Answers
Answer:
[tex]\text{B. }3x+4=3x+2\sqrt{3x-11}-10[/tex] only for [tex]3x+4\in [0, \infty)[/tex]
Step-by-step explanation:
Key formulas used:
[tex]\sqrt{x}^2=|x|[/tex] [tex](a+b)^2=a^2+2ab+c^2[/tex]Given [tex]\sqrt{3x+4}=1+\sqrt{3x-11}[/tex],
We can use the first formula on the left side of the equation.
In this case, for [tex]\sqrt{x}^2=|x|[/tex], [tex]x=3x+4[/tex], we have:
[tex]\sqrt{3x+4}^2=|3x+4|[/tex]
Similarly, we can use the second formula on the right side of the equation.
In this case, for [tex](a+b)^2=a^2+2ab+c^2[/tex], [tex]a=1, b=\sqrt{3x-11}[/tex], we have:
[tex](1+\sqrt{3x-11})^2=1^2+2\cdot 1\cdot \sqrt{3x-11}+\sqrt{3x-11}^2,\\=1+2\sqrt{3x-11}+3x-11,\\=3x+2\sqrt{3x-11}-10[/tex]
Therefore, when you square both sides of the equation, you get:
[tex]\boxed{\text{B. }3x+4=3x+2\sqrt{3x-11}-10}[/tex]
*Important:
This answer choice is actually only correct if [tex]3x+4>0[/tex], because of the first formula we used. If [tex]3x+4<0[/tex] (negative), then [tex]3x+4\neq \sqrt{3x+4}^2,\text{ if }3x-4<0[/tex]. Graphically, you can show this since the line [tex]y=\sqrt{x}^2[/tex] is not equal to [tex]y=x[/tex] but instead [tex]y=|x|[/tex]. [tex]y=\sqrt{x^2}[/tex] and [tex]y=x[/tex] only overlap if you restrict the domain to [tex][0, \infty)[/tex] (positive numbers), hence [tex]\text{B. }3x+4=3x+2\sqrt{3x-11}-10[/tex] only for [tex]3x+4\in [0, \infty)[/tex].
Related Questions
By what percent is 4.5 × 10^5 greater than 9 × 10^4
a) 200%
b) 400%
c) 500%
d) 600%
Answers
Answer:
C; 500%
Step-by-step explanation:
To get the percentage, we need to make a straight division, then multiply by 100%
We have this as;
(4.5 * 10^5)/(9 * 10^4) * 100%
= 5 * 100% = 500%
will give branliest TO ANY ACTUAL ANSWERS
Which equation does the graph of the systems of equations solve?
two linear functions intersecting at 3, negative 2
Answers
Help me out plz help me
Answers
Answer:
-15
Step-by-step explanation:
Step 1: Multiply 3 by both sides
3(2/3x)=3(-10)
Step 2: Simplify
2x=-30
Step 3: Divide both sides by 2
2x/2=-30/2
Step 4: Simplify
x=-15
Hope this helps and if it does, don't be afraid to give my answer a "Thanks" and maybe a Brainliest if it's correct?
What is the value of D
Answers
Answer:
Value of what? There’s nothing
Step-by-step explanation:
PLZ HELP IF RIGHT I WILL THEN GIVE YOU BRAINLISET!!!!!!
Answers
Answer:
1, 4, 8, 10
16, 64, 96, 160
Hope it helps u
Thank You
Please mark as brainliest
Answer:
top row is 4 and 10 bottom is 96 and 128
Step-by-step explanation:
goo
Find the Surface Area of the composite figure acellus
Answers
Answer:
653 is the total suface area
Step-by-step explanation:
i have all the math in the note book but i can explain it very simply you find the area of the big base which is 120 the side of 12 which equals 84 and the side of ten which equals 70 and multiply them all by two which gives you 548 then you multiply the base of the small figure (only count one of the shapes bases btw) and that equals 9 the you find the sides which are 24 each this gives you 96 + 548 = 644 +9 = 653 and there is your answer
Answer:
644in~2
Step-by-step explanation:
acellus 2022 ;)
log base 16 of 256 -log base 16 of 16
Answers
Answer:
What’s the question
Step-by-step explanation:
please help it’s for a final
Answers
Answer:
DAC = 54
Step-by-step explanation:
90 - 36 = 54
54 degrees
a.)Would the equation be sine or cosine if the situation was someone being on a roller coaster that starts 15 ft above ground level, goes up to 45 feet above ground level, and goes down 20 feet under ground level?
b.) What would the equation be? ford monition and the terminal is in the third quadrant
Answers
Convert 4cm to meters
Answers
Answer:0.04
Step-by-step explanation:
Answer:
0.04 meters
It's too simple
if a man died and left inheritance money$ 3990. As per his will this amount will be distributed in 15:18:17 ratio. Find the share of money each gets?
Answers
Answer:
The ratios are 15 18 and 17 which total 50
So one person will receive 15/50 = 30 per cent
Another person receives 18/50 = 36 per cent
The third person receives 17/50 = 34 per cent
1st Person 30% of 3,990 = 1,197.00
2nd Person 36% of 3,990 = 1,436.40
3rd Person 34% of 3,990 = 1,356.60
Step-by-step explanation:
Answer:
$1197 : $1436.4 : $1356.6
Step-by-step explanation:
15 + 18 + 17 = 50
3990 / 50 = 79.8
1st person : 79.8 x 15 = 1197
2nd person : 79.8 x 18 = 1436.4
3rd person : 79.8 x 17 = 1356.6
$1197 : $1436.4 : $1356.6
If this helps you, please mark brainliest!
What type of polynomial is: 2x - 4x^3 - 7 + 6x^2
A. quadratic
B. linear
C. quartic
D. cubic
Answers
Answer:
Option D
Step-by-step explanation:
Given polynomial :-
=> 2x - 4x³ -7 + 6x²
Here the highest degree of variable is 3 ,
Therefore it is a cubic polynomial .
plz any one here to follow me plz tellme any one ?
Answers
ig?
Someone plz help Which of the following equations represent f(x)=x^4 stretched vertically by a factor of 2 and horizontally by a factor of 4
Answers
Step-by-step explanation:
the answer is in the image above
Are lines l and k parallel
Answers
Answer:
yes both lines have a slope of 2, so they are parallel.
PLEASE PLEASE PLEASE HELP ME
Please look at all of the questions!
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Answers
The angle relationship is vertical angles
I don’t know the last one sorry
Help please...............................
Answers
Answer:
10cm+5cm+3cm+3cm+7cm+2cm=30cm
What is the product of (a+b) (a-b)
Answers
Answer:
[tex]a^{2}+b^{2}[/tex]
Step-by-step explanation:
(a+b)(a-b)
[tex]a^{2}[/tex]-ab+ab-[tex]b^{2}[/tex]
[tex]a^{2} + b^{2}[/tex]
which linear inequality is represented by the graph
Answers
Answer:
Step-by-step explanation:
HELP!!!
f(x) =x^2. What is g(x)?
Answers
Answer:
C. g(x) = 4x²
Step-by-step explanation:
we have one specific point on g(x) : (1,4)
so, for x=1 the functional value (y) has to be 4.
A. (4×1)² = 4² = 16 and not 4. => wrong
B. 1/4 × 1² = 1/4 and not 4. => wrong
C. 4×1² = 4 and that IS 4 => correct
D. 16×1² = 16 and not 4 => wrong
3, 6, 9, 12, 15,
Tlie common difference " is
Answers
Answer:
The common difference is definitely 3. The common difference is the difference between the numbers in a sequence. In the sequence 3,6,9,12, and 15 the common difference is 3.
Helpppppp pls
Find h.
h = [?] in
Answers
Answer:
h=rt.96=4 rt.6
Step-by-step explanation:
r=2 inches
therefore 100= root over h + 4
=>h=rt.96=4 rt.6
Convert 14 into base 2
Answers
Answer: 0b1110
Step-by-step explanation:
Multiply the following complex numbers:
(8 - 3i)(6 + 5i)
A. 33 + 221
B. 33 - 221
C. 63 + 221
O D. 63 - 221
Answers
Answer:
63+22i
Step-by-step explanation:
(8 - 3i)(6 + 5i)
FOIL
first: 8*6 = 48
outer: 8*5i = 40i
inner: -3i* 6 = -18i
last: -3i*5i = -15 i^2 = -15(-1) = 15
Add together
48+40i -18i +15
Combine like terms
63+22i
I need help please!!
What is the solution?
Answers
Answer: (5, 0) and (3, 4)
which equation has the steepest graph?
A. y=7x+3
B. y=8x-1
C. y=-10x-4
D. y=-2x+6
Answers
Find an equation of the line passing through the
point (6,5) and perpendicular to the line whose
equation is 2y + 3x = 6.
Answers
Answer:
In slope-intercept form:
[tex]\displaystyle y=\frac{2}{3}x+1[/tex]
Or, in standard form:
[tex]2x-3y=-3[/tex]
Step-by-step explanation:
We want to find the equation of the line that passes through the point (6, 5) and is perpendicular to the line whose equation is:
[tex]2y+3x=6[/tex]
Since the new line is perpendicular, its slope and the slope of the first equation will be negative reciprocals of each other.
So, find the slope of the first equation. Subtract 3x from both sides:
[tex]2y=-3x+6[/tex]
And divide both sides by two:
[tex]\displaystyle y=-\frac{3}{2}x+3[/tex]
So, the slope of the first equation is -3/2.
The slope of the new line is its negative reciprocal. So, the slope of the perpendicular line is 2/3.
Next, we also know that it passes through the piont (6, 5). We can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and (x₁, y₁) is a point.
Substitute:
[tex]\displaystyle y-(5)=\frac{2}{3}\left(x-6\right)[/tex]
And we have our equation!
If desired, we can simplify it into slope-intercept form:
[tex]\displaystyle \begin{aligned} y-5&=\frac{2}{3}x-4\\\\y&=\frac{2}{3}x+1\end{aligned}[/tex]
Or, into standard form:
[tex]\displaystyle \begin{aligned} y&=\frac{2}{3}x+1\\\\3y&=2x+3\\\\ 2x-3y&=-3\end{aligned}[/tex]
Helppp meeeee plzzzzzxxzz
Answers
Answer:
You will save $20.
Step-by-step explanation:
IMPORTANT FORMULA: TO CONVERT A NUMBER TO A PERCENT, YOU HAVE TO MULTIPLY BY 100. TO CONVERT A PERCENT TO A NUMBER, YOU HAVE TO DIVIDE BY 100.
1) Some percent of an amount is what?
Using the formula above, I can conclude that 40% is equal to 40/100=4/10=2/5
2) Translate into an equation.
It is important to keep in mind that we are trying to find 40% of $50 in order to find out how much money will be saved.
In the above step, we already found that 40% = 2/5.
I also know that, in mathematics, the word "of" means multiplication.
Therefore, I am trying to find 40% of $50 is the same as 2/5 * $50.
2/5 * $50 = x ------ (x represents the money saved)
3) Solve for variable.
$20 = x
4) Write a sentence to answer the question.
You will save $20.
Line l has a slope of . The line through which of the following pair of points is perpendicular to l?
A. (-5, -6), (3,3)
B.(-9, -6), (3,3)
C. (3,-5), (-6,3)
D. (9,-2),(-6,6)
Answers
Answer:
b is the right answer
Step-by-step explanation:
Lines RS, TV, and SW are shown.
On a coordinate plane, 3 lines are shown. Line R S goes through (negative 8, 6) and (2, 6). Line T V goes through (negative 6, negative 4) and (8, negative 4). Line S W goes through (2, 6) and (2, negative 8).
Which statements are true about these lines? Select three options.
Line RS has a slope of 6.
Line SW has an undefined slope.
Line TV has a slope of 0.
Lines RS and TV are parallel.
Line SW is perpendicular to line RS, but not to line TV.
Answers
9514 1404 393
Answer:
(b) Line SW has an undefined slope.
(c) Line TV has a slope of 0.
(d) Lines RS and TV are parallel.
Step-by-step explanation:
A horizontal line has 0 slope. Lines RS and TV are horizontal, hence are parallel and have 0 slope.
A vertical line has undefined slope. Line SW is vertical, hence has undefined slope.
Answer:
B,C,D
Step-by-step explanation: