y = x ^ 2 + 2x - 24 i need to know the points at the x-intercept ( , ) and ( , ) points at the y intercept: ( , )and i’d it’s a min or max
Answers
Question : the function in the question is given below as
[tex]y=x^2+2x-24[/tex]Step 1: Calculate the x-intercept
The x-intercept for any curve is the value of the x coordinate of the point where the graph cuts the x-axis, or we can say that the x-intercept is the value of the x coordinate of a point where the value of the y coordinate is equal to zero.
Equating the equation above to zero (0)
[tex]\begin{gathered} y=x^2+2x-24 \\ x^2+2x-24=0 \end{gathered}[/tex]Solving using the quadratic formula below,
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]The general formula of a quadratic equation is given below
[tex]ax^2+bx+c=0[/tex]By comparing the coefficient, we will have the values to be
[tex]\begin{gathered} a=1 \\ b=2 \\ c=-24 \end{gathered}[/tex]Step 2: Substitute the values into the quadratic formula to get the values of x
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-2\pm\sqrt[]{2^2-(4\times1\times-24)}}{2\times1} \\ x=\frac{-2\pm\sqrt[]{4^{}+96}}{2} \\ x=\frac{-2\pm\sqrt[]{100}}{2} \\ x=\frac{-2\pm10}{2} \\ x=\frac{-2+10}{2}\text{ or }x=\frac{-2-10}{2} \\ x=\frac{8}{2}\text{ or x=}\frac{\text{-12}}{2} \\ x=4\text{ or x=-6} \end{gathered}[/tex]Hence,
The x-intercepts are
[tex](-6,0)\text{ and }(4,0)[/tex]x-intercepts are (-6,0) and (4,0)
Step 3: Calculate the coordinate of the y-intercept
The point where a line or curve crosses the y-axis of a graph.
In other words: find the value when x equals 0
[tex]\begin{gathered} y=x^2+2x-24 \\ y=(0)^2+2(0)-24 \\ y=0+0-24 \\ y=-24 \end{gathered}[/tex]Hence,
The y-intercept is
[tex](0,-24)[/tex]The y-intercept is (0,-24)
Below is the graph of the function on the question with its x-intercepts and y-intercepts
Step 4: Determine if the graph is minimum or maximum
The first step is to determine whether your equation gives a maximum or minimum. This can be done by looking at the x^2 term. If this term is positive, the vertex point will be a minimum; if it is negative, the vertex will be a maximum.
The coefficient of the x^2 term is a positive 1
Hence,
The equation
[tex]y=x^2+2x-24\text{ }[/tex]is a minimum quadratic graph
Related Questions
1. Solve for xWxk=for x
Answers
Answer:
x=W/k
Explanation:
Given the equation
[tex]W=xk[/tex]To solve for x, we divide both sides of the equation by k.
[tex]\begin{gathered} \frac{W}{k}=\frac{xk}{k} \\ x=\frac{W}{k} \end{gathered}[/tex]2xy + 4 = -2y - x, solve for x
Answers
Answer:
x = -2/y -1
Step-by-step explanation:
2xy + 4 = -2y -----> x = -2y -y
Step 1: Divide 2y to all sides. 2xy÷2y + 4÷2y= -2y÷2y. Since we are divinding y with y it cancels out, so it will be -2÷ 2 = -1
Step 2: x + 2y = -1
Step 3: Then subtract 2y and move it to the other side.
x = -2/y -1
Another way of explaining it:
2xy + 4 = -2y
Step 1: Divide 2 to all sides. 2xy÷2 +4÷2 = -2y÷2
Step 2: xy + 2 = -y
Step 3: Subtract the 2 and move it to the other side.
xy + 2 = -y
-2. -2
Step 4: xy = -2 -y
Step 5: Then we divide the y to all sides. xy÷y = -2÷y - y÷y
Step 6: xy÷y = -2 ÷ y -2 ÷y. We're trying to get x by itself.
Step 7: x = -2/y -1. Since we are divinding y with y it cancels out, so it will be
Answer: x = -2/y -1
(Any Further Questions or Confusion Please Let Me Know)
Three vertices of a parallelogram are shown in the figure below. Give the coordinates of the fourth vertex. (7,2) (-4,0) (-6, -7)
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ANSWER:
STEP-BY-STEP EXPLANATION:
[tex]undefined[/tex]a=1.9 in, A=46.5°, C=90°Solve the right triangle. Round side lengths one decimal place.
Answers
SOLUTION
Given the following
[tex]a=1.9in,A=46.5^0,C=90^0[/tex]Consider the image below
To solve the right triangle, we need to find the following:
[tex]b=\text{?,c}=\text{?and B=?}[/tex]To find B, we use the sum of angles in a triangle
hence
[tex]\begin{gathered} A^0+B^0+C^0=180^0^{} \\ \text{where A=46.5}^0,C=90^0 \end{gathered}[/tex]Substituting into the equation we have,
[tex]\begin{gathered} 46.5^0+B+90^0=180^0 \\ 136.5+B=180^0 \end{gathered}[/tex]Subtract 136.5 from both sides
[tex]\begin{gathered} 136.5+B-136.5^0=180^0-136.5^0 \\ \text{Then} \\ B=180^0-136.5 \\ B=43.5^0 \end{gathered}[/tex]hence
B = 43.5°
To find b, we use the trigonometry ratio for tangent
From the triangle above
[tex]\begin{gathered} \tan A=\frac{a}{b} \\ \text{Where A=46.5in, a=1.9in, b=?} \end{gathered}[/tex]Substituting into the equation
[tex]\begin{gathered} \tan 46.5=\frac{1.9}{b} \\ \text{Then } \\ b=\frac{1.9}{\tan46.5} \\ \text{Where tan46.5=1.0538} \end{gathered}[/tex]Then
[tex]b=1.8030[/tex]hence
b = 1.8in to 1 decima place
To find c, we also apply trigonometry ratio for sine of an angle
[tex]\begin{gathered} \text{sinA}=\frac{opposite}{\text{hypotenuse}} \\ \text{Where } \\ A=46.5^0,\text{ opposite =1.9in},\text{ hypotenuse =c} \end{gathered}[/tex]Substituting the values into the equation we have,
[tex]\begin{gathered} \sin 46.5=\frac{1.9}{c} \\ Multiply\text{ both sides by c, we have } \\ c\times\sin 46.5=\frac{1.9}{c}\times c \\ \text{Then } \\ c\times\sin 46.5=1.9 \end{gathered}[/tex]Divide both sides by 1.9, we have
[tex]\begin{gathered} c=\frac{1.9}{\sin 46.5}=\frac{1.9}{0.7254} \\ \text{Then} \\ c=2.6193 \end{gathered}[/tex]hence
c = 2.6 in
Therefore, to solve the right triangle, we have
Answer; B = 43.5°, b = 1.8in, c = 2.6 in
-9(x-4)=81 i know what im doing im jsur stuck
Answers
Solution:
The equation in the question is given below as
[tex]-9(x-4)=81[/tex]Step 1:
Expand the brackets in the qu
You need to open the brackets and this will give:-9x+36=81.
You need to bring 36 to the other side making it negative.That is,-9x=81-36
-9x=45
We then divide both side by -9 to leave x alone.This makes x=-5
HOPE I HELP!!
What is the equation, in slope-intercept form, of the line that passes throughthe point (8, -6) and is perpendicular to y = 4x+7?
Answers
From the problem, we are given a point (8, -6) and an equation y = 4x + 7
The equation we are to obtain is perpendicular to y = 4x + 7
In Mathematical terms, it means the slope of the given equation and the one we are to find follow the relation:
[tex]\begin{gathered} m_1\text{ = }\frac{-1}{m_2_{}_{}} \\ \text{where m}_{1\text{ }}\text{represents the slope of the first equation and }m_2\text{ represents the slope of the second equation} \end{gathered}[/tex]slope of the given equation = 4
[tex]\text{Slope of the required equation = }\frac{-1}{4}\text{ = -0.25}[/tex]The required equation passes through a point (8,-6)
The formula for obtaining the equation with a given slope that passes through a point is given as :
[tex]\text{ (y - y}_1)=m(x-x_1)[/tex]By substituting;
[tex]\begin{gathered} (y\text{ - (-6)) = -0.25(x - 8)} \\ y\text{ + 6 = -0.25x + 2} \\ y\text{ = -0.25x -4} \end{gathered}[/tex]The equation in slope-intercept form is y = -0.25x - 4
[First Person To Answer Will Get 5 Stars And Brainlyest] Help Please.
Answers
Distance is the total movement of an object without any regard to direction. Total distance jogged by Linsey is 420 yards.
What is distance?
Distance is the total movement of an object without any regard to direction
Given data
vertex 1 is at ( -4, - 1)
vertex 2 is at ( - 4, 5)
vertex 3 is at (2,5)
vertex 4 is at ( 2, -1 )
Lindseys jogs along the edge of the park in order from vertex 1 to the vertex 2 , vertex 2 to vertex 3 and vertex 3 to vertex 4 and then back to vertex 1. One unit in the coordinate grid is 20 yards.
Let us calculate distance vertex 1 and vertex 2of (-4,-1) and (-4,5)
x₁=-4,x₂=-4, y₂=5, y₁=-1
Distance=√(x₂-x₁)²+(y₂-y₁)²
Substitute the values x₁=-4,x₂=-4, y₂=5, y₁=-1 in distance formula
=√(-4+4)²+(5-(-1))²
=√6²
=6
Since 1 one unit on the coordinate gride equal 20 yd.
so 6×20=120 yards.
Now for four vertices we get 4×120=480 yards.
So total distance jogged by Linsey is 420 yards.
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sixyt students are competing in a video game challenge. if 2 students comete against each other in every round how many different combinations can be made for the first round of the challenge
Answers
Answer:
i believe its 30
Step-by-step explanation:
well i think you would divide sixty by 2 which is thirty.
IM SO SORRY IF IM WRONG- THIS IS JUST WHAT I THINK!
At the craft store, Elena bought a bag of purple and blue marbles. She received 19 purple marbles and 6 blue marbles. What percentage of the marbles were purple? were purple?
Answers
She received 19 purple and 6 blue marbles, so the total number of marbles is 19 + 6 = 25
Percentage of purple marbles = 100 * 19/25 = 1900/25 = 76%
Percentage of blue marbles = 100 * 6/25 = 600/25 = 24%
Answer:
Percentage of purple marbles = 76%
Percentage of blue marbles = 24%
2. (05.03 MC)In the figure below, AABC 2 ADEF. Point C is the point of intersection between AG and BF, while point E is the point of intersection between DG and BFДАBFProve AABC AGEC. (10 points)
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Prove that Tringle ABC is congruent to tringle GEC
ind the point at which the line f ( x ) = − 4 x − 1 intersects the line g ( x ) = − 2 x + 1
Answers
Answer:
(-1,3)
Step-by-step explanation:
Where the two lines intersect, they have equal values
-4x-1 = -2x + 1
-2 = 2x
x = -1
Now, you have 'x' ....use this value in either of the equations to find 'y'
-2 (-1) + 1 = y = 3
(-1,3)
4x-3
x=2
4(2)-3
The ____ property is used here.
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According to the commutative property, the numbers we use can be moved around or swapped around without changing the solution. For addition and multiplication, the principle is true, but not for division or subtraction.
4x-3
Is x=2
4(2)-3
This uses the ___ attribute?
Answer:
(5,-5) commutative property of subtraction property is used.
Example:
It can be commutative if you retain the negative with the 2 and the positive with the 5. Edited: Subtraction is not a commutative operation; for example, 5-2=3 and 2-5=-3. The order of addition or subtraction does not important, though, if you maintain the sign of the integer, as in +5-2=3 and -2+5=3, for example.
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Help me! i need this answer now i am so dead. if i get it worng please help pls
Answers
Answer:
x = 4.8
Step-by-step explanation:
Area = Length times width
12 = 2.5x Divide both sides by 2.5
4.8 = x
Mason was creating a sundae masterpiece by adding the following chips to his ice cream. He added 1/3 cup of dark chocolate chips, 1/4 cup of milk chocolate chips, 3/4 cup of peanut butter chips, and 1/2 cup of butterscotch chips. At the last minute, he removed all of the milk chocolate chips to save to eat later. Determine how many chips he put on his sundae. Express your answer as a fraction.
Answers
Mason added 19/12 cups of chips to his sundae.
How many chips he put on his sundae?We know that Mason has a sundae and he put:
1/3 cup of dark chocolate chips.1/4 cup of milk chocolate chips (latter are removed)3/4 cup of peanut butter chips 1/2 cup of butterscotch chipsTo get the total number of chips, we just need to add these fractions (except the one for the milk chocolate chips, as these are removed).
Then we will get:
Total = 1/3 + 3/4 + 1/2 = 4/12 + 9/12 + 6/12 = 19/12
Where we used the common denominator 12 to add the fractions.
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To solve the equation x/5= 30 you will ...O divide both side by 5. The solution is x=6O multiply both sides by 5. the solution is x=150O Add 5 to both sides. The solution is x=35O Subtract 5 from both sides. The solution is x=25
Answers
You have the equation:
[tex]\frac{x}{5}=30[/tex]To solve this equation you have to clear the variable x. You can clear the variable x, as follow:
You multiply both sides of the equation by 5.
[tex](5)\frac{x}{5}=30(5)[/tex]Then the solution is:
[tex]x=150[/tex]Find θ where θ = sin-1(-.5) where 0 < θ < 2π. Select all the correct choices. Select one or more: a. 11pi/6 b. pi/6 c. 5pi/6 d. 210 degrees e. 30 degrees
Answers
The value of inverse trigonometric function θ = sin-1(-.5) is 30°
What is an inverse trigonometric function?
The inverse trigonometric functions perform the opposite operation of the trigonometric functions such as sine, cosine, tangent, cosecant, secant, and cotangent. We know that trigonometric functions are especially applicable to the right angle triangle.
Here, the given inverse trigonometric function is θ = sin⁻¹(0.5)
Now solving the given inverse trigonometric function by consider 0.5 value in terms of sine that is :
0.5 = sine (30°)
Now, substituting back this value in place of 0.5 and solve for θ :
θ = sin⁻¹(0.5)
θ = sin⁻¹(sin(30°))
Now the inverse of sinθ is θ itself
θ = 30°
Therefore, The value of inverse trigonometric function θ = sin-1(-.5) is 30°.
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Given that (9,-8) is on the graph of f(x), findthe corresponding point for the functionf(x - 2).Enter the correct answer.0000 CDONEClear allDOO
Answers
(7,-8)
1) Considering that f(x-2) is a transformation of f(x). Precisely, a horizontal translation to the right.
2) So, we can write out the following:
[tex]\begin{gathered} f(x)=x \\ f(9)=-8 \\ \\ f(x-2)=x \\ f(9-2)=-8 \\ f(7)=-8 \end{gathered}[/tex]Note that a horizontal translation just "pushes to the right". So there was no vertical shift.
3) Hence, the answer is (7,-8)
Jumping makes a frog so tired, each successive jump is 1/3 the distance of the previous hump. If a frog jumps 24 cm on its first jump, how far will the frog travel after four jumps?
Answers
Answer:
35 5/9 cm total
Step-by-step explanation:
24 + 8 + 8/3 + 8 / 9 = 35 5/9 cm
Which expression is equivalent to 7a-8-12a +4?A.-gaB.31aC. -5a - 4D.19a + 12
Answers
Step 1
Rearrange the expression to bring like terms together.
[tex]\begin{gathered} 7a-8-12a+4 \\ 7a-12a\text{ -8+4} \end{gathered}[/tex]Step 2
Simplify to get the final answer
[tex]-5a-4[/tex]Hence the right answer is option C
If f (x) = 4x2 + 3x − 5, then the quantity f of the quantity x plus h end quantity minus f of x end quantity all over h is equal to which of the following? a 4 times the quantity x plus h end quantity squared plus 3 times the quantity x plus h end quantity minus 5 minus 4 times x squared plus 3 times x minus 5 all over h b 4 times the quantity x squared plus 2 times x times h plus h squared end quantity plus 3 times the quantity x plus h end quantity minus 5 minus the quantity 4 times x squared plus 3 times x minus 5 end quantity all over h c the quantity 4 times x plus 4 times h end quantity squared plus the quantity 3 times x plus 3 times h end quantity minus 5 minus the quantity 4 times x squared plus 3 times x minus 5 end quantity all over h d 4 times the quantity x plus h end quantity squared plus 3 times x minus 5 minus 4 times x squared minus 3 times x plus 5 all over h
Answers
The difference quotient of the function f(x) = 4x² + 3x - 5 is [f(x + h) - f(x)]/h = 8x + 4h + 3
How to evaluate the difference quotient?The function is given as
f(x) = 4x² + 3x - 5
Start by calculating the function f(x + h)
So, we have the following
f(x + h) = 4(x + h)² + 3(x + h) - 5
Expand
f(x + h) = 4(x² + 2xh + h²) + 3(x + h) - 5
Open the brackets
f(x + h) = 4x² + 8xh + 4h² + 3x + 3h - 5
The difference quotient is then calculated as
[f(x + h) - f(x)]/h
This gives
[f(x + h) - f(x)]/h = (4x² + 8xh + 4h² + 3x + 3h - 5 - 4x² - 3x + 5)/h
Evaluate the like terms
[f(x + h) - f(x)]/h = (8xh + 4h² + 3h)/h
Evaluate the quotients
[f(x + h) - f(x)]/h = 8x + 4h + 3
Hence, the value of [f(x + h) - f(x)]/h is 8x + 4h + 3
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Complete question
If f(x) = 4x² + 3x - 5, then [f(x + h) - f(x)]/h is equal to which of the following?
Function ggg can be thought of as a translated (shifted) version of f(x)=x^2f(x)=x
2
f, left parenthesis, x, right parenthesis, equals, x, squared.
A parabola labeled f has a vertex at the point 0, 0. A parabola labeled g has a vertex at the point negative 4, negative 5.
Write the equation for g(x)g(x
Answers
The equation for g(x) is g(x) = x²-3
When x=0, f(x)= 0 and so has a vertex at (0,0)
Given that g(x) is a shifter version of f(x) and has a vertex at (0,-3), g(x) must be shifted down the y axis such that g(x)= x2+c when x=0 and g(x)= -3 -3=0+c c=-3 when x=3.
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Question 23 Differentiate. f(x) = (5x - 5)(6x + 1) O f'(x) = 60x - 25 O f'(x) = 30x - 25 O f'(x) = 60x - 35 f'(x) = 60x - 12.5
Answers
We have to differentiate f(x).
We can do this as:
[tex]\begin{gathered} f(x)=(5x-5)(6x+1)=30x^2-30x+5x-5=30x^2-25x-5 \\ f\text{'}(x)=30\cdot(2x)-25\cdot(1)-0 \\ f\text{'}(x)=60x-25 \end{gathered}[/tex]The answer is f'(x)=60x-25.
Once again, you're trying to get out of the classroom. The distance to the door from your desk is d meters. Your first step is 1/6 that distance. Each successive step is 1/6 the previous distance. How far have you traveled? Express each result using exponetial notation for 8 steps, 12 steps, 20 steps, and n steps.
Answers
Given:
The distance to the door from your desk is d meters.
Your first step is 1/6 that distance =
[tex]\frac{1}{6}d[/tex]Each successive step is 1/6 the previous distance.
so, the second step =
[tex]\frac{1}{6}\cdot\frac{1}{6}d=(\frac{1}{6})^2d[/tex]The third step =
[tex]\frac{1}{6}\cdot(\frac{1}{6})^2d=(\frac{1}{6})^3d[/tex]And so on,
So, for the step number n, the formula will be :
[tex]=(\frac{1}{6})^n\cdot d[/tex]So, for 8 steps
You will have traveled =
[tex]=(\frac{1}{6})^8\cdot d[/tex]For 12 steps =
[tex]=(\frac{1}{6})^{12}\cdot d[/tex]For 20 steps =
[tex]=(\frac{1}{6})^{20}\cdot d[/tex]For n steps =
[tex]=(\frac{1}{6})^n\cdot d[/tex]
The graphs below have the same shape. What is the equation of the blue graph? Gox= ?
Answers
Here, we want to deduce the equation of the blue graph
From what we have, we can see that the image of the f(x) was moved 2 units to the right and 1 unit upwards
What this mean is that, we have 1 added to the y value and 2 added to the x value
So, the equation of the blue graph is
[tex]G(x)=(x+2)^2+1[/tex]A shipping center keeps track of the number of customers in each store at Lunch times the data shows the number of customers in the 15 different stores in the shopping center last su day.
Answers
A histogram is a representation that organizes a group of data points into specified ranges.
For the given data:
4, 18 , 20, 17, 16, 23, 19, 14, 8, 8, 6, 12, 20, 14, 18
What’s the correct answer answer asap for brainlist
Answers
Answer: C
Step-by-step explanation: A is definitely not correct. not b. not d
The money was distributing un equally. Because of the great depression, the lower classes made less money
Many delivery trucks feature a "How Am I Driving?” sticker on the rear bumper, along with a phone number. This sticker allows drivers to report erratic driving by the truck driver or offer a compliment if they like. A dispatcher at the trucking station accepts calls and records information from those who call the phone number. The dispatcher reports that in the past month, 218 calls were received. Of those calls, 178 reported negative driving behaviors by the truck drivers. How might this data-collection method produce bias in obtaining an estimate of all drivers who are satisfied with the company’s truck drivers?
This sample may lead to nonresponse bias because many drivers may not call the phone number.
This sample may lead to undercoverage bias because some drivers will be more likely to be included in the sample.
The sample may lead to response bias because some who call the phone number may not provide a truthful opinion.
This sample may lead to voluntary response bias because drivers can choose to call the phone number and register an opinion.
Answers
The way in which this data-collection method produce bias in obtaining an estimate of all drivers who are satisfied with the company’s truck drivers is that: D. This sample may lead to voluntary response bias because drivers can choose to call the phone number and register an opinion.
What is sampling bias?A sampling bias can be defined as a type of bias in which members of an intended population are selected in such a way that some members have a higher or lower sampling probability (chances) than the other members.
This ultimately implies that, a sampling bias would occur when members of an intended population are selected incorrectly and as such resulting in a sample that is not representative of the entire population.
Generally speaking, a voluntary response sample is a data-collection technique (method) that is always biased because it only include individuals who choose to volunteer, unlike a simple random sample.
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ARCHAEOLOGY A farm lane in Ohio crosses two long, straight earthen mounds that may have been built about 2000 years ago. The mounds are about 200 feet apart, and both form a 63° angle with the lane, as shown. Are the mounds parallel? How do you know?
Answers
Yes. Because Mound 1 and Mound 2 form a pair of corresponding angles with that red transversal line (lane). Corresponding angles are congruent and parallel to each other.
1) Since both mounds share the same measure of the angle, then we can say that those mounds are yes, parallel to the lane since they both corresponding angles, and corresponding angles are parallel and congruent to each other.
2) So the answer is :
Yes. Because each mound 1 and Mound 2 form a pair of corresponding angles with that red transversal line. Corresponding angles are congruent and parallel to each other.
Convert 120 inches to feet. There are 12 inches in a foot. O A. 1200 feet B. 1440 feet C. 20 feet O D. 10 feet
Answers
There are 12 inches in a foot.
To convert 120 inches to feet we can use the next proportion:
[tex]\frac{12\text{ inches}}{120\text{ inches}}=\frac{1\text{ foot}}{x\text{ feet}}[/tex]Solving for x:
x = 1*120/12
x = 10 feet
Find the distance between the two points in simplest radical form.
(6,9) (9,6)
Answers
Answer:
3√2
Step-by-step explanation:
[tex] \sqrt{ {(6 - 9)}^{2} + {(9 - 6)}^{2} } [/tex]
[tex] \sqrt{ {( - 3)}^{2} + {3}^{2} } [/tex]
[tex] \sqrt{9 + 9} = \sqrt{2 \times 9} = \sqrt{2} \sqrt{9} = 3 \sqrt{2} [/tex]