4. Write the trinomial represented by each rectangle of algebra tiles. Then, determine the
dimensions of each rectangle.
Answers
Answer:
Trinomial: [tex]\boldsymbol{\text{x}^2 + 3\text{x} - 4}[/tex]
Dimensions: [tex]\boldsymbol{\text{x}+4} \text{ by } \boldsymbol{\text{x}-1}[/tex]
=======================================================
Explanation:
The big green square is x units by x units. Its area is [tex]\text{x} * \text{x} = \text{x}^2[/tex] which represents x squared.
The long vertical green rectangles are x units tall and 1 unit across. The area of one such rectangle is x times 1 = x. Since we have four of these green rectangles, so far we have x+x+x+x = 4x in additional area.
So far the area is [tex]\text{x}^2+4\text{x}[/tex]
---------------
All of the green areas mentioned so far are positive areas so to speak.
In contrast, the red areas are negative areas. They take away from the positive. You can think of it like a bank balance.
If a single green rectangle is x square units in area, then a red rectangle is negative x or -x
So we go from 4x to 4x-x = 3x
Then we subtract off 4 due to the 4 small squares
This gives a total area of [tex]\text{x}^2 + 3\text{x} - 4[/tex] and this represents the standard form of the polynomial area. It is a trinomial since it has 3 terms.
---------------
Now onto the dimensions.
Check out the diagram below. The overall figure is x+4 units across the horizontal dimension, and x-1 units tall along the vertical dimension.
If you were to use the FOIL rule, then you would find that [tex](\text{x}+4)(\text{x}-1) = \text{x}^2 + 3\text{x} - 4[/tex] which helps show how the two forms connect to one another.
This also helps show that area = length*width which is what we'd expect from any rectangular area.
Related Questions
Please help ill give whoever answers the best the brainliest answer :00
Answers
Answer: If for every independent unit(aka x), you multiply the dependent unit by the same amount(aka y).
Step-by-step explanation:
EXAMPLE:
(0,2) (1,6) (2,18) (3,54) (4,162)
As you can see, each time x increases by unit, you multiply the y unit by 3.
As an example, if you increase x by 4, you multiply the y unit by 3^4 = 81.
If this pattern is consistent with your whole table, you have an exponential function.
Hope this is useful.
Point X is the incenter of ΔABC.
Triangle A B C has point X as its incenter. Lines are drawn from the points of the triangle to point X. Lines are drawn from point X to the sides of the triangle to form right angles. Line segments X F, X G, and X E are formed.
If EX = 4z + 1, XF = 2z + 7, and mABC = 44°, find the following measures.
GX =
mABX = °
Answers
The value of GX is 13 and m ∠ABX is 22°
How to determine the angles
With the information, we have
EX = 4z + 1 and XF = 2z + 7
It is important to note that EX = XF = GX are congruent, that is, they are equal
Equate EX = XF to determine z
4z + 1 = 2z + 7
Collect like terms
2z = 6
z = 3
We know that EX = XF = GX and x = 3, substitute into the value of any one
EX = 4(3) + 1
EX = 13
EX = GX
GX = 13
To determine m ∠ABX, we divide m ∠ABC by 2
We have
m ∠ABX = 44/2
m ∠ABX = 22°
Therefore, the value of GX is 13 and m ∠ABX is 22°
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Answer: 13, 22°
Step-by-step explanation: Trust Me!
Answer is correct on Edge. Good Luck! :)
GX = 13
mABX = 22°
Which of the following graphs shows the
solution set to 2x < 6 and 3x + 2 >
-4?
Answers
Answer:
The third picture
Step-by-step explanation:
Solve for x in both equations
2x<6
Divide both sides by 2:
x<3
3x+2>-4
Subtract 2 from both sides:
3x>-6
Divide both sides by 3:
x>-2
There is this trick you can use when x is on the left side of the equation to find out which way to shade in you graph. Keep in mind this is only for the left side, it will not work if your variable is on the right.
When the symbol is facing left < then shade left, imagine it is pointing which way to shade. x<3 is represented by the 3 picture on the left. When the symbol is facing right > then shade right, again it is pointing which way to shade. x>-2 is represented by the 3 picture on the right.
The circles are not filled in because the symbol is < and > rather than [tex]\leq and \geq[/tex]. When it is greater than or equal to or less than and equal to (represented by the line under the symbol), then the circle is shaded in.
A body and tackle with a velocity ratio of 5 is used to raise a mass of 50kg through a vertical distance of 20n at a steady rate if the effort is equal to 80n. Determine (a) distance moved by effort (b)the workdone by the effort in lifting the load (c)the losses in energy involve the operating in machine
Answers
a. Distance moved by effort = 1 meter
b. Work done by effort = 80 Joules
c. Losses in energy = 18 Joules
How to determine the parametersa. Note that velocity ratio is defined as the ratio of a distance through which any part of a machine moves to the distance moved by its parts
Velocity ratio = distance moved by the effort/distance moved by the body
Where velocity ratio = 5
vertical distance = 20cm
Distance moved by effort = 5 × 0. 20 = 1 meter
b. Formula for work done is given as ;
Work done = Effort × distance moved by effort
Work done = 80 × 1
Work done = 80 Newtons
c. First, let's find the work output
Work output = m g h
Work output = 50 × 9.8 × 0. 20
Work output = 98 Joules
Losses in energy = Work output - work done
Losses in energy = 98 - 80
Losses in energy = 18 Joules
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Four cards are dealt at random without replacement from an ordinary deck of 52 cards. If it is known that the four cards have different face values, what is the probability that the first two cards are spades
Answers
Step-by-step explanation:
We gujra weeeeeeee
We gujra weeeeeeee
We gujra weeeeeeee
We gujra weeeeeeee
4 mark please help me
Answers
Answer:
There are 4 red counters
Step-by-step explanation:
1. Add the known decimals
[tex]0.25+0.35+0.3=0.9[/tex]
2. Subtract that amount from one
[tex]1-0.9=0.1[/tex]
3. multiply the result by 40
[tex](40)(0.1)=4[/tex]
Hope this helps
Step-by-step explanation:
a probability is always desired cases / total cases.
from the table and given information we know :
there are 40 blue counters.
0.25 = 40/x
x being the total number of counters in the box.
x = 40 / 0.25 = 160
the sum of all probabilities must be 1 (the always true probability), as there are only counters in the box, and one of the 4 colors is always the result.
so,
1 = 0.25 + 0.35 + 0.3 + red-probability
1 = 0.9 + red-probability
red-probability = 1 - 0.9 = 0.1
0.1 = red counters / 160
red counters = 0.1 × 160 = 16
there are 16 red counters in the box.
Each large rectangle below represents one whole.
What percent is represented by the shaded area?
Answers
Answer:
180%
Step-by-step explanation:
Given:
Large rectangle represents one (1) wholeEach rectangle is divided evenly into 5 partsThere are 2 whole rectanglesThe rectangle on the left is fully shaded in meaning that is 1 whole (100%)
The rectangle on the right is 4 / 5 shaded, 4 / 5 = 0.8 (80%)
Combining these will be 100 + 80 = 180%
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Step-by-step explanation:
there are 2 whole rectangles 1 of them is full making it 1 whole the other has 4 shaded potions and 1 unshaded potion making 4/5Mathematically writing it: 1 ⅘ (mixed fraction)we change 1 ⅘ into an improper fractionby multiplying the whole (1) by the denominator (5) and adding the numerator (4) which gives us 9/4 (improper fraction).9/4 = 9÷4 = 2.25 (decimal)Then we convert 2.25 into percentage by multiplying 2.25 by 100 2.25 x 100 = 225%Therefore the percentage represented by the shaded area is 225%. Hope this helps.Good luck ✅.Please Help!!!
Right triangle ABC is on a coordinate plane. Segment AB is on the line y = 2 and is 5 units long. Point C is on the line x = −2. If the area of ΔABC is 12.5 square units, then find a possible y-coordinate of point C.
5
6
7
8
Answers
Answer: its 7
Step-by-step explanation: hope it helps
Figure ABCD is transformed to figure A prime B prime C prime D prime, as shown: A coordinate grid is shown from negative 5 to 0 to 5 on both x- and y-axes. A polygon ABCD has A at ordered pair 2, 3, B at ordered pair 4, 4, C at ordered pair 3, 1, D at ordered pair 2, 1. A polygon A prime B prime C prime D prime has A prime at ordered pair negative 1, 3, B prime at ordered pair negative 3, 4, C prime at ordered pair negative 2, 1, D prime at ordered pair negative 1, 1. Which of the following sequences of transformations is used to obtain figure A prime B prime C prime D prime from figure ABCD? (1 point) Group of answer choices Counterclockwise rotation by 90 degrees about the origin followed by a translation to the right by 1 unit Counterclockwise rotation by 90 degrees about the origin followed by a translation to the left by 1 unit Reflection about the x-axis followed by a translation to the left by 1 unit Reflection about the y-axis followed by a translation to the right by 1 unit
Answers
Last option. The sequence that can be used to to get the figure A'B'C'D' is Reflection about the y-axis followed by a translation to the right by 1 unit.
How to get the reflection of the imageWe have an opposite orientation in this question. This based on the fact that (ABCD)' is counterclockwise. While its reflection ABCD is clockwise.
The reflection has to go over a vertical line given that (CD)' and CD are at the bottom. Hence this reflection has to go over a vertical line.
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ZA and ZB are
supplementary angles. If mA = (7x + 24)˚ and
m/B = (7x − 26)°, then find the measure of ZA.
-
Answers
The measure of ∠A is 115˚.
Given that, ∠A and ∠B are supplementary angles. ∠A=(7x + 24)˚ and ∠B=(7x − 26)°.
What are supplementary angles?Two angles are Supplementary when they add up to 180 degrees.
Now, ∠A+∠B=180°
⇒(7x + 24)˚+(7x − 26)°=180°
⇒14x− 2°=180°
⇒14x=182°
⇒14x=182°
⇒x=13°
Now, ∠A=7×13 + 24˚
⇒∠A=91˚+ 24˚=115˚
Therefore, the measure of ∠A is 115˚.
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[tex] {3}^{2x - 2} - 28( {3}^{x - 2} ) + 3 = 0[/tex]
solve for x.....
Answers
Answer:
x = 3, x = 0
Given expression:
[tex]3^{2x-2}-28\left(3^{x-2}\right)+3=0[/tex]
rewrite expression
[tex]3^{2x} \times 3^{-2}-28\left(3^{x} \times 3^{-2}\right)+3=0[/tex]
treat [tex]\sf \s3^{x}\:as\:u[/tex], then expression
[tex]u^2 \times 3^{-2}-28\left(u \times 3^{-2}\right)+3=0[/tex]
multiply both sides by [tex]\sf 3^{2}[/tex]
[tex]u^2-28\left u+27=0[/tex]
factor expression
[tex]u^2-27\left u - u + 27=0[/tex]
factor out common terms
[tex]u(u-27) -1( u - 27)=0[/tex]
collect into groups
[tex](u-1)( u - 27)=0[/tex]
set to zero
[tex]u =1, \ u=27[/tex]
Substitute [tex]\sf 3^x = u[/tex], to find x
[tex]3^x = 1, \ 3^x = 27[/tex]
[tex]3^x = 3^0, \ 3^x =3^3[/tex]
[tex]x= 0, \ x = 3[/tex]
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Graph a system of equations to solve log (−5.6x + 1.3) = −1 − x. Round to the nearest tenth.
From the least to the greatest, the solutions are:
Answers
From the least to the greatest, the solutions are x ≈ -2.1 and x ≈ 0.2
the answers are -2.1 and 0.2.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have two systems of the equation:
y = log (−5.6x + 1.3)
y = −1 − x
After plotting the above equation on the graph we will see two intersections point:
(-2.12, 1.12) and (0.221, -1.221)
So the least value is x = -2.12 ≈ -2.1
The greatest value is x = 0.221 ≈ 0.2
Thus, from the least to the greatest, the solutions are x ≈ -2.1 and x ≈ 0.2
the answers are -2.1 and 0.2.
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40 points please help!!!!
Answers
use the 3rd icon to measure 30 and 60 degrees, Then connect them with a line and add a right angle.
Answer:
Not Possible
Step-by-step explanation:
It is not possible. While it does add up to 180, if one is 90 degrees, the rest must be 45 and 45, or your not getting anything.
Let me know if this helped !!
How do I find the formula for the nth term in a sequence? Like for example the sequence:4,9,14,19 what is the next term?
Answers
Answer:
Step-by-step explanation:
Arithmetic sequence:
a = first term = 4
d = common difference = second term - first term
= 9 - 4
d = 5
[tex]\sf t_n =a +(n -1)*d[/tex]
= 4 + (n - 1) *5
= 4 + 5n - 5
= 5n -1
Check; n= 1 , first term = 5*1 - 1 = 5 - 1 = 4
n = 2, second term = 5*2 - 1 = 10 -1 = 9
n = 3, third term = 5*3 - 1 = 15 - 1 = 1
The next term, fifth term = 5*5 - 1
= 25 - 1
= 24
Emily's family loves to work together in the garden. They have a slight preference for flowers, as 60%, percent of their plants are flowers and 40%, percent are vegetables. They have 50 plants growing in the garden. How many vegetable plants do they have?
Answers
Answer:
20 vegetable plants
Step-by-step explanation:
In order to figure this out, you need to find 40% of 50. You can solve that by doing 0.40 * 50, which gives you 20. I hope that helps!
Where s is the distance traveled by an object (in meters) with an initial velocity u (in m/s) and final velocity v (in m/s), t
seconds later.
Find s when u is 6 m/s, v is 20 m/s, and t is 5 seconds.
B. 25 m
C. 130 m
= 1/2 (u + v) t
OD. 65 m
S=
Answers
The distance travelled by the object in meters is 65 meters.
How to find distance?using the formula,
s = 1 / 2 (u + v)t
where
u = initial velocityv = final velocitys = distancet = timeTherefore, the distance can be found as follows;
s = 1 / 2 (6 + 20)5
s = 1 / 2 (26)5
s = 13(5)
s = 65 m
Therefore, the distance travelled by the object in meters is 65 meters.
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Answer:
D.
Step-by-step explanation:
I had the same question
There are 135 people in a sport centre. 73 people use the gym. 59 people use the swimming pool. 31 people use the track. 19 people use the gym and the pool. 9 people use the pool and the track. 16 people use the gym and the track. 4 people use all three facilities. A person is selected at random. What is the probability that the person uses exactly one of the facilities?
Answers
The probability that the person uses exactly one of the facilities is 0.64
What is probability?Probability is the likelihood of an event happening or an event not happening.
When it is certain an event would happen the probability is 1.
Probability can be independent or mutually exclusive.
Analysis:
Find analysis in the attached file.
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Find a 10-digit number where the first digit is how many zeros in the number, the second digit is how many 1s in the number etc. until the tenth digit which is how many 9s in the number.
Answers
Answer:
9000000001
Step-by-step explanation:
.....................
Answer:
6210001000
Hope This Helps!!!
Find value of x in the 45° - 45°-90° triangle. Give
answer rounded to the nearest tenth. Geometry!! pls helppp
Answers
Answer: X = 5.0
Step-by-step explanation:
- since these are right triangles you can use trigonometry to solve this pretty easily
- for this situation, you only have to use sine/sin
sine/sin is [tex]opposite/hypotenuse[/tex]__________________________________________________________
- to start you just need to identify which side is which:
the side that is labeled 10 is the hypotenusein this case, the shared side is the opposite since you're using sin- so, for this problem the equation is: [tex]10xSin(45) = 7.071067812[/tex]
__________________________________________________________
- so 7.071067812 is the hypotenuse of the smaller triangle so you just do the same thing again
- start with identifying which side is which:
as said, the side that is shared and 7.071067812 is the hypotenusethe side labeled x is the opposite- so for this part, the equation is: [tex]7.071067812xSin(45) = 5.0[/tex]
- so X = 5.0
__________________________________________________________
hope this helps :)
Answer:
x = 5
Step-by-step explanation:
Check the file for detailed solution.
This involves SOH-CAH-TOA method, always remember that the opposite of the 90 degree mark is always the hypotenuse. Meanwhile, the position of the given angle (theta) is dependent on which side it is placed. It give either an adjacent or opposite side.
Can someone help me please?
Answers
Answer:
7.6 units
Step-by-step explanation:
Use law of sines
12 / sin C = b / sin B
sin B * 12 / sin C = b
sin (32) * 12 / sin(57) = b = 7.6
Point Y is the circumcenter of triangle DEF.
Point Y is the circumcenter of triangle D E F. Lines are drawn from the points of the triangles to point Y. Lines are drawn from point Y to the sides of the triangle to form right angles and line segments Y L, Y M, and Y N. The line segments cut the sides of the triangles into 2 equal parts.
Which statement is true about point Y?
Point Y is the center of the circle that passes through points D, F, and N.
Point Y is the center of the circle that passes through points M, N, and E.
Point Y is the center of the circle that passes through points L, M, and N.
Point Y is the center of the circle that passes through points D, E, and F.
Answers
Point Y is the centre of the circle that passes through points D, E, and F.So option A is correct.
What is circumcircle?If we draw a circle through all the vertices of a triangle then the circle obtained is the circumcircle of the given triangle.
And the circumcenter is the centre point of the circumcircle which is obtained by the point of intersection of the perpendicular bisector of all the sides of the triangle.
Therefore, since Y is the circumcenter of the triangle DEF, so, point Y is the centre of the circle that passes through points D, E, and F.
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Answer:
A
Step-by-step explanation:
gradients - pls help :)
Answers
The line which has a gradient of 6 is A. line A
To answer the question, we need to know what the gradient of a line is.
What is the gradient of a line?The gradient of a line is its slope. It is given by m = Δy/Δx where
Δy = change in y and Δx = change in x. How to find the line that has the gradient 6?Now, to find the line that has the gradient of 6, we see that the gradient
m ∝ Δy and m ∝ 1/Δx.So, for a high value of gradient, we need
a large change in y and a small change in x.Also, since 6 is positive, the gradient for the line will be positive.
The only line that meets these criteria is line A.
So, the line which has a gradient of 6 is A. line A
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A group of researchers wanted to measure the impact of playing classical music at bedtime to infants. They choose 20 infants to play music from 6:30 7:30 pm at bedtime and 20 infants to not play music at all. For each day for 3 months they observed them for 4 hours and recorded exactly how long it took for them to fall asleep. At the end of the 3 months they calculated the percentage of awake time to the time they slept for the 4 hours and compared the percentages to infants that had music played versus infants that did not. None of the answer choices Experimental Survey Observational Study A group of researchers wanted to measure the impact of playing classical music at bedtime to infants . They choose 20 infants to play music from 6:30 7:30 pm at bedtime and 20 infants to not play music at all . For each day for 3 months they observed them for 4 hours and recorded exactly how long it took for them to fall asleep . At the end of the 3 months they calculated the percentage of awake time to the time they slept for the 4 hours and compared the percentages to infants that had music played versus infants that did not . None of the answer choices Experimental Survey Observational Study
Answers
Using statistical concepts, it is found that it is an experimental study, as the music played corresponds to an experiment.
What is an experimental study?It is an study where an intervention is applied to a sample, and the effect of this intervention is studied.
In this problem, the music played is the intervention, and it's effect on the time that it takes for the infants to be asleep, hence it is an experimental study.
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A tub contains red, yellow and blue counters. There is ten more yellow than red counters, and the ratio of red to blue counters is 3:4.If there are 20 blue counters, what is the probability of picking a yellow counter?
Answers
Answer:
5/12
Step-by-step explanation:
A ratio of 3:4 means that red counters make up 3/7 of the sum of red and blue counters and blue counters make up 4/7 of the total sum of red and blue counters.
If there is 20 blue counters, then 20 is 4/7 of the sum of the total red and blue counters.
So we need to solve for the total sum.
[tex] \frac{4}{7} x = 20[/tex]
[tex]4x = 140[/tex]
[tex]x = 35[/tex]
So the total amount of red and blue counters are 35,
So this means the amount of red counters is 15.
The amount of yellow counters is 25.
So the total number of counters are 60.
So P(Yellow counters)= 25/60= 5/12
Please help For 50 points
Answers
Answer:
m = 0.875
Step-by-step explanation:
the 3 angles lie on a straight line and sum to 180° , that is
4m + 83 + 4m + 90 = 180
8m + 173 = 180 ( subtract 173 from both sides )
8m = 7 ( divide both sides by 8 )
m = [tex]\frac{7}{8}[/tex] = 0.875
work out the volume of the cone,giving your answer to 3 significant figures
Answers
The volume of the cone is 1, 139. 49 cm³
How to determine the volumeHeight of cone = 17cm
Base of cone = 16cm
Diameter = 16cm
Radius = diameter/2 = 16/2 = 8cm
Formula for volume of a cone = [tex]\pi r^{2} \frac{h}{3}[/tex]
Substitute the values
Volume = [tex]3. 142[/tex] × [tex]8[/tex] × [tex]8[/tex] × [tex]\frac{17}{3}[/tex]
Volume = [tex]201. 088[/tex] × [tex]5. 67[/tex]
Volume = 1, 139. 49 cm³
Thus, the volume of the cone is 1, 139. 49 cm³
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4. (07.06)
Write a simplified polynomial expression in standard form to represent the area of the rectangle below. (2 points)
2x - 4
O 2x² + 6x-20
2x² - 4x-20
D
2x² + 6x + 20
2x² + 10x + 20
X+5
Answers
The expression that represents the area of the rectangle is 2x² + 6x − 20. Thus, the correct option is C.
What is a rectangle?A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but reverse statement may or may not be true.
The area of the rectangle is the product of its length and its width. Therefore, the area of the given rectangle is,
Area = (2x-4)(x+5)
= 2x² + 10x - 4x - 20
= 2x² +6x - 20
Hence, the expression that represents the area of the rectangle is 2x² + 6x − 20. Thus, the correct option is C.
The complete question is:
Write a simplified polynomial expression in standard form to represent the area of the rectangle below.
2x² + 10x + 202x² + 6x + 202x² + 6x − 202x² − 4x − 20The image of the rectangle is given below.
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For every 5 minutes that Scarlett plays on the computer, she plays outside for 12 minutes. What is the ratio of minutes Scarlett plays on the computer to minutes she plays outside?
Answers
Answer:
5:12
Step-by-step explanation:
because of the new wife
Determine the slope-intercept form (y = mx + b) of the equation of the line that contains the
points (3, 5) and (5, 6)
Answers
Hello,
We have A(3, 5) and B(5, 6)
[tex]m=\frac{y_{B}-y_{A}}{x_{B}-x_{A}} =\frac{6-5}{5-3} =\frac{1}{2}[/tex]
We know the line contain the point (3, 5)
y = 1/2x + b
⇔ 5 = 1/2 × 3 + b
⇔ 5 = 3/2 + b
⇔ 5 - 3/2 = b
⇔ b = 10/2 - 3/2
⇔ b = (10 - 3)/2
⇔ b = 7/2
[tex]\boxed{y = \frac{1}{2}x + \frac{7}{2} }[/tex]
Martha climbs 40 steps to reach the first floor of a building. If the vertical and horizontal distance of each step is 1.5 ft and 1 ft, find the distance between the start and end points of each step
Answers
The distance between the initial position and the final position is 72.1ft
How to get the distance?
The initial position is (0ft, 0ft). Where the notation used is:
(horizontal position, vertical position).
Martha climbs 40 steps, then the final position is:
(40*1ft, 40*1.5ft) = (40ft, 60ft)
The distance between the initial position and the final position is:
[tex]d = \sqrt{(40ft - 0ft)^2 + (60ft - 0ft)^2} = 72.1ft[/tex]
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