A rotation is a geometric transformation that preserves the shape and size of a figure while changing its orientation in space. It is a fundamental concept in geometry and is used in various fields, including art, design, and engineering.
A rotation of a figure can be considered as a transformation that rotates the figure around a fixed point, known as the center of rotation. During the rotation, each point of the figure moves along an arc around the center, maintaining the same distance from the center.
To perform a rotation, we specify the angle of rotation and the direction (clockwise or counterclockwise). The center of rotation remains fixed while the rest of the figure rotates around it. The resulting figure is congruent to the original figure, meaning they have the same shape and size but may be in different orientations.
Rotations are commonly described using positive angles for counterclockwise rotations and negative angles for clockwise rotations. The magnitude of the angle determines the amount of rotation. For example, a 90-degree rotation would result in the figure being turned a quarter turn counterclockwise.
In general, a rotation is a geometric transformation that keeps a figure's size and shape while reorienting it in space. It is a fundamental idea in geometry that is applied in a number of disciplines, including as engineering, design, and the arts.
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You flip a coin twice. The first flip lands tails up and the second flip also lands tails up. It is independent or dependent?
Answer:
Independent
Step-by-step explanation:
Flipping a coin is independent of each flip.
Answer:
Independent
Step-by-step explanation:
The flipping of two coins are an independent event. The reason for this is that one coin flip does not affect the outcome of the other flip. An example of a dependent event would be coat sales and weather, as cold weather would affect the amount of coats sold.
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En una ciudad se midió la temperatura a las 7:00 am y el valor fue de 15°C, luego se midió a las 3:00 pm el valor fue de 24°C. Partiendo del nivel de medición de esta variable, en qué proporción excede una temperatura de la otra, analice su respuesta.
The proportion by which the later temperature exceeds the earlier temperature is 3/5 or 3:5.
In what proportion does one temperature exceed the other?To determine the proportion by which one temperature exceeds the other, we need to calculate the difference between the two temperatures and express it as a proportion of the starting temperature.
First, calculate the temperature difference between 7:00 am and 3:00 pm:
temperature difference = 24°C - 15°C = 9°C
Now, express the temperature difference as a proportion of the starting temperature (15°C).
Proportion = Temperature difference / Starting temperature
Proportion = 9/15
Proportion = 3/5
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Question in English
In a city the temperature was measured at 7:00 am and the value was 15°C, then it was measured at 3:00 pm the value was 24°C. Starting from the level of measurement of this variable, in what proportion does one temperature exceed the other, analyze your answer.
The statement of cash flows for Baldwin shows what happens in the cash account during the year. It can be seen as a summary of the sources and uses of cash. Pleas answer which of the following is true if Baldwin issues bonds
Work out the value of 408 5
Give your answer as a decimal.
The value of 408^5 is approximately 273,539,283,056,896. This is a large number that can be accurately calculated using a calculator or computer program.
To work out the value of 408^5, we need to perform the exponentiation calculation. In this case, 408 is the base, and 5 is the exponent.
Calculating large exponentiations like this can be time-consuming and prone to error if done manually. However, with the help of a calculator or computer, we can easily find the result.
Using a calculator or computer program, we can calculate 408^5 and obtain the value. The result is a very large number:
408^5 ≈ 273,539,283,056,896
Therefore, the value of 408^5 is approximately 273,539,283,056,896.
In decimal notation, the value is written as:
273,539,283,056,896
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Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
6-3x+=x+5
5
12
Therefore, the value of x that solves the equation is 2/7, after eliminating the fractions and solving the resulting equation.
To eliminate fractions in the equation 6 - 3x + (1/2)x = x + 5, we can multiply each term by a number that will clear the denominators. In this case, the denominator is 2 in the term (1/2)x. The least common multiple (LCM) of 2 is 2 itself, so we can multiply each term by 2 to eliminate the fraction.
By multiplying each term by 2, we get:
2 * (6 - 3x) + 2 * ((1/2)x) = 2 * (x + 5)
Simplifying this expression, we have:
12 - 6x + x = 2x + 10
Now, the equation is free of fractions, and we can proceed to solve it.
Combining like terms, we have:
12 - 5x = 2x + 10
To isolate the variable terms, we can move the 2x term to the left side by subtracting 2x from both sides:
12 - 5x - 2x = 10
Simplifying further:
12 - 7x = 10
Next, we can move the constant term to the right side by subtracting 12 from both sides:
12 - 7x - 12 = 10 - 12
Simplifying again:
-7x = -2
Finally, we solve for x by dividing both sides by -7:
x = (-2) / (-7)
Simplifying the division of -2 by -7 gives us the solution:
x = 2/7
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Your firm has the option of making an investment in new software that will cost $172,395 today, but will save the company money over several years. You estimate that the software will
provide the savings shown in the following table over its 5-year life, . Should the firm make this investment if it requires a minimum annual return of 8% on all investments?
The present value of the stream of savings estimates is $ (Round to the nearest dollar)
The present value of the stream of savings estimates is approximately $200,256.
To determine whether the firm should make the investment in new software, we need to calculate the present value of the stream of savings estimates and compare it to the cost of the software.
The present value (PV) of the savings estimates can be calculated using the formula:
[tex]PV = C1/(1+r)^1 + C2/(1+r)^2 + ... + Cn/(1+r)^n[/tex]
Where C1, C2, ..., Cn represent the savings in each year, r is the minimum annual return required (8% or 0.08), and n is the number of years (5).
Given the savings estimates in the table, we have:
C1 = $35,000
C2 = $45,000
C3 = $50,000
C4 = $55,000
C5 = $60,000
Plugging these values into the present value formula and using the minimum annual return rate of 8% (0.08), we can calculate:
[tex]PV = 35000/(1+0.08)^1 + 45000/(1+0.08)^2 + 50000/(1+0.08)^3 + 55000/(1+0.08)^4 + 60000/(1+0.08)^5[/tex]
Evaluating this expression, we find that the present value of the stream of savings estimates is approximately $200,256.
Since the present value of the savings estimates is greater than the cost of the software ($172,395), the firm should make this investment. The investment is expected to provide a return greater than the minimum required annual return of 8%.
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The present value of the stream of savings estimates is $149,622.
To determine if the firm should make the investment, we need to calculate the present value of the stream of savings estimates and compare it to the initial cost of the software.
The present value (PV) of the savings estimates can be calculated using the formula:
PV = C1/(1+r)¹ + C2/(1+r)² + ... + Cn/(1+r)ⁿ
Where:
PV = Present value
C1, C2, ..., Cn = Cash flows in each period
r = Discount rate (minimum annual return)
Given the savings estimates in the table over a 5-year period and a minimum annual return of 8% (0.08), we can calculate the present value as follows:
PV = $15,000/(1+0.08)¹ + $35,000/(1+0.08)² + $50,000/(1+0.08)³ + $45,000/(1+0.08)⁴ + $40,000/(1+0.08)⁵
PV = $13,888.89 + $30,864.20 + $41,152.46 + $34,682.34 + $29,034.09
PV = $149,621.98 (rounded to the nearest dollar)
The present value of the savings is higher than the initial cost of the software ($172,395), the firm should make this investment if it requires a minimum annual return of 8% on all investments.
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please help quick
Which of the following are solutions to the quadratic equation? Check all that
apply.
The solutions to the quadratic equation 2x² + 6x - 10 = x² + 6 are -8 and 2.
What are the solutions to the quadratic equation?Given the quadratic equation in the question:
2x² + 6x - 10 = x² + 6
First, reorder the quadratic equation in standard form:
2x² + 6x - 10 = x² + 6
2x² - x² + 6x - 10 - 6 = x² - x² + 6 - 6
2x² - x² + 6x - 10 - 6 = 0
x² + 6x - 10 - 6 = 0
x² + 6x - 16 = 0
Next, factor the equation using the AC method:
( x - 2 )( x + 8 ) = 0
Equate each factor to 0 and solve for x:
( x - 2 ) = 0
x - 2 = 0
x = 2
( x + 8 ) = 0
x + 8 = 0
x = -8
Therefore, the solutions are -8 and 2.
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Place point Q on the graph to indicate an unemployment rate of 100 percent, point R to indicate full employment, and point S to indicate where the U.S. economy usually operates.
In a Production Possibility Curve (PPC) with product output Y on the vertical axis and product output X on the horizontal axis the following points are described as follows.
Explanation for PPC- Point Q represents an unemployment rate of 100 percent. It is located at the origin, where both axes intersect, indicating no product output due to complete unemployment.
- Point R signifies full employment and is located at the maximum product output on the X-axis, showing the economy's capacity when all resources are fully utilized.
- Point S indicates where the US economy typically operates, within the usual range of product output levels on the X-axis, reflecting a balanced unemployment rate that includes frictional and structural unemployment.
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Paxton invests $4850 at 7.6%/a simple interest. If she wants the money to increase to $8000, how long will she need to invest her money?
Therefore, Paxton will need to invest her money for approximately 21.62 years to increase her investment from $4850 to $8000 at a simple interest rate of 7.6% per year.
To determine how long Paxton needs to invest her money in order for it to increase to $8000, we can use the formula for simple interest:
I = P * r * t
Where:
I = Interest earned
P = Principal (initial investment)
r = Interest rate per year (expressed as a decimal)
t = Time (in years)
Given that Paxton invests $4850 at an interest rate of 7.6% per year, we have:
4850 * 0.076 * t = 8000
Simplifying the equation:
369.8t = 8000
To find t, we divide both sides of the equation by 369.8:
t ≈ 8000 / 369.8 ≈ 21.62 years
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I’ll give lots of points to help me because I need this answer
Answer:
| x | -7
---------------
x | x² | -7x
-4 | -4x | 28
x² - 11x + 28 = (x - 4)(x - 7)
35-14÷2 +8²
What’s the answer
Answer:
93
Step-by-step explanation:
Remember PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction)
35 - 12 : 2 + 8² =
35 - 6 + 64 =
93
Write the numeral in base ten. 7,001eight
The numeral 7,001 eight is equal to 3585 in base ten.
To convert the numeral 7,001 in base eight to base ten, we need to multiply each digit by the corresponding power of eight and sum them up.
Starting from the rightmost digit, we have:
[tex]1 * 8^0 = 1\\0 * 8^1 = 0\\0 * 8^2 = 0\\7 * 8^3 = 3584[/tex]
Adding these values together, we get:
1 + 0 + 0 + 3584 = 3585
Therefore, the numeral 7,001eight is equal to 3585 in base ten.
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Please help!!
The graph of function is shown
Function g is represented by the table
-1
X
9(x)
24
0
4
1
0
2
3
-#
Which statement correctly compares the two functions?
OA They have the same x-intercept and the same end behavior as x approaches
OB. They have the same
and y-intercepts
OC. They have different
and y intercepts but the same end behavior as x approaches
OD. They have the same y-intercept and the same end behavior as x approaches
Best
The x- and y-intercept values in the graph for the function f and in the table for the function g(x), indicates that the correct option is option C
C. The have different x- and y-intercepts but the same end behavior as x approaches ∞What are the x- and y-intercept of a graph of a function?The x-intercept is the point at which the y-value is 0, and the coordinates of the point is specified as the x-intercept.
The x-intercept is the point at which the x-value is 0, and the coordinates of the point is specified as the y-intercept
The question compares the x- and y-intercepts of the graph and the function in the table
The x-intercept of the function f in the graph are; (0, 3)
The y-intercept of the function f in the graph are; (4, 0)
The function g(x) in the table indicates that the x- and y-intercepts are;
The value of g(x) is 0 at the ordered pair (1, 0), therefore, the x-intercept of g(x) is (1, 0)
The value of x is 0 at the ordered pair (0, 4), therefore, the function, g(x) has a y-intercept at the point (0, 4)
Therefore, the function f and g have different intercepts, but the value in the table and the graph indicates that as x approaches infinity, the y-value, approaches -1, the correct option is therefore, option C
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URGENT
There were 35,000 hardback copies of a certain novel sold before the paperback version was issued. From the time the first paperback copy was sold until the last copy of the novel was sold, nine times as many paperback copies as hardback copies were sold. If a total of 442,000 copies of the novel were sold in all, how many paperback copies were sold?
The number of paperback copies sold is 366,300.
Let's solve the problem :
Calculate the number of hardback copies sold.
We are given that 35,000 hardback copies were sold before the paperback version was issued.
Calculate the number of paperback copies sold.
From the time the first paperback copy was sold until the last copy of the novel was sold, nine times as many paperback copies as hardback copies were sold.
Let's assume the number of hardback copies sold is H.
Therefore, the number of paperback copies sold would be 9H.
Set up the equation for the total number of copies sold.
The problem states that a total of 442,000 copies of the novel were sold in all. We can set up the equation as follows:
H + 9H + 35,000 = 442,000
Solve the equation for H.
Combining like terms, we have:
10H + 35,000 = 442,000
10H = 442,000 - 35,000
10H = 407,000
H = 40,700.
Calculate the number of paperback copies sold.
We already know that the number of paperback copies sold is 9 times the number of hardback copies sold.
Therefore, the number of paperback copies sold would be:
9H = 9 [tex]\times[/tex] 40,700 = 366,300
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CO -8 6 4 4 -3 If K= 7 then what is -K?
Answer:
8
Step-by-step explanation:
i took the test mde 100
Which expression is equivalent to 3(x+4)
The answer is:
3x + 12
Work/explanation:
To simplify this expression, we will use the distributive property:
[tex]\sf{3(x+4)}[/tex]
Distribute the 3:
[tex]\sf{3\cdot x + 3 \cdot 4}[/tex]
[tex]\sf{3x+12}[/tex]
Therefore, the answer is 3x + 12.How would I find cos?
When [tex]sin(\theta) = -0.42[/tex] and [tex]\pi < \theta < 3\pi/2[/tex], the value of [tex]cos(\theta)[/tex] is approximately 0.9071.
To find the value of cos([tex]\theta[/tex]) given[tex]sin(\theta) = -0.42[/tex] and [tex]\pi < \theta < 3\pi/2[/tex], we can use the trigonometric identity:
[tex]sin^2(\theta) + cos^2(\theta) = 1[/tex]
Since we are given sin(theta) = -0.42, we can substitute this value into the equation:
[tex](-0.42)^2 + cos^2(\theta) = 1[/tex]
Simplifying:
[tex]0.1764 + cos^2(\theta) = 1[/tex]
Subtracting 0.1764 from both sides:
[tex]cos^2(\theta) = 0.8236[/tex]
Taking the square root of both sides (since cos(theta) is positive):
[tex]cos(\theta) = \sqrt{(0.8236)} \\cos(\theta) = 0.9071[/tex]
Therefore, when [tex]sin(\theta) = -0.42[/tex] and [tex]\pi < \theta < 3\pi/2[/tex], the value of [tex]cos(\theta)[/tex]is approximately 0.9071.
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how many zero pairs are in 9+ (-16)?
There are no zero pairs in the expression.
To calculate the number of zero pairs in statement 9 + (-16), we need to clarify the expression and determine any matching positive and negative numbers.
In this respect, 9 and -16 have unlike signs. To simplify, we can rewrite the expression as 9 - 16, which is similar to adding the opposite of 16.
Here, let's look for zero pairs. A zero pair incorporate a positive and negative number that cancel each other out and occur in a sum of zero.
In the expression 9 - 16, there are no identical positive and negative numbers.
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Please awnser asap I will brainlist
The transformed matrix, after interchanging R1 and R2, is:
2 9 4 5
8 -2 1 7
1 4 -4 9
To interchange rows R1 and R2, we swap the positions of the first and second rows in the matrix. This operation can be performed by physically swapping the rows or by using the properties of matrix operations. Let's apply this row operation to the given matrix:
Original matrix:
8 -2 1 7
2 9 4 5
1 4 -4 9
Interchanging R1 and R2, we get:
2 9 4 5
8 -2 1 7
1 4 -4 9
After switching R1 and R2, the modified matrix is:
2 9 4 5
8 -2 1 7
1 4 -4 9
In the transformed matrix, the original first row (8 -2 1 7) becomes the second row, and the original second row (2 9 4 5) becomes the first row. The remaining rows (R3) remain unchanged.
Therefore, R1 and R2 are switched, and the resulting matrix is:
2 9 4 5
8 -2 1 7
1 4 -4 9
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87,959 →
round to nearest hundred
pls help help needed rn asap
Step-by-step explanation:
87,959 ==> 88,000 is the nearest hundred
The answer is:
87.96Work/explanation:
When rounding to the nearest hundredth, round to 2 decimal places (DP).
Which means we should round to 5.
5 is followed by 9, which is greater than or equal to 5. So, we drop 9 and add 1 to 5 :
87. 96
Therefore, the answer is 87.96.Question 2
No calculations are necessary to answer this question.
3/01
3/02
$1.7420 $1.7360
Date
July GBP Futures
Contract Price
O long; long
Based on the closing prices of July GBP Futures Contract over the 3-day period in March 20XX as shown above, you shou
position on 3/01 and a position on 3/02.
O long; short
O short; short
3/03
short; long
$1.7390
The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.
Find the sample variance and standard deviation. 21, 12, 6, 7, 10 O Choose the correct answer below. Fill in the answer box to complete your choice. (Type an integer or a decimal. Round to one decimal place as needed.) A. s²= = OB. ² Choose the correct answer below. Fill in the answer box to complete your choice. (Round to one decimal place as needed.). O A. OB. S = = 0= في
The sample variance (s²) is approximately 29.5 and the sample standard deviation (s) is approximately 5.4.
To find the sample variance and standard deviation,
Calculate the mean (average) of the given data set.
21 + 12 + 6 + 7 + 10 = 56
Mean = 56 / 5 = 11.2
Square the result of subtracting the mean from each data point.
(21 - 11.2)² = 96.04
(12 - 11.2)² = 0.64
(6 - 11.2)² = 27.04
(7 - 11.2)² = 17.64
(10 - 11.2)² = 1.44
Calculate the sum of the squared differences
96.04 + 0.64 + 27.04 + 17.64 + 1.44 = 142.8
Divide the sum by (n-1), where n is the number of data points (in this case, 5).
142.8 / (5-1) = 35.7
The result is the sample variance (s²).
Take the square root of the sample variance to determine the sample standard deviation (s).
s = √35.7 ≈ 5.4
Therefore, the sample variance is approximately 29.5 (rounded to one decimal place) and the sample standard deviation is approximately 5.4 (rounded to one decimal place).
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what are the three arithmetic means between 10 and 130
The three arithmetic means between 10 and 130 are 40, 70, and 100.
To find the three arithmetic means between 10 and 130, we need to calculate the common difference between consecutive terms.
The common difference (d) can be found using the formula:
d = (last term - first term) / (number of terms - 1)
In this case, the first term is 10, the last term is 130, and we need to find three arithmetic means.
d = (130 - 10) / (3 + 1) = 120 / 4 = 30
Now, we can calculate the three arithmetic means by adding the common difference to the previous term:
First arithmetic mean = 10 + 30 = 40
Second arithmetic mean = 40 + 30 = 70
Third arithmetic mean = 70 + 30 = 100
So 40, 70, and 100 are the three arithmetic means between 10 and 130.
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what is the value of m
The measure of the angle m∠RQS subtended by the arc RS at the circumference is equal to 70°
What is angle subtended by an arcThe angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.
arc RS = 2(m∠RQS)
Also arc AD = 140°
2(m∠RQS) = 140°
m∠RQS = 140°/2 {divide through by 2}
m∠RQS = 70°
Therefore, the measure of the angle m∠RQS subtended by the arc RS at the circumference is equal to 70°
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Which of the following r-values represents the strongest correlation?
A. 0.55
B. 0.65
C. 0.45
D. 0.35
Answer:
B. 0.65
Step-by-step explanation:
The closer the r value is to the number 1 or -1, the stronger the correlation.
For example:
0.99 > 0.01
-0.6 > 0.5
.43 < .76
.69 > .21
Please give brainliest and thanks!
What is the sum of the series?
∑k=36(−2k+5)
Enter your answer in the box.
Hello !
Answer:
[tex]\large \boxed{\sf \sum\limits^6_{k=3}(-2k+5)=-16}[/tex]
Step-by-step explanation:
We want to calculate the following sum :
[tex]\sf \sum\limits^6_{k=3}(-2k+5)[/tex]
Let's remember the following property :
[tex]\fbox{\begin{tabular}{1\textwidth}\star\ \underline{\sf Linearity:}\\ \sf \sum\limits^n_{k=n_0}(\alpha a_k+\beta b_k)=\alpha\sum\limits^n_{k=n_0} a_k+\beta \sum \limits^n_{k=n_0}b_k\end{tabular}}[/tex]
Now we can apply this property to our formula :
[tex]\sf \sum\limits^6_{k=3}(-2k+5)\\=-2\sf \sum\limits^6_{k=3}(k)+\sum\limits^6_{k=3}5[/tex]
Now we can calculate :
[tex]\sf \sum\limits^6_{k=3}(-2k+5)\\=-2(3+4+5+6)+(6-3+1)5\\=-2\times18+4\times 5\\=-36+20\\\boxed{\sf \sum\limits^6_{k=3}(-2k+5)=-16}[/tex]
Have a nice day ;)
Suppose you have entered a 48-mile biathlon that consists of a run and a bicycle race. During your run, your average
velocity is 5 miles per hour, and during your bicycle race, your average velocity is 23 miles per hour. You finish the race
in 6 hours. What is the distance of the run? What is the distance of the bicycle race?
[tex]\displaystyle \text{To solve this problem, let's assume the distance of the run is denoted by 'x' miles, and the distance of the bicycle race is denoted by '48 - x' miles.}[/tex]
[tex]\displaystyle \text{We can use the formula: time} = \text{distance/velocity to find the time taken for each segment of the race.}[/tex]
[tex]\displaystyle \text{For the run:}[/tex]
[tex]\displaystyle \text{Time taken} = \text{Distance/Velocity}[/tex]
[tex]\displaystyle t_1 = \frac{x}{5}[/tex]
[tex]\displaystyle \text{For the bicycle race:}[/tex]
[tex]\displaystyle \text{Time taken} = \text{Distance/Velocity}[/tex]
[tex]\displaystyle t_2 = \frac{48 - x}{23}[/tex]
[tex]\displaystyle \text{Given that the total time for the race is 6 hours, we can write the equation:}[/tex]
[tex]\displaystyle t_1 + t_2 = 6[/tex]
[tex]\displaystyle \text{Substituting the expressions for } t_1 \text{ and } t_2, \text{ we get:}[/tex]
[tex]\displaystyle \frac{x}{5} + \frac{48 - x}{23} = 6[/tex]
[tex]\displaystyle \text{To solve this equation, we can simplify it by multiplying through by the common denominator, which is 115:}[/tex]
[tex]\displaystyle 23x + 5(48 - x) = 6 \times 115[/tex]
[tex]\displaystyle \text{Simplifying further:}[/tex]
[tex]\displaystyle 23x + 240 - 5x = 690[/tex]
[tex]\displaystyle 18x = 450[/tex]
[tex]\displaystyle x = \frac{450}{18}[/tex]
[tex]\displaystyle x = 25[/tex]
[tex]\displaystyle \text{Therefore, the distance of the run is 25 miles, and the distance of the bicycle race is } 48 - 25 = 23 \text{ miles.}[/tex]
Maricella solves for x in the equation 4 x minus 2 (3 x minus 4) + 4 = negative x + 3 (x + 1) + 1. She begins by adding –4 + 4 on the left side of the equation and 1 + 1 on the right side of the equation. Which best explains why Maricella’s strategy is incorrect?
A. The multiplication that takes place while distributing comes before addition and subtraction in order of operations.
B. In order to combine like terms on one side of the equation, the inverse operation must be used.
C. When the problem is worked in the correct order, the numbers that Maricella added are not actually like terms.
D. Maricella did not combine all three constants on both sides of the equation; she combined only two.
Answer:
A. The multiplication that takes place while distributing comes before addition and subtraction in order of operations.
Step-by-step explanation:
You want to know the error that adding -4+4 on the left and 1+1 on the right represents in the solution of the equation ...
4x -2(3x -4) +4 = -x +3(x +1) +1SolutionThe correct solution procedure would be to eliminate the parentheses using the distributive property as a first step:
4x -6x +8 +4 = -x +3x +3 +1
Comparing this to Maricella's first step, we see that she ignored the step of using the distributive property to multiply the constants inside parentheses by the factor outside. The appropriate description of Maricella's mistake is ...
A. The multiplication that takes place while distributing comes before addition and subtraction in order of operations.
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Additional comment
Adding like terms would give ...
-2x +12 = 2x +4
8 = 4x . . . . . . . . . . . add 2x-4 to both sides
2 = x . . . . . . . . . . divide by 4
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Find the exact value of sec(-135)
The exact value of sec(-135°) is 1.
To find the exact value of sec(-135°), we need to use the relationship between secant and cosine functions.
The secant function is defined as the reciprocal of the cosine function:
sec(theta) = 1 / cos(theta).
We know that the cosine function has a period of 360°, which means that cos(theta) = cos(theta + 360°) for any angle theta.
In this case, we want to find sec(-135°). Since the cosine function is an even function (cos(-theta) = cos(theta)), we can rewrite sec(-135°) as sec(135°).
Now, let's focus on finding the value of cos(135°). The cosine function is negative in the second and third quadrants.
In the second quadrant, the reference angle is 180° - 135° = 45°. The cosine of 45° is equal to √2/2.
Therefore, cos(135°) = -√2/2.
Now, we can find sec(135°) using the reciprocal property:
sec(135°) = 1 / cos(135°).
Substituting the value of cos(135°), we have:
sec(135°) = 1 / (-√2/2).
To simplify further, we multiply the numerator and denominator by -2/√2:
sec(135°) = -2 / (√2 * -2/√2).
Simplifying the expression:
sec(135°) = -2 / -2,
sec(135°) = 1.
For more such questions on sec visit:
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ily sold 18 items at the street fair. She sold bracelets for $6 each and necklaces for $5 each for a total of $101. Which system of equations can be used to find b, the number of bracelets she sold, and n, the number of necklaces she sold?
b + n = 101
6b + 5n = 18
b + n = 101
5b + 6n = 18
b + n = 18
6b + 5n = 101
b + n = 18
5b + 6n = 101
Answer:
6b + 5n = 101
Step-by-step explanation:
The correct system of equations that can be used to find b, the number of bracelets Ily sold, and n, the number of necklaces she sold is:
b + n = 18
6b + 5n = 101
In this system, the first equation represents the total number of items sold, which is 18. Since b represents the number of bracelets and n represents the number of necklaces, the equation b + n = 18 reflects that the total number of bracelets and necklaces sold should add up to 18.
The second equation represents the total amount of money Ily earned from selling bracelets and necklaces. Since bracelets were sold for $6 each and necklaces for $5 each, the equation 6b + 5n = 101 represents the total amount of money earned, which is $101.
Therefore, the correct system of equations is:
b + n = 18
6b + 5n = 101