Answer: [tex]5.05[/tex]
Flip
Keep: 1.8
Change: - into +
Change: -3.25 into 3.25
Your new problem
[tex]1.8+3.25[/tex]
Add
[tex]1.8+3.25=5.05[/tex]
The expression 1.8 minus negative 3.25 simplifies to 1.8 plus 3.25, which equals 5.05.
The question asks you to calculate the result of the expression 1.8 minus negative 3.25. When you have a minus sign followed by a negative sign, they cancel each other out and it becomes an addition problem. Therefore, the expression simplifies to 1.8 + 3.25.
To calculate this, you add the two numbers:
1.8+3.25Adding these numbers together gives you 5.05. So, 1.8 - (-3.25) equals 5.05.
proving the converse of the parallelogram side theorem
Answer:
* LOOK AT THE PICTURE's*
I hope this helps and is the right one
The converse of the parallelogram side theorem states, If the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
To prove this statement, we will assume that the opposite sides of a quadrilateral are congruent and demonstrate that it must be a parallelogram.
If both the opposite sides are parallel then we can easily prove that a parallelogram
Given: Quadrilateral PQRS, where PQ is congruent to RS and PR is congruent to QS.
To prove: PQRS is a parallelogram.
Proof:
Since PQ is congruent to RS (given), the segment PQ is parallel to the segment RS by the converse of the corresponding sides of congruent triangles are congruent (CPCTC). Since PR is congruent to QS (given), the segment PR is parallel to the segment QS by CPCTC.
Now we have both pairs of opposite sides of PQRS parallel, which satisfies the definition of a parallelogram.
Therefore, by proving that both pairs of opposite sides are PQRS parallel, we have shown that if the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
This completes the proof of the converse of the parallelogram side theorem.
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Convert the angle 0 = 230° to radians.
Answer:
230° is equal to [tex]\displaystyle \frac{23 \pi}{18}[/tex] radians.
General Formulas and Concepts:
Trigonometry
Degrees to Radians Conversion: [tex]\displaystyle \frac{n\pi}{180}[/tex]
n is the degreesStep-by-step explanation:
Step 1: Define
Identify variables.
n = 230°
Step 2: Find Radians
Substitute in variable [Degrees of Radians Conversion]: [tex]\displaystyle \frac{230 \pi}{180}[/tex]Simplify: [tex]\displaystyle \frac{23 \pi}{18}[/tex]∴ 230° is equal to [tex]\displaystyle \frac{23 \pi}{18}[/tex] radians.
---
Topic: Pre-Calculus
Unit: Trigonometry
1. A dog is tied to a wooden stake in a backyard. His leash is 3 meters long and he runs around in circles pulling the leash as far as it can go. How much area does the dog have to run around in?
Answer:???
Step-by-step explanation:
Answer:
As the stake is 3 m long we will take it as the radius of the circle and find the area as per:
22/7*3*3=22/7*9=198/7m^2
198/7 metre square.
A quantity with an initial value of 830 grows exponentially at a rate such that the quantity doubles every 2 weeks. What is the value of the quantity after 21 day, to the nearest hundredth?
Answer:
The value of the quantity after 21 days is 2,347.59.
Step-by-step explanation:
The exponential growth function is
[tex]A=A_0(1+r)^t[/tex]
A= The number of quantity after t days
[tex]A_0[/tex]= initial number of quantity
r= rate of growth
t= time in days.
A quantity with an initial value of 830 grows at a rate such that the quantity doubles in 2 weeks = 14 days.
Now A= (2×830)= 1660
[tex]A_0[/tex] = 830
t = 14 days
r=?
Now plug all value in exponential growth function
[tex]1660=830(1+r)^{14}[/tex]
[tex]\Rightarrow \frac{1660}{830}= (1+r)^{14}[/tex]
[tex]\Rightarrow 2= (1+r)^{14}[/tex]
[tex]\Rightarrow (1+r) ^{14}=2[/tex]
[tex]\Rightarrow (1+r)=\sqrt[14]{2}[/tex]
[tex]\Rightarrow r=\sqrt[14]{2}-1[/tex]
Now, to find the quantity after 21 days, we plug [tex]A_0[/tex] = 830, t= 21 days in exponential function
[tex]A=830( 1+\sqrt[14]{2}-1)^{21}[/tex]
[tex]\Rightarrow A=830(\sqrt[14]2)^{21}[/tex]
[tex]\Rightarrow A=830(2)^\frac{21}{14}[/tex]
[tex]\Rightarrow A=830(2)^\frac{3}{2}[/tex]
[tex]\Rightarrow A=2,347.59[/tex]
The value of the quantity after 21 days is 2,347.59.
Final answer:
To calculate the value of a quantity after 21 days when it doubles every 2 weeks with an initial value of 830, use the exponential growth formula [tex]N(t) = N_0 \times 2^{t/T}[/tex]. Plugging in the values, the quantity after 21 days is 2347.14, to the nearest hundredth.
Explanation:
Calculating Exponential Growth
To find the value of a quantity after 21 days when it has an initial value of 830 and doubles every 2 weeks, we can use the formula for exponential growth:
N(t) = N_0 × 2^(t/T)
Where:
N(t) is the future value after time t,
N_0 is the initial value (830),
t is the time period in days (21 days),
T is the doubling period in days (2 weeks = 14 days).
First, we convert 21 days into weeks: 21 days / 7 days per week = 3 weeks.
Next, let's find the value after 3 weeks. We plug our values into the exponential growth formula:
[tex]N(3) = 830 \times 2^{3/2}[/tex]
To calculate 3/2 weeks in terms of doubling periods:
3 weeks / 2 weeks per doubling period = 1.5 doubling periods.
Now we can calculate the quantity:
N(21) = [tex]830 \times 2^{1.5}[/tex] = 830 × 2.828 = 2347.14
To the nearest hundredth, the value of the quantity after 21 days is 2347.14.
2. What is the total outcome when picking a number from 1 to 30 and a
letter from the alphabet *
56
150
390
780
Answer: 780
Step-by-step explanation: 30 numbers times 26 letters.
30 x 26=780
Final answer:
To find the total number of outcomes for selecting a number between 1 and 30 and a letter from the alphabet, you multiply the outcomes of each event together, resulting in 30 numbers multiplied by 26 letters, which equals 780 total outcomes.
Explanation:
The question asks for the total number of outcomes when picking a number from 1 to 30 and a letter from the alphabet. In mathematics, to calculate the total number of outcomes for two independent events, you multiply the number of outcomes for each event. There are 30 different outcomes for picking a number from 1 to 30, and, assuming a standard English alphabet, there are 26 outcomes for picking a letter from A to Z.
To find the total number of outcomes when one event is selecting a number and another event is selecting a letter, you multiply the two: 30 (numbers) × 26 (letters) = 780 total outcomes.
There are 41 students in a Statistics class. The professor knows from experience that the time to grade one exam follows a normal distribution with average 8.8 minutes and standard deviation 3.2 minutes.
What is the average time and standard deviation to grade 41 exams
A machine fills 75 bottles of water each minute. Write an equation to represent the number of bottles, B of water the machine can fill in m minutes.
Answer:
B x m
Step-by-step explanation:
Example: 75 x minutes
So no matter how much bottles you have, you just have to multiply the minutes.
Answer:I think it would be 75 divided by b = m
Step-by-step explanation:
6. 4ab + 13b
Can someone help me find the andwers
Answer:
You cannot simplify this. One has ab, and one has only b. So that is the most simplified it can get.
Answer: There are no like terms.
Step-by-step explanation:
Using the Zero Product Property, solve for the x-values given (x-2)(x+3)=0.
Answer:
x = 2 or -3
Step-by-step explanation:
The product will be zero when one of the factors is zero.
First factor:
x - 2 = 0
x = 2 . . . . . add 2 to both sides of the equation
Second factor:
x + 3 = 0
x = -3 . . . . .subtract 3 from both sides of the equation
The values of x that solve this equation are x = 2 and x = -3.
What are the factors of x2 + 3x - 4?
(x + 4) and (x - 4)
(x + 3) and (x-4)
(x + 4) and (x - 1)
(x + 3) and (x - 1)
Answer:
C. (x + 4) and (x - 1)
Step-by-step explanation:
The middle number is 3 and the last number is -4.
Factoring means we want something like
(x+_)(x+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get 3
Multiply together to get -4
Can you think of the two numbers?
Try -1 and 4:
-1+4 = 3
-1*4 = -4
Fill in the blanks in
(x+_)(x+_)
with -1 and 4 to get...
(x + 4) and (x - 1)
You went to the mall with $52.50. You bought three shirts that each cost x
dollars. Which expression represents the amount of money, in dollars,
that you had left after you bought the shirts? *
Monique is an interior design student. As part of her internship, she is redesigning a small kitchen for a client. She would like to expand the kitchen and add a dining area. Before creating sketches for the client, she imagines the new layout in her mind, most likely using __________.A. tacit knowledge.
B. a proposition.
C. the method of loci.
D. a depictive representation.
What is a tessalation
Answer:
A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.
Step-by-step explanation:
The points A, B, C, and D are on a number line, not necessarily in that order. If the distance between A and B is 18 and the distance between C and D is 8, what is the distance between B and D ? (1) The distance between C and A is the same as the distance between C and B. (2) A is to the left of D on the number line.
Answer:
insufficient information
Step-by-step explanation:
If the order of the points is unknown, the distances AB and CD imply no particular distance for BD.
Consider the series
\sum_{n=1}^{\infty} \frac{(2 x)^n}{n}.
Find the interval of convergence of this power series by first using the ratio test to find its radius of convergence and then testing the series' behavior at the endpoints of the interval specified by the radius of convergence.
interval of convergence =
Answer:
(-\infty,-1/2) U (1/2,+\infty)
Step-by-step explanation:
You have the following series:
[tex]\sum_{n=1}^{\infty} \frac{(2 x)^n}{n}[/tex]
You calculate the radius of convergence by using the formula:
[tex]R= \lim_{n \to \infty} |\frac{a(x)_n}{a(x)_{n+1}}|= \lim_{n \to \infty} |\frac{\frac{(2x)^n}{n}}{\frac{(2x)^{n+1}}{n+1}}|\\\\=\lim_{n \to \infty} |\frac{\frac{(2x)^n}{n}}{\frac{(2x)^n(2x)}{n+1}}|=\lim_{n \to \infty}|\frac{n+1}{2xn}|=|\frac{1}{2x}|\lim_{n \to \infty}|1+\frac{1}{n}|=|\frac{1}{2x}|[/tex]
The radius of convergence is R=1/2x.
Hence, the interval of convergence is
|2x| < 1
|x| < 1/2
By evaluating in the extrems of the interval:
[tex]\sum_{n=1}^{\infty} \frac{(2 (\frac{1}{2}))^n}{n}=\sum_{n=1}^{\infty} \frac{(1)^n}{n}=0\\\\\sum_{n=1}^{\infty} \frac{(2 (-\frac{1}{2}))^n}{n}=\sum_{n=1}^{\infty} \frac{(-1)^n}{n}[/tex]
for x=-1/2 we obtain an Alternating Harmonic Series, for x=1/2 we obtain the divergent harmonic series. Thus the interval is:
(-\infty,-1/2) U [1/2,+\infty)
Answer:
Step-by-step explanation:
Recall the ratio test. Given a series [tex]\sum_{n=1}^{\infty}a_n[/tex] if
[tex] \lim_{n\to \infty} \left|\frac{a_{n+1}}{a_n}\right|<1[/tex]
Then, the series is absolutely convergent.
We will use this to the given series [tex]\sum_{n=1}^{\infty} \frac{(2 x)^n}{n}[/tex], where [tex] a_n = \frac{(2 x)^n}{n}[/tex]. Then, we want to find the values for which the series converges.
So
[tex] \lim_{n\to \infty} \left|\frac{(2x)^{n+1}}{n+1}\cdot \frac{n}{(2x)^n}\right|<1[/tex], which gives us that
[tex] |2x|\cdot\lim_{n\to \infty} \frac{n}{n+1}<1[/tex]
We have that [tex]\lim_{n\to \infty} \frac{n}{n+1}=1[/tex]. Then, we have that
[tex]|2x|<1[/tex],
which implies that |x|<1/2. So for [tex]x \in (-1/2,1/2)[/tex] the series converges absolutely.
We will replace x by the endpoints to check convergence.
Case 1, x=1/2:
In this case we have the following series:
[tex]\sum_{n=1}^{\infty} \frac{1}{n}[/tex] which is the harmonic series, which is know to diverge.
Case 2, x=-1/2:
In this case we have the following series:
[tex]\sum_{n=1}^{\infty} \frac{(-1)^n}{n}[/tex]
This is an alternating series with [tex]b_n = \frac{1}{n}[/tex]. Recall the alternating series test. If we have the following
[tex]\sum_{n=1}^\infty (-1)^nb_n [/tex] and[tex] b_n[/tex] meets the following criteria : bn is positive, bn is a decreasing sequence and it tends to zero as n tends to infinity, then the series converge.
Note that in this case, [tex]b_n = \frac{1}{n}[/tex] si always positive, its' limit is zero as n tends to infinity and it is decreasing, hence the series converge.
So, the final interval of convergence is
[tex] [\frac{-1}{2}, \frac{1}{2})[/tex]
A principal gathered data about the distance, in miles, that his teachers and bus drivers live from school. The box plots below show these data.
Answer:
We choose C
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo
Basically, interquartile range represents the width or "dispersion" of the set. [1] The interquartile range is determined by the difference between the top quartile (25% highest) and lower quartile (25% lowest) point of the data set.
From the picture, we can find that:
The interquartile range of the bus drivers is: 20 -10 = 10 The interquartile range of the teachers is: 30 -15 = 15So the interquartile range of the distances for the bus drivers is 5 miles less than the interquartile range of the distances for the teachers.
We choose C
Answer:
Step-by-step explanation:
Suppose you wanted to change the state’s constitution to require public financing for all campaigns. If you were relying on professional signature gatherers (who charge at least $1.50 per signature), what is the minimum amount of money you could reasonably expect to spend in order to qualify this amendment for the ballot?
Answer: $1.5 millions
Step-by-step explanation:
Since the population is in millions and a million is like a fraction many millions.
Therefore, the minimum amount of money you could reasonably expect to spend in order to qualify for this amendment for the ballot is $1.5 millions
need help on this math problem can someone help ax +by=cz
Answer:
a = (cx - by)/x
Step-by-step explanation:
ax + by = cz
ax = cz - by
a = (cx - by)/x
Can I get brainliest
Carl bought 7 packs of pencils. He now has 42 pencils. He writes that 42 is 6 times as many as 7. Which comparison sentence below can he use to show the comparison?
Answer:
Option b
Step-by-step explanation:
Complete question is
Carl bought 7 packs of pencils. He now has 42 pencils. He writes that 42 is 6 times as many as 7. Which comparison sentence below can he use to
show the comparison?
A. 7 more than 6 is 42.
B. 7 is 6 times as many as 42.
C. 42 is 7 times as many as 6.
D. 6 is 7 times as many as 42
Solution -
It is given that Carl has 42 pencils.
It is not sure in which pack - the one with 6 pencils or the one with 7 pencils.
But when Carl wrote that "42 is 6 times as many as 7". By this he means that the present number of pencils i.e 42 is equal to 6 times the number of pencils in the pack of 7
Then, it becomes clear that Carl has 6 times the number of pencils in the pack of 7 pencils
Option B is correct
The table shows a function. Is the function linear or nonlinear?
x y
17 8
18 10
19 12
The function shown in the given table is a linear function.
Given that, to determine whether the table shows a function is linear or non-linear.
What are functions?The connection between sets of values is what makes up a function. For instance, in the formula y=f(x), a set of y exists for each value of x. The independent variable is called x, while the dependent variable is called Y.
Here,
Table,
x = 17 18 19
y = 8 10 12
From the observation of the table, it is been observed that the value of x changes by 1 unit, and correspondingly the value of y changes by 2 units. So, the relationship arises is a linear function.
Thus, the function shown in the given table is a linear function.
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Can you please help me find the area?
Answer:
40 in
Step-by-step explanation:
A= l x w
2 x 9 = 18
2 x 11 = 22
Then add together because the shape is together:
18 + 22 =
40
Kendra needs 2 3/4 cups of flour for cookies, 4 1/2 cups of flour for bread, and cup of flour 2/3 for biscuits , How much flour does she need in all?
Answer:
7 11/12
Step-by-step explanation:
amount of the flour
= 2 3/4 + 4 1/2 + 2/3
= 11/4 + 9/2 + 2/3
= 33/12 + 54/12 + 8/12
= 95/12
= 7 11/12
make as the brainliest
Answer:
Wofford College
Step-by-step explanation:
There are two peice pf gold and silver alloy. The ratio between the gold and silver in the first piece is 2:3, in the second peice 3:7. If we want to have 8 gram of gold and silver alloy with gold-silver ratio 5:11 how much of each peice of alloy is needed.
Answer:
1 grams of one of the alloy; and 7 grams of the other corresponding alloy.Step-by-step explanation:
The ratio between the gold and silver in the first piece = 2:3
The ratio between the gold and silver in the second piece =3:7
The ratio in the mixture = 5:11
We want to have 8 gram of the new mixture.
Let the gram of alloy taken from the first piece=x
Therefore: gram of alloy would be taken from the second piece=(8-x)
This gives:
[tex]\dfrac{2}{5}x+ \dfrac{3}{10}(8-x)=\dfrac{5}{16}*8[/tex]
We simplify the equation above for the value of x.
[tex]\dfrac{2x}{5}+ \dfrac{3(8-x)}{10}=\dfrac{5}{2} \\\dfrac{4x+24-3x}{10}=\dfrac{5}{2}\\\dfrac{x+24}{10}=\dfrac{5}{2}\\2x+48=50\\2x=50-48\\2x=2\\x=1[/tex]
Therefore to create 8 gram of gold and silver alloy with gold-silver ratio 5:11, we take 1 grams of one of the alloy and 7 grams of the other alloy.
A basket full of 10 apples costs 23$, another basket full of 15 apples costs 33$. The prices of the baskets are the same. How much will a basket full of 25 apples cost? Write an equation that tells the price Y for the number of apples X. Fill in the chart.
Answer:
Equations:
y + 10x = 23
y + 15x = 33
cost of basket with 25 apples = $53
Step-by-step explanation:
A basket with 10 apples cost $23 and a basket with 15 apples cost $33. Note that these costs also include the cost of the basket, which is same in both case. Let the cost of empty basket with "y" and cost of each apple be "x"
Cost of basket and 10 apples is $23. We can transform this statement into an equation as:
y + 10x = 23 Equation 1
Similarly,
Cost of basket and 15 apples is $33. This gives us another equation:
y + 15x = 33 Equation 2
Subtracting Equation 1 from Equation 2 , we get:
y + 15x - (y +10x) = 33 - 23
5x = 10
x = 2
Using the value of x in equation 1, we get:
y + 10(2)= 23
y = 23 - 20
y = 3
This means, cost of basket is $3 and cost of each apple is $2.
Now we can calculate the cost of basket with 25 apples, which will be:
Cost of basket + Cost of 25 apples = Total Cost
3 + 25(2) = 3 + 50 = $53
Answer:
10=23
15=23
25=53
Step-by-step explanation:
Use the given qualitative data to construct the relative frequency distribution. The 2545 people aboard a ship that sank include 406 male survivors, 1651 males who died, 362 female survivors, and 126 females who died.Complete the relative frequency distribution below. Relative Frequency Category Male survivors % Males who died % Female survivors % Females who died % (Round to one decimal place as needed.)
Answer:
The data that we have is:
total people: 2545
male survivors: 406
male who died: 1651
total males: 406 + 1651 = 2057
female survivors: 362
female who died: 126
total females: 362 + 126 = 488.
We want to know:
for the percentages, we must calculate the quotient between the total numbers of the set, and the number in the particular category we are looking for.
% male survivors = (number of male survivors/total number of males)*100%.
= (406/2057)*100% = 19.73%
% male who died = (1651/2057)*100% = 80.2%
% female survivors = (362/488)*100% = 74.18%
% female who died = (126/488)*100% = 25.82%
What is the volume of a cylinder with a base radius 3 and hight 8
Answer:
Solution
V=πr2h=π·32·8≈226.19467
Step-by-step explanation:
The number of absences for one week for all students at a high school were compiled, and the probability distribution below was created. What is the probability in any given week that a randomly selected student will be absent no more than one day? Probability Distribution Days Absent: X Probability: P(X) 0 0.78 1 0.14 2 0.03 3 0.01 4 0 5 0.04 0.08 0.14 0.78 0.92
Answer:
Option D) 0.92
Step-by-step explanation:
We are given the following probability distribution in the question:
x: 0 1 2 3 4 5
P(X): 0.78 0.14 0.03 0.01 0 0.04
We have to find the probability that a randomly selected student will be absent no more than one day.
Thus, we have to evaluate:
[tex]P(x\leq1)\\=P(X=0) + P(X = 1)\\=0.78 + 0.14\\=0.92[/tex]
0.92 is the probability that a randomly selected student will be absent no more than one day.
Thus, the correct answer is
Option D) 0.92
Answer:
Option D
Step-by-step explanation:
got it right on edg
Scott is on his school's academic team. On average, it takes Scott 4 minutes, with a standard deviation of 0.25 minutes, to solve a problem at an academic bowl. How often will it take Scott more than 4.25 minutes to solve a problem at an academic bowl?
Answer:
15.87% is the chance that Scott takes more than 4.25 minutes to solve a problem at an academic bowl.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 4 minutes
Standard Deviation, σ = 0.25 minutes
We standardize the given data.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(more than 4.25 minutes to solve a problem)
[tex]P( x > 4.25) = P( z > \displaystyle\frac{4.25 - 4}{0.25}) = P(z > 1)[/tex]
[tex]= 1 - P(z \leq 1)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x > 4.25) = 1 - 0.8413 = 0.1587 = 15.87\%[/tex]
Thus,15.87% is the chance that Scott takes more than 4.25 minutes to solve a problem at an academic bowl.
The correct answer is approximately 15.87%.
To solve this problem, we can use the properties of the normal distribution. Given that the average time Scott takes to solve a problem is 4 minutes with a standard deviation of 0.25 minutes, we can calculate the z-score for the time of 4.25 minutes to determine how many standard deviations away from the mean this time is.
The z-score formula is:
[tex]\[ z = \frac{X - \mu}{\sigma} \][/tex]
where[tex]\( X \)[/tex]is the value in question[tex](4.25 minutes), \( \mu \)[/tex] is the mean (4 minutes), and [tex]\( \sigma \)[/tex] is the standard deviation (0.25 minutes).
Plugging in the values, we get:
[tex]\[ z = \frac{4.25 - 4}{0.25} = \frac{0.25}{0.25} = 1 \][/tex]
Now, we look up the z-score of 1 in the standard normal distribution table or use a calculator to find the corresponding area to the left of this z-score. This area represents the probability that Scott will take 4.25 minutes or less to solve a problem.
The area to the left of a z-score of 1 is approximately 0.8413, or 84.13%. This is the cumulative probability up to 4.25 minutes.
To find the probability that it will take Scott more than 4.25 minutes, we subtract this value from 100% (since the total area under the normal distribution curve is 1, or 100%):
[tex]\[ P(X > 4.25) = 1 - 0.8413 = 0.1587 \][/tex]
Converting this to a percentage, we get:
[tex]\[ 0.1587 \times 100\% \approx 15.87\% \][/tex]
Therefore, it will take Scott more than 4.25 minutes to solve a problem approximately 15.87% of the time.
Question Progress
Homework Progress
Sub
Describe fully the single transformation that maps triangle A onto triangle B.
-
।
Answer:
it is b
Step-by-step explanation:
HELP MEE! 100 POINTS AND BRAINLY! GIVE ME THE STEPS, AND A GOOD ANSWER OR I WILL DELETE YOUR ANSWER AND GET MY POINTS BACK!
Example: solve √(2x−5) − √(x−1) = 1
Answer:
Solve the equation for
x by finding a , b , and c of the quadratic then applying the quadratic formula.
Exact Form:
x= 7 + 2 √ 5
Decimal Form:
x = 11.47213595 …
Step-by-step explanation:
Hi there! Hopefully this helps!
Answer: 11.47(to 2 decimal places).
Isolate one of the square roots: √(2x−5) = 1 + √(x−1)
Square both sides: 2x−5 = (1 + √(x−1))^2
We have removed one square root.
Expand right hand side: 2x−5 = 1 + 2√(x−1) + (x−1)
Simplify: 2x−5 = 2√(x−1) + x
Subtract x from both sides: x−5 = 2√(x−1)
Now do the "square root" thing again:
Isolate the square root: √(x−1) = (x−5)/2
Square both sides: x−1 = ((x−5)/2)^2
We have now successfully removed both square roots.
Let's continue with the solution.
Expand right hand side: x−1 = (x^2 − 10x + 25)/4
Since it is a Quadratic Equation! let's put it in standard form.
Multiply by 4 to remove division: 4x−4 = x^2 − 10x + 25
Bring all to left: 4x − 4 − x^2 + 10x − 25 = 0
Combine like terms: −x^2 + 14x − 29 = 0
Swap all signs: x^2 − 14x + 29 = 0
Using the Quadratic Formula (a=1, b=−14, c=29) gives the solutions:
2.53 and 11.47 (to 2 decimal places)
2.53: √(2×2.53−5) − √(2.53−1) ≈ −1 Oops! Should be plus 1. So it is not the solution.
11.47: √(2×11.47−5) − √(11.47−1) ≈ 1 Yes that one works.