Can u guys tell me the answer to question 8 and 9 thank you so much
I would really appreciate it
Thank you
Answers
Step-by-step explanation:
Q8.
Step 1.
35.4 - 31 = 4.4
Step 2.
4.4 ÷ 31 = 0.1419....
Step 3.
0.1419.... x 100 = 14.19...
Step 4.
To one decimal place = 14.2% increase
Q9.
Step 1.
£10 ÷ 40 articles = £0.25 = 25p (this is the answer to part a)
Step 2.
32p x 40 articles = £0.32 x 40 articles = £12.80 (this is the answer to part b)
Step 3.
£12.80 - £10 = £2.80 (this is the answer to part c)
Step 4.
£2.80 ÷ £10 = 0.28
Step 5.
0.28 x 100 = 28% (this is the answer to part d)
Hope this was what you were looking for :)
(Also, hi to a fellow Brit - there aren't that many of us around here)
Bluey :)
Related Questions
Let a and b be real numbers where a=/b=/c=/0 which of the following functions could represent the graph below?
Answers
Answer: The second option; y = (x - a)^2*(x-b)^4
Step-by-step explanation:
Ok, we have that a and b are real numbers different than zero.
In the graph, we can see that the line touches the x-axis in two values. Now, if we would have an equation like:
y = x*(x - a)^3*(x - b)^3
then when x = 0 we would have:
y = 0*(0-a)^3*(0-b)^3 = 0
But in the graph, we can see that when x = 0, the value of y is different than zero, so we can discard options 1 and 3.
So the remaining options are:
y = (x - a)^2*(x-b)^4
y = (x - a)^5*(x - b)
Now, another thing you can see in the graph is that it is always positive.
Particularly the second option allows negative values for y because it has odd powers, then we can also discard this option.
(For example, if x > a and x < b we would have a negative value for y)
Then the only remaining option is y = (x - a)^2*(x-b)^4
Answer:
B.y = (x - a)^2*(x-b)^4
Step-by-step explanation:
EDGE 2020 Brainliest please
What is the slope of the line passing through the points (6,7) and (1,5)
Answers
Answer:
2/5
Step-by-step explanation:
(7-5)/(6-1)
A new city Mayor would like to determine the proportion of community voters who are ages 18 to 20 years. He has heard it is 10%. To test this prediction, he surveys 1000 random community voters and found that 111 of them are aged 18 to 20. The following is the setup for this hypothesis test: H0:p=0.10 H0:p≠0.10 The p-value for this hypothesis test is 0.04. At the 5% significance level, should he reject or fail to reject the null hypothesis?
Answers
Answer: He should reject the null hypothesis.
Step-by-step explanation: When using P-Values to decide if you accept or not the alternative hypothesis, compare the p-value with the chosen significance level (α).
In the Mayor's survey:
p-value = 0.04
α = 5% or 0.05
If the p-value is less than α, reject the null hypothesis and accept the alternative. If p-value is greater than or equals α, fail to reject the null hypothesis and don't accept the alternative.
Analysing the Mayor's survey:
p-value = 0.04 < α = 0.05
In conclusion, the Mayor should reject the null hypothesis and accept that the proportion of voters who are aged 18 to 20 is not equal to 10%, i.e., accept the alternative hypothesis: [tex]H_{a}[/tex]: p≠0.10
Find x and round to the nearest tenth.
Answers
Answer:
83.0°
Step-by-step explanation:
Given ∆XYZ, with 3 known sides, to find angle X, apply the Law of Cosines, c² = a² + b² - 2ab*cos(C).
For convenience sake, this formula can be rewritten to make the angle we are looking for the subject of the formula.
Thus, we would have this following:
[tex] cos(C) = \frac{a^2 + b^2 - c^2}{2ab} [/tex]
Where,
C = X = ?
a = 8 ft
b = 16 ft
c = 17 ft
Plug in the stated values into the formula and solve for X
[tex] cos(X) = \frac{8^2 + 16^2 - 17^2}{2*8*16} [/tex]
[tex] cos(X) = \frac{320 - 289}{256} [/tex]
[tex] cos(X) = \frac{31}{256} [/tex]
[tex] cos(X) = 0.1211 [/tex]
[tex] X = cos^{-1}(0.1211) [/tex]
[tex] X = 83.0 [/tex] (to nearest tenth)
Answer:
its actually 83 not 83.0
Step-by-step explanation:
im only saying this bc i know people with type 83.0 in the box
During a quality assurance check, the actual contents (in grams) of six containers of protein powder were recorded as 1530, 1532, 1495, 1508, 1528, and 1511. (a) Find the mean and the median of the contents. (b) The third value was incorrectly measured and is actually 1515. Find the mean and the median of the contents again. (c) Which measure of central tendency, the mean or the median, was affected more by the data entry error?
Answers
Answer:
Step-by-step explanation:
Given the values of the actual content of protein powder recorded as shown:
1530, 1532, 1495, 1508, 1528, and 1511
a) We are to find the mean and median of the contents.
Mean is the average sum of the numbers. It is expressed mathematically as xbar = ΣXi/N
Xi are individual values
N is the total number of values present.
N = 6
xbar = (1,530+1,532+1,495 +1,508+1,528+1,511)/6
xbar = 9104/6
xbar = 1517.33
Median of the data is the value at the middle after rearrangement. On rearranging from lowest to highest:
1,495, 1508, 1511, 1528, 1530, 1532
The two values at the centre are 1511 and 1528.
Median = 1511+1528/2
Median = 1519.5
b) If the third value was incorrectly measured and is actually 1515, then our new data will become.
1530, 1532, 1515, 1508, 1528, and 1511
xbar = (1,530+1,532+1,515 +1,508+1,528+1,511)/6
xbar = 9124/6
xbar = 1520.67
For median:
We arrange first
1508, 1511, 1515, 1528, 1530, 1532
The two values at the centre are 1515 and 1528.
Median = 1515+1528/2
Median = 1521.5
c) To know the measure of central tendency that was most affected, we will look at the difference in the values gotten for both mean and median.
∆Mean = 1520.67-1517.33
∆Mean = 3.34
∆Median = 1521.5 - 1519.5
∆Median = 2.0
It can be seen that the measure of central tendency with greater deviation is the mean. Therefore, the mean is more affected by the data entry error.
If the triangle on the grid below is translated by using the rule (x, y) right-arrow (x + 5, y minus 2), what will be the coordinates of B prime?
Answers
Answer:
B'(0,-2)
Step-by-step explanation:
the coordinates of B (-5,0)
the translation is(x+5,y-2)
B' : (-5+5,0-2)
B'(0,-2)
A pianist plans to play 5=pieces at a recital from her repertoire of 20 pieces, and is carefully considering which song to play first, second etc. to create a good flow. How many different recital programs are possible?
Answers
Answer:
2432902008176640000 programs are possible using 20 distinct (different) songs.
Step-by-step explanation:
There are 20 choices for the first song, 19 choices for the second, ...1 song for the last for a total of
N = 20*19*18*...*3*2*1 = 20!= 2432902008176640000 programs
The number 20! is the number of permutations for 20 distinct objects put in order.
20! is pronounced as 20 factorial.
Example: factorial of 5 is 5*4*3*2*1 = 120
Answer:
20*19*18*17*16=1 860 480 different programs
Step-by-step explanation:
So there are 20 pieces total and each of them can be first.
Each of residual 19 can be the second
Each of residual of 18 can be the third
Each of residual 17 can be the fourth
Each of residual 16 can be the fifth
Total amont of possible different programs ( the order of the pieces matters)
is : 20*19*18*17*16=1 860 480 different programs
A national survey of 1000 adult citizens of a nation found that 25% dreaded Valentine's Day. The margin of error for the survey was 3.6 percentage points with 90% confidence. Explain what this means.
Answers
Answer:
There is 90% confidence that the proportion of the adult citizens of the nation that dreaded Valentine’s Day is between 0.214 and 0.286.
Step-by-step explanation:
The summary of the statistics from the information given is ;
At 90% confidence interval, 25% dreaded Valentine's Day and the margin of error for the survey was 3.6 percentage points
SO;
[tex]C.I = \hat p \pm M.O.E[/tex]
[tex]C.I = 0.25 \pm 0.036[/tex]
C.I = (0.25-0.036 , 0.25+0.036)
C.I = (0.214, 0.286)
The 90% confidence interval for the proportion of the adult citizens of the nation that dreaded Valentine’s day is 0.214 and 0.286.
There is 90% confidence that the proportion of the adult citizens of the nation that dreaded Valentine’s Day is between 0.214 and 0.286.
If 2/3 of a certain number is subtracted from twice the number, the result is 20. Find the number.
Answers
Let x be the number.
Set up an equation:
2x - 2/3x = 20
Simplify:
1 1/3x = 20
Divide both sides by 1 1/3
X = 15
The number is 15
Step by Step Explanation:
Let the number be x
So, x-2/3x=20
=> x/1 - 2/3x = 20
=> (3x - 2x)/3 = 20
=> x/3 = 20
=> x= 20*3
=> x=60
Checking if the solution is correct:
So substitute the value of x in x-2/3x=20
As we know x=60
So, => 60 - 2/3*60 = 20
=> 60 - 40 = 20
As 20 = 20
So this answer is correct
f(n)=4n-3 find the 15th term of the sequence defined by the explicit rule
Answers
Answer:
57
Step-by-step explanation:
f(15)=4(15)-3
f(15)=60-3
f(15)=57
Hope that helps, tell me if you need more help
Answer:
57
Step-by-step explanation:
If you plug 15 into the equation, you get f(15)=4(15)-3
60-3
57
:)
Richard is buying a subscription for video game rentals. The plan he has chosen has an
initial fee of $20 plus $2 per video game rented. This plan can be represented by the
function f(x) = 2x + 20. How much money will Richard pay this month if he rents 5 video
games?
Answers
Answer:
Richard will pay $30.
Step-by-step explanation:
Because "x" is equivalent to the amount of video games he rents, you would replace "x" with 5. Do the math, and you would get 10+20=30! Hope this helps!
Which pairs of angles are alternate exterior angles? select yes or no
Answers
A - No
B - No
C - Yes
D - Yes
.
C and D are alternate exterior angles
Which is the value of this expression when p = 3 and q = negative 9? ((p Superscript negative 5 Baseline) (p Superscript negative 4 Baseline) (q cubed)) Superscript 0 Negative one-third Negative StartFraction 1 Over 27 EndFraction StartFraction 1 Over 27 EndFraction One-third Edge 2020
Answers
Answer:
I am pretty sure that the answer is D. The value should be 1.
Step-by-step explanation:
Answer:
Answer is D
Step-by-step explanation:
On Edge 2020
The radius of a sphere is measured to be 3.0 inches. If the measurement is correct within 0.01 inches, use differentials to estimate the error in the volume of sphere.
Answers
Answer:
ΔV = 0.36π in³
Step-by-step explanation:
Given that:
The radius of a sphere = 3.0
If the measurement is correct within 0.01 inches
i.e the change in the radius Δr = 0.01
The objective is to use differentials to estimate the error in the volume of sphere.
We all know that the volume of a sphere
[tex]V = \dfrac{4}{3} \pi r^3[/tex]
The differential of V with respect to r is:
[tex]\dfrac{dV}{dr }= 4 \pi r^2[/tex]
dV = 4 πr² dr
which can be re-written as:
ΔV = 4 πr² Δr
ΔV = 4 × π × (3)² × 0.01
ΔV = 0.36π in³
the result of two forces acting on a body has a magnitude of 80 pounds. The angles between the resultant and the forces are 20 degrees and 52 degrees. find the magnitude of the large force
Answers
Answer:
Larger force= 66.28 pounds
Step-by-step explanation:
The angle of the resultant force 80 pounds = 180-(52+20)
The angle of the resultant force 80 pounds = 180-72
The angle of the resultant force 80 pounds = 108°
The larger force is the force with 52°
Let the larger force be x
Magnitude of the larger force
x/sin52 = 80/sin108
X= sin52 *(80/sin 108)
X= 0.7880*(80/0.9511)
X = 0.7780*(84.1131)
X = 66.28 pounds
Wholemark is an internet order business that sells one popular New Year greeting card once a year. The cost of the paper on the which the card is printed is $0.05 per card, and the cost of printing is $0.15 per card. The company receives $2.15 per card sold. Since the cards have the current year printed on them, unsold cards have no salvage value. Their customers are from the four areas: Los Angeles, Santa Monica, Hollywood, and Pasadena. Based on past data, the number of customers from the each of the four regions is normally distributed with mean 2,000 and standard deviation of 500. (Assume these four are independent.)
What is the optimal production quality for the card? (Use Excel's NORMSINV{} function to find the Z-score. Round intermediate calculations to four decimal places. Submit your answer to the nearest whole number.)
Answers
Answer:
The optimal production quantity is 9,322 cards.
Step-by-step explanation:
The information provided is:
Cost of the paper = $0.05 per card
Cost of printing = $0.15 per card
Selling price = $2.15 per card
Number of region (n) = 4
Mean demand = 2000
Standard deviation = 500
Compute the total cost per card as follows:
Total cost per card = Cost of the paper + Cost of printing
= $0.05 + $0.15
= $0.20
Compute the total demand as follows:
Total demand = Mean × n
= 2000 × 4
= 8000
Compute the standard deviation of total demand as follows:
[tex]SD_{\text{total demand}}=\sqrt{500^{2}\times 4}=1000[/tex]
Compute the profit earned per card as follows:
Profit = Selling Price - Total Cost Price
= $2.15 - $0.20
= $1.95
The loss incurred per card is:
Loss = Total Cost Price = $0.20
Compute the optimal probability as follows:
[tex]\text{Optimal probability}=\frac{\text{Profit}}{\text{Profit+Loss}}[/tex]
[tex]=\frac{1.95}{1.95+0.20}\\\\=\frac{1.95}{2.15}\\\\=0.9069767\\\\\approx 0.907[/tex]
Use Excel's NORMSINV{0.907} function to find the Z-score.
z = 1.322
Compute the optimal production quantity for the card as follows:
[tex]\text{Optimal Production Quantity}=\text{Total Demand}+(z\times SD_{\text{total demand}}) \\[/tex]
[tex]=8000+(1.322\times 1000)\\=8000+1322\\=9322[/tex]
Thus, the optimal production quantity is 9,322 cards.
Use the given categorical data to construct the relative frequency distribution. Natural births randomly selected from four hospitals in a highly populated region occurred on the days of the week (in the order of Monday through Sunday) with the frequencies 53, 63, 68, 58, 61, 43, 54. Does it appear that such births occur on the days of the week with equal frequency?
Answers
Answer: Yes
Step-by-step explanation:
See explanations in the attached document
do following division with polynomials
1) (x^3-2x^2+3x-3)÷(x+2)
Answers
Explanation:
f(x) = x^3 - 2x^2 + 3x -3
Set x+ 2 = 0 => x = -2
f(-2) = (-2)^3 - 2(-2)^2 + 3(-2) - 3
f(-2) = -8 - 8 -6 - 3
f(-2) = -25
So the answer is -25
Please help! Find the perimeter and total area of the composite shape below!
Answers
Answer:
Perimeter = 19.42 in and area = 26.13 in^2.
Step-by-step explanation:
The perimeter = 2 * 5 + length of the semicircle
= 10 * 3.14 * 3
= 19.42 in.
Total area = area of the semicircle + area of the triangle
= 1/2 * 3.14 * 3^2 + 3 * 4
= 26.13 in^2.
What are the trigonometric ratios? Write all six.
Answers
Step-by-step explanation:
Check that attachment
Hope it helps :)
Hey! :)
________ ☆ ☆_________________________________________
Answer:
There are six trigonometric ratios, which will be under “Explanation”
Step-by-step explanation:
Trigonometric ratios are a measurements of a right triangle.
Here are the all the six trigonometric ratios.
1. cotangent (cot)
2. cosecant (csc)
3. cosine (cos)
4. secant (sec)
5. sine (sin)
6. tangent (tan)
Hope this helps! :)
_________ ☆ ☆________________________________________
By, BrainlyMember ^-^
Good luck!
determining probability of events. please help!
Answers
Answer:
23/90
Step-by-step explanation:
55/90 + 12/90 = 67/9090 - 67 = 2323/9023/90 balls are green or white
i hope this helps!
Given the function below, find value (s) of x if f(x)=7
Answers
Explanation:
f(x) and y are often used interchangeably. We are asked to find the x value(s) when y = 7.
Circle the rows where 7 shows up in the y column. You should find that x = -1 and x = 1 are circled as well.
So f(x) = 7 leads to x = -1 or x = 1. In other words, f(-1) = 7 and f(1) = 7 also.
For the function given the value of x can be two, one is 1 and the other one is -1 if the f(x)=7
What is a Function?
A function relates an input to an output means it is a kind of relationship between the variable y and x. It is denoted through f(x).
What is a Variable?A variable is defined as a quantity that may assume any one of a set of values.
How to find the value of x in a function?
In the question the function is given as:
Function is denoted through f(x) and f(x) shows the value of x. We know that the value of f(x)=7 which is given in the question. So we will take the value of x in the front of 7 which is written in the y column. We have got two values in this which are 1 and -1. So they both will be the values of x.
Hence the value of x for the function given in the question are -1 and 1
Learn more about functions at https://brainly.com/question/25638609
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Twice a number plus three times a second number is twenty two. Three times the first number plus four times the second is thirty one. Find the numbers
Answers
3x+4y=31
8x+12y=88
-9x-12y=-93
x=5
y=4
5 and 4.
Answer:
The numbers are 5 and 4Step-by-step explanation:
Let the first number be x
Let the second number be y
For the first equation
2x + 3y = 22
For the second equation
3x + 4y = 31
Multiply the first one by 3 and the second one by 2
That's
First equation
6x + 9y = 66
Second equation
6x + 8y = 62
Subtract the second equation from the first one
That's
6x - 6x + 9y - 8y = 66 - 62
y = 4Substitute y = 4 into 2x + 3y = 22
That's
2x + 3(4) = 22
2x = 22 - 12
2x = 10
Divide both sides by 2
x = 5Hope this helps you
let f(x) = 2x^2 + x - 3 and g(x) = x+ 2. Find (f • g) (x)
Answers
Answer:
(f • g) (x) = 2x² + 9x + 7Step-by-step explanation:
f(x) = 2x² + x - 3
g(x) = x + 2
To find (f • g) (x) substitute g(x) into every x in f (x)
That's
(f • g) (x) = 2(x + 2)² + x + 2 - 3
Expand and simplify
(f • g) (x) = 2( x² + 4x + 4) + x - 1
= 2x² + 8x + 8 + x - 1
Group like terms
= 2x² + 8x + x + 8 - 1
We have the final answer as
(f • g) (x) = 2x² + 9x + 7Hope this helps you
Find the present value of an investment that is worth $19,513.75 after earning 3% simple interest for 512 years.
Answers
Answer:
$16,750.00
Step-by-step explanation:
Simple interest:
I = Prt
Value of an investment of value P over t years at r interest rate:
F = P + Prt
F = P(1 + rt)
19,513.75 = P(1 + 0.03 * 5.5)
1.165P = 19,513.75
P = 16,750
Answer: $16,750.00
The present value of the investment was $16,750 which is worth $19,513.75 after earning 3% simple interest for 512 years.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100
We have been given data as:
Rate of Interest (R) = 3% = 3/100 = 0.03
Time (T) = 512 years
Value of an investment of value P over t years at r interest rate:
A = P + Prt
A = P(1 + rt)
19,513.75 = P(1 + 0.03 × 5.5)
19,513.75 = 1.165P
1.165P = 19,513.75
P = 19,513.75/1.165
P = 16,750
Thus, the present value of the investment was $16,750 which is worth $19,513.75 after earning 3% simple interest for 512 years.
Learn more about the simple interest here:
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find the lowest common denominator of 3/x^3y and 7/xy^4
Answers
[tex]\dfrac{3}{x^3y} +\dfrac{7}{xy^4}\\\\\\\dfrac{1}{xy}(\dfrac{3}{x^2} +\dfrac{7}{y^3})[/tex]
It's xy.
In 2009, a school population was 1,700. By 2017 the population had grown to 2,500. Assume the population is changing linearly. How much did the population grow between 2009 and 2017?
Answers
Answer:
100
Step-by-step explanation:
The population is changing linearly. This means that the population is increasing by a particular value n every year.
From 2009 to 2017, there are 8 increases and so, the population increases by 8n.
The population increased from 1700 to 2500. Therefore, the population increase is:
2500 - 1700 = 800
This implies that:
8n = 800
=> n = 800/8 = 100
The average population growth per year is 100.
Answer:
100
Step-by-step explanation:
aaaaa
How much do wild mountain lions weigh? Adult wild mountain lions (18 months or older) captured and released for the first time in the San Andres Mountains had the following weights (pounds):
69 103 126 122 60 64
Assume that the population of x values has an approximately normal distribution.
A) Use a calculator with mean and sample standard deviation keys to find the sample mean weight x and sample standard deviation s.
B) Find a 75% confidence interval for the population average weight of all adult mountain lions in the specified region.
Answers
Answer:
Step-by-step explanation:
From the information given:
Mean [tex]\overline x = \dfrac{\sum x_i}{n}[/tex]
Mean [tex]\overline x = \dfrac{69+103+126+122+60+64}{6}[/tex]
Mean [tex]\overline x = \dfrac{544}{6}[/tex]
Mean [tex]\overline x = 90.67[/tex] pounds
Standard deviation [tex]s = \sqrt{\dfrac {\sum (x_i - \overline x) ^2}{n-1}[/tex]
Standard deviation [tex]s = \sqrt{\dfrac {(69 - 90.67)^2+(103 - 90.67)^2+ (126- 90.67) ^2+ ..+ (64 - 90.67)^2}{6-1}}[/tex]
Standard deviation s = 30.011 pounds
B) Find a 75% confidence interval for the population average weight of all adult mountain lions in the specified region.
At 75% confidence interval ; the level of significance ∝ = 1 - 0.75 = 0.25
[tex]t_{(\alpha/2)}[/tex] = 0.25/2
[tex]t_{(\alpha/2)}[/tex] = 0.125
t(0.125,5)=1.30
Degree of freedom = n - 1
Degree of freedom = 6 - 1
Degree of freedom = 5
Confidence interval = [tex](\overline x - t_{(\alpha/2)(n-1)}(\dfrac{s}{\sqrt{n}})< \mu < (\overline x + t_{(\alpha/2)(n-1)}(\dfrac{s}{\sqrt{n}})[/tex]
Confidence interval = [tex](90.67 - 1.30(\dfrac{30.011}{\sqrt{6}})< \mu < (90.67+ 1.30(\dfrac{30.011}{\sqrt{6}})[/tex]
Confidence interval = [tex](90.67 - 1.30(12.252})< \mu < (90.67+ 1.30(12.252})[/tex]
Confidence interval = [tex](90.67 - 15.9276 < \mu < (90.67+ 15.9276)[/tex]
Confidence interval = [tex](74.7424 < \mu <106.5976)[/tex]
i.e the lower limit = 74.74 pounds
the upper limit = 106.60 pounds
A Microgates Industries bond has a 10 percent coupon rate and a $1,000 face value. Interest is paid semiannually, and the bond has 20 years to maturity. If investors require a 12 percent yield, what is the bond’s value? * a. $849.45 b. $879.60 c. $985.18 d. $963.15 e. None of the above
Answers
Answer:
a. $849.45
Step-by-step explanation:
In the above question, we are given the following information
Coupon rate = 10%
Face value = 1000
Maturity = n = 20 years
t = number of periods = compounded semi annually = 2
Percent yield = 12% = 0.12
Bond Value formula =
C/t × ([1 -( 1/ 1 + r/t)-^nt ÷] r/t) +( F/ (1 + r/t)^nt)
C = coupon rate × face value = 10% × 1000 = 100
Bond value:
= 100/2 × ( [1 - (1 /1 + 0.12/2)^-20×2]÷ 0.12/2)+ (1000/( 1 + 0.12/2)^20×2
= 50 × ( [1 - (1 /1 + 0.06) ^40] ÷ 0.06) + ( 1000/ (1 + 0.06) ^40
= 50 × ( [1 - (1/ (1.06) ^40] ÷ 0.06 ) + (1000/(1.06)^40)
= 50 × 15.046296872 + 97.222187709
= $849.45
Bond value = $849.45
The length of a rectangle is 7 more than the width. The area is 744 square centimeters. Find the length and width of the rectangle.
Answers
Answer:
the width of the rectangle is 24 centimeters and the length is 31 centimeters.
Step-by-step explanation:
We first have to write an equation for this, but let's just recall that the area of a rectangle is equal to the length times the width. A=L×W.
A is the area
L is the length
W is the width.
So, for our equation we can start out by putting that 744= ? times ?.
So, we are given that the length is 7 more than the width. We are going to have to translate that to represent the length.
We need a variable. Let's use the letter "W," the width of the rectangle.
W=W.
The length is 7 more than the width, so it is L=W+7.
Length represents the W+7
Width represents W.
Now, we can complete our equation.
744=W(W+7).
Simplify the expression.
744=[tex]W^{2}[/tex]+7W.
Alright, you may be thinking on how we are going to solve this problem. This equation correlates with quadratic functions.
Let's complete the square.
In a quadratic function, the standard from is y=[tex]ax^{2} +bx+c[/tex].
We need to find the c value.
We can do this by applying a formula. The formula states that c= b/2 and the whole thing squared. In other words, [tex](\frac{b}{2} )^{2}[/tex].
In this case, the b value is 7.
square 7, which is 49 and square 2 which is 4.
Now, the c value is 49/4.
We have now just created a perfect square trinomial.
Not only do we add 49/4 to W squared plus 7W, we also add 49/4 to 744.
744 plus 49/4 is 756/25.
Now, we have [tex]W^{2}+7w+\frac{49}{4} = 756.25[/tex]
Change W squared plus 7w plus 49/4 to a binomial squared.
Just take the square root of the a value, W, and 49/4 for c. the square root of W squared is W. the square root of 49/4 is 7/2.
Those values are to the power of 2.
In other words, [tex](W+\frac{7}{2})^{2} =756.25[/tex]
To isolate for W, take the square root of both sides.The square root of W plus 7/2 squared is just W+7/2. The square root of 756.25 is 27.5
There are two solutions for W because square roots be positive or negative, but we are dealing with positive since negative doesn't make sense with the context of the problem.
We have [tex]W+3.5 or \frac{7}{2}=27.5[/tex]
Isolate for W by subtracting both sides by 3.5 You get to W=24.
Therefore, the width of the rectangle is 24 centimeters.
Alright, we found the width. We now need to find the length. The problem stated that the rectangle was 7 more than the width. So, 24+7=31. Therefore, the length of the rectangle is 31 centimeters.
L=31cm
W=24cm.
I hope this was helpful! I wish you have an amazing day!