Answer:
Option C y = -4x + 9
Step-by-step explanation:
Equation of a line:The line l bisects BC. The line l passes through the midpoint of BC.
B(1, 4) ; C(3 , -2)
[tex]\sf Midpoint \ of \ BC = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]
[tex]\sf = \left(\dfrac{1+3}{2},\dfrac{4-2}2{}\right)\\\\\\=\left(\dfrac{4}{2},\dfrac{2}{2}\right)\\\\\\=(2 , 1)[/tex]
Line l passes through (2,1) and A(3 , -3),
[tex]\sf \boxed{Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{-3-1}{3-2}\\\\\\=\dfrac{-4}{1}\\\\=-4[/tex]
m = -4
Equation of line in slope intercept form: y =mx +c
Here, m is the slope and c is the y-intercept.
y = -4x + c
As the line l is passing through (2,1), substitute the point (2,1) in the above equation and find c.
1 = -4*2 + c
1 = -8 + c
1 + 8 = c
c = 9
Equation of the line l:
y = -4x + 9
quadratic cccccccccccccccccccccccc
Answer: -3 and -17
Step-by-step explanation:
When completing the square we add and subtract [tex]\frac{b}{2} ^2[/tex] in the form ax² + bx + c.
[tex]\frac{b}{2} ^2 = \frac{-6}{2} ^2=(-3)^2=9[/tex]
x² - 6x - 8 = (x - __)² - __
(x² - 6x) - 8 = (x - __)² - __
(x² - 6x + 9) - 8 - 9 = (x - __)² - __
(x - 3)² - 17 = (x - __)² - __
The blanks are 3 and 17.
PLEASE HELP REALLY IMPORTANT The price of a container of laundry detergent (in dollars)
varies with the size (x) of the container (in pounds). The
variables have a strong linear correlation and the equation
for the least squares regression line is y^= 0.86x + 0.52
Based on the regression equation, which is the best
prediction for the price of a 70-pound container of detergent?
$70
$86
$65
$60
Answer:
$60
Step-by-step explanation:
Based on the regression equation, the best prediction for the price of a 70-pound container of detergent can be found by substituting x = 70 into the equation:
y^ = 0.86x + 0.52
y^ = 0.86(70) + 0.52
y^ = 60.2 + 0.52
y^ ≈ $60.72
Therefore, the best prediction for the price of a 70-pound container of detergent is approximately $60.72. However, since we are dealing with prices, it is reasonable to round this value to the nearest dollar, which would be $61. But since none of the answers are 61 it would be $60.
In the early stages of building the Hoover Dam diversion tunnels were built to divert the flow of water away from the main construction site. Each diversion tunnel was cylindrical with a radius of 56 feet and a length of 4,000 feet. Find the volume and surface area of a diversion tunnel.
Answer:
Therefore, the volume of the diversion tunnel is approximately 9,839,916,800 cubic feet and the surface area is approximately 1,000,530.9 square feet.
Step-by-step explanation:
To find the volume and surface area of a diversion tunnel, we can use the formulas for the volume and lateral surface area of a cylinder.
The volume of a cylinder is given by the formula:
V = πr^2h
Where:
V is the volume,
π is a mathematical constant approximately equal to 3.14159,
r is the radius of the cylinder, and
h is the height (or length) of the cylinder.
Substituting the given values:
r = 56 feet
h = 4,000 feet
V = π(56^2)(4,000)
V ≈ 3.14159 * 56^2 * 4,000
Calculating the volume:
V ≈ 9,839,916,800 cubic feet
The surface area of the lateral (curved) part of a cylinder is given by the formula:
A = 2πrh
Where:
A is the surface area,
π is a mathematical constant approximately equal to 3.14159,
r is the radius of the cylinder, and
h is the height (or length) of the cylinder.
Substituting the given values:
r = 56 feet
h = 4,000 feet
A = 2π(56)(4,000)
A ≈ 2 * 3.14159 * 56 * 4,000
Calculating the surface area:
A ≈ 1,000,530.9 square feet
Therefore, the volume of the diversion tunnel is approximately 9,839,916,800 cubic feet and the surface area is approximately 1,000,530.9 square feet.
In a sample of 560 adults, 336 had children. Construct a 95% confidence interval for the true population proportion of adults with children.
Give your answers as decimals, to three places
< p <
What is the expected value of �?
The confidence interval is 0.559 < p < 0.641 and expected value is 0.600
Confidence IntervalTo construct a confidence interval for the true population proportion, we can use the formula:
p ± Z * √((p × (1 - p)) / n)
Where:
p = sample proportion (336/560)
Z = critical value for the desired confidence level
95% confidence = Z-value of approximately 1.96
n = 560
Let's calculate the confidence interval:
p = 336/560 ≈ 0.600
Z ≈ 1.96 (for a 95% confidence level)
n = 560
Plugging these values into the formula:
p ± Z × √((p × (1 - p)) / n)
0.600 ± 1.96 × √((0.600 × (1 - 0.600)) / 560)
0.600 ± 1.96 × √((0.240) / 560)
0.600 ± 1.96 × √(0.0004285714)
0.600 ± 1.96 × 0.020709611
0.600 ± 0.040564459
The confidence interval is:
0.559 < p < 0.641
Therefore, the 95% confidence interval for the true population proportion of adults with children is 0.559 < p < 0.641.
The expected valueFor proportions, the expected value is simply the sample proportion, which is approximately 0.600.
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What are the exact solutions of x2 - 5x-7= 0, where
Ox=
O
x=
X
H
-5± √3
2
5+√3
2
-5± √53
2
5± √53
2
X=
-b± √b²-4ac7
2a
Hello!
it's a quadratic equation
x = (-b ± √(b² - 4ac))/2a
= (-(-5) ± √((-5)² - 4*1*(-7)))/(2*1)
= (5 ± √(25 + 28))/2
= (5 ± √53)/2
Hello !
Answer:
[tex]\large \boxed{\sf x= \dfrac{5\pm\pl\sqrt{53}}{2} }[/tex]
Step-by-step explanation:
This equation is a quadratic equation in the form ax²+bx+c=0
The solution of this equation is given by the quadratic formula :
[tex]\sf x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Here we have :
a = 1b = +5c = -7Let's replace a, b and c with their values in the quadratic formula :
[tex]\sf x=\dfrac{-(-5)\pm\sqrt{(-5)^2-4\times1\times(-7)}}{2\times 1} \\\sf x= \dfrac{5\pm\pl\sqrt{25+28}}{2} \\\boxed{\sf x= \dfrac{5\pm\pl\sqrt{53}}{2} }[/tex]
Have a nice day ;)
If the reliability is
r = 0.25,
the equation becomes
R(n) =
0.25n
0.75 + 0.25n
.
What percent improvement is there in the reliability when the test length is doubled?
The percentage improvement in reliability when test length is doubled is 15%
R(n) = 0.25n / (0.75 + 0.25n)
For a test length of 1substitute n = 1 into the equation :
R(n) = 0.25n / (0.75 + 0.25n)
R(1) = 0.25(1) / (0.75 + 0.25(1))
R(1) = 0.25 / 1
R(1) = 0.25
For a test length of 2when test length is doubled , n = 2
substitute n = 1 into the equation :
R(n) = 0.25n / (0.75 + 0.25n)
R(2) = 0.25(2) / (0.75 + 0.25(2))
R(2) = 0.5 / 1.25
R(2) = 0.4
Percentage improvement can be calculated thus ;
R(2)-R(1)/R(1) × 100%
(0.4-0.25)/0.25 × 100%
0.15 × 100%
=15%
Therefore, percentage improvement in reliability is 15%
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Simplify the following expression:
(8t − 6t2) + 14(3t + 4)
After simplifying, what number is multiplied by the t?
We can see that the number multiplied by t is 50. Therefore, the simplified expression is -6t^2 + 50t + 56, and the number multiplied by t is 50.
To simplify the given expression (8t - 6t^2) + 14(3t + 4), we first need to apply the distributive property by multiplying 14 with both terms inside the parentheses. This gives us:
8t - 6t^2 + 42t + 56
Now, we can combine like terms by adding the coefficients of the t and t^2 terms. The t^2 term has a coefficient of -6, and there are no other t^2 terms in the expression, so we can just bring it down as it is. The t term has a coefficient of 8 + 42 = 50, so we can simplify the expression further as:
-6t^2 + 50t + 56
From this expression, we can see that the number multiplied by t is 50. Therefore, the simplified expression is -6t^2 + 50t + 56, and the number multiplied by t is 50.
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A group of ten students recorded the number of minutes they spent on one math homework problem. The
mean amount of time was 9 minutes, but the MAD was 7 minutes.
Draw a dot plot to represent a data set that matches this description. Be sure to include a title and label
your axis.
1. Create a horizontal axis labeled "Time Spent on Homework Problem (Minutes)."
2. Choose an appropriate scale for the axis, such as labeling every other unit of time from 0 to 18.
3. Plot a dot for each student's data point along the horizontal axis.
4. Arrange the dots in order from smallest to largest time spent on the problem.
5. Title the dot plot to reflect the data set being represented, such as "Math Homework Problem Time Spent: Mean 9 Minutes, MAD 7 Minutes."
6. Include a legend or key if needed to clarify the meaning of the dot plot.(The dot plot is attached below)
To draw a dot plot representing a data set where the mean amount of time spent on one math homework problem is 9 minutes and the MAD is 7 minutes for a group of ten students, we can follow these steps:
The resulting dot plot may show a spread of data between 2 and 16 minutes, with more dots around the center or mean of 9 minutes and fewer dots at the tails. The MAD of 7 minutes suggests a relatively high degree of variability in the data, with some students spending significantly less or significantly more time on the math homework problem. The dot plot can help to visualize these differences and identify any potential outliers in the data.
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how many terms are in the following Expression 2x³-4x²+2x-x-3
In the given expression, 2x³-4x²+2x-x-3, there are five terms. An expression is a mathematical phrase that can be constructed using variables, constants, and operators.
It can include any mathematical operations such as addition, subtraction, multiplication, and division. Additionally, an expression can be made up of one or more terms.In the given expression, 2x³-4x²+2x-x-3, there are five terms. The terms are:2x³: This is the first term in the expression.
It is a cubic term, which means it has an exponent of 3.4x²: This is the second term in the expression. It is a quadratic term, which means it has an exponent of 2.2x: This is the third term in the expression. It is a linear term, which means it has an exponent of 1.-x:
This is the fourth term in the expression. It is also a linear term, but it has a negative coefficient.-3: This is the fifth term in the expression. It is a constant term since it does not have any variable attached to it.In summary, the given expression has five terms, which are 2x³, -4x², 2x, -x, and -3.
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What complex number is represented by the polar coordinates (4, negative StartFraction pi Over 4 EndFraction).?
Answer:
The complex number represented by the polar coordinates (4, -π/4) is 4(cos(-π/4) + i*sin(-π/4)).
given f(x)=3x-5, solve for x when f(x)= (x-1)
Answer: Pretty sure it should be 2.
Step-by-step explanation:
maybe -2 but i dont think so
HELP! Can someone please help with the picture question below?
The probability that either event A or B will occur is 11/17.
We have,
The Addition Rule for Probability:
P(A U B) = P(A) + P(B) - P(A ∩ B),
where P(A U B) represents the probability of the union of events A and B, P(A) represents the probability of event A, P(B) represents the probability of event B, and P(A ∩ B) represents the probability of the intersection of events A and B.
Now,
P(A) = 9/17
P(B) = 2/17
There is no intersection of Q and B so,
P(A ∩ B) = 0
Now,
P(A U B) = P(A) + P(B) - P(A ∩ B),
Substituting the values.
P(A U B) = The probability that either event A or B will occur.
So,
P(A U B)
= 9/17 + 2/17 - 0
= 11/17
Thus,
The probability that either event A or B will occur is 11/17.
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Tom buys 5 shirts for $10 total. He also buys shorts for
$4.50 each. What inequality represents the situation?
He only has $50 to spend/
A. 5x + 10 < 50
B. 4.50x + 5 < 10
c. 10+ 4.5x ≤ 50
d. 5x +4.5x < 50
Answer:
c
Step-by-step explanation:
we know he spends 10$ on shirts but not how much he spends on shorts. Since we know he has $50 to spend, we can buy shorts up to the $50 limit including $50. The only inequality that includes $50 is c
C, 10+ 4.5x ≤ 50
Happy to help, have a great day! :)
PLS HELP MARKING AS BRAINLIST!
Answer:
0.90
Step-by-step explanation:
You want the probability of either event A or event B given the Venn diagram shown.
ProbabilityThe probability of an event shown in the diagram is the ratio of counts for that event to the total of all counts in the diagram. That total is 50.
The number of counts that are not part of either event is shown as 5.
P(A or B) = 1 - P(not (A or B)) = 1 - 5/50
P(A or B) = 0.90
__
Additional comment
Using the given formula, ...
P(A or B) = (25+5)/50 +(15 +5)/50 -5/50 = (25 +15 +5)/50 = 45/50
P(A or B) = 0.90
<95141404393>
A shop has jars of strawberry jam and raspberry jam in the ratio 3:1
Two customers come into the shop and randomly select a jar of jam
to purchase.
The probability that both customers select strawberry jam is 11/20
a) How many jars of jam does the shop have initially?
b) Given that the customers both chose the same type of jam, work
out the probability that they both chose strawberry.
The shop initially has 0.884 jars of jam
The probability that both customers chose strawberry jam, is 0.25.
a) Let's assume the number of jars of strawberry jam is 3x and the number of jars of raspberry jam is x.
So, the total number of jars of jam in the shop is 3x + x = 4x.
According to the given information, the probability that both customers select strawberry jam is 11/20.
So, the probability of the first customer selecting a jar of strawberry jam = (3x/4x) = 3/4,
and the probability of the second customer
= ((3x-1)/(4x-1)).
Now, (3/4) ((3x-1)/(4x-1)) = 11/20
(3/4) ((3x-1)/(4x-1)) = 11/20
20(3/4) ((3x-1)/(4x-1)) = 11
15 (3x-1) = 44 (4x-1)
45x - 15 = 176x - 44
176x - 45x = 44 - 15
131x = 29
x ≈ 29/131
Therefore, the value of x is 0.221
To find the initial number of jars of jam in the shop, we can substitute this value of x into the equation:
4x = 0.884
b) The probability of the first customer selecting strawberry jam is
= (3x)/(4x)
= 3/4.
Therefore, the probability that both customers chose strawberry jam is:
= (3/4) x ((3x-1)/(4x-1))
= (3/4) ((3 x 0.221 - 1)/(4 x 0.221 - 1))
= (3/4) ((3 x 0.221 - 1)/(4 x 0.221 - 1))
≈ 0.25
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What is a cash cycle? explain. calculate using the following information. (assume 360 days in a year). opening balances raw material 1,00,000 wip 45,000 finishes goods 1,35,000 debtors 6,00,000 creditors 8,60,000 closing balances raw material 2,00,000 wip 65,000 finishes goods 1,25,000 debtors 5,45,000 creditors 9,75,000 costs incurred during the year manufacturing costs 11,60,000 excise duty 18,80,000 selling and distribution expenses 6,20,000 admin. overheads 2,00,000 total sales 2,01,96,800 total purchases 1,46,00,000 40% of sales are on credit and 70% of purchases are on credit
The cash cycle, also known as the operating cycle or cash conversion cycle, is a financial metric that measures the time it takes for a company to convert its investments in inventory and other resources into cash flow from sales. It provides insight into the efficiency of a company's working capital management.
The cash cycle can be calculated using the following formula:
Cash Cycle = Inventory Conversion Period + Receivables Conversion Period - Payables Conversion Period
1. Inventory Conversion Period (ICP):
ICP measures the average number of days it takes for the company to convert its raw materials into finished goods. It is calculated as:
ICP = (Average Inventory / Cost of Goods Sold) x Number of Days in a Year
Average Inventory = (Opening Inventory + Closing Inventory) / 2
Cost of Goods Sold = Total Sales - Closing Inventory
2. Receivables Conversion Period (RCP):
RCP measures the average number of days it takes for the company to collect payment from its customers. It is calculated as:
RCP = (Average Receivables / Total Sales) x Number of Days in a Year
Average Receivables = (Opening Receivables + Closing Receivables) / 2
Opening Receivables = Total Sales x Percentage of Sales on Credit
Closing Receivables = Total Sales x Percentage of Sales on Credit - Collections
3. Payables Conversion Period (PCP):
PCP measures the average number of days it takes for the company to pay its suppliers. It is calculated as:
PCP = (Average Payables / Total Purchases) x Number of Days in a Year
Average Payables = (Opening Payables + Closing Payables) / 2
Opening Payables = Total Purchases x Percentage of Purchases on Credit
Closing Payables = Total Purchases x Percentage of Purchases on Credit - Payments
Now, let's calculate the cash cycle using the provided information:
Given data:
Opening balances:
Raw material: ₹1,00,000
WIP: ₹45,000
Finished goods: ₹1,35,000
Debtors: ₹6,00,000
Creditors: ₹8,60,000
Closing balances:
Raw material: ₹2,00,000
WIP: ₹65,000
Finished goods: ₹1,25,000
Debtors: ₹5,45,000
Creditors: ₹9,75,000
Costs incurred during the year:
Manufacturing costs: ₹11,60,000
Excise duty: ₹18,80,000
Selling and distribution expenses: ₹6,20,000
Admin. overheads: ₹2,00,000
Total sales: ₹2,01,96,800
Total purchases: ₹1,46,00,000
Percentage of sales on credit: 40%
Percentage of purchases on credit: 70%
1. Calculate the Inventory Conversion Period (ICP):
Average Inventory = (Opening Inventory + Closing Inventory) / 2
Opening Inventory = Raw Material + WIP + Finished Goods
Closing Inventory = Raw Material + WIP + Finished Goods
Opening Inventory = ₹1,00,000 + ₹45,000 + ₹1,35,000 = ₹2,80,000
Closing Inventory = ₹2,00,000 + ₹65,000 + ₹1,25,000 = ₹3,90,000
Average Inventory = (₹2,80,000 + ₹3,90,000) / 2 = ₹3,35,000
Cost of Goods Sold = Total Sales - Closing Inventory
Cost of Goods Sold = ₹2,01,96,800 -
Assume lines n and m are parallel. If μ(∠)1=147°
, find the following angle measures. (Type each answer as a number, in the corresponding blank below.)
The angle measures of the numbered angles from <1- 8 would be listed below as follows:
<1=147°
<2= 33°
<3= 147°
<4=33°
<5=33°
<6=147°
<7=33°
<8=147°
How to determine the measures of the missing angles?When two parallel lines a crossed by a transverse line then the following occurs:
the pair of corresponding angles is equal. That is <2=<4the pair of interior alternate angles is equal. That is; <6=<3 and <2=<7the pair of exterior alternate angles is equal. That is;<1=<8,<5=<4interior angles on the same side of transversal are supplementary.That is; <2+<3=180°Learn more about parallel lines here:
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If the radius, r, of a sphere is
7
3.14 yd, what is the surface area? Use 3.14 for π. Use pencil and paper. Explain why you can use mental math.
The surface area of the sphere is about enter your response here yd2. =
The surface area of the sphere is 98 yd².
To find the surface area of a sphere, we can use the formula:
Surface Area = 4πr²
Given that the radius, r, of the sphere is 7/3.14 yd, we can substitute this value into the formula:
Surface Area = 4 x 3.14 x (7/3.14)²
= 4 x 3.14 x 49/9.86
= 4 x 49/2
= 98 yd²
Therefore, the surface area of the sphere is 98 yd².
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I need help with this!
The length AC in the kite is 8.7 cm.
How to find the side AC in the kite?A kite is a quadrilateral that has two pairs of consecutive equal sides and
perpendicular diagonals. Therefore, let's find the length AC in the kite.
Hence, using Pythagoras's theorem, let's find CE.
Therefore,
7² - 4² = CE²
CE = √49 - 16
CE = √33
CE = √33
Let's find AE as follows:
5²- 4² = AE²
AE = √25 - 16
AE = √9
AE = 3 units
Therefore,
AC = √33 + 3
AC = 5.74456264654 + 3
AC = 8.74456264654
AC = 8.7 units
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3.2 The line drawn from the midpoint of the one side of a triangle, parallel to the second side, ... ACS is a triangle. P is a point on AS and R is a point on AC such that PSRQ is a parallelogram. PQ intersects AC at B such that B is the midpoint of AR. QC is joined. Also, CR-PS, C, -50° and BP- 60 mm. C 2 R 3 2 B/3 2 3.2.1 Calculate the size of A 3.2.2 Determine the length of QP. 2 1 P 2 (5) (3) [9]
The coordinates of midpoint P are P(-1/2, 3/2) and coordinates of midpoint Q are Q(-3/2, -4).
To find the coordinates of the midpoints P and Q of sides AB and AC, we can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint of a line segment between two points (x1, y1) and (x2, y2) are given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Using this formula, we can find the coordinates of P and Q as follows:
Coordinates of midpoint P:
P = ((2 + (-3)) / 2, (-1 + 4) / 2)
= (-1/2, 3/2)
Therefore, the coordinates of midpoint P are P(-1/2, 3/2).
Coordinates of midpoint Q:
Q = ((2 + (-5)) / 2, (-1 + (-7)) / 2)
= (-3/2, -4)
Therefore, the coordinates of midpoint Q are Q(-3/2, -4).
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Let the points A(2,-1), B(-3,4), and C(-5,-7) be the vertices of triangle A B C. Let P and Q be the midpoints of the sides AB and AC respectively. Find the coordinates of P and Q. (2 marks)
Rita's school is 5 kilometers west of her house and 5 kilometers south of her friend Jayce's
house. Every day, Rita bicycles from her house to her school. After school, she bicycles from
her school to Jayce's house. Before dinner, she bicycles home on a bike path that goes
straight from Jayce's house to her own house. How far does Rita bicycle each day? If
necessary, round to the nearest tenth
Find the difference by subtracting the second polynomial from the first.(11m^(2)n^(5)-3m^(2)n^(3)+5mn-n ) and (-6m^(2)n^(5)+3m^(2)n^(5)+m+2n )
The difference between the two polynomials is 5m^(2)n^(5) - 3m^(2)n^(3) + 5mn + m + n.
To subtract the second polynomial from the first polynomial, we need to perform term-wise subtraction. Let's break down the process step by step:
The first polynomial is: 11m^(2)n^(5) - 3m^(2)n^(3) + 5mn - n.
The second polynomial is: -6m^(2)n^(5) + 3m^(2)n^(5) + m + 2n.
To subtract the second polynomial from the first, we need to change the signs of all terms in the second polynomial and then combine like terms.
First, let's change the signs of the terms in the second polynomial:
-(-6m^(2)n^(5) + 3m^(2)n^(5) + m + 2n) = 6m^(2)n^(5) - 3m^(2)n^(5) - m - 2n.
Now, we can combine like terms by adding or subtracting coefficients of similar monomials:
(11m^(2)n^(5) - 3m^(2)n^(3) + 5mn - n) - (6m^(2)n^(5) - 3m^(2)n^(5) - m - 2n)
= 11m^(2)n^(5) - 3m^(2)n^(3) + 5mn - n - 6m^(2)n^(5) + 3m^(2)n^(5) + m + 2n
= (11m^(2)n^(5) - 6m^(2)n^(5)) + (-3m^(2)n^(3) + 3m^(2)n^(5)) + (5mn + m) + (-n + 2n)
= 5m^(2)n^(5) - 3m^(2)n^(3) + 5mn + m + n.
Therefore, the difference between the two polynomials is 5m^(2)n^(5) - 3m^(2)n^(3) + 5mn + m + n.
In summary, to find the difference, we changed the signs of all terms in the second polynomial and then combined like terms with the first polynomial. The resulting polynomial is the difference between the two original polynomials.
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NO LINKS!! URGENT HELP PLEASE!!!!
4. Use the theorems for interior and exterior angles of a polygon to find:
d. The interior angle of a regular 44-gon.
e. The number of sides in a regular polygon with an interior angle is 175°.
f. The exterior angle in a regular hexagon.
Answer:
d) 171.8°
e) 72
f) 60°
Step-by-step explanation:
Part dThe Polygon Interior Angle Theorem states that measure of the interior angle of a regular polygon with n sides is [(n - 2) · 180°] / 2.
The number of sides of a 44-gon is n = 44. Therefore, the measure of its interior angle is:
[tex]\begin{aligned}\textsf{Interior angles of a 44-agon}&=\dfrac{(44-2) \cdot 180^{\circ}}{44}\\\\&=\dfrac{42\cdot 180^{\circ}}{44}\\\\&=\dfrac{7560^{\circ}}{44}\\\\&=171.8^{\circ}\;\sf(nearest\;tenth)\end{aligned}[/tex]
Therefore, the interior angle of a 44-gon is 171.8°.
[tex]\hrulefill[/tex]
Part eThe Polygon Interior Angle Theorem states that measure of the interior angle of a regular polygon with n sides is [(n - 2) · 180°] / 2.
Given the interior angle of a regular polygon is 175°, then:
[tex]\begin{aligned} \textsf{Interior angle}&=175^{\circ}\\\\\implies \dfrac{(n-2) \cdot 180^{\circ}}{n}&=175^{\circ}\\\\(n-2)\cdot 180^{\circ}&=175^{\circ}n\\\\180^{\circ}n-360^{\circ}&=175^{\circ}n\\\\5^{\circ}n&=360^{\circ}\\\\n&=72\end{aligned}[/tex]
Therefore, the number of sides of the regular polygon is 72.
[tex]\hrulefill[/tex]
Part fAccording the the Polygon Exterior Angles Theorem, the sum of the measures of the exterior angles of a polygon is 360°.
Therefore, to find exterior angle of a regular hexagon, divide 360° by the number of sides:
[tex]\begin{aligned}\sf Exterior\;angle&=\dfrac{360^{\circ}}{\sf Number\;of\;sides}\\\\&=\dfrac{360^{\circ}}{6}\\\\&=60^{\circ}\end{aligned}[/tex]
Therefore, the exterior angle of a regular hexagon is 60°.
Answer:
4. a. 171.818°
b. 72 sides
c. 60°
Step-by-step explanation:
d. The interior angle of a regular polygon with n sides can be calculated using the formula:
[tex]\bold{Interior Angle =\frac{ (n-2) * 180\°}{n}}[/tex]
For a regular 44-gon, the interior angle would be:
[tex]\bold{Interior Angle =\frac{ (44-2) * 180\°}{44}=171.818^o}[/tex]
[tex]\hrulefill[/tex]
e. The number of sides in a regular polygon with an interior angle of 175° can be found using the formula:
[tex]\bold{n = \frac{360\° }{180\° - Interior \:Angle}}[/tex]
For an interior angle of 175°, the number of sides would be:
substituting Value,
[tex]\bold{n =\frac{ 360\° }{ 180\° - 175\°} = \frac{360\° }{ 5\° }= 72 \:sides}[/tex]
[tex]\hrulefill[/tex]
f.
The sum of the exterior angles of any polygon is always 360°.
Since a regular hexagon has six sides,
n=6
exterior angle would be [tex]\bold{\frac{360\° }{ n}}[/tex]
substituting value,
exterior angle=[tex]\bold{\frac{360\° }{ 6}=60\°}[/tex]
[tex]\hrulefill[/tex]
The following is a trapezoid. Find Angle XWZ, Angle XMY, and Angle YMZ
According to the figure of the trapezoid
angle XMZ = 115 degrees
angle XMY = 102 degrees
Angle YMZ = 78 degrees
How to find the missing anglesThe given figure is an isosceles trapezoid, hence
angle XMZ + angle XYZ = 180
angle XYZ = 39 + 26 = 65
angle XMZ + angle XYZ = 180
angle XMZ = 180 - 65
angle XMZ = 115 degrees
angle XMY
angle XMY = 180 - 39 - 39 = 180 - 78 = 102 degrees
Angle YMZ + angle XMY = 180 (angle on a straight line)
Angle YMZ = 180 - angle XMY = 180 - 102 = 78 degrees
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PLEASE HELP ME ANSWER THIS QUESTION I REALLY NEED IT
The radius 5cm, of a sphere increases at the rate of 0.4 cm/s. At what rate will the area be increasing?
a) 40 pi cm^2/s b) 24 pi cm^s/ s c) 16 pi cm^2/ s d) 10 pi cm^2/ s
The rate at which the surface area of the sphere is increasing is 16π cm^2/s.(option-c)
To find the rate at which the area of a sphere increases when its radius is increasing at a given rate, we can use the formula for the surface area of a sphere, which is A =[tex]4πr^2[/tex], where r is the radius of the sphere and A is its surface area. We can then differentiate this with respect to time t to find the rate of change of area with respect to time, which is given as dA/dt.
Given that the radius of the sphere increases at the rate of 0.4 cm/s, we can find the rate of change of area as follows:
- Differentiate the surface area formula with respect to time t:
dA/dt = d/dt [tex](4πr^2)[/tex]
- Use the chain rule to differentiate[tex]r^2[/tex]with respect to time t:
d/dt (r^2) = 2r (dr/dt)
- Substitute the value of dr/dt given as 0.4 cm/s, and the radius value as 5 cm:
dA/dt = 4π(5)^2 (2 × 0.4)
- Simplify the expression to get the rate of change of area with respect to time:
dA/dt = 16π [tex]cm^2/s[/tex]
(option-c)
The mean rounded to the nearest 10th of the following data set is 15, 16, 17, 23, 11, 19, 20, 15, 18, 22, 15, 19
Answer:
17.5
Step-by-step explanation:
You can find the mean of a data set by adding all numbers in the data set together and dividing by the amount of numbers in the given data set.
In this case, your data set is:
15 , 16 , 17 , 23 , 11 , 19 , 20 , 15 , 18 , 22 , 15 , 19 (12 numbers).
Firstly, add all the numbers together: [tex]15 + 16 + 17 + 23 + 11 + 19 + 20 + 15 + 18 + 22 + 15 + 19 = 210[/tex]
Next, divide 210 (total sum) with the amount of terms in total (12):
[tex]\frac{(210)}{(12)} = 17.5[/tex]
17.5 is already in the tenth digit place value, and so you do not need to round.
17.5 is your answer.
~
Learn more about solving for mean, here:
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Find the zeros of the function. Enter the solutions from least to greatest.
f(x) = (x-10)^2-49
Answer:f(x) = (x-10)^2-49
f(x) = (x-10+7)(x-10-7)
f(x) = (x-3)(x-17)
The zeros of the function are 3 and 17.
Step-by-step explanation:
Solve the system with elimination.
-2x + 7y =10
x - 3y = -3
Answer:
x = 9 and y = 4
Step-by-step explanation:
-2x + 7y = 10 (call this equation '1')
x - 3y = -3 (call this '2')
multiply '2' by 2:
2x - 6y = -6 (call this '3')
add '1' and '3':
(-2x + 7y = 10) + (2x - 6y = -6)
0x + y = 4
y = 4
sub that back into '1':
-2x + 7y = 10
-2x + 7(4) = 10
-2x + 28 = 10
-2x = 10 - 28 = -18
x = -18/-2 = 9
sub both y = 4 and x =9 into '2' to check if everything adds up:
x - 3y = -3
9 - 3(4) = 9 - 12 = -3
so x = 9 and y = 4
Area of a parallelogram
Find the area of this parallelogram. Be sure to include the correct unit in your answer.
16 yd
13 yd
K-12 yd →
Answer:
156yd²
Step-by-step explanation:
area of parallelogram = base X vertical height
= 12 X 13
= 156yd²
A store owner wishes to make a new tea with a unique flavor by mixing black tea and oolong tea. If he has 35 pounds of oolong tea that sells for $2.40 per pound, how much black tea worth $1.80 per pound must he mix with it so that he can sell the final mixture for $2.10 per pound?
Answer:
Step-by-step explanation:
To solve this problem, we can use the following formula:
(quantity of tea 1 x price of tea 1) + (quantity of tea 2 x price of tea 2) = total quantity x price of mixture
Let x be the number of pounds of black tea that the store owner needs to mix with the oolong tea.
We know that:
The store owner has 35 pounds of oolong tea that sells for $2.40 per pound.
The store owner wants to sell the final mixture for $2.10 per pound.
The black tea is worth $1.80 per pound.
Using the formula above, we can write:
(35 x 2.40) + (x x 1.80) = (35 + x) x 2.10
Simplifying this equation, we get:
84 + 1.8x = 73.5 + 2.1x
0.3x = 10.5
x = 35
Therefore, the store owner needs to mix 35 pounds of black tea with the oolong tea.
I hope this helps! Let me know if you have any other questions.
Answer:
Step-by-step explanation:
Let's assume the store owner needs to mix x pounds of black tea with the 35 pounds of oolong tea.
The cost of the oolong tea is $2.40 per pound, so the total cost of the oolong tea is:
Cost of oolong tea = 35 pounds × $2.40/pound = $84
The cost of the black tea is $1.80 per pound, and the final mixture needs to be sold for $2.10 per pound. To achieve an average price of $2.10 per pound, the total cost of the mixture should be:
Total cost of mixture = (35 + x) pounds × $2.10/pound = $73.5 + $2.10x
Since the cost of the mixture should equal the sum of the costs of the oolong and black teas, we can set up the equation:
$73.5 + $2.10x = $84
Now, let's solve for x to find the amount of black tea needed:
$2.10x = $84 - $73.5
$2.10x = $10.5
x = $10.5 / $2.10
x ≈ 5
Therefore, the store owner needs to mix approximately 5 pounds of black tea with the 35 pounds of oolong tea in order to sell the final mixture for $2.10 per pound.