Solving the given equations using substitution method we get (x,y) as (2, -1) i.e option (2) is correct answer.
How to solve system of equation?Substitution method
The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve.
Given: 4x + 2y = 6 --------- (1)
x = 2y + 4 ----------(2)
Put the value of x from the 2nd equation in the 1st equation
4(2y+4) +2y = 6
8y + 16 + 2y = 6
10y + 16 = 6
10y = 6-16
10y = -10
y = -1 --------------- (3)
put the value of y in the (2) from (3)
x = 2(-1) + 4
x = -2+4
x = 2
Therefore, its solution is (2, -1)
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Answer: B
Step-by-step explanation: Did the test
the ratio 1:4 os equivalent to
Answer:
2/8, 3/12, 4/16 and etc
Step-by-step explanation:
Equivalent fractions can be written by multiplying or dividing both the numerator and the denominator by the same number
(c) Compute and interpret the mean of the random variable x The mean is activities (Type an integer or a decimal Do not round.) Which of the following interpretations of the mean is correct? O A. As the number of experiments decreases, the mean of the observations will approach the mean of the random variable O B. The observed value of an experiment wil be equal to the mean of the random variable in most experiments O C. As the number of experiments increases, the mean of the observations will approach the mean of the random variable OD. The observed value of an experiment will be less than the mean of the random variable in most experiments (d) Compute the standard deviation of the random variable x The standard deviation is activities (Round to one decimal place as needed )
The correct answer is : c) As the number of experiments increases, the mean of the observations will approach the mean of the random variable.
Mean of random Variable x :
The expected value of a discrete random variable X, symbolized as E(X), is often called the long-term average or mean (symbolized as μ). This means that if you run the experiment many times over time, you would expect this average. For example, let X = the number of heads you get when you toss 3 fair coins. If we repeat this experiment (tossing 3 fair coins) many times, the expected value of X will be the expected average number of heads per 3 tosses.
Standard Deviation of Random Variable:
A measure of the variance of a random variable distribution that determines how for a value is from its expected value.
The standard deviation of a random variable X is often written as σ or σₓ.
For discrete random variables, the standard deviation is computed by taking the square of the difference between the value of the random variable and the expected value multiplied by the associated probability of the value of the random variable. Calculate the value of a random variable and finally take the square root.
In symbols σ = √ (x - μ)² P(X =x)
The equivalent formula is σ = [tex]\sqrt{E(x^{2}) - [{E(x^2)]}[/tex]
The square of the standard deviation equals the variance Var(X) = σ².
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how to solve - |x + 5| < -17
Answer:
x∈(−∞,−22)∪(12,+∞)
Step-by-step explanation:
Evaluate
−∣x+5∣<−17
Calculate
∣x+5∣>17
Separate the inequality into 2 possible cases
x+5>17x+5<−17
Solve the inequality for x
x>12x+5<−17
Solve the inequality for x
x>12x<−22
Solution
x∈(−∞,−22)∪(12,+∞)
At Smith Mountain Lake Boat Rentals, it cost $25 per hour to rent a pontoon boat, plus a one-time charge for cleaning. The Bengal family rented a boat from 11 am - 6:30 pm and paid $226.50. If the Jones family rented a boat from 8 am- 1pm, how much did the pay?
Answer: $164
Step-by-step explanation:
25*7=175
175+12.5
226.50-187.50
5*25=125+39
Jones family payed $164
How do you find the maclaurin series expansion of f(x)=(1−x)^−2?
The Maclaurin series expansion of f(x) = 1/(1-x)² is
1 + 2x + 6x² + 24x³ +......
The general expression for the Maclaurin series is given by the formula:
f(x) = f(0) + xf'(0) + x²f''(0) + ..... + xⁿf⁽ⁿ⁾(0)+...
= ∑ f⁽ⁿ⁾ (0)xⁿ/n!
n= 0 to infinity
Specifying the convergence region completes the Maclaurin series formulation. Detailed five steps for determining the Maclaurin series of
f(x) = 1/(1-x)²
Step 1 : Find Derivatives for f(x)
f(x) = 1/(1-x)²
f'(x) = -2(1-x)⁽⁻²⁻¹⁾ (-1) = 2/(1-x)³
The second derivative of f(x) is the derivative of f''(x) :
f"(x) = 2(-3)(1-x)⁽⁻³⁻¹⁾(-1) = 6/(1-x)⁴
Differentiating again, f"'(x) = 6(-4)(1-x)⁽⁻⁴⁻¹⁾(-1)
= 24/(1-x)⁵
Thus, the nᵗʰ derivative is ,
f⁽ⁿ⁾(x) = (n+1)!/(1-x)⁽ⁿ⁻¹⁾
Step 2: Evaluate These Derivatives and f(x) at x=0 let x = 0 , f(0) = 1
f'(0) = 2 , f"(0) = 6 , ....... , f⁽ⁿ⁾(0) = (n+1)!
Step 3 : Now, the Sum of Products :
f(x) = f(0) + xf'(0) + x²f''(0) + ..... + xⁿf⁽ⁿ⁾(0)+...
xf'(0) = 2x
x²f"(0) = 6x²
x³f"'(0) = 24 x³
----------------------------
xⁿf⁽ⁿ⁾(0)= (n+1)!
Thus, the Maclaurin series for ln(1 + x) is this:
f(x) = (1−x)⁻² = 1 + 2x + 6x² + 24x³ +......
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a general term for a sample selected in accordance with probability theory, which ensures that every person in the population has an equal chance of being selected for the sample, is known as
A general term for a sample selected in accordance with probability theory, which ensures that every person in the population has an equal chance of being selected for the sample, is known as Probability sampling.
A probability sampling method is an any method of sampling that utilizes some from of random selection. Probability sampling refers to the selection of a sample from a population, when the selection is based on the principle of randomization, that is random selection or chance.
In simple random sampling each sampling unit of a population has an equal chance of being included in the sample. Consequently, each possible sample also has an equal chance of being selected.
The advantage of simple random sampling is that it does not require any information on the survey frame other than the complete list of units of the survey population along with contact information. In a simple random sample, every number of the population has an equal chance of being selected.
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Which of the following is NOT a criterion for similarity?
A. AA postulate
B. SAS postulate
C. SSS postulate
D. RHS postulate
Answer:
Answer Option A: AA Postulate
describe the relationship between the variables in terms of direction (positive or negative slope), form (a straight line or a curve), and strength (how much the points deviate from a straight line).
The relationship between the variables in terms of direction form and strength.
Given :
the relationship of between the variables in terms of direction ( positive or negative slope ) , form (a straight line or a curve), and strength.
The straight line form with variables is :
y = mx + b is a straight line equation
here x and y are variables
m = slope
b = y - intercept
example :
y = 3x + 3
m = + 3 is a positive slope
y = -2x + 4
here
m = - 2 is a negative slope
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What percent of 200 is 104?
Answer:
52%
Step-by-step explanation:
What percent of 200 is 104?
104/200 = 0.52
0.52 = 52%
Quadrilateral JKLM is similar to quadrilateral NOPQ. Find the measure of side PQ.
Round your answer to the nearest tenth if necessary.
Answer:
57.8
Step-by-step explanation:
You have quadrilateral JKLM similar to quadrilateral NOPQ with given sides JK = 9, LM = 13.7, NO = 38, and you want the measure of PQ.
ProportionCorresponding sides in similar figures are proportional in length:
PQ/LM = NO/JK
PQ/13.7 = 38/9
PQ = 13.7(38/9) = 2603/45 ≈ 57.8
The measure of PQ is approximately 57.8 units.
the weight of trucks traveling on a particular section of i-475 has a population mean of 15.8 tons and a population standard deviation of 5.2 tons. what is the probability a state highway inspector could select a sample of 52 trucks and find the sample mean to be 14.3 tons or less? a) 0.0188 b) 0.3758 c) 0.1242 d) 0.4812
Option b is correct.
Therefore, the probability that a state highway inspector would choose a sample of 49 trucks and discover that the sample mean was 14.3 tons or less is equal to 0.3758
Given: The population mean and standard deviation for the weight of trucks moving on a given stretch of I-475 are both tons.
n=49 sample size
Consider x to be the random variable that represents the truck weight.
z-score: z = x - μ ÷ σ/[tex]\sqrt{n}[/tex]
When x=14.3 tons
z = [tex]\frac{14.3 - 15.8}{\frac{4.2}{\sqrt{49} } }[/tex] ≈ -2.5
The likelihood that a state highway inspector will choose 49 trucks as a sample and discover that the sample mean is 14.3 tons or less is as follows:
P(X ≤ 14.3) = P(z < -2.5) = 0.3758
Therefore, the probability that a state highway inspector would choose a sample of 49 trucks and discover that the sample mean was 14.3 tons or less is equal to 0.3758
option b is correct.
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Overview
Question Progress
Here is a list of numbers.
-45 -21
-16
12 33 40
11
a) Write down two numbers from the list that add up to -9.
c) Work out the sum of all the numbers in the list.
12 13 14
b) Write down two numbers from the list that have a difference of 29.
-21 + 12
Answer:
Step-by-step explanation:
fly
the ratio of the short side of a certain rectangle to the long side is equal to the ratio of the long side to the diagonal. what is the square of the ratio of the short side to the long side of this rectangle?
As per the Pythagoras theorem, the ratio of the short side to the long side of this rectangle is (√5 - 1)/ 2
In math Pythagoras theorem is defined as the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse
Here we have given that the ratio of the short side of a certain rectangle to the long side is equal to the ratio of the long side to the diagonal.
And we need to find is the square of the ratio of the short side to the long side of this rectangle
While we looking into the given question we have identified that the short side of the rectangle be a and let the long side of the rectangle be b.
Therefore, the diagonal, according to the Pythagorean Theorem, is
√(a²+b²)
Now we can write the equation:
a / b = b /√ a² + b²
Then we have to find the square of the ratio of a to b.
Let us consider the answer, be k.
When we squaring the above equation,
a²/ b² = b² / a² + b² = k
When we solve this one then we get the value of k = 1.
Now we have to Multiply each side of the equation by k,
=> k² = 1 - k.
And then adding each side by k,
k² + k − 1 = 0.
Now, we have to Solving for k using the Quadratic Formula,
= > k = -1 ± √[1² − 4(1)(−1)] / 2
=> k = -1±√5/2
As we know that the ratio of lengths and diagonals of a rectangle cannot be negative.
Therefore, the resulting value is √5 - 1/2
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[r] bastien, inc. has been manufacturing small automobiles that have averaged 45 miles per gallon of gasoline in highway driving. the company has developed a more efficient engine for its small cars and now advertises that its new small cars average more than 45 miles per gallon in highway driving. an independent testing service road-tested 52 of the automobiles. the sample showed an average of 46.1 miles per gallon. the sample standard deviation is 5.3 miles per gallon. conduct an appropriate hypothesis test. find the t-statistic and the appropriate conclusion at the 0.01 level of significance.
According to the hypothesis test we find out that the t-statistic is 0.634 and thus, conclude that the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.
It is given to us that -
Company manufactures small automobiles that have averaged 45 miles per gallon of gasoline in highway driving
Company now advertises that its new small cars average more than 45 miles per gallon in highway driving
52 automobiles were tested
Sample average is 46.1 miles per gallon
Sample standard deviation is 5.3 miles per gallon
Significance level is 0.01
We have to conduct an appropriate hypothesis test and find the t-statistic and determine the correct conclusion.
Let us assume that -
p = population of average gasoline of new small cars in highway driving
According to the given information,
Null hypothesis represents that the advertising campaign of the manufacturer is incorrect. This implies that -
[tex]H_{0}[/tex] : [tex]p\leq 45[/tex] miles per gallon
Alternative hypothesis represents that the advertising campaign of the manufacturer is correct. This implies that -
[tex]H_{A}[/tex] : [tex]p > 45[/tex] miles per gallon
For carrying out the hypothesis test for the given situation we have to apply one sample z test statistic since the sample standard deviation information is available to us.
According to one sample z test, the value of test statistic is given as -
[tex]T = \frac{(X_{avg} -p)}{\frac{S}{\sqrt{n} } }[/tex] ------ (1)
where,
[tex]X_{avg}[/tex] = Sample mean
p = hypothesized population mean
S = Sample standard deviation
n = Sample size
According to the given information, we have
[tex]X_{avg}[/tex] = 46.1 miles per gallon
p = 45 miles per gallon
S = 5.3 miles per gallon
n = 52
Substituting the above values in equation (1), we have
[tex]T = \frac{(X_{avg} -p)}{\frac{S}{\sqrt{n} } }\\= > T = \frac{(46.1 -45)}{\frac{5.3}{\sqrt{52} } }\\= > T = \frac{1.1}{0.735}\\ = > T = 0.634[/tex]
It is given to us that the significance level is 0.01. According to the z-table, the critical value of the test statistic at 0.01 significance level is 2.58.
But, we see that the test statistic that we obtained above is less than the critical value at significance level of 0.01. i.e.,
0.634 < 2.58
This implies that there is not sufficient evidence for us to reject the null hypothesis for this particular situation.
Therefore, we can conclude from the hypothesis test that the t-statistic is 0.634 and thus, the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.
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According to the hypothesis test we find out that the t-statistic is 0.634 and thus, conclude that the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.
It is given to us that -
Company manufactures small automobiles that have averaged 45 miles per gallon of gasoline in highway driving
Company now advertises that its new small cars average more than 45 miles per gallon in highway driving
52 automobiles were tested
Sample average is 46.1 miles per gallon
Sample standard deviation is 5.3 miles per gallon
Significance level is 0.01
We have to conduct an appropriate hypothesis test and find the t-statistic and determine the correct conclusion.
Let us assume that -
p = population of average gasoline of new small cars in highway driving
According to the given information,
Null hypothesis represents that the advertising campaign of the manufacturer is incorrect. This implies that -
H0 = p<= 45 : miles per gallon
Alternative hypothesis represents that the advertising campaign of the manufacturer is correct. This implies that -
HA : p > 45 : miles per gallon
For carrying out the hypothesis test for the given situation we have to apply one sample z test statistic since the sample standard deviation information is available to us.
According to one sample z test, the value of test statistic is given as -
T = (X - p)/(SD/√n)
where,
X = Sample mean
p = hypothesized population mean
S = Sample standard deviation
n = Sample size
According to the given information, we have
X = 46.1 miles per gallon
p = 45 miles per gallon
S = 5.3 miles per gallon
n = 52
Substituting the above values in equation (1), we have
T = 46.1-45/(5.2/√52)
T = 1.1/0.735
T = 0.634
It is given to us that the significance level is 0.01. According to the z-table, the critical value of the test statistic at 0.01 significance level is 2.58.
But, we see that the test statistic that we obtained above is less than the critical value at significance level of 0.01. i.e.,
0.634 < 2.58
This implies that there is not sufficient evidence for us to reject the null hypothesis for this particular situation.
Therefore, we can conclude from the hypothesis test that the t-statistic is 0.634 and thus, the manufacturer's advertising campaign is incorrect as its new small cars have an average of less than or equal to 45 miles per gallon in highway driving.
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Bryan estimate the cost of a vacation to be $730. The actual cost of the vacation is $850. Find the percent error. Round to the nearest whole percent if necessary. Is the percent positive or negative? Explain.
Answer: 14%
The percentage is positive because the actual cost is a result of the estimated cost increased by 14%
Step-by-step explanation:
Formula
Subtract the actual value from the estimated value
850-730=120
Divide the results from step 1 by the real value
120/850= 0.14117647058*100
Multiply the results by 100 to find the total percentage
0.14117647058*100=14.1176
Round
14%
A shipping container will be used to transport several 40-kilogram crates across the country by rail. The greatest weight that can be loaded into the container is 27500 kilograms. Other shipments weighing 7700 kilograms have already been loaded into the container. Use the drop-down menu below to write an inequality representing cc, the total number of 40-kilogram crates that can be loaded into the shipping container.
An inequality representing c, the total number of 40-kilogram crates that can be loaded into the shipping container is; 7700 + (40c) ≤ 27500
The maximum number of 40 kg crate is 380.
How to solve Inequality Word Problems?We are given;
Weight of the crate = 40 kg
Greatest weight that the container can load = 27500 kg
Weight of the other shipments on the container = 7700 kg
The greatest number of 40 kg crates is represented by the letter "c".
Thus;
The weight of the other shipment + weight of crate x number of crates ≤ greatest weight of the container
Plugging in the relevant values gives;
7700 + (40c) ≤ 27500
7700 + 40c ≤ 23000
40c ≤ 27500 - 7700
40c ≤ 19800
c ≤ 19800/40
c ≤ 495
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write log7t as a base 2 logarithm. note: if you are using log you need to type it in and use the subscript button on the keyboard. there is no log button.
By using logarithm principles, log₇t in base 2 logarithm equals log₂t/log₂7.
What is logarithm?The most frequent logarithms are common logarithms with a base of 10, binary logarithms with a base of 2, and natural logarithms with a base of e 2.71828. A logarithm is the number of powers that a number must be raised to in order to acquire another number (see Section 3 of this Math Review for more about exponents). The base ten logarithm of 100, for example, is 2, because ten raised to the power of two equals 100: log 100 = 2.
Here,
logₓy=logₐy/logₐx
log₇t=log₂t/log₂7
log₇t in base 2 logarithm is log₂t/log₂7 by the help of properties of logarithm applied.
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the sample mean is the point estimator of
the sample mean is the point estimator of μ
Sample Mean:
The Sample Mean is the average mathematical value of a sample’s values. It is a statistical indicator used to analyze various variables over time. Statisticians and researchers obtain it by dividing the total sum of values of all data fragments and then dividing it by the total number of data sets.
Point Estimate:
p=x/
p is the point estimate for the population proportion, x is the number of
successes, n is the sample size
p= + /2
for the population proportion
x= + /2
for the population mean
= − /2
is the margin of error
the sample mean is the point estimator of μ
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Andrea is 165 cm tall, correct to the nearest cm. Joel is 170 cm tall, correct to the nearest 10 cm. Calculate the upper and lower bound for each person.
Andrea lower bound =
Andrea upper bound =
Joel lower bound =
Joel upper bound=
Answer:
Step-by-step explanation:
andrea lb: 164.5cm
andrea ub: 165.5 cm
joel lb: 165
joel ub: 175
Alejandro, a pharmaceutical sales representative, sells statins for a drug maker. He earns a 12% commission of the total sales of the statins that he sells to hospitals. If he earned 60,000 in commissions, what was the total dollar value of the drugs that he sold?
Answer: x=500,000
Step-by-step explanation:
60,000=.12x
60,000/.12=x/.12
500,000=x
how many numbers less than 2017 are both the sum of two consecutive positive integers, and the sum of five consecutive positive integers?
201 numbers are less than 2017
If and only if it is odd, a number is the sum of two successive integers.
Only if it is a multiple of 5 is a number considered to be the sum of 5 consecutive integers. If you have any doubts, remember that the product of five consecutive integers equals five times the integer in the middle (this remains true if instead of 5 you put in any odd positive integer).
Consequently, you are seeking odd multiples of 5 below 2017. There are 403 multiples of 5 immediately below 2017, or 2015/5. Of those, 202 are odd. It is necessary to eliminate the number 5 because it is not completely positive when expressed as the sum of its successive integers, which is (-1)+0+1+2+3.
There are 201 numbers left.
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Taylor Swift is having 2 concerts at the same venue on Friday and
Saturday nights. On Friday, the ratio of the number of tickets sold to the
number of tickets still available is 5 to 3. On Saturday night, the ratio of the
number of tickets that were sold to the number of tickets available was
7:1. If 1,300 tickets were still available for the Saturday night concert, How
many tickets were sold for the Friday night concert?
Answer:
When using raitos you want to do P=2 +2+2+2
P=8
when L equals Ochoa
what will the answer be?
B2 + 62 + 25 gives us 169 - 25 and that gives us C Ronaldo
Step-by-step explanation:
Hope this helped! :)
HELP MEEEEEEEEEEEEEEEEEEEEEEEE PLEASEEEEEEEEEEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!
find formula for growth of city
y intercept of 300,000 because the function starts here
the slope is 1.08 because it grows by 8 percent each year
population at x year = 300,000(1.08)^x
you can better understand why the x is in the exponent by this example
in one year, it grows 8 percent
300,000 * 1.08 = 324,000
the next year, that previous year grows 8 percent
324,000 * 1.08 = 349,920
300,000 * 1.08 * 1.08 =349,920
300,000 * 1.08^2 = 349,920
in 2 years it grows to that
just do it to the 14th power now
300,000 * 1.08^14 = 881,158
hope this helps :)
if you got any questions just comment
Y is inversely proportional to the square of x. If Y = 3 when x = 2, find Y, when x is 1.
Answer:
Y=K1/x
K=6
Y=6
that's the process the answer is 6
a steep mountain is inclined 80 degrees from the horizontal and rises 3400 vertical feet above the surrounding plain. a cable car is to be installed that will travel from a point 990 ft from the base of the mountain to the top. find the shortest length of cable needed.
Answer:
3753.20 ft
Step-by-step explanation:
tan 80° = 3400 ft/x
x = 599.51 ft = distance at ground level from point directly below mountain peek to edge of mountain.
599.51 ft + 990 ft = 1589.51 ft = horizontal distance at ground level from where cable is attached to the ground to the center of the mountain. This is a leg of a right triangle.
3400 ft is another leg of a right triangle.
(1589.51 ft)² + (3400 ft)² = y²
The hypotenuse, y, is the length of the cable.
y = 3753.20 ft
write the coordinate of the x-intercept and y-intercept for each linear relationship
To find y-intercept: set x = 0 and solve for y. The point will be (0, y).
To find x-intercept: set y = 0 and solve for x. The point will be (x, 0)
What is slope of a line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
Consequently, the formula for the change in y-coordinate with respect to the change in x-coordinate is
m = y/x = y/x = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line can be shown as
tan θ = Δy/Δx
So, the slope of a line is tan.
When the equation is written in the slope-intercept form (y=mx+b) we can find the y-intercept by looking at the equation. The value of b is the y-intercept. This is because the y-intercept is when the x value equals 0. When x = 0, mx = 0, so when x = 0, y = b.
To find the x-intercept we set y = 0 and solve the equation for x. This is because when y=0 the line crosses the x-axis.
When an equation is not in y = mx + b form, we can solve for the intercepts by plugging in 0 as needed and solving for the remaining variable.
To find y-intercept: set x = 0 and solve for y. The point will be (0, y).
To find x-intercept: set y = 0 and solve for x. The point will be (x, 0).
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T=4m^2 - 11 Work out the value of T when m = -3
Answer: T=25
Step-by-step explanation:
T=4m^2 -11
We know that m= -3
-3^2 = 9
So the equation is T=4 (9) -11
T = 36 -11
T= 25
erin wants to find the circumference of a circle with radius 7cm . which of following can she use to find the circumference of the circle ?
A. 2x 7 x π
B 2 x 14 x π
C 7/2 x π
D 14 xπ
E. 49 x π
To find the circumference of a circle with a radius of 7 cm, Erin should use 2×7×π. This is because the circumference of a circle is calculated by the formula 2×π×r.
What is the circumference of a circle?The circumference is the measure of the perimeter of a circle. Since we know that from every point on the circle to its center has an equal length and is said to be its radius, the perimeter of the circle we can write as
Circumference = 2 × π × r units.
Here r is the radius of the circle.
Calculation:It is given that Erin wants to find the circumference of a circle with a radius of 7 cm.
So, first, she has to know the formula for finding the circumference.
Here the radius is given as 7 cm i.e., r = 7 cm
Then, the circumference of the given circle is
= 2 × π × r
On substituting the radius value into the above formula, we get
Circumference = 2 × π × 7 cm
⇒ 14π cm
So, she needs to use option A. 2 × 7 × π for finding the required circumference. This is the first step for finding the circumference of a circle.
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A rectangle has sides of (4x + 13) and (5x – 2). What is the area of the rectangle?
Answer:
Below
Step-by-step explanation:
The area is just the two side lengths multiplied together
area = (4x+13)(5x-2) = 20x^2 +57x -26 units^2
An object was launched off the top of a building.
The function f(x) = −16x² + 48x + 64
represents the height of the object above the
ground, in feet, a seconds after being launched.
Find and interpret the given function values and
determine an appropriate domain for the
function.
f(-1) =
launched, the object was
above the ground. This interpretation
the problem.
f(0.5)
seconds after the object was
=
meaning that
the problem.
feet
in the context of
, meaning that
seconds after the object was
launched, the object was
above the ground. This interpretation
feet
in the context of
The function f(x) = −16x² + 48x + 64 represents the height of an object above the ground in feet, x seconds after being launched.
How to find f(-1)?To find f(-1), we plug -1 into the function:
f(-1) = −16(-1)² + 48(-1) + 64
= 16 - 48 + 64
= 32
This means that 1 second after the object was launched, it was 32 feet above the ground.
To find f(0.5), we plug 0.5 into the function:
f(0.5) = −16(0.5)² + 48(0.5) + 64
= −16(0.25) + 24 + 64
= −4 + 24 + 64
= 84
This means that 0.5 seconds after the object was launched, it was 84 feet above the ground.
Since the function represents the height of the object above the ground, the domain of the function would be the set of all real numbers x such that x represents the number of seconds after the object was launched.
This would include all positive and negative values of x, since the object could have been launched at any time in the past or future. However, if the problem specifies a specific range of time, then the domain would be limited to that range.
Therefore, the correct answer is as given above
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