The location at which a function is not differentiable is a Vertical tangent line
A function may not be differentiable at some points. Such points are known as non-differentiable points. Let's take a look at each of the given terms to figure out the non-differentiable points. Discontinuity: A discontinuity is when a function's graph is interrupted by a break or hole.
It occurs when a function is undefined at a certain point. It may be classified into three categories: removable, jump, and infinite. Functions may not be differentiable at removable discontinuities but are differentiable at jump and infinite discontinuities. A discontinuous point is not the same as a non-differentiable point because it may be differentiable at other points of the function.
Cusp: A cusp is a sharp corner formed by a curve. It happens when the slope of the function approaches infinity. The curve is not differentiable at the cusp. Horizontal Tangent Line: When the slope of a function approaches zero, it creates a horizontal tangent line. The function may or may not be differentiable at this point depending on the shape of the graph.
It may be differentiable or not differentiable. Therefore, it is not a non-differentiable point. Vertical Tangent Line: When a function's slope approaches infinity, it creates a vertical tangent line. The function is non-differentiable at this point. A vertical tangent line is always a non-differentiable point.
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The function C (t) = StartFraction 4 t Over t squared + 2 EndFraction models the cost per student of a field trip when x students go on the trip. How is the parent function On a coordinate plane, 3 curves are shown. One curve opens up and to the right in quadrant 1 and goes through (2, 4) and (4, 1). Another curve approaches x = negative 2 in quadrant 2, changes direction at (0, 0), and then decreases in quadrant 4 and approaches y = 2. The third curve opens down and to the left in quadrant 3 and goes through (negative 4, negative 1) and (negative 2, negative 4). transformed to create the function On a coordinate plane, 2 curves are shown. One curve opens up and to the left in quadrant 2 and goes through (negative 4, 8) and (negative 6, 6). Another curve opens down and to the right and goes through (negative 1, negative 3), (0, 0), and (6, 3).?
It is vertically stretched by a factor of 200.
It is vertically stretched by a factor of 200 and shifted 10 units leftt.
It is vertically stretched by a factor of 200 and shifted 10 units up.
It is vertically stretched by a factor of 200 and shifted 10 units right.
It is vertically stretched by a factor of 200 and shifted 10 units up.
What is a function?A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.
How do you write a function?You write functions with the function name followed by the dependent variable.
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Answer:
Step-by-step explanation:
i cant see the answer
The center of an ice rink is located at (0, 0) on a coordinate system measured in meters. Susan is skating along a path that can be modeled by the equation y = 6x – x2 – 5. Luke starts at (10, –21) and skates along a path that can be modeled by a quadratic function with a vertex at (8, –9). If the rink is a circle with a radius of 35 meters, which statement best interprets the solution(s) of a system of equations modeling the paths of the skaters?
The skaters’ paths intersect once, but that point is outside the rink.
The skaters’ paths intersect once, and that point is inside the rink.
The skaters’ paths intersect twice, but only one of those points is inside the rink.
The skaters’ paths intersect twice, and both points are inside the rink.
Answer:
Option C: The skaters path intersect twice, but only one of those points is inside the rink.
Step-by-step explanation:
Coordinates of center of ice rink: (0,0) Radius of ice rink circle = 35 m
We know that the equation of a circle with center coordinates (a,b) and radius of (r) is given as; (x - a)² + (y - b)² = r²
Thus, the total area on which the skaters are skating will be given by the equation;
x² + y² = 35²
Now, we are told the path along which Susan is skating is modeled by the equation: y = 6x - x² - 5
While Luke starts at (10, –21) and skates along a path that can be modeled by a quadratic function with a vertex at (8, –9)
From equation of a parabola, the path along which like is skating can be modeled by;
(x - 8)² = 4a(y + 9)
To find a, we will substitute the coordinate started at to get;
(10 - 8)² = 4a(-21 + 9)
4 = 4a × -12
Divide both sides by 4 to get;
a = -1/12
Thus;
(x - 8)² = 4(-1/12)(y + 9)
(x - 8)² = (-1/3)(y + 9)
This gives: 3(x - 8)² = -(y + 9)
I've drawn the graph on demos and attached it.
From the graph we can see that the skaters points intersect twice but one is inside the rink circle while the other is outside the rink circle. The point at which they intersect outside the rink was slightly cropped out because of size. But it is clearly seen that they are both approaching point of intersection.
Thus, correct answer is Option C.
-10+30+58=9-54 X 50-4=
Answer:
Hi
Step-by-step explanation:
SOLUTION STEPS
−10+30+58=9−54×50−4=
Add −10 and 30 to get 20.
20+58=9−54×50−4
Add 20 and 58 to get 78.
78=9−54×50−4
Multiply 54 and 50 to get 2700.
78=9−2700−4
Subtract 2700 from 9 to get −2691.
78=−2691−4
Subtract 4 from −2691 to get −2695.
78=−2695
Compare 78 and −2695.
Calculate 441 ÷ 3 by using long division
Answer:
the answer is 147
Step-by-step explanation:
I have attached a picture with the work. Hope this helps :)
The answer is 147 0 Remainder
EXPLANATION: MY A$* (not that hard lol)
Step 1:
Start by setting it up with the divisor 3 on the left side and the dividend 441 on the right side like this:
Step 2:
The divisor (3) goes into the first digit of the dividend (4), 1 time(s). Therefore, put 1 on top:
Step 3:
Multiply the divisor by the result in the previous step (3 x 1 = 3) and write that answer below the dividend.
Step 4:
Subtract the result in the previous step from the first digit of the dividend (4 - 3 = 1) and write the answer below.
Step 5:
Move down the 2nd digit of the dividend (4) like this:
Step 6:
The divisor (3) goes into the bottom number (14), 4 time(s). Therefore, put 4 on top:
Step 7:
Multiply the divisor by the result in the previous step (3 x 4 = 12) and write that answer at the bottom:
Step 8:
Subtract the result in the previous step from the number written above it. (14 - 12 = 2) and write the answer at the bottom.
Step 9:
Move down the last digit of the dividend (1) like this:
Step 10:
The divisor (3) goes into the bottom number (21), 7 time(s). Therefore put 7 on top:
Step 11:
Multiply the divisor by the result in the previous step (3 x 7 = 21) and write the answer at the bottom:
Step 12:
Subtract the result in the previous step from the number written above it. (21 - 21 = 0) and write the answer at the bottom.
You are done, because there are no more digits to move down from the dividend.
The answer is the top number and the remainder is the bottom number.
Therefore, the answer to 441 divided by 3 calculated using Long Division is:
147
0 Remainder
ur welcome dummyboi
So this question really confuses me LOL SO PLEASE HELP LOL ;-; I WILL GIVE BRAINLIEST
The proportional equation us y = 2.5x and the constant is 2.5
6 bottles would have a volume of 15 liters.
How to solve an equation?An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.
Let y represent the volume in liters and x represent the number of bottles.
A proportional relationship is in the form:
y = kx; where k is the constant of proportionality.
From the table, using the value (2, 5):
y = kx
substituting:
5 = 2k
k = 2.5
The proportional equation us y = 2.5x and the constant is 2.5
For 6 bottles:
y = 2.5(6) = 15 liters
6 bottles would have a volume of 15 liters.
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3x+y=4 pls help me with this i need to get this right
Answer: y - intercept is c = 4.
Step-by-step explanation:
The line equation is 3x + y = 4.
The slope-intercept form of the line equation is y = mx + c.
Where m is the slope of line c is the y-intercept.
The equation is 3x + y = 4.
subtract 3x from each side.
y - intercept is c = 4.
To practice for a competition, Ava swam 0.69 kilometer in the pool each day for 4 weeks. How many meters did Ava swim in those 4 weeks? 1 km = 1,000 m
Answer:
14490 meters
Step-by-step explanation:
0.69 x 3weeks which is (21) days , so 0.69•21 =14.490km 14.490km=14490 meters
A cylinder has a volume of 72 cubic inches. What is the volue of a cone with the same height and radius as the cylinder
A cone with the same height and radius as a cylinder has a volume of 24 cubic inches.
If a cylinder has a volume of 72 cubic inches, we can use the formula for the volume of a cylinder to find its height and radius. The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.
So, we have:
72 = πr^2h
We can solve this equation for h:
h = 72/(πr^2)
Now, we can use the formula for the volume of a cone to find the volume of a cone with the same height and radius as the cylinder. The formula for the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius, and h is the height.
So, we have:
V = (1/3)πr^2(72/(πr^2))
Simplifying this equation, we get:
V = 24
Therefore, the volume of a cone with the same height and radius as the cylinder is 24 cubic inches.
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Help please with this maths I need to check it it’s right
Answer:
9999
Step-by-step explanation:
99x10=990
99x1=99
9999
Answer:9999
I hope it is helpful:)
Step-by-step explanation:
we can see 99 is 100-1 and 101 is 100+1
we can rewrite this as,
99*101=(100-1)(100+1)
let's use short mltiplication formula,
[tex]a^{2}-b^{2}=(a-b)(a+b)\\(100-1)(100+1)=100^{2}-1^{2}=10000-1=9999[/tex]
Find the domain and the range of the function and compute the following values of f(x). 10 points. f(x)={x2+3−x+1. if x<1 if x≥1} a. Domain b. Range
The domain of the given function is (-∞, 1) ∪ [1, ∞) and the range of the function is [1/4, ∞)
The domain of a function is the set of all possible values for which the function is defined. In the given function, there are two separate definitions: one for x < 1 and another for x ≥ 1. Hence, we can say that the domain of the given function is (-∞, 1) ∪ [1, ∞).b. Range: The range of a function is the set of all possible values that the function can take. Since the function is a quadratic function, it is always positive, and the minimum value occurs at x = -b/2a. The minimum value of the function occurs at x = -b/2a = 1/2.
Thus, the range of the function is [1/4, ∞). Computing the values of f(x): Now, we have to compute the following values of f(x): f(0), f(1/2), and f(2).f(0): The value of the function when x = 0 is given by the second part of the definition:f(0) = (0² + 3 - 0 + 1) = 4f(1/2): The value of the function when x = 1/2 is given by the first part of the definition: f(1/2) = (1/4 + 3 - 1/2 + 1) = 13/4f(2): The value of the function when x = 2 is given by the second part of the definition: f(2) = (2² + 3 - 2 + 1) = 8Therefore, f(0) = 4, f(1/2) = 13/4, and f(2) = 8.
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Solve for vertex algebraically x^2+4x+6
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{+6} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 4}{2(1)}~~~~ ,~~~~ 6-\cfrac{ (4)^2}{4(1)}\right) \implies \left( - \cfrac{ 4 }{ 2 }~~,~~6 - \cfrac{ 16 }{ 4 } \right) \\\\\\ \left( -2 ~~~~ ,~~~~ 6 -4 \right)\implies (-2~~,~~2)[/tex]
PLEASE HELP!! ITS DUE IN 40 MINUTES!!
Measure the lengths of the following segments in BOTH centimeters and
millimeters.
The measure of the lengths of the following line segments using online ruler are given as follows:
KL = 5.11cm or = 51.1mm
FG = 8.67cm or = 86.7mm
Length is a physical quantity that refers to the measurement of the extent of an object or distance between two points. It is usually measured in units such as meters, centimeters, or feet.
A line segment is a part of a line that is bounded by two distinct endpoints. It is the shortest distance between two points on a straight line.
To convert cm to mm, we multiply by 10 because there are 10 millimeters in 1 centimeter.
Therefore, to convert 5.11 cm to mm, we can multiply 5.11 by 10:
5.11 cm * 10 = 51.1 mm
So, 5.11 cm is equal to 51.1 mm.
Also to convert 8.67 cm to mm, we can multiply 8.67 by 10:
8.67 cm * 10 = 86.7 mm
So, 8.67 cm is equal to 86.7 mm.
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Full Question:
Although part of your question is missing, you might be referring to this full question: See attached image.
What are the multiples of 12, of which the square root is 6
The only multiple of 12 with a square root of 6 is 12 times 3, or 36 using generate multiples of 12 .
The multiples of 12 are numbers that are divisible by 12 without a remainder. We can generate multiples of 12 by multiplying 12 by any integer. For example, the first few multiples of 12 are 12, 24, 36, 48, 60, and so on.
To find which multiples of 12 have a square root of 6, we can use the following formula:
√(12n) = √(12) * √(n)
Since the square root of 12 is equal to 2 times the square root of 3, we can simplify the formula as follows:
√(12n) = 2 * √(3n)
If the square root of 12n is equal to 6, then we can set up an equation and solve for n:
2 * √(3n) = 6
√(3n) = 3
3n = 9
n = 3
In summary, we can use the formula √(12n) = 2 * √(3n) to find which multiples of 12 have a square root of 6. By solving for n, we find that the only multiple of 12 with a square root of 6 is 36.
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A frustum is made by removing a small
rectangular-based pyramid from a similar, larger
pyramid, as shown.
Work out the volume of the frustum.
If your answer is a decimal, give it to 1 d.p.
30 cm
10 cm
6 cm
40 cm
Not drawn accurately
The volume of the frustum is 19840cm³
What is a frustum?A frustum is a cut out section of a defined shape. The volume of the frustum is calculated as;
Volume of the Big shape - Volume of the small shape.
The shape here is a pyramid. And the volume of a pyramid is given as ;
1/3 bh
The height of the big pyramid is obtained by using similar shape theorem
10/10+x = 6/30
= 60+6x = 300
6x = 240
x = 240/6 = 40
Therefore the height of the pyramid = 40+10 = 50cm
Therefore volume of the big pyramid = 1/3 × 30×40× 50
= 10× 40 × 50
= 20000cm³
The volume of the small pyramid = 1/3 bh
The width of the small pyramid = 6/30 = x/40
30x = 240
x = 8
= 1/3 × 8× 6× 10
= 8× 2 × 10
= 160cm³
therefore the volume of the frustum = 20000-160
= 19840cm³
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i need help on this question please
Vοlume οf cylinder is and when height tripled then its vοlume alsο tripled but when radius tripled its vοlume becοme which is nineth times οf οriginal vοlume.
What dο yοu mean by Vοlume?Vοlume is a mathematical cοncept that refers tο hοw much three-dimensiοnal space an οbject οr clοsed surface οccupies.
Vοlume οf cylinder = πr²h
= π × 4² × 10
= 160π m³
When the height is tripled, h becοmes 3h
So, new height = 3 × 10 = 30m
Volume of a Cylinder (when height is tripled) = π × (4)² × 30
= π × 16 × 30
= 480π m³
When height is tripled then vοlume alsο tripled.
When the radius is tripled, r becοmes 3r
So, new radius = 3 × 4 = 12m
Volume of a Cylinder (when radius is tripled)
= π × (12)² × 10
= 1440 m³
But when radius is tripled the vοlumes becοme Nine times.
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2. The distance by road from Newport to London is 140 miles. Tom travels by coach from Newport to London. The coach leaves Newport at 1. 30 pm (a) He assumes the coach will travel at an average speed of 50 mph Use his assumption to work out the arrival time in London.
Tom will arrive in London at 4.10 pm, after travelling 140 miles at an average speed of 50 mph.
The formula to calculate the time taken is: Time = Distance/Speed
Using Tom's assumption that the coach is travelling at an average speed of 50 mph, the time taken for the journey from Newport to London can be calculated as follows:
Time = 140 miles/50 mph = 2.8 hours
Therefore, Tom will arrive in London at 1.30 pm + 2.8 hours = 4.10 pm.
To put this in context, it means that the coach will travel at an average speed of 70 km/h, covering a distance of 224 km in 2.8 hours. This is equivalent to covering 80 km in an hour.
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Which values in the data set are outliers? Show all work
72, 81, 82, 83, 83, 85, 100, 54, 75, 81,83
List the follow (and show work if needed): Q1, Median, Q3, IQR, Lower Fence, Upper Fence and outliers
Answer: The outliers are 54 and 100.
Step-by-step explanation:
And outlier is a number that doesnt belong. Learn more about outliers here https://www.itl.nist.gov/div898/handbook/prc/section1/prc16.htm#:~:text=An%20outlier%20is%20an%20observation,what%20will%20be%20considered%20abnormal.
(If you were also asking about the q1, medians, and q3 please make that a seperate question.
A sculpting tool is in the shape of a solid triangular prism. the tool is made of 12 in.3 of metal and is 4 in. long. what is the height of the base if it is 2 in. wide? 1.5 in. 3 in. 48 in. 96 in.
The height of the base if it is 2 in. wide is 3 inches. Option B
How to calculate The height of the baseLet's call the height of the triangular base h (in inches).
The volume of the triangular prism can be calculated using the formula:
Volume = (1/2) x Base x Height x Length
In this case, the length is given as 4 inches, the width (or base) is given as 2 inches, and the volume is given as 12 cubic inches. Substituting these values into the formula, we get:
12 = (1/2) x 2 x h x 4
Simplifying this equation, we get:
12 = 4h
Dividing both sides by 4, we get:
h = 3
Therefore, the height of the triangular base is 3 inches.
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Answer: 3
Step-by-step explanation:
Can someone help asap with this please?
By looking at the degree, we conclude that we have 4 roots.
How many roots has the function?Here we want to see how many roots the function:
x⁴ - 2x³ - 6x² + 22x - 15 = 0
The numer of roots (repeated, complex, or real) is given by the degree of the g
In this case we can see that the maximum exponent is 4, so the degree is 4, which means that we have 4 roots
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Find g(x), where g(x) is the translation 1 unit left of f(x)=7x–5.
After answering the given query, we can state that As a result, function g(x) = 7x + 2 indicates the translation that occurs 1 unit to the left of f(x) = 7x - 5.
what is function?Mathematicians research numbers, their variations, equations, associated structures, shapes, and possible configurations of these. The relationship between a group of inputs, each of which has a corresponding outcome, is referred to as a "function." A function is a relationship between inputs and outputs where each input results in a unique, distinct output. Each function has a domain, codomain, or scope assigned to it. Functions are commonly denoted by the letter f. (x). An cross is entered. On functions, one-to-one capabilities, so several capabilities, in capabilities, and on functions are the four main categories of available functions.
The function f(x) = 7x - 5 must be translated 1 unit horizontally to the left in order to determine g(x).
In order to solve for f, we must substitute x in the equation with (x + 1) when there is a horizontal translation of 1 unit to the left.(x). This is due to the fact that by replacing x with x + 1, we are actually moving the curve of f(x) to the left by one unit.
So, g(x) = f(x + 1) can be expressed as:
g(x) = 7(x + 1) - 5
g(x) = 7x + 2
As a result, g(x) = 7x + 2 indicates the translation that occurs 1 unit to the left of f(x) = 7x - 5.
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events. a. A∣B b. A∣B ′ c. A∣B ' d. Are events A and B independent? a. P(A∣B)= (Round to two decimal places as needed.) b. P(A∣B ′ )= (Round to two decimal places as needed.) c. P(A ′ ∣B ′ )= (Round to two decimal places as needed.) d. Are events A and B independent? A and B are not independent. A and B are independent.
The A and B are independent then P(A∣B) = P(A).Since P(A) = 0.60 and P(A∣B) = 0.60, it can be said that A and B are not independent.
P(A∣B)= 0.60 (Round to two decimal places as needed.)b. P(A∣B ′ )= 0.45 (Round to two decimal places as needed.)c. P(A ′ ∣B ′ )= 0.20 (Round to two decimal places as needed.)d. Are events A and B independent? A and B are not independent.Explanation:A∣B means that the event A occurs when the event B occurs. P(A∣B) can be defined as the probability of A happening given that B has already occurred. By definition, A and B are independent if P(A∣B) = P(A).a. P(A∣B)= P(A∩B)/P(B)0.60 = 0.36/0.60= 3/5 b. P(A∣B ′ )= P(A∩B ′ )/P(B ′ )0.45 = 0.27/0.60= 9/20c. P(A ′ ∣B ′ )= P(A ′ ∩B ′ )/P(B ′ )0.20 = 0.12/0.60= 1/5d. If A and B are independent then P(A∣B) = P(A).Since P(A) = 0.60 and P(A∣B) = 0.60, it can be said that A and B are not independent.
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A population proportion is 0.61. Suppose a random sample of 659 items is sampled randomly from this population. Appendix A Statistical Tables Answer D and E only! will thumbs up! (Round values of z to 2 decimal places, e.g. 15.25 and final answers to 4 decimal places, e.g. 0.2513.) d. What is the probability that the sample proportion is between 0.56 and 0.59? e. What is the probability that the sample proportion is less than 0.51?
D)probability that the sample proportion is between 0.56 and 0.59 is 0.7912.
E)Probability that the sample proportion is less than 0.51 is 0.0002
D. To calculate the probability that the sample proportion is between 0.56 and 0.59, we can use the Standard Normal Probability Distribution Table. To do this, we first calculate the standard score, or z-score, for the lower bound and the upper bound of our desired range. The formula for calculating the z-score is:
z = (x - μ) / σ
where x is the value for which you want to find the z-score, μ is the population mean, and σ is the population standard deviation. In this case, x is the sample proportion, μ is 0.61, and σ is 0.01. Therefore, the z-score for the lower bound (0.56) is -2.90, and the z-score for the upper bound (0.59) is -0.33. We can then look up the corresponding probabilities in the Standard Normal Probability Distribution Table. The probability that the sample proportion is between 0.56 and 0.59 is 0.7912.
E. To calculate the probability that the sample proportion is less than 0.51, we can use the same process as above. The z-score for 0.51 is -3.90. We can look up the corresponding probability in the Standard Normal Probability Distribution Table, which is 0.0002. Therefore, the probability that the sample proportion is less than 0.51 is 0.0002.
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The line I passes through the points (3,−4) and (2, 2).
Find the gradient of line L.
Ray only wants to cover the lateral area of his paper weight. How many square inches of paper will he need? Round your answer to the nearest square inch.
The lateral area of this paper weight is 61.42 sq inches.
What is lateral surface area?Every solid object's lateral area may be calculated using the lateral area formula. Every figure's lateral area only includes the non-base faces. Calculating the lateral surface area of various forms, such as a cuboid, cube, cylinder, cone, or sphere, is made easier with the use of lateral area formulae. The object's base and the face parallel to the base are not included in the lateral area.
The surface area of the composite figure is the addition of the area of all the shapes.
The area of triangle with height 3.5 in is:
A1 = 1/2(6.5)(3.5)
A1 = 11.375 sq. in.
There are two such triangles thus, 2A1 = 2(11.375) = 22.75.
The area of the two triangle with height 6.5 in is:
A2 = 2(1/2)(4.3)(6.5) = 27.95 sq. in.
The area of the rectangle is:
A3 = (l)(w)
A3 = (6.5)(4.2) = 27.3 sq. in.
The total lateral area is:
LA = 11.375 + 22.75 + 27.3 = 61.42 sq inches.
Hence, the lateral area of this paper weight is 61.42 sq inches.
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In the figure, three lines intersect at point P. If x = 65 and y = 75, what is the value of z?
The value of angle Z is 40 degrees. (Option 3). In this problem, we are given that three lines intersect at point P and we need to find the value of angle Z.
We know that angle X is 65 degrees and angle Y is 75 degrees. We also know that all six angles formed by the intersection of the three lines add up to 360 degrees.
Using these facts, we can set up an equation as
2X + 2Y + 2Z = 360.
We can simplify this equation to
X + Y + Z = 180.
We can then substitute the given values of X and Y to get
65 + 75 + Z = 180.
Simplifying this equation, we get Z = 40, which means Z is equal to 40 degrees.
Therefore, the answer is option C.
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Complete Question:
In the figure, 3 lines intersect at point P. If x = 65 and y = 75, what is the value of z?
140804020what is the average rate of change of f(x) from x=-4 to x=0?
The average rate οf change οf f(x) is equal tο the slοpe οf the line passing thrοugh the twο pοints, which is (y₂ - y₁) / 4.
What is the average rate οf change?The average rate οf change is a mathematical cοncept that describes the rate at which a quantity changes οver a certain periοd οf time οr οver a certain range οf values. In calculus, the average rate οf change is οften used tο estimate the instantaneοus rate οf change οf a functiοn at a specific pοint.
Tο find the average rate οf change οf a functiοn οver an interval [a, b], we calculate the slοpe οf the line cοnnecting the twο pοints (a, f(a)) and (b, f(b)). This is given by the fοrmula:
average rate οf change = (f(b) - f(a)) / (b - a)
Tο calculate the average rate οf change οf f(x) frοm x=-4 tο x=0, we need tο find the slοpe οf the line cοnnecting the twο pοints.
The fοrmula fοr the slοpe οf a line passing thrοugh twο pοints (x₁, y₁) and (x₂, y₂) is:
slοpe = (y₂ - y₁) / (x₂ - x₁)
In this case, the twο pοints are (-4, f(-4)) and (0, f(0)). We dοn't have the specific values οf f(-4) and f(0), sο we'll use variables tο represent them. Let's say f(-4) = y₁ and f(0) = y₂.
Then the slοpe οf the line is:
slοpe = (y₂ - y₁) / (0 - (-4)) = (y₂ - y₁) / 4
Sο the average rate οf change οf f(x) frοm x=-4 tο x=0 is equal tο the slοpe οf the line passing thrοugh the twο pοints, which is (y₂ - y₁) / 4.
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Mr. Tomas is making a rectangular concrete pad for shed. The area of a pad is 17. 5 square yards. The length of the pad is 5 yards. What is the width of the pad?
If the area of a pad is 17. 5 square yards, the length of the pad is 5 yards, the width of the pad is 3.5 yards.
The formula for the area of a rectangle is:
Area = length x width
We know that the area of the pad is 17.5 square yards, and the length is 5 yards. We can use this information to solve for the width.
Let's substitute the values we know into the formula:
17.5 = 5 x width
To solve for the width, we need to isolate it on one side of the equation. We can do this by dividing both sides by 5:
17.5/5 = width
Simplifying the left side gives:
3.5 = width
In conclusion, Mr. Tomas should make a rectangular concrete pad that is 5 yards long and 3.5 yards wide to have an area of 17.5 square yards.
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In 2009 A.D., the number of tourist who visited Nepal was 2,50,000. In 2010, was decreased by 5% and in 2011 it was increased by 40%. How many touris visited Nepal in 2011?
There were 332500 tourists who traveled to Nepal in 2011.
What is unitary method?"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."
We always count the unit or amount value first and then calculate the more or less amount value.
For this reason, this procedure is called a unified procedure.
Many set values are found by multiplying the set value by the number of sets.
A set value is obtained by dividing many set values by the number of sets.
Number of tourists in 2010 = 95% of number of tourists in 2009
= 0.95 x 250000
= 237500
Number of tourists in 2011 = 140% of number of tourists in 2010
= 1.4 x 237500
= 332500
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Help me ill give you brainliest and extra points Find the average rate of change of g(x)=-x²+4x+2 from x=3 to x=7
The average rate of change of g(x) from x = 3 to x = 7 is -5.
To find the average rate of change of the function g(x) = -x² + 4x + 2 over the interval [3, 7], we need to calculate the change in the function values over this interval and divide by the length of the interval.
The change in the function values between x = 3 and x = 7 is:
g(7) - g(3) = (-7² + 47 + 2) - (-3² + 43 + 2) = (-49 + 28 + 2) - (9 + 12 + 2) = -20
Therefore, the average rate of change of g(x) over the interval [3, 7] is:
average rate of change = change in function values / length of interval
= -20 / (7 - 3)
= -5
This means that on average, the function g(x) decreases by 5 units for every 1 unit increase in x over the interval [3, 7].
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Determine if triangle BCD and triangle EFG are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale. )
We can conclude that the triangles are similar, based on the Side-Angel-Side Theorem (SAS).
Hence, the answer is The third option.
Given the triangles EFG and BCD, you can identify that:
By definition, two triangles are similar if the lengths of the corresponding sides are in proportion and their corresponding angles are congruent.
In this case, you can identify that you know two pairs of corresponding sides. Then, you can find that they are in proportion. Set up that:
[tex]\frac{EF}{BC}=\frac{FG}{CD}[/tex]
Substituting values and simplifying, you get:
[tex]\frac{18}{90}=\frac{16}{80}\\\\\frac{1}{5}=\frac{1}{5}[/tex]
Notice that they are in proportion.
You can also identify that the corresponding angles F and I are congruent because they have equal measures.
Therefore, since you know that two sides are proportionate and the included angles are congruent, you can conclude that the triangles are similar, based on the Side-Angel-Side Theorem (SAS).
Hence, the answer is The third option.
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