Answers
Answer:
Using the Pythagorean theorem, we know that in a right-angle triangle, we have:
a^2 + b^2 = c^2
where c is the hypotenuse.
From the given information, we have:
ab = 11 - x
a = x
b = 11
c = 11 (given)
We can use the given values to eliminate a or b from the Pythagorean theorem:
a^2 + (11 - x)^2 = 11^2
Expanding and simplifying, we get:
a^2 + 121 - 22x + x^2 = 121
a^2 + x^2 - 22x = 0
Substituting a = x into the above equation, we get:
x^2 + x^2 - 22x = 0
2x^2 - 22x = 0
2x(x - 11) = 0
So, either x = 0 or x - 11 = 0.
Since x cannot be zero (as it represents a length), we have x - 11 = 0.
Therefore, x = 11.
Hence, the value of x in its simplest form with a rational denominator is 11/1 or just 11.
Answer:
\(x=11\sqrt{2}\)
Step-by-step explanation:
The given right triangle is an isosceles right triangle since its legs are equal in length (denoted by the tick marks).
Side x is the hypotenuse of the isosceles right triangle.
Given both legs are 11 units in length, we can use Pythagoras Theorem to calculate the length of the hypotenuse.
\(\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}\)
As a and b are the legs, and c is the hypotenuse, substitute the following values into the formula and solve for x:
a = 11b = 11c = xTherefore:
\(\implies 11^2+11^2=x^2\)
\(\implies 121+121=x^2\)
\(\implies 242=x^2\)
\(\implies x^2=242\)
\(\implies \sqrt{x^2}=\sqrt{242}\)
\(\implies x=\sqrt{242}\)
To simplify the radical, rewrite it as a product of prime numbers:
\(\implies x=\sqrt{11^2 \cdot 2}\)
\(\textsf{Apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)
\(\implies x=\sqrt{11^2}{\sqrt{2}\)
\(\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0\)
\(\implies x=11\sqrt{2}\)
Therefore, the length of side x in simplest radical form is 11√2.
Related Questions
A shirt was originally priced at $20. The store is having a 40% off sale.
How much will you pay for the shirt after the discount (not including tax)?
$
Round to two decimal places if needed.
Answers
Answer:
$12
Step-by-step explanation:
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answers
The three true statements are:
The standard form of the equation is (x – 1)² + y² = 3.
The center of the circle lies on the x-axis.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
What is the center of the circle?
A circle is named by the point in the center. A radius is a line segment from the center of the circle to the edge. A diameter is a line segment that passes through the center of a circle.
The true statements are:
The standard form of the equation is (x – 1)² + y² = 3.
The center of the circle lies on the x-axis.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Given an equation of x2 + y2 – 2x – 8 = 0, we can make the following observations:
We can complete the square to get the equation in standard form. (x – 1)² + y² = 3². This is true statement.
The center of the circle is (1,0) which is on the x-axis, this statement is true.
The radius is 3 units, which is the same as the radius of the circle x² + y² = 9 (3²). This statement is true.
The center of the circle does not lie on the y-axis as its x-coordinate is not 0.
Hence, The three true statements are:
The standard form of the equation is (x – 1)² + y² = 3.
The center of the circle lies on the x-axis.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
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Is 2x - 3 = -7 x + 2 > y a true or false statement?
Answers
On Monday, Marie walks her dog 3/8 mile, and Randy walks his dog 1/4 mile. how far do they walk in all
Answers
Answer:
5/8 mile
Step-by-step explanation:
3/8 + 1/4 = 3/8 + 2/8 = 5/8
Leslie is making these two recipes. Which takes
longer to make, the strawberry bread or the
spaghetti sauce? How many minutes longer
Answers
Based on the information in the image, we can infer that the recipe that takes the longest is the one for spaghetti sauce.
How to identify the recipe that takes the longest?To find the recipe that takes the longest we must take into account the information of each of the recipes. In this case, we have preparation time and cooking time. To know the total time we must add these two values.
Additionally, we must establish a magnitude to be able to relate all the values, in this case the most appropriate would be the number of minutes.
So, the preparation of the spaghetti sauce takes 10 minutes and its cooking takes an hour and a half, that is, 90 minutes. On the other hand, strawberry bread takes 20 minutes to prepare and 55 to cook:
10 + 90 = 100 minutes20 + 55 = 75 minutesAccording to the above, the spaghetti sauce takes longer because it takes 25 minutes longer than the strawberry bread.
Note: This question is incomplete. Here is the complete information:
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A rancher wants to construct a rectangular pen by extending an existing 100 ft stone wall by an additional x feet of fencing. If the farmer has a total of 700 ft of fencing to complete the pen, find the dimensions that will maximize the enclosed area.
Answers
Answer:
175ft by 175ftStep-by-step explanation:
Let the length of the rectangular pen be L
let the width be W
Perimeter of the pen P = 2L+2W
Area A = LW
Given
P = 700ft
L = 100+x
P = 2(100+x) + 2w
P = 200+2x+2w
700 = 200+2x+2w
500 = 2x+2w
250 = x+ w
w = 250-x..... 1
A = (100+x)w ....2
substitute 1 into 2;
A = (100+x)(250-x)
A = 25000-100x+250x-x²
A = 25000+150x-x²
To maximize the area, dA/dx = 0
dA/dx = 150-2x
150-2x = 0
150 = 2x
x = 150/2
x = 75ft
Since
x+w = 250
75+w = 250
w = 250-75
w = 175ft
The width of the rectangular pen will be 175ft
The length will be 100+x = 100+75 = 175ft
Hence the dimension that will maximize the enclosed area is 175ft by 175ft
-8x+y=6
-8x+3y=-14
How would you solve this using the elimination method? Thanks!
Answers
Answer:
x = -1,375
y = -5
Step-by-step explanation:
{-8x + y = 6, / : (-1)
{-8x + 3y = -14;
Multiply the first equation by -1, so that we could eliminate 8x:
+ {8x - y = -6,
{-8x + 3y = -14;
----------------------
4y = - 20 / : 4
y = -5
Now, make x the subject from the first equation (you can do it from the 2nd one instead):
8x = -6 + y / : 8
x = -0,75 + 0,125y
x = -0,75 + 0,125 × (-5) = -0,75 - 0,625 = -1,375
Write a polynomial function of least degree with rational coefficients so that P(x) = 0 has the given roots.
X= - 2, x = 10
Answers
Answer:
Hope this helps ;) don't forget to rate this answer !
Step-by-step explanation:
To write a polynomial function of least degree with rational coefficients that has the given roots, we can use the factor theorem. The factor theorem states that if r is a root of a polynomial function P(x), then x - r is a factor of P(x).
In this case, the roots of the polynomial are x = -2 and x = 10. We can use the factor theorem to write a polynomial function that has these roots as follows:
P(x) = (x + 2)(x - 10)
This polynomial function has degree 2, which is the least degree possible, and all of its coefficients are rational numbers. It has roots x = -2 and x = 10, as required.
2/7 = 4/5 + 1/7 q answe for q
Answers
Answer:
??
Step-by-step explanation:
Answer:
what
Step-by-step explanation:
Callie runs 30 minutes a day. She has already run 90 minutes this week. How many days will it take her to run at least 240 minutes?
Answers
150/30=5 MORE days (or 8 TOTAL days if that’s what you’re looking for)
help im bad at math AHHHHHHHHHHHHHHHHHHHHH
Answers
Answer:
36
Step-by-step explanation:
Answer:
The answer is D
Step-by-step explanation:
because am very good at math
change each mixed number into an improper fraction 6 2/5
Answers
Answer:
32/5
Step-by-step explanation:
Convert the mixed number 6 2/5 into an improper fraction by multiplying the denominator by the whole number and then add the numerator.
Ex: 6 2/5 = 5 x 6 +3
The IQ scores and science test scores of fourth grade students is given by the line of best fit ŷ = −20.3 + 0.7489s, where ŷ is the predicted science score and s is the IQ score. An actual science test score for a student is 52.6 with an IQ of 100.
Find and interpret the residual.
−1.99; The line of best fit underpredicts the student's science test score.
1.99; The line of best fit overpredicts the student's science test score.
1.99; The line of best fit underpredicts the student's science test score.
−1.99; The line of best fit overpredicts the student's science test score.
Answers
-19.99; The line of best fit underpredicts the student's science test score.
So correct option is A.
What do you mean by prediction?A prediction is an estimation or forecast about future events or conditions, based on past data and trends, current information, and/or mathematical models. Predictions can be made in various fields, such as finance, weather, sports, social sciences, and natural sciences. The accuracy of predictions depends on many factors, including the quality of the data used, the assumptions made, the complexity of the system being analyzed, and the reliability of the methods used. Predictions are not always accurate and are often subject to revision as new information becomes available.
The predicted science score for the student with IQ 100 can be calculated using the line of best fit:
ŷ = −20.3 + 0.7489 * 100 = 71.59
The residual is the difference between the actual science test score and the predicted science score:
residual = actual score - predicted score = 52.6 - 71.59 = -19.99
So the line of best fit underpredicts the student's science test score by 19.99 points.
Therefore, the residual is:
-19.99; The line of best fit underpredicts the student's science test score.
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Would be wonderful, if anyone could help me understand what steps you should do for this one.
Answers
The value of x is 6 is proved by equating line segment PM and MR as M is the midpoint of line PR.
What is midpoint of line segment?
The midpoint divides the line segment into two equal parts. As the number line progresses, the leftmost numbers become smaller, and the rightmost numbers become larger. Adding, subtracting, and multiplying can also be done using a number line like for addition move towards right and for subtraction move towards left.
It is given that M is the midpoint of line segment PR which implies M will divide PQ into two equal parts that is PM (2x + 5) equals MR (4x - 7). now calculating x value first :
PM = MR
2x+5 = 4x -7
4x -2x = 5 + 7
2x = 12
x = 12/2
x = 6
Hence proved that the value of x is 6
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Find the values of x and y if (2x + y, 2) = (1, x - y).
Answers
Answer:
We have, 2x+y=3 .......(1)
xy=1....(2)
In equation (2), we get
y=
x
1
..........(3)
y put in the equation (1)
2x+
x
1
=3
2x
2
+1=3x
2x
2
−3x+1=0
2x
2
−3x−1x+1=0
2x(x−1)−1(x−1)=0
x=1, x=
2
1
We take the value of x=1
x value put in equation (1)
2(1)+y=3
y=3−2
y=1
x=1
x and y value put (x+y)
x−y
=(1+1)
(1−1)
=2
0
=1
Hence, this is the answer
Was this answer helpful?
2x + y = 1
+ (x - y = 2)
3x=3
X=1. Plug back into one of the equations.
1-y=2. Isolate y.
Y=-1
The Answer is (1,-1)
A triangle has an angle measures of (x+3)º,(5x-8)º, and (2x+1)º
What is the measure of the smallest angle of the triangle in degrees?
Answers
The measure of the smallest angle is 26 degree.
We have,
Triangle's angle measures of (x+3)º,(5x-8)º, and (2x+1)º
Using Angle Sum Property
(x+ 3) + (5x - 8) + (2x + 1)= 180
8x - 4 = 180
8x = 184
x = 184/8
x = 23
Thus, the measure of angles are
x+ 3 = 23+ 3 = 26
5x-8 = 5(23) - 8 = 107
2x +1 = 2(23) + 1 = 47
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I need the reasons for this
Answers
Answer:
Reflexive Property
ASA
CPCTC
Step-by-step explanation:
Solve 1/2w=16. What is w?
Answers
0.5w=16 -> w= 16/0.5= 32
Answer is 32.
Step-by-step explanation:
The answer you are looking for is w=32.
Solution/Explanation:
Writing out the equation first
1/2w=16
Multiplying 2 to both sides of the equation
(1/2w)(2)=(16)(2)
(1/2w)(2)=w
(16)(2)=32
You will get w=32.
So, therefore, the final answer to this problem is w=32.
Hope this helped answer your question for you. Good day to you.
Find the first four terms of the sequence defined by a(n subscript)= 1/n (separated by a comma).
Answers
Answer:
1,1/2,1/3,1/4
Step-by-step explanation:
an = 1/n
n is the term number
a1 = 1/1 =1
a2 = 1/2
a3= 1/3
a4 = 1/4
The first 4 terms are 1,1/2,1/3,1/4
what is one thousandth less than 0.061
Answers
Answer:
one thousandth is greater than 0.061
Step-by-step explanation:
What happened to the U.S. dollar when President Nixon closed the gold
window?
Answers
Archie bought 100 shares of stock in an ice cream company 2 years ago. He paid $60.65 per share. He just sold all of his shares for $67.68 per share. How much did he gain?
Answers
Answer:
Step-by-step explanation:
First, we need to find the difference between the price that he sold the shares for and the price that he bought them at: (67.68-60.65) = 7.03
That means that there was a gain of $7.03 per share for Archie.
That being said, since Archie bought 100 shares, we can multiply that number by 100 to find the total gain from selling the shares:
(7.03x100)= 703
The answer then is:
Archie gained $703 from selling all of his shares.
determine whether the following procedure results in a binomial distribution or a distribution that can be treated as binomial (by applying the 5% guideline for cumbersome calculations). If it is not binomial and cannot be treated as binomial, identify at least one requirement that is not satisfied.
Treating 20 bald men with a special shampoo and recording how they say their scalp feels
Choose the correct answer below.
A. It is binomial or can be treated as binomial.
B. It is not binomial because the probability of success does not remain the same in all trials.
C. It is not binomial because there are more than two possible outcomes.
D. It is not binomial because there are more than two possible outcomes and the trials are not independent.
Answers
The given procedure results as not binomial and cannot be treated as binomial. It is not binomial because the probability of success does not remain the same in all trials. The correct answer is option B.
What is binomial distribution?Binomial distribution compiles the number of trials, or observations when each trial has the same probability of attaining one particular value. Binomial distribution controls the probability of observing a specified number of successful outcomes in a specified number of trials.
In a binomial distribution, the probability of getting a success have to remain the same for the trials we are investigating. For example, when tossing a coin, the probability of flipping a coin is half or 0.5 for every trial we conduct, because there are only two possible outcomes.
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Need help with this one please
Answers
Answer:
100°
Step-by-step explanation:
I'm sorry, I don't quite remember the name of the four sided shape when it fits into a circle but when it does, the opposite angles are equal to 180° therefore we say 180° - 80° and get 100° for the opposite angle which is U
making $40 payments each Friday,
6. Emily borrowed $1,000 from her parents to put towards a down payment on a car. She has
already paid back $350. Her parents do not charge any interest and Emily is planning on
Write an equation that represents the number of weeks it will take Emily to repay her
b. Is the solution to the equation the actual number of weeks it will take Emily to repay her
Lesson 1.5.
parents? Explain your answer.
a.
parents if she pays $40 each Friday.
Answers
1d. Are the points on the line included in the solution set? Explain how youknow. *
Answers
Given the following question:
\(2y-x>1\)Graph the following inequality:
First option or above the line is the answer.
Write the absolute value equations in the form | x - b |= c (where b is a number and C can be either a number or an expression) that has the following solution set. All numbers such that x <= 5
Answers
The absolute value equations in the form | x - b |= c is x-5<=0
What is absolute value?
A number's absolute value is defined as how far it is from the origin of a number line. The symbol |a|, which represents the size of any integer "a," is used to represent it. Any integer's absolute value is a real number, regardless of its sign or whether it is positive or negative. Two vertical lines are used to depict the modulus of an as |a|.
Given,
The absolute value equations in the form | x - b |= c
Where b is a number and C can be either a number or an expression
The equation must be written down for x <= 5
All numbers will be such that x <= 5
So, x-5<=0
Hence the correct answer is x-5<=0.
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how to graph y+9= -3x and find x-intercept
Answers
When you graph y=-3x-9 you find that the x-intercept is -9
What is a translation
Answers
Answer:
the process of translating words or text from one language into another.
Answer: words that have been changed from one language into a different language words that have been translated or the act or process of translating something into a different language also the act or process of changing something from one form to another hopefully i helped
Step-by-step explanation:
Fill in the table using this function rule. y=27-3x
x y
1 blank
2 blank
3 blank
4 blank
5 blank
Answers
Answer:
plz
Step-by-step explanation:
can any one answer this