Answer:
[tex]= \frac{2x-3\sqrt{x} }{x-1}[/tex]
Step-by-step explanation:
Given the expression
[tex]\frac{(\sqrt{x} +1)^{2} +(\sqrt{x} -1)^{2} )}{(\sqrt{x} +1)(\sqrt{x} -1)} -\frac{3\sqrt{x} +1}{x-1}[/tex]
Expand
[tex]\frac{(\sqrt{x} +1)^{2} +(\sqrt{x} -1)^{2} )}{(\sqrt{x} +1)(\sqrt{x} -1)} -\frac{3\sqrt{x} +1}{x-1}\\= \frac{x+2\sqrt{x}+1+(x-2\sqrt{x} +1) }{x-1}- \frac{3\sqrt{x} +1}{x-1}\\= \frac{2x+1}{x-1} - \frac{3\sqrt{x} +1}{x-1}\\= \frac{2x+1-(3\sqrt{x} +1)}{x-1}\\= \frac{2x-3\sqrt{x} +1-1}{x-1}\\= \frac{2x-3\sqrt{x} }{x-1}[/tex]
This gives the simplified form
Alice, Bernice, and Carol have £600 altogether. The ratio of Alice’s money to Bernice’s money is 3:7. Carol has £60 more than Alice. What is the amount of money each girl got?
Answer:
Alice - £124.62
Bernice - £290.77
Carol - £184.62
Step-by-step explanation:
Let the amount of money Alice has be a. This way, the sentence "The ratio of Alice’s money to Bernice’s money is 3:7." can be translated into a proportion:
Alice's money / Bernice's money = 3 / 7
We can substitute Alice's money with a, and cross multiply and solve for Bernice's money:
a / Bernice's money = 3 / 7
7a = 3(Bernice's money)
Bernice's money = 7/3 a
Now, we can represent Carol's money in terms of Alice's money, she has 60 more, or a + 60. We can create can equation to represent the total:
Alice's money + Bernice's money + Carol's money = total
We can plug in what we have and solve for a:
a + 7/3 a + a + 60 = 600
13/3 a = 540
a = 124.62
This means Alice has £124.62
Bernice has 7/3 a amount of money, so we can substitute the value of a to get Bernice has 7/3 (124.62), or £290.77
We can do the same for Carol who has 60 more, 124.62 + 60 is £184.62
Four spheres of radius 6 cm just fit inside a cylinder.
Calculate the volume inside the cylinder that is empty.
Leave your answer in terms of pi.
Answer:
1152\pi\
Step-by-step explanation:
If f(x) = 5x, what is rx)?
Answer:
18x
Step-by-step explanation:
If f(x) is 5x which can also be expressed 5(x)
Then r(x) is a number then x
f is the fifth digit in the alphabet
So fx is 5x
r is the 18 th letter so
18x
does anyone know the answer?
Answer:
multiply the bottom equation by 6
Jason rolls a fair number cube labeled 1 through 6 and then he flips a coin what is the probability that he rolls a 3 and flips a head
There are 6 numbers on the cube.
The probability of getting a 3 would be 1 out of 6, 1/6
The probability of getting heads on a coin toss is 1/2
The probability of getting both a 3 and a head = 1/6 x 1/2 = 1/12
Answer: 1/12
Chef Antonio works at a Latin restaurant and doing a great job. During his yearly evaluation, the owner increased his salary from $42,500 to $46,000. What is the percent of increase, to the nearest whole percent, in Chef Antonio's salary?
Answer:
8%
Step-by-step explanation:
To find the percent change, we first have to find the amount changed, which is (46000-42500) = 3500. Then, we find what percentage that is of the original amount. Remember that when calculating percentage change, it's important to calculate change with respect to the initial value.
To find the percentage, we can divide 3500 by 42500, and multiply that by 100, resulting in 8 being our nearest whole percent
Use numerals instead of words
Answer:
Step-by-step explanation:
Put in the 3 and 4 so it is the square root of 3^4 - -6^2
The square root of 3^4 + 6^2
The square root of 3^4 is 3^2 so
9 + 6^2
=> 9 + 36
=> 45
45 in numerals is XLV
I need help but they are getting confused with the z as a 2 please don’t get confused the z is a z
Step-by-step explanation:
everything can be found in the picture
Answer:
w = - (7/2) z
Step-by-step explanation:
5w + 9z = 2z + 3w
Subtract 3w from both sides
2w + 9z = 2z
Subtract 9z from both sides
2w = -7z
Divide both sides by 2
w = - (7/2) z
Which best describes the strength of the model?
O a weak positive correlation
O a strong positive correlation
O a weak negative correlation
O a strong negative correlation
Answer:
A weak positive correlation
Step-by-step explanation:
The table of values of the women's age to shoe size is presented as follows;
Women's Age and Shoe Size
[tex]\begin{array}{ccc} Age&&Shoe \, size\\18&&7\\30&&10\\52&&6\\64&&9\end{array}[/tex]
We get;
The correlation coefficient, r, is given as follows;
[tex]r = \dfrac{\sum \left(x_i - \overline x \right ) \cdot \left(y_i - \overline y \right )}{\sqrt{ \sum \left(x_i - \overline x \right )^2 \cdot \sum \left(y_i - \overline y \right )^2}}[/tex]
From MS Excel, we have;
[tex]\sum \left(x_i - \overline x \right ) \cdot \left(y_i - \overline y \right )[/tex] = 2
[tex]\sqrt{ \sum \left(x_i - \overline x \right )^2 \cdot \sum \left(y_i - \overline y \right )^2}[/tex] = √13,000 = 10·√130
∴ r = 2/(10·√130) ≈ 0.01754
Therefore, given that the calculated correlation coefficient, r is positive and less than 0.2 (weak), we have
The correlation is a weak and positive.
Given two similar cylinders with a height ratio of 2:3 what is the ratio of their volumes?
Answer:
8 : 27
Step-by-step explanation:
The ratio of the volumes is the ratio of the scale factor cubed
2^3 : 3^3
8 : 27
Answer:
8 : 27
Step-by-step explanation:
Given 2 similar cylinders with height ratio = a : b , then
ratio of volumes = a³ : b³
Here height ratio = 2 : 3
ratio of volumes = 2³ : 3³ = 8 : 27
How to sketch the graph?
Step-by-step explanation:
sketch the mother function of |x| then go 3 steps to the right horizontally and that's it
What is the area of triangle ABC?
3 square units
O 7 Sguare units
11 square units
15 square units
Answer:
3
Step-by-step explanation:
base = 4-1
= 3
height = 3-1
= 2
Area = 1/2 (b)(h)
= 1/2 (3)(2)
= 3
therefore the answer is 3 square unit
3g - 4 = 17
show ur work
Answer:
g = 7
Step-by-step explanation:
3g - 4 = 17
+ 4 + 4
3g = 21
÷3 ÷3
g = 7
Answer:
g=7
Step-by-step explanation:
First add 17+4=21 to find out how much 3g needs to equal. 3g needs to get to 21. Next, do 21/3=7. g=7
Hope this helps!
Two workers paint lines for angled parking spaces. One worker paints a line so that m∠1=65. The other worker paints a line so that m∠2=65. Are their lines parallel? Explain your answer.
The image of the car park showing the 2 angles is attached.
Answer:
Their lines are parallel.
Step-by-step explanation:
From the attached image, we can see that ∠1 and ∠2 form a pair of alternate exterior angles. Thus; ∠1 = ∠2.
Now since they are congruent, it means that their lines will be parallel.
Thus, we can conclude that their lines are parallel.
Express your answer as a polynomial in standard form.
f(x) = 2x + 7
g(x) = 2x2 - 6x +5
Find: g(f(x))
Answer:
[tex]16x^{2}+44x+61[/tex]
Step-by-step explanation:
g(f(x)) means that you substitute f(x) as x in g(x)
[tex]2(2x+7)^{2}-(6)(2x+7)+5[/tex]
expand
(2x+7)(2x+7)=
4x^2+28x+49
(2)(2x+7)(2x+7)=16x^2+56x+98
16x^2+56x+98-12x-42+5
16x^2+44x+61
Which expression has a value of 3
A. (12 + 6) ÷ (3 + 3)
B. 12 + (6 ÷ 3 + 3)
C. (12 + 6) ÷ 3 + 3
D. 12 + 6 ÷ (3 + 3)
Answer:
(12 + 6) / (3 + 3) = 18 / 6 = 3
your answer is : (12 + 6) / (3 + 3)
Answer:
A
Step-by-step explanation:
A) 18/6 = 3
B) 12+5 = 17
C) (18 / 3) + 3 = 9
D) 12 +(6/6) = 13
Help me please I need help .
Answer:
cos A =1.0
sin B=0.02
tan C=9.1
Find the length of the third side. If necessary, round to the nearest tenth.
2
3
Answer:
The third side is 3.6
Step-by-step explanation:
Incomplete question;
The parameter from the complete question can be summarized as follows:
[tex]Side\ 1 =2[/tex]
[tex]Side\ 2 =3[/tex]
Required
Determine the third side (hypotenuse)
Let the third side be x;
So:
[tex]x^2 = Side\ 1^2 + Side\ 2^2[/tex]
[tex]x^2 = 2^2 + 3^2[/tex]
[tex]x^2 = 4 + 9[/tex]
[tex]x^2 = 13[/tex]
Take square roots of both sides
[tex]x = 3.6[/tex]
HELP
Use the definition of continuity and the properties of limits to show that’s the function…
Answer with Step-by-step explanation:
We are given that
[tex]g(x)=(x^2-3x-10)(x^2+2x^2-5x+4)[/tex]
x=-1
Using property of limit
[tex]\lim_{x\rightarrow -1}g(x)=\lim_{x\rightarrow -1}(x^2-3x-10)(3x^2-5x+4)[/tex]
=[tex](1+3-10)(3+5+4)[/tex]
=[tex](-6)(12)[/tex]
=[tex]-72[/tex]
[tex]g(-1)=(1+3-10)(1+2+5+4)[/tex]
[tex]g(-1)=(-6)(12)=-72[/tex]
[tex]\lim_{x\rightarrow -1}g(x)=g(-1)[/tex]
Hence, the function is continuous at x=-1
Natasha was thinking of a number. Natasha subtracts 9.3 from the number and gets an answer of 86.7. Form an equation with
x
Answer:
x-9.3 = 86.7
Step-by-step explanation:
expand (y+1)(y-4) !!!!!!
Answer:
Step-by-step explanation:
y^2 - 4y + y - 4
y^2 - 3y - 4
(2x2 + 4x + 1) + (3x2 + 6x + 5)
Answer:
5x^2+10x+6
Step-by-step explanation:
PLZ HELP ITD MEAN THE WORLD
dude its just 3 rooms. yes
Answer:
3 rooms
Step-by-step explanation:
For 1 1/4 rolls of electric wire = 1 room
For 3 3/4 rolls of electric wire = 3 3/4 ÷ 1 1/4
= 15/4 ÷ 5/4
= 15/4 x 4/5
= 15/5
= 3 rooms
Classify the following triangle. Check all that apply.
Answer:
Option(B) & Option(C)
Step-by-step explanation:
Right angled triangle (One angle is 90 degree)
Isosceles(Two sides of triangle are equal)
Please help, I might give brainliest.
Answer:
1. The two decimals are 1.06 and 1.28. 2. The numbers 1.06 and 1.28 are both between 1 and 2.
A small pebble is stuck in Jim's bike tire. The wheel has a radius of 34 cm. Determine the equation of the function that expresses the height of the pebble from the ground in terms of the distance that the bike travels from the point where the pebble got stuck in the tire. How high off the ground will the pebble be after the tire has rolled 150 cm?
Answer:
distance = 68 pie x
Step-by-step explanation:
Hope this helps
Jo invests 20 000.
in the first year her investment grows 20%
then in the second year her investemnt loses 10% of its value.
work out the investment after 2 years?
Answer:
21600
Step-by-step explanation:
20000*1.2*.9=21600
Anyone know the answer to this ?!?
Answer:
12/25 = 48/100 = .48 = 48%
Step-by-step explanation:
The conditional relative frequency table was calculated by row using data from a survey of one station’s television programming. The survey compared the target audience with the type of show, either live or recorded, over a 24-hour time period.
A 4-column table with 3 rows titled television programming. The first column has no label with entries adult, children, total. The second column is labeled live with entries 0.625, 0.5, nearly equal to 0.583. The third column is labeled recorded with entries 0.375, 0.5, nearly equal to 0.417. The fourth column is labeled total with entries 1.0, 1.0, 1.0.
Which is the best description of the value 0.375 in the table?
Given that the program was targeted at adults, there is a 37.5% chance that it was recorded.
Given that the program was recorded, there is a 37.5% chance that it was targeted at adults.
37.5% of the programs are targeted at adults.
37.5% of the programs are recorded.
Answer:
37.5% of the programs are targeted at adults
Step-by-step explanation:
The following figure shows the given four column table for the target audience of television programming
[tex]\begin{array}{lllc}&Television \ Programming \\& Live&Recorded&Total\\Adult&0.625&0.375&1.0\\Children&0.5&0.5&1.0\\Total&\approx 0.583& \approx 0.417&1.0\end{array}[/tex]
From the table, we have that the best description of the value 0.375 in the table is that the percentage of television program targeted at adults is 37.5%
Answer:
The answer is a “Given that the program was targeted at adults, there is a 37.5% chance that it was recorded”
Step-by-step explanation:
i did the test
Kharter goes to a gas station near his house where it costs $2.95 per gallon. Kharter’s car hold’s 13.2 gallons. The gas station near Devin’s house sells gas for $3.03 per gallon and his car holds 11.8 gallons