The values of the expressions are x = √6, y = 2√3 and z = √2
How to evaluate the expressions?From the question, we have the following parameters that can be used in our computation:
[tex]x =\sqrt{12-3\sqrt{7} } - \sqrt{12 + 3\sqrt{7} }[/tex]
[tex]y = \sqrt{7-4\sqrt{3 } } - \sqrt{7 + 4\sqrt{3} }[/tex]
[tex]z = \sqrt{2 + \sqrt{3} } - \sqrt{2 - \sqrt{3} }[/tex]
We have
[tex]x =\sqrt{12-3\sqrt{7} } - \sqrt{12 + 3\sqrt{7} }[/tex]
Take the square of both sides
So, we have
[tex]x^2 =12-3\sqrt{7} + 12 + 3\sqrt{7} - 2(\sqrt{12-3\sqrt{7} } * \sqrt{12 + 3\sqrt{7} })[/tex]
This gives
x² = 12 - 3√7 + 12 + 3√7 - 2√81
Evaluate the roots
So, we have
x² = 12 - 3√7 + 12 + 3√7 - 18
Evaluate the sum and the difference
x² = 6
Take the square roots of both sides
x = √6
Using the same steps above, we have
[tex]y = \sqrt{7-4\sqrt{3 } } - \sqrt{7 + 4\sqrt{3} }[/tex]
Square both sides
So, we have
[tex]y^2 = 7 - 4\sqrt 3 + 7 + 4\sqrt 3 - 2 * \sqrt{7-4\sqrt{3 } } * \sqrt{7 + 4\sqrt{3} }[/tex]
This gives
[tex]y^2 = 7 - 4\sqrt 3 + 7 + 4\sqrt 3 - 2 * 1[/tex]
Evaluate
y² = 12
Take the square root of both sides
y = 2√3
Lastly, we have
[tex]z = \sqrt{2 + \sqrt{3} } - \sqrt{2 - \sqrt{3} }[/tex]
Square both sides
[tex]z^2 = 2 + \sqrt 3 + 2- \sqrt 3 - 2 * \sqrt{2 + \sqrt{3} } * \sqrt{2 - \sqrt{3} }[/tex]
This gives
z² = 4 - 2 *1
Evaluate
z = √2
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1. If a rubber ball is dropped from a height of 10 feet, the function
f(x) = 20 (0.6)* gives the height in feet of each bounce, where
x is the bounce number. What will be the height of the 5th bounce?
Round to the nearest tenth of a foot.
2. A population of pigs is expected to increase at a rate of 4% each
year. If the original population is 1000, the function f(x) = 1000 (1.04)*
gives the population in x years. What will be the population in 12 years?
Please help
If a rubber ball is dropped from a height of 10 feet, The height of the 5th bounce and the population in 12 years
2.4 feet1700 pigs What will be the height of the 5th bounce?Generally, For the first problem, the height of the 5th bounce can be calculated by plugging in 5 for x in the function
f(x) = 20 (0.6)^x:
f(5) = 20 (0.6)^5
= 20 (0.12)
= 2.4 feet
What will be the population in 12 years?For the second problem, the population in 12 years can be calculated by plugging in 12 for x in the function f(x) = 1000 (1.04)^x:
f(12) = 1000 (1.04)^12
= 1000 (1.70)
= 1700 pigs
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#6: Clayton is flying a model helicopter. The helicopter starts
on the roof of a building that is 85 feet above the ground.
Clayton makes the helicopter climb at a constant rate. After
10 seconds, the helicopter is 120 feet above the ground. How
many feet above the ground will the helicopter be after 20
seconds?
A. 130 B. 155 C. 205 D. 240
Answer:
155 feet
Step-by-step explanation:
the building is 85 feet high that's where drone starts
the drone flies to 120 feet in 10 seconds from 85 feet so the rate equals 35 feet per 10 second
in 20 seconds the drone would be 70 feet higher.
so the final height would be 85 feet plus 70 feet which equals 155 feet.
hope that helps
what effect does increasing the sample size have on the probability? provide an explanation for this result.
Increasing the given sample size will decreases the probability because σx will decreases as n value increases.
In Statistitics whenever we test a hypothesis for testing a statistic, we use confidence interval. Confidence interval is on either side of an assumed value a margin of error. Margin of error is calculated as critical value * sigma/sqrt of n. Thus we find that whenever n increases, margin of error decreases.
Thus making confidence interval narrower and thus making probability for accepting null hypothesis a less value. As the pattern sizes increase, the range of every sampling distribution decreases so they emerge as more and more leptokurtic. The variety of the sampling distribution is smaller than the variety of the authentic populace. Therefore, as a pattern length increases, the pattern imply and general deviation might be nearer in fee to the populace imply μ and general deviation σ.
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There are four people in Haydens family. Each person always eats 3/4 of a cheese pizza. How many whole pizzas should they order?
In linear equation,3 whole pizzas should they order .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
total people = 4
Each person always eats 3/4 of a cheese pizza.
3/4 + 3/4 + 3/4 + 3/4
= 3 + 3 + 3 + 3 /4
= 12/4
= 3
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The volume of water in a tank is modeled by the function y = 1.15x3 – 0.1x2 + 2 where x is the number of minutes after the faucet filling the tank is turned on. . How long will it take for the tank to fill to 247 feet.
Answer:
2
Step-by-step explanation:
: in this context, the y-intercept represents the volume of water already in the tank
(Get 30 points for answer, please answer truthfully)
Carter and his children went into a movie theater and he bought $33 worth of drinks and candies. Each drink costs $4.50 and each candy costs $3. He bought 3 times as many drinks as candies. Determine the number of drinks and the number of candies that Carter bought.
Answer:
6 drinks
2 boxes of candy
==================================================
Explanation:
x = number of drinks
y = number of boxes of candy
These two variables represent positive integers.
"He bought 3 times as many drinks as candies" which means we can set up the equation x = 3y
-------------
1 drink costs $4.50
x drinks cost 4.50x dollars
1 box of candy costs $3
y boxes of candy cost 3y dollars.
4.50x + 3y = total cost = 33 dollars
Therefore, we arrive at the second equation of 4.50x+3y = 33
-------------
We have this system of equations
[tex]\begin{cases}x = 3y\\4.50x+3y = 33\end{cases}[/tex]
I'll use substitution to solve. Replace x with 3y in the second equation, then isolate y.
[tex]4.50x+3y = 33\\\\4.50(3y)+3y = 33\\\\13.50y+3y = 33\\\\16.50y = 33\\\\y = 33/16.50\\\\y = 2\\\\[/tex]
This tells us he bought 2 boxes of candy.
Use that value to find x.
[tex]x = 3y\\\\x = 3*2\\\\x = 6\\\\[/tex]
Carter also bought 6 drinks.
-------------------------------
Check:
6 drinks = 6*4.50 = 27 dollars2 boxes of candy = 2*3 = 6 dollarsTotal cost = 27+6 = 33 dollarsThe answers are confirmed.
Another way to confirm the answers is to plug (x,y) = (6,2) into each equation of the system I mentioned earlier. After simplifying, you should get the same thing on both sides.
A visual way to confirm the answers is to graph each equation on the same xy grid. The two lines intersect at (6,2). You can use a graphing tool such as Desmos or GeoGebra.
6,526,572,333 lottery tickets were sold last year. This year 3,223,526,869 lottery tickets were sold. About how many more tickets were sold last year than this year?
Answer:
2,570,869,636 more tickets
Step-by-step explanation:
Suppose sine (x) = four-fifths and cos(x) < 0. What is the value of cos(2x)? negative startfraction 14 over 25 endfraction negative startfraction 7 over 25 endfraction startfraction 7 over 25 endfraction startfraction 14 over 25 endfraction.
Because the value of x is 126° and the value of cos 2x is -0.301, which is fractionally identical to -7/25, the value of cos 2x will be -7/25.
What is trigonometry?Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circle functions) that make up trigonometry. The sine, cosine, and tangent are the three fundamental trigonometric operations. The cotangent, secant, and cosecant functions are derived from these three basic functions. On these functions, all trigonometrical concepts are built.
Here,
sin x=4/5
x=126°
Cos 126°=-0.588
cos (2*126)=-0.310
The value of cos 2x will be -7/25 because value of x is 126° and that of cos 2x is -0.301 that is fractionally equal to -7/25.
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Answer:
B
Step-by-step explanation:
on edge
Which equation is equivalent to the formula d = rt? r equals d over t r = dt t equals r over d t = dr
The equation is equivalent to the r = d/t.
There are numerous ways in which one may define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.
We have to find which equation is equivalent to the formula d = rt.
Formula given: d = rt
Divide both sides by t
d/t = rt / t
d/t = r
Thus, the equation is equivalent to the r = d/t.
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A salesman priced a car at 3,500 the first day the second day he reduced the price by 10% what was the new price
Answer: 3150 is the answer
Step-by-step explanation:
Find value of K for which
Y=2x+K is tangent to
y=x²-4x+4
To find the value of K, we need to find the point at which the line Y=2x+K is tangent to the parabola Y=x^2-4x+4. This means that the line and the parabola will have the same y-value at this point, and the line will be tangent to the parabola (meaning it will just touch the parabola at this point, without intersecting it).
To find the point at which the line and parabola are tangent, we can set Y=2x+K equal to Y=x^2-4x+4 and solve for x:
2x + K = x^2 - 4x + 4
x^2 - 4x + 4 - 2x - K = 0
(x-2)^2 = K
x = 2 +/- sqrt(K)
Since the line is tangent to the parabola, it will just touch the parabola at this point, which means that the parabola will have a minimum value at this point. This means that the value of K must be nonnegative, because the square root of a negative number is not a real number. Therefore, K must be equal to or greater than 0.
So, the value of K for which Y=2x+K is tangent to Y=x^2-4x+4 is K >= 0.
For the function: y = startroot x minus 7 endroot minus 1 the domain is : x ≥ the range is: y ≥
The function's range is in the interval (1, ∞).
What is function's range ?Members of a set can congregate in mathematics.
These sets' constituents are referred to as elements. The correspondence between the two groups is known as a relation when the elements of each group are paired up together.
So, between two sets, a relation is a collection of ordered pairs of elements.
The term "function" refers to a particular type of relation where each element in the first group, referred to as the domain, corresponds to exactly one element in the second group, referred to as the range.
The elements in the domain couple with exactly one element in the range, and this is how a function is a pairing between two sets.
According to our question-
[7, ] is the interval notation.
The function's range falls between the numbers (1, ).
provided function
Determine the function's domain:
You do not want to use a counterargument to the square root in this situation (you cannot find the solution of a negative square root, at least as a real number).
What you actually do is "impose" that the argument always ends in a yes or a no (you know the square root of a positive number or zero).
You then solve for x to determine the variable's ALLOWED values by setting the argument greater than or equal to zero:
Consequently, the function is in the domain.
Find the function's range:
The set of all y values in the function's range is when,
range of the function is in the interval (1, ∞).
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Answer: first 7,1 second 7, -1
Step-by-step explanation: edge 2023
In an arithmetic sequence, each term after the first is found by multiplying the previous term by a constant.
True false question.
True
False
Answer: False
Step-by-step explanation:
The statement you are giving is for the Geometric Sequence, not the arithmetic sequence. So this is false!
The measures of two vertical angles are given by the expressions (x+16)° and (2x - 3).
Find the value of x . What is the measure of each angle?
Answer:
see explanation
Step-by-step explanation:
vertical angles are congruent , then
2x - 3 = x + 16 ( subtract x from both sides )
x - 3 = 16 ( add 3 to both sides )
x = 19
Then
x + 16 = 19 + 16 = 35°
since the angles are congruent , then
the measure of each angle is 35°
On the first day of winter, an entire field of trees starts losing its flowers. The number of locusts
remaining alive in this population decreases rapidly due to the lack of flowers for them to eat.
The relationship between the elapsed time, t, in days, since the beginning of winter, and the
total number of locusts, N(t), is modeled by the following function:
N(t) 8950 (0.49)^t/2
Complete the following sentence about the daily rate of change in the locust population.
Round your answer to two decimal places.
Every day, the locust population is multiplied by a factor of ____.
Answer:
0.7
Step-by-step explanation:
Good points please answer
The values of given functions are Sin2x = 120/169, Cos2x = 119/169 and tan2x = 120/119.
What are trigonometric equation?Trigonometric equation is a condition including at least one trigonometric ratios of obscure points. It is communicated as proportions of sine(sin), cosine(cos), tangent(tan), cotangent(cot), secant(sec), cosecant(cosec) points. For instance, cos2 x + 5 sin x = 0 is a mathematical condition.
According to question:We have,
Cosx = 12/13
Use sin^2(x) + Cos^2(x) = 1
sinx = [tex]\sqrt{1-cos^{2}x}[/tex] = 5/13
We know that
Sin2x = 2sinxcosx
Sin2x = 2(5/13)(12/13)
Sin2x = 120/169
Using cos2x = 2cos^2x - 1
cos2x = 2(12/13)^2 - 1
Cos2x = 119/169
Then, using tanx = sinx/cosx
tan2x = sin2x/cos2x
tan2x = [tex]\frac{\frac{120}{169} }{\frac{119}{169} }[/tex] = 120/119
Thus, required values Sin2x = 120/169, Cos2x = 119/169 and tan2x = 120/119
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Required solution is
[tex]Sin2x=-\frac{120}{169} \\\\\\Cos2x=-\frac{119}{169} \\\\\\Tan2x=\frac{120}{119}[/tex]
What is trigonometric ratios?
The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
[tex]cos2x=cos^2x-sin^2x[/tex]
[tex]sin2x=2sinxcosx\\\\tan2x=(2tanx)/(1-tan2x)[/tex]
..
[tex]sinx= -\frac{12}{13}[/tex]
you are working with a (5-12-13) reference right triangle in quadrant IV where sin<0,cos>0,tan<0
[tex]sinx=-\frac{12}{13} (given)\\\\\cosx=\frac{5}{13} \\\\tanx=-\frac{12}{5}[/tex]
..
[tex]cos2x=cos^2x-sin^2x=\frac{25}{169-144} \times \frac{1}{69} =-\frac{119}{169} \\\\\\sin2x=2sinxcosx=2\times(-\frac{12}{13}) \times (\frac{5}{13} )=-\frac{120}{169} \\\\\\tan2x=\frac{2tanx}{1-tan^{2}x } \\\\\\=2(-12/5)/(1-(144/25))=(-24/5)/(-119/25)=(-24/5)(25/119)=\frac{120}{119}[/tex]
required solution is
[tex]Sin2x=-\frac{120}{169} \\\\\\Cos2x=-\frac{119}{169} \\\\\\Tan2x=\frac{120}{119}[/tex]
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Kendra owns a restaurant. She charges $1.50 for 2 eggs and one piece of toast and $0.90 for one egg and one piece of toast. Write a system of equations that can be used to
determine how much she charges for each egg and each piece of toast.
Enter your answer in the space below.
√x
Answer:
Each egg costs $0.60
Each piece of toast costs $0.30
Step-by-step explanation:
Let's assume that the cost of a single egg is E
And the price of a toast as T
Kendra charges $1.50 for one toast and two eggs
The equation above will be
2E + T = $1.50
And the other equation is
E + T = $0.90
For the second equation, we make E the subject of the formula
E = 0.90 - T
Now substitute for this in equation 1
2E + T = 1.50
It will now be 2(0.90 - T) + T = 1.50
1.80 - 2T + T = 1.50
T= $0.30
price of one toast is $0.30
And now, for the price of an egg, we substitute T = 0.30 in the equation
E= $0.60
33 points! Help please! Simplify 8 - (4)(3)/cube root 8 + 5
A. 12/7
B. -12/7
C. 4/7
D. -4/7
The given expression is simplified as -4/7. So, the correct option is D.
What is simplify?To simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.
Given that, (8-(4)(3))/(∛8 +5).
The given expression can be simplified as follows
Numerator of fraction simplified as 8-(4)(3)
= 8-12
= -4
Numerator of fraction simplified as (∛8 +5)
We know that, cube root of 8 (∛8) is 2
=(2 +5)
= 7
Thus, the fraction is -4/7
So, the expression (8-(4)(3))/(∛8 +5) is reduced to -4/7.
The simplified form of expression is -4/7. Therefore, option D is the correct answer.
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there are two formulas that can be used to find the volume of a rectangle prism. Find the volume using both formulas
Step-by-step explanation:
Formula 1: V = lwh
V = 10 x 8 x 6
V = 480
Formula 2: V = 2lw + 2lh + 2wh
V = 2(10 x 8) + 2(10 x 6) + 2(8 x 6)
V = 480
Solve for y in the equation, y = mx when m = 13/40 and x = 362 feet.
y = [1] feet
Round your answer to the nearest tenth.
Answer:117.7
Step-by-step explanation: m is 13/40, I converted that to decimal form which was .325. I then multiplied 362 by .325 to get 117.65, then rounded to the nearest tenth
Given the following information, determine which lines, if any, are parallel. State the converse that justifies your answer. Please helppp
Lines a, b, and c are parallel, and d and e are also parallel to each other.
What are parallel lines?No matter how far they may reach in either direction, parallel lines are ones that are equidistant from one another and never cross. Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline. In this essay, let's study more about parallel lines.
Given the 5 lines and the angles made by them,
if ∠1 = ∠3 then a║b Because they intersect on the same line.
if ∠4 = ∠6 then c║b Because they intersect on the same line.
if ∠1 = ∠7, ∠2 = ∠8, ∠23 = ∠5, ∠11 = ∠17, ∠2 = ∠8, ∠24 = ∠18, ∠6 = ∠12, and some more than d║e Because they intersect on the same line.
Therefore from the above figure, if two lines intersect another line with the same angle then they are parallel lines.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the
blanks.
Tony is starting a business selling handmade necklaces. He has decided to invest an initial amount of
$381 for advertising, and materials cost $8 for each necklace he makes. Tony can sell his creations for
$9 per necklace. Once he makes and sells a certain number of necklaces, he will break even, with
identical expenses and sales. How many necklaces would that take? What would the total expenses and
sales be then?
After selling
necklaces, Tony would have total expenses and sales of $
It will take the sales of 381 necklaces to reach break-even.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
An equation is an expression that shows the relationship between two or more numbers and variables.
We are given that Tony invest an initial amount of $381 for advertising, and materials cost $8 for each necklace he makes. Tony can sell his creations for $9 per necklace.
Let the number of necklace be x then;
8x + 381 = 9x
Solving;
9x - 8x = 381
x = 381
Therefore, Total expenses = 8x + 381
8(381) + 381
= 3429
Thus, Total sale = 9x = 3429
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Determine the value of x.
Options:
03√2
03√3
3
6
Answer:
x=
[tex]3 \sqrt{3} [/tex]
Step-by-step explanation:
because tan30⁰=
[tex] \frac{ \sqrt{3} }{3 } \\ \[/tex]
3/x=root 3 over3
[tex]3 \sqrt{3} [/tex]
What is the slope of this line?
Answer:
m = 2/5
:)))))))))))))))))))))))))))
Original Equation: y = 2x + 7
Which equation will shift the graph of the original equation up 2 units?
Responses
A y = 2x + 9y = 2x + 9
B y = 2x + 5y = 2x + 5
C y = 2x + 2y = 2x + 2
D y = 2x - 2y = 2x - 2
E y = 4x + 7
Therefore the solution to the given question equation will shift the graph of the original equation up 2 units in y=2x + 9
What is equation?equation, a declaration of equivalence between two expressions with variable- and/or number-filled expressions. In essence, equations are questions, and efforts to discover a method for answering them have fueled the growth of mathematics. Equations range in complexity from straightforward addition-and-multiplication equations in mathematics through differential equations, exponential equations that use exponential expressions, and integral equations.
Here,
It follows a linear function. y=mx + b
If A is the location where the y-axis intersects, then x = 0 and y = b are the coordinates of A.
In order to move the graph up by 2 units, you must add 2 units to b.
In our case, b was originally equal to 7, so shifting it up makes b become 7+2=9, and the new function is y=2x + 9.
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Add the equations.
3x - y = -5
7x + y=15
A. -4x = 10
B. -4x = -20
C. 10x = 10
D. 10x-2y = -20
Answer:
its c
Step-by-step explanation:
Evaluate 150 - (2 + x) to the power of 3 when x = 2.
Answer:
3,112,136
Step-by-step explanation:
x=2
replace x with 2
2+2=4
150-4= 146
146 to the third power is 146 x 146 x 146
146 x 146 x 146 = 3112136
hope this helps, tell me if i'm wrong
An angle meaure 48° le than the meaure of it upplementary angle. What i the meaure of each angle?
Answer:
132
Step-by-step explanation: Supplementary=180 So all you have to do is subtract 48 from 180 and should give you 132.
Hope that helps!
In order to walk to school from your house, you walk 0. 8 mi north and 0. 5 miles east. What is the direct distance from your house to school
The direct distance from your house to school as calculated from the given data is 0.9434 miles.
Let
the distance walked North = A = 0.8 miles
the distance walked East= B = 0.5 miles
the direct distance between house and school be C
On using pythagoras theorem,
C² = A² + B²
= 0.8 ²+ 0.5 ²
= 0.89
C =0.9434 miles
A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem.
According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle. This theorem can be expressed as the Pythagorean equation, which is an equation relating the lengths of the sides a, b, and the hypotenuse c , C² = A² + B².
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A year hence a father will be 5 times as old as his son. Two years ago, he was three times as old as his his son will be four years hence. Find their present age.