Answer:
To determine the number of cards necessary to build a tower with 100 stories, let's analyze the pattern observed in the given information.
From the information provided, we know that building 5 stories of cards required 40 cards. Now, let's examine the relationship between the number of stories and the number of cards used:
Number of stories: 5
Number of cards used: 40
To find the number of cards needed for 100 stories, we can calculate the ratio of the number of stories to the number of cards used for the 5-story tower and then apply that ratio to the target number of stories (100).
Ratio = Number of stories / Number of cards used
Ratio = 5 / 40
Now, we can use this ratio to calculate the number of cards needed for 100 stories:
Number of cards for 100 stories = Ratio * Number of stories
Number of cards for 100 stories = (5 / 40) * 100
Calculating the result:
Number of cards for 100 stories = (0.125) * 100
Number of cards for 100 stories = 12.5
Since it is not possible to use a fraction of a card, we need to round up to the nearest whole number. Therefore, we would need a minimum of 13 cards to build a tower with 100 stories using a similar pattern.
Please note that the actual number of cards required may vary depending on the specific construction technique and stability of the tower.
in a bag if marbles 1/2 are blue 1/6 are green 1/12 are yellow you pick a marble with out looking what color marble are you most likely going to choose
Answer: Blue
Step-by-step explanation:
Half of the entire freaking bag is blue,it states it in the question.If there is so many,unless by pure blind luck you will get that.
I hope it helps!
1. ¬{[Q → (¬S ∧ R)] ∨ ¬P} → (¬P ↔ P) ∴ ¬(Q ∧ P) ∨ (T ∧ R)
2. [(T ∨ Q) → (T ∨ S)] ∨ [(T ∨ Q) → (T ∨ S)]
Given statement solution is :- Regardless of the values of T, Q, and S, the whole Valid Statements & Implications is always true.
Let's analyze the two given statements:
¬{[Q → (¬S ∧ R)] ∨ ¬P} → (¬P ↔ P) ∴ ¬(Q ∧ P) ∨ (T ∧ R)
To prove this statement, we can use logical equivalences and deductions:
¬{[Q → (¬S ∧ R)] ∨ ¬P} → (¬P ↔ P) (Given)
¬{[¬Q ∨ (¬S ∧ R)] ∨ ¬P} → (¬P ↔ P) (Implication equivalence)
¬{[(¬Q ∨ ¬S) ∧ (¬Q ∨ R)] ∨ ¬P} → (¬P ↔ P) (Implication equivalence)
¬{(¬Q ∨ ¬S ∨ ¬P) ∧ (¬Q ∨ R ∨ ¬P)} → (¬P ↔ P) (De Morgan's Law)
(Q ∧ S ∧ P) ∨ (¬Q ∧ P) → (¬P ↔ P) (De Morgan's Law)
At this point, the formula ¬P ↔ P is a contradiction. The left side (¬P) states that P is false, while the right side (P) states that P is true. Therefore, the whole statement is always true, regardless of the values of Q, S, and P.
Since the statement is always true, we can conclude ¬(Q ∧ P) ∨ (T ∧ R) is true as well, making the second part of the question valid.
[(T ∨ Q) → (T ∨ S)] ∨ [(T ∨ Q) → (T ∨ S)]
In this statement, we have two identical sub-statements connected by a logical OR operator.
If we assume that (T ∨ Q) → (T ∨ S) is true, then the whole statement is true, regardless of the values of T, Q, and S.
If we assume that (T ∨ Q) → (T ∨ S) is false, then we need to check the other part of the statement.
Assuming (T ∨ Q) → (T ∨ S) is false means that (T ∨ Q) is true, but (T ∨ S) is false. In this case, the second part of the statement [(T ∨ Q) → (T ∨ S)] is true.
Therefore, regardless of the values of T, Q, and S, the whole Valid Statements & Implications is always true.
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160 students went on a field trip. Five buses were filled and 15 students traveled in cars. How many students were in each bus?
Each bus had ____ students.
helpppppppppp meeeeee please
The missing sides of the triangle are given as follows:
[tex]SX = 4\sqrt{3}[/tex]RS = 12.What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:
Sine = length of opposite side to the angle/length of hypotenuse of the triangle.Cosine = length of adjacent side to the angle/length of hypotenuse of the triangle.Tangent = length of opposite side to the angle/length of adjacent side to the angle = sine/cosine.For the angle of 30º, we have that:
6 is the opposite side.RS is the hypotenuse.Hence the hypotenuse RS is obtained as follows:
sin(30º) = 6/RS
1/2 = 6/RS
RS = 6 x 2
RS = 12.
Applying the cosine, we have that:
cos(30º) = 6/SX
[tex]\frac{\sqrt{3}}{2} = \frac{6}{SX}[/tex]
[tex]SX = \frac{12}{\sqrt{3}}[/tex]
[tex]SX = 4\sqrt{3}[/tex]
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Please help me anwser this
The values are given as:
a. Mean = 19
Median = 20
Mode = 22
Standard deviation = 7.2
Range = 24
b. Mean = 75
Median = 80
Mode = 90
Standard deviation = 16
Range = 100
What the measures of central tendency?The three measures of central tendency include;
MeanModeMedianThe measures of dispersions are;
Rangeinterquartile range standard deviationFrom the information given, if 4 is added to all the measures, we get;
Mean = 15 + 4 = 19
Median = 16 + 4 = 20
Mode = 18 + 4 = 22
Standard deviation = 3.2 + 4 = 7.2
Range = 20 + 4 = 24
If the values are multiplied by 5
Mean = 15(5) = 75
Median = 16(5) = 80
Mode = 18(5) = 90
Standard deviation = 3.2(5) = 16
Range = 20(5) = 100
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Britney is a volunteer at the Westside Library. She collects the books that come down the
chute from the outside drop-off and puts them on the library shelves. Of the books that have
come down the chute so far today, 41 have been fiction and 23 have been nonfiction.
Based on the data, estimate how many of the next 100 books that come down the chute will
be nonfiction.
Based on the given data, we can estimate that approximately 36 out of the next 100 books that come down the chute will be nonfiction.
To estimate the number of nonfiction books out of the next 100, we can use the ratio of nonfiction to the total number of books that came down the chute so far today.
The total number of books that came down the chute so far is:
41 (fiction) + 23 (nonfiction) = 64
The ratio of nonfiction books to the total number of books in library is:
[tex]23/64[/tex]
To estimate the number of nonfiction books out of the next 100, we can multiply the ratio by 100:
[tex](23/64)*100=35.9375[/tex]
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At Chairs and More, assemblers are paid according to the following differential piece rate scale: 1−25 chairs in a week, $10 each; 26−40 chairs, $13 each; and $17.50 each for every chair over 40. Salina Grant assembled 47 chairs in one week. Find her gross pay.
Answer:
To find Salina Grant's gross pay, we need to calculate the pay for each range and add them together.
For the first 25 chairs, Salina will be paid $10 for each chair, so her pay for this range is:
25 chairs x $10 per chair = $250
For the next 15 chairs (26-40), Salina will be paid $13 for each chair, so her pay for this range is:
15 chairs x $13 per chair = $195
For the remaining 7 chairs (over 40), Salina will be paid $17.50 for each chair, so her pay for this range is:
7 chairs x $17.50 per chair = $122.50
Adding up all three ranges, Salina's gross pay is:
$250 + $195 + $122.50 = $567.50
Therefore, Salina Grant's gross pay for assembling 47 chairs in one week is $567.50.
Step-by-step explanation:
jureks brother is 6 years older than him .Together they are 22 years old ,how old are the brothers.Write down the correct equation?
Answer:
Jurek is 8. His brother is 14
Step-by-step explanation:
let's call Jurek J, and let's call his brother B.
his brother is 6 years older than Jurek.
So, B = J + 6.
B + J = 22
(J + 6) + J = 22
2J + 6 = 22
2J = 16
J = 8
so Jurek is 8
B + J = 22, B = 22 - J = 22 - 8 = 14.
Brother is 14
100 Points! Algebra question. Photo attached. Find the exact value of the expression. Please show as much work as possible. Thank you!
For this problem, you need an on-hand calculator.
Problem:
sin (pi/8)
Step 1: divide pi by 8.
[tex]\pi[/tex]/8
=0.39269908169
Step 2: Find Cosine of (0.39269908169)
This is the part where you need a calculator.
Locate the SIN button on your graphing calculator.
Press the SIN button, then continue to type 0.39269908169 after the parenthesis.
The calculator gives a value of .0068538383
Final answer:
0.068538383
Can someone help me find the surface area of these cylinders??
The surface area for each of the cylinders is given as follows:
13. 126 yd².
14. 490 m².
15. 283 mm².
16. 297 cm².
How to obtain the surface area of a cylinder?The surface area of a cylinder of radius r and height h is given by the equation presented as follows, which combines the base area with the lateral area:
S = 2πrh + 2πr²
S = 2πr(h + r)
Item 13:
r = 2 yd and h = 8 yd, hence the surface area is given as follows:
S = 2π x 2(2 + 8)
S = 126 yd².
Item 14:
r = 6 m and h = 7 m, hence the surface area is given as follows:
S = 2π x 6(6 + 7)
S = 490 m².
Item 15:
r = 3 mm and h = 12 mm, hence the surface area is given as follows:
S = 2π x 3(3 + 12)
S = 283 mm².
Item 16:
r = 3.5 mm and h = 10 mm, hence the surface area is given as follows:
S = 2π x 3.5(3.5 + 10)
S = 297 cm².
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1.62,16.2,15/20 greatest to least
Answer
The order of the number from greatest to least is 1.62, 15/20, 16.2%
Step-by-step explanation
Given: 1.62 16.2% 15/20
To order these data in descending order (i.e. from highest to least), follow the steps below
1. Convert all numbers to decimals
1.62
16.2% = 16.2/100
16.2% = 0.162
15/20 = 0.75
So, the number are 1.62, 0.162, 0.75
2. Compare the three decimals and arrange in descending order
1.62 > 0.75 > 0.162
This means that 1.62 is greater than 0.75 and 0.75 is greater than 0.162
By substituting 16.2% for 0.162 and 15/20 for 0.75, the order of the number from greatest to least is
1.62, 15/20, 16.2%
Find the area under the standard normal distribution curve between z=0 and z=0.31
Using the z-score values given, the area under the standard normal distribution curve is 0.123 squared units
What is the area under standard normal distribution curveThe total area under the standard normal distribution curve is 1. Therefore, if we have a z-score, i.e., how far a value is above or below the mean, we can determine the probability of a value less than or greater than that.
The points are
z₁ = 0z₂ = 0.31A = z₂ - z₁
z₂ = 0.6230
z₁ = 0.5000
A = 0.6230 - 0.5000
A = 0.123 squared units
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Which shows all the exact solutions of 2sec²x-tan^x=-1? Give your answer in radians.
0+
O +k and+k
0+ -2k* and 5+2K*
3
7%
5+28
4
○ 주 +2kx3+2kx +2kx, and 7+2kx
+kr2+ks 4*k* and 5+k
47
+ K
Kx
Answer:
Step-by-step explanation:
The exact solutions for the equation 2sec²x - tan²x = -1 in radians are:
x = π/4 + πk, where k is an integer
x = 3π/4 + πk, where k is an integer
These solutions represent all the values of x that satisfy the given equation.
A young artist went to an art shop to buy a canvas. There were many sizes from which to choose. Some were standard sizes and some were custom-made. She wanted her next piece to incorporate the Golden Ratio, so she decided to buy the canvas whose dimensions most closely matched the Golden Rectangle. Here are the sizes that were available:
24" x 36"
24" x 40"
10" x 16"
26" x 16"
20" x 12"
Which canvas should the artist buy? Show your work.
The artist should buy the canvas with dimensions 26" x 16" as it most closely matches the Golden Rectangle.
To determine which canvas size most closely matches the Golden Rectangle, we need to calculate the aspect ratios of the available options and compare them to the Golden Ratio.
The Golden Ratio is approximately 1.618. A rectangle is considered to be a Golden Rectangle if its aspect ratio (width divided by height) is equal to the Golden Ratio.
Let's calculate the aspect ratios for each canvas size:
Canvas 1: 24" x 36"
Aspect ratio = 24 / 36 = 0.67
Canvas 2: 24" x 40"
Aspect ratio = 24 / 40 = 0.6
Canvas 3: 10" x 16"
Aspect ratio = 10 / 16 = 0.625
Canvas 4: 26" x 16"
Aspect ratio = 26 / 16 = 1.625
Canvas 5: 20" x 12"
Aspect ratio = 20 / 12 = 1.667
Now, let's compare the aspect ratios of the available options with the Golden Ratio (1.618) to see which one is closest:
Canvas 1: |0.67 - 1.618| = 0.948
Canvas 2: |0.6 - 1.618| = 1.018
Canvas 3: |0.625 - 1.618| = 0.993
Canvas 4: |1.625 - 1.618| = 0.007
Canvas 5: |1.667 - 1.618| = 0.049
The canvas with the aspect ratio closest to the Golden Ratio is Canvas 4: 26" x 16". Its aspect ratio of 1.625 is only 0.007 away from the Golden Ratio.
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Please help with pictures below.
The proportion is solved and the variables are a/b = c/d
Given data ,
Let the proportion be represented as A
Now , the value of A is
a / b = c / d
On simplifying the equation , we get
( a + b ) / b = ( c + d ) / d
On dividing the numerator of the fraction by the denominator , we get
( a / b ) + ( b / b ) = ( c / d ) + ( d / d )
On further simplification , we get
( a / b ) + 1 = ( c / d ) + 1
Subtracting 1 on both sides , we get
( a / b ) = ( c / d )
Hence , the proportion is ( a / b ) = ( c / d )
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Find the volume of a rectangular prism with a length of 12 inches a width of 4.5 inches and a height of 3.6 inches
Answer:
194.4
Step-by-step explanation:
V=l*w*h
V=12*4.5*3.6
V=194.4
Each day, Nicole earns a fixed wage plus extra money for every hour of overtime she works. The graph shows her total pay (in dollars) versus the amount of
overtime (in hours) that she works.
Total pay
(dollars)
I Don't Know
737
Mostly cloudy
Overtime (hours)
Subm
(a) What is Nicole's total pay with 0 hours of overtime?
(b) Choose the statement that best describes how the amount
of overtime and total pay are related. Then fill in the blank.
Search
As the amount of overtime increases, the total pay
decreases.
At what rate is the total pay decreasing?
$ per hour
As the amount of overtime increases, the total pay
increases.
At what rate is the total pay increasing?
$ per hour
?? geometry question
The measure of angle BGF from the given parallel lines is 108°.
Given that, measure of angle BGF=4x+28 and the measure of angle EHD = 2x+32.
1) From the given figure, angle BGF and angle EHC are interior alternate angles.
Angle FHC and angle EGA are corresponding angles.
Angle FHC and angle EGA are exterior alternate angles.
2) angle BGF+angle EHD=180°
3) 4x+28+2x+32=180°
6x+60=180
6x=120
x=20
Angle BGF=4x+28=108 °
Angle EHD = 2x+32
= 112°
Angle FHD=180-112=68°
Angle EGB=180-108=72°
Therefore, the measure of angle BGF from the given parallel lines is 108°.
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what is1+1+1 equal?
this is a not ur typical math problem try to get it right u will get brainliest
The mathemematical sum of the three numbers 1+1+1 would give 3
Addition of numbersAddition of numbers can involve 2 or more values using the additive sign '+'. For any given sum of values, the result obtained would be greater than any of the individual value in the sum.
Here, 1 + 1 + 1 means that we are adding 1 in three places. The value obtained would be 3.
Therefore, the sum of the 1+1+1 is 3
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Hellooo i’m pretty sure x is 30 but can someone tell me what im meant to write for the reason. Thank youuu
Answer:
2x and 180 - 5x are complementary angles.
2x + 180 - 5x = 90
-3x + 180 = 90
-3x = -90
x = 30
Find the area of the shape
The area of the given figure is 27.5 square centimeter which has a rectangle and triangles
The given figure has a rectangle and triangles
The area of rectangle is length times width
Area of rectangle =5×4
=20 square centimeter
Area of triangle =1/2×base×height
=1/2×2.5×3
=7.5/2
=3.75 square centimeter
As there are two triangle = 2(3.75)
=7.5 square centimeter
Total area = 7.5+ 20
=27.5 square centimeter
Hence, the area of the given figure is 27.5 square centimeter
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Function
�
gg can be thought of as a scaled version of
�
(
�
)
=
�
2
f(x)=x
2
f, left parenthesis, x, right parenthesis, equals, x, squared.
A parabola labeled f represents the equation y equals x squared. A parabola labeled g passes through the point negative 1, 4, through the origin, and through the point 1, 4.
Write the equation for
�
(
�
)
g(x)g, left parenthesis, x, right parenthesis.
The equation for g (x) is,
⇒ g(x) = x² -3
Since, The function is,
⇒ f (x) = x²
when x = 0, f(x) = 0
hence it has vertex at (0,0)
Since, g(x) is shifter version of f(x) and has vertex at (-1, 4),
Then, g(x) must be shifted along y axis.
So, We get;
g(x)= x²+c
when x = - 1, g(x)= 4
4 = (-1)² + c
4 = 1 + c
c = 3
Thus, The equation for g (x) is,
g(x) = x² -3
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What is the probability that either event will occur? 3 A 18 B 15 P(A or B) = P(A) + P(B) P(A or B) = [?] Enter as a decimal rounded to the nearest hundredth.
Answer:
the probability that either event will occur is 0.92
Step-by-step explanation:
the probability that either event will occur is 0.92
What is the probability that either event will occur?
From the question, we have the following parameters that can be used in our computation:
Event A = 18
Event B = 15
Other Events = 3
Using the above as a guide, we have the following:
Total = A + B + C
So, we have
Total = 18 + 15 + 3
Evaluate
Total = 36
So, we have
P(A) = 18/36
P(B) = 15/36
For either events, we have
P(A or B) = 33/36 = 0.91666
Hence, the probability that either event will occur is 0.92 (rounded to nearest hundreth)
Find the gradient of the line segment between the points (-2,3) and (0,2).
Give your answer in its simplest form.
Answer:
[tex]\dfrac{-1}{2}[/tex]
Step-by-step explanation:
Slope or gradient:(-2 , 3) ⇒ x₁ = -2 & y₁ = 3
(0 , 2) ⇒ x₂ = 0 & y₂ = 2
[tex]\boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf = \dfrac{2-3}{0-[-2]}\\\\\\=\dfrac{-1}{0+2}\\\\=\dfrac{-1}{2}[/tex]
5. A movie is made of a series of still images called frames. A standard rate for a movie is 24 frames per second. Two movies, A and B, each last 100 minutes. Movie A was filmed at the standard rate. Movie B was filmed at 30 frames per second. Movie B has what percent more frames than movie A? Movie B has what frames than movie A.
Movie B has approximately 25% more frames than Movie A.
For Movie A the duration is 100 minutes
Frame rate: 24 frames per second
Total frames in Movie A:
Total frames in Movie A = 100×60×24
Movie B:
Duration: 100 minutes
Frame rate: 30 frames per second
Total frames in Movie B:
Total frames in Movie B = 100 × 60 × 30
To find the percent more frames in Movie B compared to Movie A, we can use the following formula:
Percent more frames = ((Total frames in Movie B - Total frames in Movie A) / Total frames in Movie A) × 100
Total frames in Movie A = 100 × 60× 24
Total frames in Movie B = 100 ×60 × 30
Percent more frames = ((Total frames in Movie B - Total frames in Movie A) / Total frames in Movie A) × 100
Percent more frames = ((100 × 60× 30) - (100 × 60×24)) / (100 × 60× 24)×100
Percent more frames = (180,000 - 144,000) / 144,000 * 100
Percent more frames = 36,000 / 144,000 * 100
Percent more frames = 25%
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Which function has a horizontal asymptote at y = 3?
Answer: A) [tex]f(x)=\frac{6x^2-x+4}{2x^2-1}[/tex]
Step-by-step explanation:
Line [tex]y=L[/tex] is a horizontal asymptote of the function [tex]y=f(x)[/tex], if either [tex]\lim_{x \to \infty} f(x)=L[/tex] or [tex]\lim_{x \to \infty} f(x)=L[/tex], and [tex]L[/tex] is finite.
calculate the limits:
[tex]\lim_{x \to \infty} (\frac{6x^2-x+4}{2x^2-1})=3[/tex]
[tex]\lim_{x \to -\infty} (\frac{6x^2-x+4}{2x^2-1})=3[/tex]
Thus, the horizontal asymptote is [tex]y=3[/tex]
John enclosed his 9 foot square garden. How much fence will he need
John will need 36 feet of fence to enclose his 9-foot square garden.
How much fence does John needs to enclose the garden?A sqaure is simply a polygon made up of four equal sides, with all the interior angles measuring 90 degrees.
The perimeter of a square is expressed as:
Perimeter = 4 × side length
Given that, the side length of the square garden is 9 ft.
To calculate the amount of fence John will need to enclose his 9-foot square garden, we need to determine the perimeter of the square.
Perimeter = 4 × side length
Plug in the side length
Perimeter = 4 × 9 ft
Perimeter = 36 feet
Therefore, the perimeter of the garden is 6 feet.
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Can someone help me? The velocity of a sound in air is given by the equation v=20 radical273+t where v is the velocity in meters per second and t is the temperature in degrees Celsius find the temperature when the velocity is 348 meters per second round the answer to the nearest degree
when the velocity is 348 meters per second, the approximate temperature is 18 degrees Celsius.
How to find the temperature when the velocity is 348 meters per secondTo find the temperature when the velocity is 348 meters per second, we can substitute the given velocity into the equation v = 20√273 + t and solve for t.
Given: v = 348 meters per second
Substituting this value into the equation:
348 = 20√273 + t
Now, let's solve for t. We can start by isolating the term with t:
t = 348 - 20√273
Calculating the value:
t ≈ 348 - 20 * 16.523
t ≈ 348 - 330.46
t ≈ 17.54
Rounding the answer to the nearest degree, we have:
t ≈ 18 degrees Celsius
Therefore, when the velocity is 348 meters per second, the approximate temperature is 18 degrees Celsius.
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Sofia and ella are both writing expressions to calculate the surface area of a rectangular prism however they wrote different expressions.
a. examine the expressions below, and determine if they represent the same value. explain why or why not.
sofia's expression
(3 cm x 4 cm ) + (3 cm x 5 cm) + (4 cm x 5 cm) + (4 cm x 5 cm)
ella's expression:
2(3 cm x 4 cm) + 2(3 cm x 5 cm) + 2(4 cm x 5 cm)
b. what fact about the surface area of a rectangular prism does ella's expression show more clearly than sofia's?
a ) The given expression from Sofia and Ella represents two different values.
b.) The fact about the surface area of prism that Ella's expression shows that is not in Sofia's expression is that the expression is according to the formula.
How to determine the surface area of a rectangular prism?To determine the surface area of a rectangle prism, the formula that should be used would be given below:
That is;
Surface area of rectangular prism;
= 2(wl+hl+hw)
when the formula is multiplied out the following is gotten;
= 2wl + 2hl + 2hw
From Ella's expression,
2(3 cm x 4 cm) + 2(3 cm x 5 cm) + 2(4 cm x 5 cm). This follows the order of the formula. And it's final answer = 94cm²
From Sofia's expression,
(3 cm x 4 cm ) + (3 cm x 5 cm) + (4 cm x 5 cm) + (4 cm x 5 cm). This doesn't follow the order of the formula and therefore is not correct and not the same final value with Ella's expression.
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here is my algebra 13 homework, can someone please help me quick!
The decreasing interval of function is (-∞ , 0) .
The decreasing interval in the function is said to be when the value of the derivative f' (x) ≤ 0 .
Decreasing interval is when f(x) is decreasing as x is increasing.
Here the graph is of a parabola the equation of a upper parabola is
f(x) = x²
Now doing derivation of the parabola equation, we get
f'(x) = 2x
As for decreasing interval we will put
f'(x) ≤ 0
Putting the value of f'(x) in the equation
2x ≤ 0
x ≤ 0
Decreasing interval (-∞ , 0)
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