To find the distance they traveled, we can use the formula:
distance = rate × time
In this case, the rate is 65 miles per hour and the time is 3 hours.
So, the distance they traveled is:
distance = 65 × 3 = 195 miles
Therefore, Lily's family traveled 195 miles from Chicago to Wisconsin Dells.
i need to know the answer
area of trapezium is 30 in².
Define trapeziumA trapezium is a four-sided geometric figure that has only one pair of parallel sides. It is also known as a trapezoid in some countries. The parallel sides of a trapezium are called the bases, and the non-parallel sides are called the legs. The height (or altitude) of a trapezium is the perpendicular distance between the two bases.
The area of a trapezium is given by the formula:
A =½(a×b)h
where "a" and "b" are the lengths of the parallel sides of the trapezium, and "h" is the height (or perpendicular distance) between the parallel sides.
Length of two parallel side
a=7.7in
b=2.3in
Height of trapezium, h=6in
Area of trapezium=½(a×b)h
=½(7.7+2.3)×6
=3×10
=30in²
Hence, area of trapezium is 30 in².
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A research scholar wants to know how many times per hour a certain strand of virus reproduces. He wants to construct the 90%
confidence interval with a maximum error of 0.16
reproductions per hour. Assuming that the mean is 6.2
reproductions and the variance is known to be 5.29
, what is the minimum sample size required for the estimate? Round your answer up to the next integer.
The minimum sample size required for the estimate, considering the z-distribution, is given as follows:
560.
What is a z-distribution confidence interval?The bounds of the confidence interval are given by the rule presented as follows:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.The margin of error is modeled as follows:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
The parameters for this problem are given as follows:
[tex]M = 0.16, \sigma = \sqrt{5.29} = 2.3, z = 1.645[/tex]
Hence the sample size is obtained as follows:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.16 = 1.645\frac{2.3}{\sqrt{n}}[/tex]
[tex]0.16\sqrt{n} = 1.645 \times 2.3[/tex]
[tex]\sqrt{n} = \frac{1.645 \times 2.3}{0.16}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.645 \times 2.3}{0.16}\right)[/tex]
n = 560. (rounded up).
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what fraction of the numbers from 1 to 20 contain digit 1
Answer:
11/20
Step-by-step explanation:
1,10,11,12,13,14,15,16,17,18,19 All have the number "1"
there are 11 of them so 11/20 have the digit 1.
:)
Answer:
To find the fraction of the numbers from 1 to 20 that contain the digit 1, we can count the number of such numbers and divide by the total number of numbers from 1 to 20.
The numbers from 1 to 20 are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.
The numbers that contain the digit 1 are: 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19.
Therefore, there are 11 numbers from 1 to 20 that contain the digit 1.
The fraction of the numbers from 1 to 20 that contain the digit 1 is:
fraction = number of numbers containing 1 / total number of numbers
fraction = 11 / 20
So, the fraction of the numbers from 1 to 20 that contain the digit 1 is 11/20 or 0.55.
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Seven times the difference of a number and two is equal to nine subtracted from x
Answer:
9.2(x- 7) = 9
Step-by-step explanation:
I tried my best to solve this sorry if it is wrong.
Have a good day :)
What are the minimum and maximum values on the interval?
Answer:
Min = -1
Max = 3
Step-by-step explanation:
Evaluate the values on the ends of the interval
[tex]f(-10) = \sqrt[3]{-10+9}[/tex]
[tex]f(-10)=\sqrt[3]{-1}[/tex]
[tex]f(-10)= -1[/tex]
[tex]f(18)=\sqrt[3]{18+9}[/tex]
[tex]f(18)=\sqrt[3]{27}[/tex]
[tex]f(18)=3[/tex]
can yall help me out?
Answer:
107 degrees
Step-by-step explanation:
since the two angles are on a straight line, and a straight line is 180 degrees,
180-73=x
x=107
Convert 2-³
=
into logarithmic form.
O log₂ (¹) = -3
O log₂ (-3) =
○ log(:) (−3) = 2
O log_3 (2) =
1/8
The expression 2⁻³ = 1/8 into logarithmic form is log₂(1/8) = -3
How to convert the expression into logarithmic form.In logarithmic form, the equation 2⁻³ = 1/8 can be written as log base 2 of 1/8 = -3.
Mathematically, we have
log₂(1/8) = -3
This means that the exponent that gives 2⁻³ is -3, and the logarithm base 2 of 1/8 is -3.
Logarithmic form is often used to solve exponential equations where the variable is in the exponent.
In logarithmic form, the variable is moved from the exponent to the logarithm, making it easier to solve for the unknown variable.
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The probability of picking a quarter from a jar of coins is 0. 125. If Noah has 250 coins in the jar, about how many quarters are in the jar?
There are approximately 31 quarters in a jar of 250 coins.
The probability of picking a quarter from a jar of coins is 0.125. To calculate the number of quarters in a jar of 250 coins, we need to use the following formula:
Number of Quarters = Total Number of Coins * Probability of Picking a Quarter
Number of Quarters = 250 * 0.125
Number of Quarters = 31.25
So, there are approximately 31 quarters in a jar of 250 coins.
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please answer this with solution thankyouuu
Therefore , the solution of the given problem of probability comes out to be 0 0.015, 0.018, 0.045 , 0.061 and 0.045.
What is probability?Every procedure's criteria-based approaches have as their main objective determining the likelihood that a statement is accurate or that an event will take place. Any number from one to one, where 0 typically represents chance and 1 typically reflects degree of certainty, can be used to symbolize chance. A probability illustration shows the likelihood that a particular occurrence will occur.
Here,
The formula below can be used to calculate the likelihood of drawing precisely k red balls in 4 draws:
=> P(b = k) = (C(6, k) * C(5, 4-k))/C.(11, 4)
By applying this method, the probability distribution for b can be determined as follows:
=> P(b = 0) = (C(6, 0) * C(5, 4-0)) / C(11, 4) = (1 * 5) / 330 = 0.015
=> P(b = 1) = (C(6, 1) * C(5, 4-1)) / C(11, 4) = (6 * 1) / 330 = 0.018
=> P(b = 2) = (C(6, 2) * C(5, 4-2)) / C(11, 4) = (15 * 1) / 330 = 0.045
=> P(b = 3) = (C(6, 3) * C(5, 4-3)) / C(11, 4) = (20 * 1) / 330 = 0.061
=> P(b = 4) = (C(6, 4) * C(5, 4-4)) / C(11, 4) = (15 * 1) / 330 = 0.045
As a result, the following is the probability distribution for the random variable b that represents the number of red balls pulled in 4 subsequent draws from the box:
b P(b)
0 0.015
1 0.018
2 0.045
3 0.061
4 0.045
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A right-angled triangle is shown below.
By first writing an equation involving tan 63°, calculate the length r.
Give your answer in metres to 2 d.p..
13.85 m
63°
The calculated length of r is 27.18 meters
Calculating the length of rFrom the question, we have the following parameters that can be used in our computation:
The right triangle
Using the tangent of angle 63 degrees, we have
tan(63) = r/13.85
So, we have
r = 13.85 * tan(63)
When evaluated, we have
r = 27.18
Hence, the length of r is 27.18
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Rhombus JKLM with vertices J(-10, 2), K(-2, 8), L(6,2), and M(-2, -4): k = ¹/2
help im literally clueless when it comes to math
(help with both of these but if cant its fine)
The location of Connor's work place with respect to his home is √10 units.
The location of Vikram's martial art school with respect to his home is √34 units.
How to determine the distance between the coordinates for each location?In Mathematics and Geometry, the distance between two (2) points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
Next, we would determine Connor's location with respect to his home as follows;
Distance = √[(-2 - 1)² + (2 - 3)²]
Distance = √[(-3)² + (-1)²]
Distance = √[9 + 1]
Distance = √10 units.
For Vikram, we have:
Distance = √[(-2 - 3)² + (4 - 1)²]
Distance = √[(-5)² + (3)²]
Distance = √[25 + 9]
Distance = √34 units.
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What inverted describes 50 feet below sea level
The integer that describes 50 feet below sea level is -50.
How to determine the integerThe integer that describes 50 feet below sea level is -50. Negative integers are used to represent values below zero.
In this case, the value of 50 feet below sea level is represented by a negative integer because it is below the reference point of sea level, which is typically defined as zero.
Sea level is the average height of the surface of the sea, and is often used as a reference point for measuring elevations and depths.
When a location is above sea level, positive integers are used to represent the height or elevation, while negative integers are used to represent depths or elevations below sea level.
In summary, the integer -50 represents 50 feet below sea level because it is a negative integer that describes a depth below the reference point of sea level.
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Complete question
What integer describes 50 feet below sea level
The mean of 3, 15, and my number is 40. What is my number?
We can start by using the formula for the mean (average):
Mean = (sum of numbers) / (number of numbers)
We are given that the mean of 3, 15, and another number is 40, so we can set up an equation:
40 = (3 + 15 + x) / 3
Multiplying both sides by 3 yields:
120 = 3 + 15 + x
Simplifying this equation gives:
102 = x
Therefore, the missing number is 102.
13) Ellen wanted to buy the following items: A DVD holder for $19.95, headphones for $41.25, and a personal stereo for $30.65. How much money does Ellen need?
Answer: $91.85
Step-by-step explanation:
19.95 + 41.25 + 30.65
= 91.85
And bro, its not that hard to simply calculate it in your head, or even on a paper. Like literally, there's calculators too
i need help pls!!!!! question is attached
The value of the investment after 3.5 years is $ 2000.
What is the interest rate?
The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate. The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.
Here, we have
Given: if $2000 is invested at 4% interest compounded monthly, the value of the investment after t years is given by 2000(12.04/12)¹²ⁿ.
We have to find the value of the investment after 3.5 years.
= 2000(12.04/12)¹²ⁿ
n = 3.5
= 2000(12.04/12)¹²⁽³°⁵⁾
= = 2000(12.04/12)⁴²
= 2000(1)
= $ 2000
Hence, the value of the investment after 3.5 years is $ 2000.
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On a certain route, an airline carries 9000 passengers per month, each paying $30 . A market survey indicates that for each $1 increase in the ticket price, the airline will lose 50 passengers. Find the ticket price that will maximize the airline's monthly revenue for the route. What is the maximum monthly revenue?
Let's start by finding the current monthly revenue of the airline for the given number of passengers and ticket price:
Monthly revenue = number of passengers x ticket price
Monthly revenue = 9000 x $30
Monthly revenue = $270,000
Now, let's find the number of passengers for each $1 increase in the ticket price:
Number of passengers lost = 50
So, for a ticket price increase of $x, the number of passengers will be:
Number of passengers = 9000 - 50x
The ticket price will then be $30 + $x, and the revenue will be:
Revenue = (9000 - 50x) x ($30 + $x)
Revenue = 270,000 - 1500x + 30x + x^2
Revenue = x^2 - 1470x + 270,000
To find the ticket price that will maximize the revenue, we need to find the vertex of the parabola given by the revenue equation. The x-coordinate of the vertex is:
x = -b/2a
Where a = 1, b = -1470, and c = 270,000.
x = -(-1470)/2(1)
x = 1470/2
x = 735
So, the ticket price that will maximize the revenue is $30 + $735 = $765. The maximum monthly revenue is then:
Revenue = (9000 - 50(735)) x ($30 + $735)
Revenue = 105 x $765
Revenue = $80,325
Therefore, the ticket price that will maximize the airline's monthly revenue for the route is $765, and the maximum monthly revenue is $80,325.
can you do a step by step explanation please and thank you!!!
The total area of the shaded region is 67.92 sq. in.
What is sector of a circle?A sector is a section of a circle that may be described using the following four criteria:
Two radii and an arc surround a section of a circle. The two sectors that make up a circle are referred to as the minor and major sectors. The main sector of the circle is the larger area, while the minor sector is the smaller area. The circle is split into two equally sized sections in the case of semicircles.
Let us suppose the central angle of the shaded portion = x.
From the given figure we observe that angle DEC = 143 degrees, and angle AEB are equal as they are vertically opposite angles.
The angle formed by the shaded regions are same as they are vertically opposite angles.
Thus,
143 + 143 + x + x = 360
286 + 2x = 360
2x = 74
x = 37
Now, the area of the sector is given as:
A = α/360 πr²
Here, r = 10.4 in.
Substituting the values:
A = (37/360)π(10.4)²
A = (0.10)(3.14)(10.4)²
A = 33.96 sq in.
There are two shaded portions thus:
Total area = 2(33.96)
Total area = 67.92 sq. in.
Hence, the total area of the shaded region is 67.92 sq. in.
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3.What is the measure of angle d₁º?
4.What is the tangent ratio of angle c₂?
Step-by-step explanation:
remember answer 2.
3. I answered already in my other answer.
remember, the diagonals split the angles in half.
so,
d1 = 50°
4. the tangent ratio is sine/cosine (that is the definition of tangent).
c2 = 40°
sin(40) × 5 = OD (half of BD)
cos(40) × 5 = OC
the tangent ratio is
(sin(40) × 5) / (cos(40) × 5) = sin(40)/cos(40) = OD/OC =
≈ 3.2 / 3.8 = 1.6/1.9 =
= 0.842105263...
control : tan(40) = 0.839099631... close enough (we used round numbers with 3 2 and 3.8 - see again 1. and 2.).
y=3x-1
y=2x+7
solve by substitution
Therefore, the solution to the system of equations is x = 8 and y = 23.
What is equation?An equation is a statement that shows the equality between two mathematical expressions using symbols, numbers, and/or variables. Equations are used to describe relationships between different quantities, and they are commonly used in many fields, including mathematics, physics, chemistry, engineering, and economics.
by the question.
Let's solve the first equation for y:
y = 3x - 1
Now we substitute this expression for y in the second equation:
2x + 7 = y
We can substitute 3x - 1 for y in this equation:
2x + 7 = 3x - 1
Now we can solve for x:
2x - 3x = -1 - 7
-x = -8
x = 8
Now we can substitute x = 8 into either equation to solve for y. Let's use the first equation:
y = 3x - 1
y = 3(8) - 1
y = 24 - 1
y = 23
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The hire purchase for motor bike is GHC 540.00, if this is to be paid in twenty equal monthly installments, what amount is paid each monthly installments
Answer:
The monthly installment for the hire purchase of the motorbike is GHC 27.00
Step-by-step explanation:
To calculate the monthly installment for the hire purchase, we can divide the total cost by the number of months:
Monthly installment = Total cost / Number of months
In this case, the total cost is GHC 540.00 and the number of months is 20:
Monthly installment = GHC 540.00 / 20
Monthly installment = GHC 27.00
Therefore, the monthly installment for the hire purchase of the motorbike is GHC 27.00
One pump can fill a swimming pool in 4 hours. A second pump can fill the pool in 6 hours. If the pool starts empty, what part of the pool will be filled in each situation? The first pump works for 5 hours and the second pump works for 6 hours.
According to the solving this word problem It will take the slowest pump [tex]\frac{7}{2}[/tex] hours to complete filling the pool.
What does a math word puzzle entail?A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve a problem from "real life." In order for kids to understand the word problem, they must be acquainted with the vocabulary that goes along with the mathematical symbols that they are used to.
According to the given information,
The first pump can fill the pool in 4 hours, so its rate is 1/4 of the pool per hour.
The second pump can fill the pool in 6 hours, so its rate is 1/6 of the pool per hour.
The total work done in fraction by both pumps in an hour is:
[tex]\frac{1}{4} + \frac{1}{6} = \frac{5}{12}[/tex]
The remaining work to be completed by the slowest pump is:
[tex]1 - \frac{5}{12} = \frac{7}{12}[/tex]
The ratio of the amount of work left to be done by the weakest pump's work rate determines how long it will take to fill the pool:
[tex]\frac{7}{12} \frac{1}{6} = \frac{7}{12} * 6 = \frac{7}{2}[/tex]
According to the solving It will take the slowest pump [tex]\frac{7}{2}[/tex] hours to complete filling the pool.
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How do debt payments relate to gross income in terms of the debt-to-income (DTI) ratio?
O total gross income is divided by total debt payments
total debt payments are subtracted from total gross income
total gross income is added to total debt payments
total debt payments are divided by total gross income
Debt payments relate to gross income in terms of the debt-to-income (DTI) ratio by total debt payments are divided by total. gross income.
How do debt payments relate to gross income?
The debt-to-income (DTI) ratio is a financial measurement used by lenders to assess a borrower's ability to manage debt payments. It is calculated by dividing the borrower's total debt payments by their total gross income. The resulting ratio is expressed as a percentage and indicates the portion of the borrower's income that goes towards paying their debt obligations.
For example, if a borrower has total debt payments of $1,000 per month and a gross income of $4,000 per month, their DTI ratio would be 25% ($1,000 divided by $4,000). A lower DTI ratio indicates that a borrower has more disposable income available after paying their debts and is generally viewed as a positive factor by lenders when considering a borrower for a loan or credit.
So, correct option is total debt payments are divided by total gross income.
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Answer:
D. total debt payments are divided by total gross income
Step-by-step explanation:
D. total debt payments are divided by total gross income
PLEASE ANSWER USE PEMDAS
What is the correct mathematical description of the expression (14.8 ÷ 2) + 6 x 3 − 12?
14 and 8 tenths divided by 2 plus 6 times 3 minus 12
14 and 8 tenths divided by 2 plus 6 times the difference of 3 minus 12
The quotient of 14 and 8 tenths divided by 2 plus six times 3 minus 12
The quotient of 14 and 8 tenths divided by 2 plus the product of 6 and 3 minus 12
Answer: D or the Fourth Choice-The quotient of 14 and 8 tenths divided by 2 plus the product of 6 and 3 minus 12
PEDMAS means Parentheses, Exponents, Divide, Multiply,Add,Subtract. The first thing we must solve is what is in the parentheses, that is 14.8 divided by 2. We don't have any exponents, so we move to divide. We have already solved the division sentence that was in the parentheses, so we have to multiply 6x3 next. 6x3 will then be added to the answer that was divided by 14.2 and 2, and lastly we will subtract 12. The only answer choice that follows that pattern is D or The quotient of 14 and 8 tenths divided by 2 plus the product of 6 and 3 minus 12.
I hope this helped & Good Luck <3!!!!
Samples of four people were asked whether gun laws should be more stringent. Respondents had a choice to answer "yes" or "no." The sampling distribution of the proportion of people who respond "yes" in the samples of 4 individuals is binomial because the number of people who respond "yes" has binomial distribution not possible to say because the sample size it too small not possible to say because population distribution is not known normal
According to the student question, the sampling distribution of the proportion of people who respond "yes" in the samples of 4 individuals is binomial because the number of people who respond "yes" has binomial distribution. The correct answer is A.
The sampling distribution of the proportion of people who respond "yes" in the samples of 4 individuals is binomial because the sample size is sufficiently small and each person's response is independent of the others.
Binomial distribution is used to model the number of successes in a fixed number of independent trials, where the probability of success is constant for each trial. In this case, the proportion of people who respond "yes" is the number of successes out of the total number of trials (i.e., 4 people).
Moreover, the responses of each individual are independent of each other, meaning that the probability of one person answering "yes" does not affect the probability of another person answering "yes." The correct answer is A.
Your question is incomplete but most probably your full question was
Samples of four people were asked whether gun laws should be more stringent. Respondents had a choice to answer "yes" or "no." The sampling distribution of the proportion of people who respond "yes" in the samples of 4 individuals is
a. Binomial because the number of people who respond "yes" has binomial distribution
b. Not possible to say because the sample size it too small
c. Not possible to say because population distribution is not known
d. Normal
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4 3/4 plus 1/3 what does it equal
Find all values of $c$ such that $\dfrac{c}{c-5} = \dfrac{4}{c-4}$.
If you find more than one, then list the values separated by commas. If the solutions are not real, then they should be written in $a + bi$ form.
By applying the quadratic formula to simplify the following statement, it is possible to find the value of x, which is 3, 5.
The problem is asking us to find all values of $c$ that satisfy the given equation:
[tex]\frac{c}{c-5} =\frac{c}{c-4}[/tex]
To solve for $c$, we can start by cross-multiplying:
[tex]c(c-4)= 4(c-5)[/tex]
Expanding both sides gives:
[tex]c^2-4c=4c-20[/tex]
Simplifying and rearranging terms, we get:
[tex]c^2-8c+20=0[/tex]
We can now calculate $c$ using the quadratic formula:
[tex]c=[/tex] -b ±[tex]\sqrt{b^2-4ac}[/tex]/2a
Plugging in the values $a = 1$, $b = -8$, and $c = 20$, we get:
c= 8 ± [tex]\sqrt{8^2-4(1)(20)}[/tex]/2(1)
Simplifying, we get:
c = 8 ±[tex]\sqrt{64-80}[/tex]/2
c = 8±[tex]\sqrt{-16}[/tex]/ 2
c = 8 ±[tex]\sqrt{4}[/tex]/2
c = 8± 2/2
c = 4±1
So the solutions are:
c= 3,5
Therefore, the values of $c$ that satisfy the equation are $c = 3$ and $c = 5$.
The complete question is:-
Find all values of [tex]'x'[/tex] such that [tex]\frac{c}{c-5} =\frac{c}{c-4}[/tex].
If you find more than one, then list the values separated by commas. If the solutions are not real, then they should be written in [tex]$a + bi$[/tex] form.
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7 ∊ D (f)
f(7) - f(-7) = ?
if f is an even function
Answer:
0
Step-by-step explanation:
if f is an even function, it means that:
f(x) = f(-x) for every x of the domain
So, because 7 is in f's domain, f(7) = f(-7),
and so f(7) - f(-7) = 0
what is the value of the expression
v/2 +(3/4 +w)
when v=1 and w= 5/8
a 1/8
b 3/8
c 5/8
d 1
The value of v/2 +(3/4 +w) when v = 1 and w = 5/8 is 1 7/8
What is substitution of variables?substitution of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables.
Since V = 1 and W = 5/8, by substituting 1 for V and 5/8 for w in the expression
v/2 +(3/4 +w) = 1/2+ ( 3/4 + 5/8)
= 1/2 + (6+5)/8
= 1/2 + 11/8
= (4+11)/8
= 15/8
= 1 7/8
Therefore the value of v/2 +(3/4 +w) when v is 1 , and w is 5/8 is 1 7/8
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Find and prove algebraically the solutions (coordinate points) to the system of equations?
fx=x²+2x-1 and g x=x+1
Answer:
(x, y) = (-2, -1) or (1, 2)
Step-by-step explanation:
You want to find the algebraic solutions to the system of equations ...
f(x) = x² +2x -1g(x) = x +1SolutionThe x-value of the solutions will be the solutions to ...
f(x) = g(x)
f(x) -g(x) = 0
(x² +2x -1) -(x +1) = 0 . . . . substitute for f(x) and g(x)
x² +x -2 = 0 . . . . . . . . . simplify
(x +2)(x -1) = 0 . . . . . factor
The zero product rule says the solutions will be values of x that make one or the other of the factors zero.
x = -2 or +1 . . . . . . . values that make the factors zero
y = x +1 = -1 or +2 . . . . from the equation for g(x)
Solutions are (x, y) = (-2, -1) or (1, 2).
ProofWe already know that g(x) is satisfied by these x- and y-values.
f(x) = x² +2x -1 = (x +2)x -1
f(-2) = (-2 +2)(-2) -1 = 0 -1 = -1 . . . . . (-2, -1) is a solution
f(1) = (1 +2)(1) -1 = 3 -1 = 2 . . . . . . . . . (1, 2) is a solution
These values agree with the above, so we have shown the solutions satisfy both equations in the system of equations.