The graph below shows a company's profit f(x), in dollars, depending on the price of pens x, in dollars, sold by the company:
Graph of quadratic function f of x having x intercepts at ordered pairs 0, 0 and 6, 0. The vertex is at 3, 120.
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit?
Part B: What is an approximate average rate of change of the graph from x = 3 to x = 5, and what does this rate represent?
Part C: Describe the constraints of the domain.
Answers
The Domain of the function would be the interval [0, 6].The increasing interval represents the point where the company is pricing the pens appropriately, resulting in increasing profit.Average rate of change = (f(5) - 120) / (5 - 3)
Part A:
The x-intercepts of the graph, located at the ordered pairs (0, 0) and (6, 0), represent the points where the profit function intersects the x-axis. In the context of the problem, these x-intercepts indicate the price values at which the company sells pens, resulting in zero profit. When the price is $0, the company does not make any profit, and when the price is $6, the company also does not make any profit. The x-intercepts represent the break-even points where the company covers its costs but does not generate any profit.
The maximum value of the graph, located at the vertex (3, 120), represents the peak profit achieved by the company. The vertex is the highest point on the graph and indicates the optimal price at which the company can maximize its profit. In this case, when the price of pens is $3, the company achieves a maximum profit of $120.
Regarding the intervals of increasing and decreasing profit, the function is decreasing to the left of the vertex (3, 120) and increasing to the right of the vertex. This means that for prices less than $3, the profit decreases, and for prices greater than $3, the profit increases. The decreasing interval represents the point where the company is pricing the pens too low, resulting in decreasing profit. The increasing interval represents the point where the company is pricing the pens appropriately, resulting in increasing profit.
Part B:
To find the approximate average rate of change of the graph from x = 3 to x = 5, we need to calculate the slope of the line segment connecting the two points. The average rate of change represents the average amount by which the profit changes per unit increase in price over the given interval.
Using the coordinates (3, 120) and (5, f(5)) on the graph, we can determine the change in profit and price:
Change in profit = f(5) - 120
Change in price = 5 - 3
Substituting the values of the points into the equation, we can calculate the approximate average rate of change:
Average rate of change = (f(5) - 120) / (5 - 3)
Part C:
The constraints of the domain refer to the limitations or restrictions on the values that x (the price of pens) can take. Based on the given information, the x-intercepts of the graph are at (0, 0) and (6, 0), indicating that the price cannot be negative or exceed $6. Therefore, the domain of the function would be the interval [0, 6]. The constraint is that the price of the pens must be within this range for the profit function to be applicable.
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Note the full question may be :
A bakery sells cupcakes for $2 each. The bakery's total revenue from selling cupcakes is given by the function R(x) = 2x, where x represents the number of cupcakes sold.
Part A: What does the x-intercept of the graph of R(x) represent? Explain its significance in the context of the bakery's revenue.
Part B: What is the slope of the graph of R(x)? Interpret the meaning of this slope in terms of the bakery's revenue and the price of cupcakes.
Part C: If the bakery wants to maximize its revenue, what should be the ideal number of cupcakes to sell? Explain your answer based on the graph of R(x).
Related Questions
The side lengths of ABC are AB = 12, BC= 19, and AC = 11. List the
angles of the triangle in order from smallest to largest.
Answers
The angles of the triangle are ordered as follows:
<B, <C and <A.
What is the law of sines?We consider a triangle with side lengths and angles related as follows:
Side length of a is opposite to angle A.Side length of b is opposite to angle B.Side length of c is opposite to angle C.Then the lengths and the sines of the angles are related as follows:
sin(A)/a = sin(B)/b = sin(C)/c.
By the law of sines, we have that the greater angle measures are opposite to the greater side lengths.
Hence the angle measures for this problem are ordered as follows:
<B -> opposite to AC = 11.<C -> opposite to AB = 12.<A -> opposite to BC = 19.More can be learned about the law of sines at https://brainly.com/question/4372174
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The angles of triangle ABC is arranged below
angle b - smallest
angle c
angle a - largest
How to arrange the measure of the anglesTo determine the angles of triangle ABC in order from smallest to largest, we can use use the knowledge that the side with higest length will face the largest angle.
Let the angles be
angle c is opposite AB = 12
angle b is opposite AC = 11
angle a is opposite BC = 19
Using the knowledge as introduced we have that
angle a > angle c > angle b
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The support beams of truss bridges are triangles. James made a model of a truss bridge with a scale of 1 inch = 4 feet. If the height of the tallest triangle on the model is 9 inches, what is the height of the tallest triangle on the actual bridge?
Answers
The height of the tallest triangle on the actual bridge is 12 feet.
If James made a model of a truss bridge with a scale of 1 inch = 4 feet, we can use this information to find the height of the tallest triangle on the actual bridge.
Let x be the height of the tallest triangle on the actual bridge. Since the scale of the model is 1 inch = 4 feet, the height of the tallest triangle on the model can be converted to feet by multiplying by 4. Therefore, the height of the tallest triangle on the model is:
9 inches * (1 foot / 12 inches) * 4 = 3 feet
We can use the similarity of triangles to set up a proportion to find x. The corresponding sides of similar triangles are proportional. In this case, the height of the triangle on the model corresponds to the height of the triangle on the actual bridge, and the scale factor from the model to the actual bridge is 1/4 (since 1 inch on the model represents 4 feet on the actual bridge). Therefore, we have:
height of triangle on model / height of triangle on actual bridge = scale factor
3 feet / x = 1/4
Multiplying both sides by x, we have:
3 feet = (1/4) x
Multiplying both sides by 4, we have:
12 feet = x
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What is the equation for this line?
Answers
y=2/3x-4 is the equation of the line where 2/3 is the slope.
We have to find the equation of line which is passing through points (0, -4) and (3, -2).
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁.
Slope = -2+4/3-0
=2/3
Now let us find the y intercept.
-4=2/3(0)+b
b=-4
The equation of line is y=2/3x-4.
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For triangle XYZ, m∠X = (2g + 16)° and the exterior angle to ∠X measures (4g + 38)°. Find the measure of ∠X and its exterior angle.
Answers
The angles in the triangle are as follows:
∠X = 58°
Exterior angle of ∠X = 122°
How to find the angle of a triangle?The sum of angles in a triangle is 180 degrees. The sum of the exterior angle and the interior angle of a triangle is 180 degrees.
Therefore, let's find the measure of ∠X in the triangle XYZ.
Hence,
m∠X = (2g + 16)°
The exterior angle of m∠X measures 4g + 38 degrees.
Hence,
2g + 16 + 4g + 38 = 180
6g + 54 = 180
6g = 180 - 54
6g = 126
g = 126 / 6
g = 21
Therefore,
∠X = (2(21) + 16)° = 42 + 16 = 58 degrees
Exterior angle of ∠X = 4(21) + 38 = 84 + 38 = 122
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In quantitative literacy
Answers
In quantitative literacy, the solution involves finding the LCM of the numbers and then squaring it to obtain the smallest square number that satisfies the given conditions.
In quantitative literacy, finding the smallest square number that is divisible by 8, 12, 15, and 20.
To solve the problem, we need to determine the least common multiple (LCM) of these four numbers.
Let's list the multiples of each number until we find a common multiple:
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, ...
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, ...
Multiples of 20: 20, 40, 60, 80, 100, 120, ...
From the lists above, we can see that 120 is the smallest common multiple of all the numbers. To find the smallest square number, we need to square 120:
120^2 = 14,400
The smallest square number that is divisible by 8, 12, 15, and 20 is 14,400.
In quantitative literacy, the solution involves finding the LCM of the numbers and then squaring it to obtain the smallest square number that satisfies the given conditions.
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A rectangular room is tiled with tiles 1
2
inches long and 1
2
inches wide. If the room is L tiles long and W tiles
wide, find the room’s area, in square inches.
Answers
The room’s area, in square inches is,
⇒ A = 144LW square inches.
We have to given that,
A rectangular room is tiled with tiles 12 inches long and 12 inches wide.
And, The room is L tiles long and W tiles wide.
Hence, Lenght of L tiles,
= 12L
And, Length of W tiles,
= 12W
Since, We know that,
Area of rectangle is,
⇒ A = Length x width
Substitute given values, we get;
⇒ A = 12L x 12W
⇒ A = 144LW square inches.
Therefore, The room’s area, in square inches is,
⇒ A = 144LW square inches.
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
Answer: D
Step-by-step explanation: -135
I need help graphing this!! I cent do my table right please help ASAP!
y= 2(1/3^x)-2
Answers
Answer: Your line should start at (-1,6) then it should cross (0,0) so, straight down and a small curve. Then you should be at (0 -2), continue the small curve you made. DO not make it a parabola. it is basically just a straight line down, then a really long curve. Make sure you make the curve go across the entire graph.
Steve is going shopping. This matrix shows his shopping list:
How much will Steve spend if he shops at S2?
Round to the nearest cent
Answers
$27.71 is the amount Steve spend if he shops at S2.
Given that Steve is going shopping
The shopping list of steve has 2 cereal, 4 soups , 2 soda, 1 milk and 4 candy.
We have to find the cost spend by Steve when he purchase in shop 2, S2.
In S2, the cereal cost 2.15, soup cost 2.75, soda cost is 3.00, Milk cost 3.25 and candy costs 0.79.
Total cost = 2×2.15 + 4×2.75+2×3+1×3.25+4×0.79
=4.3+11+6+3.25+3.16
=27.71
Hence, $27.71 is the amount Steve spend if he shops at S2.
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(3a - 5b)(, + 5b)(a ^ 2 + ab - b ^ 2)
Answers
The solution after resolving into factors are,
⇒ 8 (a - 3b) (a - b)
We have to given that,
Resolve into factors the expression,
⇒ (3a - 5b)² - (a + b)²
Now, We can simplify for resolving the factors as,
⇒ (3a - 5b)² - (a + b)²
Since, WE know that,
⇒ x² - y² = (x - y) (x + y)
Hence,
⇒ (3a - 5b)² - (a + b)²
⇒ [(3a - 5b) - (a + b)] [ (3a - 5b) + (a + b)]
⇒ [3a - 5b - a - b] [4a - 4b]
⇒ (2a - 6b) (4a - 4b)
⇒ 2 (a - 3b) × 4 (a - b)
⇒ 8 (a - 3b) (a - b)
Thus, The solution after resolving into factors are,
⇒ 8 (a - 3b) (a - b)
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
a^2 = b^2 + c^2 - 2(b)(c)cosx
In this case we need to find the angle of f, so for a we use the length f is. It’s set up like this:
30^2 = 20^2 + 25^2 -2(20)(25)cosx
Next multiple and simply everything
900 = 1025 -1000cosx
Now subtract 1025
-125 = -1000cosx
Divide by -1000 to get cosx by itself
.125 = cosx
Now take the inverse of cos
Cos^-1 (.125)
And you get 82.8 or 83
So the answer should be A
Hope that helps. Lmk if there are questions.
An artist makes a hanging sculpture out of rhombus-shaped pieces. Each rhombus shape has diagonals of 3.5 centimeters and 5 centimeters. What is the area of each rhombus? 4.25 cm2 8.5 cm2 8.75 cm2 17.5 cm2
Answers
The area of each rhombus is 8.75 [tex]cm^2[/tex]. The correct option is 8.75 [tex]cm^2.[/tex]
To find the area of each rhombus, we can use the formula for the area of a rhombus:
Area = (diagonal1 × diagonal2) / 2
Given that the diagonals of the rhombus-shaped pieces are 3.5 centimeters and 5 centimeters, we can substitute these values into the formula:
Area = (3.5 cm × 5 cm) / 2
Area = 17.5 [tex]cm^2[/tex] / 2
Area = 8.75 [tex]cm^2[/tex]
Therefore, the area of each rhombus is 8.75 [tex]cm^2[/tex]. The correct option is 8.75 [tex]cm^2.[/tex]
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i need the whole problem done and i don’t understand, i need a step by step to show my work. its at 12. PLS HELP
Answers
The surface area of given triangular prism = 24 ft².
For the given triangular prism
Base = 2 ft
height = 3 ft
side = 3ft
We know that,
Surface area of triangular prism
= side x base + 3x base x height
= 3 x 2 + 3x2x3
= 6 + 18
= 24 ft²
Thus,
Surface area = 24 ft²
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Need some help on this question!!!!!
Answers
The greater number of packages that can fit in the truck is 24000.
The volume of the part of the truck that is being filled is 375 cubic feet.
We have,
To determine the greater number of packages that can fit in the truck, we need to calculate the volume of both the packages and the part of the truck that is being filled.
The volume of a cube-shaped package:
The side length of the cube-shaped package is 1/4 feet.
The volume of a cube is given by V = s³, where s is the side length.
Therefore, the volume of each package is (1/4)³ = 1/64 cubic feet.
The volume of the part of the truck being filled:
The dimensions of the rectangular prism-shaped part of the truck are:
Length = 8 feet
Width = 6(1/4) feet = 6.25 feet
Height = 7(1/2) feet = 7.5 feet
The volume of a rectangular prism is given by V = length × width × height.
Therefore, the volume of the part of the truck being filled is:
8 × 6.25 × 7.5
= 375 cubic feet.
To calculate the greater number of packages that can fit in the truck, we divide the volume of the part of the truck by the volume of each package:
= 375 cubic feet / (1/64 cubic feet)
= 375 × 64
= 24000 packages.
Therefore,
The greater number of packages that can fit in the truck is 24000.
The volume of the part of the truck that is being filled is 375 cubic feet.
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Which graph shows the solution set for -4.421.6x-3.6?
←++
-3
←++
-3
-2 -1 0
←+++
-7
-2
-1 0
-7 -6 -5 -4
-6 -5 -4
1
1
-3
♡
2
2
3
-2
3
-2 -1
-1
Answers
The graph shows the solution set for -4.4 ≥ 1.6x - 3.6 is Graph I.
To solve the inequality -4.4 ≥ 1.6x - 3.6, we can follow these steps:
Add 3.6 to both sides of the inequality to isolate the term with x:
-4.4 + 3.6 ≥ 1.6x - 3.6 + 3.6
-0.8 ≥ 1.6x
Divide both sides of the inequality by 1.6
-0.8 / 1.6 ≥ 1.6x / 1.6
-0.5 ≥ x
So, the solution to the inequality is x ≤ -0.5.
Now, from the solution the graph for the inequality start with closed dot from 0.5 and move towards the points -0.6, -0.7, -0.8, ....
Thus, the graph shows the solution set for -4.4 ≥ 1.6x - 3.6 is Graph I.
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Find the area of the following regular hexagon.
10
Round your answer to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
Find the equation using the point slope formula or slope intercept formula for the two sets of points. (19,-16) (-7,-15)
Answers
The equation of the Line passing through the points (19, -16) and (-7, -15) is: y = (-1/26)x - 397/26
The equation of a line using the point-slope formula or the slope-intercept form, we need either the slope of the line or the y-intercept. Let's calculate the slope of the line using the given points (19, -16) and (-7, -15).
The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (19, -16) as (x1, y1) and (-7, -15) as (x2, y2), we can substitute these values into the slope formula:
m = (-15 - (-16)) / (-7 - 19)
m = (-15 + 16) / (-7 - 19)
m = 1 / (-26)
m = -1/26
Now that we have the slope of the line, we can use either the point-slope formula or the slope-intercept form to find the equation.
Using the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept, we can substitute the slope (-1/26) and one of the given points (19, -16) into the equation:
-16 = (-1/26) * 19 + b
To solve for b, we can simplify the equation:
-16 = -19/26 + b
To isolate b, we can add 19/26 to both sides of the equation:
-16 + 19/26 = b
Now, we can find the common denominator of 26 and add the fractions:
(-416 + 19) / 26 = b
-397/26 = b
Therefore, the equation of the line passing through the points (19, -16) and (-7, -15) is: y = (-1/26)x - 397/26
This equation represents the line with a slope of -1/26 and a y-intercept of -397/26.
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Change these fractions into decimals. Do not round your answers:
a. 3 8
b. 1 9
Answers
Step-by-step explanation:
3/8 = 0.375
1/9 = 0.1111111111
Answer:
Step-by-step explanation:
(-20,13) (16,15)
Can some find the slop for this question
Answers
Slope (m) = (y2 - y1) / (x2 - x1)
Given the points (-20, 13) and (16, 15), we can assign the coordinates as follows:
x1 = -20, y1 = 13
x2 = 16, y2 = 15
Now, we can substitute these values into the slope formula:
Slope (m) = (15 - 13) / (16 - (-20))
= 2 / 36
= 1 / 18
Therefore, the slope of the line passing through the points (-20, 13) and (16, 15) is 1/18.
1. A research poll was conducted to investigate opinions about global warming. The respondents (1 point)
who answered yes when asked if there is solid evidence that the Earth is getting warmer were
then asked to select a cause of global warming. The results were arranged between male and
female responses. Using a 0.05 significance level, a test statistic of 0.792 and a critical value of
5.991 are found. Test the claim that the gender of the respondent is independent of the choice
for the cause of global warming. State the initial and final conclusion
OReject the null hypothesis; there is not sufficient evidence to warrant rejection of the claim that the
gender of the respondent is independent of the choice for the cause of global warming.
OReject the null hypothesis; there is sufficient evidence to warrant rejection of the claim that the gender
of the respondent is independent of the choice for the cause of global warming.
Fail to reject the null hypothesis; there is not sufficient evidence to warrant rejection of the claim that
the gender of the respondent is independent of the choice for the cause of global warming.
OFail to reject the null hypothesis; there is sufficient evidence to warrant rejection of the claim that the
gender of the respondent is independent of the choice for the cause of global warming.
Answers
The initial and final conclusion would be Fail to reject the null hypothesis; there is not sufficient evidence to warrant rejection of the claim that the gender of the respondent is independent of the choice for the cause of global warming. Option C
Why does it fail to reject the null hypothesis?The initial hypothesis is that the gender of the respondent is independent of the choice for the cause of global warming.
The alternative hypothesis is that the gender of the respondent is dependent on the choice for the cause of global warming.
The test statistic of 0.792 is less than the critical value of 5.991. Therefore, we do not reject the null hypothesis.
Looking at the statistic that has been provided, we do not have enough evidence to conclude that the gender of the respondent is related to the choice of the cause of global warming at the 0.05 significance level.
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Write the equation of the line, in slope-intercept form, with the
following information:
rate of change: undefined
point: (-3,2)
Answers
y = -3x + 2 is the equation of the line, in slope-intercept form, with the following information.
Thus, The most "popular" type of a straight line is one with a slope-intercept. Due of its simplicity, this is helpful to a lot of kids.
The slope and y-intercept of the straight line can be easily determined or read off from this form, making it possible to describe its properties without having access to the graph.
You may learn how to determine the equation of a line from any two points that this line passes through using the slope intercept form calculator.
Continue reading to find out what a linear equation's slope intercept form is, how to calculate a line's equation, and the significance of the slope intercept form equation in practical applications.
Thus, y = -3x + 2 is the equation of the line, in slope-intercept form, with the following information.
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a triangle has angle measurements of 51 89 and 40 what kind of triangle is it?
(20 points, please answer quick)
Answers
The correct classification for this triangle is an acute triangle.
How to solveThe angle measures given are 51, 89, and 40 degrees.
There are no angles that are either equal to or greater than 90 degrees among those mentioned. Consequently, the triangle does not contain any angles that are either right or obtuse.
To categorize a triangle according to its angles, the total of the angles within the triangle, which is invariably 180 degrees, is taken into account.
51 + 89 + 40 = 180
Given that the total of the angles is 180 degrees, we can deduce that this particular triangle is acute in nature. An acute-angled triangle is a type of triangle that has three angles which are each smaller than 90 degrees.
Therefore, the correct classification for this triangle is an acute triangle.
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What is the meaning of "we call a class R an n-ary relation if all its elements are n-tuples"?
Answers
The statement is saying that a class R is considered an n-ary relation if all its elements are n-tuples.
The symbol R⊂Vⁿ represents that the class R is a subset of Vⁿ, which is the class of all n-tuples.
Here, Vⁿ represents the set of all possible n-tuples, and R is a subset of that set.
The notation Cⁿ is used to denote the set of n-tuples with elements from the set C, and C×D represents the Cartesian product of sets C and D.
The statement defines an n-ary relation as a class where all its elements are n-tuples, and it establishes a connection between the class R and the set of all n-tuples (Vⁿ).
The notation Cⁿ and C×D are used to describe sets of n-tuples and Cartesian products, respectively, in a mathematical context.
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The additional growth of plants in one week are recorded for 11 plants with a
sample standard deviation of 3 inches and sample mean of 10 inches.
t at the 0.05 significance level = Ex: 1.234
Margin of error = Ex: 1.234
Confidence interval = [ Ex: 12.345 Ex: 12.345 ]
[smaller value, larger value]
Answers
1. The t-value of the data is 1.833
2. The margin of error is 1.66
3. The confidence interval is between 11.66 to 8.34
What is the margin of error?From the question given;
sample size = 11
sample mean = 10 inches
standard deviation = 3 inches
1.The t-value of the data with a degree of freedom equal to 10 at 0.05 significance level = 1.833
2. Using the formula below, the margin of error is;
[tex]ME = t * \frac{SD}{\sqrt{n} }[/tex]
ME = margin of errort = t-valueSD = standard deviationn = sample sizeSubstituting the values into the formula above;
ME = 1.833 * 3/√11
ME = 1.66
3. The confidence interval of the data is;
CI = mean ± ME
where CI is the confidence interval, mean is the sample mean, and ME is the margin of error. In this case, the confidence interval is calculated as follows:
CI = 10 +/- 0.96 = 9.04 to 10.96 inches
CI = 10 ± 1.66 = 11.66 to 8.34
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What is the rate of change for f(x) = 7 sin x-1 on the interval from x = 0 to x = pi/2
A)14/pi
B)pi/14
C)pi/4
D)4/pi
Answers
Answer:
a]14/pi
Step-by-step explanation:
The following number is a BASE-7 NUMBER. Convert this to a base 10 number and enter your answer in the box.
463421
(Remember, the above number is in Base 7!)
Number in base 10:
Answers
The base 10 equivalent of the base 7 number 463421 is 83174.
To convert a number from base 7 to base 10, we multiply each digit of the base 7 number by the corresponding power of 7 and sum up the results.
For the number 463421 in base 7:
= 4 x 7⁵ + 6 x 7⁴ + 3 x 7³ + 4 x 7² + 2 x 7¹ + 1 x 7⁰
= 4 x 16807 + 6 x 2401 + 3 x 343 + 4 x 49 + 2 x 7 + 1 x 1
= 67228 + 14406 + 1029 + 196 + 14 + 1
= 83174
Therefore, the base 10 equivalent of the base 7 number 463421 is 83174.
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P(-1; -1) S(-3; -7) Q(4; 2) R(7; -5) Determine (correct to one decimal place): 3.2 3.1 the acute angle between QR and the x-axis the angle of inclination of PQ POR 3.3 3.4 the angle of inclination of SP 3.5 SPR 3.6 PSR.
Answers
1. Acute angle between QR and the x-axis:
The angle between QR and the x-axis can be found by calculating the arctan of the slope of QR. The slope (m) can be found using the formula: m = (y2 - y1) / (x2 - x1).
Given points Q(4, 2) and R(7, -5):
m(QR) = (-5 - 2) / (7 - 4) = -7/3
Using the arctan function, we can find the acute angle (A1):
A1 = arctan(-7/3) ≈ -68.2 degrees
2. Angle of inclination of PQ:
The angle of inclination of PQ can be found using the same method as above with points P(-1, -1) and Q(4, 2):
m(PQ) = (2 - (-1)) / (4 - (-1)) = 3/5
The angle of inclination (A2) can be found by taking the arctan of the slope:
A2 = arctan(3/5) ≈ 30.96 degrees
3. Angle of inclination of POR:
The angle of inclination of POR can be found using points P(-1, -1) and R(7, -5):
m(POR) = (-5 - (-1)) / (7 - (-1)) = -6/8 = -3/4 = -0.75
The angle of inclination (A3) can be found using the arctan function:
A3 = arctan(-0.75) ≈ -36.87 degrees
4. Angle of inclination of SP:
To find the angle of inclination of SP, we can use points S(-3, -7) and P(-1, -1):
m(SP) = (-1 - (-7)) / (-1 - (-3)) = 6/2 = 3
The angle of inclination (A4) can be found using the arctan function:
A4 = arctan(3) ≈ 71.57 degrees
5. Angle SPR:
To find angle SPR, we can use the Law of Cosines. Using the distance formula, we can find the lengths of sides SP, SR, and PR. Let's denote SP as a, SR as b, and PR as c:
a = sqrt((-3 - (-1))^2 + (-7 - (-1))^2) = sqrt(4^2 + 6^2) = sqrt(52) ≈ 7.21
b = sqrt((-3 - 7)^2 + (-7 - (-5))^2) = sqrt(10^2 + 2^2) = sqrt(104) ≈ 10.2
c = sqrt((-1 - 7)^2 + (-1 - (-5))^2) = sqrt((-8)^2 + 4^2) = sqrt(80) ≈ 8.94
Now we can apply the Law of Cosines to find the angle SPR (A5):
cos(A5) = (a^2 + b^2 - c^2) / (2ab)
A5 = arccos((7.21^2 + 10.2^2 - 8.94^2) / (2 * 7.21 * 10.2)) ≈ 42.1 degrees
6. Angle PSR:
To find angle PSR, we can subtract the angle SPR (A5) from the angle of inclination of SP (A
help please show work
Answers
The slope of line AD will be 4/3
Given,
ABCD is a square.
AB ⇒ y = -3/4 x + 7
Now,
AB is straight line.
Straight line equation ⇒ y =mx + c
m = slope of line
c = y intercept
Here,
m = -3/4 ( slope of line AB )
Now for slope of line AD,
ABCD is a square. Thus AB and AD are perpendicular to each other.
According the relation,
[tex]m_{1} m_{2} = -1[/tex]
[tex]m_{1}[/tex] = slope of line 1
[tex]m_{2}[/tex] = slope of line 2
So,
-3/4 [tex]m_{2}[/tex] = -1
[tex]m_{2}[/tex] = 4/3.
Hence slope of AD is 4/3 .
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A health store sells two different sized square granola bars. the side length of the smaller granola bar, C(x), is modeled by the function C(x)=1/4 square root x +2, where x is the area of the larger granola bar in square inches. which graph shows C(x)
Answers
The graph that best represents these characteristics is the one that shows an increasing curve with a flattened slope and is shifted upward. Option C
The function C(x) = (1/4)√x + 2 represents the side length of the smaller granola bar, where x is the area of the larger granola bar in square inches. To determine which graph shows C(x), we need to analyze the characteristics of the function.
First, let's consider the behavior of the function C(x) = (1/4)√x + 2:
Square Root Function: The term √x indicates that the function involves the square root of x. This means that as x increases, C(x) will also increase, but at a decreasing rate.
Scaling Factor: The coefficient (1/4) scales the square root of x. It affects the steepness of the function and causes C(x) to increase more slowly compared to a simple square root function.
Vertical Shift: The constant term (+2) shifts the entire function vertically upward by 2 units. This means that the graph will be raised by 2 units compared to a standard square root function.
Based on these characteristics, we can conclude that the graph of C(x) will be an increasing curve with a flattened slope compared to a simple square root function, and it will be shifted upward by 2 units.
Among the answer choices, the graph that best represents these characteristics is the one that shows an increasing curve with a flattened slope and is shifted upward. Without the actual graphs provided, it is difficult to specify the exact choice, but it should exhibit these features described above.
It is essential to refer to the available graphs or visually analyze the functions to determine the correct graph that shows C(x). Option C is correct.
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Vertex for y=2(x-3)^2 +1
Answers
The vertex of the equation of the parabola y = 2( x - 3 )² + 1 is (3,1).
What is the vertex of the parabola?Given the equation of the parabola in the question:
y = 2( x - 3 )² + 1
To determine the vertex of the parabola, we use the vertex form of a parabola which is expressed as:
Vertex form: y = a(x - h)² + k
Where (h, k) represents the vertex of the parabola.
The given equation is already in the vertex form:
y = 2( x - 3 )² + 1
Hence, comparing the given equation, y = 2(x - 3)² + 1, with the vertex form, we can see that:
h = 3 and k = 1
Therefore, the vertex is (3,1).
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