If [tex]\frac{3+\sqrt{8} }{3-\sqrt{8} } +\frac{3-\sqrt{8} }{3+\sqrt{8} }=a+b\sqrt{2}[/tex], the value of a and b is given as a = 34 and b = 0
What is an equation?An equation is an expression that shows the relationship between two or more variables or numbers.
[tex]\frac{3+\sqrt{8} }{3-\sqrt{8} } +\frac{3-\sqrt{8} }{3+\sqrt{8} }\\ \\\frac{9+6\sqrt{8}+8+9-6\sqrt{8}+8 }{(3-\sqrt{8} )(3+\sqrt{8} )} \\\\\frac{34}{9-8} =34+0\sqrt{2}[/tex]
If [tex]\frac{3+\sqrt{8} }{3-\sqrt{8} } +\frac{3-\sqrt{8} }{3+\sqrt{8} }=a+b\sqrt{2}[/tex], the value of a and b is given as a = 34 and b = 0
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Express in simplest radical form.
5x√192x³+√3x5
please help!!
[tex]-5x\sqrt{192x^3} + \sqrt{3x^5}\\\\=-5x\left(192x^3 \right)^{\tfrac 12} + \left(3x^5 \right)^{\tfrac 12}\\\\=-5\cdot (192)^{\tfrac 12} \cdot x \cdot x^{\tfrac 32} + 3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\=-5\left( 64 \cdot 3 \right)^{\tfrac 12} \cdot x^{1+\tfrac 32} + 3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\=-5\cdot 8\cdot 3^{\tfrac 12} \cdot x^{\tfrac 15} + 3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\=-40\cdot 3^{\tfrac 12} \cdot x^{\tfrac 52}+3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\[/tex]
[tex]=-39\cdot 3^{\tfrac 12} \cdot x^{\tfrac 52}\\\\=-39\sqrt 3 \sqrt{x^5}[/tex]
Help and please show work!
Factor sin^8Θ + 2sin^4Θcos^4Θ + cos^8Θ
hi
Step-by-step explanation:
I
don't
know
see you in next question
Melissa rolls 2 fair dice and adds the results from each.
Work out the probability of getting a total less than 12.
Answer:
It would be 35/36
Step-by-step explanation:
so if you did like 1+1, 1+2, 1+3....2+1,2+2, 2+3 yada yada
the only possible number combo that would equal twelve is 6+6 and there is 36 possible combos so your answer is 35/36
- a former algebra 2 student
A 2-ft vertical post casts a 20-in shadow at the same time a nearby cell phone tower casts a 115-ft shadow. how tall is the cell phone tower?
the cell phone tower is _ ft
The height of the cell phone tower will be 138 feet.
What are ratio and proportion?A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.
A 2-ft vertical post casts a 20-in shadow at the same time a nearby cell phone tower casts a 115-ft shadow.
Then the height of the cell phone tower will be
Let x be the height of the cell phone tower.
x / 2 = 115 x 12 / 20
x = 69 x 2
x = 138 feet
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x⁶y⁴/xy²
how would I simplify?
Answer choices:
A: x⁵y²
B:x⁶y²
C:x²y⁵
D:(xy)⁷
Step-by-step explanation:
please mark me as brainlest
can you solve the question but tell me how to do it I'm trying to study but don't know how to solve it?
Answer:
8x+19=9x+9
Step-by-step explanation:
Simplifying
(8x + 19) = (9x + 9)
Reorder the terms:
(19 + 8x) = (9x + 9)
Remove parenthesis around (19 + 8x)
19 + 8x = (9x + 9)
Reorder the terms:
19 + 8x = (9 + 9x)
Remove parenthesis around (9 + 9x)
19 + 8x = 9 + 9x
Solving
19 + 8x = 9 + 9x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-9x' to each side of the equation.
19 + 8x + -9x = 9 + 9x + -9x
Combine like terms: 8x + -9x = -1x
19 + -1x = 9 + 9x + -9x
Combine like terms: 9x + -9x = 0
19 + -1x = 9 + 0
19 + -1x = 9
Add '-19' to each side of the equation.
19 + -19 + -1x = 9 + -19
Combine like terms: 19 + -19 = 0
0 + -1x = 9 + -19
-1x = 9 + -19
Combine like terms: 9 + -19 = -10
-1x = -10
Divide each side by '-1'.
x = 10
Simplifying
x = 10
Answer:
x = 10Step-by-step explanation:
they are opposite angles, therefore congruentwe solve with an equation8x + 19 = 9x +9
19 - 9 = 9x - 8x
10 = 1x
x = 10
check
-------------------
8 * 10 + 19 = 9 * 10 + 9
80 + 19 = 90 + 9
99 = 99
the answer is good
As seen in the diagram below, Shandra is building a walkway with a width of xx feet to go around a swimming pool that measures 8 feet by 6 feet. If the total area of the pool and the walkway will be 168 square feet, how wide should the walkway be?
The total surface area of the building is the sum of the total faces an object contains. The walkway should be about 2.57feet
How to calculate the total surface area the building?The total surface area of the building is the sum of the total faces an object contains. The formula is expressed as:
TSA = 2(lw + wh + lh)
where
l is the lengthw is the widthh is the heightGiven the following parameters
TSA = 168 square feet
length = 8feet
Height = 6 feet
Required
Width of the walkway
Substitute
168 = 2(lw + wh + lh)
84 = (8(6) + 6w + 8w)
84 = 48 + 14w
14w = 84 - 48
14w = 36
w = 2.57feet
Hence the walkway should be about 2.57feet
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Suppose that $b$ is a positive integer greater than or equal to $2.$ When $197$ is converted to base $b$, the resulting representation has $4$ digits. What is the number of possible values for $b$
Suppose that b is a positive integer greater than or equal to 2. When 197 is converted to base b, the resulting representation has 4 digits. What is the number of possible values for b?
The possible values of b are 4 and 5
How to determine the possible numbers of b?The conditions are given as:
b is at least 2When 197 in base b has 4 digits.So, we start by converting 197 to base 2 and above.
This is done as follows:
197 to base 2
2 | 197
98 R 1
49 R 0
24 R 1
12 R 0
6 R 0
3 R 0
1 R 1
0 R 1
So, we have:
197 = 11000101 in base 2
11000101 has more than 4 digits.
This means that b cannot be 2
Using the above method of conversion, we have:
197 = 21022 in base 3197 = 3011 in base 4197 = 1242 in base 5197 = 525 in base 6197 = 401 in base 7See that as the base increases, the number of digits decreases.
The numbers in base 4 and 5 have 4 digits.
Hence, the possible values of b are 4 and 5
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Find the midpoint of A and B where A has coordinates (2, 3)
and B has coordinates (8, 9).
Step-by-step explanation:
Solution,Given,Coordinates of A and B are (2,3) and(8,9) respectively. Let A(2,3)= (x1,y1) and B(8,9)=(x2,y2)Midpoint of AB(m)=?Now,using midpoint formulam= {(x1+x2)/2 ,(y1+y2)/2}or m= {(2+8)/2,(3+9)/2}.°. m=(5,6)Answer:Mxy= [(Xa+Xb/2);(Ya+Yb/2)]
=(2+8/2);(3+9/2)
Midpoint= (5, 6)
Step-by-step explanation:
Please help me!!!! I would really appreciate it!!!
Answer:
x=-(7 [tex]\pm i\sqrt(7)[/tex])
Step-by-step explanation:
Solve for d given -4d+6>10
Answer:
Scientific notation: 4 ⋅ 10 -4
expanded form: 0.0004
Explain how the expression 32 relates to the diver's depth
Answer:
See below
Step-by-step explanation:
Each 32 feet of depth is 1 more atmosphere of pressure on the diver
Shelby mixes a 25% bleach solution with 5 cups of a 10% bleach solution, resulting in a 20% bleach solution. The table shows the amount of each solution used.
A table titled Bleach Solution showing Cups, Bleach concentration, and Total. The first row shows 10 percent Bleach with 5, 0.10, and 0.5. The second row shows, 25 percent bleach, with x, 0.25, and 0.25 x. The third row shows Mixture, with 5 plus x, 0.20, and 3.
What is the value of x?
Answer: is C
Step-by-step explanation: like i said making it easier .
A trellis consists of overlapping wooden slats.
1.What is the position of the indicated angles?
2.What should the value of x be in order for the two slats to be parallel?
3. Which theorem or postulate will you use to prove the parallel slats?
4. Find the measure of the indicated angle
The position of the angles are corresponding angles.
The value of x should be 6 for the slats to be parallel.
The theorem use to prove the parallel slat is the corresponding angle theorem.
The measure of the indicated angles are 42 degrees.
How to know a corresponding angles?Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal.
Therefore, the position of the angles are corresponding angles
Since the angles are corresponding angles, they are congruent.
Therefore,
3x + 24 = 7x
24 = 7x - 3x
24 = 4x
x = 6
The theorem use to prove the postulate is the corresponding angle theorem.
The measure of the indicated angle can be calculated as follows:
7(6) = 42 degrees.
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Carmen used a random number generator to simulate a survey of how many children live in the households in her town. There are 1,346 unique addresses in her town with numbers ranging from zero to five children. The results of 50 randomly generated households are shown below.
Children in 50 Households
Number of Children
Number of Households
0
5
1
11
2
13
3
10
4
9
5
2
Using a proportion, what can you infer about the number of households in her town that have more than three children?
About 242 households have more than three children.
About 269 households have more than three children.
About 296 households have more than three children.
About 565 households have more than three children.
About 296 households have more than three children. Then the correct option is C.
How to find that a given condition can be modeled by binomial distribution?Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as
The expected value will be
E(X) = np
Carmen used a random number generator to simulate a survey of how many children live in the households in her town.
There are 1,346 unique addresses in her town with numbers ranging from zero to five children.
The results of 50 randomly generated households are shown below.
Children in 50 Households
Number of Children Number of Households
0 5
1 11
2 13
3 10
4 9
5 2
Then the value of p and n will be
p = 11/50
n = 1346
Then the expected value will be
E(x) = (11/50) x 1346
E(x) = 296.12 ≈ 296
Then the correct option is C.
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can someone help me out?
The factor if the root is 2 is x - 2 and the factor if the root is -3 is c + 3
Factors of a polynomialAccording to the question, we are to find the factors of the polynomial expression
Given the polynomial expression
y = x² + x - 6
Factorize
y = x² + 3x - 2x - 6
y = x(x+3)-2(x+3)
y = (x-2)(x+3)
Hence the factor if the root is 2 is x - 2 and the factor if the root is -3 is c + 3
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A bakery sold a total of 400 cupcakes in a day, and 43% of them were vanilla flavored. how many of the cupcakes sold that day were vanilla flavored?
The number of the cupcakes sold that day that were vanilla flavored is 172.
How do we calculate a number from a percentage?The number of the cupcakes sold that day that were vanilla flavored can be calculated using the following formula:
Number of vanilla flavored cupcakes sold = Total number of cupcakes sold * Percentage that were vanilla flavored .............. (1)
Substituting the relevant values into equation (1), we have:
Number of vanilla flavored cupcakes sold = 400 * 43% = 172
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1
2
X
-5
-4
-3
2
1
0
1
2
3
6
f(x)
-6
-2
0
4
4
0
-2
-6
-10
Based on the table, which best predicts the end
behavior of the graph of f(x)?
O As x, f(x)→∞, and as x→→∞, f(x)→∞.
O As x→∞, f(x)→∞, and as x→∞, f(x)→→∞
O As x, f(x)→∞, and as x→→∞, f(x)→∞
O As x→∞, f(x)→∞, and as x→∞, f(x)→
818
The statement that best describes the end behavior of the graph is given as follows:
As [tex]x \rightarrow -\infty, f(x) \rightarrow -\infty[/tex], and as [tex]x \rightarrow -\infty, f(x) \rightarrow \infty[/tex].
What is the end behavior of a function?It is given by it's limits as x goes to negative and positive infinity.
From the given table, it is found that f(x) starts with negative values, increases until it's maximum value then decays again, hence the correct statement is:
As [tex]x \rightarrow -\infty, f(x) \rightarrow -\infty[/tex], and as [tex]x \rightarrow -\infty, f(x) \rightarrow \infty[/tex].
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Find the volume of the sphere. Round your answer to the nearest tenth.
A sphere is shown with a radius of 7 feet.
The volume is about
cubic feet.
So we all know the FORMULA for a sphere is v=4/3 x π x r^3
So, now we SUBSTITUTE ,V=4/3 x π x 7^
This leaves us with the answer of 1436.76 ft ^2 maybe?
(hope this is correct!)
A flower bed in your yard is in the shape of a right triangle. The perpendicular sides of the bed measure 14 feet and 11 feet. Calculate the area of the flower bed.
The area of the flower bed is 77 square feet
How to determine the area?The given parameters are:
Shape = TrianglePerpendicular sides = 14 feet and 11 feetThe area of the flower bed is calculated as:
Area = 0.5 * Product of perpendicular sides
So, we have:
Area = 0.5 * 14 * 11
Evaluate
Area = 77
Hence, the area of the flower bed is 77 square feet
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Factor 4x² - 121 a) (2x + 11) (2x + 11) b) (2x - 11) (2x - 11) (2x + 11) (2x - 11) d) (4x + 11) (4x - 11)
Answer:
(2x-11)(2x+11)
Step-by-step explanation:
2x-11 × 2x+11 yields
4x^2 + 22x -22x +121
22x subtracts itself and final result is
4x^2 -121
Courtney was making curtains from some fabric she had in her closet. She measured 7 3/4 yards of fabric and needed to make 4 curtains that were the same size. How much fabric does she need for each curtain? Estimate:
Answer:
About 32
Step-by-step explanation:
It says 7 3/4 and she makes 4 curtains ESTIMATE!! So you round the 7 3/4 to 8 and do 8 x 4 since she made 4 curtains. Hope this helped!
100 points plus brainliest
Answer:
45 degrees
Step-by-step explanation:
so we know there is one 90 degree angle
and the other two angles are congruent
so the math would go like this
180-90=90
90/2= 45
(the 2 represents the two angles)
Answer:
x = 22.62° (nearest hundredth)
Step-by-step explanation:
As this is a right triangle, we can use the cosine trigonometric ratio to find x.
[tex]\sf \cos(\theta)=\dfrac{A}{H}[/tex]
where:
[tex]\theta[/tex] is the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)Given:
[tex]\theta=x[/tex]A = 12H = 13Substitute the given values into the formula and solve for x:
[tex]\implies \cos(x)=\dfrac{12}{13}[/tex]
[tex]\implies x=\cos^{-1}\left(\dfrac{12}{13}\right)[/tex]
[tex]\implies x=22.61986495...^{\circ}[/tex]
[tex]\implies x=22.62^{\circ}\:\: \sf(nearest\:hundredth)[/tex]
Find the equation of the line shown.
y
X
0 1 2 3 4 5 6 7 8 9 10
10
987654321
Answer:
y = 2x
Step-by-step explanation:
The graph is of a straight line through the origin. Its slope can be determined from the grid points it passes through. That slope will be the constant of proportionality for the proportion represented.
__
When the graph is a line through the origin, it is a representation of a proportion that can have the equation ...
y = kx
where k is the constant of proportionality, also the slope of the line.
The value of k will be the y-value when x=1. Reading from the graph, we find the line goes through point (1, 2), so y = 2 when x = 1. That means k = 2 and the equation of the line is ...
y = 2x
PLEASE HELP ME!!!!!!!!!!!!!!!
Answer:
hypotenuse(h)^2 = 3^2 + 7^2
h^2 = 9 + 49
h = √58
h = 7.6
The graph of a quadratic function passes through the points (0,-4) and (-2,0). what is a zero of the function
Answer:
-2
Step-by-step explanation:
the zero of the function is -2 because it's the root of the equation when y= 0
How many solutions are in 17x-8=3x+16
Consider the original triangle and the scale drawing enlargement.
A triangle with a side measurement of 2 centimeters. 2 triangles have corresponding side lengths of 2 centimeters and 8 centimeters.
Figures not drawn to scale.
What is the scale factor?
Answer:
scale factor = 4
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, image to original
scale factor = [tex]\frac{8}{2}[/tex] = 4
Simon easily defeats the kidnapper in
hand-to-hand combat outside the water tower,
but to get inside the tower he must figure out the
last digit to the combination lock on the door.
A riddle was left for Simon to solve, giving him the
number he needs... if he can solve it in time!
The riddle reads:
2
"A rectangle has an area given by x² + 2x - 24.
The number you seek is the sum of its length
and width when x = 5."
9) Find the last digit to the password by solving
the riddle! (A /4) hint factor to get the dimensions of the rectangle
The dimensions of the rectangle will be 4 and 6.
How to solve the value?From the information given, we are told that the area is given by x² + 2x - 24. We will expand this as follows:
x² + 2x - 24
x² + 6x - 4x - 24
x(x + 6) + 6(x - 4)
x - 4 = 0
x = 0 + 4
Therefore, the other dimension will be:
= 24/4
= 6
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A rescue mission is being conducted using a plane to drop supplies and medical personnel. A helicopter
is also sent from the same base station to rescue wounded persons. If the plane flies 400 mph, the
helicopter flies 200 mph, and they leave at the same time, how far away is the rescue site if the
helicopter arrives 1 hour after the plane arrives?
If t represents the time that the plane flies, which of the following equations could be used to solve the
problem?
400/t = 200/(t+1)
400t = 200(t+1)
400t = 200t+1
400 miles away is the rescue site if the helicopter arrives 1 hour after the plane arrives and the expression 400t = 200(t + 1) represents the time that the plane flies option second is correct.
What is distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
We have:
A helicopter is sent from the same base station to rescue wounded persons. If the plane flies 400 mph, the helicopter flies 200 mph, and they leave at the same time.
Let's suppose the plane takes t hours
We know,
Distance = speed×time
400×t = 200(t + 1)
or
400t = 200(t + 1)
After solving we get:
t = 1 hour
Distance = 400×1 = 400 miles
Thus, 400 miles away is the rescue site if the helicopter arrives 1 hour after the plane arrives and the expression 400t = 200(t + 1) represents the time that the plane flies option second is correct.
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