Answer:
Area of rectangle = [tex]196\,m^2[/tex]
Length of rectangle = 14 m
Width of rectangle = 14 m
Step-by-step explanation:
Given:
Perimeter of rectangle is 56 m
To find: the maximized area of a rectangle and the length and width
Solution:
A function [tex]y=f(x)[/tex] has a point of maxima at [tex]x=x_0[/tex] if [tex]f''(x_0)<0[/tex]
Let x, y denotes length and width of the rectangle.
Perimeter of rectangle = 2( length + width )
[tex]=2(x+y)[/tex]
Also, perimeter of rectangle is equal to 56 m.
So,
[tex]56=2(x+y)\\x+y=28\\y=28-x[/tex]
Let A denotes area of rectangle.
A = length × width
[tex]A=xy\\=x(28-x)\\=28x-x^2[/tex]
Differentiate with respect to x
[tex]\frac{dA}{dx}=28-2x[/tex]
Put [tex]\frac{dA}{dx}=0[/tex]
[tex]28-2x=0\\2x=28\\x=14[/tex]
Also,
[tex]\frac{d^2A}{dx^2}=-2<0[/tex]
At x = 14, [tex]\frac{d^2A}{dx^2}=-2<0[/tex]
So, x = 14 is a point of maxima
So,
[tex]y=28-x=28-14=14[/tex]
Area of rectangle:
[tex]A=xy=14(14)=196\,m^2[/tex]
Length of rectangle = 14 m
Width of rectangle = 14 m
How do I write an equation represented by the line?
Answer:
This line can be represented by the line y = 3/4x + 2.
Step-by-step explanation:
The slope is identified as the m in y = mx + b. The slope is the rise/run of your line (AKA how many units it goes upwards/downwards and then goes to the right/left to meet the second given point).
In this case, the line rises 3 units from 2 to 5, and then goes to the right by 4 units to meet the coordinate (4, 5).
B in the equation refers to the y-intercept, or where the line intersects/crosses the y-axis. In this case, it is the coordinate (0, 2).
Finally, x is irrelevant and is placed in the equation for no reason (at least that I am aware of in my several years of high school math).
Therefore, your final equation is y = 3/4x + 2.
The width of the pond shown is x ft. What is the value of x.
Answer:
Width (x) = 160ft
See explanation below
Step-by-step explanation:
The information given is incomplete as we are not told if the shape of the pond. This is about determining the surface area of a water body.
Looking at the question, we can tell we are to find the width of a pond whose shape wasn't given.
Assuming the shape of the pond is either a rectangular or square pond, let's consider the following question:
The acreage of a rectangular pond is 1.54 acres and the length is 420ft. The width of the pond shown is x ft. What is the value of x.
Find attached the diagram used for solving the question.
Formula for calculating the acreage of
a Square or Rectangular Ponds is multiplying average length (in feet) times average width (in feet) and dividing the result by 43,560 to derive our answer in acres.
That is: Average Length (ft) × Average Width (ft) ÷ 43,560 = Acres
Since we have been given acreage and length, we would make width subject of formula.
Width = (Acreage × 43500)/length
Width (x) = (1.54 × 43,560)/420
=67082.4 ÷ 420 = 159.72
Width (x) = 160ft (nearest feet)
Please answer this math quesiton im desperate !! tysm!! will give brainliest!!
Answer: i am pretty sure it is C dont get your hopes up but
Step-by-step explanation:
from what i see if you take the y=3 over 2 and make that a decimal you can now take y = that number and make a line and so on then after that step you want to now take your final answer which is x and subtract it by 3 i MIGHT be wrong but i tried.
Answer:
The Answer is C I hope this helped
Step-by-step explanation:
I did it on my quiz!
the length of a rectangular park excerdees its width of 17m if the perimeter of the park find the dimension of the park
Answer:
math papa look on that website
Step-by-step explanation:
A high tech company operates a satellite which can measure the size of features on the surface of the earth. They use this technology to measure a particular rectangular field and find it's length to be 311 \pm± 1.89 (in meters) and it's width to be 354 \pm± 1.39 (in meters). They plan to report the area of the field as A\pm\Delta AA ± Δ A in units of acres. (1 acre = 4840 square yards & 1 meter = 1.094 yards) What is \Delta AΔ A?
Answer:
1 acre
Step-by-step explanation:
in a certain town there were 113 robberies last year this year the number of robberies has gone down 14% how many robberies were there this year to the nearest whole number
Answer:
99 robberies
Step-by-step explanation:
What you are basically doing is taking the discount.
1 + 14% = 1.14
113 / 1.14 = 99.12
Which of the given expressions results in 0 when evaluated at x = 5? A. 5x(x − 7) B. (x − 8)(x − 5) C. (x + 7)(x − 2) D. (x + 5)(x − 8)
Answer:
B. (x - 8)(x - 5)
Step-by-step explanation:
If you plugged in x = 5 into the 2nd equation, you would see that you would be multiplying by 0, which would turn everything zero.
m-n/m^2-n^2 + ?/(m-1)(m-2) - 2m/m^2-n^2
Answer:
The answer is "[tex]\bold{\frac{(m-1)(m-2)}{(m-n)}}[/tex]"
Step-by-step explanation:
Given:
[tex]\bold{\frac{(m-n)}{m^2-n^2} + \frac{?}{(m-1)(m-2)} - \frac{2m}{m^2-n^2}=0}\\\\[/tex]
let, ? = x then,
[tex]\Rightarrow \frac{(m-n)}{m^2-n^2} + \frac{x}{(m-1)(m-2)} - \frac{2m}{m^2-n^2}=0\\\\\Rightarrow \frac{(m-n)}{m^2-n^2} - \frac{2m}{m^2-n^2}=- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{(m-n)-2m}{(m^2-n^2)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{m-n-2m}{(m^2-n^2)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{-n-m}{(m^2-n^2)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{-(m+n)}{(m+n)(m-n)} =- \frac{x}{(m-1)(m-2)} \\\\\Rightarrow \frac{-1}{(m-n)} =- \frac{x}{(m-1)(m-2)} \\\\[/tex]
[tex]\Rightarrow -((m-1)(m-2))=-x(m-n) \\\\\Rightarrow x= \frac{- (m-1)(m-2)}{- (m-n)} \\\\\Rightarrow \boxed{x= \frac{(m-1)(m-2)}{(m-n)}} \\[/tex]
In a particular month, Ezhil spent one-fifth of her salary on shopping. Two-fifth of the remaining she gave to her sister. If she has Rs 11 , 040 left, what was her salary in that month?
Answer:
[tex]Salary = Rs23000[/tex]
Step-by-step explanation:
Given
[tex]Shopping = \frac{1}{5}[/tex]
[tex]Sister = \frac{2}{5}R[/tex]
[tex]Left over = Rs11,040[/tex]
Required
Her salary in that month
Given that she spent [tex]\frac{1}{5}[/tex] of her salary on shopping, this implies that she has [tex]\frac{4}{5}[/tex] of her salary left
From what's left, she gave her sister [tex]\frac{2}{5}[/tex]
This means she gave her sister [tex]\frac{2}{5} * \frac{4}{5}[/tex]
Sister = [tex]\frac{8}{25}[/tex]
Calculating a fraction of what's left
[tex]Left over = 1 -Shopping - Sister[/tex]
[tex]Left over = 1 - \frac{1}{5}- \frac{8}{25}[/tex]
[tex]Left over = \frac{25 - 5 - 8}{25}[/tex]
[tex]Left over = \frac{12}{25}[/tex]
Recall that she has Rs11,040
This means that
[tex]\frac{12}{25} of Salary = Rs11,040[/tex]
Multiply both sides by [tex]\frac{25}{12}[/tex]
[tex]\frac{12}{25} * \frac{25}{12} * Salary = Rs11,040 * \frac{25}{12}[/tex]
[tex]Salary = Rs11,040 * \frac{25}{12}[/tex]
[tex]Salary = \frac{Rs276000}{12}[/tex]
[tex]Salary = Rs23000[/tex]
Hence, her salary for that month was Rs23000
Answer:
Her salary = Rs 23000
Step-by-step explanation:
In a month, Ezhil spent 1/5 of her salary on shopping.
Let
Her salary = a
she spent 1/5 of a on shopping
Amount spent on shopping = 1a/5
She gave 2/5 of the remaining to her sister .
The remaining money = a - 1a/5 = 5a - a/5 = 4a/5
She gave 2/5 of 4a/5 to her sister. Therefore,
The amount she gave to her sister = 2/5 × 4a/5 = 8a/25
Out of her salary she is left with Rs 11040 .Therefore,
a - 1a/5 - 8a/25 = 11040
25a - 5a - 8a/25 = 11040
12a/25 = 11040
12a = 11040 × 25
12a = 276000
divide both sides by 12
a = 276000/12
a = 23000
Her salary = Rs 23000
(WITH IMAGE) What is the value of m?
Answer:
10
Step-by-step explanation:
The two marked angles are a linear pair, so have a sum of 180°.
(2m +10) +(5m +100) = 180
7m +110 = 180 . . . . . . . collect terms
7m = 70 . . . . . . . . . . . . subtract 110
m = 10 . . . . . . . . . . . . . divide by 7
the line of symmetry for the quadratic equation y=ax^2+8x-3 is x=4. What is the value of “a”?
Answer:
The value of a is -1.
Step-by-step explanation:
The line of symmetry of a parabola is a vertical line that divides the parabola into two congruent halves.
For a quadratic function in standard form, [tex]y=ax^2+bx+c[/tex], the line of symmetry is a vertical line given by [tex]x=-\frac{b}{2a}[/tex].
We know that the quadratic equation, [tex]y=ax^2+8x-3[/tex], has x = 4 as line of symmetry. Therefore, the value of a is:
[tex]4=-\frac{8}{2a}\\\\4=-\frac{4}{a}\\\\4a=-4\\\\a=-1[/tex]
Answer:
a=-1
Step-by-step explanation:
so that the other person could get brainliest
Can someone help?
Find the mean of the data in the bar chart below.
Answer:
b
Step-by-step explanation:
Answer:
2.5
Round this up to 3
Step-by-step explanation:
Add all the numbers of the graph together
1+4+3+2 = 10
Divide by 4 because it has 4 categories in total
= 2.5
Round up because its asking for puppets and theres not 1/2 of a puppet.
At a certain gas station, 40% of the customers use regular gas (A1), 35% use plus gas (A2), and 25% use premium (A3). Of those customers using regular gas, only 40% fill their tanks (event B). Of those customers using plus, 80% fill their tanks, whereas of those using premium, 70% fill their tanks.
Required:
a. What is the probability that the next customer will request extra unleaded gas and fill the tank?
b. What is the probability that the next customer fills the tank?
c. If the next customer fills the tank, what is the probability that regular gas is requested?
Answer:
A) 0.28
B) 0.615
C) 0.26
Step-by-step explanation:
We are given;
Probabilities of customers using regular gas:P(A1) = 40% = 0.4
Probabilities of customers using plus gas: P(A2) = 35% = 0.35
Probabilities of customers using premium gas: P(A3) = 25% = 0.25
We are also given with conditional probabilities of full gas tank:
P(B|A1) = 40% = 0.4
P(B|A2) = 80% = 0.8
P(B|A3) = 70% = 0.7
A) The probability that next customer will requires extra unlead gas(plus gas) and fill the tank is:
P(A2 ∩ B) = P(A2) × P(B|A2)
P(A2 ∩ B) = 0.35 × 0.8
P(A2 ∩ B) = 0.28
B)The probability of next customer filling the tank is:
P(B) = [P(A1) • P(B|A1)] + [P(A2) • P(B|A2)] + [P(A3) • P(B|A3)]
P(B) = (0.4 × 0.4) + (0.35 × 0.8) + (0.25 × 0.7)
P(B) = 0.615
C)If the next customer fills the tank, probability of requesting regular gas is;
P(A1|B) = [P(A1) • P(B|A1)]/P(B)
P(A1|B) = (0.4 × 0.4)/0.615
P(A1|B) = 0.26
After collecting the data, Christopher finds that the total snowfall per year in Reamstown is normally distributed with mean 94 inches and standard deviation 14 inches. What is the probability that, in a randomly selected year, the snowfall was greater than 52 inches? Use the empirical rule. Provide the final answer as a percent rounded to two decimal places.
Answer:
99.85
Step-by-step explanation:
$99.85\text{ %}$
Notice that 52 inches is three standard deviations less than the mean. Based on the Empirical Rule, 99.7% of the yearly snowfalls are within three standard deviations of the mean. Since the normal distribution is symmetric, this implies that 0.15% of the yearly snowfalls are less than three standard deviations below the mean. Alternatively, 99.85% of the yearly snowfalls are greater than three standard deviations below the mean.
What is the volume, to the nearest whole cubic inch, of a cylinder with a height of 10 inches and a radius of 8 inches? Use
* = 3.14 and round your answer to the whole number.
cubic inches
Answer:
2,009.6 inches³
Step-by-step explanation:
The formula for the volume of a cylinder:
V = πr²h
Let's substitute into the given equation:
V = πr²h
V = (3.14)(8²)(10)
Solve:
V = (3.14)(8²)(10)
V = (3.14)(64)(10)
V = (200.96)(10)
V = 2,009.6
Therefore, the volume of the cylinder is 2,009.6 cubic inches.
In a recent survey of 200 elementary students, many revealed they preferred math than English. Suppose that 80 of the students surveyed were girls and that 120 of them were boys. In the survey, 60 of the girls, and 80 of the boys said that they preferred math more.
Required:
a. Calculate an 80% confidence interval for the difference in proportions.
b. What is the standard error of the difference in the probability between that girls prefer math more and boys prefer math more?
1. 0.4097
2. 0.0042
3. 0.0833
4. 0.0647734
c. What is the difference in the probability between that girls prefer math more and boys prefer math more?
1. 0.0833
2. 0.5
3. 0.0042
4. 0.4097
Answer:
Step-by-step explanation:
a) Confidence interval for the difference in the two proportions is written as
Difference in sample proportions ± margin of error
Sample proportion, p= x/n
Where x = number of success
n = number of samples
For the girls,
x = 60
n1 = 80
p1 = 60/80 = 0.75
For the boys
x = 80
n2 = 120
p2 = 80/120 = 0.67
Margin of error = z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.8 = 0.2
α/2 = 0.2/2 = 0.1
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.1 = 0.9
The z score corresponding to the area on the z table is 1.282. Thus, z score for confidence level of 80% is 1.282
Margin of error = 1.282 × √[0.75(1 - 0.75)/80 + 0.67(1 - 0.67)/120]
= 1.282 × √0.00418625
= 0.081
Confidence interval = 0.75 - 0.67 ± 0.081
= 0.08 ± 0.081
b) The formula for determining the standard error of the distribution of differences in sample proportions is expressed as
Standard error = √{(p1 - p2)/[(p1(1 - p1)/n1) + p2(1 - p2)/n2}
Therefore,
Standard error = √{(0.
75 - 0.67)/[0.75(1 - 0.75)/80 + 0.67(1 - 0.67)/120]
Standard error = √0.08/0.00418625
Standard error = 4.37
c) the difference in the probability between that girls prefer math more and boys prefer math more is
0.75 - 0.67 = 0.08
10. How many different combinations are there of the digits 46987?
25.
Look at this:
There are 5 digits in 46987.
There will be 5 combinations.
5 times 5 = 25.
You have your answer.
A total of 31 possible combinations are there for number 46987.
What is a expression? What is a mathematical equation? What is Equation Modelling?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have a 5 - digit number 46987.
Assume that there are [y] possible combinations. For a [x] digit number, the total possible combinations are -
y = 2ˣ - 1
So, for [x] = 5, we will have -
y = 32 - 1
y = 31
Therefore, a total of 31 possible combinations are there for number 46987.
To solve more questions on Equations, Equation Modelling and Expressions visit the link below -
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In a recent survey, a random sample of 130 families were asked about whether they have a pet, and 67 reported that they have a pet. What value of z should be used to calculate a confidence interval with a 90% confidence level
Answer:
z = 1.645 should be used.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]z = 1.645[/tex].
z = 1.645 should be used.
Find the number of unique permutations of the letters in the word: ONGOING
Answer:
The Number of unique permutation is 6,615Step-by-step explanation:
This particular permutation deals with words that have repeated letters.
Given word = "ONGOING"
the formula for the permutation is
[tex]= \frac{n!}{mA! mB!.....mZ!}[/tex]
where n is the amount of letters in the word, and m A , m B , ... , m Z are the occurrences of repeated letters in the word. Each m equals the amount of times the letter appears in the word.
So in the word "ONGOING"
n= 7
mO= 2
mN= 2
mG=2
[tex]permutations = \frac{7!}{2!2!2!} \\\\permutations= \frac{7*6*5*4*3*2*1}{(2*1)*(2*1)*(2*1)}[/tex]
[tex]permutations= \frac{52920}{8} \\permutation = 6,615[/tex]
A restaurant uses 4/5 ounce of gravy for each serving of meat loaf. If 45 people
ordered meat loaf, how much gravy will the restaurant need?
ounces
Answer:
36
Step-by-step explanation:
Hope this helps and please rate brainliest!!!
Answer:
36 ounces
Step-by-step explanation:
We want to find the total amount of gravy the restaurant will need.
Multiply the gravy needed for one serving by the number of servings.
gravy for one serving × number of servings.
The restaurant uses 4/5 of an ounce for each serving, and 45 people ordered meatloaf. Therefore, the gravy for one serving is 4/5, and the number of servings is 45.
4/5 × 45
45 is equivalent to 45/1.
4/5 × 45/1
Multiply across the numerator (the top numbers: 4 and 45) and denominator (the bottoms numbers: 5 and 1)
(4× 45)/(5× 1)
180/5
Divide
36
Add appropriate units. In this case, the units are ounces.
36 ounces
The restaurant needs 36 ounces of gravy for 45 servings of meatloaf.
The point (-1,4) is on the terminal side of angle theta in standard position. What are the values of sine, cosine, tangent of theta
Answer:
cosФ = 0.97
sinФ = 0.292
tanФ = -4
Step-by-step explanation:
A general point P(x,y) with an angle Ф has the following trigonometrical functions:
[tex]sin\phi=\frac{y}{r}\\\\cos\phi=\frac{x}{r}\\\\tan\phi=\frac{y}{x}\\\\r=\sqrt{(x)^2+(y)^2}[/tex]
For the point P(-1 , 4) you obtain:
[tex]r=\sqrt{(-1)^2+(4)^2}=\sqrt{17}\approx 4.123[/tex]
[tex]sin\phi=\frac{4}{4.123}=0.97\\\\cos\phi=\frac{-1}{4.123}=0.242\\\\tan\phi=\frac{4}{-1}=-4[/tex]
(-36)1/2= -6 1/6
a.-6
b.1/2
c.no real numbers
Answer:
c
Step-by-step explanation:
Jenny had 188 but she is spending 14 per week
Answer:
14×7=98
188-98=90 so she had 90 left
What us the slope of the points, (0,20) and, (4,0)?
Answer:
-5
Step-by-step explanation:
The equation to find the slope between two points is y₂-y₁/x₂-x₁.
In this case that would be 0-20/4-0 which simplifies into -20/4=-5
So your slope is -5
Answer:
-5Solution,
Let the points be A and B
A(0,20)---------> (X1,y1)
B(4,0)------------>(x2,y2)
Now,
[tex]slope = \frac{y2 - y1}{x2 - x1} \\ \: \: \: \: \: \: \: \: \: = \frac{0 - 20}{4 - 0} \\ \: \: \: \: \: = \frac{ - 20}{4} \\ \: \: \: \: = - 5[/tex]
hope this helps...
Good luck on your assignment....
An Epson inkjet printer ad advertises that the black ink cartridge will provide enough ink for an average of 245 pages. Assume that this claim is accurate and that the standard deviation for this population is 15 pages. A random sample of 33 customers was surveyed about the number of pages they were able to print with their black ink cartridges. What the probability that the sample mean will be 246 pages or more?
Answer:
35.2% probability that the sample mean will be 246 pages or more
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 245 \sigma = 15, n = 33, s = \frac{15}{\sqrt{33}} = 2.61[/tex]
What the probability that the sample mean will be 246 pages or more?
This is 1 subtracted by the pvalue of Z when X = 246. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{246 - 245}{2.61}[/tex]
[tex]Z = 0.38[/tex]
[tex]Z = 0.38[/tex] has a pvalue of 0.6480.
1 - 0.6480 = 0.3520
35.2% probability that the sample mean will be 246 pages or more
Suppose there are 310 first-year lawyers in a particular metropolitan area with an average starting salary of $156,000 and a standard deviation of $13,000. What is the standard error of the mean for a random sample of 33 first-year lawyers?
Answer:
$ 2263
Step-by-step explanation:
In this case to calculate the standard error of the mean, we only need the standard deviation (sd) and the number of the random sample (n).
sd = 13000
n = 33
SE = sd / (n ^ (1/2))
replacing:
SE = 13000 / (33 ^ (1/2))
SE = 2263.01
What the standard error of the mean for a random sample of 33 first-year lawyers means is $ 2263
The standard error of the mean is $2263
Calculation of the standard error of the mean:Since here are 310 first-year lawyers in a particular metropolitan area with an average starting salary of $156,000 and a standard deviation of $13,000.
So, the standard error is
[tex]= 13000 \div (33 ^ {(1\div 2))}[/tex]
= 2263.01
Therefore, we can conclude that The standard error of the mean is $2263
learn more about salary here: https://brainly.com/question/6078275
8 1/6 divide 1 7/8?
The quotient is close to _____
Answer:
4.35 rounded to the nearest hundredth
4.3 rounded to the nearest tenth
4 rounded to the nearest whole number.
Step-by-step explanation:
[tex]8\frac{1}{6}[/tex] ÷ [tex]1 \frac{7}{8}[/tex] =
[tex]\frac{49}6}[/tex] ÷ [tex]\frac{15}{8} =[/tex]
[tex]\frac{49}{6} *\frac{8}{15} =[/tex]
[tex]\frac{392}{90} =[/tex]
[tex]4 \frac{32}{90} =[/tex]
[tex]4\frac{16}{45}[/tex] ≈ 4.35
Which number line shows the solution set for StartAbsoluteValue 2 p minus 4 EndAbsoluteValue greater-than-or-equal-to 6?
Answer:
B on edge 2022
Step-by-step explanation:
The three sides of a right-angled triangle are x, x+1 and 5. Find x and the area, if the longest side is 5.
Answer:
x = 3
area = 6
Step-by-step explanation:
using phytagoras's. theorem
a² + b² = c² (with c is the longest one)
x² + (x+1)² = 5²
x² + x² + 2x + 1 = 25
2x² + 2x - 24 = 0 (divide all by 2)
x² + x -12 = 0 then factorize
(x-3)(x+4) = 0
we get x = 3 and x = -4. Take the positive one.
so now we have x = 3 then x + 1 must be 4.
the area is
A = ½ . 3 . 4 = 6
Suppose you want to have $400,000 for retirement in 30 years. Your account earns 4% interest.
a) How much would you need to deposit in the account each month?
Answer:
if he wants to have $400000 on gis bank in 30 years at 4 %rate then he needs to deposit $15151.5 per month