For Part 1 of 2 (a): The exact distance between the points (2,73) and (-22,3) is 74.
For Part 2 of 2 (b): The midpoint of the line segment whose endpoints are the given points is (−10,38).
(a) The exact distance between the points is found using the distance formula:
d = √[(x2 - x1)² + (y2 - y1)²]
Where (x1, y1) and (x2, y2) are the coordinates of the given points. Plugging in the values from the given points:
d = √[(-22 - 2)² + (3 - 73)²]
Simplifying:
d = √[(-24)² + (-70)²]
d = √[576 + 4900]
d = √[5476]
d = 74
Therefore, the exact distance between the points is 74.
(b) The midpoint of the line segment whose endpoints are the given points is found using the midpoint formula:
M = [(x1 + x2)/2, (y1 + y2)/2]
Where (x1, y1) and (x2, y2) are the coordinates of the given points. Plugging in the values from the given points:
M = [(2 + (-22))/2, (73 + 3)/2]
Simplifying:
M = [(-20)/2, (76)/2]
M = [-10, 38]
Therefore, the midpoint is (-10, 38).
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Apply the Empirical RuleA 3-column table has 1 row. The first column is labeled Age with entry 7 years. The second column is labeled Mean with entry 49 inches. The third column is labeled Standard Deviation with entry 2 inches. According to the empirical rule, 68% of 7-year-old children are between inches and inches tall.
The empirical norm therefore states that 68% of 7-year-old kids are between 47 and 51 inches tall.
What does a table column mean?A column in a table is a collection of cells which are arranged vertically. A field, like the received field, is a sort of element that contains only one item of data. A column in a table usually contains the values for just a single field.
The empirical rule states that in a normal distribution, 68% of the data fall within one average standard deviation. In this instance, the mean difference is 2 inches, while the average height of 7-year-old kids is 49 inches.
We must identify the range among heights that is within one average standard deviation in order to apply the scientific rule. To accomplish this, we can add and subtract the standard variance from the median as follows:
Mean ± (Standard Deviation) = 49 ± 2
As a result, the height range which falls within the standard deviation from the average is between 47 and 51 inches.
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3/4d-11=1/4d-6 1/2 please help!!!
The solution for d in the one-variable equation as required to be determined is; d = 9.
What is the value of d in the given equation?As evident in the task content; the given equation is;
3/4d - 11 = 1/4d - 6½
¾d - 11 = ¼d - 13/2
Therefore, we have that;
¾d - ¼d = 11 - 13/2
½d = 9/2
d = 9
Ultimately, the value of d which holds true for the given equation is; 9.
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On a certain route, an airline carries 9000 passengers per month, each paying $150. A market survey indicates that for each$1 decrease in the ticket price, the airline will gain 50 passengers. Express the monthly revenue for the route, R, as a function of the ticket price, x.
The monthly revenue for the route, R, as a function of the ticket price, x, can be expressed as R(x) = (9000 + 50(150 - x))x.
The airline carries 9000 passengers per month, and each pays $150, so the initial monthly revenue is R(150) = 9000 x $150 = $1,350,000.
If the ticket price is decreased by $1, the airline will gain 50 passengers, so the new monthly revenue can be calculated by adding the revenue gained from these additional passengers to the initial revenue, and subtracting the revenue lost from the decrease in ticket price. The revenue gained from the additional passengers is 50(x - $150), since each passenger pays the new ticket price x instead of $150. The revenue lost from the decrease in ticket price is 9000($150 - x), since each of the 9000 passengers pays $150 - x instead of the initial price of $150.
Putting these together, we get:
[tex]R(x) = R(150) + 50(x - $150) - 9000($150 - x)[/tex]
R(x) = (9000 x $150) + 50x - 50($150) - 9000($150) + 9000x[tex]R(x) = R(150) + 50(x - $150) - 9000($150 - x)[/tex]
[tex]R(x) = (9000 + 50(150 - x))x[/tex]
Thus, the monthly revenue for the route, R, as a function of the ticket price, x, is [tex]R(x) = (9000 + 50(150 - x))x[/tex]
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A group of friends wants to go to the amusement park. They have no more than $425 to spend on parking and admission. Parking is $14.75, and tickets cost $18.75 per person, including tax. Which inequality can be used to determine x, the maximum number of people who can go to the amusement park? 425 18.75(x + 14.75), 425 14.75 +18.75x 4252 14.75 +18.75, 425 18.75(x + 14.75)
Answer:
14.75 + 18.75x ≤ 425
Step-by-step explanation:
Total amount they have is $425
Parking for the entire group = $14.75
If x is the number of persons in the group, the cost of x tickets at $18.75 per head
= 18.75x
The total cost incurred
= Parking Cost + Ticket Cost
= 14.75 + 18.75x
This has to be less than equal to 425
So the inequality is
14.75 + 18.75x ≤ 425
i cannot make out the given answer choices clearly, it appears the constant 425 is on the left side in each answer choice - choose the one which is closest to the given answer
The exact same experiment was conducted 15 times. How many times should the results have been similar for them to be valid?
A. 6
B. 15
C. 9
D. 8
Convert the following angles measures to degrees or radius.
Answer:
a) [tex]\frac{2\pi }{3}[/tex]
b) 330
Work:
a) To convert degrees to radians you multiply by [tex]\frac{\pi }{180}[/tex]
[tex]\frac{120}{1}[/tex] x [tex]\frac{\pi }{180}[/tex]
= [tex]\frac{6}{1}[/tex] x [tex]\frac{\pi }{9}[/tex]
= [tex]\frac{2\pi }{3}[/tex]
b) To convert radians to degrees you multiply by [tex]\frac{180}{\pi }[/tex]
[tex]\frac{11\pi }{6}[/tex] x [tex]\frac{180}{\pi }[/tex]
= [tex]\frac{11}{1}[/tex] x [tex]\frac{30}{1}[/tex]
= 330
In a direct variation, the variable k is the ?
Answer: slope of the line
Step-by-step explanation: I'm not sure if we're talking about the same thing though
Answer: The slope (stands in for m)
Step-by-step explanation:
In a direct variation, the variable m (slope) is swapped for k.
Look for a pattern in the table. Find the missing addends and sums
Looking at the table, we can see that the addends follow a pattern where each subsequent pair of addends adds up to 1/5. Specifically, the missing addend is 2/5 - 3/10, which equals 1/10. The missing sums are 1/2 and 4/10.
The addends in the table are as follows:
1/10 + 1/5 = 3/10, 1/5 + 1/5 = 2/5
3/10 + 1/5 = 1/2
We can observe that the first two pairs of addends add up to 1/5 less than the subsequent sums. This pattern indicates that the missing addend must be
1/5 - 1/10 = 1/10
which would make the third pair of addends add up to
1/2 - 1/10 = 4/10
Therefore, the missing sums are 1/2 and 4/10, respectively. This pattern can be helpful in solving similar problems where pairs of addends add up to a specific sum or difference.
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log2(9x^10/y²)
Can someone explain it step by step?
Answer:
We can use the properties of logarithms to simplify this expression:
log2(9x^10/y²) = log2(9) + log2(x^10) - log2(y²)
Now we can apply the power rule of logarithms to the second term:
log2(x^10) = 10 log2(x)
Substituting back into the original expression:
log2(9x^10/y²) = log2(9) + 10 log2(x) - log2(y²)
This is the simplified form of the expression.
2
Alice went to a toy store. She paid for 2 jigsaw
puzzles and 4 packs of cards with 3 ten dollar bills.
The price for a pack of cards is $2. She received
$4 in change.
What was the total cost of the 2 jigsaw puzzles?
A $9
B $18
C $22
D $26
Answer:
Alice paid for the 4 packs of cards with 4 x $2 = $8.
She used 3 ten dollar bills, which is 3 x $10 = $30.
Therefore, the cost of the 2 jigsaw puzzles is:
Total cost of the purchase - Cost of the packs of cards
= ($30 + $4 change) - $8
= $26
So, the total cost of the 2 jigsaw puzzles was $26.
The answer is (D) $26.
Answer:
C. $22
Step-by-step explanation:
You have $30, then you multiply 4x2=8(Price of the Cards)
next subtract the $8 from $30 (30-8)
Your final answer is 22
For every tile you draw in a game, you lose 5 points. For every tile you play, you gain 3 points. What is your score if you draw 9 tiles and play 12 tiles?
Answer:
Your score is -9.
Step-by-step explanation:
An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, the altitude cuts the base into two equal segments. The length of the altitude is 9 inches, and the length of the base is 7 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch. Thanks!!!
Answer:
26.3 inchesStep-by-step explanation:
We separate into 2 congruent triangles. Both have a base of 3.5 and a height of 9 inches. Using pythagoran theorum, we will square 9 and 3.5
81 and 12.25
Add them up and it's 93.25
[tex]\sqrt{93.25}[/tex]=9.65660395791
Now since it's isosceles, the other side will also be 9.65660395791.
9.65660395791 + 9.65660395791 + 7 =26.3132079158
You want it rounded to the nearest tenth, so 26.3
Select all the expressions that have the same value 892 ÷ 7.
answer choices
A. 8920 ÷ 80 =
B. 894 ÷10 =
C. 89.2 ÷ 0.08 =
D. 8.92 ÷ 0.8 =
E. 892 ÷ 0.008 =
Answer: if there is a none of the above answer I would choose that otherwise your best bet might be A.
cancelleddddddddddddddddddd
Answer:
Step-by-step explanation:
Using the given functions: f(x)=2x^(2)-5x-3,g(x)=x-3 and h(x)=2x+5, what is the product of (g*f)(x) ? 2x^(3)+11x^(2)+18x+9 2x^(3)-z^(2)-18x+9 2x^(3)-x^(2)-12x+9
Using the given functions, the product of (g*f)(x) is 2x³ - 11x² + 12x + 9.
A relation between a set of inputs having one output each is called a function. The product of (g*f)(x) can be found by multiplying the functions f(x) and g(x) together.
Since f(x) = 2x² - 5x - 3 and g(x) = x - 3, then the product of (g*f)(x) can be solved as follows:
(g*f)(x) = g(x)*f(x) = (x - 3)(2x² - 5x - 3)
Use the distributive property:
(g*f)(x) = 2x³ - 5x² - 3x - 6x² + 15x + 9 = 2x³ - 11x² + 12x + 9.
Therefore, the correct answer is 2x³ - 11x² + 12x + 9.
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What is the difference of the LCM and GCF of 30 and 55?
Answer:
The difference between the LCM and the GCF of 30 and 55 are that the LCM is the smallest positive integer that is divisible and the GCF is the largest positive integer that divides each of the integers.
Step-by-step explanation:
Find the present value PV of the annuity necessary to fund the withdrawal given. HINT [See Example 3.] (Assume end-of-period withdrawals and compounding at the same intervals as withdrawals. Round your answer to the nearest cent.) $500 per month for 15 years, if the annuity earns 6% per year PV = $
The present value PV of the annuity necessary to fund the withdrawal is $5,354.82, rounded to the nearest cent.
The present value of an annuity is calculated using the following formula:
PV = A[((1+i)n-1)/(i(1+i)n)]
where A = amount of each annuity payment, i = interest rate, and n = number of payments.
For this problem, A = $500, i = 6%, and n = 15 years.
Therefore, the present value of the annuity necessary to fund the withdrawal is:
PV = $500[((1+0.06)15-1)/(0.06(1+0.06)15)]
PV = $500[5.72982/0.105638]
PV = $5,354.82
Therefore, the present value PV of the annuity necessary to fund the withdrawal is $5,354.82, rounded to the nearest cent.
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The graph of f(x)=x^2 was transformed to create g(x)=2/3x^2 Mark the statement. True or False
The graph of g(x) will be wider than f(x)
Graph of g(x) will be wider than f(x) is false.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The graph of f(x)=x² was transformed to create g(x)=2/3x².
The transformation applied to f(x) to create g(x) is a vertical compression by a factor of 2/3.
This means that the graph of g(x) will be narrower than the graph of f(x), not wider.
Specifically, the parabola of g(x) will be compressed vertically towards the x-axis by a factor of 2/3, making it more pointy than the original graph of f(x).
Hence, graph of g(x) will be wider than f(x) is false.
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Karen used 186 digits to number a book from page 4 to the end. What is the number of the last page?
Answer:
Step-by-step explanation:
its 190 because you started on page 4 and you add 186
Help with my home work
An indoor soccer field can be rented for personal use. The total cost for renting the field can be found by using the equation y= 225x. The x-variable is the number of hours the field is
being rented, and the y-variable is the total cost, in dollars.
Which statement is true based on the given equation?
A) The equation shows a linear relationship, but not a proportional relationship.
B) The equation shows a linear relationship and a proportional relationship
C) The equation does not show a linear relationship or a proportional relationship
D) The equation shows a proportional relationship,but not a linear relationship.
PLS HELP!!
Answer:
The equation y=225x represents a proportional relationship between the number of hours the field is being rented and the total cost. This means that as the number of hours increases, the total cost will increase proportionally. Therefore, statement D) "The equation shows a proportional relationship, but not a linear relationship" is true based on the given equation.
Looking at the bookshelf in the library Neil notices that the number of books that he
has read is
7
of the books he did not read. If he reads one more book from the
bookshelf and puts it back this fraction becomes 1. How many books are there on
the bookshelf?
6
There are 14 books on the bookshelf as a result.
How was the number of books on the shelf determined?Assume that there are x total books on the bookshelf. Neil has read 7 out of a total of 7 + (x-7) = x-0 books, which means that he has read 7/14 of the books, according to the problem. This is reduced to 1/2.
Now that he has read 8 out of 15 books, his percentage of books read will be 8/15 if he reads one more (the original 7 books he read plus the one he read now). This implies:
8/15 = 8/(x+1)
In order to find x, we can cross-multiply:
8(x+1) = 15(8) (8)
8x + 8 = 120
8x = 112
x = 14
There are 14 books on the bookshelf as a result.
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I bought a toy car for $7.55, a pizza for $3.75 and a pencil for $0.75. How much money did I spend altogether?
Answer:
To find the total amount of money spent on the toy car, pizza, and pencil, we simply need to add the individual prices together:
$7.55 (toy car) + $3.75 (pizza) + $0.75 (pencil) = $12.05
Therefore, you spent $12.05 altogether on the toy car, pizza, and pencil.
Solve this system of equations: y=x-4 y=6x - 10
The system of equations are solved and the value of x and y are 6/5 and -14/5 respectively
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
y = x - 4 be equation (1)
y = 6x - 10 be equation (2)
On simplifying , we get
x - 4 = 6x - 10
Subtracting x on both sides , we get
5x - 10 = -4
Adding 10 on both sides , we get
5x = 10 - 4
5x = 6
Divide by 5 on both sides , we get
x = 6/5
So , the value of y = ( 6/5 ) - 4
y = -14/5
Hence , the value of x and y are 6/5 and -14/5 respectively and the equations is solved
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Pls solve asap helpppppppp please immediately it due soon
The number of squares wide needed is 7 squares and the number that can be used to replace A is 0.1 km.
What are Grid squares:Grid squares are a way to represent two-dimensional space using a grid of squares, with each square representing a unit of length.
Grid squares are often used in various fields, such as computer graphics, geographic information systems, and mathematics, to represent and manipulate two-dimensional data.
Here we have
The table shows the distance traveled in a time period
The maximum time is shown in a table = 35 minutes
Let 1 unit = 5 minutes
Number of squares used to represent 35 minutes = 35/5 = 7
Therefore, the number of squares wide needs = 7 blocks
Given that the grid is 20 squares tall
The maximum distance in a table = 1.8 km
Let's take the total distance = 2 km
The number of squares along length = 2 km/20 = 0.1
Therefore,
The number of squares wide needed is 7 squares and the number that can be used to replace A is 0.1 km.
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What is the height (in inches) of a triangle with an area of 720
square inches and base of 32 inches?
The height (in inches) of a triangle with an area of 720 square inches and base of 32 inches is 45 inches.
The height of a triangle can be found using the formula for the area of a triangle: A = (1/2)bh, where A is the area, b is the base, and h is the height.
In this case, we are given the area (720 square inches) and the base (32 inches) and are asked to find the height.
First, we can plug in the given values into the formula:
720 = (1/2)(32)(h)
Next, we can simplify the equation by multiplying both sides by 2:
1440 = 32h
Finally, we can solve for the height by dividing both sides by 32:
h = 45 inches
Therefore, the height of the triangle is 45 inches.
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Evaluate log3 3^(2x+1)
[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{ \textit{let's use this one} }{log_a a^x = x}\qquad \qquad a^{log_a (x)}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_3(3^{2x+1})\implies 2x+1[/tex]
The equations y1 = 2x + 1 and intersect at a point. After three cycles of successive approximation, without rounding the answers, the approximate x-value of the point of intersection is
The intersection point on the graph has an approximate x-value of 1a.
Describe graphs?Making the curve that represents a function on a coordinate plane is the process of graphing a function. If the curve (or graph) represents the function, then each point on the curve will satisfy the function equation.
The line, also called the "curve," has a point at each point that fulfils the function.
The three lines are contemporaneous if they all cross at the same point.
From the second equation,
x = 8y + 19
Putting value of x,
2(8y + 19) + 3y = 0 9(8y + 19) + 5y = 17
16y + 38 + 3y = 0 72y + 171 + 5y = 17
19y = -38 77y = -154
y = -2 y = -2
You'll see that the y value for the answer is the same for the two equations. Simply evaluate the second equation now to find x. Hence, we are aware that the y-coordinate is negative two at some x number.
x = 8(-2) + 19
x = -16 + 19
x = 3
The single point that these three equations share is (3, -2).
4x - 3y = 13 eq1
-6x + 2y = -7 eq2
Use the elimination method. Multiply eq1 by eq2 and multiply eq2 by eq3.
8x - 6y = 26 eq1
-18 + 6y = -21 eq2
Adding the equations to eliminate the y terms.
-10x = 5
x = -1/2
Substituting this value of x into any of the equations to solve for the value of y.
Substituting the first equation into the second equation. In terms of x, this will translate the second equation. From that freshly created equation, find x. Once you solved for x, substitute that value of x into the first equation to solve for y.
You have a vertical line that passes all points that have the x coordinate 7 and you have a horizontal line that passes all point that have the y coordinate -5.
If you were to graph these two lines, they will be intersecting at (7, -5).
Now, draw the following lines on a coordinate system:
i) A vertical line passing through the points (3, 0).
ii) A horizontal line passing through the point (0, 6).
iii) A line passing through the points (0,0) and (1, -3).
Once you have drawn these lines, look for 3 points of intersection.
Area = (base × height) / 2
Lines that have the same slope never intersect. Put both equations in y=mx+b form where the slope is the coefficient of x.
2x + 3y = > 3y = -2x + 23
y = (-2 / 3) x + 23/3
7x + py = 8
py = -7x + 8
y = (-7 / p) x + 8/p
Set the slopes equal to each other.
-2 / 3 = -7 / p
Cross-multiply.
-2p = -21
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(a) Let E be an intermediate field of the extension K⊂F and assume that E=K(u1,…,ur)
where the ui are (some of the) roots of fεK [x]. Then F is a splitting field of f over K if and only if F is a splitting field of f over E. (b) Extend part (a) to splitting fields of arbitrary sets of polynomials.
All the roots of all the polynomials in {f1, ..., fn}.
(a) Let E be an intermediate field of the extension K⊂F and assume that E=K(u1,…,ur) where the ui are (some of the) roots of fεK [x]. Then F is a splitting field of f over K if and only if F is a splitting field of f over E.
(b) We can extend part (a) to splitting fields of arbitrary sets of polynomials by first noting that the field E must contain the coefficients of all the polynomials in the given set. This implies that for a given set of polynomials {f1, ..., fn}, the field F is a splitting field over K if and only if it is a splitting field over E, where E is the smallest field containing the coefficients of {f1, ..., fn}. In other words, F must contain all the roots of all the polynomials in {f1, ..., fn}.
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Help similar triangles
The value of x for the similar triangles is 57.5 units.
What is the value of x?The value of x is determined by applying the principle of similar triangles as shown below.
In the given diagram, we can assume the following for the similar triangles;
length 46 is congruent to length (16 + 46)
length 20 + x is congruent to length x
So we will have the following equation;
46/x = (16 + 46 ) / ( 20 + x )
46/x = ( 62 ) / ( 20 + x )
46 ( 20 + x ) = 62x
920 + 46x = 62x
920 = 16x
x = 920 / 16
x = 57.5
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