Answer:
43.96 = 2πr
r = 21.98/π
A = π(21.98/π)^2 = 483.1204/π = 153.78 square meters
A = 483.1204/3.14 = 153.86 square meters
Calculator
What is the volume of this figure?
Enter your answer in the box.
ft³
4
3 ft
5 ft
6 ft
7 ft
2 ft
Answer:
The answer should be 1,260
Answer:
75
Step-by-step explanation:
.
Find the area of the triangle:
(Please show work so I can learn how to do it)
Step-by-step explanation:
Area of a traingle = 1/2 * base * height
area = 1/2 * 6 * 4 = 12 cm^2
sketch the graph of each function.
22. g(x)= -2x³-8x2 +18x+72
The graph of the cubic equation is in the equation of the end.
How to sketch the graph of the function?To do it, we need to find some points that are solutions of the equation. Then we can graph these points on a coordinate axis and then connect these points with a curve proper of a cubic relation.
when x = 0
g(0) = -2*0³-8*0² +18*0+72 = 72
So we have the point (0, 72)
when x = 1
g(1) = -2*1³-8*1² +18*1+72
= -2 - 8 + 18 + 72 = 80
So we have the point (1, 80)
when x = -1
g(-1) = -2*-1³-8*-1² +18*-1+72
= 2 - 8 - 18 + 72 = 48
(-1, 48)
And so on, when you have enough points, you can connect them. The graph that should you get is one like the graph in the image at the end.
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I'm needing help with setting up these equations
The sides show that we have an equilateral triangle
What is the measure of each of the sides?An equilateral triangle is a triangle in which all three sides are of equal length. Since all three sides are equal, all three angles are also equal and measure 60 degrees each.
We know that;
12x - 22 = 10x - 6
Collect like terms;
12x - 10x = -6 + 22
2x = 16
x = 8
Thus the sides of the triangle are;
12(8) - 22 = 74
10(8) - 6 = 74
7(8) + 18 = 74
In the second triangle;
4x - 25 = x + 14
4x - x= 14 + 25
3x = 39
x = 13
Thus the sides are;
4(13) - 25 = 27
13 + 14 = 27
6(13) - 51 = 27
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3x+10<3 or 2x-5 ≥ 5 solve the inequality
Answer: x is greater than or equal to 5 (I can't put the symbol in)
Step-by-step explanation:
Add 5 to both sides then simplify, which will get you 2x is greater than or equal to 10, then divide by 2.
Answer:
Step-by-step explanation:
3x+10<3
3x<3-10
3x<-7
x<-7/3
2x-5≥5
2x≥5+5
2x≥10
x≥10/2
x≥5
so x<-7/3 or x≥5
You invest $4000 in an account to save for college.
a. Option 1 pays 5% annual interest compounded semi-annually. What would
be the balance in the account after 2 years?
b. Option 2 pays 4.5% annual interest compounded continuously. What would
be the balance in the account after 2 years?
c. At what time t (in years) would Option 1 give you $100 more than Option 2?
The answers to the given questions about annual interest are given below:
a. $4,415.25b. $4,376.70c. 2.27986 yearsHow to solvea.
A = 4,000 (1 + 0.05/2)^(2 x 2)
= $4,415.25
b.
A = 4,000 x e^(0.045 x 2)
= $4,376.70
c. $100 more than option 2 = 4,376.70 + 100
= $4,476.70
t (in years) = ln(4,476.70/4,000) / ln(1 + 0.05/2)
= 2.27986 years
Annual interest denotes the rate of interest levied or gained on a loan or investment for a duration of one year. This indicates the portion, expressed as a percentage, of the original amount that is utilized for interest payments or gained as a profit within a twelve-month period.
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33% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say cashews are their favorite nut is (a) exactly three, (b) at least four, and (c) at most two. If convenient, use technology to find the probabilities. Due Saturday night
The cumulative probability is
P(at most 2 ) = 0.187560896 [answer]
How to solvea)
Note that the probability of x successes out of n trials is
P(n, x) = nCx p^x (1 - p)^(n - x)
where
n = number of trials = 12
p = the probability of a success = 0.33
x = the number of successes = 3
Thus, the probability is
P ( 3 ) = 0.21509867 [answer]
***********
b)
Note that P(at least x) = 1 - P(at most x - 1).
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 12
p = the probability of a success = 0.33
x = our critical value of successes = 4
Then the cumulative probability of P(at most x - 1) from a table/technology is
P(at most 3 ) = 0.402659566
Thus, the probability of at least 4 successes is
P(at least 4 ) = 0.597340434 [answer]
***************
c)
Using a cumulative binomial distribution table or technology, matching
n = number of trials = 12
p = the probability of a success = 0.33
x = the maximum number of successes = 2
Then the cumulative probability is
P(at most 2 ) = 0.187560896 [answer]
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I am unsure about how to do this problem, pictured below.
Answer:
Step-by-step explanation:
150/2 = 75
500/75 = 6.6666666667 hours
it will take 6.2/3 hours to reach 500 bacteria cells
NOT SURE ABOUT EXPERSION BUT YOU COULD TRY THIS
p = 75t
Given that a culture of bacteria grows at a rate proportional to its size. Where the culture starts with 50 cells, then grows 150 after time, "t" equals 2 hours.
We are asked to:
> (a) Find an expression, P(t), to model the number of cells present after "t" hours.
> (b) Determine the time at which the population is at 500 cells.
For part (a):
Since the culture of bacteria grows at a rate proportional to its size, we can model it as the following differential equation.
[tex]\Rightarrow \frac{dP}{dt}=kP; \ Where \ P =P_0 \ at \ t=0 \ and \ P=3P_0 \ at \ t=2[/tex]
Solve the first-order separable differential equation with the given initial condition.
[tex]\Longrightarrow \frac{dP}{dt}=kP \Longrightarrow \frac{1}{P}dP=kdt \Longrightarrow \int\limits {\frac{1}{P} } \, dP=\int\ {k} \, dt \Longrightarrow ln(P)=kt+c[/tex]
[tex]\Longrightarrow e^{ln(P)}=e^{kt}+e^{c} \Longrightarrow P=ce^{kt}[/tex]
Plug in the initial condition.
[tex]\Longrightarrow P_0=ce^{k(0)} \Longrightarrow P_0=c(1) \Longrightarrow \boxed{c=P_0}[/tex]
[tex]\Longrightarrow P=ce^{kt} \Longrightarrow \boxed{P=P_0e^{kt}}[/tex]
Use the second initial condition to find "k."
[tex]\Longrightarrow 3P_0=P_0e^{k(2)} \Longrightarrow 3=e^{k(2)} \Longrightarrow 3=e^{2k} \Longrightarrow ln(3)=ln(e^{2k})[/tex]
[tex]\Longrightarrow k=\frac{ln(3)}{2} \Longrightarrow \boxed{k \approx 0.5493}[/tex]
Thus, the equation to model the situation is,
[tex]\boxed{\boxed{P(t)=50e^{0.5493t}}} \therefore Sol.[/tex]
For part (b):
[tex]P=10P_0[/tex]
[tex]\Rightarrow 10P_0=P_0e^{0.5493t} \Longrightarrow 10=e^{0.5493t} \Longrightarrow ln(10)=ln(e^{0.5493t})[/tex]
[tex]\Longrightarrow ln(10)=0.5493t \Longrightarrow t=\frac{ln(10)}{0.5493} \Longrightarrow \boxed{t=4.192 \ hrs}[/tex]
Thus, the time it takes the population to reach 500 is approx. 4.192 hours.
Which of the following has the polar coordinates negative five comma two pi over 3
Options:
Q
R
U
W
the french club is holding a car wash fundraiser. They are going to charge $20 per car, and expect between 30 and 100 cars. Identify the independent and dependent quality in the situation, and find reasonable domain and range values
Correct option is,
A: number of cars; money raised; 30 to 100 cars; $600 to $2000 is the right option.
Since, An independent variable is a variable that represents a quantity that is being controlled in an experiment.
A dependent variable represents a quantity whose value depends on how the independent variable is controlled.
Now, In the given question;
The number of cars represents the independent variable while money raised represents independent variable .
Domain is the set of values the independent variable can take .
The number of cars 30 to 100 represents the Domain.
The range is corresponding y values .
The charge per car is $20.
Hence, Range = 30 x 20
=600
to Range = 100 x 20
= 2000.
Thus, Correct option is,
A: number of cars; money raised; 30 to 100 cars; $600 to $2000 is the right option.
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Complete question is,
The French club is holding a car wash fundraiser. They are going to charge $20 per car, and expect between 30 and 100 cars. Identify the independent and dependent quantity in the situation, and find reasonable domain and range values.
A: number of cars; money raised; 30 to 100 cars; $600 to $2000
B: money raised; number of cars; 30 to 100 cars; $600 to $2000
C: number of cars; money raised; $600 to $2000; 30 to 100 cars
D: money raised; number of cars; $600 to $2000; 30 to 100 cars
Prove by mathematical induction that:
[tex]2 + 4 + 8 + ... + {2}^{n} = {2}^{n + 1} - 2 [/tex]
By the principle of mathematical induction, the statement holds for all positive integers n.
How did we arrive at this assertion?Using mathematical induction:
Base case:
For n=1, results into:
2 = 2^2 + 1 - 2
which is true.
Inductive step:
For some positive integer k, we have:
2+4+8+...+2^k = 2^(k+1) + 1 - 2
This implies the statement for n=k+1, i.e.,
2+4+8+...+2^k+2^(k+1) = 2^(k+2) + 1 - 2
From the left-hand side of the equation, we can rewrite it as:
2+4+8+...+2^k+2^(k+1) = (2+4+8+...+2^k) + 2^(k+1)
Applying the induction hypothesis, substitute the expression for 2+4+8+...+2^k:
2+4+8+...+2^k+2^(k+1) = (2^(k+1) + 1 - 2) + 2^(k+1)
Simplify:
2+4+8+...+2^k+2^(k+1) = 2^(k+2) - 1
Using the formula for the sum of a geometric series to simplify the right-hand side of the original statement:
2^(k+2) + 1 - 2 = 2^(k+2) - 1
Thus, the statement holds for n=k+1, supposing it holds for n=k. By the principle of mathematical induction, the statement holds for all positive integers n.
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Question 4 A study has been conducted to compare male and female test performance on a standardised science exam. In this hypothetical study, the researchers reported with a sample size of n = 50, the 95% confidence interval was found to be between 0.15 and 0.55.
What would happen to the 95% confidence interval if the sample size was increased?
The 95% confidence interval would remain the same Cannot be determined from the information provided The 95% confidence interval would decrease The 95% confidence interval would increase
If the sample size was increased, the 95% confidence interval would decrease. A larger sample size would provide more precise and accurate data, resulting in a narrower confidence interval.
A confidence interval is a range of values within which a population parameter is estimated to lie with a certain level of confidence. It is commonly used in statistical inference to estimate the true value of a population parameter based on a sample from that population.
If the sample size was increased, the 95% confidence interval would likely decrease. This is because a larger sample size typically leads to more precise estimates and less variability in the data, resulting in a narrower confidence interval. However, the exact size of the decrease would depend on various factors such as the amount of variability in the data and the level of statistical significance chosen for the study.
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Find the surface area of the prism
The surface area of the triangular prism is 70.2 yd²
What is surface area of prism?A prism is a solid shape that is bound on all its sides by plane faces.
The surface area of a prism is expressed as ;
SA = 2B +ph
where h is the height,
B is the base area and
p is the perimeter of the base
Base area = 1/2 bh( since the base Is a triangle)
Base area = 1/2 × 3 ×3 = 4.5yd²
The other side of the triangle is calculated as;
x= √ 3²+3²
x = √9+9
x = √18
x = 4.2
Therefore perimeter = 4.2 + 3+3 = 10.2yds
SA = 2× 4.5 + 10.2 × 6
SA = 9 + 61.2
SA = 70.2 yd²
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HELPPP DUE TOMORROW
Answer: 1/2 cup oats 2/3 cup flower
A wallet contains 34 notes, all of which are either $5 or $10 notes. If it amounts to $235, how many $10 notes are there?
Answer:
For this question, you can use the simultaneous equation to solve this problem.
Equation 1 reads: x + y = 34. (There are 34 notes in total.)
Equation 2: 5x + 10y = 235 (The notes are worth a total of $235.)
To find x in terms of y, we can apply equation 1:
x = 34 - y
When we use this expression to replace x in equation 2, we obtain:
5(34 - y) + 10y = 235
By condensing and figuring out y, we get at:
y = 15
There are 15 $10 bills in the wallet as a result.
Consider the line y=8x-7
Find the equation of the line that is parallel to this line and passes through the point (5,-3)
Find the equation of the line that is perpendicular to this line and passes through the point (5,-3)
Answer:
Parallels lines:
y = 8x - 43
Perpendicular line:
y = [tex]\frac{-1}{8}[/tex]x - [tex]\frac{19}{8}[/tex]
Step-by-step explanation:
y = 8x -7
Parallel lines have the same slope.
The slope will be 8. We will use the x from the point (5,-3) and the y from the point (5,-3) to find the y-intercept (b)
y = mx + b Substitute in -3 for y, 8 for m, and 5 for x.
-3 = 8(5) + b
-3 = 40 + b Subtract 40 from both sides
-3 - 40 = 40 - 40 + b
-43 = b
Substitute in 8 for m and -43 for b to write the equation
y = mx + b
y = 8x - 43
Perpendicular slope are opposite reciprocals of each other, so the perpendicular slope is [tex]\frac{-1}{8}[/tex]
Substitute [tex]\frac{-1}{8}[/tex] doe m, -3 for y and 5 for x.
y = mx + b
-3 = [tex]\frac{-1}{8}[/tex](5) + b
-3 = [tex]\frac{-5}{8}[/tex] + b add [tex]\frac{5}{8}[/tex] from both sides
-3 + [tex]\frac{5}{8}[/tex] = [tex]\frac{-5}{8}[/tex] + [tex]\frac{5}{8}[/tex] + b
[tex]\frac{-24}{8}[/tex] + [tex]\frac{5}{8}[/tex] = b
[tex]\frac{-19}{8}[/tex] = b
Substitute [tex]\frac{-1}{8}[/tex] for m and [tex]\frac{-19}{8}[/tex] for b
y = mx + b
y = [tex]\frac{-1}{8}[/tex]x - [tex]\frac{19}{8}[/tex]
Helping in the name of Jesus.
Can someone help me please
The expansion and simplification of the expression (x - 2)² is x² - 4x + 4.
What is an expression?An algebraic expression is a combination of variables with constants, numbers, and values using the mathematical operands addition, subtraction, multiplication, or division.
Algebraic Expression:(x - 2)²
Expanding the square:
(x - 2)² = (x - 2)(x -2)
Distributing the square:
x(x - 2) - 2(x - 2)
x² - 2x - 2(x -2)
x² - 2x - 2x + 4
Solution:x² - 4x + 4
Thus, after expanding and simplifying the algebraic expression (x - 2)², the solution is x² - 4x + 4.
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At their practices, the volleyball team ran a total of 10 miles in 14 days. The tennis team ran a total of 8 miles in 7 days. Which team ran more miles per day?
Answer:
tennis team
Step-by-step explanation:
because they ran 8 miles is 7 days to get equal amount of days you multiply by 2 on both 8 miles and 7 days so they ran 16 miles in 14 days thats y tennisbteam ran more miles
The distance between cities A and B on a map is 12.5 in. The distance from city B to city C, is 8.5 in, and the distance from C to A is 16.25 in. If the bearing
from A to B is N75°E, find the bearing from C to 4. Round to the nearest tenth of a degree.
Answer:
90
Step-by-step explanation:
Answer:
It seems like the chat transitioned to a different topic. However, based on the search results, it appears that the query was related to solving distance problems using linear equations. One common application of linear equations is in distance problems, where you can create and solve linear equations to find the distance between two points or the rate of travel. Here's an example problem:
Joe drove from city A to city B, which are 120 miles apart. He drove part of the distance at 60 miles per hour (mph) and the rest at 40 mph. If the entire trip took three hours, how many miles did he drive at each speed?
To solve this problem, you can use a system of two linear equations. Let x be the number of miles driven at 60 mph, and y be the number of miles driven at 40 mph. Then you have:
x + y = 120 (total distance is 120 miles) x/60 + y/40 = 3 (total time is 3 hours)
To solve for x and y, you can multiply the second equation by 120 to eliminate fractions and then use the first equation to solve for one of the variables. For example:
x/60 + 3y/120 = 3 x/60 + y/40 = 3 2x/120 + 3y/120 = 3 x/60 + y/40 = 3 x/60 = 3 - y/40 x = 180 - 3y/2 (from the first equation)
Substitute the expression for x into the second equation and solve for y:
x/60 + y/40 = 3 (180 - 3y/2)/60 + y/40 = 3 3 - 3y/160 + y/40 = 3 3 - 3y/160 = 2.75 -3y/160 = -0.25 y = 20
Substitute y = 20 into the expression for x to get:
x = 180 - 3y/2 x = 120
Therefore, Joe drove 120 - 20 = 100 miles at 60 mph and 20 miles at 40 mph.
Step-by-step explanation:
POSSIBLE POINTS: 10
Find the area of the composite figure below. Area of Triangle = bh, Area of Rectangle = lb Use Pythagorean formula to find the length () of the
Rectangle.
7 mm
10.4 mm
15.3 mm
The total surface area of the composite figure is: 288.62 mm²
What is the area of the composite figure?From the attached image, we can see that the composite figure is made up of 2 triangles and one rectangle. Thus:
Formula for area of rectangle is:
A = Length * Width
Formula for area of triangle is:
A = ¹/₂ * base * height
Using Pythagoras theorem, length of rectangle is:
L = √(10.4² + 15.3²)
L = 18.5 mm
Thus:
TSA = (18.5 * 7) + 2(¹/₂ * 15.3 * 10.4)
TSA = 129.5 + 159.12
TSA = 288.62 mm²
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a rock is thrown straight up with an initial velocity of 3m/s. The mass of the rock is approximately 0.2kg. Air resistance acts on the rock with a force numerically equal to 0.5v where v is the velocity of the rock. Acceleration due to gravity is 9.8 m/s^2. Set up and solve a differential equation to find the velocity of the rock as a function of time
The velocity of the rock as a function of time is given by:
[tex]v(t) = 3 - 4.9exp(-2t/0.2) m/s[/tex]
where 4.9 is the value of mg in SI units.
The forces acting on the rock are the force due to gravity and the force due to air resistance. The force due to air resistance is given by 0.5v, where v is the velocity of the rock.
The force due to gravity is given by the mass of the rock (0.2 kg) times the acceleration due to gravity [tex](9.8 m/s^2)[/tex]. Using Newton's second law, we can set up the following differential equation:
[tex]m(dv/dt) = -mg - 0.5v[/tex]
where m is the mass of the rock, g is the acceleration due to gravity, and v is the velocity of the rock as a function of time t.
We can simplify this differential equation by dividing both sides by m:
[tex]dv/dt = (-g - 0.5v/m)v[/tex]
This is a separable differential equation, which we can solve using the separation of variables:
[tex](1/(-g - 0.5v/m)) dv = dt[/tex]
Integrating both sides gives:
[tex]-2ln(-g - 0.5v/m) = t + C[/tex]
where C is a constant of integration.
Solving for v gives:
[tex]v(t) = -0.5mg + C'exp(-2t/m)[/tex]
where C' = exp(C).
We can find the value of C' using the initial condition that the initial velocity of the rock is 3 m/s:
[tex]v(0) = -0.5mg + C' = 3[/tex]
[tex]C' = 0.5mg + 3[/tex]
Substituting this into the equation for v(t) gives:
[tex]v(t) = -0.5mg + (0.5mg + 3)exp(-2t/m)[/tex]
Therefore, the velocity of the rock as a function of time is given by:
[tex]v(t) = 3 - 4.9exp(-2t/0.2) m/s[/tex]
where 4.9 is the value of mg in SI units.
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Square with top and left sides labeled 1. The square is divided into 6 equal sections vertically and the first section is divided into 2 equal sections horizontally. The first of these sections is shaded.
Number line from 0 to 1. There are 5 large tick marks equally spaced between 0 and 1. There are 3 equally spaced smaller tick marks between every pair of large tick marks. The first of these smaller tick marks has a dot on it.
Question
Raj combined white sand with black sand to make 14 pound mixture of sand. Raj then put an equal amount of this sand mixture into each of 5 vases. All of Raj's sand mixture went into the vases.
How much sand was in each vase?
Responses
140 lb
1 over 40, , lb
120 lb
, 1 over 20, , lb
14 lb
1 fourth, , lb
45 lb
4 over 5, , lb
The amount of sand in each vase is 2.8 pounds by dividing the total amount by the number of vases.
Given that,
Raj combined white sand with black sand to make 14 pound mixture of sand.
Total amount of sand = 14 pounds
Number of vases to which sand is put = 5 vases
Amount of sand in each vase can be found by dividing the total amount by the number of vases.
Amount of sand in each vase = 14 / 5 = 2 4/5 pounds = 2.8 pounds
Hence the total amount of sand is 2.8 pounds.
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Find the multiplying integers -2x24=
The multiplying integers -2x24= -48
Multiplication of Integers:Here is some rules of multiplication of integers:
1. Positive integer × negative integer = negative.
2. Positive integers × Positive integers = positive.
3. Negative integers × Negative integers = positive.
Here, To find the the multiplying integers
-2x24 = -48
When you multiply integers :
Negative x Positive = Negative
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NO LINKS!!! URGENT HELP PLEASE!!!!
Please assist me with these problems.
Answers in bold
7. Not congruent
8. Congruent by the HL theorem
HL = hypotenuse leg
==========================================
Explanation for problem 7
The tickmarks on segments MA and AT tell us that these segments are congruent. Another pair of congruent segments would be AE = AE by the reflexive property.
Then angle EMA = angle ETA because of the similar arc markings for those angles.
We have these congruence facts:
MA = AT (side)AE = AE (side)angle EMA = angle ETA (angle)But recall that the "side side angle" rule isn't a valid congruence theorem. Search out "SSA ambiguous case" for more information.
We cannot use SAS because the angle is not between the sides mentioned.
Therefore, we don't have enough information to determine if the triangles are congruent or not. We can't say they are congruent, so the only thing we can do is say "not congruent" until more info comes along.
------------
Explanation for problem 8
We use the HL (hypotenuse leg) theorem. It works for right triangles only.
The congruent legs are segment ON = segment ON because of the reflexive property.
The congruent hypotenuses are MN = RO because of the tickmarks.
In short, the triangles are congruent by the HL theorem.
Find the amount in the account for the given principal, interest rate, time, and compounding period. P = $700, r=7%, t=8 years; compounded quarterly
Answer:
$1092
Step-by-step explanation:
QUICK, I’LL MARK U BRAINLIEST!! Help me solve this problem!
Based on the information, bIda would owe $3700 at the end of 12 months.
Ida would owe $3808 at the end of 12 months.
How to calculate the interestThe formula will be:
I = P * r * t
I = 2500 * 0.04 * 12 = $1200
So, Ida would owe $2500 + $1200 = $3700 at the end of 12 months.
b. For option b, , the monthly interest rate is:
r = 0.01 * 4.33 = 0.0433
Using the same simple interest expression:
I = 2500 * 0.0433 * 12 = $1308
Ida would owe $2500 + $1308 = $3808 at the end of 12 months.
Therefore, option a is the better choice due to the fact she would owe less in total with a simple interest rate of 4% annually.
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Need help solving this problem please help
The height of tree is given as follows:
40 ft.
How to obtain the height of the tree?The height of the tree is obtained applying the proportions in the context of this problem.
The proportions are applied as a rule of three can be formed between the heights and the shadows for both the tree and the person, as follows:
h/30 = 6/4.5
Applying cross multiplication, the value of h is obtained as follows:
4.5h = 30 x 6
4.5h = 180
h = 180/4.5
h = 40 ft.
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Joey's current monthly expenses include a rent payment of $1,100, a $178 car payment, and a combined minimum payment of $220 for his credit card debt. His current gross monthly income is $3,600. If Joey moves to a new apartment, what is the maximum monthly rent payment he can make and still maintain a DTI ratio of 36%?
a.
$702
b.
$898
c.
$922
d.
$960
Based on Joey's debt-to-income ratio, the maximum monthly rent payment he can make and still maintain the DTI ratio would be; b. $898.
WE are given that Joey has a DTI ratio of 36% which means that his maximum debt payment should be 36% of his income.
This amount would be:
= DTI x monthly income
= 36% x 3,600
= $1,296
Maximum monthly rent can be found as:
= Maximum monthly debt payment - Car payment - Credit card payment
= 1,296 - 178 - 220
= $898
In conclusion, option B is correct.
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Solve (x+1)2 =13/4 using the square root property
Answer:
Starting with the equation:
(x + 1)^2 = 13/4
We can use the square root property, which states that if a^2 = b, then a is equal to the positive or negative square root of b.
Taking the square root of both sides, we get:
x + 1 = ±√(13/4)
Simplifying under the radical:
x + 1 = ±(√13)/2
Now we can solve for x by subtracting 1 from both sides:
x = -1 ± (√13)/2
Therefore, the solutions to the equation are:
x = -1 + (√13)/2 or x = -1 - (√13)/2
Step-by-step explanation:
Use the graph of g(x) to answer the following question. The graph of g(x) is a translation of f(x)=x^2 Write the equation for g(x) in vertex form.
The equation for g(x) in vertex form is g(x) = (x - 2)^ + 3
Writing the equation for g(x) in vertex form.From the question, we have the following parameters that can be used in our computation:
The graph of g(x)
Also, we have
The graph of g(x) is a translation of f(x)=x^2
From the graph, we can see that
Using the above as a guide, we have the following:
g(x) = f(x - 2) + 3
Substitute the known values in the above equation, so, we have the following representation
g(x) = (x - 2)^ + 3
Hence, the equation for g(x) in vertex form is g(x) = (x - 2)^ + 3
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