Answer:
75cm
Step-by-step explanation:
If a and b are rational numbers and a+b√3=1/2-√3,find a:b=?
The value of the ratio a:b is 2:1
What is a surd?Surds are values of a square roots that cannot be simplified as whole numbers or integers. They are usually called irrational numbers.
Example of some surds are the square root of prime numbers.
Analysis:
a + b[tex]\sqrt{3}[/tex] = [tex]\frac{1}{2 - \sqrt{3} }[/tex]
Rationalizing the right hand side by the conjugate surd which is 2 + [tex]\sqrt{3}[/tex]
[tex]\frac{1}{2 - \sqrt{3} }[/tex] x [tex]\frac{2 + \sqrt{3} }{2 +\sqrt{3} }[/tex] = [tex]\frac{2 + \sqrt{3} }{4 -2\sqrt{3} +2\sqrt{3} -3}[/tex] = [tex]\frac{2 + \sqrt{3} }{1}[/tex] = 2 + [tex]\sqrt{3}[/tex]
Equating,
a + b[tex]\sqrt{3}[/tex] = 2 + [tex]\sqrt{3}[/tex]
Comparing the variables,
a = 2, b[tex]\sqrt{3}[/tex] = [tex]\sqrt{3}[/tex], b = 1
The ratio, a: b = 2:1
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30 points please help i dont understand
Answer:
502.4 ft²
Step-by-step explanation:
To find the individual area of the ring, you first need to find the area of the white circle. Then, you need to find the area of the circle and the ring (which can be found by adding the width of the ring to the radius of the circle). Finally, you can find the area of the ring through subtraction.
Area (White Circle)
radius = 1/2 diameter
radius = (1/2) x 36 ft
radius = 18 ft
Area = πr²
Area = π(18 ft)²
Area = π(324 ft²)
Area = 1017.36 ft²
Area (White Circle + Ring)
radius = 1/2 diameter + width of ring
radius = (1/2 x 36 ft) + 4 ft
radius = 22 ft
Area = πr²
Area = π(22 ft)²
Area = π(484 ft²)
Area = 1519.76 ft²
Area (Ring)
Area (Ring) = Area (White Circle + Ring) - Area (White Circle)
Area (Ring) = 1519.76 ft² - 1017.36 ft²
Area (Ring) = 502.4 ft²
the price for 5/6 l of liquid x is $80. what is the price per litre of liquid x
Answer:
$96.
Step-by-step explanation:
5/6 costs 80
Multiply both parts by 6/5:
5/6 * 6/5 ( = 1 ) costs 80 * 6/5
= 16 * 6
= $96.
Someone help me please
Answer:30 degress
3 angles in a triangle equal 180-120=60 60÷2=30
Step-by-step explanation:
If the hypotenuse has a length 7√2, then both legs have a length
Of what
Answer:
7
Step-by-step explanation:
this is probably a 45-45-90 triangle if its both legs
The graph at left in the ap-plane shows p, the atmospheric pressure of Earth in pounds per square inch (psi),
The best interpretation of 0.8^a in this exponential equation is that: C. For each mile that the altitude increases, the atmospheric pressure decreases 20%.
What is an exponential function?An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function is represented by this formula:
f(x) = aeˣ
How to interpret this equation modeling the atmospheric pressure?Based on the information provided, we can logically deduce that the atmospheric pressure (p) exerted on an airplane flying at an altitude of a miles above sea level is defined by the following exponential function:
p = 14.63 × 0.8^a
Next, we would evaluate as follows;
At a = 0, we have:
p = 14.63 × 0.8^(0)
p = 14.63 psi.
At a = 1, we have:
p = 14.63 × 0.8^(1)
p = 11.704 psi, and this is 20% less than a mile before.
At a = 2, we have:
p = 14.63 × 0.8^(2)
p = 9.3632 psi, and this is 20% less than a mile before.
At a = 2, we have:
p = 14.63 × 0.8^(3)
p = 7.4906 psi, and this is 20% less than a mile before.
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Complete Question:
Atmospheric pressure, measured in pounds per square inch (psi) is the force exerted by Earth's atmosphere over a given area. The atmospheric pressure, p, exerted on an airplane flying at an altitude of a miles above sea level can be approximated by the model shown below. What is the best interpretation of 0.8^a in this equation?
p = 14.63 × 0.8^a
A. If the airplane reaches the outer extent of the Earth's atmosphere, the atmospheric pressure will be 0.8 psi.
B. If the airplane is at sea level, the atmospheric pressure will be 0.8 psi.
C. For each mile that the altitude increases, the atmospheric pressure decreases 20%.
D. For each mile that the altitude increases, the atmospheric pressure increases 20%.
Can someone help please?
Answer:
A
Step-by-step explanation:
From left to right of the graph, we can observe that the generally the points are going down. This means that the trend line drawn will have a negative slope.
In the slope-intercept form, which is the form the given equations are in, we have y= mx +c, where m is the slope and c is the y-intercept.
We are only interested in the slope in this case, since no actual values are given. Thus, let's focus on the coefficients of x to determine whether the slope is positive or negative.
Option A: Slope= -⅔ (negative)
Option B: Slope= 3 (positive)
Since we have a negative slope, option A would be the best answer.
The attached image shows 2 graphs. The graph in blue shows the shape of a graph with negative slope, while the graph in red has a positive slope.
Given the series 2 two-thirds startfraction 4 over 9 endfraction startfraction 8 over 27 endfraction startfraction 16 over 81 endfraction startfraction 32 over 243 endfraction ellipsis, which partial sums are correct? check all that apply. s1 = 2 s2 = 4 s subscript 3 = startfraction 28 over 9 endfraction s subscript 4 = startfraction 10 over 9 endfraction s subscript 6 = startfraction 292 over 81 endfraction
The partial sums are correct are That is: (2) and (28/9).
What is a partial sum?A partial sum (simply put) refers to the sum of the various parts that make up a sequence. One of a series of sums of elements of a given sequence, the first sum being the first element, the second sum being the first element added to the second element, the third sum being equal to the sum of the first three elements, and so on.A partial sum of an infinite series is the sum of a finite number of consecutive terms beginning with the first term. When working with infinite series, it is often helpful to examine the behavior of the partial sums.A partial sum would be:
2 + (2/3).
In this case, thus,
Series 1 = 2 - This is correct.
Series 2 = 2 + (2/3) = 8/3 - incorrect
Series 3 = (8/3) + (4/9) = (28/9) Correct
Series 4 = (28/9) + (8/27) = (92/27)
Series 5 = (92/27) + (16/81) = 292/81
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A submarine model starts at 8 m above the bottom of the pool. It gradually goes down at a rate of 1\2 m\s
a) Graph the relation on the grid provided. Label the axes.
b) Write an equation to represent the relation.
Pleasee
The equation that represents the relation is y = 8 - 0.5x
How to graph the relation?The given parameters are:
Start = 8m
Rate = 1/2 m/s
The linear equation that represents the submarine movement is:
y = Start - Rate * x
This gives
y = 8 - 1/2 * x
Evaluate
y = 8 - 0.5x
Hence, the equation that represents the relation is y = 8 - 0.5x
See attachment for the graph
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i need help with question 2
Answer:
Please see the answer below.
Step-by-step explanation:
A square has side lengths of 9, which of the following is a correct formula for finding the area of a square
Answer:
9 x 9 = 81
Step-by-step explanation:
area = width x height
Since it's a square, width = height
What quadrant does the terminal side of this angle lie in?
A) Quadrant III
B) Quadrant II
OC) Quadrant IV
OD) Quadrant I
Answer:
Quadrant III
Step-by-step explanation:
Top-right quadrant = QI
Top-left quadrant = QII
Bottom-left quadrant = QIII
Bottom-right quadrant = QIV
A 2-column table with 5 rows. Column 1 is labeled x with entries 1, 3, 6, 9, 12. Column 2 is labeled y with entries 3, 9, 18, 27, 36.
Given that y varies directly with x in the table, find the value of y if the value of x is 5.
Given that y varies directly with x in the above table, if the value of x is 5, the value of y is 15.
How to calculate direct variation?According to this question, a 2-column table with 5 rows is given.
Column 1 is labeled x with entries 1, 3, 6, 9, 12 Column 2 is labeled y with entries 3, 9, 18, 27, 36If y varies directly with x, the mathematical representation is as follows:
y = kx
Since y = 3, when x = 1
3 = k × 1
k = 3
The relationship between x and y is as follows: y = 3x
Therefore, if the value of x is 5, the value of y = 3 × 5 = 15.
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Owen has enough materials to build up to 10 birdhouses in shop class. each birdhouse needs 12 square feet of wood. the function w(b) = 12b represents the total amount of wood that owen would need to build b birdhouses. what domain and range are reasonable for the function?
Domain of the function is [tex]0\leq b\leq 10[/tex] and range of the function is [tex]0\leq W\leq 120[/tex].
What is domain and range of a function?The range of values that we are permitted to enter into our function is known as the domain of a function.
A function's range is the collection of values it can take as input.
Each birdhouse uses 12 square feet of wood. Owen has enough to build 10 birdhouses, so he has 120 square feet of wood.
The function has an input of the number of birdhouses, b, and W as an output of the amount of wood needed. b is domain, and W is the range. The domain is 0 to 10 and range is 0 to 120.
Therefore, the domain of the function is [tex]0\leq b\leq 10[/tex] and the range of the function is [tex]0\leq W\leq 120[/tex].
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Need some help with trigonometry
Answer:
e) B. 45°
f) A. 30°
Step-by-step explanation:
e) sec theta = 1/ cos theta
the value of cos theta is 1/√2 at 45°
so , sec 45° = √2 and theta = 45°
f) cot theta = 1/ tan theta
the value of tan theta is 1/ √3 at 30°
so, cot 30° = √3 , theta = 30°
The answers are :
e) B
f) A
For part (e), convert into terms of cosθ.
secθ = 1/cosθcosθ = 1/√2θ = cos⁻¹ (1/√2)θ = 45°For part (f), convert into terms of tanθ.
cotθ = 1/tanθcotθ = 1/√3θ = cot⁻¹ (1/√3)θ = 30°Type the correct answer in each box.
Find the elements of matrix A.
help PLS!!
Answer:
a = 2
b = 11
c = 11
d = -2
Step-by-step explanation:
[tex]\sf \left[\begin{array}{cc}a&b\\c&d \end{array}\right] *\left[\begin{array}{ccc} 22&11&7\\ 6&-9&-15 \end{array}\right] =\left[\begin{array}{ccc} 22a+6b&11a-9b&7a-15b\\22c+6d&11c-9d&7c-15d \end{array}\right][/tex]
[tex]\sf \left[\begin{array}{ccc} 22a+6b&11a-9b&7a-15b\\22c+6d&11c-9d&7c-15d \\ \end{array}\right] =\left[\begin{array}{ccc} 110&-77&-151\\230&139&107 \\ \end{array}\right][/tex]
On comparing to right side, we get,
22a + 6b = 110
Divide the entire equation by 2
11a + 3b = 55 ------------(I)
11a - 9b = -77 -------------(II)
Subtract equation (II) from (I)
11a + 3b = 55
11a - 9b = -77
- + + {Now subtract}
12b = 132
b = 132/12
[tex]\sf \boxed{\bf \ b = 11}[/tex]
Substitute the value of b in eqaution (I)
11a + 3*11 = 55
11a + 33 = 55
11a = 55 - 33
11a = 22
a = 22/11
[tex]\sf \boxed{\bf \ a = 2}[/tex]
22c + 6d = 230
Divide by 2
11c + 3d = 115 -----------------(III)
11c - 9d = -139 ------------------(IV)
Subtract (IV) from (III)
11c + 3d = 115
11c - 9d = 139
- + -
12d = -24
d = -24/12
[tex]\sf \boxed{\bf \ d = -2}[/tex]
Plugin d = - 2 in equation (III)
11c + 3*(-2) = 115
11c - 6 = 115
11c = 115 + 6
11c = 121
c = 121/11
[tex]\sf \boxed{\bf \ c = 11}[/tex]
With a perfectly balanced roulette wheel, in the long run, red numbers should turn up 18 times in 38. To test its wheel, one casino records the results of 3,800 plays, finding 1,890 red numbers. Is that too many reds
It is not too many reds, but it is also not a perfectly balanced roulette wheel.
How to find whether the roulette wheel is balanced or not?It is given that the red numbers should come up 18 times when the roulette wheel is played 38 times.
Therefore, the ratio of red numbers to the total number of plays is = 18:38
It is also given that a casino tests the wheel with 3800 plays and noticed that the red numbers came up 1890 times.
The ratio is given as 1890:3800.
We have to simplify this.
1890/3800 = 18.9/38
If the roulette wheel was perfect, it should've been 18:38.
Therefore, we can say that the roulette wheel is not perfectly balanced.
Therefore we have found that it is not too many reds, but it is also not a perfectly balanced roulette wheel.
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What is piaget's term for cognitive development between the ages of about 2 and 6?
Q1. suppose that lim(,)â(3,1)(,)=6. what can you say about the value of (3,1) ? what if is continuous?
Answer:39084620
Step-by-step explanation:
New questions in Mathematics
19 ft 4 ft l Find l. l = √ [?] ft
flying against the jet stream, a jet travels 3000 in 3 hours. Flying with the jet stream, the same jet travels 5360 miles in 4 hours. What is the rate…e of the jet in still air and what is the rate of the jet stream?
Please help! Express the area of the region bounded by the x-axis, y = 1/2x - 2, and y equals the cubed root of x, using definite integrals.
Solve the equation 7/4x-2=-5x+1
How to Convert 11010112 to base 10?
Answer the following. (a) A certain solution has a hydrogen ion concentration of 0.00000896 moles per liter. Write this number in scientific notation…. (b) A humpback whale can weigh up to ×1.1105 pounds. Write this number in standard notation.
Evaluate the expression if a=2,b=-3,C=-1, and D=4 -2(b^2-5c)
Evaluate the expression if a=2,b=-3,C=-1, and D=4 -2(b^2-5c)
The set of all triples of real numbers with the standard vector addition but with scalar multiplication defined by k(x, y, z) = (k2 x,k2 y,k2 z)
Evaluate each expression if a=2,b=-3,C=-1, and d=4 5+d(3b-2d)
Jessica purchased a dvd that was on sale for 12% off. the sales tax in her county is 3%. let y represent the original price of the dvd. write an expression that can be used to determine the final cost of the dvd. how do i solve a problem like this ? khan academy
Jessica purchased a DVD that was on sale for 12% off.
The sales tax in her county is 3%.
Let, y represent the original price of the DVD.
We can simply solve this mathematical problem by using the following mathematical process.
Here, we will form an algebraic expression, according to the given data.
So,
The original price of the DVD = y
Discount on the original price :
y * 12/100
=3y/25
Price after discount :
y - 3y/25
=25y - 3y/25
=22y/25
Sales tax amount :
22y/25 * 3/100
11y/25 * 3/50
=33y/1250
Final price including the sales tax :
22y/25 + 33y/1250
1100y + 33y/1250
1133y/1250
(This will be considered as the final result.)
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Please help thank you
no links
1) in 1992, the average was credit card debt for an
american family was $3275. in 2006, the
average credit card debt for a family was $8900.
find the average rate of change of credit card
debt with respect to time.
a) 390.80
yr
b) 401.79
yr
c) 412.68
yr
d) 423.575
yr
e) 434.46
yr
The average rate of change of credit card is $ 401.79 /year.
What is Average Rate?A single rate that is a weighted average of the different rates that are applicable to property in various locations.An average is a single number calculated as the average of a set of numbers, typically calculated as the sum of the numbers divided by the total number of numbers in the set (the arithmetic mean).Solution
The difference of credit card debt between the year 2006 and 1992 = 8900 - 3275 = $5625
The difference of years between the year 2006 and 1992 = 2006 - 1992 = 14
average rate of change of credit card debt with respect to time = [tex]\frac{difference of credit card debt}{difference of years}[/tex]
average rate = [tex]\frac{5625}{14}[/tex] = $ 401.79 / year
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Ilean works as a welder and
web designer. As a welder, she earns $18 per hour. Last week she
worked x hours as a welder and her friend paid her $75 to design a web page. Write an
expression to represent the total amount llean earned last week.
The expression which can be used to represent the total amount llean earned last week is 75 + 18x
EquationAmount llean earns per hour welding = $18Number of hours worked as welder = xAmount earned as a web page designer = $75An expression to represent the total amount llean earned last week = Amount earned as a web page designer + (Amount llean earns per hour welding × Number of hours worked as welder)
= 75 + (18 × x)
= 75 + 18x
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Determine the coordinates of the point p on the line y=-x+6 such that p is equidistant from the points a(10,-10) and o(0,0) (that is, so that pa=po). express your answer as an ordered pair (a,b).
Solution,
Let P = ( x, -x + 6) = (x, 6 - x)
We want to solve this
( Distance from P to (0,0) )^2 = (Distance from P to (10, -10) )^2
x^2 + (6 - x)^2 = [ ( x - 10)^2 + ( 6 - x + 10)^2
x^2 + x^2 - 12x + 36 = x^2 - 20x + 100 + x^2 - 32x + 256 simplify
-12x + 36 = -52x + 356
40x = 320
x = 8
And y = -(8) + 6 = -2
So...P = ( 8, -2)
In mathematics, an equation is an equation that expresses two equations by joining them with an equal sign =. Equations in other languages and the word their relatives can have slightly different meanings; for example, in French, an equation is defined as containing one or more variables, but in English, it is an equal sign.
A well-formed expression consisting of two combined equations is an equation, and a variable makes the equation true. The variable for which the equation must be solved is also called the unknown, and the value of the unknown that satisfies the equation is called the solution of the equation. There are two types of equations: identities and constraint equations. The ID applies to all values of the variable. Constraint equations apply only to specific values of variables
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Draw the graph of the linear equation 2x – y + 1 = 0. From the graph find the values of h and k if the graph passes through the point (h,4) and (1/2 , k)
Answer + Step-by-step explanation:
2x – y + 1 = 0
We know that the graph of a linear equation is a line.
So ,in order to draw it we need to find two points A and B of the line
Afterward, we join A and B to get the graph.
2x – y + 1 = 0
If x = 0 → y = 1 ⇒ A(0 , 1) lie on the line AB (the graph)
If x = 1 → y = 3 ⇒ B(1 , 3) lie on the line AB
Now ,all we have to do is plotting A and B
on the coordinates plane ,then connecting then with a line.
According to the graph (check the attached image) :
If (h,4) ∈ line AB ⇒ h = 3/2
If (1/2 , k) ∈ line AB ⇒ k = 2
Page 3. Calculate the semi inter quartile range and its coefficients from the table Marks (below) 20 30 40 50 60
No of students 5 12 27 40 50
SOMEONE HELP ME
1. The semi inter quartile range is 10
2. The coefficient of quartile deviation is 0.2
1. How to determine the semi inter quartile rangeMark: 20, 30, 40, 50, 60Freq: 5, 12, 27, 40, 50Com. freq: 5, 17, 44, 84, 134Semi inter quartile range =?1st quartile (Q₁) = (134 + 1) / 4 = 33.75th = 40
3rd quartile (Q₃) = 3 (134 + 1) / 4 = 3 × 33.75 = 101.25th = 60
Semi inter quartile range = (Q₃ - Q₁) / 2
Semi inter quartile range = (60 - 40) / 2
Semi inter quartile range = 10
2. How to determine the coefficient1st quartile (Q₁) = 403rd quartile (Q₃) = 60Coefficient of quartile deviation =?Coefficient of quartile deviation = (Q₃ - Q₁) / (Q₃ + Q₁)
Coefficient of quartile deviation = (60 - 40) / (60 + 40)
Coefficient of quartile deviation = 0.2
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Which sequence of transformations produces A’B’C’ from ABC?
On a coordinate plane, triangle A B C has points (3, negative 1), (4, negative 4), (1, negative 2). Triangle A prime B prime C prime has points (negative 2, 3), (1, 4), (negative 1, 1).
a translation up 3 and then a 90º counterclockwise rotation about the origin
a 90º counterclockwise rotation about the origin and then a translation up 3
a reflection over the x-axis and then a translation left 2 and down 1
a translation left 5 and down 2 and then a reflection over the x-axis
Answer:
The first chose is correct
Step-by-step explanation:
You can see in the first picture that graphed both of the triangles and then I followed the directions. It is very, very helpful if you have tracing paper. You can trace the original and then translate it three up. For the 90 rotation, put a small + on the origin of your tracing paper, then move the tracing paper one one turn on the plus sign. That would be 90 degrees.
The coordinates of three vertices of a rectangle are (3,7), (-3,5), and (0,-4). What are the coordinates of the fourth vertex
The coordinates of the fourth vertex are (6, -2)
What are the coordinates of the fourth vertex?The coordinates of three vertices of a rectangle are given as: (3,7), (-3,5), and (0,-4).
Calculate the slope of the first two coordinates using
m = (y2 - y1)/(x2 - x1)^2
Substitute the known values in the above equation
d = (7 - 5)/(3 + 3)
Let the fourth coordinate be (x, y)
Calculate the slope of the other two coordinates using
m = (y2 - y1)/(x2 - x1)^2
Substitute the known values in the above equation
m = (y + 4)/x
Equate both slope equations
(y + 4)/x = (7 - 5)/(3 + 3)
Simplify the fraction
(y + 4)/x = 1/3
Cross multiply
x = 3y + 12
Let y = -2
So, we have:
x = 3 *-2 + 12
Evaluate
x = 6
Substitute x = 6 and y = -2 in (x, y)
This gives (6, -2)
Hence, the coordinates of the fourth vertex are (6, -2)
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Triangle \triangle A'B'C'△A
′
B
′
C
′
triangle, A, prime, B, prime, C, prime is the image of \triangle ABC△ABCtriangle, A, B, C under a rotation about the origin, (0,0)(0,0)left parenthesis, 0, comma, 0, right parenthesis.
From the information given, the rotated triangle is same as the original triangle. This is because, vertices of the rotation remain at the origin - (0,0).
What is the proof the above?Notice that the question states: △A'B'C' is the image of △ABC. Given that the △ without primes is the original and the one with primes depict the rotated triangle,
under a rotation about the origin, (0,0) (0,0) (0, 0), indicating no movement,
△A'B'C' is in the same position with △ABC.
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Answer: D: 60 degrees
Step-by-step explanation:
khan
Charlie owns a computer repair service. For each computer, they charge $50 plus $45 per hour of work. A linear equation that expresses the total amount of money Charlie earns per computer is y
The linear equation is 45x+50
Linear equation is the equation having the degree 1
Given that the charge per computer repair service is $50
The charge per hour of work is $ 45
We need to show the linear equation that expresses the total amount of money Charlie earns per computer is y
So , Let the number of hours be x
Therefore, the Charlie working hours charge will be 45x
The total amount of money Charlie earns per computer is y
Therefore the linear equation will be
y = 50+45x
Where y = Total amount of money
x = number of hours
Hence the linear equation is y = 45x+50
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Which of the following is correct based on this picture?
Applying the trigonometry ratios, the correct option is: B. none of these are correct.
What are the Trigonometry Ratios?The trigonometry ratios are SOH CAH TOA, which are used for solving a right triangle.
Use the trigonometry ratio to find out which option is correct.
Cos Z = adj/hyp = 61/CZ, so option A is incorrect.
Sin Z = opp/hyp = 73/CZ, so option C is incorrect.
Tan Z = opp/adj = 73/61, so option D is incorrect.
Thus, the answer is: B. none of these are correct.
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