The quadrilateral given is Parallelogram.
What are Quadrilaterals?Quadrilaterals are four sided polygons which also have four vertices and four angles.
Sum of all the interior angles of a quadrilateral is 360 degrees.
(a) The quadrilateral is sketched as shown in the graph below.
(b) We have to write the equation of four lines AB, BC, CD and AD in the form y = mx + b. m is slope and b is intercept along Y axis.
Coordinates of vertices are A(-5, 2), B(-2, 6), C(3, 5) and D(0,1).
Equation of line AB :
Slope = (6 - 2) / (-2 - -5) = 4/3
Equation in point slope form is
(y - 2) = 4/3(x - -5)
y - 2 = 4/3 x + 20/3
y = 4/3 x + 26/3
Equation of line BC :
Slope = (5 - 6) / (3 - -2) = -1/5
Equation in point slope form is,
(y - 6) = -1/5 (x - -2)
y - 6 = -1/5 x - 2/5
y = -1/5 x + 28/5
Equation of line CD :
Slope = (1 - 5) / (0 - 3) = -4/-3 = 4/3
Equation in point slope form is,
y - 5 = 4/3 (x - 3)
y - 5 = 4/3 x - 4
y = 4/3x + 1
Equation of line AD :
Slope = (1 - 2) / (0 - -5) = -1/5
Equation in point slope form is,
y - 1 = -1/5 (x - 0)
y - 1 = -1/5 x
y = -1/5 x + 1
(c) Opposite sides are having the same slope.
From the sketch, opposite sides are equal.
So quadrilateral is either parallelogram or rectangle.
But if the figure is rectangle, adjacent sides are perpendicular and therefore the product of their slope is -1.
But it is not the case here.
So it is parallelogram.
Hence the given figure is a parallelogram.
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Prove the following boolean equations using the axioms and theorems of boolean algebra. Write down explicitly which theorems are used in each step of the derivation. a) BACD + ABDC + ACBD + ADBC + DCBA = BCD + ACD + ABD + ABC b) YQX + XQYŽ + XZQ7 = (Y(X + 2) + XZ)Q
The proofs of both the conditions are given below: we used the distributive property, identity x(x+y) = xy + x^2, identity x + xy = x(1 + y) and identity x + xy = x(1 + y) to prove the given equation.
a) BACD + ABDC + ACBD + ADBC + DCBA = BCD + ACD + ABD + ABC
Using the distributive property:
BACD + ABDC + ACBD + ADBC + DCBA = (B + A)(C + D)(A + B + C + D)
Using the identity x(x+y) = xy + x^2:
BACD + ABDC + ACBD + ADBC + DCBA = BCD + ACD + ABD + ABC
b) YQX + XQYŽ + XZQ7 = (Y(X + 2) + XZ)Q
Using the distributive property:
YQX + XQYŽ + XZQ7 = YQ(X + Z) + XQ(Y + Z)
Using the identity x + xy = x(1 + y):
YQX + XQYŽ + XZQ7 = YQ(X + Z) + XQ(Y + Z) = (YQ + XQ)(X + Y + Z)
Using the identity x + xy = x(1 + y):
YQX + XQYŽ + XZQ7 = (YQ + XQ)(X + Y + Z) = (YQ + XQ)(X + (Y + Z))
Using the distributive property:
YQX + XQYŽ + XZQ7 = (YQ + XQ)(X + (Y + Z)) = (YQX + XQY + YQZ + XQZ) = (Y(X + Q) + XQ)(Y + Z)
Finally, using the identity x + xy = x(1 + y):
YQX + XQYŽ + XZQ7 = (Y(X + Q) + XQ)(Y + Z) = (Y(X + Q) + XZ)Q
In this derivation, we used the distributive property, identity x(x+y) = xy + x^2, identity x + xy = x(1 + y) and identity x + xy = x(1 + y) to prove the given equation.
Therefore, we used the distributive property, identity x(x+y) = xy + x^2, identity x + xy = x(1 + y) and identity x + xy = x(1 + y) to prove the given equation.
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The graph models the temperature, in degrees Fahrenheit, of a cup of hot water placed in a refrigerator.
Based on the graph, what was the original temperature, in degrees Fahrenheit, of the cup of hot water?
Since the graph of a straight line passing through the origin represents two variables in direct variation, with the slope as the coefficient of proportionality,
what was the original temperature, in degrees Fahrenheit, of the cup of hot water?
The initial temperature of a cup of hot coffee is T(0)=175∘F T ( 0 ) = 175 ∘ F . The cup is placed in a room temperature of T∞=70∘F T ∞ = 70 ∘ F . The temperature T(t) of the coffee at time t can be approximated by Newton's law of cooling as dTdt+kT(t)=kT(∞) d T d t + k T ( t ) = k T ( ∞ ) where k is a constant.Definition and conversion. Historically, on the Fahrenheit scale the freezing point of water was 32 °F, and the boiling point was 212 °F (at standard atmospheric pressure). This put the boiling and freezing points of water 180 degrees apart.OSHA recommends you keep your water heater at 140 degrees Fahrenheit so your risk of being exposed to microorganisms and Legionella is reduced. Various recommendations for safe water temperature is not only varies from safety agency to health agency.To learn more about temperature refers to:
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Which of the following did you include in your explanation? Check all of the boxes that apply. There is a unique solution. The solution is x = 0, y = 0, and z = 0. The system intersects at one point. The system is independent and consistent.
This two options I am going to include in my explanation
a) There is a unique solution.
d) The system is independent and consistent.
The given system of equations can be represented as a matrix equation [A|B] where A is the coefficient matrix and B is the constant matrix.
|1 1 1 | 0 |
|2 -1 3 | 0 |
|3 2 -1 | 0 |
The above system of equation can be written as AX=B, where X=[x,y,z] and A,B are as above.
We can check the rank of A and [A|B], if they are equal then the system is consistent and has a unique solution.
Using Gaussian elimination method, it can be observed that the rank of A and [A|B] both are 3, which means the system is consistent and has a unique solution.
Thus the given system of equations is consistent and has a unique solution.
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The Complete Question is -
Consider the following system of equations:
x + y + z = 0
2x - y + 3z = 0
3x + 2y - z = 0
Which of the following statements are true about this system of equations?
a) There is a unique solution.
b) The solution is x = 0, y = 0, and z = 0.
c) The system intersects at one point.
d) The system is independent and consistent.
Please check all of the box that apply.
(HELP!)
What are the leading coefficient and degree of the polynomial?
-23+3u+23u8
Leading coefficient:
Degree:
Leading coefficient: 23
Degree: 8 (The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the highest power of the variable "u" is 8, so the degree of the polynomial is 8.)
Answer:
i) 23
ii) 8
Step-by-step explanation:
i) leading coefficient:
23
ii) Degree
The degree of the polynomial is the highest power in the polynomial.
So,
degree of polynomial=8
The Parkers are getting a new pet. Alan wants a cat, but his sister Jessica wants a dog. Both want a fair method to determine who gets to choose the new pet. Alan devised a method using the given spinner. They will spin the arrow twice and record the outcomes. If the product of the outcomes is even, Alan gets to choose the new pet. If the product of the outcomes is odd, Jessica gets to choose the new pet. Determine if the method is fair. If it is not, how can it be adjusted to make it fair?
A. The method is not fair. This can be resolved by using the sum of the two outcomes instead of the product.
B. The method is not fair. This can be resolved by using the same method with a spinner with only two same-sized sections instead of four.
C. The method is fair.
D. The method is not fair. This can be resolved by finding the product of the outcomes of three spins instead of two.
The method proposed is not fair, it can be adjusted by giving each sibling equal chance of winning.
What is algebra ?
Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It includes the study of operations such as addition, subtraction, multiplication, division, and the extraction of roots, as well as the properties of operations such as commutativity, associativity, and distributivity.
The method proposed by Alan is not fair because it does not take into account the probability of each outcome. The product of the outcomes being even or odd does not guarantee an equal probability of winning for both siblings. To make it fair, each sibling should have an equal chance of winning. A fair method could be to have the arrow spun once, and the sibling whose number is spun gets to choose the new pet. Another fair method could be to have a coin flipped, and the sibling whose side of the coin is facing up gets to choose the new pet.
So , The method proposed is not fair, it can be adjusted by giving each sibling equal chance of winning.
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Unit 2 Lesson 12 Math cool down 12.4 is the point on the line?
Answer:
please open the following image for the answer
Find the length of the arc of a sector of a circle whose angle at the centre is 120° and area of the sector is 462 cm².
The area of the sector is 113.14 square cm.
Find length and area of a sector?Step1:
Given, central angle, θ = 120°
Radius of circle, r = 21 cm
We have to find the area of a sector of the circle.
Area of sector = πr²θ/360°
= π(21)²(120°)/360°
= π(21)²(1/3)
= (22/7)(21)(21)(1/3)
= (22/7)(21)(7)
= (22)(21)
= 462 square cm.
Step2:
Therefore, the area of the sector is 462 square cm.
the area of a sector of circle of radius 12 cm and central angle 90°.
central angle, θ = 90°
Radius of circle, r = 12 cm
We have to find the area of a sector of the circle.
Area of sector = πr²θ/360°
= π(12)²(90°/360°)
= (22/7)(12)(12)(1/4)
= (11/7)(6)(12)
= 113.14 square cm
Therefore, the area of the sector is 113.14 square cm.
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the length l (in centimeters) of a scalloped hammerhead shark can be modeled by the function l = 266-219e -0.05t where t is the age (in years) of
the shark. how old is a shark that is 175 centimeters long? round your answer to the nearest tenth
With the help of equations we can say that the shark is 18 years old.
What are 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.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value
To determine the value A statement is not an equation if it has no "equal to" sign.
A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.
Hence, the shark is 18 years old.
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A polling agency is investigating the voter support for a ballot measure in an upcoming city election. The agency will select a random sample of 500 voters from one region, Region A, of the city. Assume that the population proportion of voters who would support the ballot measure in Region A is 0.47. The polling agency will take another sample from a different region, Region B, of the city. The agency plans to select a random sample of 400 voters. Assume that the population proportion of voters who would support the ballot measure in Region B is 0.51.
b. What is the probability that the two sample proportions will differ by more than 0.05?
As per the concept of the normal distribution and the central limit theorem, the probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50.
The term normal distribution is defined as a symmetrical plot of data around its mean value, where the width of the curve is defined by the standard deviation.
Here we have given that agency will select a random sample of 500 voters from one region, Region A, of the city and here we also know that The proportion is of 0.47.
Then the mean and the standard deviation are 0.47 and 0.0223 respectively.
Here the probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50 is 1 subtracted by the p-value of Z when X = 0.5 is calculated as,
=> Z = (0.5 - 0.47) / 0.0223
=> Z = 1.34
Then by using the Z table we have identified the value of P as 0.9099.
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Can someone help me with this?
The formula for the area of a trapezoid is A = 1/2 h(b₁ + b₂), and where h is its height and b₁ and b₂ are the lengths of each base. Rewrite the area formula to solve for the height
are the lengths of each base.
Answer:
i think its A=12BH+12BiH
------------------------------------
Suppose that a point (x, y) is chosen from the unit square S = [0,1]×[0,1] using the uniform probability law — the probability that (x, y) is in a subset A of S is equal to the area of A:
P ((x, y) ∈ A) = area(A) for all A ⊂ S.
(a)What is the probability that x + y <1/3 ?
(b)What is the probability that x + y <3/2 ?
(c)Find an algebraic expression F(u) for
F(u) = P (x + y ≤ u).
The probability that x + y <1/3 is 1/18, the probability that x + y < 3/2 is 0.875 and the algebraic expression for F(u) is: F(u) = 0, if u < 0; F(u) = 0.5u^2, if 0 <= u <= 1; F(u) = 1 - 0.5(2 - u)^2, if 1< u < 2; F(u) = 1, if u >= 2.
(a) The set of points (x,y) in the unit square S for which x+y < 1/3 is a triangle with vertices at (0,0), (1/3,0), and (0,1/3).
The area of this triangle is
0.5(1/3)^2 = 1/18
Therefore, the probability that a point (x,y) chosen from the unit square using the uniform probability law is in this triangle is 1/9.
(b) The set of points (x,y) in the unit square S for which x+y < 3/2 is a polygon with vertices at (0, 0), (1, 0), (1, 0.5), (0.5, 1) and (0, 1) as S = [0,1]×[0,1] refer figure for clarity.
The area is
1*1 - 0.5*0.5²
= 1 - 0.125
= 0.875
Therefore, the probability that a point (x,y) chosen from the unit square using the uniform probability law is in this triangle is 0.875
(c) To find an algebraic expression for F(u), we need to consider different cases for the value of u:
if u < 0, then the set of points (x,y) for which x+y <= u is empty, so F(u) = 0
if 0 <= u < 1, then the set of points (x,y) for which x+y <= u is a triangle with vertices at (0,0), (u,0), and (0,u). The area of this triangle is u^2, so
F(u) = 0.5u^2
if 1 <= u < 2, then the set of points (x,y) for which x+y <= u is a polygon with vertices at (0,0), (1,0) (1, u-1), (u-1, 1) and (0, 1). The area can be obtained by subtracting the area of triangle with vertices (1, u-1), (u-1, 1) and (1, 1), from area of square, that is 1 sq units.
F(u) = 1 - 0.5(2 - u)²
if u >= 1, then the set of points (x,y) for which x+y <= u is the entire unit square, so
F(u) = 1.
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Is infinity 1 0 or undefined?
1/0 is undefined but not infinity.
In mathematics, expressions like 1/0 are undefined. But the limit of the expression 1/x as x tends to zero is infinity.
i.e limx→0 1/x = infinity
Similarly, expressions like 0/0 are undefined. But the limit of some expressions may take such forms when the variable takes a certain value and these are called indeterminate. limit tends to some value of x varies with the expression so as there is limit of some value i.e x but not a particular limit 0f 1/x as x tends to zero is infinity. But 1/0 is not infinity and 0/0 is not indeterminate, since division by zero is not defined.
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The complete question is:
Is 1/0 infinty or undefined?
Check each of the components below that you included in your response. The standard deviation will decrease when the outlier is removed. Standard deviation represents the spread of data from the mean. Removing a high-value outlier decreases the spread of data from the mean. Removing a low-value outlier decreases the spread of data from the mean. In both cases the standard deviation decreases.
To put it simply, any outlier with a high or low value has the same impact on the data set. The standard deviation goes down when the outlier is taken out.
What is outlier?Outliers are data points that deviate from the distribution's typical pattern. a value that is "outside" of the record's typical range (either significantly lower or substantially greater).
The standard deviation increases when the outlier's value is higher than the average of the data, compared to when it doesn't exist. When the outlier is eliminated, the mean decreases if the outlier was lower than the majority of the data, and the standard deviation is once more higher than it would be without the outlier. What makes it different is that, as opposed to a fall in the mean, the removal of the outlier would cause an increase.
To put it simply, any outlier with a high or low value has the same impact on the data set. The standard deviation goes down when the outlier is taken out.
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find 35% of 230
give simple working out please :)
Answer:
Step-by-step explanation:
35% of 230 can be found by first converting 35% to a decimal. To do this, divide 35 by 100.
35/100 = 0.35
Next, multiply the decimal by the total number you want to find the percentage of, which is 230 in this case.
0.35 * 230 = 80.5
So 35% of 230 is 80.5.
Fi nd the height of 20 peron of your belonging collect data. Find mean, median andmode uing the data
The mean, median, and mode of the heights of 20 people belonging to the same group were found to be 160.95 cm, 160 cm, and 160 cm respectively.
Mean:
Add all the heights together:
160 + 160 + 170 + 180 + 160 + 160 + 175 + 170 + 160 + 160 + 160 + 160 + 160 + 160 + 160 + 175 + 160 + 160 + 170 + 160 = 2605
Divide the sum by the number of data points (20):
2605 / 20 = 160.95
Median:
Arrange the data in numerical order:
160, 160, 160, 160, 160, 160, 160, 160, 160, 160, 170, 170, 175, 175, 180
The median is the middle value, which is 160.
Mode:
The mode is the most common value, which is 160.
The mean, median, and mode of the heights of 20 people belonging to the same group were calculated by adding all the heights together and dividing the sum by the number of data points (20). The mean was found to be 160.95 cm. The data was then arranged in numerical order and the median was found to be the middle value, which was 160 cm. Lastly, the mode was determined to be the most common value, which was also 160 cm.
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Question 1
Divide £1530 in the ratio 5 : 12
kayla did this problem in class determine where kayla made an error
-4(x+2)=23+x
Solve for d: 1/4(d-2)=6
The value of d = 26.
What are Equations:A mathematical statement that maintains the equality of two expressions that are joined by the equals sign "=" is known mathematically as an equation.
A mathematical equation can be solved by adding or subtracting the same number on both sides or multiplying or dividing the same number into both sides.
Here we have
1/4(d-2) = 6
Solve the above equation as follows
=> 1/4(d-2) = 6
Multiply by the same number on both sides
=> 4[ 1/4 (d - 2) ] = 4 × 6
=> (d - 2) = 24
Add '2' on both sides
=> (d - 2) + 2 = 24 + 2
=> d = 26
Therefore,
The value of d = 26
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One of the roots of the equation 2x^2-bx-20=0 is -2.5. Find the other root.
Answer: If one of the roots of the equation 2x^2-bx-20=0 is -2.5, then by Vieta's Formulas, the other root is x = (20 + b)/4.
Step-by-step explanation:
Answer:
x=4
Step-by-step explanation:
Given equation: 2x^2 - bx - 20 = 0
We are also given one of the solutions, which is -2.5.
We can start off by substituting -2.5 in place of x, in the given equation.
This is what it will look like:
2 * (2.5) ^2 - b (-2.5) - 20 = 0
After simplifying, the equation will now look like this:
12.5 + 2.5b - 20 = 0
Now, move all of the similar terms to one side of the equation:
2.5b = 20 - 12.5, which is basically 2.5b = 7.5
Divide 2.5 from both sides of the equation:b = 7.5/2.5, which is b = 3
Now that we know what the value of "b" is, let's go back to the given equation (2x ^2 - bx - 20 = 0), and substitute "3" in place of "b".
It will look like this:
2x^2 - 3x - 20 = 0
We can now apply the Quadratic formula. The formula looks like this:
(-b ± √b^2 -4ac)
2a
Substitute the values from the new equation into the formula:
3 ± √9 + 160
4
Simplify that:
3 ± 13
4
You should now have two solutions:
x1 = 3 + 13, which is x1 = 16/4 = 4
4
x2 = 3 - 13 , which is x2=-10/4, = -2.5
4
Now, the root that was given to us at the start of the problem was -2.5, so the other solution is 4, which we just solved for.
I hope this helps!!
How many right triangles have integer leg lengths a and b and a hypotenuse of length b 1, where b < 100
The possible number of the right triangle is 6. Hence option A is the correct option.
What is the right triangle?
A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly known as a rectangle triangle, is a triangle with one right angle, i.e. two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.
Given that △ABC is a right triangle.
The legs of the △ABC are a and b which are integers. The hypotenuse is b+1. Since b is an integer thus b+1 is an integer.
Pythagorean theorem:
The sum of the square of the legs of a right triangle is the square of the hypotenuse.
According to Pythagorean theorem,
a² + b² = (b+1)²
Applying the algebraic formula (a+b)² = a² + b² + 2ab
a² + b² = b² + 2b +1
Cancel out b² from both sides:
a² = 2b + 1
2b is always a positive number since 2 is multiplied with b. Thus 2b+1 is an odd number.
Since a² = 2b + 1, thus a² is an odd number.
The square of an odd number is an odd number. Thus a is an odd number.
Again given that,
b<100
2b < 200
2b + 1< 201
Putting 2b + 1 = a²:
a² < 201
Now putting a=1 in a² < 201:
1² < 201 (true)
Now putting a=3 in a² < 201:
3² < 201 (true)
Now putting a=5 in a² < 201:
5² < 201 (true)
Now putting a=7 in a² < 201:
7² < 201 (true)
Now putting a=9 in a² < 201:
9² < 201 (true)
Now putting a=11 in a² < 201:
11² < 201 (true)
Now putting a=13 in a² < 201:
13² < 201 (true)
Now putting a=15 in a² < 201:
15² < 201 (false)
If a = 1, 2b+1 = 1 which implies b = 0. The length of a side of a triangle is never zero. Therefore a ≠ 1.
Thus the possible values of a are 3,5,7,9,11,13.
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Find the least common denominator of these fractions.
38 518
The least common denominator of the given fractions, can be found to be 72.
How to find the least common denominator ?The least common denominator of two or more fractions, is the least common multiple of the denominators of the fractions.
With the given fractions of 3 / 8 and 5 / 18 therefore, the least common denominator would be the least common multiple of 8 and 18.
The least common multiple of 8 and 18 is the value of 72 so this must be the least common denominator for the fractions.
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the bonneville salt flats, located in utah near the border with nevada, not far from interstate i80, cover an area of over 30000 acres. a race car driver on the flats first heads north for 4.69 km, then makes a sharp turn and heads southwest for 2.75 km, then makes another turn and heads east for 3.89 km. how far is she from where she started?
A race car driver is 3.79 km away from where she started.
Assume that a race car driver turns southwest, at an angle of 45 degrees.
Also she turns East making another 45 degree angle.
So, we get a right triangle.
Let ABC be right triangle with A = 90°, B = 45° and C = 45°
For right triangle ABC, a = 2.75km, b = y km and c = x km (the distance she has traveled east before crossing her northern path)
Consider the sine of angle B
sin(B) = Opposite side of angle B / Hypotenuse
sin(45) = x / 2.75
x = 1.94
sin(C) = Opposite side of angle C / Hypotenuse
sin(45) = y/2.75
y = 1.94
So, the distance to north before paths crossed would be,
N = 4.69 - y
N = 3.31
And the distance after she passed her northern path.
E = 3.89 - x
E = 1.85
Let m be the distance from Starting Point to End Point.
Using Pythagoras theorem,
m² = N² + E²
m² = (3.31)² + (1.85)²
m = 3.79 km
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a four-term sequence is formed by adding each term of a four-term arithmetic sequence of positive integers to the corresponding term of a four-term geometric sequence of positive integers. the first three terms of the resulting four-term sequence are 57, 60, and 91. what is the fourth term of this sequence?
The fourth term of the resulting four-term sequence is 206.
Let the four terms of the arithmetic sequence be a a+d, a+2d, and a+3d (where d is common difference)
Let the four terms of the geometric sequence be b, br, br^2, and br^3 (where r is the common ratio)
An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is always the same. The difference is called the common difference.
The resulting four-term sequence is a+b, a+d+br, a+2d+br^2, a+3d+br^3
Given that the first three terms of the resulting four-term sequence are 57, 60, and 91, we can set up the following equations:
a + b = 57
a + d + br = 60
a + 2d + br^2 = 91
By substituting the first equation into the second and third equations we get:
d + b(r-1) = 60 - 57 = 3
2d + b(r-1)^2 = 91 - 57 = 34
By substituting the first equation and the second equation into the third one we get:
2(3) + b(r-1)^2 = 34
6+b(r-1)^2 = 34
b(r-1)^2 = 28
Note that either b=28 or b=7. We proceed with casework:
If b=28, then r=2,a=29, and d=25.The arithmetic sequence is 29,4,-21,-46, arriving at a contradiction.
If b=7, then r=3,a=50, and d=-11.The arithmetic sequence is 50,39,28,17, and the geometric sequence is 7,21,63,189. This case is valid.
Therefore, The fourth term of the resulting four-term sequence is [tex]a+3d^{2}+br^{3}= 17 +189 =206[/tex].
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Which of the following notations correctly describe the end behavior of the polynomial graphed below
The notations correctly describe the end behavior of the polynomial graphed is,
x → -∞ ⇒ f(x) → -∞
x → ∞ ⇒ f(x) → -∞
What is end behavior of polynomial?
The polynomial function's leading term can be used to determine the end behavior. The behavior of the leading term will dominate the graph because it has the highest power, which means it will grow significantly faster than the other terms as x gets very large or very small.
From the graph we know that the vertex of this parabola is V(0, 8).
This is a maximum y-value. We also know that the parabola opens downward, so the leading coefficient is negative.
Given that the function is even and the leading coefficient is negative, it follows that the graph falls to the left and right.
In a mathematical language this is:
x → -∞ ⇒ f(x) → -∞
x → ∞ ⇒ f(x) → -∞
Hence, the notations correctly describe the end behavior of the polynomial graphed is,
x → -∞ ⇒ f(x) → -∞
x → ∞ ⇒ f(x) → -∞
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The price of an item has been reduced by 95%. The original price was $75.
Use the ALEKS calculator to find the price of the item now.
sin^2A.cos2B- sin^2B.cos2A= cos^2B-cos^2A
show in step by step explanation
Answer: hoped this help. bye.:)
A straw is placed inside a rectangular box that is 10 inches by 3 inches by 5 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw
The length of the straw is equal to the length of the space diagonal of rectangular box, that is 11.6 inches.
The length of the straw is equal to the space diagonal of the rectangular box. Space diagonals are three-dimensional diagonals.
If the length of the sides of the box is a, b, and c, then the space diagonal can be computed by applying the Pythagorean Theorem.
D = √(a² + b² + c²)
Substitute the following dimensions:
a = 10 inches
b = 3 inches
c = 5 inches
Then,
D = √(10² + 3² + 5²)
D = √(100 + 9 + 25)
D = √134 = 11.6 inches
Hence, the length of the straw is 11.6 inches.
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PLSSS HELPPP!!! WILL GIVE BRAINLIEST!!
Answer:
You cut the question out so it is impossible to tell but i can guess that
W is the midpoint or something, so WR = 136.8/2 = 68.4
This is just a guess, i can't tell properly as i don't know the question.
To obtain a retail price, a dress shop adds $20 to
the wholesale cost x of every dress. when the shop
has a sale, every dress is sold for 75% of the retail
price. if f(x) = x + 20 and g(x) = 0.75x, find [gf](x)
to describe this situation.
In this situation, the wholesale cost x of every dress is first increased by $20 to obtain the retail price. This is represented by the function f(x) = x + 20.
How is this calculated?Then, during a sale, every dress is sold for 75% of the retail price. This is represented by the function g(x) = 0.75x.
To find the composite function gf that describes this situation, we need to substitute f(x) into g(x) and simplify.
gf = g(f(x)) = g(x + 20) = 0.75(x + 20) = 0.75x + 0.75(20) = 0.75x + 15
Therefore, gf = 0.75x + 15 describes the situation where the wholesale cost x of every dress is first increased by $20 to obtain the retail price, and then during a sale, every dress is sold for 75% of the retail price. So, the final cost of the dress is (0.75x + 15)
So, the composite function gf = 0.75x + 15, describes the situation where the shop adds $20 to the wholesale cost, and then sells it for 75% of the retail price.
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The graph shows the volume of water in a sink x minutes after the faucet is turned on.
8
9
Volume (gal)
O
0
2
Water in Sink
4
Time (min)
6 8
a) Find the slope of the line.
b) What does the slope of the line mean? Explain.
a) The slope of the line is given as follows: 0.5.
b) The meaning of the slope is that the volume increases by 0.5 gallons per minute.
What is a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For which the parameters are given as follows:
m is the slope, representing the rate of change of the output variable y relative to the input variable x.b is the intercept, representing the value of y when x = 0.From the graph, when x increases by 8, y increases by 4, hence the slope m is obtained as follows:
m = 4/8 = 0.5.
As x is the time in minutes and y is the volume in gallons, the meaning of the slope is that the volume increases by 0.5 gallons per minute.
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