Select the correct answer.Which expression has a value closest to 1? (Use 3.14 as the value of T.)OA.77V10OB. V75-V74OC. 37-V26OD3V5 V20V2
Answers
the expression has a value closest to 1 is √37 - √26 (option C)
Explanation:
To determine the expression, we need to solve each of the options.
a) 7π/√10 = 7(3.14) /√10 = 21.98/3.1623
= 6.95
b) √75 - √74 = 8.66 - 8.60
= 0.06
c) √37 - √26 = 6.083 - 5.099
= 0.984
d) (3√5 - √20)/√2 = (6.708 - 4.472)/1.414 = 2.236/1.414
= 1.58
√37 - √26 = 0.984 is closest to 1
From the above, the expression has a value closest to 1 is √37 - √26 (option C)
Related Questions
Factor the polynomial below. To earn full credit please share all work/calculations/thinking. You may want to do this work by hand and then upload an image of that written work rather than try to type it all out. 12t^2+t-13
Answers
Given:
The polynomial is,
[tex]12t^2+t-13[/tex]Factor the polynomial,
[tex]\begin{gathered} 12t^2+t-13=12t^2-12t+13t-13 \\ =\mleft(12t^2-12t\mright)+\mleft(13t-13\mright) \\ =12t(t-1)+13(t-1) \\ =\mleft(t-1\mright)(12t+13) \end{gathered}[/tex]Answer:
[tex]12t^2+t-13=(t-1)(12t+13)[/tex]Lisa is saving for college. The account is modeled by the function:
f(x) = 250(1.25)^x
,when x represents how many years she has saved.
Xavier is also saving college. His account is modeled by this table:
X g(x)
0 200
1 270
2 364.5
3 492.08
1. After 3 years, how much does Lisa's account have in it? (Round to the hundredths
decimal place.)
2.After 3 years, how much does Xavier’s account have in it?
3.What is the positive difference in their accounts after 3 years?
Answers
Using exponential functions, it is found that:
a) Lisa's account has $489 after 3 years.
b) Xavier's account has $493 after 3 years.
c) The difference is of $4.
An exponential function is what, exactly?According to the following principle, an exponential function is modelled where the following description of the parameters is given:
The value of the function at x = 0 is known as its initial value, or a.The function's rate of change is denoted by bLisa's function is already given, while for Xavier's, the parameters are given as follows:
a = 200
b = 270/200
= 1.35
g(x) = 200 × [tex]1.35^{x}[/tex]
In 3 years, the amounts in each account will be given by the numeric values of the functions as follows:
Lisa = f(3)
= 250 (1.25)³
= 489$
Xavier = f(3)
= 200 (1.35)³
= 493$
The positive difference is given by the subtraction of the greater amount by the lesser amount, hence:
493 - 489 = 4$
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A rocket is launched straight up and it takes 83 seconds to hit the ground. How long did it take the rocket to get to the top of its path?
Answers
It would take 41.5 to get to the top of its path if the rocket is launched straight up and it takes 83 seconds to hit the ground by solving through finding speed.
Given that the time that rocket took to hit the ground is 83 seconds.
We are required to find the time that it took the rocket to get to the top of its path.
Suppose the height from the ground is h.
To cover the distance of 2h it would take 83 seconds.
We know that speed=Distance/time
Speed=2h/83
So, to cover the distance of h, the time will be :
Time=Distance/Speed
=h/2h/83
=(h*83)/2h
=83/2
=41.5
Hence it would take 41.5 to get to the top of its path if the rocket is launched straight up and it takes 83 seconds to hit the ground by solving through finding speed.
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Write and solve a direct variation equation to find the answer
Answers
Direct Variation
If y varies directly with x, then they are related by the equation:
y = kx
Where k is a constant called the proportionality factor.
It's given that y = -38 when x = 19. Substituting those values in the equation, we can find the value of k:
-38 = k*19
Dividing by 19:
k = -38 / 19
k = -2
Now our model is complete:
y = -2x
Now it's required to find the value of x when y = -4. Substituting:
-4 = -2x
Dividing by -2:
x = -4 / (-2)
x = 2
Angelina can type 150 words in 5 minutes. At this rate, how many words can she type in 1 minute?
Answers
Answer:
30 words per minute
Step-by-step explanation:
Answer:
30 words
Step-by-step explanation:
her typing speed is 150 words for 5 minutes.
Since we know that she can type 5 times as much in 5 minutes than in 1 minute, we know that 150 words is 5 times as much as she would be able to type in 1 minute. The question that should be asked is "5 times what would equal 150?" The answer would be 30 words.
Shorter answer: 150 words / 5 minutes = 30 words/minute
Question 14<>The table summarizes results from 981 pedestrian deaths that were caused by automobileaccidents.Pedestrian DeathsDriver Pedestrian Intoxicated?Intoxicated?NoYesYes5584No248594If one of the pedestrian deaths is randomly selected, find the probability that the driver was notintoxicated but the pedestrian was. Please enter a decimal to 4 places.Calculator
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
If one of the pedestrian deaths is randomly selected.
Find the probability that the driver was not intoxicated but the pedestrians were.
We are expected to enter 4 decimal places.
Now, from the table, we can see clearly that:
[tex]\begin{gathered} \text{Probability ( the driver was not intox}icated\text{ but the pedestrians were)} \\ =\text{ }\frac{248}{981} \\ =\text{ 0.2528 ( 4 decimal places)} \end{gathered}[/tex]CONCLUSION:
The final answer is 0. 2528 ( 4 decimal places).
which graph represents the equation 2 x + y =2?
Answers
start by writing the equation in the slope-intercept form
[tex]\begin{gathered} 2x+y=2 \\ y=-2x+2 \end{gathered}[/tex]this meand that the line has a slope of -2 and cuts the y-axis over 2.
the graph should look like this
A bacteria population is modeling by b(t) = 10e^5t million bacteria after t days. how fast is the population growing after 3 days?
Answers
The population of this bacteria is growing at the rate of 10.897 trillion per day.
What is the growth rate?The growth rate refers to the change from one period to another.
It also refers to the average growth per day, especially in the case of bacteria.
Bacteria population = b(t) = 10e^5t million
The number of days, t = 3
e = 2.71828
10e^5t million = 10 x 2.71828^5x3 million
= 10 x 2.71828^15 million
= 10 x 3268984.38894 million
= 32,689,843,889,400
Growth per day = 10.897 trillion
Thus, we can conclude that the bacteria is increasing at the growth rate of 10.897 trillion per day.
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1 Type the correct answer in each box. Use numerals instead of words, Consider this quadratic equation, x2 + 2x + 7 = 21 The number of positive solutions to this equation is The approximate value of the greatest solution to the equation, rounded to Reset
Answers
Answer:
The number of positive solutions to this equation is;
[tex]1[/tex]The approximate value of the greatest solution to the equation is;
[tex]2.87[/tex]Explanation:
Given the equation;
[tex]x^2+2x+7=21[/tex]Let us subtract 21 from both sides;
[tex]\begin{gathered} x^2+2x+7-21=21-21 \\ x^2+2x-14=0 \end{gathered}[/tex]We can now solve for x using the quadratic formula;
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]from the equation;
[tex]\begin{gathered} a=1 \\ b=2 \\ c=-14 \end{gathered}[/tex]substituting;
[tex]\begin{gathered} x=\frac{-2\pm\sqrt[]{2^2-4(1)(-14)}}{2(1)} \\ x=\frac{-2\pm\sqrt[]{4+56}}{2} \\ x=\frac{-2\pm\sqrt[]{60}}{2} \end{gathered}[/tex]so, we have;
[tex]\begin{gathered} x=\frac{-2\pm\sqrt[]{60}}{2} \\ x=\frac{-2+\sqrt[]{60}}{2} \\ x=2.87 \\ \text{and} \\ x=\frac{-2-\sqrt[]{60}}{2} \\ x=-4.87 \end{gathered}[/tex]Therefore, the number of positive solutions to this equation is;
[tex]1[/tex]The approximate value of the greatest solution to the equation is;
[tex]2.87[/tex]Find the difference of (4y2 - 2y - 5) and (y² - y + 8).4у2 - 3у - 133у2 - у - 135y2 - 3y + 33у2 - 3у + 3
Answers
We must find the difference between the following polynomials:
[tex]\begin{gathered} f_1(y)=4y^2-2y-5, \\ f_2(y)=y^2-y+8. \end{gathered}[/tex]The difference between the polynomials is obtained by subtracting the coefficient of terms with equal power of y:
[tex]\begin{gathered} f_1(y)-f_2(y) \\ =\left(4y^2-2y-5\right)-\left(y^2-y+8\right) \\ =\left(4y^2-y^2\right)+\left(-2y+y\right)+\left(-8-5\right) \\ =3y^2-y-13. \end{gathered}[/tex]Answer3y² - y - 13
the 7th grade fundraiser gives away a large container of gumballs to the student who is closest to guessing the correct number of gumballs in the container noticing that the container is a cube. Sally decides to count the number of gumballs along the length of one side if Sally get 729 gumballs how many gumballs did she count along one side of the container
Answers
If the container is a cube, every side is a square, so the length and the width are the same.
To get the number of gumballs based on the number of gumballs in one side, we can use the following equation
[tex]TotalGumballs=x^3[/tex]Where x is the number of gumballs along one side. So, replacing the total by 729 and solving for x, we get:
[tex]\begin{gathered} 729=x^3 \\ \sqrt[3]{729}=x \\ 9=x \end{gathered}[/tex]Answer: She counts 9 gumballs along one side of the container
At a fruit stand , apples sell for $ 1.20 per pound . One week , the stand sold $600 worth of apples and pears . The equation below describes the situation , where A is the number of pounds of apples and P is the number of pounds of pears . 0.8a + 1.2p = 600 Which graph represents the equation?
Answers
we can calculate two points in order to know what graph corresponds to the equation
when a=0
1.2p=600
p=600/1.2
p=500
the point is (0,500) red point
when b=0
0.8a=600
a=600/0.8
a=750
the point is (750,0) green point
the answer is B
Identify the function in which y varies directly with x.
Answers
Let the function in which "y" varies directly with "x" be y = kx where "k" is the proportionality constant and y ∝ x
As per the question statement, We are supposed to write any function in which "y" varies directly with "x" i.e., y ∝ x
Let's say y = kx be the function where "k" is the proportionality constant and y ∝ x.
Now let x = 3 and y = 6, so 6 = k*3
or k = 3
Hence for any value of "x" value of "y" would be k times the value of x and this is called the direct proportion relationship.
Hence, the function in which "y" varies directly with "x" be y = kx where "k" is the proportionality constant and y ∝ x
Function: An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable).Proportionality constant: The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant ratio is another term for the constant of proportionality.To learn more about function and proportionality constant, click on the link given below:
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How many weeks can Shanika withdraw money from her account
Answers
Step 1
Given;
[tex]\begin{gathered} Money\text{ in her account \$500} \\ Money\text{ that will be left is \$200} \\ She\text{ withdraws \$25 weekly} \end{gathered}[/tex]Hence the equation from the question will be;
[tex]\begin{gathered} 500-25x=200 \\ where\text{ x= number of weeks} \end{gathered}[/tex][tex]\begin{gathered} 500-200=25x \\ 300=25x \\ x=\frac{300}{25} \\ x=12 \end{gathered}[/tex]Hence, the answer will be;
[tex]12\text{ or less weeks}[/tex]The formula a = m – n represents the actual cost, a, of an item with original price m after a coupon for n dollars off is applied. Solve the formula for the amount of the coupon.
Answers
The formula for amount of the coupon is given by n = m - a.
This question can be solved using simple Linear equation. A linear equation may be defined as an expression which can be written in the form y = ax + b where a, b are coefficients and x, and y are independent and dependent variables respectively. According to question we have a formula a = m - n where a is the actual cost, m is original price and n is coupon discount. The actual cost of an item will depend on the coupon discount as well as the original cost of the item. To find the coupon amount from the formula we rearrange the equation as
a = m - n
a - m = -n
=> n = m - a which will be the required formula.
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shshshdggdgdgdggddgegegegegegs
Answers
We need to solve the following equation by completing the square:
[tex]x^2-4x-9=0[/tex]we first pass the 9 to sum in the right side
[tex]x^2-4x=9[/tex]now we add 4 in both sides of the equation, because (4/2)^2=4, obtaining
[tex]x^2-4x+4=9+4[/tex]simplifying
[tex](x-2)^2=13[/tex]then
[tex](x-2)=\pm\sqrt[]{13}[/tex]adding 2 in both sides of the equation we have that the solution is:
[tex]x=2\pm\sqrt[]{13}[/tex]Lena sells earrings from a booth at the arts fair. She pays $200 to rent the booth.She makes $5 from each pair of earrings she sells. Her profit, P, can be foundusing the following equation, where n is the number of pairs of earrings sold.P = 5n – 200How many pairs of earrings must Lena sell to earn a profit of $450?1- 1402- 1303- 1004- 150
Answers
P = 5n - 200
where
P: profit
n: number of pairs of earrings sold.
To find how many pairs of earrings must Lena sell to earn a profit of $450, we have to replace P = 450 into the equation and solve for n, as follows:
450 = 5n - 200
200 is subtracting on the right, then it will add on the left
450 + 200 = 5n
650 = 5n
5 is multiplying on the right, then it will divide on the left
650/5 = n
130 = n
Lena must sell 130 pairs of earrings to earn a profit of $450.
Which of the following investments will earn the smallest amount of interest?
Answers
Part a: will earn the smallest amount of interest at 321.2 when 8030 is invested for 2 years at 2%
We will use the formula for all the parts:
Simple interest is interest that is simply charged on the principal amount, which is the original amount borrowed or deposited. The interest charge will only be applied once, regardless of how frequently it is applied.
Simple interest = P*R*T/100
where P = principal amount invested
R = rate of interest
T = time in years
Part a:
Simple interest = 8030*2*2/100
= 321.2
Part b:
Simple interest = 1901*8*4/100
= 608.32
Part c:
Simple interest = 5330*6*2/100
= 639.6
Part d:
Simple interest = 3970*6*4/100
= 952.8
Although a part of your question is missing, you might refer to this full question: Which of the following investments will earn the smallest amount of interest? a. $8,030, invested for 2 years at 2.0% interest b. $1,901, invested for 8 years at 4.0% interest c. $5,330, invested for 6 years at 2.0% interest d. $3,970, invested for 6 years at 4.0% interest
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PLEASE THIS IS DUE IN AN HOUR PLEASE HELP ME PLEASE :(
Answers
The expression is:
f(-2) = 23, f(3) = 5, f(4) = 5, f(6) = 5, f(9) = -3
The function is
f(x) = 5x² + 3 x< 3
= 5 3≤x ≤ 6
= 6-x x>6
a) f(-2) for x<3
So we have 5x² + 3
5(-2)² + 3
= 5 × 4 + 3
= 20 + 3
= 23
b) f(3)
as the range is 3≤ x ≤6
for which we have a value 5
So f(3) = 5
c) f(4)
As the range is 3≤ x ≤ 6 for which the value is 5.
So f(3) = 5
d) f(6)
As the range is 3≤ x ≤ 6
So the value is 5
f(6) = 5
e) f(9)
The range is x>6 for this we have 6-x
So 6-x
= 6 - 9
= -3
Therefore the value of the function is f(-2) = 23, f(3) = 5, f(4) = 5, f(6) = 5 and f(9) = -3.
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y varies jointly as a and b , and inversely as the square root of c. y=54 , a = 3 , b=9 , and c=25. Find y when a=5 , b=6 , c=36
Answers
When a=5 , b=6 , c=36, the value of y will be 50.
Here, we are given that y varies jointly as a and b and inversely as the square root of c.
⇒ y ∝ ab/[tex]\sqrt{c}[/tex]
Let k be a constant, then we can say that-
y = kab/[tex]\sqrt{c}[/tex]
We are given that y = 54 , a = 3 , b = 9 , and c = 25.
substituting these values in the above equation, we can calculate the value of k as follows-
54 = (k*3*9)/[tex]\sqrt{25}[/tex]
54 = 27k/5
54*5 = 27k
270 = 27k
27k = 270
k = 270/27
k = 10
Now, when a=5 , b=6 , c=36, the value of y will be-
y = (10*5*6)/[tex]\sqrt{36}[/tex]
y = 300/6
y = 50
Thus, when a=5 , b=6 , c=36, the value of y will be 50.
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Determine if the following system of equations has no solutions , infinitely many solutions or exactly one solution .- Infinitely Many Solutions - One Solution - No Solutions
Answers
Let's begin by identifying key information given to us:
[tex]\begin{gathered} x+3y=8----1 \\ x-3y=-6---2 \\ A\text{dd equations 1 \& 2, we have:} \\ x+x+3y-3y=8-6 \\ 2x=2 \\ x=1 \\ \text{Substitute the value of ''x'' into equation 1, we have:} \\ 1+3y=8 \\ \text{Subtract ''1'' from both sides, we have:} \\ 1-1+3y=8-1 \\ 3y=7 \\ y=\frac{7}{3} \end{gathered}[/tex]Therefore, the system of equations has one solution
i need help with this question it’s for a test. i’m doing summer school to help me prepare for college.
Answers
Ok, so
We got these triangles:
We know that two triangles are similar if there's a ratio between their sides.
So, if we compare,
We got this ratio:
As you can notice, if we relation side by side, the ratio is the same. So, we could say that the bigger triangle is 1.5 times the smaller one. So, they are similar.
What are the x and y-intercepts of the line described by the equation?
-6x+3y=18.9
Answers
Answer:
Y=6.3 and X=-3.15
Step-by-step explanation:
Plug in 0 for x and y in separate equations
-6(0)+3y=18.9
3y=18.9
3/3y=18.9/3
y+6.3
-6x+3(0)=18.9
-6x+18.9
-6/-6x+18.9/-6
x=-3.15
Ordering Decima
A) Write each set of decimals in increasing order.
1)
14.78, 46.1, 25.5, 14.8, 32.32
2)
37.44, 9.32, 16.49, 9.67, 37.91
Answers
Increasing order :
1) 14.78 , 14.8 , 25.5 , 32.32 , 46.1
2) 9.32 , 9.67 , 16.49 , 37.44 , 37.91
What is ascending order ?
Numbers can be arranged in ascending order, from least value to highest value. The arrangement is left to right. Increasing order is another name for ascending order.The base-10 number system is known as the decimal system.The accepted method for representing both integer and non-integer numbers is the decimal numeral system.It is the extension to non-integer numbers.Decimal notation is the term used to describe the method of representing numbers in the decimal system.To learn more about ascending order refer :
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A survey found that women's heights are normally distributed with mean 63.6 in. and standard deviation 3,8 in. The survey also found that men's heights are normally distributed with
mean 67.6 in. and standard deviation 3.6 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 56 in. and a maximum of 62 in.
Complete parts (a) and (b) below.
a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusement park?
The percentage of men who meet the height requirement iS
(Round to two decimal places as needed.)
%.
Since most men
the height requirement, it is likely that most of the characters are
b. If the height requirements are changed to exclude only the tallest 50% of men and the shortest 5% of men, what are the new height requirements?
The new height requirements are a minimum of
in. and a maximum of in.
(Round to one decimal place as needed.)
Answers
The percentage of men meeting the height requirement is 5.93%.The new height requirements are a minimum of 61.7 inches and a maximum of 67.6 inches.
What is probability?Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty. The likelihood or chance that a specific event will occur is represented by a probability. Both proportions between 0 and 1 and percentages between 0% and 100% can be used to describe probabilities. A measure of how likely something is to happen is called a probability. It gauges how likely the occurrence is to occur. The probability equation reads as follows: P(E) = Number of Favorable Outcomes/Total Outcomes.
For mean deviation of women
σ = 3.8
μ = 63.6
For mean deviation of men
σ = 3.6
μ = 67.6
The probability for men
= 5.93%
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Two different floor plans are being offered in a new housing
Answers
We kwot that the probability of an union of eventes (that can be written with the "or" sentence) is given by:
[tex]P(X\cup Y)=P(X)+P(Y)-P(X\cap Y)[/tex]where X and Y are the events.
In this case, let X be the event "The buyer preferred Plan A" and let Y be the event "The buyer is in the 40 to 49 year old age group). We know that the probability is given by:
[tex]P=\frac{\text{number of favorable outcomes}}{\text{ number of possible outcomes}}[/tex]Adding all the values in the table we have that the total number of possible outcomes is 68.
For event X, we have a total of 38 favorable outcomes; hence its probability is:
[tex]P(X)=\frac{38}{68}[/tex]For event Y, we have a total of 24 favorable outcomes, hence its probabiliy is:
[tex]P(Y)=\frac{24}{68}[/tex]From the table we notice that 16 buyers preferred plan A and are in the 40 to 49 year old age group. This means that the probability of the intersection of the events is:
[tex]P(X\cap Y)=\frac{16}{68}[/tex]Plugging our probabilities in the formula for the union we have:
[tex]\begin{gathered} P(X\cup Y)=\frac{38}{68}+\frac{24}{68}-\frac{16}{68} \\ P(X\cup Y)=\frac{46}{68} \\ P(X\cup Y)=0.676 \end{gathered}[/tex]Therefore, the probability we are looking for is 0.676
Which does NOT represent a valid argument?Anyone who buys a boat will go water skiing.Ivan bought a boat.Ivan will go water skiing.Everyone who went to the football gamecheered.Maria cheered.Maria went to the football game.If the Nationals win the playoffs, then I will behappy.O if I am happy, then I will have a party.If the Nationals win the playoffs, then I will have aparty.Everyone who studies Geometry will pass theSOL.Everyone who passes the SOL will be exemptfrom the exam.Everyone who studies Geometry will be exemptfrom the exam,
Answers
the statement that does not represent a valid arguement is,
Everyone who went to the football game cheered.
Maria cheered.
Maria went to the football game.
Solve for X
3-4x+5=2(8-2x)
Answers
Value of x will be 0.
What is equation?A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. Based on the degree, there are three different sorts of equations. Equations that are linear, quadratic, and cubic. In mathematics, an equation is a relationship between two expressions that is expressed as an equality on each side of the equal to sign. An equation would be 3y = 16, for instance.
Given Data
3-4x+5=2(8-2x)
3 - 4x + 5 = 16 -4x
3 + 5 -16 = -4x+4x
-8 = 0
Value of x will be 0.
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Kendall is investing in the stock market and has a maximum budget of $9,900 with which to purchase stock in two promising companies. Stock in the software company currently sells for $38 per share. Stock in the robotics company is currently trading at $49 per share.
Answers
The solution is 38x+49y<9,900 of investing in the stock market.
What is the Equation of inequality?The idea of inequality can be used to understand this query.
Let x represent the number of stocks purchased in software firms, and y represents the number of stocks purchased in robotics companies.
$38 was placed in one software company stock.
$ was placed in one robotics firm's stock.
Total investment in the equity of the software company = 38*x
Cost of robotics firm stock as a whole: 49*y
Therefore, the overall cost should be lower than 9,900.
As a result, the equation is
38x+49y<9,900.
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hurry brainiest! if right
Determine which set of side measurements could be used to form a right triangle.
square root of 2, square root of 3, 5
square root of 2, 3, square root of 11
7, 9, 11
5, 10, 14
which set of side measurements could be used to form a right triangle.
square root of 2, square root of 3, 5
square root of 2, 3, square root of 11
7, 9, 11
5, 10, 14
Answers
Answer:
Option 2
Step-by-step explanation:
The side lengths satisfy the Pythagorean theorem.
Answer:
square root of 2, 3, square root of 11
Step-by-step explanation:
