The growth in x years for the gym will be represented as [tex]y = 840(1.25)^x[/tex].
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
City Fitness, a popular gym currently has 840 members. Based on its membership statistics since opening a few years ago, City Fitness expects to grow its membership by a factor of 1/4.
The expression can be written as,
[tex]y = 840(1.25)^x[/tex].
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How does the value of a number change when you divide by 10 100 1000?
Answer: It gets smaller
Step-by-step explanation: When you divide something by anything, the place value of the digits decreases. The digits move to the right since the number gets smaller, but remember, the decimal point does not move.
A circle is inscribed in quadrilateral , tangent to at and to at . Given that , , , and , find the square of the radius of the circle.
The square of the radius of the given circle is [tex]$OP^2 = 703$[/tex]
What is quadrilateral?A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus. Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties.
We can use the concept of the power of a point, which states that the square of the distance of a point from a line is equal to the product of the distances of the point from the two tangents to the line that are drawn from the point.
Let [tex]$O$[/tex] be the center of the inscribed circle.
The power of point O with respect to AB and CD is [tex]$(OPOQ) = (1937) = 703$[/tex]
Since the Circle is tangent to AB and CD at P and Q respectively, so [tex]$OP = OQ$[/tex]
So, [tex]$OP^2 = 703$[/tex]
Hence, the square of the radius of the circle is [tex]$OP^2 = 703$[/tex]
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Complete question is: A circle is inscribed in quadrilateral [tex]$A B C D$[/tex], tangent to [tex]$\overline{A B}$[/tex] at [tex]$P$[/tex] and to [tex]$\overline{C D}$[/tex] at [tex]$Q$[/tex]. Given that [tex]$A P=19, P B=26, C Q=37$[/tex], and [tex]$Q D=23$[/tex], find the square of the radius of the circle.
Please help! ;)
The vectors VN−→{−8;3} and MT−→{2;10} are given. Calculate: 7⋅VN−→3⋅MT−→ =
Answer: { ; }.
Answer:
Step-by-step explanation:
To calculate 7⋅VN−→3⋅MT−→, we need to perform scalar multiplication on the two vectors. Scalar multiplication is simply multiplying each of the components of the vector by the scalar value.
So for the first vector, we have: 7⋅VN−→ = {7⋅(-8); 7⋅3} = {-56; 21}.
For the second vector, we have: 3⋅MT−→ = {3⋅2; 3⋅10} = {6; 30}.
Then to add the two vectors, we simply add the corresponding components: {-56; 21} + {6; 30} = {-50; 51}.
Therefore, the final result is {-50; 51}.
Add the following polynomials, then place the answer in the proper location on the grid. Write the answer in descending powers of a. Add: 3a 3 8a - 6 and 4a 2 - 9a 11
Adding the polynomial 3a³ + 8a - 6 and 4a² - 9a + 11 gets 3a³ + 4a² - a + 5.
The answer in descending powers of a is 3a³ + 4a² - a + 5.
A polynomial is a mathematical expression consisting of a sum of powers in one or more variables (indeterminates) with non-negative integer exponents.
Adding the polynomial 3a³ + 8a - 6 and 4a² - 9a + 11
(3a³ + 8a - 6) + (4a² - 9a + 11) = 3a³ + 4a² - a + 5
The coefficients of a³, a², a and 1 is 3, 4, -1 and 5 respectively.
Descending powers of a in the polynomial is a³, a², a. So the answer in descending powers of a is 3a³ + 4a² - a + 5.
--The question is incomplete, answering to the question below--
"Add the following polynomials, then place the answer in the proper location on the grid. Write the answer in descending powers of a.
Add: 3a³ + 8a - 6 and 4a² - 9a + 11"
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Mariana spent $166.50 on games played at a laser tag arena
last year. If the laser tag arena charges $4.50 per game, how
many games did Mariana play at the arena last year?
Answer: 37
Step-by-step explanation:
divide the total that she spent over how much each game is (166.50/4.50). this will give you the number of games that she played.
What are the 15 types of angles?
There are various classifications of angles, some of which include: Acute angles, Right angles, Obtuse angles, Straight angles, Reflex angles, Complementary angles, Supplementary angles, Adjacent angles, Linear pair, Vertically opposite angles, Alternate interior angles, Alternate exterior angles, Corresponding angles, Conjugate angles, and Explementary angles.
It's important to note that this is not an exhaustive list and the classification may vary depending on the context.
Acute angles which measure less than 90 degrees, Right angles that measure exactly 90 degrees, Obtuse angles that measure more than 90 degrees but less than 180 degrees.
There is also Straight angles that measure exactly 180 degrees, Reflex angles that measure more than 180 degrees but less than 360 degrees, Complementary angles which add up to 90 degrees, Supplementary angles which add up to 180 degrees.
Then there is Adjacent angles that share a common vertex and a common side but no common interior points, Linear pair which add up to 180 degrees and share a common side, Vertically opposite angles that are formed by two intersecting lines and are opposite to each other, Alternate interior angles that are formed by two intersecting lines on opposite sides of a transversal and inside parallel lines, Alternate exterior angles that are formed by two intersecting lines on opposite sides of a transversal and outside parallel lines, Corresponding angles that are formed by two intersecting lines in the same relative position.
Conjugate angles are angles which are supplementary but non-adjacent, and Explementary angles are angles which add up to 90 degrees.
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How do you find an inverse?
Answer:
by using 1 to divide the value
Step-by-step explanation:
the inverse of 5/8 is 8/5.
A water sample must be taken from water at least 20 feet deep. Find the depth of the water feet from shore
The depth of water from the shore is 15 feet.
What is a proportion?
A proportion is an equation that states that two ratios are equal. It can be written in the form of a/b = c/d. The two ratios, a/b and c/d, are called the terms of the proportion.
The cross-products of a proportion are also equal, so ad = bc.
To solve for d in the equation 5/1.5 = 50/d, you can start by multiplying both sides of the equation by 1.5 to cancel out the denominator on the left side. This gives:
5 = 50/d * 1.5
Next, you can simplify the right side of the equation by multiplying 50 and 1.5, which gives:
5 = 75/d
To solve for d, you can now cross-multiply to get:
75 = 5d
Finally, you can divide both sides of the equation by 5 to get:
d = 75/5
d = 15
the value of d is 15.
Hence, the depth of water from the shore is 15 feet.
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The depth of water from the shore is 15 feet.
What is a proportion?
A proportion is an equation that states that two ratios are equal. It can be written in the form of a/b = c/d. The two ratios, a/b and c/d, are called the terms of the proportion.
The cross-products of a proportion are also equal, so ad = bc.
To solve for d in the equation 5/1.5 = 50/d, you can start by multiplying both sides of the equation by 1.5 to cancel out the denominator on the left side. This gives:
5 = 50/d * 1.5
Next, you can simplify the right side of the equation by multiplying 50 and 1.5, which gives:
5 = 75/d
To solve for d, you can now cross-multiply to get:
75 = 5d
Finally, you can divide both sides of the equation by 5 to get:
d = 75/5
d = 15
the value of d is 15.
Hence, the depth of water from the shore is 15 feet.
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Circumference question
1. Suppose a bottle of Buckley's has a radius of 2cm. If you created a label for this product. What is the length of this label?
2. Assumes the company uses 22cm x 12cm boxes for delivery to stores. How many vials will be in each box?
suppose the price of each vial is $5.00. What is the cost of a box?
2 The displacement of a mass is given by the function
y = sin 3t. 3t is measured in radians.
The tasks are to:
a) Draw a graph of the displacement y against time t
for the time t = 0s to t = 2.s.
b)
Identify the position of any turning points and
whether they are maxima, minima or points of
inflexion.
c) Calculate the turning points of the function using
differential calculus and show which are maxima,
minima or points of inflexion by using the second
derivative.
Compare your results from parts b and c.
The graph is attached and the point of maximum as y"(π/6) < 0 and at point of minimum y"(π/2) > 0.
What is turning point and inflexion point?An inflection point is where a graph's curvature changes, from concave up to concave down or vice versa. It is also known as a turning point, flex, inflection, or "point of diminishing returns."
A concave down graph resembles an upside-down U or a cap, while a concave up graph resembles the letter U (or a "cup"). The intersection of a "cup" and a "cap" marks the inflection point.
Given displacement of mass by function,
y = sin(3t), where 3t is in radians,
the graph for t = 0 and t = 2 sec.
2: The position of turning point,
differentiate the equation we get,
y' = 3cos(3t)
the turning points are t = π/6 and t = π/2
y'(π/6) = y'(π/2) = 0
3: inflexion points,
again differentiate the equation we get,
y" = -9sin(3t)
and inflection at π/3
because y"(π/3) = 0
Maximum and minimum points are π/6 and π/2 respectively,
as the point of maximum t = π/6 as y"(π/6) < 0,
and point of minimum at t = π/2 as y"(π/2) > 0.
Hence the graph is attached and maximum at t = π/6, and minimum at t = π/2, and inflection at π/3.
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Eight rooks are placed at positions sampled randomly without replacement on an chessboard. Two rooks attack each other if they are in the same row or in the same column. What is the probability that none of them attacks any of the others
There is a 60% chance that none of them will assault any of the others.
Explain about the Probability?Only the likelihood that something will happen is included in probability. When we don't know how something will turn out, we could talk about the possibility of one or the likelihood of different outcomes. The scientific study of events that fit into a probability distribution is known as statistics.
It is based on the probability that something will happen. The fundamental principle of theoretical probability is the explanation of probability. For instance, when a coin is flipped, there is a 12% chance that it will land on its head.
Probability is a statistic that is used to show the possibility or likelihood that an event will happen. Probabilities can be expressed as fractions from 0 to 1 or as percentages from 0% to 100%.
= 64/8 = 8
= 8 - 2
= 4
= 64- 4
= 60
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man travels 60 miles to work at an average speed of 40mph. He travels home the same route at an average speed of 60mph. What is the average speed of his round trip
Answer:1881 6040mph 18x
An object is moving at a speed of 3 yards per month. Express this speed in centimeters per day.
The speed of the object is 9.14 cm per day.
What is unit conversion?A unit conversion expresses the same property as a different unit of measurement. For instance, time can be expressed in minutes instead of hours, while distance can be converted from miles to kilometers, or feet, or any other measure of length.
Given that, An object is moving at a speed of 3 yards per month. we are asked to express this speed in centimeters per day.
For this, we will have to convert the units,
1 yard = 91.44 cm
3 yards = 91.44 × 3 = 274.32 cm
Therefore, we can say the object is moving 274.32 cm per month
Now,
If it moves 274.32 cm in one month,
Therefore, in day, it will move = 274.32 / 30 [1 month = 30 days]
= 9.144
Hence, the speed of the object is 9.14 cm per day.
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Write the equation of the line that passes through the points (6, 1) and
(6, -8). Put your answer in fully simplified point-slope form, unless it
is a vertical or horizontal line.
something noteworthy is that the x-coordinate is the same for each point, so Check the picture below.
Find the volume of the cylinder to the nearest tenth. Use 3.14 for
4 in.
I
7 in.
in³
On solving the provided question we can say that - Height(h) = h; Radius(r) = r; Length(l) = l Volume of cylinder A(V)=Volume of cylinder B(v) => [tex]4\pi R^2H = \pi r^2h[/tex]
what is cylinder?One of the most fundamental curved geometric forms is the cylinder, which is often a three-dimensional solid. It is referred to as a prism with a circle as its base in elementary geometry. Several contemporary fields of geometry and topology also define a cylinder as an indefinitely curved surface. A three-dimensional object known as a "cylinder" consists of curving surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure that has two bases that are both identical circles joined by a curving surface at the height of the cylinder, which is determined by the distance between the bases from the center. Examples of cylinders are cold beverage cans and toilet paper wicks.
Cylinder A
Height(h) = H; Radius(r) = 2R; Length(l) = L
Cylinder A
Height(h) = h; Radius(r) = r; Length(l) = l
Volume of cylinder A(V)=Volume of cylinder B(v)
[tex]4\pi R^2H = \pi r^2h[/tex]
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When you use substitution What are the steps used to find the solution to a system of linear equations?
In one of the equations, separate one of the two variables. In the other equation, replace the expression with the value of the isolated variable from Step 1. Consequently, a linear equation with just one variable ought to emerge.
What constitutes the substitution system's solution?The one y-value in the substitution method is replaced with the other. We'll give an example to illustrate this. Since y = y, we can replace y in the second equation with y from the first equation. The linear system's solution is (1, 6).
What are the three possible types of solutions for a linear equation?Numerous solutions, no solutions, and a singular solution.
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Find the lengths of the diagonals of rectangle WXYZ
WY = 14x + 10
XZ = 11x + 22
The length of each diagonal is
units.
A rectangle is a four-sided geometric shape where opposite sides are parallel and congruent. The diagonals of a rectangle are two lines that connect the opposite corners of the rectangle, and they bisect each other at 90 degrees.
Briefly defined, what is rectangle?
A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.
Given the sides of rectangle WXYZ are WY = 14x + 10 and XZ = 11x + 22. We can find the length of the diagonals using the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the diagonal of the rectangle) is equal to the sum of the squares of the other two sides (the sides of rectangle)
Diagonal WX: √(14x+10)^2 + (11x+22)^2 = √(196x^2 + 456x + 100 + 121x^2 + 484x + 484) = √(317x^2 + 940x + 584)
Diagonal YZ: √(14x+10)^2 + (11x+22)^2 = √(196x^2 + 456x + 100 + 121x^2 + 484x + 484) = √(317x^2 + 940x + 584)
So, the lengths of the diagonals of rectangle WXYZ are √(317x^2 + 940x + 584) units.
Note that the diagonals of a rectangle are congruent and the value of x is not a known, the diagonal of rectangle is the value of the square root of the expression.
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Answer: 66
Step-by-step explanation:
I skipped it to see the answer hope this helps
Question content area top Part 1 Without using paper and pencil, how would you find the sum of 8.8 and 5.5 and ?
The sum of 8.8 and 5.5 is 14.3
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
To find the sum of 8.8 and 5.5 without using pen and pencil:
First, we break the term in simple manner.
8.8 = 8 + 0.3 + 0.5
And 5.5 = 5 + 0.5
And now adding the terms one by one,
0.5 + 0.5 = 1.0
0.3 = 0.3
8 + 5 = 13
Addition,
13 + 1 + 0.3 = 14.3
Therefore, the value is 14.3
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James is building a doll house that is proportional to his own house. He is using a scale of 0. 5inch = 1foot. If the doll house is 12. 3inches tall, how tall is his house. ?
James's house is 24.6 feet tall because he is using a scale of 0.5 inch per 1 foot. To get this measurement, he multiplied 12.3 inches (the height of the doll house) by 2.
1. Take the height of the doll house (12.3 inches).
2. Multiply 12.3 inches by 2.
3. The result is 24.6 feet which is the height of James's house.
James is building a doll house that is proportional to his own house. He is using a scale of
0.5 inch = 1 foot,
which means that for every 0.5 inch in the doll house, 1 foot is represented in his house. To calculate how tall his house is, we need to figure out how many inches the doll house is. The doll house is 12.3 inches tall. To get the height of James's house, we need to multiply this by 2. Thus, 12.3 inches multiplied by 2 equals 24.6 feet, which is the height of James's house. This is because for every 0.5 inch in the doll house, 1 foot is represented in his house. Therefore, with the scale of 0.5 inch = 1 foot, the height of James's house is 24.6 feet.
1. Determine the scale of the doll house (0.5 inch = 1 foot).
2. Measure the height of the doll house (12.3 inches).
3. Multiply 12.3 inches by 2.
4. The result is 24.6 feet which is the height of James's house.
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I need to factor completely to get an answer for
n²-10n+24
I need to get factors in parenthesis like (n +/- #) (n +/- #)
I need it before tomorrow
Answer:
(n - 6)(n -4)
Step-by-step explanation:
Find two numbers that add to - 10 and multiply to +24.
In this case, -6 * -4 satisfies these requirements.
Please help
The graph shows the reciprocal parent function
Which statement best describes the function
The statement that best represents the function must be identified by reading the graph.
Let's check which of the following statements best characterizes the function:A) When x < 0, the function is negative.
This is accurate; as you can see, the function is negative for x < 0 because it is below the horizontal axis.
We shall see that choice A is the proper one. "When x < 0, the function is negative."
The function tends to infinity on the positive side at an x close to zero.
The function tends to negative infinity at x close to zero on the negative side.
The function tends to zero as x's absolute value grows.
So we can conclude that this is an inverse function similar to:
y = f(x) = 1/x
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victoria took a test and got 80% of the questions right. she answered 20 questions correctly. how mnay queestions were on the test
Answer:
25
Step-by-step explanation:
let there be x questions on the test
80% of x = 20
80% * x = 20
80% = 0.8
0.8 * x = 20
divide both sides by 0.8 to isolate x
x = 20/0.8 = 25
A coin is tossed, a number cube is rolled, and a letter is picked from the word framer. 10. P(tails, 5, m)
Answer: The function you provided describes an experiment in which a coin is tossed, a number cube is rolled, and a letter is picked from the word "framer". The outcome of the experiment is represented by the ordered triple (tails, 5, m).
P(tails, 5, m) refers to the probability of the outcome (tails, 5, m) occurring. To find this probability, you would need to know the probability of each individual event:
The probability of getting tails is 1/2,
The probability of getting a 5 on a number cube is 1/6
and probability of getting letter "m" in the word "framer" is 1/6
So P(tails, 5, m) = (1/2) * (1/6) * (1/6) = 1/72
It is to be noted that in order for the inverse function to exist, the function must be one-to-one, meaning each y value has one unique x value, meaning the random variables in question should be independent. But in this case the events are dependent on one another.
Step-by-step explanation:
Help quickly this is for a final!
The polygons are similar.
The perimeter of pentagon RSTPQ is ___ units.
Answer:
unidentified
Step-by-step explanation:
could you please send the other polygon or send an attachment of the whole question because this information is not enough
What is the additive inverse of 6 /- 5 of Class 8?
The additive inverse of 6 /- 5 is 6/5
We know that for any real number 'a' an additive inverse is a number 'b' such that a + b = 0
i.e., b = -a
An additive inverse of 'a' is -a.
The means, an additive inverse is nothing but changing sign + to - OR - to +
Here we have been given a rational number 6/(-5)
Let m be the additive inverse of number 6/(-5)
From the definition of additive inverse,
6/(-5) + m = 0
[6/(-5) + m] - 6/(-5) = -6/(-5)
[6/(-5) - 6/(-5)] + m= -6/(-5) ...........(associative property of addition)
0 + m = 6/5
m = 6/5
Hence, the additive inverse is 6/5
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Bella has a cell phone plan in which she pays of each call minute and text message she sends. The total number of minutes used and text messages sent last month was 561. If call minutes cost 8€ each and text messages cost 5€ each and her pill was $34. 26, how many minutes did she use?
If the total number of minutes used and text messages sent last month was 561 , then the number of minutes she use is 207 minutes .
The total number of minutes used and text messages is = 561 ;
the cost for per minute cost is = 8 cents ;
the cost for per text message is = 5 cents ;
Bella's total bill amount is = $34.26 = 3426 cents
let the number of minutes used be = x minutes ; and
let the number of text messages be = y ;
So ,According to the question ,
the equations representing the situations are ,
[tex]x+y=561[/tex] and [tex]8x+5y=3426[/tex]
Substituting the values of [tex]y=561-x[/tex] in the equation [tex]8x+5y=3426[/tex] ,
we get ;
[tex]8x + 5(561-x)= 3426[/tex]
On solving ,
we get ; x = 207 minutes ;
So , the number of text messages (y) = [tex]561-207[/tex]
= 354 text messages.
Therefore , the number of minutes is = 207 minutes .
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Mr. Spears was purchasing supplies for his math classroom. He had $25 to spend. Mechanical pencils and erasers come in bundles of 10. Each eraser costs $0.50. Fill in the missing place in the equation to compute the cost of each mechanical pencil.
x+y=10 and ax+0.50y=25 are the system of equations to compute the cost of each mechanical pencil.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Mr. Spears was purchasing supplies for his math classroom.
He had $25 to spend.
Mechanical pencils and erasers come in bundles of 10
Let x represents the Mechanical pencils
y represents the erasers
x+y=10
y=10-x
Each eraser costs $0.50
ax+0.50y=25
a is the cost of the each mechanical pencil.
Hence, x+y=10 and ax+0.50y=25 are the system of equations to compute the cost of each mechanical pencil.
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Show that f is continuous on (−[infinity], [infinity]). f(x) = 1 − x2 if x ≤ 1 ln(x) if x > 1
On the interval
(−[infinity], 1),
f is function; therefore f is continuous on
(−[infinity], 1).
On the interval
(1, [infinity]),
f is function; therefore f is continuous on
(1, [infinity]).
The function [tex]$$f(x)= \begin{cases}1-x^2 & x \leqslant 1 \\ \ln (x) & x \geqslant 1\end{cases}$$[/tex] is continuous on (-∞, ∞).
As per the given data the function f(x) is given by:
[tex]$$f(x)= \begin{cases}1-x^2 & x \leqslant 1 \\ \ln (x) & x \geqslant 1\end{cases}$$[/tex]
Here we have to determine that the function f(x) is continuous on (-∞, ∞)
If we show that f(x) is continuous at x = 1 then f(x) is continuous on (-∞, ∞)
What are continuous function?
A continuous function in mathematics is one where changes in the parameter cause constant changes in the function's value (i.e., a change without a leap). This shows that there are no abrupt changes in value or discontinuities.
To show f(x) is continuous at x = 1
[tex]\lim _{x \rightarrow 1^{-}} f(x)=\lim _{x \rightarrow 1^{+}}[/tex] f(x)
[tex]\rightarrow \lim _{x \rightarrow 1^{-}} f(x) & =\lim _{x \rightarrow 1^{-}}\left(1-x^2\right) \\[/tex]
= 1 - 1
= 0
[tex]\lim _{x \rightarrow 1^{+}} f(x) & =\lim _{x \rightarrow 1^{+}} \ln (x) \\[/tex]
= ln 1
= 0
Therefore [tex]\lim _{x \rightarrow 1^{+}} f(x) & =\lim _{x \rightarrow 1^{-}} f(x)-0[/tex].
Hence f(x) is continuous on (-∞, ∞)
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5
Drag each length to the correct location on the image. Each length can be used more than once, but not all lengths will be used.
What are the missing segment lengths shown in the image?
20
10 10√3
20√3 10 2 20√2
45° 45°
4
45°
20
00
45°
The missing segment lengths are CD = 10√2, AC = 10√2, BC = 10 and AB = 10.
Drag each length to the correct location accordingly
How to find the missing segment lengths?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
In ΔACD,
sin 45° = CD/20 (sin = opp/hyp)
(√2)/2 = CD/20
CD = (√2)/2 × 20
CD = 10√2
cos 45° = AC/20 (cos = adj/hyp)
(√2)/2 = AC/20
AC = (√2)/2 × 20
AC = 10√2
In ΔABC,
sin 45° = BC/10√2 (sin = opp/hyp)
(√2)/2 = BC/10√2
BC = (√2)/2 × 10√2
BC = (10 × 2)/2
BC = 10
cos 45° = AB/10√2 (cos = adj/hyp)
(√2)/2 = AB/10√2
AB = (√2)/2 × 10√2
AB = 10
Drag each length of the missing segment to the correct location
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What do you call two angles whose measures have a sum of 180?
Answer:
supplementary angles
Step-by-step explanation:
for instance, 50 + 130 = 180.