Perimeter = 36 units
width = x
length = 4x - 2
Equation of perimeter = 2width + 2length
Substitution
36 = 2(x) + 2(4x - 2)
Expanding
36 = 2x + 8x - 4
36 = 10x - 4
36 + 4 = 10x
40 = 10x
x = 40/10
x = 4
Someone help me ASAP!!!plsss
Answer:
See my photo bro. hope it can help
part (a) Solve for x: 1 /x − 1 /x + 1 = 3.
part (b) Solve for t: 2 = Square root √ (1 + t) power of 2 + (1 − 2t) power of 2
part (c) Solve for t: 3/√5 = Square root √(1 + t) power of 2 + (1 − 2t)power of 2
part (d) Solve for t: 0 = Square root √ (1 + t)power of 2 + (1 − 2t)power of 2
The value of x in part (a) is [-3+√21]/6 and [-3-√21]/6, the value of t in part (b) is (1/5+√11/5) and (1/5-√11/10), the value of t in part (c) is 1/5 and the value of t in part (d) is 1/5-3/5i and 1/5+3/5i.
Part a. Solving for x,
1/x - 1/(x+1) = 3
(1-x+x)/x(x+1) = 3
1/(x²+x) = 3
1 = 3x²+3x
3x²+3x-1=0
Solving the quadratic by using quadratic formula,
x = [-b±√(b²-4ac)]/2a
Here,
a = 3
b = 3
c = -1
Putting all the values,
x= [-3±√(3²-4(3)(-1)]/6
x = [-3±√21]/6
We get,
x = [-3+√21]/6 and
x = [-3-√21]/6
Part b. Solving for t;
2 =√[(1+t)²+(1-2t)²]
Squaring both sides,
4 = (1+t)²+(1-2t)²
4 = 1+t²+2t+1+4t²-4t
2 = 5t²-2t
5t²-2t-2=0
Solving the equation by using quadratic formula,
t= [-b±√(b²-4ac)]/2a
Here,
a = 5
b = -2
c = -2
Putting all the values,
t = [2±√(4-4(5)(-2))]/10
t = [2±√44]/10
We get
t = (1/5+√11/5) and (1/5-√11/10)
Part c. Solving for t;
3/√5 = √[(1 + t)² + (1 − 2t)²]
Squaring both sides,
9/5 = (1+t)²+(1-2t)²
9/5 = 1+t²+2t+1+4t²-4t
9 = 5+5t²+10t+5+20t²-20t
25t²-10t+1=0
t = [-b±√(b²-4ac)]/2a
Here,
a = 25
b = -10
c = 1
Putting all the values,
t = [10±√(100-4(25))]/50
t= [10±0]/50
t= 1/5
Part d. Solving for t;
0 = √[(1 + t)²+(1 − 2t)²]
Squaring both sides,
(1+t)² =-(1-2t)²
1+t²+2t = -(1+4t²-4t)
1+t²+2t = -1-4t²+4t
5t²-2t+2=0
Solving the equation by using quadratic formula,
t = [-b±√(b²-4ac)]/2a
Here,
a = 5
b = -2
c = 2
Putting all the values,
t = [2±√(4-4(5)(-2)]/10
t = [2±√(-36)]/10
t = [2±6√(-1)]/10
√-1 is 'iota' or i.
t = (2±6i)/10
We get,
t = 1/5-3/5i and 1/5+3/5i
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Alondra bought a $1,700 television on an installment plan. The installment agreement included a
$170 down payment and 18 monthly payments of $105 each. What is the total finance charge?
The total finance charge is $360.
Given:
Alondra bought a $1,700 television on an installment plan.
The installment agreement included a $170 down payment and 18 monthly payments of $105 each.
Total amount paid = down payment + payment of each month * number of months.
= 170 + 105 * 18
= 170 + 1890
Total amount paid = $2060
Total finance charge = total amount paid - $1700
= $2060 - $1700
= $360.
Therefore the total finance charge is $360.
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The graph shown below expresses a radical function that can be written in the form f(x) = a(x+k)lin+c. What does the graph tell you about the value of k in this function? 1 1 15 1 1 1 1 1 1 1 1 1 1 1: 18 4 A kis greater than zero. B. It is not possible to tell whether kis greater than or less than zero. c. kis less than zero. D. kequals zero.
Given,
The function of the graph is,
[tex]undefined[/tex](Type an integer or decimal rounded to the nearest tenth as needed.)
The slope of the wooden beam is 39.8 ft
STEP - BY -STEP EXPLANATION
What to find?
The slope of the wooden beam.
Let y be the slope length.
To determine the slope length of the wooden beam we will follow the steps below.
Step 1
Write down the formula in calculating the sloping beam.
rise² + run² = slope length²
Step 2
Observe from the given diagram;
The value of the rise =12
The value of the run =76/2 = 38
Step 3
Substitute the values into the formula.
12²+ 38² = y²
Step 4
Simplify the above.
144 + 1444 = y²
1588 = y²
Step 5
Take the square root of both-side of the equation.
y = 39.8 ft
Therefore, the length of the sloping beam is 39.8 ft
Find a quadratic equation in standard form given its roots are 2+/- i square root of 3/2
We want to find a quadratic equation with the following roots:
[tex]\begin{gathered} x_+=2+i\sqrt{\frac{3}{2}} \\ x_-=2-i\sqrt{\frac{3}{2}} \end{gathered}[/tex]Then we have:
[tex]\begin{gathered} y=(x-x_+)\cdot(x-x_-) \\ y=(x-2-i\sqrt{\frac{3}{2}})\cdot(x-2+i\sqrt{\frac{3}{2}}) \\ y=x^2-2x+i\sqrt{\frac{3}{2}}x-2x+4-i2\sqrt{\frac{3}{2}}-i\sqrt{\frac{3}{2}}x+i2\sqrt{\frac{3}{2}}+\frac{3}{2} \\ y=x^2-4x+\frac{11}{2} \end{gathered}[/tex]solve using properties of logarithm round two decimal places1. 5e^ (-0.4t) = 1.506
To solve the exercise, we can use the following property of logarithms:
[tex]\ln (e^x)=x[/tex]Then, we can solve the equation like this:
[tex]\begin{gathered} 1.5e^{-0.4t}=1.506 \\ \text{ Divide by 1.5 from both sides of the equation} \\ \frac{1.5e^{-0.4t}}{1.5}=\frac{1.506}{1.5} \\ e^{-0.4t}=1.004 \\ \text{ Apply }\ln \text{ from both sides of the equation} \\ \ln (e^{-0.4t})=\ln (1.004) \\ \text{ Apply the mentioned property of logarithms} \\ -0.4t=\ln (1.004) \\ \text{ Divide by -0.4 from both sides of the equation} \\ \frac{-0.4t}{-0.4}=\frac{\ln(1.004)}{-0.4} \\ t\approx-0.01\Rightarrow\approx\text{ it reads "approximately"} \end{gathered}[/tex]Therefore, the solution of the equation rounded to two decimal places is -0.01.
The history museum charges a $10 fee plus $15 per student for a field trip.
The aquarium charges a $20 fee plus $10 per student. The lines in the graph
represent the cost of each field trip,
For what number of students will the total cost of each field trip be the same,
and what will that cost be?
O A. 120 students: $10
O B. 2 students: $40
O G. 40 students: $2
OD. 10 students: $120
Need help fast
Method 1
Write an equation for the total cost for each trip.
The history museum
Let the number of students = n
Total cost = 10 + 15n
The aquarium
Let the number of students = n
Total cost = 20 + 10n
Next, equate the two equations to find what number of students will the total cost of each field trip be the same.
[tex]\begin{gathered} 10\text{ + 15n = 20 + 10n} \\ 15n\text{ - 10n = 20 - 10} \\ 5n\text{ = 10} \\ n\text{ = }\frac{10}{5} \\ n\text{ = 2} \end{gathered}[/tex]The number of students = 2
The cost = 20 + 10(2) = 20 + 20 = $40
Answer
2 studnets; $40
Method 2:
To find number of students will the total cost of each field trip be the same.
From the graph, look for the point where the two graphs intercept.
Read the number of students as 2 and the cost as $40
Final answer
2 studnets; $40 Option B
F(x)=x+2 g(x)=x-4 (f g)(x)=
Given functions are:
[tex]\begin{gathered} f(x)=x+2 \\ g(x)=x-4 \end{gathered}[/tex]So:
[tex]\begin{gathered} f(x)\times g(x)=(x+2)(x-4) \\ f(x)\times g(x)=x^2-4x+2x-8 \\ f(x)\times g(x)=x^2-2x-8 \end{gathered}[/tex]06 WS Solving Systems of Equations and Inequalities Word Problems
Systems of Equations: Use two equations with two variables to solve each of the following problems.
(1) The sum of two numbers is 51 and their difference is 13. Find the two numbers.
som of
One Saturday the theat
The two numbers are 19 and 32 respectively.
What is equation?
Equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
According to question, let x and y be two numbers
x + y = 51 and
x- y = 13
from equation two,
x = 13+y
put this in equation one,
y+13+y = 51
2y = 51 - 13
2y = 38
y = 38/2 = 19
x = 13+y
x = 13+19
x = 32
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grgrgrgrggrdfb rgedg ee
Personal finance Funding a retirement goal. Austin Miller wishes to have $800,000 in a retirement fund 20 years from now. He can create the retirement fund by making a single lump-sum deposit today. How much would Austin need to have on deposit at retirement in order to withdraw $35,000 annually over the 15 years if the retirement fund earns 4 percent? To achieve his annual withdrawal goal of $35,000 calculated in part b, how much more than the amount calculated in part a must Austin deposit today in an investment earning 4 percent annual interest?
Answer:
$389,200
$21,200
Since,
[tex]\text{PMT}=\frac{PV}{\text{PVA}}[/tex]We are to find PV when the PMT is $35000. Since the PVA is 11.12,
[tex]PV=\text{PVA}\cdot\text{PMT}[/tex][tex]PV=(11.12)(35000)=389200[/tex]Hence, Austin would need to deposit $389,200.
For the last part, we first need to solve the PV at 4% in 20 years.
The PVIF would be:
[tex]\text{PVIF}=\frac{1}{(1+0.04)^{20}}=0.46[/tex]Then, solving for the PV:
[tex]PV=800000(0.46)=368000[/tex]Now, to know how much more should Austin deposit, we need to subtract the original PV from the PV that we got from part B.
That would be,
[tex]389200-368000=21200[/tex]Austin would need to deposit $21,200 more to achieve his withdrawal goal.
I need to know the answer quick because I have to go somewhere
First, we need to remember to rules when working with exponents:
[tex]\begin{gathered} \frac{1}{b^a}=b^{-a} \\ \text{and} \\ b^a\cdot b^c=b^{a+c} \end{gathered}[/tex]So, going back to our problem
[tex]\begin{gathered} \frac{2^{\frac{3}{4}}}{2^{\frac{1}{2}}} \\ =2^{\frac{3}{4}}\cdot2^{-\frac{1}{2}}=2^{\frac{3}{4}-\frac{1}{2}}=2^{\frac{1}{4}} \end{gathered}[/tex]And this last result is equal to
[tex]\begin{gathered} 2^{\frac{1}{4}}=\sqrt[4]{2} \\ \Rightarrow\frac{2^{\frac{3}{4}}}{2^{\frac{1}{2}}}=\sqrt[4]{2} \end{gathered}[/tex](1) In the 1970’s the popular advice columnist Ann Landers published a letter from a young couple about to be married. The letter said, “so many of our friends seem to resent their children. They envy us and our freedom to go and come as we please. Then there’s the matter of money. They say their kids keep them broke. Will you please ask your readers the question: 'If you had it to do over again – would you have children?' ” Nearly 10,000 of her readers responded. 70% said “no.” (2) The Good Housekeeping magazine published the results of the poll with a sidebar that said, “All of us at Good Housekeeping know that no mother will be able to read Ann Landers’ report without passionately agreeing or disagreeing. We would like to know what your reaction is. Won’t you therefore, take a minute or two to let us know how you would answer the question: 'If you had it to do over again, would you have children?' ” The results for the Good Housekeeping poll were 95% “yes.” These two polls gave opposite results! What i
Now that the poll has been published in magazines and newspapers, it is up to the readers to decide whether they want to participate. Consequently, the findings are biased by D. volunteer responses.
How to illustrate the information?Option A is incorrect since the estimate need not be underrepresented.
Option B is incorrect since it omits mentioning the good housekeeping magazine.
Option C is incorrect since the discrepancy isn't the result of sampling variance. Both resources' audiences are distinct and do not accurately reflect the general population.
Therefore, this is a voluntary answer, Option D is accurate.
Note that the complete question is attached.
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Tony is laying out the design for a concrete path. The path is to be L-shaped as shown in the plan. The measurements are in millimetres. Question prompt and response areaFill in all answer spaces Lengths of timber, called formwork, mark out the edges of the path. When ordering the timber for the formwork Tony adds an extra 10% to the measured length to allow for wastage. The timber supply company sells the formwork timber in lengths of 3600 mm. How many lengths of timber does Tony need to order?
Shape area of timber measured in millimeters is 10.8 m2.
Given:
Rectangle 1's length is 4000 mm, or 4 meters.
Rectangle 1's width is 1200 mm, or 1.2 meters.
Rectangle 2's length is [6200-1200] mm, or 5 meters.
Rectangle width 2 = 1200 mm = 1.2 m
Area of the form,
Shape's area is equal to the sum of its two rectangles.
Shape area equals [(4)(1.2)] plus [(5)(1.2)].
Shape's area equals 4.8 + 6.
Length area of the shape is 10.8 m2.
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4. How many integers are in the solution set of the inequality x² - 10 ≤ 0?
(a)1
(b) 2
(c) 3
(d) 6
(e) 7
Answer: 7
Step-by-step explanation: There are an infinite number of integers that satisfy the inequality. There are only seven integers that don't satisfy the inequality which are -3, -2, -1, 0, 1, 2 and 3.
I need to know the Highest, Second Highest, Middle, Second lowest, and lowest interest rate in that order.
Norman, this is the solution to the exercise:
According to the information provided, we have:
• Highest interest rate = 8.81%
,• Second highest interest rate = 8 4/5 % = 8.8%
,• Middle interest rate = 8 1/2 % = 8.5%
,• Second lowest interest rate = 8.313%
,• Lowest interest rate = 8.3%
The solution of a quadratic equation are called it’s ____1- x-intercepts2- zeros 3- roots4- all of the above
ANSWER
All of the above.
EXPLANATION
The solutions to a quadratic equation are the points where the graph of the equation touches the x-axis of the coordinate grid. This is why the solutions are called x-intercepts.
When solving for the solutions of a quadratic equation, the equation is equated to 0. This is why the solutions to a quadratic equation are called zeros of the equation or roots of the equation.
Hence, the correct option is All of the above.
This is the problem I am having.
Answer:
Can you send a better picture please thanks.
Step-by-step explanation:
Find the end behavior of the polynomial function y = 9x2 + 8x + 9.
SOLUTION
[tex]\begin{gathered} Given \\ y=9x^2+8x+9 \end{gathered}[/tex]The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity. The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.
The first option is the correct answer.
This probability distribution shows thetypical grade distribution for a Geometrycourse with 35 students.GradeАBсDFFrequency 5101532Using the frequencies given, find theprobability that a student earns a grade of A.p = [?]
Probability is expressed as
number of favourable outcomes/total number of possible outcomes
Looking at the given scenario, the number os students that earned a grade of A is 5. Since we are concerned with these students, then, the number of favourable outcomes is 5.
The total number of students for all grades is 35. This means that the total number of possible outcomes is 35
Thus, the probability that a student earns a grade of A is
5/35
= 0.14
Susana is enrolled in a photography class and has been Complete each statement.
pricing entry-level DSLR cameras. The prices are
Normally distributed.
Use the z-table to answer the question.
w
88%
-2 -1
Z-score
1 2 3
The Z-score of about
tells us that 88% of
the observations in the distribution are at or below
standard deviations above the mean.
The Z-score of about
tells us that 12%
of the observations in the distribution are at or below
standard deviations below the mean.
Answer:
Step-by-step explanation:
1.175
1.175
-1.175
1.175
First find the closest values possible to 0.88 (88%) on the z-score table. Once found we can see that it is located at positive 1.1 and directly in-between .07 and .08. Therefore we take the half of the two, .075, and get the answer of 1.175. The positive z-score, 1.175, tells us that we are 1.175 standard deviations above the mean.
Second find the closest values possible to 0.12 (12%) on the z-score table. We find it at -1.1 and perfectly in-between .07 and .08. We repeat the same steps as before and get -1.175. The negative z-score, -1.175, tells us the we are 1.175 standard deviations below the mean.
Answer:
The z-score of about
✔ 1.175
tells us that 88% of the observations in the distribution are at or below
✔ 1.175
standard deviations above the mean.
The z-score of about
✔ –1.175
tells us that 12% of the observations in the distribution are at or below
✔ 1.175
standard deviations below the mean.
Step-by-step explanation:
edge 2023
Work out a)4/5-1/5 b)9/11+5/11 c)3/4+1/8
The solutions are:
a) 3/5
b) 14/11
c) 7/8
What are the steps of adding and subtracting fractions?The steps for adding and subtracting fractions are as follows:
Step 1: Match the denominators.
Step 2: Add and subtract the numerators.
Step 3: Make the fraction simpler.
Fractions with different denominators can be added or subtracted by using Least Common Multiple(LCM) to convert them to like fractions.
a) 4/5 - 1/5
The denominators of the fractions are the same so we have to just subtract the numerators.
= (4 - 1)/5
= 3/5
b) 9/11 + 5/11
Similarly, the denominators of these fractions are also equal so we have to just add the numerators.
= (9 + 5)/11
= 14/11
c) 3/4 + 1/8
First, we find the Least Common Multiple (LCM) of the denominators to convert them into like denominators and then add the respective numerators.
LCM of 4 and 8 = 8
= [tex]\frac{6+1}{8}[/tex] = 7/8
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You deposit $3000 each year into an account earning 8% interest compounded annually. How much will youhave in the account in 20 years?
The rule of the compounded interest is
[tex]A=P\frac{\lbrack(1+\frac{r}{n})^{nt}-1\rbrack}{\frac{r}{n}}[/tex]A is the final amount
P is the amount each year
r is the interest rate in decimal
t is the time
n is the number of periods per year
Since you deposit $3000 each year, then
P = 3000
Since the annual rate is 8%, then
r = 8/100 = 0.08
n = 1
Since the time is 20 years, then
t = 20
Substitute them in the rule above to find A
[tex]\begin{gathered} A=\frac{3000\lbrack(1+\frac{0.08}{1})^{1(20)}-1\rbrack}{\frac{0.08}{1}} \\ A=\frac{3000\lbrack(1.08)^{20}-1\rbrack}{0.08} \\ A=137285.8929 \end{gathered}[/tex]You will earn $137 285.8929 after 20 years
Evaluate the expression when c=4 and x=-4.-C+2x
ok
c = 4 x = 4
-c + 2x
Substitution
-4 + 2(4)
-4 + 8
Result
4
The answer for the second question is 2v + 15
DATA ANALYSES AND STATISTICSUnderstanding likelihoodThere are two boxes containing only blue and purple pens.Box A has 6 purple pens and 2 blue pens.Box B has 12 purple pens and 8 blue pens,A pen is randomly chosen from each box,List these events from least likely to most likelyEvent 1: choosing a purple or blue pen from Box B.Event 2: choosing a blue pen from Box B.Event 3: choosing a red pen from Box A.Event 4: choosing a purple pen from Box A.Least likelyMost likelyEvent ). Event | Event | .Event
Answer
Event 3, Event 2, Event 4, Event 1.
Explanation
Given data:
Box A has 6 purple pens and 2 blue pens.
Box B has 12 purple pens and 8 blue pens.
Let X represents purple, Y represents blue, and Z represents red.
Box A: n(X) = 6, n(Y) = 2, and n(Z) = 0. Hence, n(S) = 6 + 2 + 0 = 8
Box B: n(X) = 12, n(Y) = 8, and n(Z) = 0. Hence, n(S) = 12 + 8 + 0 = 20
So if a pen is randomly chosen from each box, the probability of:
Event 1: choosing a purple or blue pen from Box B. will be:
[tex]\begin{gathered} p(X\text{ or Y})=p(X)+p(Y)=\frac{n(X)}{n(S)}+\frac{n(Y)}{n(S)}=\frac{12}{20}+\frac{8}{20}=\frac{12+8}{20}=\frac{20}{20}=1 \\ \end{gathered}[/tex]Event 2: choosing a blue pen from Box B will be:
[tex]p(Y)=\frac{8}{20}=\frac{1}{5}=0.4[/tex]Event 3: choosing a red pen from Box A will be:
[tex]p(Z)=\frac{n(Z)}{n(S)}=\frac{0}{8}=0[/tex]Event 4: choosing a purple pen from Box A wil be:
[tex]p(X)=\frac{n(X)}{n(S)}=\frac{6}{8}=\frac{3}{4}=0.75[/tex]If a pen is randomly chosen from each box, the list of the events from least likely to most likely are:
Event 3, Event 2, Event 4, Event 1.
An insurance agent estimates that it takes 2/3 of an hour to
process a customer's claim. If the agent spends 22 hours per
week processing claims, about how many claims does he
process in a week?
Graph the line that has an z-intercept at (1,0) and a y-intercept at (0, - 4). What is the slope of this line? And what is m=
Answer: m= -5
Step-by-step explanation:
Answer:
m = 4
Step-by-step explanation:
Change in y over change in x
[tex]\frac{-4-0}{0-1}[/tex] = [tex]\frac{-4}{-1}[/tex] = 4
From the ordered pairs are in the form (x,y)
so your y's are -4 and 0
your x's are 0 and 1
Jacqueline took out a personal line of credit in her senior year of college with an annual simple interest rate of 4%.she takes 51 months to pay off the loan in full and pays 1530 in interest. A. How much was the original line of credit amount.B. How much did Jacqueline pay in total.
Given data:
The given annual interest is r=4%.
The given time is t=51 months= 4 year+3 months=4.25 years.
The interest ammount is i=1530.
A)
The expression for the simple innterest is,
i=(Prt)/100
Substitute the given values in the above expression.
1530=P(4)(4.25)/100
P=9000.
Thus, the original amount credit is 9000.
B)
The expression for the total amount is,
A=P+i
Substitute the above calculated values.
A=9000+1530
=10530
Thus, the total amount is 10530.
What matrix results from B+ A?
Enter your answer by filling in the boxes.
Answer:
[tex]\begin{bmatrix}6 & -5\\-5 & 1\\13 & 6\\-15 & -9\\\end{bmatrix}[/tex]
======================================================
Explanation:
In the top left corner of matrix B is the value 7
For matrix A, the top left corner is -1
The values add to 7+(-1) = 6 which is the result in the top left corner box of the answer matrix.
Add the other corresponding values the same way.
As you can see, the two matrices must be the same size in order to add them. They must have the same number of rows, and the same number of columns.
Matrix addition is commutative allowing us to write B+A = A+B