Answers
Answer:
Step-by-step explanation:
Simplify Surd: Multiply the denominator and numerator with the conjugate of the denominator.Conjugate of denominator:[tex]\sf (\sqrt{x+1}) + (\sqrt{x-1})[/tex]
[tex]\sf\dfrac{\sqrt{x+1} +\sqrt{x-1}}{\sqrt{x+1}-\sqrt{x-1}} = \dfrac{(\sqrt{x+1} +\sqrt{x-1})(\sqrt{x+1} +\sqrt{x-1})}{(\sqrt{x+1} -\sqrt{x-1})(\sqrt{x+1} +\sqrt{x-1})}\\[/tex]
When doing so, in the numerator, we get in the form of the identity (a +b)² and in the denominator a² - b²
[tex]\sf =\dfrac{(\sqrt{x+1} +\sqrt{x-1})^2}{(\sqrt{x+1})^2 - (\sqrt{x-1})^2}\\\\=\dfrac{(\sqrt{x+1})^2+(\sqrt{x-1})^2+2*\sqrt{x+1}*\sqrt{x-1}}{x + 1 - (x - 1)}\\\\=\dfrac{x+1 +x -1 + 2*\sqrt{(x+1)(x-1)}}{x + 1 - x + 1}\\\\=\dfrac{x+ x + 1 - 1 +2\sqrt{x^2-y^2}}{x-x+1+1}\\\\=\dfrac{2x+2\sqrt{x^2-y^2}}{2}\\\\= \dfrac{2x}{2}+\dfrac{2\sqrt{x^2-y^2}}{2}\\\\=x + \sqrt{x^2-y^2}[/tex]
Related Questions
The table shows the change in the price of a stock. At the end of the week, the price is $17.17.
Answers
The price of the stock after the change in price on Thursday is $16.76.
The price of the stock at the beginning of the week is $16.81.
What are the price changes?The price at the end of the week is a function of the total changes in price and the price at the beginning of the week.
$17.17 = beginning price + 0.21 + 0.09 - 0.03 - 0.02 + 0.11
$17.17 = beginning price + 0.36
Beginning price = $17.17 - 0.36 = $16.81
Price on Thursday = $16.81 + 0.21 + 0.09 - 0.03 - 0.02 = $16.76
Here are the questions:
What was the price of the stock after the change in price on Thursday?
What was the price of the stock at the beginning of the week?
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A group of people were surveyed, and the data about their age and hemoglobin levels was recorded in a two-way table. Based on the data in the
table, match each probability with its correct value.
Age
Hemoglobin Level
Less than 25 Years 25-35 Years Above 35 Years Total
Less than 9
21
32
76
129
Between 9 and 11
49
52
46
147
Above 11
69
44
40
153
Total
139
128
162 429
the probability that a person older
than 35 years has a hemoglobin
level less than 9
the probability that a person
younger than 25 years has a
hemoglobin level above 11
the probability that a person in the
25-35 age group has a hemoglobin
level less than 9
the probability that a person older
than 35 years has a hemoglobin
level between 9 and 11
0.25
0.47
0.28
0.50
Answers
The probability that a person older than 35 years has a hemoglobin level less than 9 is 0.47.
The probability that a person younger than 25 years has a hemoglobin level above 11 is 0 .50
the probability that a person in the 25-35 age group has a hemoglobin
level less than 9 is 0.25.
The probability that a person older than 35 years has a hemoglobin level between 9 and 11 is 0.28.
What are the probabilities?The probability that a person older than 35 years has a hemoglobin level less than 9 = number of people order than 35 that have a hemoglobin level less than 9 / total number of people over 35
= 76 / 167 = 0.47
The probability that a person younger than 25 years has a haemoglobin level above 11 = people over 25 that have a haemoglobin level above 11 / total number of people above 25
69/139 = 0 .50
The probability that a person in the 25-35 age group has a hemoglobin
level less than 9 = people between 25 - 35 that have a haemoglobin level less than 9 / total number of people between 25 - 35
= 32/128 = 0.25
The probability that a person older than 35 years has a hemoglobin level between 9 and 11= number of people order than 35 that have a hemoglobin level 9 - 11 / total number of people over 35
46 / 162 = 0.28
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Someone please help
Answers
Answer:
Part (a)Given:
[tex]\displaystyle \int\limits_{1}^{3} x^2 \:dx[/tex]
Trapezium Rule
[tex]\displaystyle \int\limits_{a}^{b} y \:dx \approx \dfrac{1}{2}h\left[(y_0+y_n)+2(y_1+y_2+...+y_{n-1})\right] \quad \textsf{where }h=\dfrac{b-a}{n}[/tex]
Calculate the width of each strip (h).
Given:
a = 1b = 3n = 5[tex]\implies h=\dfrac{3-1}{5}=0.4[/tex]
Create a table with the x and y values:
[tex]\large\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} x & 1 & 1.4 & 1.8 & 2.2 & 2.6 & 3\\\cline{1-7} y & 1 & 1.96 & 3.24 & 4.84 & 6.76 & 9\\\cline{1-7}\end{array}[/tex]
Put all the values into the formula:
[tex]\begin{aligned}\displaystyle \int\limits_{1}^{3} x^2 \:dx & \approx \dfrac{1}{2}(0.4)\left[(1+9)+2(1.96+3.24+4.84+6.76)\right]\\& = 0.2\left[10+2(16.8)\right]\\\\& = 0.2\left[10+33.6\right]\\\\& = 0.2\left[43.6\right]\\\\& = 8.72 \end{aligned}[/tex]
Part (b)[tex]\begin{aligned}\displaystyle \int\limits_{1}^{3} x^2 \:dx &=\left[\dfrac{1}{3}x^3\right]^3_1\\& = \dfrac{1}{3}(3)^3-\dfrac{1}{3}(1)^3\\& = 9-\dfrac{1}{3}\\& = \dfrac{26}{3}\end{aligned}[/tex]
The exact area as a decimal is [tex]\sf 8.\dot{6}[/tex]. Therefore, the estimated answer of 8.72 is an overestimate.
Part (c)Answer to (a) = 8.72
To find the maximum possible error:
Identify the last non-zero digit to the right of the decimal point → 2The precision of the number is the place value: 0.01Divide the precision by 2Therefore, the maximum possible error for 8.72 is 0.005.
Part (d)Trapezoid Error formula
[tex]|E| \leq \dfrac{(b-a)^3}{12n^2}\left[\textsf{max}|f''(x)|\right],\quad a \leq x \leq b[/tex]
Calculate the second derivative:
[tex]f(x)=x^2[/tex]
[tex]f'(x)=2x[/tex]
[tex]f''(x)=2[/tex]
Input the values into the formula:
[tex]\implies |E| \leq \dfrac{(3-1)^3}{12n^2}(2) < 0.001[/tex]
[tex]\implies 16 \leq 0.012n^2[/tex]
[tex]\implies 36.5148...\leq n[/tex]
[tex]\implies 37\leq n[/tex]
If angles A and B are consecutive interior angles, what is the measure of
angle B if angle A measures 75°?
Answers
Answer:
105
Step-by-step explanation:
Consecutive interior angles need to add up to 180 degrees.
Therefore, 180 - 75 = 105
Answer:
105°
Consecutive interior angles are always supplementary, they add upto 180°
.
.
Angle A = 75°
Angle B = 180 - 75 = 105°
Step-by-step explanation:
I hope it helps u dear ^_^
Suppose that a sample is taken from a population whose mean value is 45. As the sample size increases, which value will the sample mean approach?
Answers
Suppose that a sample is taken from a population whose mean value is 45, the sample mean will approach
[tex]\mu=45[/tex]
Which value will the sample mean approaches?Generally, the equation for the standard deviation is mathematically given as
Standard deviation sample mean [tex]\mu = \frac{\sigma}{\sqrt{n}}[/tex]
Therefore, where a population whose mean value is 45 for any sample
size, Hence mean of the sample mean is
[tex]\mu = \=x[/tex]
[tex]\mu=45[/tex]
In conclusion, the value the sample mean approach is
[tex]\mu=45[/tex]
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I need help please asap?!!!
Answers
Answer:
3660
Step-by-step explanation:
'milli..' in the metric system means 1000 th
there are 1000 milliliters in a liter
3.66 liters * 1000 ml/liter = 3660 ml
Gordon had $200,000 in a CD at Lots
a Loot Bank, which just failed. If the
FDIC insurance limit per depositor,
per bank, is $250,000, how much
will Gordon get back?
Answers
Given the FDIC insurance limit, the amount that Gordon would get back is $200,000.
How much would Gordon get back?
The Federal Deposit Insurance Corporation (FDIC) was established after the great depression with the aim of insuring the deposits of customers in banks.
If the limit on insurance is $250,000, depositors with $250,000 or less would get the full amount of their deposits in case of bank failure. If the deposit is greater than $250,000, they would get $250,000.
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Given that ƒ(x) = 3x, identify the function g(x) shown in the figure.
A)
g(x) = −(1∕3)x
B)
g(x) = 3−x
C)
g(x) = −3−x
D)
g(x) = −3x
Answer: D
Answers
Answer:
the answer is D
hope it will help
Building A is 875 feet tall and contains 71 stories. Building B contains 109 stories. If the two buildings have the same number of feet per floor, approximate the height of building B rounded to the nearest foot.
Answers
Answer:
Approx. 1343 feet
Step-by-step explanation:
Building A is 71 stories at 875 feet tall. Since the two buildings have the same number of feet per floor, we can divide building A's stories to find the height of 1 story, and then multiply by the stories of building B.
Building A
71 ÷ 71 = 1 story
875 ÷ 71 = 12.32 feet
Each story is approximately 12.32 feet tall
Building B
1 story × 109 = 109 stories
12.32 feet × 109 = 1343.31 feet
Rounded to the nearest foot is 1343 feet.
I got this question while practicing MAP, can someone lend a hand?
Answers
Answer:
see the attachment photo!
Eugene and three of his friends went out to eat. They decided to split the bill evenly. Each person paid $11. What was the total bill?
Answers
Answer:
Step-by-step explanation:
Je calcule la facture totale
11x4=44
La facture totale d'Eugène et ses trois amis était de 11$
HELP I'LL GIVE 50 POINTS IF YOU CAN HELP WITH THIS MATH QUESTION
IMAGE BELOW...
Answers
Answer:
last one is the answer brother
Triangel ABC has vertices A(-2,1) B(2,2), and C(2,y). The area of the triangle is 4 square units.
Y=
Answers
Answer:
i wish i knew
Step-by-step explanation:
The volume of a cylinder is given by the formula y = ²h, where r is the radius of the cylinder and h is the height.
Suppose a cylindrical can has radius (x + 8) and height (2x + 3). Which expression represents the volume of the can?
Ozx³ +19x²+112x+192
O 27x³ +35mx² +80*x+48
O 27x³ +35x² +1767x+1927
O 47x³+447x² +105x+72
Answers
The expression represents the volume of the can is 2x³ + 35x² + 176x + 192.
What is Volume?Volume is a mathematical term that describes how much three-dimensional space an object or closed surface occupies. The measurement for volume is in cubic units, such m3.
Expression: (Math Operator, Number/Variable, Math Operator)
We have,
radius = (x + 8) and, height = (2x + 3)
So, Volume of can
= πr²h
= π(x+8)² (2x+3)
= π (x² + 16x + 64) (2x+3)
= π (2x³ + 3x² + 32x² + 48x + 128x + 192)
= π (2x³ + 35x² + 176x + 192)
So, the Expression for volume is 2x³ + 35x² + 176x + 192.
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Use triangle XYZ to answer questions 3-5.
1) Use special right triangles to help find the length of segment XY. What is the exact height of triangle XYZ?
Click the keyboard button to enter your answer.
2)What is the exact area of triangle XYZ? Leave your answer in radical terms.
Click the keyboard button to enter your answer. Show your work.
3)What is the area of triangle XYZ to the nearest tenth of a square in?
Answers
Answer:
Step-by-step explanation:
Part A: Describe the solution(s) to 9x² - 36x + 36 = 0 by just determining the radicand. Show your work. (10 points) Part B: Describe the solution (s) to x²-x + 4 = 0 by just determining the radicand. Show your work. (10) points) Part C: Solve 4x² + 23 – 35 using an - appropriate method. Show the steps of your work and explain why you chose the method used. (15 points) (35 points)
Answers
The solution to the equations are:
9x² - 36x + 36 = 0 has two equal real solutionsx² - x + 4 = 0 has no real solutionsThe factored expression of 4x² + 23 – 35 is 4(x² -3)Part A: Describe the solutionThe equation is given as:
9x² - 36x + 36 = 0
The above equation is a quadratic equation which can be represented as:
ax² + bx + c = 0
The discriminant (d) is calculated as:
d = b² - 4ac
So, we have:
d = (-36)² - 4 * 9 * 36
d = 0
A discriminant of 0 means that the equation has two equal real solutions
Hence, 9x² - 36x + 36 = 0 has two equal real solutions
Part B: Describe the solution
The equation is given as:
x² - x + 4 = 0
The above equation can be represented as:
ax² + bx + c = 0
The discriminant (d) is calculated as:
d = b² - 4ac
So, we have:
d = (-1)² - 4 * 1 * 4
d = -15
A discriminant of -15 means that the equation has no real solutions
Hence, x² - x + 4 = 0 has no real solutions
Part C: The solution to the expression
We have:
4x² + 23 – 35
Evaluate the difference
4x² -12
Factor out 4
4(x² -3)
Hence, the factored expression of 4x² + 23 – 35 is 4(x² -3)
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Using only the markings given in the diagram, which triangle congruence criterion can be used to prove that PQR and STU are congruent?
Answers
Answer: HL
Step-by-step explanation:
If the hypotenuse and one leg of the two triangles are congruent, then the triangles are congruent. The correct option is D, HL.
What is the HL theorem?According to the HL theorem, If the hypotenuse and one leg of the two triangles are congruent, then the triangles are congruent. therefore, the hypotenuse will be congruent to each other, and the corresponding sides will be congruent to each other.
In the two of the given triangle, ΔPQR and ΔSTU, the following things can be seen,
PR ≅ SU (Leg of the triangle)
RQ ≅ TU (Hypotenuse)
Also, since the two of the triangles are right angle triangle, and the length of the one leg of the two triangles is equal, also, the hypotenuse of the two triangle is equal. Therefore, Using the HL postulate. The two triangles can be said to be congruent.
Hence, the triangle congruence criterion can be used to prove that PQR and STU are congruent is HL Congruency.
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4. What is the total cost of 400 square feet of land if it sells for
$110 per square foot?
Answers
The total cost of 400 square feet of land if it sells for $110 per square foot is $ 44,000.
what is Area?Area is the quantity that expresses the extent of a region on the plane or on a curved surface.
Here, Total area = 400 sq. units
Cost per square foot = $ 110
Total Cost = Total area X Cost per unit area
TC = 400 X 110
TC = 44,000
Thus, the total cost of 400 square feet of land if it sells for $110 per square foot is $ 44,000.
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How do you find the length of an unknown leg in a right triange
Answers
By using the pythagoras theorum you can find an unknown leg of right angled triangle.
Hypotenuse side is in the front of the 90 degree angle and other two sides can be taken as base and perpendicular, so formula goes as :-
(Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2
H^2 = B^2 + P^2
Step-by-step explanation:
Hope it helps you!!I need this answer asap (fast)
Of the 12.4 million species of organisms in the world today, 64% (almost two thirds) are insects.
Estimate to the nearest million the number of insect species.
Answers
Answer:
8 million insect species
Step-by-step explanation:
Solving :
⇒ Number of species = Total organisms × % of the species
⇒ Number of species = 12.4 × 64%
⇒ Number of species = 0.124 × 64
⇒ Number of species = 7.936 million ≈ 8 million insect species
HELPPP HELP MEH plane intersects a prism parallel to the base of the prism. The cross section is a polygon with eight sides. The base of the prism has__ sides.
Answers
The minimum number of sides that the polygon at the base of the prism must has 4 sides.
What is a Polygon?This refers to the plane figure in geometry that has three or more sides and angles in a finite straight line.
As we know the minimum number of sides a polygon does the base of the polygon have 4 side.
Now, as the plane intersect a prism parallel to base of the prism so the polygon of 5 sides will form then at least the base of the polygon will have 4 sides.
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Pls help me i need quick responses TwT
Answers
Answer:
56%
Step-by-step explanation:
i think your missing some info.
Please help! This is a math question and due soon I don’t understand the charting part please help , thank you
Answers
Answer:
it's 0 I think ok hope this helped stay safe
4,5,5,6,10,11,12,13 mode
Answers
Answer: 5 is the mode
Step-by-step explanation: The mode is the number that is appeared most often in the data, so the mode in this case (4, 5, 5, 6, 10, 11, 12, 13) is 5.
Which expression is equal to
5(2x²-1) + 3(7x² + 1)?
11x² + 2
11x-2
31x² + 2
31x²-2
Answers
Answer:
d
Step-by-step explanation:
What is the probability that student A choses yellow and student b choses yellow from their skittles at the same time
Answers
Solve for (x): (14.5x − 5(x + 2) ≤ 4 + 4(4 − 1/8x)
Answers
Answer:x ≤ 3
Step-by-step explanation:
(14.5x − 5(x + 2) ≤ 4 + 4(4 − 1/8x)
14.5x - 5x-10 ≤ 4 + 16 - 1/2x Get rid of the parenthesis
9.5x-10 ≤ 20-1/2x Combine like terms
10x - 10 ≤ 20
10x/10 ≤ 30/10
x ≤ 3
using the digits 4,5,6,and 7,write the greatest 4 digit number you can without repeating any of the digits.
Answers
Answer:
7,654
Step-by-step explanation:
Arrange the digits in order to create the highest possible number.
7000 + 600 + 50 + 4 = 7654
Miriam reduced a square photo by cutting 3 inches away from the length and the width so it will fit in her photo album. The area of the reduced photo is 64 square inches. In the equation (x – 3)2 = 64, x represents the side measure of the original photo. What were the dimensions of the original photo?
Answers
The dimensions of the original photo is: X = 11
Meaning of dimension.A dimension can be defined as the parameters, measurement, scale or size of an object or figure.
A dimension is so important as is gives us a visual representation of an object.
Analysis(x-3[tex])^{2}[/tex] = 64
(x-3) = [tex]\sqrt{64}[/tex]
x = 8 + 3
x = 11
In conclusion, The dimensions of the original photo is: X = 11
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Which of the following describes the best method of solving two-step equations? A. Apply the multiplication property of equality first, and then apply the addition property of equality to isolate the variable. B. Apply the addition property of equality first, and then apply the multiplication property of equality to isolate the variable. C. Apply only the multiplication property of equality to isolate the variable. D. Apply only the addition property of equality to isolate the variable.
Answers
The best method of solving two-step equation is "Apply the multiplication property of equality first, and then apply the addition property of equality to isolate the variable"
How to solve two step equationFor instance:
40 = 5(x) - 5
40 = 5x - 5
Add 5 to both sides40 + 5 = 5x
45 = 5x
x = 45/5
x = 9
Therefore, the correct answer is "Apply the multiplication property of equality first, and then apply the addition property of equality to isolate the variable".
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