All 45-45-90-degree triangles have sides that are in a unique ratio. The two legs are exactly the same length.
This triangle is important because any time we're given one side of a 45-er triangle, we can figure out the other two sides.
If one leg is given, the hypotenuse is calculated by multiplying this length by the square root of 2.The hypotenuse is given, and the leg is calculated by dividing the hypotenuse by the square root of 2.The 30-60-90 degree triangle is half of an equilateral triangle, cut straight down the middle along its altitude. This triangle has angles of 30°, 60°, and 90°.
The shortest leg is over from the 30-degree angle, the length of the hypotenuse is always double the length of the shortest leg,If the hypotenuse is given, the long leg is calculated by dividing the hypotenuse by 2.If the long leg is given, the hypotenuse is calculated by dividing this side by the square root of 3.Read more about 30-60-90 degree triangle:
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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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Write an exponential function to represent the spread of Ben's social media post. Write an exponential function to represent the spread of Carter's social media post
So, y = ab^x and y = ac^x are the exponential functions to represent the spread of Ben's and Carter's social media posts respectively.
An exponential function has the form y = ab^x, where a and b are constants and x is the independent variable (in this case, time).
For Ben's social media posts:
y = ab^x
For Carter's social media post:
y = ac^x
Please note that the value of a, b, and c will be different for Ben and Carter's post, as it will depend on the number of shares, likes, views, etc., and the rate of spread of the post.
This is an exponential function that represents the spread of Ben's social media posts and Carter's social media post.
Complete Question:
1. Write an exponential function to represent the spread of Ben's social media post 2. Write an exponential function to represent the spread of Carter's social media post. 3. Graph each function using at least three points for each curve. All graphs should be placed together on the same coordinate plane, so be sure to label each curve. You may graph your equation by hand on a piece of paper and scan your work, or you may use graphing technology. 4. Using the functions for each student, predict how many shares each student's post will be received on Day 3 and then on Day 10. Justify your answers 5. If Amber decides to mail copies of her photo to the 45 residents of her grandmother's assisted living facility, the new function representing her photo shares is . How does this graph compare with the original graph of Amber's photo share? 6. Based on your results, which students' post travels the fastest? How is this shown in the equation form of the functions? 7. If you had to choose, would you prefer a post with fewer friends initially but more shares, like Amber, or more friends initially but fewer shares? Justify your answer with your calculations from previous questions
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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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What is the negation of ∃?
In order to find the negation of an expression we simply put the not operator in front of them . Therefore, the negation of ∃ is that â is not ^ to f.
The term negation means opposite , that is the negation of a statement is the opposite of the given mathematical statement. If we will take the example of P , let P be a statement, then the negation of P will be represented by ~P.
There are two symbols which are used to represent the negation of a statement which are “~” or “¬”. Therefore, ~P is known as the negation of P.
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Find the gradients of lines A and B.
Answer: The Gradient of line A and B are
2 and -1
Step-by-step explanation:
For the given two points A(x1, y1) and B(x2, y2)
The gradient of the line AB is y2-y1/x2-x1
So the gradient of line A is
5-1/2-0
2
the gradient of line B is
5-0/0-5
-1
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
18+x=27
please answer soon:)
Answer:
x = 9
Step-by-step explanation:
18 + x = 27
x = 27 - 18
x = 9
please assist with helping in the image below!!
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.
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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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.
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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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 slope. please help
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 $0.50
ax+0.50y=25
a is the cost of the each mechanical pencil.
Hence, x+y=10 and ax+0.50y=25 are the system of equations to compute the cost of each mechanical pencil.
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what is the answer to 16(5-4v)=-5-v
A circle is inscribed in quadrilateral , tangent to at and to at . Given that , , , and , find the square of the radius of the circle.
The square of the radius of the given circle is [tex]$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.
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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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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For a project in her Geometry class, Violet uses a mirror on the ground to measure the height of her school’s football goalpost. She walks a distance of 6.65 meters from the goalpost, then places a mirror flat on the ground, marked with an X at the center. She then walks 4.25 more meters past the mirror, so that when she turns around and looks down at the mirror, she can see the top of the goalpost clearly marked in the X. Her partner measures the distance from her eyes to the ground to be 1.75 meters. How tall is the goalpost? Round your answer to the nearest hundredth of a meter.
Answer: To find the height of the goalpost, we can use the information provided in the problem and the concept of similar triangles. Since Violet is looking down at the mirror, the line of sight from her eyes to the top of the goalpost forms a right angle with the ground. This right angle creates two similar triangles, one between her eyes, the ground, and the top of the goalpost, and the other one between the mirror on the ground, the goalpost, and a point on the ground that is the same distance from the mirror as the top of the goalpost is from Violet's eyes.
Since similar triangles have the same angle measures, we can set up the following proportion:
(distance from mirror to point on the ground) / (distance from mirror to top of goalpost) = (distance from Violet's eyes to ground) / (height of goalpost)
We can now use the information provided in the problem to solve for the height of the goalpost.
(6.65+4.25)/x = 1.75 / H
x = (6.65+4.25) * (1.75/H)
Where x is the distance from mirror to top of the goalpost.
Substitute the known values and solve for H
H = 1.75*(6.65+4.25) / x = 1.75*10.9 / x
We know that x = 4.25, so
H = 1.75*10.9 / 4.25 = 4.093 m
The height of the football goalp
Step-by-step explanation:
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:
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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Please hurry its timed and i really need help!
Hello!:
Let's take this problem in steps:
[tex]sinx-\sqrt{3-3sin^2(x)}=0\\\\\text{We know that } sin^2(x) + cos^2(x)=1 \text{ and that } cos^2x=1-sin^2(x)\\\\sin(x)-\sqrt{3(1-sin^2(x))}=0\\\\sin(x)-\sqrt{3*cos^2(x)}=0\\\\sin(x)-\sqrt{3}*cos(x)=0[/tex]
Now we need to find the value of sin(x) and cos(x) where the value becomes zero:
--> and it so happens to be:
[tex]sin(30)=\dfrac{1}{2} \\\\cos(120)=\dfrac{\sqrt{3}}{2}[/tex]
Thus:
[tex]sin(30)-\sqrt{3}*cos(120)=0\\\\\dfrac{1}{2} -\sqrt{3}*\dfrac{\sqrt{3} }{2} =0\\\\\\\dfrac{1}{2} -\dfrac{1}{2} =0\\\\0=0[/tex]
Answer: (B)
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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What does ∠ABC mean?
The measure of angle ABC means, vertex B lies in between A and C, whose value is to be obtained.
Explain the term angles?Whenever two straight lines as well as rays intersect at a single endpoint, an angle is created. The vertex of the an angle is the location where two points come together.
Measure or "the measure of" are indicated by the "m." Consequently, m1 and m2 stand for "the measure for angle one" and "this same measure of angle two," respectively.The total of a triangle's three internal angles is 180 degrees, as stated by the angle sum feature of a triangle.A closed shape with both inner and exterior angles, a triangle is created by three line segments.When the values of the remaining two angles are known, then angle sum property is utilised to determine the measure of an uncertain interior angle.Thus, the measure of angle ABC means, vertex B lies in between A and C, whose value is to be obtained.
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the length breadth and height of a cuboid are in the ratio 7:5:2 its volume is 35840cm³
[tex] \longmapsto \: 7x + 5x + 2x = 35820 \\ \\ x = \frac{35840}{14} = 2560[/tex] length equals to 7 into 2560 = 1792
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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The table shows data for 4 cyclists during one day of training.
Complete the table by finding the rate of speed for each cyclist. Use the formula r = d ÷ t.
Cyclist Distance (mi) Time (hr) Rate (mi per hr)
Alisha 40 4
Jose 30 2
Raul 40 4
Ruthie 80 5
Rate of speed of each cyclist is:
Alisha 10mi/hr
Jose 15mi/hr
Raul 10mi/hr
Ruthie 16mi/hr
Data given of each cyclist;
Formula used: [tex]r=\frac{d}{t}[/tex]
here,
r=rate of speed
d=distance
t=time
Alisha: Distance=40mi; Time=4hr
applying the formula
[tex]r=\frac{d}{t} \\r=\frac{40}{4} =10mi/hr[/tex]
Jose: Distance=30mi; Time=2hr
applying the formula
[tex]r=\frac{d}{t}\\ r=\frac{30}{2} =15mi/hr[/tex]
Raul: Distance=40mi; Time=4hr
applying the formula
[tex]r=\frac{d}{t} \\r=\frac{40}{4}=10mi/hr[/tex]
Ruthie: Distance=80mi; Time=5hr
applying the formula
[tex]r=\frac{d}{t} \\r=\frac{80}{5} =16mi/hr[/tex]
Alisha= 10mi/hr
Jose= 15mi/hr
Raul= 10mi/hr
Ruthie= 16mi/hr
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What is the formula of third side?
The formula for the third side of a triangle, given the lengths of two other sides and the angle between them, is:
side_3 = sqrt(side_1^2 + side_2^2 - 2 * side_1 * side_2 * cos(angle))
The formula for the third side of a triangle, given the lengths of two other sides and the angle between them, is:
side_3 = sqrt(side_1^2 + side_2^2 - 2 * side_1 * side_2 * cos(angle))
This formula is derived from the Law of Cosines, which states that the sum of the squares of any two sides of a triangle is equal to the square of the third side, minus twice the product of those two sides multiplied by the cosine of the angle between them.
In other words, the formula states that:
side_3^2 = side_1^2 + side_2^2 - 2 * side_1 * side_2 * cos(angle)
which is then solved for side_3 by taking the square root of both sides. Thus, the formula for the third side can be written as:
side_3 = sqrt(side_1^2 + side_2^2 - 2 * side_1 * side_2 * cos(angle))
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Is the triangle with sides of length 5 cm 3 cm and 4 cm a right angled triangle If yes why?
The triangle with sides of length 5 cm 3 cm and 4 cm is a right angled triangle because (3, 4, 5) is a Pythagorean triple.
We know that if non zero real numbers a, b, c follows Pythagoras theorem c² = a² + b², the numbers a, b, c is called as a Pythagorean triple.
And these numbers are nothing but the sides of right triangle.
Here we have been given the triangle with sides of length 5 cm 3 cm and 4 cm
Assume that p = 5 cm, q = 3 cm and r = 4 cm
p² = 25
q² = 9
and r² = 16
Consider q² + r² = 16 + 9
q² + r² = 25
q² + r² = r²
Since given numbers follows Pythagoras theorem, (3, 4, 5) is a Pythagorean triple.
And p = 5 cm, q = 3 cm and r = 4 cm are the lengths of sides of right triangle.
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