√(x2−2x−2)+√(2x−3)=5
Answers
[tex]\\ \sf\longmapsto \sqrt{(x^2-2x-2)}+\sqrt{2x-3}=5[/tex]
We know
if x=√a+√b then
x^2=a+b+2√ab[tex]\\ \sf\longmapsto x^2-2x-2+2x-3+2\sqrt{(x^2-2x-2)(2x-3)}=5^2[/tex]
[tex]\\ \sf\longmapsto x^2-3+2\sqrt{2x^3-4x^2-4x-3x^2+6x+6}=25[/tex]
[tex]\\ \sf\longmapsto 2\sqrt{2x^3-7x^2+2x+6}=25-x^2+3=28-x^2[/tex]
[tex]\\ \sf\longmapsto \sqrt{2x^3-7x^2+2x+6}=\dfrac{28-x^2}{2}[/tex]
[tex]\\ \sf\longmapsto 2x^3-7x^2+2x+6=\dfrac{(28-x^2)^2}{4}[/tex]
[tex]\\ \sf\longmapsto 2x^3-7x^2+2x+6=\dfrac{784-56x^2+x^4}{4}[/tex]
[tex]\\ \sf\longmapsto 8x^3-28x^2+8x+24=784-56x^2+x^4[/tex]
[tex]\\ \sf\longmapsto x^4-8x^3-28x^2-8x+760=0[/tex]
Solving furtherThe equation has no real solutions .(attached a pic of calculator )
Answer:
[tex]{ \rm{ \sqrt{( {x}^{2} - 2x - 2) } + \sqrt{(2x - 3)} = 5 }}[/tex]
• let's first collect like terms
[tex]{ \rm{ \sqrt{( {x}^{2} - 2x - 2)} = 5 - \sqrt{(2x - 3)} }}[/tex]
• Then, let's take a square:
[tex]{ \rm{ {( \sqrt{( {x}^{2} - 2x - 2)}) }^{2} = {(5 - \sqrt{(2x - 3)} )}^{2} }} \\ \\ { \rm{ {x}^{2} - 2x - 2 = (5 - {(2x - 3)}^{ \frac{1}{2} } )(5 - {(2x - 3)}^{ \frac{1}{2} }) }} \\ \\ { \rm{ {x}^{2} - 2x - 2 = 25 - 10 \sqrt{2x - 3} - 2x - 3 }} \\ \\ { \rm{ {x}^{2} - 2x + 2x - 2 - 22 + 10 \sqrt{2x - 3} = 0}} \\ \\ { \rm{ {x}^{2} + 10 \sqrt{2x - 3} - 22 = 0}} \\ \\ { \rm{the \: roots \: of \: the \: equation \: are \: not \: real}}[/tex]
Answer: x = 3(-1 + i) or 3(-1 - i)
Related Questions
Find the point-slope equation of the line with slope -3 that passes
through the point (2, -10).
Answers
Answer:
Step-by-step explanation
(-y-y1)/(x-x1)= m
y-(-10)/(x-2)= -3
y= -3x -4
Answer:
[tex]y+10=-3(x-2)[/tex]
Step-by-step explanation:
First we must know the format of point-slope form.
This would be: [tex]y-y1 = m (x-x1)[/tex]
Given x = 2, y = -10, and that our slope MUST be -3
Lets solve for "b" in the slope-intercept form using the variables provided to us. Remember that slope-intercept form is: [tex]y=mx+b[/tex] where "m" is the slope.
-10 = -3(2) + b
-10 = -6 + b
-4 = b
Congrats! We now have our b variable, which means we can write out our slope-intercept form for our equation. This would be: [tex]y=-3x-4[/tex]
We aren't done though, we now must convert this into point-slope form! Remember that x = 2 and y = -10
Lets plug in -3 for the "m" spot, -10 for the "y1" spot, and 2 for the "x1" spot in the point-slope equation.
[tex]y+10=-3(x-2)[/tex]
(Why are we adding 10 instead of subtracting you might ask? Remeber that two negatives equal a positive; when we plugged in -10 into the "y1" spot it was already negative, it would essentially be this: [tex]y - (-10)[/tex] which turns into a positive!)
Huzzah! We now have our equation in point-slope form which is equivalent to: [tex]y=-3x-4[/tex]
Feel free to check on the Desmos graphing calculator if you wish!
If you have any questions feel free to ask! Hope this helped!
what does it mean when y tends to increase as x increases, the two data sets have a
Answers
Answer:
1] She would not have to change a diaper, they said. In fact, she would not have to do anything at all. Mrs. Winter said that Charles would not wake while she and Mr. Winter were out at the movies. He was a very sound sleeper, she said. No need to have a bottle for him or anything. Before the Winters left they said absolutely please not to look in on the sleeping baby because the door squeaked too loudly.
[2] Harriet had never held a baby, except for one brief moment, when she was about six, when Mrs. Antler next door had surprisingly bestowed¹ on her the tight little bundle that was their new baby, Andrea. Harriet had sat very still and her arms had begun to ache from the tension by the time Mrs. Antler took back her baby. Andy was now a plump seven-year-old, older than Harriet had been when she held her that day.
[3] After two hours of reading all of the boring mail piled neatly on a desk in the bedroom and looking through a depressing wedding album filled with photographs of dressed-up people in desperate need of orthodonture² (Harriet had just ended two years in braces and was very conscious of malocclusion³ issues) while flipping channels on their television, Harriet turned the knob on the baby's door very tentatively, but it seemed locked. She didn’t dare turn the knob with more pressure because what if she made a noise and woke him and he started to cry?
[4] She stood outside the door and tried to hear the sound of a baby breathing but she couldn’t hear anything through the door but the sound of the occasional car that passed by on the street outside. She wondered what Charles looked like. She wasn’t even sure how old he was. Why had she agreed to baby-sit when Mr. Winter approached her at the swim club? She had never seen him before, and it was flattering that he took her for being capable, as if just being a girl her age automatically qualified her as a baby-sitter.
[5] By the time the Winters came home, Harriet had eaten most of the M & M's in the glass bowl on their coffee table: first all the blue ones, then the red ones, then all the green ones, and so on, leaving, in the end, only the yellow.
[6] They gave her too much money and didn’t ask her about anything. Mrs. Winter seemed to be waiting for her to leave before checking on the baby. Mr. Winter drove her home in silence. When they reached her house he said, My wife. He hesitated, then he said, You understand, don't you? and Harriet answered Yes without looking at him or being sure what they were talking about although she did really know what he was telling her and then she got out of his car and watched him drive away.
___________
¹ Bestow (verb): to give or present
² Orthodonture refers to the branch of dentistry dealing with the prevention or correction of irregularities of the teeth.
³ Malocclusion refers to a misalignment of teeth.
Step-by-step explanation:
Comment on the impact of the flashback in paragraph 2. How does it contribute to the story? Use textual evidence to justify your response.
helppp meee
^ this is the question
MONTHLY EXPENSE
Randy spends an average of $25 per week on gasoline and $45 every three months on the daily newspaper.
Answers
I need help pleAse and thank you
Answers
Answer:
The last
Step-by-step explanation:
6^2 = 36 and (-6)^2=36 so the last is the correct answer.
Answer:
Last Option
Step-by-step explanation:
1: Take the square root of both sides.
[tex]\sqrt{x^2}[/tex] = ± [tex]\sqrt{36}[/tex] [tex]x[/tex] = ± [tex]\sqrt{36}[/tex] [tex]x = 6[/tex] or [tex]x = -6[/tex]2. Now, the points, q and p, on the last option are at -6 and 6. Therefore, the last option is the correct answer.
Answer the question in the photo please.
Answers
Answer:
The answer is -2
Step-by-step explanation:
2 to the 3rd power would be the same as saying 2x2x2 which is 8. Now with that, you know that y is 6 and o is 4, so you would do 8-6-4. I hope this helps!
8 - 6 - 4
2 - 4
-2
The answer is -2
I hope this helps
I'm confused- how do I form the equation with 2 pts?
Write the equation of the line given the y-intercept and x-intercept.
y-intercept is (0, –6), x-intercept is (–2, 0)
Answers
Answer:
the equation of the line is y = -3x - 6
Step-by-step explanation:
Note that since (0, -6) is the y-intercept, we can write the slope-intercept equation of the line as y = mx - 6. The other given point is (-2, 0) (which happens to be the x-intercept also). Starting with y = mx - 6, replace y with 0 and x with -2:
0 = m(-2) - 6. We now solve this for the slope, m: 0 = -2m - 6 becomes
2m = -6, or m = -3.
With m = -3 and b = -6, the equation of the line is y = -3x - 6
please help me i dont understand
Answers
Answer:
you are multiplying by 7
Step-by-step explanation:
so like 3 x 7 = 21
4 x 7 = 28
6 x 7 = 42
9 x 7 = 63
10 x 7 = 70
hope it helps
7,9
Step-by-step explanation:
3x4=21
4x7=28
6x7=42
9x7=64
10x7=70
Construct a quadrilateral ABCD, AB = 4cm BC = 3cm,
AD= 2.5cm, AC= 4.5cm, BD= 4cm.
Answers
Answer:
steps below
Step-by-step explanation:
1. use ruler to draw a segment of 4 units AB
2. center the compasses needle at A and draw arc with radius of 5 and intersect with another arc centered at B with radius of 3 at point C
3. center the compasses needle at B and draw arc with radius of 4.5 and intersect with another arc centered at A with radius of 2.5 at point D
4. connect BC, CD and AD to form quadrilateral ABCD
. Write the equation of a line with a y-intercept of 2 and a slope of - Graph the equation 3
Answers
Answer:
y=3/4x+2
Step-by-step explanation:
Idont know how to graph on brainly
show -12 as a fraction
Answers
Answer:
[tex]-\frac{12}{1}[/tex]
Step-by-step explanation:
show -12 as a fraction
- 12/100Solve for X.
- 4x + 60<72
OR
14x+ 11 < -31
Choose 1 answer:
Answers
-4x + 60 < 72
= -4x > 72 - 40
= -4x > 12
= x > 12/-4
= x > -3
Answer the question in the photo please
Answers
Answer:
Brian because if you do the math correctly it should be Brian
Answer:
Laurie
Step-by-step explanation:
Laurie
12 +3 (3² + (-9)) = 12 +3 (9 +(-9)) {Here, 3² is calculated}
= 12 + 3 *0 {9 - 9 = 0}
= 12 + 0 {Anything multiplied by 0 = 0}
= 12
Provide an example of linear equation. The example should show that the output doubles or increases as the input increases and reduces when the input reduces too.
Answers
Answer:
[tex]y=2x+1[/tex]
Step-by-step explanation:
Use the formula [tex]y=mx+b[/tex]
Switch out any number for '[tex]m[/tex]' and for '[tex]b[/tex]' and your input would be '[tex]x[/tex].'
Just make sure your '[tex]m[/tex]' is larger than your '[tex]b[/tex].'
An example could be, [tex]y=2x+1[/tex]
Select all of the following expressions that require
use of the distributive property to simplify
Answers
Answer:
√5(√7-√2)
(√5+√2)(-√7)
Step-by-step explanation:
i got it right on edge .
The correct expressions that require the use of the distributive property to simplify are √5(√7-√2) and (√5+√2)(-√7)
What is Number system?A number system is defined as a system of writing to express numbers.
Given the integers A, B, and C.
According to the distributive property;
A(B + C) = AB + AC
From the expression, you can see that A is distributed over B and C
So for distributive property, there must be a factor and the sum of terms in parenthesis.
Based on the given options the correct expressions that require the use of the distributive property to simplify are √5(√7-√2) and
(√5+√2)(-√7)
Hence, the correct expressions that require the use of the distributive property to simplify are √5(√7-√2) and (√5+√2)(-√7)
To learn more on Number system click:
https://brainly.com/question/22046046
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Passing through (-2,-6) and parallel to the line whose equation is y=-3x+4
Write an equation for the line in point-slope form
Answers
Answer:
y = -3x - 12
Step-by-step explanation:
Lines that are parallel have the same gradient.
Therefore using the point (-2,-6) you can make your own equation.
-6 will be y, -2 will be x
All you have to do is find the y-intercept which is C in y=mx+c
-6 = -3(-2) + c
-6 = 6 + c
-12 = c
Therefore;
y = -3x - 12
please help I'm gonna fail
Answers
Answer:
Ask me things ill try my best!
A bad contains 35 colored maebles. There are 6 blue marbles. 7 red marbles. 12 yellow marbles and 10 clear marbles. What is the ratio of blue marbles to clear marbles
Answers
Simplify the expression 2x²6 when x = 5
Answers
Answer:
300
Step-by-step explanation:
First we simplify the exponent to get 25, then multiply it buy 2 and then 6.
25*2*6=300
Answer:
Below,...!
Step-by-step explanation:
[tex]2x^26[/tex]
[tex]2*x^2*6[/tex]
x = 5
[tex]2*5^2*6[/tex]
[tex]2*25*6[/tex]
[tex]50*6[/tex]
[tex]300[/tex]
Chow,...!
The graph of y=f(x) is shown. Please answer, will mark BRAINELIST!
Answers
Answer:
a) -2
b) -5
Mark me bailiest
Please help
The black graph is the graph of
y = f(x). Choose the equation for the
red graph.
a. y = f (x - 1)
b. y = f (6)
y - 1 = f(x)
d. 3 = f(x)
Answers
Answer:
answer is B
Step-by-step explanation:
Answer: a
Step-by-step explanation:
3 x 10⁹ divided by 2.28 x 10⁸, In scientific notation.
Answers
Answer:
0.131579 x 10^2
Step-by-step explanation:
Hope It helps
solve pls brainliest
Answers
Answer: (a.) 3x18= +54 meters. (b.) (-12)+(-12)+(-12) =-36 Celsius
Step-by-step explanation:
WHERE DO THEY GO??? PLEASE HELP MEEE
Answers
Answer:
Step 1: 2x - 6 = 4x
Step 2: -6 = 2x
Step 3: -3 = x
Step-by-step explanation:
Step 1: Start off with the distributive property, multiplying 2 by x and -3.
2(x - 3) = 4x ------> 2x - 6 = 4x
Step 2: Subtract 2x from both sides.
2x - 6 = 4x ------> -6 = 2x
Step 3: Divide by 2 to solve for x.
-6 = 2x ------> x = -3
ngl you should probably know this...
Answer:
4, 3, then 5
Step-by-step explanation:
1. 2x-6=4x
2. -6=2x
3. -3=x
Hep help help a lay done 5 more
Answers
Answer:
9and 12at the top is the answer
Answer:
9^12
Step-by-step explanation:
please mark me as brainlest
Please help me out please
Answers
9514 1404 393
Answer:
(a) m = 0.47, b = 154.30
(b) b = fixed costs, listed as insurance and car payments.
Step-by-step explanation:
(a) All you're required to do here is recognize that the fixed costs of $154.30 for insurance and car payments represent the constant part of the monthly expense. And, the $0.47 per mile represents the mileage-related part of the monthly expense. Of course the mileage-related charge is the product of the per-mile charge ($0.47) and the number of miles (x).
Then the monthly charge is ...
monthly cost = mileage-related cost + constant (fixed) cost
y = mx + b
y = 0.47x + 154.30 ⇔ m = 0.47, b = 154.30
__
(b) The 'b' in the equation is the fixed monthly cost: $154.30 for insurance and car payment.
x : (x + 3) = 2 : 3
Work out the value of x
Answers
Step-by-step explanation:
x : (x + 3) = 2 : 3
[tex] \frac{x}{x + 3} = \frac{2}{3} [/tex]
[tex]3x = 2x + 6[/tex]
[tex]3x - 2x = 6[/tex]
[tex]x = 6[/tex]
The value of x on simplifying the expression x : (x + 3) = 2 : 3 is 6.
What is the ratio?If b is not equal to 0, an ordered pair of numbers a and b, denoted as a / b, is a ratio. A proportion is an equation that equalizes two ratios. It is the contrast of two different quantities. For instance, if your father weighs 90 kg, and you weigh 30 kg, the weight ratio is 1:3.
Given:
x : (x + 3) = 2 : 3,
Calculate the value by simplifying the expression,
3x = 2 (x + 3)
3x = 2x + 6
x = 6
To know more about Ratios:
https://brainly.com/question/13419413
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20% of a full tank is 80 liters.
Answers
Step-by-step explanation:
you have to multiply 20 by 80
Answer:
How many liters are in a full tank? ----- Answer:
Step-by-step explanation:
20 % of 80 = 16
(I really don't know what your asking for, your missing pieces to the question.)
Sorry, :(
Need help with math in Spanish
Answers
Answer:
wheres the math
Step-by-step explanation:
Solve for z
THANK U SM
I WILL MARK BRAINILIEST
Answers
Answer:
z=7
Step-by-step explanation:
Combine like terms: 2z=14
Reduce the greatest common factor on both sides of the equation z=7
answer: z= 7
Answer:
z = 7
Step-by-step explanation:
6z + z - 4z + 4z - 5z = 14
Collect like terms
6 + 1 - 4 + 4 - 5
-4 and 4 cancel out each other so remove it from the equation
6 + 1 - 5 = 2
2z = 14
Divide by 2 to isolate z
z= 7
The equation y=6.5x represents a proportional relationship. What is the constant of proportionality?
Answers
Answer:
The constant of proportionality is 6.5.
Step-by-step explanation:
The constant of proportionality is the same thing as the slope and the equation of a line is y = mx + b, where m is the slope. Therefore, 6.5 is the slope because it is multipying by x.