Answers
Answer:
Step-by-step explanation:
I'm assuming that strange looking thing is a 9, so begin by multiplying both sides by that denominator to get:
[tex]x-9=\sqrt{x}+3[/tex] then subtract 3 from both sides to get
[tex]x-12=\sqrt{x}[/tex] and then square both sides to get
[tex]x^2-24x+144=x[/tex] and get everything on one side to solve for x by factoring:
[tex]x^2-25x+144=0[/tex] and factor that however it is you have learned to factor second-degree polynomials to get that
x = 16 and x = 9. We have to check for extraneous solutions because anytime you manipulate an equation, as we did by squaring both sides, you run the risk of these solutions that actually don't work when you plug them back into the original equation. Let's try 16 first:
[tex]\frac{16-9}{\sqrt{16}+3 }=1[/tex] If 16 is a solution, then this statement will be mathematically true.
[tex]\frac{7}{4+3}=1[/tex] and [tex]\frac{7}{7}=1[/tex] so 16 works. Let's try 9:
[tex]\frac{9-9}{\sqrt{9}+3 }=1[/tex] We know that one doesn't work, because 9-9 = 0 and 0 over anything = 0, not 1.
x = 16 is the only solution.
Answer:
x = 16
Step-by-step explanation:
[tex]\frac{x-9}{\sqrt{x}+3}=1[/tex]
Cross multiply,
x - 9 = √x + 3
Subtract 3 from both sides
x - 9 - 3 = √x
x - 12 = √x
Square both sides
(x -12)² = (√x)²
x² - 2 * x*12 + 12² = x
x² - 24x + 144 = x
x² - 24x + 144 - x = 0
x² - 25x + 144 = 0
Sum = -25
Product = 144
Factors = -9 , -16 {(-9)+(-16) = -25 & (-)*(-16) = 144}
x² - 25x + 144 = 0
x² - 16x - 9x + (-9)*(-16) = 0
x(x - 16) - 9(x - 16) = 0
(x - 16) (x - 9) = 0
x - 16 = 0 ; x - 9 = 0
x = 16 ; x = 9
x = 9 is an extraneous solution.
When we plug in 9 in the LHS of the equation,
LHS = [tex]\frac{9-9}{\sqrt{9}+3}[/tex]
[tex]= \frac{0}{3+3}[/tex]
= 0 ≠ RHS
So, x = 16 is the only solution
Related Questions
Practice Problems
Lance and Dimetri are playing a marble game. According to their rules, 3 points are awarded for
each red marble collected and 2 points are awarded for each green marble collected.
The number of points per player is found using the following expression:
3r + 29
How many points would be given for 5 red and 6 green marbles?
PLEASE QUICK I WILL GIVE 5 stars
Answers
12 green marbles
15+12 = 27 marbles in total
In the following situations, state what the constant of proportionally represents.
1, The time taken for a journey is inversely proportional to the speed travelled?
2, The amount of VAT paid on an item varies directly as the cost of the item?
3,The length of a rectangle is indirectly proportional to its width?
4, The length of an original photograph is directly proportional to the length of an enlargement of the photograph?
5, The height of a cylinder is inversely proportional to the area of the base of the cylinder?
Answers
Answer:1, Thời gian thực hiện một hành trình tỉ lệ nghịch với vận tốc đi được?
2, Số thuế GTGT được trả cho một mặt hàng thay đổi trực tiếp như giá vốn của mặt hàng đó?
3, Chiều dài của hình chữ nhật tỉ lệ thuận với chiều rộng?
4, Chiều dài của một bức ảnh gốc tỷ lệ thuận với chiều dài khi phóng to bức ảnh?
5, Chiều cao của hình trụ tỉ lệ nghịch với diện tích đáy củ on:
Which figure shows an example of symmetry?
A.
B.
C.
D.
Answers
Answer:
D
Step-by-step explanat:
Answer:
Option D
Step-by-step explanation:
Option D has the only figure whose mirror image is the exact same; Option A, B and C are not symmetrical because their mirror image is different.
Can someone help me on this please
Answers
Answer:
x=0,1,±2
Step-by-step explanation:
x^3(x^2-5)=-4x
x^2(x^2-5)=-4
Take x^2=a, we have
a*(a-5)=-4, a^2-5a+4=0, (a-1)(a-4)=0, a=1,4
x^2=0, 1, 4. x=0,1,±2
Answer:
x = 1 and x = 2
Step-by-step explanation:
[tex] {x}^{5} - 5 {x}^{3} = - 4x \\ {x}^{4} - 5 {x}^{2} + 4 = 0 \\ ( {x}^{2} - 4)( {x}^{2} - 1)=0[/tex]
x² = 4 or x² = 1
x = ±√4 = -2 or 2x = ±√1 = -1 or 1Since x > 0, the negative integers are rejected and the solutions to this equations are x = 1 and x = 2
PLEASE HELP QWQ AsAp with these 4 questions
Answers
Answer:
Step-by-step explanation:
I can't believe I'm doing this for 5 points, but ok!
For the first 3, we are going to multiply to find the value of that 3 x 3 matrix by picking up the first 2 columns and plopping them down at the end and then multiplying through using the rules for multiplying matrices:
[tex]\left[\begin{array}{ccccc}7&4&6&7&4\\-4&8&9&-4&8\\1&8&7&1&8\end{array}\right][/tex] and from there find the sum of the products of the main axes minus the sum of the products of the minor axes, as follows (I'm not going to state the process in the next 2 problems, so make sure you follow it here. This is called the determinate. The determinate is what you get when you evaluate or find the value of a matrix. Just so you know):
[tex](7*8*7)+(4*9*1)+(6*-4*8)-[(1*8*6)+(8*9*7)+(7*-4*4)][/tex] which gives us:
392 + 36 - 192 - [48 + 504 - 112] which simplifies to
236 - 440 which is -204
On to the second one:
[tex]\left[\begin{array}{ccccc}-8&-4&-1&-8&-4\\1&7&-3&1&7\\8&9&9&8&9\end{array}\right][/tex] and multiplying gives us
[tex](-8*7*9)+(-4*-3*8)+(-1*1*9)-[(8*7*-1)+(9*-3*-8)+(9*1*-4)][/tex] which gives us:
-504 + 96 - 9 - [-56 + 216 - 36] which simplifies to
-417 - 124 which is -541, choice c.
Now for the third one:
[tex]\left[\begin{array}{ccccc}-2&-2&-5&-2&-2\\2&7&-3&2&7\\8&9&9&8&9\end{array}\right][/tex] and multiplying gives us
[tex](-2*7*9)+(-2*-3*8)+(-5*2*9)-[(8*7*-5)+(9*-3*-2)+(9*2*-2)][/tex] which gives us:
[tex]-126+48-90-[-280+54-36][/tex] which simplifies to
-168 - (-262) which is 94, choice c again.
Now for the last one. I'll show you the set up for the matrix equation; I solved it using the inverse matrix. So I'll also show you the inverse and how I found it.
[tex]\left[\begin{array}{cc}-4&-5&\\-6&-8\\\end{array}\right][/tex] [tex]\left[\begin{array}{c}x\\y\\\end{array}\right][/tex] = [tex]\left[\begin{array}{c}-5\\-2\\\end{array}\right][/tex] and I found the inverse of the 2 x 2 matrix on the left.
Find the inverse by:
* finding the determinate
* putting the determinate under a 1
* multiply that by the "mixed up matrix (you'll see...)
First things first, the determinate:
|A| = (-4*-8) - (-6*-5) which simplifies to
|A| = 32 - 30 so
|A| = 2; now put that under a 1 and multiply it by the mixed up matrix. The mixed up matrix is shown in the next step:
[tex]\frac{1}{2}\left[\begin{array}{cc}-8&5\\6&-4\end{array}\right][/tex] (to get the mixed up matrix, swap the positions of the numbers on the main axis and then change the signs of the numbers on the minor axis). Now we multiply in the 1/2 to get the inverse:
[tex]\left[\begin{array}{cc}-4&\frac{5}{2}\\3&-2\\\end{array}\right][/tex] Multiply that inverse by both sides of the equation. This inverse "undoes" the matrix that's already there (like dividing the matrix that's already there by itself) which leaves us with just the matrix of x and y. Multiply the inverse matrix by the solution matrix:
[tex]\left[\begin{array}{c}x&y\end{array}\right] =\left[\begin{array}{cc}-4&\frac{5}{2} \\3&-2\end{array}\right] *\left[\begin{array}{c}-5&-2\\\end{array}\right][/tex] and that right side multiplies out to
x = 20 - 5 which is
x = 15 and
y = -15 + 4 which is
y = -11
(It works, I checked it)
Help!!!! Please!! Thanks
Answers
never saw an indian guy asking for help in so simple question
Step-by-step explanation:
ans of 3rd given statement is true, conclusion, mb=nb
ans of 4th given statement is true, conclusion alt int angles of paralel lines are equal
∠ABM＝∠ABN
MB＝NB
△AMB≌△ANB (SAS)
∠CBM＝∠ADM
∠BCM＝∠DAM
∠BMC＝∠DMA
△BCM∽△DAM (AAA)
Hope my answer helped u :)
convert 123000000 milligram into gram
Answers
Answer:
123,000 grams
Step-by-step explanation:
1000 mg is equivalent to 1 gram.
Answer:
123000g
Step-by-step explanation:
1000mg=1g
123000000mg= xgrams
cross multiplying,
you'll have
[tex] \frac{123000000}{1000} = 123000[/tex]
Question 6 of 10
Which of the following graphs represents the equation y- 4 = 3(x - 1)?
Answers
Graph D
Step-by-step explanation:
The following equation: y - 4 = 3 (x - 1) is written in Point-Slope Form.
In Slope-Intercept Form, it would look like this: y = mx + b where m = slope and b = y-intercept.
*****************************************************Point-Slope Form: y - y1 = m (x - x1)
Slope-Intercept Form: y = mx + b
*****************************************************
To graph the equation we’ll need it to be in Slope-Intercept Form.
y-intercept = 1 because when x reaches 0, y = 1
The first two points are: (0, 1) (1, 4) as we can see that from (1, 4) to (0, 1) or (0, 1) to (1, 4), the slope is 3
Therefore, the Slope-intercept form: y = 3x + 1
The graph that best represents the following equation is Graph D because it contains the point (1, 4)
The average weight of 10 boys is 77.0 pounds. If the
youngest boy is excluded, the average weight of the
9 remaining boys is 78.0 pounds. What is the weight,
in pounds, of the youngest boy?
Answers
Answer:
68 pounds.
Step-by-step explanation:
Find the total weight when there are 10 boys and when there are 9 boys then calculate the difference.
I'll let x = total weight.
[tex]\frac{x}{10}=77\\(10)\frac{x}{10}=77(10)\\x=770\\\\ \frac{x}{9}=78\\(9)\frac{x}{9}=78(9)\\x=702\\\\ 770-702=68[/tex]
Therefore, the youngest boy weighs 68 pounds.
find the surface area of each figure. Round your answer to the nearest tenth if necessary.
Answers
Answer:
556
Step-by-step explanation:
Surface area of the cuboid=2*(lb+bh+lh)
Surface area=2*(110+80+88)=556
Can someone plz help me
Answers
Answer:
37500
Step-by-step explanation:
pattern is multiplying by -5.
-7,500*-5 = 37,500
Have a nice day! :-)
Which of the following is the function for the graph? Choices/graph below.
Answers
set x=0 to get insights.
at x=0 to the functions are
-2(0-2)²+3 = -5
-2(0+2)²-3 = -11
-2(0-2)²+3 = -5
-2(0-2)²-3 = -11
weird, for some reason option 1 and 3 seem to be the same, maybe that's an accident by the author.
maybe a + was intended inside the parentheses, dunno.
option 1 and 3 seem fine, although I think there is an error in the options. they shouldn't be exactly the same
x-1/x > 1/2
(x>0;x>1)
Answers
Step-by-step explanation:
its on the picture.........
Darnell bought 6 packs of baseball cards. There were 6 cards In each pack. Darnell put all his cards in a card book. He put 9 cards on each page. How many pages of the card book did Darnell use ?
Answers
Answer:
Darnell used 4 of the pages.
Step-by-step explanation:
6 times 6 is 36, and 9 goes into 36 4 times. Therefore, if Darnell put 9 cards on every page, he used 4 pages.
Darnell bought 6 packs of baseball cards. There were 6 cards In each pack. Darnell uses 4 pages of the card book.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Darnell bought 6 packs of baseball cards.
There were 6 cards In each pack.
Darnell put all his cards in a card book. He put 9 cards on each page.
1 pack: 6 cards
6 packs: x cards.
x = 6 x 6
= 36
Darnell bought 36 baseball cards.
1 page: 9 cards
x pages: 36 cards
x = 36/9
= 4
Therefore, Darnell used 4 pages of his card book.
Learn more about the unitary method;
https://brainly.com/question/23423168
#SPJ2
Answer always, sometimes, or never
Answers
Answer:
9. Always
10. Never
11. Always
12. Sometimes
Step-by-step explanation:
Natural numbers are any positive whole numbers (e.g. 1, 2, 3, 4….)Integers are any whole number, positive or negative (e.g. -2, -1, 0, 1, 2…)Rational numbers are any number that can be put into a fraction (or if it’s a decimal, a number that ends)Irrational numbers are any number that cannot be put into a fraction (like a never ending decimal; e.g. pi)Real numbers are any and all numbers (rational or irrationa)convert the following fraction into decimals 3/8
Answers
Answer:
0.375
Step-by-step explanation:
Hope this helps!
Answer:
0.375
Step-by-step explanation:
Dividing:
8)3.000(0.375
24
60
56
40
40
..
18. PLEASE HELP ME
Solve the equation using square roots.
x2 – 14 = –10
A. ±2
B. 2
C. no real number solutions
D. ±4
Answers
9514 1404 393
Answer:
A. x = ±2
Step-by-step explanation:
Add 14, then take the square root.
x^2 -14 +14 = -10 +14
x^2 = 4
x = ±√4
x = ±2
Answer:
A
Step-by-step explanation:
X^2-14=-10
X^2=14-10
X^2=4
√X2=√4
X=±2
What is the equation of the following graph in vertex form?
Y=(X-3)^2-1
Y=(X+3)^2-1
Y=(X-4)^2-2
Y=(X-4)^2+8
Answers
Answer:
Hello,
answer B
Step-by-step explanation:
Vertex is (-3,-1)
The equation of the parabola should be:
y=k*(x+3)²-1
(0,8) is a point of the parabola:
8=k*(0+3)²-1
8+1=9k
k=1
Equation is y=(x+3)²-1
Answer B
What is the number of the parking space covered by the car?
Answers
Answer:
The answer is 87
Step-by-step explanation:
Because the parking space are number from 86 to 91
From 86 they add 1 to every number
The Yogurt Packaging company is now re-designing their factory. They are going to construct a building in
the shape of a square box. Their contractor has told them that the diagonal braces needed to make the roof
are 150 feet long.(please help)
1. What would be the floor plan of the building? Label the diagonal braces
2. Find the dimensions of the new factory
3.Find the perimeter of the new factory
4.the yogurt machines will be placed along the wall of the new factory . Each machine is 10 feet wide.
Find the company fit 40 of the machines in the building Why or Why not ?
Answers
Answer:
1. see attached diagram
2. The dimensions are 75 sqrt(2) by 75 sqrt(2) ft
3. The perimeter is 300 sqrt(2) ft
4. cannot fit 40 machines along the walls
Step-by-step explanation:
We are using a top down view. We have a square building with side length s. The diagonal is 150 ft
Using the Pythagorean theorem
s^2 + s^2 = 150^2
2s^2 = 22500
s^2 =11250
Taking the square root of each side
sqrt(s^2) = sqrt(11250)
s = sqrt(6225*2)
s = 75 sqrt(2)
The dimensions are 75 sqrt(2) by 75 sqrt(2) ft
The perimeter of a square is given by
P = 4s = 4(75 sqrt(2)) =300 sqrt(2) ft
The perimeter is 300 sqrt(2) ft
Assuming the machines are square ( that they are as wide as they are long) 75 sqrt(2) is approximately 106 ft so you can fit 10 along the wall
Putting them along the top and bottom walls = 20 machines
We are only left with 86 ft along the side walls
86/10 = 8 machines
machines * 2 walls = 16
We can fit 20+16 machines = 36 machines not 40
Stuart needs to run by the store on his way to school. He begins at home, which on a coordinate plane is represented by the point (0,4). He walks to the store, which is the equivalent of walking 2 units right and 4 units down. After grabbing something to eat for lunch, he walks 3 units to the left and 5 units up to school. What point represents the school
Answers
Need help nsjsisjejskskkdof
Answers
Answer:
8×4=32 and 8 groups of 4 equals 32.
1st point: (1,2)
2nd point: (4,4)
Answers
Answer:
y = 2/3x + 4/3
Step-by-step explanation:
i found the slope using [tex]\frac{rise}{run}[/tex]. so it would be 2/3. next i just kinda tested similar numbers in the graph to find b.
if you aren't allowed to put factions i would say put:
y = 0.67x + 1.33
Answer:
[tex]2x - 3y + 4 = 0[/tex]
Step-by-step explanation:
The formula of finding equation of two different point is
[tex] \frac{x - x1}{x1 - x2} = \frac{y - y1}{y1 - y2} [/tex]
here, x1 =1, x2=4, y1= 2 and y2= 4
hope you can understand.
What is the answer to P(4)=4n + 5
Answers
Answer:
P(x) = 4n+5
P(4) = 4(4)+5
P(4) = 16+5
P(4) = 21
The answer is 21.
Let me know if this helps!
A trinomial of the 2nd degree with a leading coefficient of 1 and a constant of 4.
Answers
Answer:
x^2+1x+4
Step-by-step explanation:
here; degree is =2.
cofficient is= 1
and constant =4
True or False: The function y = (x2 – 4)/(x2 – 4) is continuous for all values of x
Answers
Answer:
False
Step-by-step explanation:
The function isn't continuous at x=±2 as a function isn't continuous at the point where the function becomes undefined, this function becomes undefined when the denominator is equal to 0. So x^2-4=0 => x=±2.
help please!!! i don’t understand
Answers
Answer:
The answer is D: 990
Step-by-step explanation:
G(-10) = f( 3(-10) )
g(-10) = f(-30)
F (-30) = (-30) ^2 -3(-30)
900 + 90
990
Can someone help me pleasee
Answers
2*3=6
So it’s 3x^6
Answer:
it's 9x^6.
hope it may help you
PLEASE HELP ME!. I will give thanks, 5 star rating, and brainly to the most helpful answer, and I will report unrelated answers, so don't try me.
Three vertices of a parallelogram are (0,1), (2,0), and (2,5). Label all the possible location(s) of a fourth vertex.
Answers
Answer:
(0, 6), (4, 4), and (0, -4)
Step-by-step explanation:
basically you pick 2 sides (each with endpoints at two of the three verticies) to be the adjacent sides, and then you can easily find the fourth vertex for each case.
In a function g(x), g(1) = 5. Which could be the function
of g(x)?
Answers
Answer:
Step-by-step explanation:
It could be almost anything.
g(x) = 5*x
g(x) = 5*(x)^2
g(x) = 2.5(2x)
g(x)= 4x *(5/3)
g(x) 10x / 2
