are the coordinates of the other endpoint?
5.
Ray AC is in the interior of angle BAD. Write an equation using the Angle Addition
Postulate. If the measure of angle BAD = 52º and the measure of angle BAC = 2x - 3
and the measure of angle CAD = 7x + 1, what are the measures of angle BAC and
angle CAD?
Answers
Answer:
4. (9, -8)
(✿◠‿◠)
Related Questions
C(x) = 0.05x2 + 22x + 340, 0 < < 150. (A) Find the average cost function C(x). (B) List all the critical values of C(x). Note: If there are no critical values, enter 'NONE'. (C) Use interval notation
Answers
A) The average cost function C(x) can be obtained by dividing the total cost function by the quantity x:
C(x) = (0.05x^2 + 22x + 340) / x
Simplifying this expression, we get:
C(x) = 0.05x + 22 + 340/x
Therefore, the average cost function C(x) is given by 0.05x + 22 + 340/x.
B) To find the critical values of C(x), we need to determine the values of x where the derivative of C(x) is equal to zero or is undefined. Taking the derivative of C(x) with respect to x, we have:
C'(x) = 0.05 - 340/x^2
Setting C'(x) equal to zero and solving for x, we find:
0.05 - 340/x^2 = 0
Rearranging the equation, we have:
340/x^2 = 0.05
Simplifying further, we get:
x^2 = 340/0.05
x^2 = 6800
Taking the square root of both sides, we find two critical values:
x = ± √(6800)
Therefore, the critical values of C(x) are x = √(6800) and x = -√(6800)
C) Using interval notation, we can express the domain of x where the function C(x) is defined. Given that the range of x is from 0 to 150, we can represent this interval as (0, 150).
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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
Answers
The class that lost the most pencils overall based on the data displayed is D. Mr. Johnson's class; it has a wide spread in the data
How to explain the informationThe answer is Mr. Johnson's class. The median is the middle value in a set of data. In Mr. Johnson's class, the median is 11 pencils. This means that half of the students in his class lost 11 or fewer pencils, and half of the students lost 11 or more pencils.
In Mr. Simpson's class, the median is 14.5 pencils. This means that half of the students in his class lost 14.5 or fewer pencils, and half of the students lost 14.5 or more pencils.
Since the median for Mr. Johnson's class is lower than the median for Mr. Simpson's class, we can conclude that Mr. Johnson's class lost more pencils overall.
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What is the inverse of:
If a = b and b = c, then a = c
1) a = b and b = c if, and only if, a = c
2) If a ≠ c then a ≠ b or b ≠ c
3) If a ≠ b or b ≠ c, then a ≠ c
4) If a = c, then a = b and b = c
Answers
Answer:
1
Step-by-step explanation:
Is the correct way to do it
Find the generating function of the sequence {an}n≥0 determined by an = an−1 + 6an−1 with initial conditions a0 = 1, a1 = 3. You need to find the closed form of the generating function, but you don’t need find the closed form of the coefficients.
Answers
The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.
To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.
The given recurrence relation is: an = an-1 + 6an-2
We are also given the initial conditions: a0 = 1 and a1 = 3.
To find the generating function, we define the generating function A(x) as:
a(x) = a0 + a1x + a2x² + a3x³ + ...
Multiplying the recurrence relation by x^n and summing over all values of n, we get:
∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)
Now, let's express each summation in terms of the generating function a(x):
a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾
Simplifying and rearranging the terms, we have:
a(x)(1 - x - 6x²) = a0 + (a1 - a0)x
Using the given initial conditions, we have:
a(x)(1 - x - 6x²) = 1 + 2x
Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):
a(x) = (1 + 2x) / (1 - x - 6x²)
Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).
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A group of 40 students from your school is part of the audience for a TV game show. The total number of people in the audience is 150 What is the theoretical probability of 5
students from your school being selected as contestants out of 8 possible contestard spots?
P(5 students selected)
(Type an integer or decimal rounded to three decimal places as needed)
Cus
Answers
The theoretical probability of randomly selecting 5 students from my schools is 0.00000001237
probability of an eventprobability = required outcome / total possible outcomes
Required outcome = 5 students from the 40. Here , we have
40C5 = 65008
Total possible outcomes = 8 students From the total contestants . Here , we have
150C8 = 5257211409450
Hence, selecting 5 students from my school :
P(5 from my school) = 65008/5257211409450
P(5 from my school ) = 0.00000001237
Hence, the theoretical probability is 0.00000001237
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Find the maximum volume of a cylindrical soda can such that the sum of its height and its circumference is 150 cm.
Answers
20371.83 cm³ is the maximum volume of a cylinder.
What is volume?The space occupied within an object's borders in three dimensions is referred to as its volume.
It is sometimes referred to as the object's capacity.
So, consider a cylinder with a radius of r and a height of h.
The cylinder's volume is: V = πr²h
Because its height plus circumference equals 120 cm.
h + 2πr
h = 120 - 2πr
Changing the value of h in the cylinder's volume equation:
V = πr² (120-2πr)
V = 120πr² - 2π²r³
To get the biggest volume, compare the above expression to r and equate it to zero:
dV/dx = 240πr - 6π²r² = 0
6πr(πr-0) = 0
r = 0, r = 40/π
The cylinder's radius is: r = 40/π
Now: h = 120 - 2π(40/π) = 80cm
Changing the values of r and h in the cylinder's volume formula:
V = π(40/π)²*40 = 20371.83 cm³
Value of π = 3.14
Therefore, 20371.83 cm³ is the maximum volume of a cylinder.
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I need help please
Which value is the closest to
0.9 • 997
a. 1,000
b. 81
c. 10,000
d. 10
Answer with supporting work:
Answers
Explanation: 0.9 x 997 equals to 897.3
897.3 rounds to 900 which is close to 1000 so it is that
In the given figure ABCD, prove that
angleBCD= angleBAD+ angle ABC+angle ADC.
[Hint: Join A and C then extended AC to the point E]
Answers
We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.
To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:
Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.
Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.
Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).
Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.
Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).
Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.
Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.
Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.
Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.
Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.
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Given: Quadrilateral \(\displaystyle\sf ABCD\)
To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)
Proof:
1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).
2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).
3. In triangle \(\displaystyle\sf ACD\):
- \(\displaystyle\sf \angle ACD = \angle BAD + \angle ADC\) (Angles of a triangle add up to \(\displaystyle\sf 180^\circ\)).4. In triangle \(\displaystyle\sf BCE\):
- \(\displaystyle\sf \angle BCE = \angle BAD + \angle ABC\) (Angles of a triangle add up to \(\displaystyle\sf 180^\circ\)).5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):
- \(\displaystyle\sf \angle BCE = \angle BCD\).6. Combining the equations from steps 3 and 4:
- \(\displaystyle\sf \angle BCD = \angle ACD = \angle BAD + \angle ADC\). - \(\displaystyle\sf \angle BCD = \angle BCE = \angle BAD + \angle ABC + \angle ADC\).Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).
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the hypotenuse of a right triangle is 6 1 /2cm and its area is 7 1/2sq.cm. Calculate the length of its perpendicular sides.
Answers
Answer:
The Length of the triangle = 2.307 cm
Step-by-step explanation:
Step(i):-
Given hypotenuse of a right triangle is = 6 1 /2 cm
Let assume the height of the triangle h = \(\frac{13}{2} c m\)
Given Area of the triangle = 7 1/2 sq.cm.
A = \(\frac{15}{2} sq .c m\)
Step(ii):-
We know that Formula
Area of the triangle
\(A = \frac{1}{2} base X height\)
\(\frac{15}{2} = \frac{1}{2}X b X \frac{13}{2}\)
On calculation , we get
Base of the triangle (b) = \(\frac{30}{13} = 2.307 c.m\)
Conclusion:-
The length of the triangle = 2.307 c.m
find the area and missing angle x
Answers
This is an isosceles triangle, meaning that two sides and angles are the same.
x + x + 28 = 180
2x = 152
x = 76
76 degrees
using the Pythagorean Theorem, 4^2 + h^2 = 9^2
h = sqrt(65), area is 8*sqrt(65)/2 = 4*sqrt(65)
we can also check using heron's formula. area = sqrt(s(s-a)(s-b)(s-c)) = sqrt(13*4*4*5).
Which of the following is not an item in the income statement? SELECT ONLY ONE a. Discount allowed b. Furniture & Fixture c. Furniture & Fixture d. Discount received
Answers
The item that is not an item in the income statement is b. Furniture & Fixture as it is considered a fixed asset and is reported on the balance sheet instead.
The income statement, also known as the profit and loss statement, provides a summary of a company's revenues, expenses, gains, and losses over a specific period. It helps to assess the financial performance of a business. The income statement typically includes various items such as revenues, cost of goods sold, operating expenses, interest income or expense, and other gains or losses.
a. Discount allowed is a revenue item that represents the discounts given to customers as an incentive for early payment or other reasons. It is usually reported as a deduction from sales revenue.
c. Furniture & Fixture is not typically included in the income statement. Instead, it is considered a non-operating or non-recurring item and is generally classified as a fixed asset on the balance sheet. Fixed assets represent long-term investments made by a company for its operations.
d. Discount received is also not an item in the income statement. It represents the discounts received by a company from its suppliers for early payment or other reasons. Similar to discount allowed, it is usually reported as a deduction from the respective expense account.
In summary, b. Furniture & Fixture is the item that is not included in the income statement. It is considered a fixed asset and is reported on the balance sheet instead.
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the population of the united states is aging. at right is the stemplot of the percentage of residents aged 65 and older in each of the 50 states, according to the 2010 census. there are three outliers: alaska has the lowest, utah has the second lowest, and florida has the highest. what is the percentage for utah?
Answers
The percentage for Utah is 9.0%.
The collection of data is gathered and chosen from a statistical population with the use of some prescribed techniques in both statistics and quantitative methodology. Data sets may be divided into two categories: sample and population.
All the components of the data set are included in the population, which also contains quantifiable qualities like mean and standard deviation.
A sample is made up of one or more observations that are taken from the population, and a statistic is what makes a sample quantifiable. The act of sampling is the selection of a sample from a population.
Thus, The percentage for Utah is 9.0%.
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Translate this phrase into an algebraic expression. 9 increased by twice a number
use the variable n to represent the unknown number
Answers
Which value of a,b, and c correctly represent the answer in simplest form?
Answers
Answer:
A
Step-by-step explanation:
first, you turn 3 1/2 into 3 2/4'ths and change 3 two fourth's into 14/4 fraction.
next, you change 2 one fourth into 9/4th's fraction
your equation would be 14/4 divided by 9/4th's = a times b/c
when you used divide, you get get flip one of the fractions being divided, and it could turn into 14/4 TIMES 4 over 9 = a times b/c.
wait this area down here could be wrong:
when you get your equation, multiply them together and you get 56 over 36 equals a times b/c.
A times B /C is equal to 56/36 which can simple out to 28/18 which AGAIN simpled out to 14/9
C IS 9 BECAUSE IT IS THE DENOMINATOR
and because of that, A would be the answer.
Gerard concluded that the triangle with sides feet, 8 feet, and cannot be used as a building frame support on the house because it is not a right triangle. How did gerard come to that conclusion? explain.
Answers
Gerard concluded that triangle with given sides cannot be used as building-frame support because it is not right triangle, he come to this conclusion because the Pythagoras-theorem is not satisfied.
In order to check if a triangle is "right-triangle", Gerard used the Pythagorean theorem. According to this theorem, in right triangle, the square of length of hypotenuse (the side opposite the right angle) is equal to sum of squares of other two sides,
So, the squares of the given sides are :
Square of √95 feet = (√95)² = 95 feet
Square of 8 feet = 8² = 64 feet
Square of √150 feet = (√150)² = 150 feet
We see that, 95 feet + 64 feet = 159 feet ≠ 150 feet,
Since the square of the longest side (√150) is not equal to the sum of the squares of the other two sides (√95 and 8), the Pythagorean-theorem is not satisfied.
Therefore, Gerard concluded that the triangle with sides √95 feet, 8 feet, and √150 feet is not a right triangle.
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The given question is incomplete, the complete question is
Gerard concluded that the triangle with sides √95 feet, 8 feet, and √150 cannot be used as a building frame support on the house because it is not a right triangle. How did Gerard come to that conclusion? explain.
Find the perimeter and the area of the polygon with the given vertices N (-4,2) , P (5,2) , Q (5,5) , R (-4,5) PLEASE ANSWER
Answers
Answer:
Perimeter = 24; Area = 27
Step-by-step explanation:
If you draw out the coordinates on paper you can clearly see side lengths be seeing how far away they are from eachother on the axis'
From Point N to point P it travels the x axis by 9 units.
Therefore the bottom side is 9 units long.
From Point N to Point R it travels the y axis by 3 units
therefore the left side length is 3 units long
Area = b*h = 9*3 = 27
Perimeter = 2b + 2h = 2*9 + 2*3 = 24
help me can you help with the second part
Answers
Answer:
12 packages with 2 toothbrushes and 3 soaps each
Step-by-step explanation:
The distance a body falls from rest varies as the square of the time the body is falling. If a body falls 64 ft. in two seconds, how far will it fall in seven seconds?
Answers
Answer:
224
Step-by-step explanation:
Answer:
224 feet
Step-by-step explanation:
So because the body falls from rest at 64 feet in two seconds, we can divide that by two so that the body falls from rest at 32 feet in one second. Since we are talking about in seven seconds, multiply 32 by 7 which equals 224 feet which is your answer.
Write the function for the graph.
A. f(x)= 4•(2)^x
B. f(x)= 2•(4)^x
C. f(x)= 8•(4)^x
D. f(x)= 4•(8)^x
Answers
A) f(x) = 4•(2)^x
Step-by-step explanation:When substituting in the values of x and y into the functions, the only function that works for both (0,4) and (1,8) is A.
8 = 4•(2)^1 = 4 x 2 = 8
4 = 4•(2)^0 = 4 x 1 = 4
thing
Fill in the blank with the correct response.
The slope of the graph of y= 5x is
ao
Answers
Answer:
slope is 5
Step-by-step explanation:
y = 5x
This is in the form
y = mx+b where m is the slope and b is the y intercept
The slope is 5 and the y intercept is 0
In slope intercept form, y=mx+b, m is the slope. You can see that 5 is in the place of m, so the slope is 5
i feel absolutely unintelligent and cannot get past this assignment. all my friends finished school but im not done yet. can someone help me please!
Answers
Step-by-step explanation:
Probability of A is 10 + 5 =15
Probability of B is 9 + 5 ( but you already counted the '5')
so just count 9
9+ 15 = 24
this is 24 out of 16 + 10 + 5 + 9 = 40
or 24/40 which reduces to 3/5 or .6 or 60%
Using the equation given:
P(A) + P(B) - P(A and B)
15 + 14 - 5 = 24 this is out of the entire number 40
24/40 = same as above
9.
Kim is 15 more than three times her nephew's age. If Kim is 36, how old is her nephew?
Answers
Answer:
7 years old
Step-by-step explanation:
36=3x+15
x=21/3=7
Answer:
X = 7
Step-by-step explanation:
nephew ---- x
Kim ------ 3x + 15
3x+15 = 36
3x = 36-15
3x = 21
x = 7
Write the slope of 4x + 5y = -5
Answers
Answer:
4
Step-by-step explanation:
the number before x is the slope
^^^^^^^^^^^^^^^^^^^^^^^^
solve the quadratic equations
1)a20-3a+2=0
2)x2-6x+9=0
3)y2+8y+16=0
4)z2-4z=0
5)z2-4=0
Answers
A20-3a+2=0
22-3a=0
-3a=-22
a=22/3
A= 7,3
It is known that 2x-3/x = x + 1 What is the value of x^2 -x + 3
Answers
The value of the equation x² - x + 3 is 37/9.
We have,
We can start by multiplying both sides of the equation by x:
2x - 3/x = x + 1
2x - 3 = x^2 + x
Rearranging and simplifying, we get:
x^2 - x + 3 = (2x - 3) + x^2
x^2 - x + 3 = x^2 + 2x - 3
-x + 3 = 2x - 3
5 = 3x
x = 5/3
Now we can substitute x into the equation x^2 - x + 3:
x^2 - x + 3 = (5/3)^2 - 5/3 + 3
x^2 - x + 3 = 25/9 - 15/9 + 27/9
x^2 - x + 3 = 37/9
Therefore,
The value of x² - x + 3 is 37/9.
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y = 1/3x - 4
2x - 6y = -24
solve by elimination or substitution
Answers
A car is traveling at a speed of 75 miles per hour. What is the car's speed in miles per minute? How many miles will the car travel in 20 minutes? Do not round your answers.
Answers
Answer:
1.25MilesPerMinute
Step-by-step explanation:
Sarah met three members of the Harris family and they all had red hair. She made a conjecture that everyone in the Harris family has red hair. Choose a counterexample that prove this conjecture false
Answers
Answer:
3. Sarah met Charlie Harris, the grandson of Ed and June, and he had a blond hair
Step-by-step explanation:
2 diamond rings and 4 silver rings cost $1300. A diamond ring and a silver ring cost $510. How much is a diamond ring?
Answers
Answer:
370
Step-by-step explanation:
510 times 2 is 1020 - cost for 2 diamond and 2 silver
1300-1020 is 280 - cost for remaining 2 silver
280 divided by 2 = 140 - cost for each silver
510-140 is cost for 1 dimond = 370
which of the following verified that ABC is similar to DEF
Answers
Answer:
D
Step-by-step explanation:
The two triangles are similar by the property side angle side.
What is the similarity?
If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.
Here in the triangles, the angle is equal and the sides are dilated by factor two from 18 to 9. It means that the sides are similar to each other and the angle is the same.
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