The answer is 9.5
You tube is awesome for explaining this
x³ multiplied by x²
plz help and show an explanation not just the answer.
Answer:
[tex]x^{5}[/tex]
Step-by-step explanation:
We simply add the exponents together. This depicts the exponent product rule, which states that when multiplying together two values with the same base (x) but different exponents, we can solve the answer by adding together the exponents with the base staying the same.
Explanation / Proof:
[tex]2^{2} * 2^{3} = 4 * 8 = 32\\\\2^{2} * 2^{3} = 2^{5} = 2*2*2*2*2 = 32[/tex]
As you can see, adding together the exponents will give the same answer. Therefore, the answer is [tex]x^{5}[/tex].
Aaron bought a new television that has a 92 in. 76 in. screen. It has a feature that splits the screen to allow him to watch 4 channels at once. What is the scale factor and size for each channel when this feature is turned on? (SHOW WORK)
Answer:
The scale factor is equal to 1/2
The dimensions of each channel when splits the screen is 46 in x 38 in
Step-by-step explanation:
we know that
The dimensions of the new television is 92 in x 76 in
Remember that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let
A1 -----> the area of the new television
A2 ----> the area of each channel when splits the screen
z-----> the scale factor
[tex]z^{2} =\frac{A2}{A1}[/tex]
we have that
The area of the new television is 4 times the area of each channel
[tex]A1=4A2[/tex]
[tex](A2/A1)=1/4[/tex]
[tex]z^{2} =\frac{1}{4}[/tex]
[tex]z=\frac{1}{2}[/tex] -----> the scale factor
so
When splits the screen, the dimension of each channel is equal to
92/2 in x 76/2 in
so
46 in x 38 in
Remember, if two figures are similar then the scale factor is equal to the ratio of their corresponding sides
Verify the value of the scale factor
92/46=1/2
or
76/38=1/2
Which point lies on a circle with a radius of 5 units and center at P(6, 1)?
A. Q(1, 11)
B. R(2, 4)
C. S(4,-4)
D. T(9,-2)
Answer:
The correct answer is R(2, 4)
Step-by-step explanation:
What is .5x5 equal???
Answer:
The answer is 25
Step-by-step explanation:
Marcel and Floyd are playing games at an arcade. Marcel has $8.25 and is only playing $0.25 games. Floyd has $9.75 and is only playing $0.75 games. Jorge wants to find the number of games after which Marcel and Floyd will have the same amount of money remaining. Jorge’s work is shown below.
Let x = the number of games played.
Jorge knows his answer is incorrect because it does not make sense to have a negative number of games. What is Jorge’s error?
A. The variable x should represent the amount of money left.
B. From Step 1 to Step 2, Jorge did not add 0.25x correctly to both sides.
C. The equation should have sums on both sides.
D. From Step 2 to Step 3, Jorge should have subtracted 0.50x from both sides.
Answer:
The mistake is that from Step 1 to Step 2, Jorge did not add 0.25 correctly to both sides.
Step-by-step explanation:
If Marcel has $8.25 and is only playing $0.25 games, then the equation will be given by: 8.25 - 0.25X.
If Floyd has $9.75 and is only playing $0.75 games, then the equation will be given by: 9.75 - 0.75X.
If we want to find the number of games after which Marcel and Floyd will have the same amount of money remaining, we need to solve the system of equations:
Equation: 8.25 - 0.25X = 9.75 - 0.75X
Step 1: -1.50 - 0.25X = - 0.75X
Step 2: -1.50 = - 0.50X
Step 3: x=3
The mistake is that from Step 1 to Step 2, Jorge did not add 0.25 correctly to both sides.
Answer: Option B
From Step 1 to Step 2, Jorge did not add 0.25x correctly to both sides.
Step-by-step explanation:
To solve this problem, let's consider the initial equation that Jorge had.
[tex]8.25-0.25x=9.75-0.75x[/tex]
Subtract 9.75 on both sides of equality
[tex]8.25-9.75-0.25x=9.75-9.75-0.75x[/tex]
[tex]-1.50-0.25x=-0.75x[/tex]
Add 0.25x on both sides of equality
[tex]-1.50-0.25x+0.25x=-0.75x+0.25x[/tex]
[tex]-1.50=-0.50x[/tex]
[tex]x=3[/tex]
You can see then that Jorge's error was adding [tex]-0.75x + 0.25x[/tex]
When this sum is correctly done, the result is [tex]-0.50x[/tex]
The answer is the option B.
to solve the system of equations below, grace isolated the variable y in the first equation and then substituted into the second equation. what was the resulting equation? 3y=12x x^2/4+y^2/9=1
Answer:
The resulting equation is
x^2/4+16x^2/9=1
Step-by-step explanation:
The given equations are:
3y=12x eq(1)
x^2/4+y^2/9=1 eq(2)
We need to isolate variable y in equation 1
Divide both sides of the equation with 3
3y/3 = 12x/3
y = 4x
Now, substitute the value of y=4x in second equation
x^2/4+y^2/9=1
x^2/4 + (4x)^2/9 = 1
The resulting equation is
x^2/4+16x^2/9=1
Answer:
[tex]\frac{x^2}{4}+\frac{(4x)^2}{9}=1[/tex]
Step-by-step explanation:
Given system of equations,
[tex]3y=12x-----(1)[/tex]
[tex]\frac{x^2}{4}+\frac{y^2}{9}=1----(2)[/tex]
As per statement,
Isolating the variable y in the first equation,
[tex]y=\frac{12}{3}x=4[/tex]
Now, substituting into the second equation,
[tex]\frac{x^2}{4}+\frac{(4x)^2}{9}=1[/tex]
Which is the resulting equation,
Simplifying the equation,
[tex]\frac{x^2}{4}+\frac{16x^2}{9}=1[/tex]
[tex]\frac{9x^2+64x^2}{36}=1[/tex]
[tex]73x^2=36[/tex]
what is the slope of the line graphed below? (-1,3) (-2,-1)
Answer:
m=4
Step-by-step explanation:
3-(-1)/-1-(-2)=3+1/-1+2=4/1
Answer:
4
Step-by-step explanation:
Slope formula:
↓
[tex]\frac{\huge Y_2-Y_1}{\huge X_2-X_1}=\frac{Rise}{run}[/tex]
[tex]Y_2=(-1)\\Y_1=3\\X_2=(-2)\\X_1=(-1)\\[/tex]
[tex]\frac{(-1)-3}{(-2)-(-1)}=\frac{-4}{-1}=4[/tex]
Therefore, the slope is 4.
4 is the correct answer.
I hope this helps you, and have a wonderful day!
an equation in slope-intersept form the lines that passes thought (-8,1) and is perpindicular to the y=2x-17.
Answer:
y = (-1/2)x -3
Step-by-step explanation:
We are given
y = 2x-17
which is in slope-intercept form: y = mx +b
Where m is the slope. so, m= 2
But this is perpendicular, When a line is perpendicular then the slope become -1/m so in our case the slope m will be = -1/2
Using the point(-8,1) we can find the b i.e the y intercept
We have x = -8, y =1 and m=-1/2
y = mx + b
1 = (-1/2)(-8) + b
1 = 4 + b
=> b = 1-4
b = -3
The equation of slope intercept form will be
y = mx + b
Putting value of m= -1/2 and b = -3
y = (-1/2)x -3
Find the nth term of this quadratic sequence:
4, 7, 12, 19, 28
Answer:
n² + 3
Step-by-step explanation:
It's a quadratic sequence, so it follows the form:
y = ax² + bx + c
We're given five points that satisfy the equation. (1, 4), (2, 7), (3, 12), (4, 19), and (5, 28). Picking any three points, we can form a system of equations.
If we pick (1, 4), (2, 7), and (4, 19):
4 = a(1)² + b(1) + c
7 = a(2)² + b(2) + c
19 = a(4)² + b(4) + c
4 = a + b + c
7 = 4a + 2b + c
19 = 16a + 4b + c
Through substitution, elimination, or trial and error, we can find a = 1, b = 0, and c = 3.
y = x² + 3
So the nth term of the sequence is n² + 3.
Answer:
a(n) = a(n-1) + (2n - 1)
Step-by-step explanation:
Start by analyzing the pattern:
7 is 3 more than 4;
12 is 5 more than 7;
19 is 7 more than 12, and so on.
Each step is an odd number and is 2 greater than the previous step.
a(2) = 7 = 4 + step = 4 + 3 = 7
a(3) = 12 = 7 + step = 7 + 5 = 12
a(4) = 12 + 7 = 19
a(5) = 19 + 9 = 28
and so on.
Looking at a(2), we see that the step is 2+1, or 3;
Looking at a(3), we see that the step is 2(3) - 1, or 5;
Looking at a(4), we see that the step is 2(4) - 1, or 7; and so on.
Looking at a(n), we see that the step is 2n - 1.
Thus, a(n) = a(n-1) + (2n - 1)
Determine the end behavior for function f(x)=-x^4+5x^3-3
Answer:
Step-by-step explanation:
The dominant term of this function is x^4. The graph of x^4 starts in Quadrant II and continues in Quadrant I.
If we have y = -x^4, the graph starts in Quadrant III and continues in Quadrant IV. This is the end behavior for f(x)=-x^4+5x^3-3.
A teacher wanted to buy a chair, a bookshelf, two tables and a desk. She spent $900 for all five items and the chair and the desk combined 70% of her total. If the bookshelf cost $50, how much did each of the tables cost?
Find the cost of the chair and desk by multiplying the total amount pent by the 70%
Chair and desk = 900 x 0.70 = $60
Subtract that cost from the total spent:
900 - 630 = $270 was spent on the other three items.
Subtract the cost of the bookshelf:
270 - 50 = 220
The two tables cost 220.
For the price of one table divide that cost by 2:
220/2 = 110
One table cost $110.
The cost of each table is $110.
Given that
There are five items i.e. chair, bookshelf, 2 tables, and a desk.
The total amount incurred for these 5 items should be $900.
And, the chair + desk = 70% of total.
The cost of the bookshelf is $50.
Since 70% of total = chair + desk
That means
Chair + desk = 0.70 of $900 = $630
So the other items cost should be
= $900 - $630
= $270
And, the cost of bookshelf is $50
So, the two tables cost should be
= $270 - $50
= $220
So for one it should be
= $220 ÷ 2
= $110
Therefore we can conclude that the cost of each table is $110.
Learn more about the cost here: brainly.com/question/5282141
Please Help I Will Offer 30!!!!
Answer:
Step-by-step explanation:
Compare y = (1/2)x - 3 and y = (-1/2)x - 3.
They have different slopes but the same y-intercept (0, -3). Eliminate the first answer choice.
They have different slopes. Eliminate the second answer choice.
Their graphs intersect, so they have a solution. Eliminate the third choice.
They have different slopes but the same intercept, so they have one solution. The fourth answer choice is the correct one.
Answer:
the fourth one is the corect one
Step-by-step explanation:
the fourth one is the corect one because i did the mathand i checked it twice and its right and also i asked my friend and he said it the fourth one
hope that helps you
Find the factored form of
-14a-a^2=0
Answer:
-a (14 +a) =0
Step-by-step explanation:
-14a-a^2=0
Factor out -a
-a (14 +a) =0
Using the zero product property
-a =0 14+a =0
a =0 a = -14
What is f[g(7)] for the following functions?
f(x) = 3x2 − 4
g(x) = 2x − 5
A.) f[g(7)] = 9
B.) f[g(7)] = 143
C.) f[g(7)] = 239
D.) f[g(7)] = 281
Answer:
C
Step-by-step explanation:
To evaluate f(g(7)), substitute x = 7 into g(x), then substitute the result into f(x)
g(7) = (2 × 7) - 5 = 14 - 5 = 9, then
f(9) = 3(9)² - 4 = 243 - 4 = 239 → C
Option C is correct.
Composite function :Given functions are, [tex]f(x)=3x^{2} -4,g(x)=2x-5[/tex]
We have to find [tex]f(g(7))[/tex].
[tex]g(7)=2*7-5=14-5=9[/tex]
So that, [tex]f(g(7))=f(9)[/tex]
[tex]f(9)=3*(9)^{2}-4\\ \\f(9)=243-4=239\\\\f(g(7))=f(9)=239[/tex]
Learn more about the composite function here:
https://brainly.com/question/10687170
I ONLY NEED THE 2nd ONE !!
Answer:
The length of the missing side of the triangle is represented by the equation:
(6a + 2b - 5) - (2a - 3b) - (a - 3)
= 6a + 2b - 5 - 2a + 3b - a + 3
= 3a + 5b - 2
Nina graphs the function y = ⌊x⌋ to learn the properties of the parent floor function. What is the value of y when x =5.7?
Answer:
5
Step-by-step explanation:
When you given input of "x" into a floor function y = ⌊x⌋ , it gives as output the "greatest integer less than or equal to x"
For example, if we were to given 1.4 as the input for floor function, it will return the greatest integer that is less than or equal to 1.4, so it would be 1.
So, if we put 5.7 into this function, the floor function would give "5" as the output.
Thus value of y would be 5
Answer:
5
Step-by-step explanation:
PLEASE HELP!!!
Point A, located at (-2, 4), is translated down 6 units. What are the coordinates of A'?
(-8, 4)
(-8, -2)
(-2, -2)
(-2, 4)
Point B, located at (-4, -7), is reflected over the y-axis. What are the coordinates of B'?
(-4, 7)
(4, -7)
(4, 7)
(-4, -7)
Answer for A. (-8,-2)
answer for B. (4,-7)
Compute the distance between the two points. (–3, 4) and (21, 11)
For this case we have that by definition, the distance between two points is given by:
[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]
We have the following points:
[tex](x_ {1}, y_ {1}): (- 3,4)\\(x_ {2}, y_ {2}) :( 21,11)[/tex]
We replace:
[tex]d = \sqrt {(21 - (- 3)) ^ 2+ (11-4) ^ 2}\\d = \sqrt {(21 + 3) ^ 2 + (11-4) ^ 2}\\d = \sqrt {(24) ^ 2 + (7) ^ 2}\\d = \sqrt {576 + 49}\\d = \sqrt {625}\\d = 25[/tex]
Thus, the distance between the two points is 25 units.
Answer:
25
Answer:
The distance is 25 units
Step-by-step explanation:
Points to remember
Distance formula
Length of a line segment with end points (x1, y1) and (x2, y2) is given by,
Distance = √[(x2 - x1)² + (y2 - y1)²]
To find the distance between given points
Here (x1, y1) = (-3, 4) and (x2, y2) = (21, 11)
Distance = √[(x2 - x1)² + (y2 - y1)²]
= √[(21 - -3)² + (11 - 4)²]
= √[(21 +3)² + (11 - 4)²]
= √[24² + 7²]
= √(576 + 49)
= √625
=25
Therefore the distance is 25 units
find the derivative in the form dy/dx
Answer:
dy/dx = [tex]\frac{1}{(4x^{3}-7)}*[\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4})}{(3x^{5}+1)}][/tex]
Step-by-step explanation:
* Lets revise some rules for the derivative
- The derivative of ㏑(f(x)) = 1/f(x) × f'(x)
- The derivative of u/v = (vu'-uv')/v²
- The derivative of the constant is 0
* Lets solve the problem
∵ y = ㏑[(4x³ - 7)/(3x^5 + 1)]
- Let u = 4x³ - 7 and v = 3x^5 + 1
∵ u = 4x³ - 7
∴ u' = 4(3)x^(3-1) - 0 = 12x²
∵ v = 3x^5 + 1
∴ v' = 3(5)x^(5-1) + 0 = 15x^4
∵ The derivative of u/v = (vu' - uv')/v²
∴ The derivative of u/v = [tex]\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4})}{(3x^{5}+1)^{2}}[/tex]
∵ The derivative of ㏑(f(x)) = 1/f(x) × f'(x)
∴ dy/dx = [tex]\frac{1}{\frac{(4x^{3}-7)}{(3x^{5}+1)}}*[\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4}}{(3x^{5}+1)^{2}}][/tex]
- Simplify by cancel bracket (3x^5 + 1)from the 1st fraction with the
same bracket in the 2nd fraction
∴ dy/dx = [tex]\frac{1}{(4x^{3}-7)}*[\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4})}{(3x^{5}+1)}][/tex]
Find the perimeter of the region that is NOT shaded.
39 ft
29 ft
58 ft
See the attached picture:
Write the point-slope form of an equation of the line through the points (-2, -3) and (-7, 4).
Answer:
y+3 = -7/5(x+2)
Step-by-step explanation:
First we need to find the slope
m = (y2-y1)/(x2-x1)
= (4--3)/(-7--2)
= (4+3)/(-7+2)
=7/-5
= -7/5
The point slope form is y-y1 = m(x-x1)
y--3 = -7/5(x--2)
y+3 = -7/5(x+2)
We could use the second set of points
y-4 = -7/5(x--7)
y-4 =-7/5(x+7)
At which value of x does the graph of the function F(x) have a vertical asymptote?
Answer:
x = -8 & x = 3
Step-by-step explanation:
Vertical asymptote occur when denominator is 0.
So to find the x-values, we need to middle term factor the denominator. Shown below:
[tex]x^2+5x-24\\=(x+8)(x-3)\\x=3, -8[/tex]
Thus, at x = 3 and at x = -8 -- there is vertical asymptote.
Which expressions are equivalent to the given expression? Check all that apply.
(–2.4a – 1.8b) – (–3.8a – 4.4b) + (2.0a + 3.0b)
A. 3.4b – 3.2a
B. 3.4a – 3.2b
C. 5.6b + 3.4a
D. 3.2b + 3.4a
E. 3.4a
Answer:
5.6b + 3.4a
Step-by-step explanation:
Simply evaluate be match each term with its corresponding variable, and watch out for where you have to distribute negatives, meaning that you have a couple of double negatives in there.
Double Negative = Positive
Answer:
it’s C and E
Step-by-step explanation:
X+3y=28 find the value of y when x equals 28
Answer:
y = 0Step-by-step explanation:
x + 3y = 28
Put x = 28 and solve for y:
28 + 3y = 28 subtract 28 from both sides
28 - 28 + 3y = 28 - 28
3y = 0 divide both sides by 3
3y : 3 = 0 : 3
y = 0
Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. Persons taking a 70-hour review course average a score of 785. Find a linear function which fits this data.
Answer:
y = 4.125x + 496.25
Step-by-step explanation:
Set the data up as points. Then deal with the points.
Givens
(30,620)
(70,785)
y2 = 785
y1 = 620
x2 = 70
x1 = 30
Formula
Slope = (y2 - y1) / (x2 - x1)
Solution
Slope = (785 - 620)/(70 - 30)
Slope = 165 / 40
Slope = 4.125
===================
Now you need the y intercept. Either one of the two given points will give you that.
y = 620
x = 30
m = 4.125
y = mx + b
620 = 4.125*30 + b
620 = 123.75 + b
620 - 123.75 + b
b = 496.25
the linear function that describes the relationship between study hours and exam scores is:
y = 4.125x + 496.25
To find a linear function that fits the data provided, we'll use the points (30, 620) and (70, 785), which represent the number of hours spent studying and the corresponding exam scores. The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
First, we calculate the slope (m):
m = (y2 - y1) / (x2 - x1) = (785 - 620) / (70 - 30) = 165 / 40 = 4.125
Next, we use one of the points to solve for b (y-intercept). Let's use the point (30, 620):
620 = 4.125(30) + b
b = 620 - (4.125 × 30) = 620 - 123.75 = 496.25
So the linear function that describes the relationship between study hours and exam scores is:
y = 4.125x + 496.25
Triangle QRS is dilated according to the rule DO,2 (x,y).
What is true about the image △Q'R'S'? Check all that apply.
DO,2 (x,y) = (2x, 2y)
Side Q'S' lies on a line with a slope of -1.
QR is longer than Q'R'.
The vertices of the image are closer to the origin than those of the pre-image.
The distance from Q' to the origin is twice the distance from Q to the origin.
Answer:
True options:
[tex]D_{O,2} (x,y) = (2x, 2y)[/tex]
Side Q'S' lies on a line with a slope of -1.
The distance from Q' to the origin is twice the distance from Q to the origin.
Step-by-step explanation:
Triangle QRS is dilated according to the rule [tex]D_{O,2} (x,y).[/tex] This dilation has the rule
[tex](x,y)\rightarrow (2x,2y)[/tex]
So,
[tex]S(-1,1)\rightarrow S'(-2,2)\\ \\Q(-3,3)\rightarrow Q'(-6,6)\\ \\R(2,4)\rightarrow R'(4,8)[/tex]
True options:
[tex]D_{O,2} (x,y) = (2x, 2y)[/tex]
Side Q'S' lies on a line with a slope of -1.
The distance from Q' to the origin is twice the distance from Q to the origin.
False options:
QR is longer than Q'R', because QR is twice shorter than Q'R'.
The vertices of the image are closer to the origin than those of the pre-image, because the vertices of the per-image are closer to the origin than those of the image (see attached diagram).
Answer:
1, 2, 5 on Ed
Step-by-step explanation:
Which are possible first steps in solving the equation 4x + 3 = 18?
Answer:
C D and E
Step-by-step explanation:
The only one you probably can never do is B. It get's you no where. The way A is written, it is not much help to write 18 in base 2. So A and B both won't work. The common logs and the natural logs will both work
Log(4^(x + 3)) = Log(18)
(x + 3) Log(4) = log (18)
(x + 3) * 0.6021 = 1.2553
x + 3 = 1.2553/0.6021
x + 3 = 2.08496
Now all you need do is subtract 3 from both sides. The natural logs will give you the same answer.
You could take base-4 logs of both sides and it is a possible first step, but d and e are much more efficient. You have to change both sides to base 4 before you can proceed. This one is kind of iffy. It does say possible first steps.
Answer:
C.Take the base-4 logarithm of each side.
D.Take the natural logarithm of each side.
E. Take the common logarithm of each side.
Step-by-step explanation:
PLZZZZ GEOMETRY HELP solve for HI
Answer:
2 units
Step-by-step explanation:
ok, so, the line below says HJ is (x+1) units long. therefore:
2x-16+8 = x+1
now, let's isolate the variable.
2x-x = 1+16-8
x = 9
since we now defined variable x, we can add it to the equation that determines the length of HI.
2x-16
2(9)-16
18-16
2
the length of line segment HI is 2 units
hope this helped!
HI + IJ = HJ
With this knowledge you can from an equation like so...
2x - 16 + 8 = x + 1
Now combine like terms and solve for x
2x + (- 8 + 8) = x + 1 + 8
2x = x + 9
2x - x = x - x + 9
x = 9
To find HI plug 9 in for x and simplify
2(9) - 16
18 - 16
2
The length of HI is 2!!!
Hope this helped!
~Just a girl in love with Shawn Mendes
What is 7% of £14.50? Please show me the working outs in a simplest way possible. Thank you
[tex]\text{Hey there!}[/tex]
[tex]\text{The word \bf{of}}\text{ means multiply in mathematical terms.}[/tex]
[tex]\text{Percentages (\%) usually run out of 100}[/tex]
[tex]\text{First, put the numbers set to multiply from each other.}[/tex]
[tex]\text{7\%}\times\text{14.50}[/tex]
[tex]\text{(You can convert the percentage into a decimal (if you want but it is mandatory)}[/tex] [tex]\leftarrow\text{in order for you to convert them into a decimal you have to divide 7\%}[/tex] [tex]\text{from 100}[/tex]
[tex]\dfrac{7\%}{100}[/tex]
[tex]\dfrac{7\%}{100}=0.07[/tex]
[tex]\text{Next, solve for your answer.}[/tex]
[tex]\text{0.07}\times\text{14.50 = ?}[/tex]
[tex]\text{Solve the one above, and you SHOULD get your result!}[/tex]
[tex]\boxed{\boxed{\bf{Thus,\ your\ answer\ is: 1.015}}}\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
what the length of the hypotenuse of an isosceles right triangle whose legs are 1 unit in length.
Answer: ≈ 1.414
Step-by-step explanation:
You can use the pythagorean theorem, a^2 + b^2 = c^2
a^2 and b^2 are the legs and c^2 is the hypotenuse.
1^2 + 1^2 = c^2
1 + 1 = c^2
2 = c^2
√ 2 = √ c^2
c = ≈ 1.414