Answer:
g(f(4)) = 106.
Step-by-step explanation:
To find f(g(4)), we first need to find
g(4):g(4) = 5(4)^2 - 4(4) + 1 = 80 - 16 + 1 = 65
Now that we know g(4) is 65, we can find
f(g(4)):f(g(4)) = f(65) = 2(65) - 3 = 127
Therefore,
f(g(4)) = 127.
To find g(f(4)), we first need to find f(4):f(4) = 2(4) - 3 = 5
Now that we know f(4) is 5, we can find g(f(4)):
g(f(4)) = g(5) = 5(5)^2 - 4(5) + 1 = 125 - 20 + 1 = 106
Therefore, g(f(4)) = 106.
if it takes three people 4 hours to clean a warehouse how long will it take 4 people to clean the warehouse
The solution is ,if it takes three people 4 hours to clean a warehouse , then 3 hours will it take 4 people to clean the warehouse.
Here, we have,
given that.
if it takes three people 4 hours to clean a warehouse
now, we have to find that how long will it take 4 people to clean the warehouse.
i.e. we have,
3 people take to clean = 4 hours
let, 4 people will take to do it x hours.
now, we have,
3 people take to clean = 4 hours
so, 1 people take to clean = 4*3 hours
so, 4 people take to clean = 4*3 / 4 hours
i.e. we get,
x = 4*3 / 4 hours
or, x = 12/4 hours
= 3 hours
Hence, if it takes three people 4 hours to clean a warehouse , then 3 hours will it take 4 people to clean the warehouse.
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In the coordinate plane, the point A (-2, -4) is translated to the point A' (-3, -1). Under the same translation, the points B (0, -7) and C (-5, -8) are translated to B' and C', respectively. What are the coordinates of B' and C'?
The coordinates of the points B' and C' are B' = (-1, 10) and C' = (-6, -5)
Calculating the coordinates of B' and C'?From the question, we have the following parameters that can be used in our computation:
A = (-2, -4)
This point is translated to
A' = (-3, -1)
This means that the rule of transformation is
(x, y) = (x - 1, y + 3)
Given that
B = (0, 7) and C = (-5, -8)
When this transformation is applied on B and C, we have
B' = (0 - 1, 7 + 3) and C' = (-5 - 1, -8 + 3)
Evaluate
B' = (-1, 10) and C' = (-6, -5)
Hence. the coordinates of B' and C' are B' = (-1, 10) and C' = (-6, -5)
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For the nonextreme weather months, a company charges $5.10 plus 5.747 cents per kilowatt-hour
(kWh) for customers using up to 1300 kWh, and charges 5.788 cents per kilowatt-hour (kWh) for the
extra kWh used after the first 1300 kWh, if more than 1300 kWh are used.
a. What is the charge for 1300 kWh?
(round to three decimal places)
dollars
For a company that charges $5.10 plus 5.747 cents per kilowatt-hour (kWh) for customers using up to 1300 kWh, and charges 5.788 cents per kilowatt-hour (kWh) for the extra kWh used after the first 1300 kWh, if more than 1300 kWh are used, the total charge for 1,300 kWh is $79.811.
How is the total charge computed?The total charge is the product of the multiplication of the unit rate by the total kilowatt-hours used by the customer plus the fixed rate.
Multiplication operation is one of the four basic mathematical operations, including addition, subtraction, and division.
Multiplication involves the multiplicand, the multiplier, and the product.
Fixed charge = $5.10
Variable charge per kilowatt-hour = 5.747 cents ($0.05747)
Total usage = 1,300 kWh
The total charge = $79.811 ($5.10 + $0.05747 x 1,300)
Thus, the total charge for 1,300 kWh for the nonextreme weather month is $79.811.
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How many
1/4-foot cubes would fill the inside of the prism?
Write the answer in the box.
There are 4 cubes of size 1/4 foot would fill the inside of the prism.
We have to given that;
Height of cuboid = 3 feet
Length of cuboid = 3/4 feet
Width of cuboid = 1/2 feet
We know that;
Volume of cuboid = Length x width x height
Hence,
V = 3/4 x 3 x 1/2
V = 9/8
Thus, Number of 1/4-foot cubes which would fill the inside of the prism is,
= (9/8) ÷ (1/4)
= (9/8) x 4
= 9/2
= 4.5
Thus, There are 4 cubes of size 1/4 foot would fill the inside of the prism.
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Mr. Oakley class surveyed 200 students about their favorite type of pie. The double bar graph below shows the result of the survey. What is the difference in the total number of students who chose peach pie as their favorite type of pie and the total number of students who chose apple pie? Show all your work. Explain why you did each step.
The difference in the students who chose peach pie and apple pie is 46
What is the difference in the students who chose peach pie and apple pie?From the question, we have the following parameters that can be used in our computation:
Number of students = 200Proportion of students that choose peach = 38%Proportion of students that choose apple = 15%From the above, we have the percentage difference to be
Difference = 38% - 15%
When the given values are substituted, we have
Difference = 23%
This means that
Students = 23% * 200
Evaluate
Students = 46
Hence, the number of students is 46
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5m) Change to metres. a) 1.241 km D) 3.4 km (b) 6.002 km (e) 21.32 km (c) 5.168 km (f) 0.895 km
The distances in meters are:
a) 1241 m
b) 6002 m
c) 5168 m
d) 3400 m
e) 21320 m
f) 895 m
We have,
To convert kilometers (km) to meters (m), we need to multiply the distance by 1000.
a) 1.241 km = 1.241 × 1000 m = 1241 m
b) 6.002 km = 6.002 × 1000 m = 6002 m
c) 5.168 km = 5.168 × 1000 m = 5168 m
d) 3.4 km = 3.4 × 1000 m = 3400 m
e) 21.32 km = 21.32 × 1000 m = 21320 m
f) 0.895 km = 0.895 × 1000 m = 895 m
Therefore,
The distances in meters are:
a) 1241 m
b) 6002 m
c) 5168 m
d) 3400 m
e) 21320 m
f) 895 m
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Bills and sliding scale tariffs.
In a local municipality the first 50khw of electricity cost 0.55c per kWh and the next 60khw cost 0.82c per kWh . calculate the cost using.
A 45khw of electricity
B 60khw of electricity
C 100khw of electricity
A) The total cost for 45khw of electricity is 27.50c.
B) The total cost for 60khw of electricity is 76.70c.
C) Total cost for 100khw of electricity is 76.70c.
To calculate the cost of electricity for different amounts of kWh, we need to use the sliding scale tariffs provided by the local municipality. Here are the calculations for the given scenarios:
A. For 45 kWh of electricity:
The first 50 kWh cost 0.55c per kWh, so the cost is 50 x 0.55 = 27.50c
There is no electricity used beyond the first 50 kWh, so the total cost is 27.50c.
B. For 60 kWh of electricity:
The first 50 kWh cost 0.55c per kWh, so the cost is 50 x 0.55 = 27.50c
The next 10 kWh cost 0.82c per kWh, so the cost is 10 x 0.82 = 8.20c
The total cost is 27.50c + 8.20c = 35.70c.
C. For 100 kWh of electricity:
The first 50 kWh cost 0.55c per kWh, so the cost is 50 x 0.55 = 27.50c
The next 60 kWh cost 0.82c per kWh, so the cost is 60 x 0.82 = 49.20c
The remaining 40 kWh are not covered by the sliding scale tariff and their cost is unknown.
The total cost is 27.50c + 49.20c = 76.70c.
In summary, the cost of electricity varies depending on the amount of kWh used, and we need to use the sliding scale tariffs to calculate it correctly.
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A human heart pumps about 7 × 10-2 liter of blood pe-
heartbeat. The average human heart beats about 72 times per minute.
How many liters of blood does a heart pump in 1 year? 70 years?
The heart will pumps 31,536 litres in 1 year and pumps 2,207,520 liters in 70 years.
Simple solution to how blood is pumpedThere are 72 heartbeats in a minute.
If heart pumps 7 × 10⁻² litre per heartbeat,
then in 1 min,
7 × 10⁻² x 72 = 5.04 litres/minute
In one year (365 days), the heart pumps:
5.04 x 60 x 24 x 365 = 31,536 litres/year
Hence in 1 year, heart pumps 31,536 litres
In 70 years, the heart would pump:
31,536 x 70 years = 2,207,520 litres
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An employee receives a 3% raise once per year. If the employee's initial salary is $65,800.00, what will the employee's salary be after 7 years?
Answer:
$79,618
Step-by-step explanation:
7 years x 3% = 21%
$65,800 x 21% = $13,818
$65,800 + $13, 818 = $79,618
To answer my problem view the image
To be 90% certain that the sample percentage is within 5.5 percentage points of the genuine population percentage, we need to survey at least 384 randomly chosen plane passengers.
To calculate the sample size required for the survey, we can use the formula:
[tex]n = \dfrac{(Z^2 \times p \times q)} { E^2}[/tex]
where:
Z = the z-score associated with the level of confidence (90% in this case), which is 1.645
p = the estimated proportion of passengers who prefer aisle seats (unknown)
q = 1 - p
E = the maximum allowable error (5.5 percentage points)
Since we don't know the proportion of passengers who prefer aisle seats, we can assume a conservative estimate of 50%. This means that p = 0.5 and q = 0.5.
Substituting these values into the formula, we get:
[tex]n = \dfrac{(1.645^2 \times 0.5 \times 0.5)} { (0.055^2) }= 383.8[/tex]
We need to round up to the nearest integer, so the minimum sample size required is:
n = 384
Therefore, we need to survey at least 384 randomly selected air passengers to be 90% confident that the sample percentage is within 5.5 percentage points of the true population percentage.
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Which of the following interpretations for the given expression is correct?
(x + 9)² - 4
A.The sum of the square of x and 9 - 4.
B. The difference of the square of x and 9 - 4.
C. The sum of the square of x, 9, and -4.
D. The difference of the square of x + 9 and 4.
Answer:
D
Step-by-step explanation:
First consider a part of the numerator 5 + 3y2. This can be verbally described as "the sum of 5 and 3 times the square of y".
Then, the entire expression in the numerator, (5 + 3y2)3, can be written as "the cube of the sum of 5 and 3 times the square of y".
Next, consider a part of the denominator (4y), which can be verbally described as "the product of 4 and y".
Then, the entire expression in the denominator, (4y)3, can be written as "the cube of the product of 4 and y".
Dividing the two expressions yields the complete expression shown below.
So, the given expression can be interpreted as "the cube of the sum of 5 and 3 times the square of y divided by the cube of the product of 4 and y".
6ft=____yd
Remember to convert to a larger unit divide
Answer:
2 yards
Step-by-step explanation:
2 yards equals 6 feet because 2x3=6 or 72 inches because 6x12 equals 72. 1 yard is equal to 3 feet.
for the function g(x)=-1/2x^2+2x+5, write the function in vertex form. ANSWER ASAP! Will Give Branliest!!! No Fake answers! Thx!
I NEED THE ANSWER! IM SO CONFUSED!!
[tex]\blue{\boxed{\bold{\mathbb{SOLUTION}}}}[/tex]
[tex]\cos C=\dfrac{CE}{AC}\\=\dfrac{8}{\sqrt{8^2+3^2}}\\=\dfrac{8}{\sqrt{64+9}}\\=\dfrac{8}{\sqrt{73}}\\=\boxed{0,936}[/tex]
[tex]\aqua{\boxed{\mathfrak{Thank \: You}}}\\\aqua{\boxed{\boxed{\mathfrak{answered \: by: \: akbarsdtazm}}}}[/tex]
2. The million-dollar question! Suppose you
want to have $1,500,000 for retirement in
30 years. If you deposit the same amount
each month into an annuity that earns 6%
interest annually (and compounded
monthly),
what is the amount you need to
deposit each month?
Show your work
using the formula.
The formula to calculate the monthly payment needed to achieve a future value in an annuity is:
PMT = FV * (r / 12) / [(1 + r / 12)^(n * 12) - 1]
where PMT is the monthly payment, FV is the future value, r is the annual interest rate (as a decimal), and n is the number of years.
In this case, FV = $1,500,000, r = 0.06, and n = 30. Plugging these values into the formula, we get:
PMT = $1,500,000 * (0.06 / 12) / [(1 + 0.06 / 12)^(30 * 12) - 1]
PMT = $1,500,000 * 0.005 / [1.06^(360) - 1]
PMT = $1,500,000 * 0.005 / 5.743
PMT = $1,244.23 (rounded to the nearest cent)
Therefore, the amount that needs to be deposited each month to achieve a future value of $1,500,000 in 30 years is $1,244.23.
Answer:
the guys above me is correct
Step-by-step explanation:
because i did it and the answer was correct for me
Anders owns a hat shop.During a scale,he sells all his hats for 20% off.Is this a markup or a markdown
Rectangle LMNP is similar to rectangle WXYZ.
The length of LM is 19 in, the area of rectangle LMNP is 140.6 in2, and the length of XY is 2.22 in.
What is the difference between the perimeters of the two rectangles?
A. 31.96 in
B. 36.96 in
C. 15.84 in
D. 41.96 in
The required, difference between the perimeters of the two rectangles is 46.03 in. None of the options is correct.
Since rectangles LMNP and WXYZ are similar, their corresponding sides are proportional. Let's denote the scale factor as k. Then:
k = XY / LM = 2.22 / 19
To find the value of k, we can divide 2.22 by 19:
k ≈ 0.117
The area of rectangle LMNP is given as 140.6 in^2. We can use this to find the length of NP:
LM * NP = area of LMNP
19 * NP = 140.6
NP ≈ 7.4 in
Since the sides of WXYZ are proportional to those of LMNP, we can find the length of YZ:
XY / YZ = LM / NP
2.22 / YZ = 19 / 7.4
YZ ≈ 1.167 in
Now we can calculate the perimeters of both rectangles:
Perimeter of LMNP = 2(LM + NP) = 2(19 + 7.4) = 52.8 in
Perimeter of WXYZ = 2(XY + YZ) = 2(2.22 +1.167) = 6.77in
The difference between the perimeters is:
52.8 - 6.77 = 46.03 in
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Select all the conditions for which it is possible to construct a triangle
A triangle with angle measures 50, 40, and 10°
A triangle with angle measures 80, 40, and 60
A triangle with angle measures 60, 80, and 80
A triangle with angle measures 100°, 30°, and 50
A TV singing competition is airing on channel 8. A contestant named Jimmy gives an exceptional performance. Jimmy's performance appears from 6:06 pm until 6:14 pm in the 30 min program. Suppose a viewer turns to channel 8 at a random time during the show. What is the probability that the viewer will turn to channel 8 during Jimmy's performance? Give your answer as a percentage rounded to the ones place.
The probability that a viewer will turn to channel 8 during Jimmy's performance is 2.67%.
The show is 30 minutes long, which is equivalent to 1800 seconds. Jimmy's performance starts at 6:06 pm, which is 366 seconds into the show, and ends at 6:14 pm, which is 414 seconds into the show. Therefore, Jimmy's performance lasts for 48 seconds.
The probability of a viewer turning to channel 8 during Jimmy's performance can be calculated by dividing the length of Jimmy's performance by the length of the entire show:
P = (length of Jimmy's performance) / (length of entire show) = 48 / 1800 = 0.0267
Multiplying by 100 gives the probability as a percentage: 2.67%
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Let f (x) = log2(x) + 2 and g(x) = log2(x3) – 6. Part A: If h(x) = f (x) + g(x), solve for h(x) in simplest form. (4 points) Part B: Determine the solution to the system of nonlinear equations. (6 points)
The simplified expression for h(x) is h(x) = 4 log₂(x) - 4.
Given information:
f(x) = (log₂(x) + 2) and g(x) = (log₂(x³) - 6)
h(x) = f(x) + g(x) = (log₂(x) + 2) + (log₂(x³) - 6)
Using the rules of logarithms, we can simplify g(x) as follows:
g(x) = log₂(x³) - 6
= 3 log₂(x) - 6.
Now we can substitute this into the expression for h(x):
h(x) = (log₂(x) + 2) + 3 log₂(x) - 6
= 4 log₂(x) - 4
Therefore, the simplified expression for h(x) is h(x) = 4 log₂(x) - 4.
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Paula is investing $5,000 in an account that earns 4.10% APR compounded quarterly. How much
money will she have in 25 years?
$15,556.84
Paulanwill have approx $15,556.84 if she investb$5k that earns 4.10% apr compound quarterly..
Answer:
I’m pretty sure it’s $11,780.60
Step-by-step explanation:
We can use the formula for compound interest to determine how much money Paula will have in 25 years:
A = P(1 + r/n)^(nt)where:A = the total amount of money after t years
P = the principal amount (the initial investment)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, we have:
P = $5,000
r = 4.10% = 0.041 (as a decimal)
n = 4 (compounded quarterly)
t = 25 years
Plugging these values into the formula, we get:
A = $5,000(1 + 0.041/4)^(4*25)
A = $5,000(1 + 0.01025)^100
A = $5,000(1.01025)^100
A = $5,000(2.356)
A = $11,780.60
Therefore, Paula will have approximately $11,780.60 in her account after 25 years.
I need help with this, thx! (Pls show working and steps so I would know how to do other questions!)
Answer:
t = [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
calculate the gradient (slope) of AB using the slope formula and equate to the slope of the perpendicular line.
given line with slope 1 [tex]\frac{1}{4}[/tex] = [tex]\frac{5}{4}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{5}{4} }[/tex] = - [tex]\frac{4}{5}[/tex]
calculate [tex]m_{AB}[/tex] using slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = A (2, - 3 ) and (x₂, y₂ ) = B (- 2, t )
[tex]m_{AB}[/tex] = [tex]\frac{t-(-3)}{-2-2}[/tex] = [tex]\frac{t+3}{-4}[/tex]
equating corresponding slopes
[tex]\frac{t+3}{-4}[/tex] = - [tex]\frac{4}{5}[/tex] ( multiply both sides by - 4 to clear the fraction )
t + 3 = - [tex]\frac{4}{5}[/tex] × - 4 = [tex]\frac{16}{5}[/tex] ( subtract 3 from both sides )
t = [tex]\frac{16}{5}[/tex] - 3 = [tex]\frac{16}{5}[/tex] - [tex]\frac{15}{5}[/tex] = [tex]\frac{1}{5}[/tex]
Can someone please solve this y = 5x² + 2x + 7
The roots of the quadratic equation y = 5 · x² + 2 · x + 7 are contained by x = - 1 / 5 ± i √34 / 5.
How to solve a quadratic equation
In this problem we must solve a quadratic equation, whose roots must be found. This can be done by using algebra properties, by completing the square. First, write the entire quadratic equation:
y = 5 · x² + 2 · x + 7
Second, use algebra properties to find all roots:
y = 5 · [x² + (2 / 5) · x + 7 / 5]
y = 5 · [x² + (2 / 5) · x + 1 / 25] + 5 · (34 / 25)
y = 5 · (x + 1 / 5)² + 34 / 5
Third, use y = 0:
5 · (x + 1 / 5)² + 34 / 5 = 0
5 · (x + 1 / 5)² = - 34 / 5
(x + 1 / 5)² = - 34 / 25
x + 1 / 5 = ± √(- 34) / 5
x = - 1 / 5 ± √(- 34) / 5
x = - 1 / 5 ± i √34 / 5
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A bag of marbles has 4 red, 3 blue, 2 green, and 1 yellow marbles. If Aisha reaches into the bag, what is the probability she picks a red marble?
There are a total of 4 + 3 + 2 + 1 = 10 marbles in the bag. The probability of picking a red marble is the number of red marbles divided by the total number of marbles:
Probability of picking a red marble = 4/10 = 2/5
Therefore, the probability Aisha picks a red marble is 2/5 or 0.4 when written as a decimal.
The numbers: 76.4 72.1 78.5 46.3 63.2 59.6 55.4 62.1 71.5 64.5 52.9 64.8 72.8 54.0 55.8 62.7 68.2 69.3 63.4 88.8 78.4 57.9 52.7 75.3 72.9 38.6 65.2 75.3 84.2 76.3 62.8 52.3 69.1 72.0 68.0 47.9 33.5 78.2 48.9 59.9 89.2 59.0 58.2 75.0 63.3 52.8 59.1 76.9 78.4 62.3 75.8 59.5 78.0 84.2 76.9 42.7 65.4 87.6 79.0 65.0
Pt1: A well respected wild life researcher recently conducted a study of wild Jackalopes. He trapped and weighed 60 adult wild Jackalopes in an attempt to gauge their health. As a population, if a species loses weight it could be a signal that the health of the population is in danger. Research conducted 10 years prior found that the population mean was 69.9 pounds. Test the claim that population mean of wild Jackalopes is equal to 69.9 lbs. Use a significance level of .01.
Pt 2: You have recently been notified by the US Fish and Wildlife Service that grants are available to help reestablish wild populations of Jackalopes if their health is in danger. These grants could total several millions of dollars for research. Without changing the data or the given population mean, what change could be made to show that the population is actually in danger. Prove this by conducting another hypothesis test with the needed changes.
Claim:
Null Hypothesis: _________________________
Alternative Hypothesis: ___________________________
Test Statistic: (state the statistic and find it’s value):
Find the pvalue for the given test statistic: ________________
At the 0.01 significance level would you reject the null or fail to reject the null? Justify your answer.
What final conclusion could you draw from your research? What will your report to the US Fish and Wildlife Service say?
The study conducted on wild Jackalopes population shows a sample mean weight of 69.9 pounds, with a test statistic of -1.327 and a p-value of 0.190. Therefore, at a significance level of 0.01, the null hypothesis can be rejected, indicating that the population mean weight is different from 65 pounds. This suggests the population health is in danger, and grants may be needed to re-establish their wild populations.
Pt1
Null Hypothesis The population mean of wild Jackalopes is equal to 69.9 lbs.
Alternative Hypothesis The population mean of wild Jackalopes is not equal to 69.9 lbs.
Test Statistic t = (X - μ) / (s / √n), where X is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.
Using a calculator or statistical software, we find that the test statistic is t = -1.327 and the p-value is 0.190.
At the 0.01 significance level, we fail to reject the null hypothesis. There is not enough evidence to conclude that the population mean of wild Jackalopes is different from 69.9 lbs.
Pt2
To show that the population is actually in danger, we could change the null hypothesis to reflect a lower population mean weight. For example:
Null Hypothesis The population mean of wild Jackalopes is equal to 65 lbs.
Alternative Hypothesis The population mean of wild Jackalopes is greater than 65 lbs.
Using the same formula for the test statistic, we find that the test statistic is t = -5.457 and the p-value is 2.29 x 10⁻⁷, which is much smaller than the significance level of 0.01.
At the 0.01 significance level, we reject the null hypothesis. There is strong evidence to conclude that the population mean weight of wild Jackalopes is greater than 65 lbs. This suggests that the health of the population is in danger and that grants to help reestablish wild populations should be pursued.
Our report to the US Fish and Wildlife Service should reflect these findings and suggest taking action to support the health and survival of wild Jackalopes.
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he data collected on the number of points scored in a basketball season are represented in the box plot. A box plot uses a number line from 13 to 33 with tick marks every one-half unit. The box extends from 16 to 31 on the number line. A line in the box is at 24. The lines outside the box end at 14 and 32. The graph is titled Number of Points, and the line is labeled Points Scored in Basketball. What value does 25% of the data lie above? Find the value. Lower quartile (Q1) = 14 Lower quartile (Q1) = 16 Upper quartile (Q3) = 24 Upper quartile (Q3) = 31
The value that lie above 25% of the data of the box plot is 31 and the lower quartile (Q1) = 14 upper quartile (Q3) = 31
Given data ,
The minimum value, which is 14
Now , the lower quartile, which is 16 (25% of the data is below this value)
And , the median, which is 24 (50% of the data is below this value)
Now , the upper Quartile, which is 31 (75% of the data is below this value)
And , the maximum value is 32.
The upper and lower quartiles of a box plot, also known as the 75th percentile (Q3) and 25th percentile (Q1) respectively, represent the range within which the middle 50% of the data falls.
Lower quartile (Q1) = 14
Upper quartile (Q3) = 31
Hence , 25% of the data lie above 31, which is the upper quartile.
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Factor each polynomial using difference of squares. Check for common factors first.
a) x² – 36
b) 3x² - 12
Factor the following using the trinomial method. Check for common factor first.
a) x² + 6x + 9
b) 4x² - 8x - 60
PLS HELP!!!!!
The factorised forms of the Polynomials using difference of squares are;
a). (x - 6) (x + 6)
b). 3 (x - 2) (x + 2).
The factorised forms of the polynomials using the trinomial method are;
a). (x + 3)²
b). 4 (x -5) (x + 3)
What are the factorised forms of the polynomials?Recall that from the difference of squares concept;
a² - b² = (a - b) (a + b) where a² and b² are perfect squares.
Therefore, if we have; x² - 36; we have; x² - 6²
x² - 36 = (x-6) (x + 6).
For, 3x² - 12; = 3 (x² - 4)
= 3 (x -2) (x + 2).
For the trinomials;
x² + 6x + 9;. x² + 3x + 3x + 9
= (x + 3) (x + 3) = (x+3)².
Also, for 4x² - 8x - 60; we have
4 (x² - 2x - 15)
= 4 (x - 5) (x + 3).
Read.more on difference of squares;
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Add 2x+ 3 y + 7 and 4x-7y-8 PLLSSS QUICKKK
Answer:
3
Step-by-step explanation:
The sum of three numbers is 144. The first number is 6 less than the third. The second number is 4 times the third. What are the numbers?
Answer:
19, 100, and 25
Step-by-step explanation:
Let's call the first number "x", the second number "y", and the third number "z". We know that:
x + y + z = 144 (the sum of three numbers is 144)
We also know that:
x = z - 6 (the first number is 6 less than the third)
y = 4z (the second number is 4 times the third)
We can substitute the expressions for x and y into the first equation:
x + y + z = 144
(z - 6) + 4z + z = 144
Combining like terms, we get:
6z - 6 = 144
Adding 6 to both sides:
6z = 150
Dividing by 6:
z = 25
Now that we know z, we can use the other equations to find x and y:
x = z - 6 = 25 - 6 = 19
y = 4z = 4(25) = 100
So the three numbers are 19, 100, and 25.
Let first number be a
second number be b
Third number be c
As per the question The first number is 6 less than the third. The second number is 4 times the third.
First number, a = c - 6 ....(i)
second number, b = 4c ....(ii)
Also sum of the three numbers is 144.
a + b + c = 144
c - 6 + 4c + c = 144
c + 4c + c = 144 + 6
6c = 150
c = 150/6
c = 25
Put value of c in equation (i) & (ii)
in equation (i)
a = c - 6
a = 25 - 6
a = 19
in equation (ii)
b = 4c
b = 4 × 25
b = 100
Hence thee required numbers will be 19, 100 and 25.
100 POINTS!!!
The magnitude and direction of two forces acting on an object are 100 pounds, S80°E, and 90 pounds, N55°E,
respectively. Find the magnitude, to the nearest hundredth of a pound, and the direction angle, to the nearest tenth
of a degree, of the resultant force.
Answer:
175.58 poundsN 78.7° EStep-by-step explanation:
You want the resultant force equivalent to the two forces ...
100 pounds S 80° E90 pounds N 55° EResultantThere are a number of ways the resultant force can be found. One of them is to add the components of the two forces. Another makes use of the law of cosines:
r² = u² +v² -2uv·cos(θ)
where θ is the supplement of the angle between the two forces.
r² = 100² +90² -2·100·90·cos(135°) ≈ 30827.922061
r ≈ 175.579 ≈ 175.58
The resultant force is about 175.58 pounds.
DirectionThe angle added to that of v can be found using the law of sines:
sin(φ)/100 = sin(135°)/175.58
φ = arcsin(sin(135°)·100/175.58) ≈ 23.749°
The angle East of North is then ...
55° +23.7° = 78.7°
The direction of the resultant is N 78.7° E.
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Additional comment
The angles used in the second attachment are bearing angles measured clockwise from north. The rectangular coordinates shown as the sum of the forces represent (north) + (east)i.
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