Answer:
-2 + i
Step-by-step explanation:
The midpoint is the average:
[ (-7 + 4i) + (3 − 2i) ] / 2
Combine like terms:
(-4 + 2i) / 2
Divide:
-2 + i
Graph the given relation or equation and find the domain and range. Then determine whether the relation or equation is a function. (3.9, 5.9), (–1.1, 5.9), (–4.1, 3.9), (–4.1, –2.1)
Answer:
See attachment
The relation is not a function.
The domain is [-4.1,3.9]
The range is [-2.1,5.9]
Step-by-step explanation:
The given relation has ordered pairs (3.9, 5.9), (–1.1, 5.9), (–4.1, 3.9), (–4.1, –2.1)
It is implied in the ordered pairs that the relation is a continuous function.
We plot the points and connect them with straight lines as shown in the attachment.
The relation is not a function because its graph fails the vertical line test.
In other words, we have an x-coordinate that corresponds to more than one y-coordinate.
-4.1 corresponding to 3.9 and -2.1 at the same time.
The domain is the set of values for which the function is defined.
The domain is [-4.1,3.9]
The range refers to the corresponding y-values for which the function exists.
The range is [-2.1,5.9]
If seamstress is paid 7.85 per hour and works 18.75 hours in one week, how much is she paid in one week?
[tex](12 {x}^{2} + 13y)(4x \times 2xy)[/tex]
need help solving? can anyone help
Answer:
[tex]96x^4y+104x^2y^2[/tex]
is the simplified form of
your given problem:
[tex](12x^2+13y)(4x \times 2xy)[/tex].
Step-by-step explanation:
So the given problem is this:
[tex](12x^2+13y)(4x \times 2xy)[/tex]
I'm going to do the multiplication in the second ( ).
Nothing can be done in the first ( ) because the operation is addition and those two terms aren't like terms.
[tex](12x^2+13y)(8x^2y)[/tex]
I got x^2 because of x(x) part.
Now we get to distribute 8x^2y to both terms in the ( ).
[tex]12x^2 \cdot 8x^2y+13y \cdot 8x^2y[/tex]
Adding exponents on bases that have the same variable:
[tex]96x^4y+104x^2y^2[/tex]
The figure below is a right rectangular prism. which expression represents the volume of the prism?
Answer: The expression (equation/formula) for the volume of a:
" right rectangular prism " ; is represented by:
____________________________________________________
→ " V = L * w * h " ;
____________________________________________________
in which: all the dimensions are in the same "units of measurement" (or converted to the same "units of measurement" ;
and in which:
" V " is the "volume" of the right rectangular prism; in the "cubic units" ; or written as: "units³ " ; or, [insert the particular units used}^ ³ " ;
→ that is, [units] raised to the "3rd [third] power" ; assuming these units are the same same "fundamental units of measurement" as the "other 2 (two) values in the expression".
If we are given no specific units of measurement whatsoever, then we use the generic term, "units" as the "units of measurement" ; and we express the "volume; "V" ; of a "right rectangular prism" as: " units ³ " ; or "cubic units" ;
in our answer— if we are asked to solve for the:
"volume; "V"; of a "right rectangular prism" ;
_________________________________________________
and in which:
"L" represents the "length" of a "right rectangular prism" ;
"w" represents the "width" of a "right rectangular prism" ;
"h" represents the "height" of a "right rectangular prism" .
_________________________________________________
To given an example:
Say we have a "right rectangular prism" ; with the given measurements:
width , "w" : w = 2 units;
length, "L" : L = 3 units ;
height, "h" : h = 8 units.
_________________________________________________
We are asked to "find the volume " ; of this "right recentangular prism" .
The formula for the volume; "V" ; of this "right rectangular prism" ;
is:
_________________________________________________
→ Volume = Length * width * height ;
that is:
→ V = L * w * h ;
Solve for the volume; "V" .
_________________________________________________
→ V = L * w * h ; Now plug in the values given:
→ V = (3 units) * (2 units) * (8 units) ;
= 3 * 2 * 8 * (units) * (units) * (units) ;
= 3 * 2 * 8 * units ³ ;
= 48 units ³ .
_________________________________________________
Hope this answer— and explanation—is helpful to you!
Wishing you the best in your academic pursuits
— and within the "Brainly" community!
_________________________________________________
Answer: A
Step-by-step explanation:
I filled 6/9 of the prescriptions for the pharmacist to review. The pharmacist returns and reviews 2/3 of the prescriptions. How many more prescriptions does the pharmacist have left to review that I filled?
[tex]\left(1-\dfrac{2}{3}\right)\cdot\dfrac{6}{9}=\dfrac{1}{3}\cdot \dfrac{2}{3}=\dfrac{2}{9}[/tex]
The pharmacist has 2 more prescriptions left to review that you filled.
To find out how many prescriptions the pharmacist has left to review, we can follow these steps:
1. Calculate the total number of prescriptions filled by you:
[tex]\[ \text{Total filled prescriptions} = \frac{6}{9} \times \text{Total prescriptions} \][/tex]
2. Calculate the number of prescriptions reviewed by the pharmacist:
[tex]\[ \text{Prescriptions reviewed by pharmacist} = \frac{2}{3} \times \text{Total filled prescriptions} \][/tex]
3. Calculate the number of prescriptions left for the pharmacist to review:
[tex]\[ \text{Prescriptions left to review} = \text{Total filled prescriptions} - \text{Prescriptions reviewed by pharmacist} \][/tex]
Let's put the numbers into these equations. Assuming there were initially 9 prescriptions:
1. Total filled prescriptions:
[tex]\[ \text{Total filled prescriptions} = \frac{6}{9} \times 9 = 6 \][/tex]
2. Prescriptions reviewed by pharmacist:
[tex]\[ \text{Prescriptions reviewed by pharmacist} = \frac{2}{3} \times 6 = 4 \][/tex]
3. Prescriptions left to review:
[tex]\[ \text{Prescriptions left to review} = 6 - 4 = 2 \][/tex]
What is the vertex of the parabola? Assume p > 0.
Final answer:
The vertex of a parabola in the form y = ax + bx² can be found using the vertex formula x = -b/(2a). The vertex represents the highest or lowest point on the graph depending on whether a is positive or negative.
Explanation:
The vertex of a parabola in the form y = ax + bx² can be found using the vertex formula. The vertex formula is x = -b/(2a), which gives the x-coordinate of the vertex. To find the y-coordinate of the vertex, substitute the x-coordinate into the equation y = ax + bx². The vertex of the parabola represents the highest or lowest point on the graph, depending on whether the coefficient a is positive or negative.
One third of the sum of 5 times a number and 3 is less than one fourth the sum of six times that number and 5
Answer:
x < 3/2.
Step-by-step explanation:
1/3( 5x + 3) < 1/4(6x + 5)
5/3 x + 1 < 3/2x + 5/4
5/3 x - 3/2 x < 5/4 - 1
1/6 x < 1/4
x < 6/4
x < 3/2.
The value of the variable x is less than 3/2.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Let x be the number.
One-third of the sum of 5 times a number and 3 is less than one-fourth the sum of six times that number and 5. Then the equation will be
(1/3)(5x + 3) < (1/4)(6x + 5)
Simplify the inequality, then the value of x will be
20x + 12 < 18x + 15
2x < 3
x < 3/2
The value of the variable x is less than 3/2.
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Factor 3h2 – 11h - 42
A. (3h – 7)(h + 6)
B. 3(h + 7)(h - 6)
C. (34 – 6)(h + 7)
D. (3h + 7)(h – 6)
Answer:
The correct answer is option D. (3h + 7)(h – 6)
Step-by-step explanation:
It is given a quadratic function ,
3h² - 11h - 42
To find the factors of given function
3h² - 11h - 42 = 3h² - 18h + 7h - 42
= 3h(h -6) + 7(h - 6)
=(h - 6)(3h + 7)
= (3h + 7)(h – 6)
The correct answer is option D. (3h + 7)(h – 6)
Solve for x
X^2+6x+9=20
Answer:
x = 1.47 or x = -7.47
Step-by-step explanation:
x²+6x+9=20
This is a quadratic equation
x²+6x+9-20=0
x²+6x-11=0
Step 1 : Write the quadratic formula
x = -b±√b²-4(a)(c)
2a
Step 2 : Substitute values in the formula
a = 1
b = 6
c = -11
x = -6±√6²-4(1)(-11)
2(1)
x = -6±√80
2
x = -3 + 2√5 or x = -3 - 2√5
x = 1.47 or x = -7.47
!!
Answer:
x=1.472 or x=-7.472
Step-by-step explanation:
Lets begin by rearranging the equation into the format ax²+bx+c=0
The equation will be:
x²+6x+9-20=0
x²+6x-11=0
We shall use the quadratic formula to solve the equation.
x=[-b±√(b²-4ac)]/2a
=[-6±√(6²-4×1×-11)]/2
=[-6±√80]/2
=[-6±8.944]2
x= Either (-6+8.944)/2 or x= (-6-8.944)/2
Solving for x in each case gives:
x=1.472 or x=-7.472
Which sentence demonstrates the multiplicative identity?
1/2 • 2= 1
1/2• 1= 1/2
1/2 + 0 = 1/2
Answer:
1/2 • 1 = 1/2
Step-by-step explanation:
It shows that anything multiplied by 1 is itself.
Answer:
1/2· 1= 1/2
Step-by-step explanation:
When multiplying by 1, you will get the same number.
The Rangers won 5 of their first 8 games. At this rate,how many games should the Rangers win out of 56 games? F. 28 games. G. 32 games. H. 35 games. I. 37 games.
Answer: H. 35 games
Step-by-step explanation: Set up a proportion.
5/8 = X/56
Cross multiply.
5 x 56 = 280
8 x X = 8x
The cross multiplied equation will be 280=8x.
Divide by 8 in order to isolate x.
x=35
They will win 35 games.
Answer:
The answer is H. 35 games
If a triangle has one angle measuring 40 degrees and a second angle measuring 100 degrees, what is the measurement of the third angle
A. 80
B.40
C.140
D.120
Answer:
B. 40
Step-by-step explanation:
All triangle angles equal 180
100+40=140
180-140=40
B. 40 is the answer.
About what percentage of Guadalupe's payments so far have gone to paying
interest?
Answer: C. 96% -------- APEX :D
find the length of wire required to fence a rectangle field with three round, whose length and breadth are 150 m and 80m respectively
Answer:
1380 meters
Step-by-step explanation:
perimeter of a rectangle :2(l+b)
2(150 +80)
2(230)
460 meters of wire for one round
for three rounds :3×460=
1380 meters
Which equation represents a line that passes through (-2, 4) and has a slope of 1/2?
Answer:
[tex]\large\boxed{y-4=\dfrac{1}{2}(x+2)\text{- point-slope form}}\\\boxed{y=\dfrac{1}{2}x+5\text{- slope-intercept form}}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
We have the slope [tex]m=\dfrac{1}{2}[/tex] and the point [tex](-2, 4)[/tex].
Substitute:
[tex]y-4=\dfrac{1}{2}(x-(-2))[/tex]
[tex]y-4=\dfrac{1}{2}(x+2)[/tex] - point-slope form
Convert to the slope-intercept form (y = mx + b):
[tex]y-4=\dfrac{1}{2}(x+2)[/tex] use the distributive property
[tex]y-4=\dfrac{1}{2}x+1[/tex] add 4 to both sides
[tex]y=\dfrac{1}{2}x+5[/tex] - slope-intercept form
suppose a figure is located in Quadrant l. which of the following sequences will result in an image that is located in Quadrant lll?
Answer:
Step-by-step explanation:
A will.
Suppose the object is placed on (5,4)
If you rotate it 180o counterclockwise, the point will become (-5,-4) (both x and y will change signs.)
Moving one unit down will still leave you in quadrant III.
If you start in another quadrant, this answer will not be correct. If the point started out in quadrant 2, rotating it 180o counterclockwise will put you in quad 4. For example
Object Start: (-2,3) Starts in quad 2
Image found: (- -2, - 3) = (2, - 3) which is in quad 4.
The graph shows Melissa's heart rate in beats per minute be) during the tirst few minutes other cool down after
jogging
Melissa's Heart Rate
Heart Rate -
Answer:
The domain is {1,2,3,4,5}
The range is {150,135,120,105,90}
Step-by-step explanation:
Domain is the set of x-values (x axis) and Range is the set of y-values (y axis).
Now if you look at the relation (points given), you can see the 5 points corresponds to 1,2,3,4, adn 5 in the x axis (minutes). So this is the domain - 1,2,3,4,5.
If we look at the y-axis (Heart Rate) , the values corresponding to 1,2,3,4,and 5 are 150, 135, 120, 105, and 90. These are the range.
Hence the last choice is the correct answer.
Answer: Domain = {1,2,3,4,5}
Range = {150,135, 120,105, 90}
Step-by-step explanation:
We know that,
Domain : Set of all input values .
Range : Set of output values.
In a graph, x values are the input values and y values are output values.
Given : The graph shows Melissa's heart rate in beats per minute be) during the first few minutes other cool down after jogging .
In the graph, number of minutes are shown by x-values and heart rate are shown by y-values.
Thus from graph, Domain = {1,2,3,4,5}
Range = {150,135, 120,105, 90}
A farmer feeds his cows 200 pounds of feed each day and has 700 pounds of feed in his barn. Another farmer feeds his cows 350 lbs of feed each day and has 1000 lbs of feed in his barn. In how many days will the two farmers have the same amount of feed left?
Answer:
The farmers will have the same amount of feed (300 lbs) in 3 days
Step-by-step explanation:
After dividing the total amounts of feed by the daily feed amounts, it’s found that the two farmers will have the same amount of feed left after approximately 3.5 days.
Explanation:To solve this problem, you need to find out how many days it takes for both farmers to run out of feed. For the first farmer, divide the total amount of feed (700 pounds) by the amount he uses each day (200 pounds). This comes to 3.5 days. For the second farmer, divide his total feed (1000 pounds) by the amount he uses each day (350 pounds), which comes to approximately 2.857 days.
Since we want to know when they will have the same amount of feed left, we look for the higher number, because the first farmer will still have feed left when the second farmer runs out. Therefore, the two farmers will have the same amount of feed left after around 3.5 days.
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What is the solution to the system of equations? {x=5 y=2x−1} (5, 9) (9, 5) (5, 11) (11, 5)
Answer:
(5, 9)
Step-by-step explanation:
Given the 2 equations
x = 5 → (1)
y = 2x - 1 → (2)
x = 5 is the value of the x- coordinate.
Substitute x = 5 into (2) for the corresponding value of y
y = (2 × 5) - 1 = 10 - 1 = 9
Solution is (5, 9 )
What is the slope of the line?
y + 1 = 3 (x - 4)
A. 1/3
B. -4/3
C. -3/4
D. 3
Answer:
D. 3
Step-by-step explanation:
In the Point-Slope Formula, y - y₁ = m(x - x₁), m represents the rate of change [slope], which in this case is 3.
I am joyous to assist you anytime.
The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
The slope of the line y + 1 = 3 (x - 4) is 3.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The equation of a line y + 1 = 3 (x - 4)
y + 1 = 3 (x - 4)
Subtract 1 on both sides.
y = 3(x - 4) - 1
y = 3x - 12 -1
y = 3x - 13
This is in the form of y = mx + c
Now,
Slope = m
m = 3
Thus,
The slope of the line y + 1 = 3 (x - 4) is 3.
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- the following functions.
f = {(-4,1),(5, 1), (1, -1)}
and
8 = {(5, 1), (1,4)}
2: Find (f + g)(1).
Answer:
(f+g)(1)
equals
3
Step-by-step explanation:
(f+g)(1) is f(1)+g(1).
f(1) means what y corresponds to x=1 so f(1)=-1.
g(1) means what y corresponds to x=1 so g(1)=4.
So (f+g)(1)=f(1)+g(1)=-1+4=3.
If two cylinder are similar and the ratio between the lengths of their edges is 4;3 what is the ratio of their volumes
Answer:
64 : 27
Step-by-step explanation:
Given 2 similar figures with
ratio of lengths = a : b, then
ratio of volumes = a³ : b³
For 2 cylinders with ratio of lengths = 4 : 3, then
ratio of volumes = 4³ : 3³ = 64 : 27
Answer:
Its 64:27
Step-by-step explanation:
what is 144^1/2=12 written in logarithmic form
Answer:
[tex]\log_{144}(12)=\frac{1}{2}[/tex]
Step-by-step explanation:
First step identify the base. The base is 144.
The exponent is the logarithm.
The number not mentioned is the one that goes inside.
In other words [tex]a^x=b[/tex] is equivalent to [tex]log_a(b)=x[/tex]
There are some restrictions on what a and b can be.
You read [tex]log_a(b)=x[/tex] as log base a of b equals x
x is the exponent
a is the base
So we have log base 144 of 12 equals 1/2
[tex]\log_{144}(12)=\frac{1}{2}[/tex]
which of the following is an equation of the line passing through the points (-1, 4) and (1, 2)?.
Answer:
y-4 =-1(x+1) point slope form
y-2 = -1(x-1)
y = -x +3 slope intercept form
Step-by-step explanation:
We have 2 points, we can find the slope
m = (y2-y1)/(x2-x1)
= (2-4)/(1--1)
(2-4)/(1+1)
-2/2
=-1
The slope is -1
Then we can use point slope form to find an equation
y-y1 =m(x-x1)
y-4 = -1(x--1)
y-4 =-1(x+1) point slope form
Using the other point
y-2 = -1(x-1)
Distribute the -1
y-2 = -1x +1
Add 2 to each side
y-2+2 = -x+1+2
y = -x +3 slope intercept form
The time it takes to read a book depends on the number of pages in the book
The situation "The time it takes to read a book depends on the number of pages in the book" in function notation is: A. Time(pages).
In Mathematics, a function is typically used in mathematics for uniquely mapping an input variable (domain or independent value) to an output variable (range or dependent value).
This ultimately implies that, an independent value represents the value on the x-axis of a cartesian coordinate while a dependent value represents the value on the y-axis of a cartesian coordinate.
In this context, we can logically deduce that time is a function of the number of pages, so it should be written in function notation as follows:
Time(pages).
Complete Question:
Which of the following shows the situation below in function notation?
The time it takes to read a book depends on the number of
pages in the book.
A. Time(pages)
B. Book(pages)
C.Pages(time)
D. Book(time)
Which three pairs of measurements are possible side length for the triangle?
Answer:
A, B, E, F
Step-by-step explanation:
In a 30-60-90 triangle, the hypotenuse is twice the length of the short leg.
That makes choice E possible.
In a 30-60-90 triangle, the long leg is sqrt(3) times the length of the short leg.
That makes choices A, B, and F possible.
Answer:
First option.
Option 5.
Option 6.
Step-by-step explanation:
The formula for a 30-60-90 triangle is this:
1) Side opposite to 30 will be value [tex]a[/tex].
2) Side opposite to 60 will be value [tex]a\sqrt{3}[/tex].
3) Hypotenuse will be [tex]2a[/tex].
So let's look and see:
First option: [tex]AB=4[/tex] and [tex]BC=4\sqrt{3}[/tex]
AB is opposite of the angle with 30 degree measurement.
BC is opposite of the angle with 60 degree measurement.
So [tex]a=4[/tex] here.
So the side opposite of 60 using the formula should be [tex]4 \sqrt{3}[/tex] which it is here.
So first option looks good.
Second option: [tex]BC=2\sqrt{3}[/tex] and [tex]AC=2[/tex].
We aren't given the side opposite to 30.
AC is the hypotenuse so 2a=2 which means the side opposite to 30 is a=2/2=1.
This means using the formula that the side opposite to 60 will be [tex]1\sqrt{3}=\sqrt{3}[/tex] but we don't have that.
So not option 2.
Third option: [tex]AB=3[/tex] and [tex]AC=3\sqrt{3}[/tex]
AB is the side opposite of 30, so we have [tex]a=3[/tex]
AC is the hypotenuse so that side should be [tex]2a=6[/tex] and it isn't.
Option 3 is not working.
Fourth option: [tex]BC=10[/tex] and [tex]AC=4\sqrt{3}[/tex]
So we have that [tex]2a=4\sqrt{3}[/tex] which means [tex]a=2\sqrt{3}[/tex] and so [tex]a\sqrt{3}=2\sqrt{3}\sqrt{3}=2(3)=6[/tex] but that is a contradiction because we have this value should be 10.
Not option 4.
Option 5: [tex]AB=7[/tex] and [tex]AC=14[/tex]
So we have [tex]a=7[/tex] and [tex]2a=14[/tex] so this looks good.
Option 6: [tex]AB=11[/tex] and [tex]BC=11\sqrt{3}[/tex]
[tex]a=11[/tex] so [tex]a\sqrt{3}=11\sqrt{3}[/tex] which is what we have.
Option 6 works.
help please also thank you so much if you do
Answer:
Step-by-step explanation:
100 cm = 1 meter
200 cm = 2 meters
100 cm = 1 meter
150 cm = 150 / 100 = 1.5 meters.
1 meter = 100 cm
6.5 meters = 6.5 * 100 = 6500 cm
1 km = 1000 meters.
5 km = 5 * 1000 meters = 5000 meters.
1 meter = 100 cm
1.68 m = 100 * 1.68
1.68 m = 168 cm
1 km = 1000 meters.
8.25 km = 8.25 * 1000 m = 8250 meters.
PLEASE HELP AGAIN WILL MARK BRAINLEST !!!!!
Answer:
3
Step-by-step explanation:
g(-1) means what is g(x) when x=-1.
So find -1 under the column labeled x and then scroll directly to the right of that and you should see what g(-1). It is 3
Here are my examples:
g(-8)=6
g(-5)=-2
g(-1)=3
g(0)=-5
Add the following lengths: 4'9" + 7"
Answer:
5'4"
Step-by-step explanation:
In terms of height, the apostrophe ( ' ) stands for feet and the quotation mark ( " ) stands for inches.
Your first term includes 4 feet and 9 inches. There are 12 inches in a foot, so we can simplify this as being 57 (48+9) inches.
Your second term includes 7 inches.
Add your two terms (57 and 7) together, and you have 64 inches.
Again, there are 12 inches in a foot, so to convert 64 inches to feet, count how many times you can put 12 into 64 without surpassing 64.
12 / 24 / 36 / 48 / 60
This will result in 5 times, so you have 5 feet and 4 inches left over.
In the figure, a square is inside another bigger square.
If a = 4 units and b = 3 units, the length of the diagonal of the outside square rounded to the nearest tenth is _____
units and the length of the diagonal of the inside square rounded to the nearest tenth is _____ units.
Answer:
Part 1) The length of the diagonal of the outside square is 9.9 units
Part 2) The length of the diagonal of the inside square is 7.1 units
Step-by-step explanation:
step 1
Find the length of the outside square
Let
x -----> the length of the outside square
c ----> the length of the inside square
we know that
[tex]x=a+b=4+3=7\ units[/tex]
step 2
Find the length of the inside square
Applying the Pythagoras Theorem
[tex]c^{2}= a^{2}+b^{2}[/tex]
substitute
[tex]c^{2}= 4^{2}+3^{2}[/tex]
[tex]c^{2}=25[/tex]
[tex]c=5\ units[/tex]
step 3
Find the length of the diagonal of the outside square
To find the diagonal Apply the Pythagoras Theorem
Let
D -----> the length of the diagonal of the outside square
[tex]D^{2}= x^{2}+x^{2}[/tex]
[tex]D^{2}= 7^{2}+7^{2}[/tex]
[tex]D^{2}=98[/tex]
[tex]D=9.9\ units[/tex]
step 4
Find the length of the diagonal of the inside square
To find the diagonal Apply the Pythagoras Theorem
Let
d -----> the length of the diagonal of the inside square
[tex]d^{2}= c^{2}+c^{2}[/tex]
[tex]d^{2}= 5^{2}+5^{2}[/tex]
[tex]d^{2}=50[/tex]
[tex]d=7.1\ units[/tex]
If a = 4 units and b = 3 units, the length of the diagonal of the outside square rounded to the nearest tenth is 9.9 units
units and the length of the diagonal of the inside square rounded to the nearest tenth is 7.1 units
Let's solve its step by step
step 1
Find the length of the outside square
Let
x -----> the length of the outside square
c ----> the length of the inside square
we know that
x=a+b=4+3=7 units
step 2
Find the length of the inside square
Applying the Pythagoras Theorem
[tex]c^(2)= a^(2)+b^(2)[/tex]
substitute
[tex]c^(2)= 4^(2)+3^(2)[/tex]
[tex]c^(2)=25[/tex]
c=5 units
step 3
Find the length of the diagonal of the outside square
To find the diagonal Apply the Pythagoras Theorem
Let
D -----> the length of the diagonal of the outside square
[tex]D^(2)= x^(2)+x^(2)[/tex]
[tex]D^(2)= 7^(2)+7^(2)[/tex]
[tex]D^(2)=98[/tex]
D=9.9 units
step 4
Find the length of the diagonal of the inside square
To find the diagonal Apply the Pythagoras Theorem
Let
d -----> the length of the diagonal of the inside square
[tex]d^(2)= c^(2)+c^(2)[/tex]
[tex]d^(2)= 5^(2)+5^(2)[/tex]
[tex]d^(2)=50[/tex]
d=7.1 units