Solve √5r - 9 - 3 = √r +4-2
Answers
Answer:
r = 5
Step-by-step explanation:
Solving radical equations often results in extraneous solutions. These can be avoided by using a graphing calculator for the solution.
GraphThe attached shows that the value of r that makes both sides of the equation have the same value is r = 5.
Check:
√(5·5 -9) -3 = √(5 +4) -2 ⇒ 4 -3 = 3 -2 . . . true
Analytical solutionSolution of an equation like this is typically done by isolating the radical expressions, then squaring the equation.
We can add 3, square the equation, then isolate the radical and square again:
[tex]\displaysyle \sqrt{5r-9}-3=\sqrt{r+4}-2\\\\\sqrt{5r-9}=\sqrt{r+4}+1\qquad\text{add 3}\\\\5r-9=(r+4)+2\sqrt{r+4}+1\qquad\text{square both sides}\\\\(4r-14)^2=4(r+4)\qquad\text{subtract $(r+5)$ and square again}\\\\16r^2-116r+180=0\qquad\text{rewrite in standard form}\\\\4(4r -9)(r -5) = 0\qquad\text{factor}\\\\r=\{\dfrac{9}{4},\ 5\}\qquad\text{solutions to the factored form}[/tex]
Trying these values in the original equation, we get ...
√((5(9/4) -9) -3 = √(9/4 +4) -2 ⇒ 1.5 -3 = 2.5 -2 . . . . . false
√(5(5) -9) -3 = √(5 +4) -2 ⇒ 4 -3 = 3 -2 . . . . . true
The solution is r = 5.
Related Questions
Select the three inequalities that have n = 3 in the solution set
A. n + 5 < 9
B. 13 n < 1
C. 3n + 1 >7
D. 3n > 9.5
E. n-2<5
Answers
Answer:
Its just E
I'm sorry if I'm wrong
Answer: A, C, E
Solve for all the inequalitites.
n + 5 < 9
n < 9 - 5
n < 4
∴ n = 3 is a part of the solution set.
13n < 1
n < 1/13
∴ This definitely doesn't include n = 3.
3n + 1 > 7
3n > 6
n > 2
∴ n = 3 is part of the solution because n is larger than 2.
3n > 9.5
n > 9.5 ÷ 3
n > 3.16666666
∴ n = 3 is not part of the solution set.
n - 2 < 5
n < 5 + 2
n < 7
∴ n = 3 is a part of the solution set.
Three students in a painting class made green paint by mixing blue and yellow paint. The table below shows the comparison of ounces of blue paint to ounces of yellow paint that each student mixed. Whose green paint mixture has a yellow-to-blue unit rate of 6 ounces to 1 ounce?
Answers
Answer:
Clara
Step-by-step explanation:
PLEASE HELPP!!!!
ive been stuck on this for 3 days i feel clueless
Answers
Answer:
C.
Step-by-step explanation:
I think im right!
Hopefully it helps!
Answer:
the answer is letter C I'm sure
Complete the sentence.
Answers
Answer:
50 more
Step-by-step explanation:
Answer:
50 more than............
Please help me! 20 points!
Enter your answer and show all the steps that you use to solve this problem in the space provided.
simplify
(in attachment)
Answers
Answer:
12 1/4 or (Decimal: 12.25)
Step-by-step explanation:
(3 1/2) (3 1/2)
= 7/2 (3 1/2)
= 7/2 (7/2)
= 49/4
= 12 1/4
I hope I helped you!!
Step-by-step explanation:
When we multiplying, we find the sum of the exponents so
[tex]3 {}^{ \frac{1}{2} } \times 3 {}^{ \frac{1}{2} } \\ {3}^{ \frac{1}{2} + \frac{1}{2} } \\ = {3}^{ \frac{2}{2} } \\ = 3[/tex]
9. Which points are on the graph with the equation -6x + y = 6. Select all that apply.
A. (0,6)
B. (6,2)
C (-1,0)
D. (-2, 3)
Please answer
Answers
This would be your answer!
A cell phone costs $750 and loses 28% of its value each year. Write an exponential decay function to represent this situation.
1. f(x)= 750 • 0.72^x
2. f(x)= 0.72 • 750^x
3. f(x)= 750 • 0.28^x
4. f(x)= 0.28 • 750^x
Answers
Answer:
1. [tex]f(x) = 750\cdot 0.72^{x}[/tex]
Step-by-step explanation:
The cell phone experiments an exponential depreciation, which is defined by the following formula:
[tex]f(x) = C_{o}\cdot (1-r)^{x}[/tex], for [tex]0<r< 1[/tex]. (1)
Where:
[tex]C_{o}[/tex] - Initial cost, measured in monetary units.
[tex]r[/tex] - Depreciation rate, no unit.
[tex]x[/tex] - Time, measured in years.
[tex]f(x)[/tex] - Current value of the cell phone, measured in monetary units.
If we know that [tex]C_{o} = \$\,750[/tex] and [tex]r = 0.28[/tex], then the exponential decay function that represents the situation is:
[tex]f(x) = 750\cdot 0.72^{x}[/tex]
Which means that correct answer is 1.
A lumberjack needs to climb a tree to place a satellite tower in the tree top in the woods. The satellite signal needs to reach a horizontal distance of 3500 meters along the ground. If the angle of elevation from the farthest distance along the ground that the satellite reaches to the satellite in the tree is 18 degrees, what is the radius of the satellite signal? Round your answer to the nearest meter.
Radius of the satellite signal = meters
Answers
Answer: I use clickcaculators.com ;)
Step-by-step explanation:
which of the given values will make the inequality n-93>175 true?
n=82
n=105
n=268
n=300
n=312
Answers
Answer:
n = 300 and n = 312
Step-by-step explanation:
n - 93 > 175
n > 175 + 93
n > 268
Therefore only the two last answers are are possible n values (n has to be more than 268, not equal)
The two numbers 300 and 312 will make the inequality n-93>175 true which are correct option (D)300 and (E)312.
What is inequality?Inequality is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is not equal.
Given inequality as:
n - 93 > 175
n > 175 + 93
n > 268
Therefore, n must be greater than 268 and not equal.
Hence, the two numbers 300 and 312 will make the inequality n-93>175 true.
Learn more about inequalities here:
brainly.com/question/20383699
#SPJ2
The Milgram Family drove 440 miles on 20 gallons of gas. At this rate, how many miles can they drive on 25 gallons of gas? *
Answers
Answer:550
Step-by-step explanation: first you need to find the unit rate ( or how many miles per gallon) by dividing 440 by 20 which would get 22, then you would take that and multiply it by 25 to get 550. Hope this helps!
hi help again lol :)
Answers
Answer:
Please mark brainleiest
Step-by-step explanation:
Answer is B
Step-by-step explanation:
B if you divided all the y values by x you will get 0.9
Each pair of polygons is similar. Find each missing side measure. two polygons 12 on top 5 on bottom second polygon 48 on top x on bottom
Answers
Answer:
[tex]x = 20[/tex]
Step-by-step explanation:
Given
First Polygon:
[tex]Top = 12[/tex]
[tex]Bottom =5[/tex]
Second Polygon
[tex]Top = 48[/tex]
[tex]Bottom =x[/tex]
Required
Find x
Since both polygons are similar, then:
[tex]Ratio = Top:Bottom[/tex]
For the first:
[tex]Ratio = 12:5[/tex]
For the second
[tex]Ratio = 48:x[/tex]
Equate both ratios
[tex]12:5 = 48:x[/tex]
Express as fraction
[tex]\frac{12}{5} = \frac{48}{x}[/tex]
Cross Multiply
[tex]12 * x = 48 * 5[/tex]
Solve for x
[tex]x = \frac{48 * 5}{12}[/tex]
[tex]x = \frac{240}{12}[/tex]
[tex]x = 20[/tex]
Classify the triangle 3 8 12
Answers
Write each ratio in three different ways based on the table. Party Mix Makes 8 Cups 3 cups pretzels 3 cups bagel chips 1 cup cheese crackers 1 cup peanuts
Answers
To answer
Solve the system of linear equations by elimination x + 2y = 13 --x+y=5
Answers
Answer:
{x,y} = {1,6} Have a great day
Answer: welp its already answred
Step-by-step explanation:
Steve studies math for 7/8 of an hour and history for 2/3 of an hour. How many hours did he study?
Answers
Answer:
The answer is 1 13/24 hours or 1 hour, 32.5 minutes
Step-by-step explanation:
Find a common multiple of the denominators 3 and 8, which would be 24. Convert the fractions:
7/8 x 3/3 = 21/24.
2/3 x 8/8 = 16/24
Add the two numerators = 37/24 or 1 13/24.
1/24 of an hour is 2.5 minutes, so 13/24 is 32.5 minutes.
The answer is 1 13/24 hours or 1 hour, 32.5 minutes
Which shows the numbers ordered from least to greatest? 9.129, 9.37, 9.3, 9.219
Answers
Hope this helps.
Answer:
9.129 then , 9.219 then , 9.3 then , 9.37
Step-by-step explanation:
Please answer will give brainlyest! :D
Answers
Let's just ignore memorizing any formulas for perimeters of a rectangle and just remember this!!
The opposite sides are the same right? and there are 2 pairs? that's why we just need to find one side in each pair and multiply the sum of them by 2!
Here we already know what 2 of the sides are! Therefore we find the sum.
((5/4)x+3)+3x-2= (17/4)x+1
Then we need to multiply this sum by 2
((17/4)x+1)*2=(17/2)*x+2
*Note I left the result as a fraction not a mixed number because this is how you are suppose to write it in higher math but if your teacher wants you to convert it into a mixed number, then go ahead!
Hope this helped!!
Answer:
P = (8.5x + 2)Step-by-step explanation:
Given
l = (5/4x + 3) and w = (3x - 2)Find the perimeter
P = 2(l + w)P = 2(5/4x + 3 + 3x - 2) = 2(17/4x + 1) = 17/2x + 2 = 8.5x + 2What is the solution of the system of equations? Enter the solution as an ordered pair (use decimal rounded to the nearest hundredth if necessary)
=32+54−2+8=−25
Answers
please help and quick cause im giving a lot of points
Answers
Answer: it might be C let me know if im wrong
Step-by-step explanation:
A recipe calls for 4 spoons of sugar for every 40g of flour if 240g of flour is used how much sugar would be needed
Answers
Answer:
24 spoons of sugar
Step-by-step explanation:
240/40= 6
6x4= 24
3
Gürkan bisikletiyle birinci gün 3.1 km, ikinci gun 4.5 km ve puncu
gun 4.25 km yol almıştır Gürkan üç günde toplam kaç km yol aims
tir? Tahmin ediniz Tahmininizi işlem yaparak kontrol ediniz.
Answers
tahmin etmek için yuvarlama yapmak gerekir 3,1=3 4,5=5 4,25=4,20 hepsini toplarsak 12,20
what's
[tex](4 \sqrt{2} ) {}^{2} [/tex]
Answers
Answer:
32
Step-by-step explanation:
(4√2)^2=4^2×(√2)^2
=16×2
=32
A scale model of a house is 1/10 the size of the actual house. One of the bedrooms in the house is 16 feet long. Which expression will help you find the length of the same bedroom in the model?
Answers
yeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeees
Write a similarly comparing the three triangles in the diagram
Answers
Answer:
ΔBCE similar to ΔECD similar toΔBED
Step-by-step explanation:
ΔBCE similar to ΔECD similar toΔBED
Given the expression below, identify its factors.
3a + 4b– 7c - 12
Answers
Answer:
i dont think you can solve this because
The expression is not factorable with rational numbers.
there are no like terms
what is 3/7 as decimal
Answers
Answer:
0.428571429
Step-by-step explanation:
Simplify (3xy3141x?). Use ^ when identifying your exponents
My solution is:
??
Answers
Answer:
3x^2y^3141
Step-by-step explanation:
A sum of money is divided between Mohan and Sohan in the ratio 5:7 . If Sohan's share is ₹665, find the total amount.
please help me fast.
Answers
Answer:
1140
Step-by-step explanation:
7u-> 665
1u->95
7+5=12
12u->1140
Determine if the two triangles are congruent.
Answers
Answer:
sas
Step-by-step explanation:
vertical angle stuffs