[tex] \sqrt{29 \: - \: 12 \sqrt{5} } [/tex]
Factor the indicated expression:[tex] \sqrt{(3 \: - \: 2 \sqrt{5}) ^{2} } [/tex]
Simplified the index the root and also the exponent using the number 2.[tex] \boxed{ \bold{2 \sqrt{5} \: - \: 3}}[/tex]
MissSpanish[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{29-12\sqrt{5}} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{20-12\sqrt{5}+9} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{4\cdot \:5-12\sqrt{5}+9} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{\left(\sqrt{4}\right)^2\left(\sqrt{5}\right)^2-12\sqrt{5}+\left(\sqrt{9}\right)^2} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{4}=2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{9}=3 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 2\cdot2\cdot3\sqrt{5}=12\sqrt{5} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{2^2\left(\sqrt{5}\right)^2-2\cdot \:2\cdot \:3\sqrt{5}+3^2} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Apply\:the\:formula\:from\:binomial\:to\:square:(a-b)^2=a^2-2ab+b^2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 2^{2}(\sqrt{5})^{2}-2\cdot2\cdot3\sqrt{5}+3^{2}=(2\sqrt{5}-3)^{2} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{\left(2\sqrt{5}-3\right)^2} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Apply \ the \ laws \ of \ exponents:\sqrt[n]{a^{2} }=a \end{gathered}$}[/tex]
[tex]\sqrt{(2\sqrt{5}-3)^{2} } =2\sqrt{5 }-3.[/tex]
[tex]\red{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \red{=2\sqrt{5}-3 } \end{gathered}$}}} \ \ \red{\Rightarrow} \ \ \bf{\red{Answer}}[/tex]
↓
[tex]\red{\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\red{MyHeritage}} \end{gathered}$}}}}[/tex]
The graph of y=x² + 11x + 24 is equivalent to the graph of which equation?
y=(x+8)(x+3)
y=(x + 4)(x+6)
y=(x +9)(x + 2)
y=(x + 7)(x+4)
Answer:
y = (x+8)(x+3)
Step-by-step explanation:
If you multiply
(x+8)(x+3),
you get x^2 + 3x + 8x + 24
This simplifies to x^2 + 11x + 24, same as the original question.
The graph of y=x² + 11x + 24 is equivalent to the y=(x+8)(x+3).
What is Polynomial?An algebraic expression known as a polynomial requires that all of its exponents be whole numbers. Any polynomial must have variable exponents that are non-negative integers. Constants and variables are components of a polynomial.
We have Graph whose equation is
y=x² + 11x + 24
Now, factories the above equation using splitting the middle term
y=x² + 11x + 24
y=x² + 8x + 3x + 24
y = x(x+8) + 3(x+8)
y= (x+3)(x+8)
Thus, the factors are (x + 3)(x+8).
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In 20 words or fewer write a conjecture about rectangles and quadrilaterals
A quadrilateral comprises a rectangle, which is a specific kind of quadrilateral.
What is conjecture?A conjecture is a conclusion made on the basis of speculation rather than proof.
Rectangle has four sides and is a polygon. The internal angle total is 360 degrees. The opposing sides of a rectangle are parallel and equal, and each angle is 90 degrees.
In the first place, your search for a pattern before making an educated assumption or hypothesis about it. In the introduction, you look for a pattern and then form an educated guess or conjecture about it.
A quadrilateral comprises a rectangle, which is a specific kind of quadrilateral.
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Which of the following equations has a slope of 5 and y-intercept of 4 ?
Answer:
Equation in Slope intercept form :
y = 5x + 4
I need the answers with work someone please help if not ima fail math
Answer:
I am sorry if you feel mad but I do not know this question I am very sorry . . . . . . . . . .
Nick walked 5 miles to reach his aunt's house. from there he traveled 8 miles to the shopping mall on a bicycle. he traveled 80% faster on the bicycle than on foot. let r represent his rate of walking in miles per hour. identify the expression that represents the number of hours nick took to reach the shopping mall in terms of r. then find the time taken by nick to reach the shopping mall if he walked at an average speed of 3 miles per hour.
The expression of time in terms of r is T = 85/9r. If he walked at an average speed of 3 miles per hour. Then the time taken by nick to reach the shopping mall will be 3 hours and 60 minutes.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
Nick walked 5 miles to reach his aunt's house.
From there he traveled 8 miles to the shopping mall on a bicycle.
He traveled 80% faster on the bicycle than on foot.
Let r represent his rate of walking in miles per hour. Then the 1.8r will be the rate of cycling in miles per hour.
Then the number of hours nick took to reach the shopping mall in terms of r will be
T = t₁ + t₂
Where t₁ is the time taken to reach his aunt's house and t₂ is the time taken to reach the shopping mall from his aunt's house. Then we have
T = 5 / r + 8 / 1.8r
T = 1/r (5 + 8/1.8)
T = 85/9r
If r is 3 miles per hour, then the time taken by nick to reach the shopping mall will be
T = 85 / (9 x 3)
T = 3.15 hours
T = 3 hours and 9 minutes
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Which represent geometric sequences? check all that apply.
a. 3/16, 3/8, 3/4, 3/2, . . .
b. 13/20, 10/20, 7/20, 4/20, . . .
c. 2, 4, 6, 8, . . .
d. 3, 9, 27, 81, . . .
e. f(x) = x/4 -9
f. f(x) = -4(4/9)^x
g. f(x) = -4/9x^4
Only three are geometric sequences, a which is 3/16, 3/8, 3/4, 3/2, d which is 3,9,27,81 and f which is -4(4/9)^x
What is a geometric sequence?A geometric sequence is a sequence of numbers or functions in which successive member differ by a constant term called the common ratio.
Analysis:
For a, the first term is 3/16, second term is 3/8. if we divide the second term by the first we have 2. If we do same with the third and second we still have 2. so this is a geometric sequence
For d, if we divide 9 by 3 we have 3, if we divide 27 by 9 we have 3. so this is a geometric sequence.
For f, if we make x equal to a nonzero integer, we have first term as -16/9, second term as -64/81 and third term as -256/729. if we divide the second term by the first we have -4/9, if we divide the third by the second we have-4/9.
In conclusion, Only three are geometric sequences, a which is 3/16, 3/8, 3/4, 3/2, d which is 3,9,27,81 and f which is -4(4/9)^x
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MATHH!!! find the surface area of the composite figure. Please answer correctly & tell me how you got your answer
The total area of the given composite figure is; 84.8 ft²
How to find the area of a composite figure?
We are given;
Area of triangle = 5.6 ft²
Thus, area of 2 triangles = 2 * 5.6 = 11.2 ft²
Area of rectangles = 2(3.6 * 2) + 2(2 * 4) + 3(4 * 3.6)
Area of rectangles = 14.4 + 16 + 43.2
Area of rectangles = 73.6 ft²
Total Area of composite figure = 73.6 ft² + 11.2 ft²
Total Area of composite figure = 84.8 ft²
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There are 12 apples in a basket. Out of these, 3 apples are rotten. Find the probability of choosing a good apple.
Help me out pls
Answer:
the probability is 3/4
Step-by-step explanation:
probability = possible outcome/total outcome
Possible outcome= 12-3=9
Total outcome = 12
Probability = 9/12 = 3/4
So the chance of u getting a good apple is 3/4
$75 before tax. Disc: 10% Tax: 7%, Tip: 20% what’s the total?
Answer:
$102.75
Step-by-step explanation:
Given the following question:
We are given a cost of 75 dollars and are being asked to find the total cost after adding a tip, tax, and disc to the cost. To find this answer we will use the formula to calculate percentages making sure we use 75 as our base for each addition to our total cost.
Formula to calculate percentages:
[tex]\frac{p\times n}{100}[/tex]
First the disc:
[tex]\frac{10\times 75}{100}[/tex]
[tex]10\times75=750[/tex]
[tex]750\div100=7.5[/tex]
[tex]=7.5[/tex]
Next the tax:
[tex]\frac{7\times75}{100}[/tex]
[tex]7\times75=525[/tex]
[tex]525\div100=5.25[/tex]
[tex]=5.25[/tex]
Last but not least the tip:
[tex]\frac{20\times75}{100}[/tex]
[tex]20\times75=1500[/tex]
[tex]1500\div100=15[/tex]
[tex]=15[/tex]
Finally add:
[tex]75+7.50+5.25+15=102.75[/tex]
[tex]=102.75[/tex]
The total cost after adding the disc, tax, and the tip will be "$102.75."
Hope this helps.
Which equation represents a nonlinear function? x(y – 5) = 2 y – 2(x 9) = 0 3y 6(2 – x) = 5 2(y x) = 0
The equation that represents a nonlinear function is x(y – 5) = 2
How to determine the equation?Nonlinear functions are functions that do not have a uniform slope.
A linear function is represented as:
y = mx + b
This means that all other forms are nonlinear function.
From the list of given options, x(y – 5) = 2 is a nonlinear function
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Answer:
A
Step-by-step explanation:
Factor quadratic trinomials
need help on a worksheet due early tomorrow
The correct numbers to get to the media or mean are 10, 33, 3, and 2.
What is the difference between median and mean?The media is obtained by organizing the values given and selecting the one that is in the middle; while the mean is obtained by adding all values and dividing the total by the number of values.
What value makes the median 5 and 25?A. 2,4,5,9,1,7 = 1,2,4,5,7,9,10 x= 10B.32,23,15,30,12 = 12,15,23,25,30,32,33 x= 33What value makes the mean 5 and 3?A. 7+8+2+5 +3 = 25/5 = 5 x= 3B. 6+1+7+4+1+0+2= 21/7 =3 x=2Learn more about numbers in: https://brainly.com/question/17429689
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Three solid shapes a, b and c are similar.
the volume of shape a is 27 cm
the volume of shape b is 64 cm
the ratio of the surface area of shape b to the surface area of shape c is 8:15
work out the ratio of the height of shape a to the height of shape c.
The ratio of the height of shape A to the height of shape C is [tex]\frac{3}{10}[/tex]
Calculations and Parameters:First step:Recall that similar figures have the same scale factor squared due to the ratio of its surface area.
Hence,
We would make:
z-----> the scale factorx----> surface area shape Ay----> surface area shape B[tex]z^2 = x/y\\z= 2/5[/tex]
Therefore, the ratio of the height of shape A to the height of shape B is = [tex]\frac{hA}{hB} = \frac{2}{5}[/tex]
Next step:To find the ratio of the height of shape B to the height of shape C, we would perform a similar operation which is:
[tex]z^3 = 27/64\\z= 3/4[/tex]
The ratio is:
[tex]\frac{hB}{hC} = \frac{3}{4}[/tex]
Final step:To find the ratio of the height of shape A to the height of shape C would be:
[tex](\frac{hA}{hB}) (\frac{hB}{hC} )= \frac{hA}{hC}[/tex]
= 6/20
= 3/10
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Which equation represents a population of 300 animals that increases at an annual rate of 23% ?
Answer:
300+(300 + 0.23x)
Step-by-step explanation:
I'm not sure what you are asking but this is the only equation I can get
Alex's favorite number is 175% of Winnie's favorite number. Winnie's favorite number is 48 less than Alex's favorite number. What is Winnie's favorite number?
Answer:
64
Step-by-step explanation:
The information can be written as:
Let Alex's number = x
Winnie's number = y
x = 1.75y
x = y + 48
Substitute 1.75y for x:
1.75y = y +48
0.75 y = 48
3/4 y = 48
y = 64
Winnie's favourite number = 64.
On Monday, 56 biographies were
checked out at the library. This is 8 less
than twice the amount of fiction books
checked out that day. How many fiction
books were checked out on Monday?
Nathaniel works as a baker and makes several batches of muffins every morning. each batch requires 1 1/7 cups of sugar. for a large meeting, nathaniel needs 4 4/7 times more nuffins than what a regular batch makes. how much sugar will he use? if each batch fills 3 boxes, how many boxes will be needed to pack the muffins for the meeting?
The amount of sugar he will use is 5.22 cups of sugar, and the number of boxes needed to pack the muffins is 13.71 boxes.
How do we solve a word problem?This word problem question can be solved as follows:
Amount of sugar he will use = 1 1/7 * 4 4/7 = 1.142857142857143 * 4.0.571428571428571 = 5.22 cups of sugar
Number of boxes needed to pack the muffins for the meeting = 4 4/7 * 3 = 4.0.571428571428571 * 3 = 13.71 boxes
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consider the following pattern: 5;8;11; ... ; ...
a) determine the common difference of the pattern
b) write the next two terms of the pattern
c) determine the general term
d) determined T²⁰ of the pattern
Answer:
Step-by-step explanation:
The common difference is 8-5 = 3
The first next term is 11 + 3 = 14
The next (second) term is 14 + 3 = 17
tn = 5 + (n - 1)*3 This is part c
t20 = 5 + (20 - 1)*3
t20 = 5 + 19*3
t20 = 5 + 57
Answer t20 = 62
Ali needs $60 to purchase a flute. She has $32. She can earn $4 an hour babysitting. Which equation could be used to find h, the number of hours Ali needs to babysit to earn enough money to purchase the flute?
A. 60=(32 x 4)h
B. 60=(32 x 4)h
C. 60=(32 + 4)h
D. 60=(32 - 4)h
PLS HELP FAST
Answer:
A formula to express this would be:
60 = 32 + 4h
This simplifies down to 7 for h
Jaxon has a bag of marbles. He draws one marble from the bag. Before drawing another marble from the bag, what could Jaxon do to ensure that the events are independent of each other?
keep the marble he initially drew from the bag
return the marble he initially drew from the bag
add more marbles to the bag
remove all marbles that are the same color as the first one
Answer:
Return the marble he initially drew from the bag
Step-by-step explanation:
Choose the equation that represents the fraction 1/12
Answer:
1/24 + 1/24 = 1/12
Step-by-step explanation:
1/24 + 1/24 = 1/12 I think it’s this.
I don’t have any options though so I just thought of that.
a circle has a radius of 8cm the measure or the arc of the shaded region is 72 which is closest to the area of the shaded region of the circle
Answer:
just tell me when you find the answer
Calvin throws 12 sheets of paper up in the air and randomly catches one of the sheets as they float down. Of the 12 sheets of paper, 9 are white and 3 are red.
The probability that Calvin caught a white sheet is
. It is
that this event occurs. The probability that Calvin caught a red sheet is
. It is
that this event occurs.
Reset
Answer:Calvin throws 12 sheets of paper up in the air.
He randomly catches one of the sheets as they float down.
Of the 12 sheets of paper, 9 are white and 3 are red.
Probability = Number of favorable outcomes/ total number of outcomes
The probability that Calvin caught a white sheet is = or 75%.
It is likely that this event occurs as above 70% we say that the event is likely and here the probability is 75%.
The probability that Calvin caught a red sheet is = or 25%
This is unlikely to happen. Thus, we can say that it is not likely event.
Pls help!!!
Write an exponential equation for the graph shown
below.
Explain how you determined the equation.
The exponential equation of the graph is y = 1.59 * 1.26^x
How to determine the exponential equation?On the graph, we have the following points
(x,y) = (2,1) and (4,4)
An exponential function is represented as;
y = ab^x
So, we have:
ab^1 = 2 and ab^4 = 4
Divide both equations
b^3 = 2
Take the cube root of both sides
b = 1.26
Substitute b = 1.26 in ab^1 = 2
1.26a = 2
Divide both sides by 1.26
a = 1.59
So, we have:
y = ab^x
y = 1.59 * 1.26^x
Hence, the exponential equation of the graph is y = 1.59 * 1.26^x
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Two large numbers of the fibonacci are F(51) = 20,365,011,074 and F(52) = 32,951,280,099 if these two numbers are added together what number results
If these two numbers F(51) and F(52) are added together. Then the number of results will be 53,316,291,173.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Two large numbers of the Fibonacci are given below.
F(51) = 20,365,011,074 and F(52) = 32,951,280,099.
The sum of the F(51) and F(52) will be
20, 365, 011, 074
+ 32, 951, 280, 099
53, 316, 291, 173
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A 6.1 foot tall camper is standing on a 98 foot cliff looking down at his tent. The tent is 65 feet from the base of the
cliff, find the angle of depression to the nearest tenth.
Answer:
58.0 degrees
Step-by-step explanation:
Let the angle of depression be x.
tan x=104.1/65
x=58.0 degrees
Answer:
the angle of depression is 32°
Step-by-step explanation:
Help me please!!!
M
What is m
Answer
in the m∠C it means measure of C
Step-by-step explanation:
Hope this helps!
If not, I am sorry.
A number, increased by four times the number, is 35. Find the number.
How do I solve
x² - 10x-3=0
Answer:
x = 5±2√7
Step-by-step explanation:
This quadratic cannot be factorised via the factorisation method, so we use the quadratic formula :
x = [tex]\frac{-b + \sqrt{b^{2} -4ac} }{2a}[/tex] or x = [tex]\frac{-b - \sqrt{b^{2} -4ac} }{2a}[/tex]
(The reason I did 2 equations is because brainliest does not allow me to do the ± in the equation insert thing )
x = [tex]\frac{-(-10) + \sqrt{-10^{2} -4(1)(-3)} }{2(1)}[/tex] or x = [tex]\frac{-(-10) - \sqrt{-10^{2} -4(1)(-3)} }{2(1)}[/tex]
x = [tex]\frac{10 + \sqrt{100+12} }{2}[/tex] or x= [tex]\frac{10 - \sqrt{100+12} }{2}[/tex]
x = [tex]\frac{10 + {4\sqrt{7}} }{2}[/tex] or x = [tex]\frac{10 - {4\sqrt{7}} }{2}[/tex]
x = [tex]5+2\sqrt{7}[/tex] or x = [tex]5 -2\sqrt{7}[/tex]
Hope this helped and brainliest please
What is the measure of 1, 2 and 3?
Answer:
angle 1= 59 degree, angle 2= 61 degree and angle 3 = 119 degree
Step-by-step explanation:
because in the figure angle 2 and 61 degree are alternative angle so they are equal