How do I solve this problem and check all the solutions?

How Do I Solve This Problem And Check All The Solutions?

Answers

Answer 1

Answer:

x-5=sqrt(2x+5)

then square both sides

x2-10x+25=2x+5

x2-8x+20=0

rest is trivial

Step-by-step explanation:

Answer 2

Answer:

x = 10

Step-by-step explanation:

Given

x - [tex]\sqrt{2x+5}[/tex] = 5 ( subtract x from both sides )

- [tex]\sqrt{2x+5}[/tex] = 5 - x ( divide all terms by - 1 )

[tex]\sqrt{2x+5}[/tex] = x - 5 ( square both sides )

2x + 5 = (x - 5)²

2x + 5 = x² - 10x + 25 ( subtract 2x + 5 from both sides )

0 = x² - 12x + 20 ← in standard form

0 = (x - 2)(x - 10) ← in factored form

Equate each factor to zero and solve for x

x - 2 = 0 ⇒ x = 2

x - 10 = 0 ⇒ x = 10

As a check

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions

x = 2

2 - [tex]\sqrt{4+5}[/tex] = 2 - [tex]\sqrt{9}[/tex] = 2 - 3 = - 1 ≠ 5

Thus x = 2 is an extraneous solution

x = 10

10 - [tex]\sqrt{20+5}[/tex] = 10 - [tex]\sqrt{25}[/tex] = 10 - 5 = 5 = right side

Thus x = 10 is the solution


Related Questions

What is the domain and range please?

Answers

Answer:

Both infinate.

Step-by-step explanation:

What is the value of (2x)° + 1​

Answers

Answer:

=2x+1

Step-by-step explanation:

I am pretty sure that is the answer

Sebastian drove for 2.2 hours at an average rate of 43.5 miles per hour. He calculates that he drove 95.7 miles. He knows the answer should be near 80, because 40 times 2 is 80. Which best explains Sebastian’s actual solution?
The actual product is reasonable because it is near 80 but greater than 80. Both factors were rounded down, making the estimate lower than the actual product.
The actual product is unreasonable. It should be near 80 but less than 80 because both factors were rounded down.
The actual product is reasonable because the estimate and actual answers both have two places to the left of the decimal.
The actual product is unreasonable because the estimate has zero places to the right of the decimal and the actual product has one decimal place to the right of the decimal.

Answers

Answer:

The actual product is reasonable because it is near 80 but greater than 80. Both factors were rounded down, making the estimate lower than the actual product.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

A player located 18.6 ft from the basket launches a successful jump shot from a height of 10 ft (level with the rim of the basket), at an angle θ = 36º and an initial velocity of v = 25 ft/s. Find the change of distance Δs of the toss if the angle changes by an amount Δθ. Hint: Use the following fact derived from Newton's Laws: An object released at an angle θ with initial velocity v ft/s travels a total distance [tex]s=\frac{1}{32} v^{2} sin(2\theta)[/tex]

Answers

Answer:

Step-by-step explanation:

You suck free points

The change of the distance travelled by the ball when the angle of launch

changes can be found by linear approximation.

The change in the distance, Δs, when the angle changes by Δθ in radians is  approximately 0.211·Δθ.

Reasons:

The distance of the player from the basket = 18.6 ft.

Height from which the jump shot is launched = 10 ft.

Angle of the jump shot = 36°

The initial velocity = 25 ft./s

According to Newton's Law of motion, the distance an object travels when

released at an angle θ, with an initial velocity, v, is given by the following

horizontal range formula equation;

[tex]s = \dfrac{1}{32} \cdot v^2 \cdot sin(2 \cdot \theta)[/tex]

   

[tex]\dfrac{ds}{d\theta} =\dfrac{d}{d\theta } \left( \dfrac{1}{32} \cdot v^2 \cdot sin(2 \cdot \theta) \right)= \dfrac{v^2 \cdot cos(2 \cdot \theta)}{16}[/tex]

By linear approximation, we have;

[tex]\Delta s = \dfrac{ds}{d\theta} \times \Delta \theta[/tex]

Which gives;

[tex]\Delta s =\dfrac{25^2 \cdot cos(2 \times 36^{\circ})}{16}\times \Delta \theta \approx 12.07 \times \Delta \theta[/tex]

360° = 2·π radians

[tex]12.07 ^{\circ} = \dfrac{2 \cdot \pi}{360} \times 12.07 \approx 0.211 \ radians[/tex]

Δs ≈ 0.211·Δθ

Therefore;

The change in the distance, Δs, when the angle changes by Δθ is 0.211·Δθ.

Learn more here:

https://brainly.com/question/17026396

Rounding Decimals 5.5252; ones

Answers

Answer:

6

Step-by-step explanation:

Identify the ones place and check the number to the right.

5.5252

Since we round up if the number to the right is greater than or equal to 5, and the number is a 5, we round up.

Therefore,

5.5252 ≈ 6

Hope this helps.

what is the solution to this??
4x + 12x =320
then using the solution to this do _x=_

Answers

Answer:

x=20

Step-by-step explanation:

Add like terms:

4x + 12x = 16x

16x = 320

320/16 = 20

2. Convert 25.2625° from decimal degrees to degrees-minutes-seconds.

Answers

Answer:15

Step-by-step explanation:

How many solutions exist for the system of equations in the graph?

one
two
three
four

Answers

Answer:

2 solutions

Step-by-step explanation:

The solutions are found at the points where the 2 graphs intersect.

From the graph there are 2 points of intersection, thus 2 solutions.

PLEASE HELP!!!!! 2.) What is the perimeter of a polygon with vertices at (-3, 1), (5, 1), (-3, 4), (5, 4)? 30 points if you can help

Answers

Answer:

22 units

Step-by-step explanation:

Known Quantities:

AB = CD and AC = BD

Calculations:

AB = 8AC = 3CD = 8BD = 3

Final Calculations:

perimeter = 2 x (3+8)perimeter = 22

Answer this question and get it right I will mark right one Brainliest
I am thinking of a number from 1-10 what is it ?

Answers

Answer:

6

Step-by-step explanation:

6 is the most common lol

Answer:

I'll say 5

Step-by-step explanation:

Hoped this helped!

What are the domain and range of each relation?

Drag the answer into the box to match each relation.

Answers

Answer:

Step-by-step explanation: Domain is the x coordinates and range is the y coordinates

5, 18, 6, 18, 13 WHATS THE INTERQUARTILE RANGE??

Answers

Answer: 12.5

Step-by-step explanation:

25th Percentile: 5.5

50th Percentile: 13

75th Percentile: 18

Interquartile Range: 12.5

Can somebody just answer this in simplify form plz!!! Make sure it’s a correct answer :)

(I’m still new to this and idek what “simplify it” means...?
WILL MARK BRAINLIEST
PROMISE!

Answers

7-2 is 5 and multiple by 3 equal 15

Write the numbers from least to greatest
8.062, 8.26, 8.026, 8.6

Answers

Answer:

8.026, 8.062, 8.26, 8.6

Step-by-step explanation:

Answer:

Hi! I'm happy to help!

Step-by-step explanation:

8.026, 8.062, 8.26, 8.6

Write an equation for the line parallel to the given line that contains C.
y =

Answers

Answer:

y=3/7x+46/7

Step-by-step explanation:

Parallel lines have the same slope. This means in the equation y=mx+b, m=3/7 for sure. Then, it gives us the point (1,7). The line has to go through this point so we plug it in: 7=3/7(1)+C. Then, we solve for C using algebra.

7-3/7=C

C=46/7

At Cheng's Bike Rentals, it costs 31 to rent a bike for 6 hours.
How many hours of bike use does a customer get per dollar?

Answers

Answer:

0.2hrs/dollars

Step-by-step explanation:

Given parameters:

Cost of bike = $31

Time duration  = 6hrs

Unknown:

Hours customers get per dollar = ?

Solution:

The number of hours customer gets per dollar is;

      Number of hrs/dollar = [tex]\frac{time duration }{cost}[/tex]

    Number of hrs/dollar  = [tex]\frac{6hrs}{31}[/tex]  

    Number of hrs/dollar = 0.2hrs/dollars

The bottom one Staples has 9 cases of crayons with 1452 boxes in each case
Office Depot has 6 cases of crayons with 504 boxes in each cate
How many total boxes of crayons do both stores hove?

Answers

Answer:

d. 16,092

Step-by-step explanation:

Staples: 1452 x 9 = 13,068

Office Depot: 504 x 6 = 3,024

13,068 + 3,024 = 16,092

A car travels 61 miles per hour. At this rate, how far will the car travel in 5 hours?​

Answers

Answer:

305 miles per hour

Step-by-step explanation:

61 miles per hour

61(5)= 305 miles/ hour

305 miles travled in the past 5 hours going 61 miles

There were 42 mangoes in each crate. 12 such crates of mangoes were delivere to a factory. 4 mangoes were rotten and had to be thrown away. The remaining mangoes were packed into boxes of 10 mangoes each. How many mangoes were left after the 4 rotten ones were thrown away? * Your answer​

Answers

Answer: 50

Step-by-step explanation: 42x12=504. 504-4=500. 500/10=50.

Answer:

Total Mangoes = 50

Rotten =  46

Step-by-step explanation:

50 divided by 10 = 5.

50 minus 4 is 46.

Anna makes unique jewelry. The owner of the "Unique" store agreed with Anna to deliver 20 bracelets a week. At the moment, Anna has 80 bracelets made, and can make 17 bracelets a week. For how many consecutive weeks will Anna be able to supply her bracelets to the "Unique" store?

Answers

Answer:

7 weeks

Step-by-step explanation:

80 ÷ 20 = 4

She over those four week she makes 17 per week. So,

17 × 4 = 68

Next, divide the product by 20:

68 ÷ 20 = 3.4

But 3.4 is only 3 full weeks so then its 3.

Lastly, add the 3 weeks we just solved for the the 4 weeks from before and you get 7 weeks.

So, Anna will be able to supply the "Unique" store for 7 weeks.

I HOPE I HELPED!!!!!!!!!! :))))))

A rock is thrown from a cliff into a ravine. The function ℎ() = −16^2 + 19 + 2560 describes the height, in feet, of the rock from the ground seconds after it is thrown. What is the height of the rock, in feet, 2 seconds after it is thrown?

Answers

Answer:

d

Step-by-step explanation:

Simplify.

Rewrite the expression in the form 4^x.

4^4 x 4^3 = ??

Answers

Answer:

[tex]4^{7}[/tex]

Step-by-step explanation:

To simplify the expression [tex]4^{4}\times4^{3}[/tex], we can use the first law of the law of indices which states that the exponent is added together when multiplying numbers with the same base. Eg: [tex]a^{x}\times a^{y} = a^{x+y}[/tex].

[tex]4^4 \times4^3=4^{4+3}[/tex]

[tex]=4^{7}[/tex]

Hope this helps :)

A carpenter use 65 shelves to make 13 bookcases. She uses the same number of shelves for each bookcase. Are 32 shelves enough to build 6 more bookcases?

Answers

Answer:

Yes.

Step-by-step explanation:

First, find the unit rate for 1 bookcase.

65 ÷ by 13 = 5 (unit rate)

Then, multiply the unit rate by the bookcases the carpenter wants to make.

6 · 5 = 30

Finally, subtract the shelves the carpenter wants to use by 30.

32 - 30 = 2 shelves.

Therefore, 32 shelves is enough to build 6 more bookcases. <3

I need to know what's 1131÷29 pronto

Answers

the answer is 39 because you need to divide.

39 because you have to divide the equation

Who can't wait for Cyberpunk to come out

Answers

Answer:

i got it, hella good game but reallllyyy buggy

Step-by-step explanation:

feel free to ask questions abt it, I know, lore, controls, gameplay, etc.

what is the value of q in the equation 4/5q = 32

Answers

Answer:

40

Step-by-step explanation:

4/5 * q = 32

First you divide 4/5 by itself so you can eliminate it from the equation and then you have to divide 32 by 4/5 n when you do that you get 40. So q = 40.

Mr. Smith had 262 markers in the art room. He threw away the markers that dried out, and now he has 99 markers. How many markers dried out?​

Answers

Answer:

163

Step-by-step explanation:

262-99=163

Answer:163

Step-by-step explanation: subtract 262 and 99

a university department administers a survey regardring student satisfaction based on the survey results the department provides a confidence interval estimate of 60% to 80% for student satisfaction if the department wishes to construct a confidence interval the more accurate represents the proportion of a student satisfaction how should the design be altered

Answers

Answer:

Change the confidence interval.

Step-by-step explanation:

The confidence interval should be altered . If a 95 % or 90% confidence interval is set then better results can be obtained for student satisfaction.

A 90 or 95  or 99 percent confidence interval will show  a greater range of the data that lies within or without the given criteria.

95 % confidence interval does not mean that the probability is 95% . It means that we are 95% of the data lies  or does not lie within the specific range.

This gives better results as compared to 60- 80 % confidence intervals.

If 95% of the students are satisfied as compared to 60% or 80% , this shows more accuracy.

Samantha claims that 4x + 2 is equivalent to the expression x + 17 + 3x − 15. Check whether Samantha’s equivalent expression is correct using x = 2. Samantha is incorrect because when using x = 2, the resulting values in both expressions are different. Samantha is incorrect because the expressions cannot be checked using x = 2. Samantha is correct because when using x = 2, the resulting values in both expressions are equal.

Answers

Answer:

The correct answer is c

Answer:

Answer is c

Step-by-step explanation:

Your welcome

The temperature increases from 18° F to 27° F.
What is the percent increase of the temperature?
A
3%
B
9%
С
33%
D
50%

Answers

Either 50% or 9%
Because it can be both

The percent increase in the temperature is 50%.

To understand more, check below explanation.

Percentage increase:

The temperature increases from 18° F to 27° F.

       Increase in temperature = 27 - 18 = 9

The percent increase in the temperature is computed as,

                                  [tex]=\frac{27-18}{18}*100\\ \\=\frac{9}{18}*100\\ \\=\frac{1}{2}*100=50\%[/tex]

Learn more about the percentage here:

https://brainly.com/question/24304697

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