The three vertices drawn on a complex plane at represented by 0+0i, 4+0i, and 0+3i. What is the length of the hypotenuse
Answers
you can pretty much get the values for "a" and "b" from the grid.
Related Questions
The perimeter of a triangle is 133 inches. If one side of the triangle is five more than the shortest side, and the longest side is 14 more than the shortest side, find the lengths of the three sides?
Answers
side 1 = x
side 2 = x+5
side 3 = x+14
perimeter = side 1 + side 2 + side 3
133 = x + (x+5) + (x +14)
133=3x + 19
114=3x
x=114/3 = 38
side 1 = 38
side 2 = x+5 = 38+5 = 43
side 3 = x+14 = 38+14 = 52
38+43+52 = 133
side lengths are 38, 43 & 52
Which ratio is equivalent to 7 : 8?
A) 28 : 40
B) 21 : 24
C) 49 : 64
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I need to simplify this equation and don't know how, please help!
[tex] \frac{ \frac{y}{x} - \frac{x}{y}}{ \frac{1}{y}-\frac{1}{x}} [/tex]
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[tex]\bf \cfrac{\frac{y}{x}-\frac{x}{y}}{\frac{1}{y}-\frac{1}{x}}\implies \cfrac{\textit{LCD of \underline{xy}}}{\textit{LCD of \underline{xy} also}}\implies \cfrac{\frac{y^2-x^2}{xy}}{\frac{x-y}{xy}}\implies \cfrac{y^2-x^2}{\stackrel{ }{xy}}\cdot \cfrac{\stackrel{ }{xy}}{x-y} \\\\\\ \cfrac{y^2-x^2}{x-y}\implies \cfrac{(y-x)(y+x)}{x-y}\implies \cfrac{\stackrel{ }{(y-x)}(y+x)}{-\stackrel{ }{(y-x)}}\implies \cfrac{y+x}{-1} \\\\\\ -(y+x)\implies -y-x[/tex]
With 400,000 sq ft or 16% of total office space. How much space did the city have
Answers
well then [tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 400,000&16\\ x&100 \end{array}\implies \cfrac{400000}{x}=\cfrac{16}{100}[/tex]
solve for "x".
Choose the correct description of the graph of the inequality x − 3greater than or equal to 5
Answers
x ≥ 8
Answer:
Move all terms not containing x to the right side of the inequality. x≥8
Closed circle on 8, shading to the right.
Two examples where the law of detachment does not apply.
Answers
If the following statements are true, use the Law of Detachment to derive a new true statement.
1) If you are a penguin, then you live in the Southern Hemisphere.
2) You are a penguin.
Remember if p then q
The law of detachment, or modus ponens, doesn't apply when the antecedent is false or when premises lack conditional statements, making deductions invalid in these cases.
The law of detachment, also known as modus ponens, is a fundamental principle in classical logic that allows us to make valid deductions. However, there are situations where it does not apply:
Invalid Antecedent: In modus ponens, we start with a conditional statement (if-then statement) as our premise and then affirm the consequent. If the antecedent (the "if" part) of the conditional statement is false, the law of detachment cannot be applied. For example, if we have the statement "If it is raining, then the ground is wet" and we know that the ground is not wet, we cannot conclude anything about whether it's raining or not, as the antecedent is false.
Lack of a Conditional Statement: Modus ponens requires a conditional statement as its premise. If we are given unrelated or non-conditional premises, we cannot apply this rule. For instance, if we know that "John is a doctor" and "The sun is shining," we cannot use modus ponens to deduce anything because there is no conditional relationship between the statements.
In summary, while modus ponens is a valid and powerful inference rule in classical logic, it cannot be applied when the antecedent is false or when the premises do not involve conditional statements.
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Complete question below:
Could you provide two examples where the law of detachment does not apply in logic?
help me? idk the answer :P
Answers
[tex]\bf \left( 2^8\cdot \cfrac{1}{3^5}\cdot 1 \right)^{-2}\implies \left( \cfrac{2^8}{3^5} \right)^{-2}\implies \left( \cfrac{3^5}{2^8} \right)^{2}\implies \cfrac{3^{2\cdot 5}}{2^{2\cdot 8}}\implies \boxed{\cfrac{3^{10}}{2^{16}}}\\\\ -------------------------------\\\\ \textit{now the second group}\qquad \left( \cfrac{3^{-2}}{2^3} \right)^4\implies \left( \cfrac{\frac{1}{3^2}}{2^3} \right)^4\implies \left( \cfrac{1}{2^3\cdot 3^2} \right)^4[/tex]
[tex]\bf \cfrac{1^4}{2^{4\cdot 3}\cdot 3^{4\cdot 2}}\implies \boxed{\cfrac{1}{2^{12}\cdot 3^8}}\\\\ -------------------------------\\\\ \textit{so we end up with\qquad }\cfrac{3^{10}}{2^{16}}\cdot \cfrac{1}{2^{12}\cdot 3^8}\cdot 2^{28}\implies \cfrac{3^{10}\cdot 2^{28}}{2^{16}\cdot 2^{12}\cdot 3^8} \\\\\\ \cfrac{3^{10}\cdot 2^{28}}{2^{16+12}\cdot 3^8}\implies \cfrac{3^{10}\cdot 2^{28}}{2^{28}\cdot 3^8}\implies 3^{10}\cdot 2^{28}\cdot 2^{-28}\cdot 3^{-8}[/tex]
[tex]\bf 3^{10-8}\cdot 2^{28-28}\implies 3^2\cdot 1\implies 3^2\implies 9[/tex]
Which equation does the graph of the systems of equations solve? two linear functions intersecting at 4, 1 the answers are one fourthx + 2 = 2x − 7 one fourthx + 2 = −2x − 7 −one fourthx + 2 = 2x − 7 −one fourthx + 2 = −2x − 7
Answers
-1/4x + 2 = 2x - 77 + 2 = 2x + 1/4x9 = 8/4x + 1/4x9 = 9/4x9 * 4/9 = x4 = x
y = 2x - 7y = 2(4) - 7y = 8 - 7y = 1
solution is : -1/4x + 2 = 2x - 7 letter c
What is the area of parallelogram ABDC?
Answers
A = bh/2
Triangle 1:
3*3 = 9
9/2 = 4.5
Triangle 2:
3*3 = 9
9/2 = 4.5
4.5 + 4.5 = 9
Answer: The area of the parallelogram is 9 cm^2
Hope this helps :)
Please give brainliest
Answer:
9cm
Step-by-step explanation:
Solve for v 14v-8v=24
Answers
Subtract 8v from 14v
6v=24
Divide 24 by 6
Final Answer: v = 4
Reorganize this problem to: 14(v)-8(v)-24 ➡️?
6v ➡️ 24
6(1)➡️ 6
6(2) ➡️ 12
6(3) ➡️18
6(4) ➡️24
✅v ➡️ 4 ✅
or you can do this method
v - 4 ➡️0
✔️v ➡️4 ✔️
The number of solution is 1 and v=4
The Jurassic Zoo charges $14 for each adult admission and $9 for each child. The total bill for the 214 people from a school trip was $2081. How many adults and how many children went to the zoo?
Answers
a=adult
c=child
a+c=214
c=214-a
9c+14a=2081
9(214-a)+14a=2081
1926-9a+14a=2081
5a=155
a=155/5=31
31 adults
183 children
check
31*14 = 434
183*9=1647
1647+434=2081
Consider the words typically associated with geometry. Are there any words that would be hard to precisely define? What words can you think of?
Answers
Other words like line, segment, circle, angle may be defined from other word based of the notion of point.
But point is a very abstract notion, because it does not have length, so a point is an imaginary think.
Once, you have the notion of point, you can figure out that a line is an infinite succession of points, and from that define other concepts.
Angle may also be found a dificcult word to define because it is the opening or amount of turn between two lines that have a common end point.
The words typically associated with geometry are:
Points, Lines, Plane, and angle.
We have,
In geometry,
There are some words that can be challenging to precisely define or may have different interpretations.
Here are a few examples:
- Point: While a point is commonly understood as a location with no size or dimension, providing an exact definition can be difficult without relying on terms like "location" or "position."
- Line: A line is often described as a straight path extending infinitely in both directions. However, defining it without using similar geometric concepts like "straight" or "infinitely" can be challenging.
- Plane: A plane is typically defined as a flat, two-dimensional surface that extends infinitely in all directions. However, explaining it without referencing terms like "flat" or "two-dimensional" can be complex.
- Angle: An angle is formed by two intersecting lines or line segments. Describing it precisely without using terms like "intersects" or "measures" can be difficult.
Thus,
These words require a level of understanding of basic geometric concepts and often rely on other geometric terms for precise definitions.
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Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities.
A newspaper finds that the mean number of typographical errors per page is
six
six. Find the probability that (a) exactly
four
four typographical errors are found on a page, (b) at most
four
four typographical errors are found on a page, and (c) more than
four
four typographical errors are found on a page.
Answers
The probability of a given number, x, of occurrences is given by
P(x)=m^x*e^(-m)/x!
where m is the mean number of occurrences.
In the case of mean, m=6, the probability reduces to
P(x)=6^x*e^(-6)/x!
(a) x=4
P(4)=6^4*e^(-6)/4!=0.13385
(b) x<=4
P(X<=4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)
=0.00248+0.01487+0.04462+0.08924+0.13385+0.28506
=0.28506
(c) x>4
P(X>4)=1-P(X<=4)
=1-0.28506
=0.71494
At what points does the helix r(t) = sin t, cos t, t intersect the sphere x2 + y2 + z2 = 65? (round your answers to three decimal places. if an answer does not exist, enter dne.)
Answers
To determine the intersection points of the helix and the sphere, we substitute the helix's parametric expressions into the sphere's equation, simplify, and solve for t, resulting in two points of intersection upon further substitution back into the helix's equation.
Explanation:The question asks at what points the helix r(t) = (sin t, cos t, t) intersects the sphere x2 + y2 + z2 = 65. To find the intersections, we substitute the parametric equations of the helix into the equation of the sphere. Thus, we get (sin2t) + (cos2t) + t2 = 65. Using the Pythagorean identity sin2t + cos2t = 1, the equation simplifies to 1 + t2 = 65, which further simplifies to t2 = 64. Solving for t, we find t = ±8. Thus, the helix intersects the sphere at the points generated by these t values, which can be found by substituting t back into the helix equations, resulting in (sin(8), cos(8), 8) and (sin(-8), cos(-8), -8), with approximate numerical values after calculations.
Sal bought three CDs for 1598 each a computer cable for 3995 and a case for his MP3 player for 2499 sales tax is 7% to the nearest cent what is the total cost of his purchases
Pleaseee helppppppp
Answers
7% taxes (always taxes!): 112.88 * 1.07= 120.7816
Rounded to cents: 120.78
112.88(1.07) = 120.78 <=
Analyzing the graphs of a periodic functions (need help)
Answers
[tex]\bf \bullet \textit{ stretches or shrinks}\\ \left. \qquad \right. \textit{horizontally by amplitude } |{{ A}}|\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]
[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\[/tex]
[tex]\bf \bullet \textit{function period or frequency}\\ \left. \qquad \right. \frac{2\pi }{{{ B}}}\ for\ cos(\theta),\ sin(\theta),\ sec(\theta),\ csc(\theta)\\\\ \left. \qquad \right. \frac{\pi }{{{ B}}}\ for\ tan(\theta),\ cot(\theta)[/tex]
now, with that template above in mind, let's see.
reflected over the x-axis, that means A is negative.
vertically shrunk by 0.25 or 1/4, that means A is negative 4, or -4.
shifted to the left, that means C/B is positive
shifted by 65°, that means, we could use the default B = 1, and C = 65°, that way we end with C/B = 65/1 or just +65
and shifted downwards by 1 unit, that means D = -1.
[tex]\bf f(x)=-4sin(1x+65^o)-1\implies f(x)=-4sin(x+65^o)-1[/tex]
and looks more or less like the picture below.
The sum of differences between the group mean and the grand mean summed over all groups for a given set of observations is called _____ variance.
Answers
EASY 5 POINTS!!! You want to help build an awards podium for a track meet. If the podium has the dimensions shown, what is its volume?
Answers
Answer:
The volume is equal to [tex]18\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of each figure is equal to
[tex]V=LWH[/tex]
where
L is the length
W is the width
H is the height
Step 1
Find the volume of figure N 1
[tex]V1=1.5*2*3=9\ cm^{3}[/tex]
Step 2
Find the volume of figure N 2
[tex]V2=1.5*2*2=6\ cm^{3}[/tex]
Step 3
Find the volume of figure N 3
[tex]V3=1.5*2*1=3\ cm^{3}[/tex]
Step 4
Find the total volume
[tex]V=V1+V2+V3=9+6+3=18\ cm^{3}[/tex]
Answer:
[tex]\text{Volume of podium}=18\text{ ft}^3[/tex]
Step-by-step explanation:
We have been given a graph of podium for a track meet and we are asked to find the volume of our given podium.
To find the volume of podium we will find volume of each podium using volume of cuboid formula.
[tex]\text{Volume of cuboid}=l*b*h[/tex], where,
[tex]l=\text{ Length of cuboid}[/tex],
[tex]b=\text{ Breadth of cuboid}[/tex],
[tex]h=\text{ Height of cuboid}[/tex].
Upon substituting our given values in cuboid formula we will get,
[tex]\text{Volume of cuboid 1}=\text{3 ft*2 ft*1.5 ft}[/tex]
[tex]\text{Volume of cuboid 1}=9\text{ ft}^3[/tex]
[tex]\text{Volume of cuboid 2}=\text{2 ft*2 ft *1.5 ft}[/tex]
[tex]\text{Volume of cuboid 2}=6\text{ ft}^3[/tex]
[tex]\text{Volume of cuboid 3}=\text{1 ft*2 ft *1.5 ft}[/tex]
[tex]\text{Volume of cuboid 3}=6\text{ ft}^3[/tex]
Let us add volume of each cuboid to find the volume of our given podium.
[tex]\text{Volume of podium}=9\text{ ft}^3+6\text{ ft}^3+3\text{ ft}^3[/tex]
[tex]\text{Volume of podium}=18\text{ ft}^3[/tex]
Therefore, volume of our given podium is 18 cubic feet.
What is the inverse of y equals x squared + 2
Answers
[tex]\bf \boxed{y}=\boxed{x^2}+2\qquad inverse\implies \boxed{x}=\boxed{y^2}+2 \\\\\\ x-2=y^2\implies \sqrt{x-2}=y\impliedby f^{-1}(x)[/tex]
What is 24/126 simplified
Answers
24/126.
First, let's try to divide both numbers by 2, as the numbers in the ones place are even.
24 / 2 = 12
126 / 2 = 63
12/63
Divide both numbers by 3.
12 / 3 = 4
63 / 3 = 21
4/21. This is your simplified fraction.
I hope this helps!
126= 2*3*3*7
The GCF= 2*3 or 6
Divide the numerator and denominator by the GCF
24/6=4
126/6=21
Final answer: 4/21
20. Archetypes are a type of _______ that appear throughout history.
A. motif
B. prototype
C. foreshadowing
D. subgenre
Student Answer: A
Answer: Incorrect
Answer is B Prototype
Answers
For Penn Foster the answer you find the answer to this qrestion In the section called Analysis of “ Paul’s Case” 4 th paragraph an Archetype appears repeatedly throughout history -It’s a prototype . So the qrestion people are asking is. Archetypes are a type of _______ that appear throughout history? A. foreshadowing B. prototype C. subgenre D. motif
Answer true and correct B. PROTOTYPE
I made a hundred on this test for pf
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Find the area of the equilateral triangle if a side is 14√3 ft. Round to the nearest whole number.
Answers
Answer:
Answer is C
Step-by-step explanation:
Area of an equilateral triangle can be found by the following formula,
A=[tex]\frac{\sqrt{3}} {4} a^{2}[/tex]
Where "a" is the length of one side of the triangle.
Now we can substitute the value given to the equation above and find the area of the given equilateral triangle.
A=[tex]\frac{\sqrt{3}} {4}(14\sqrt{3})^ {2}[/tex]
=[tex]\frac{\sqrt{3}} {4} 196*3[/tex]
=[tex]\frac{\sqrt{3}*196*3} {4}[/tex]
=[tex]254.611[/tex]
A=[tex]255[/tex] square feet.
Answer is C
In Ellen's math class, there are 2 boys for every 3 girls . What is the the following ratio of boys to girls in the class ?
A . 17/21
B . 14/21
C . 7/14
D. 11/17
Answers
(15+23)+7=15+(___+7)
Answers
he IQ scores of 500 college football players are randomly selected. Which graph would be most appropriate for these data: histogram, bar chart, pie chart, multiple bar graph, or slack plot?
Answers
A local hamburger shop sold a combined total of 693 hamburgers and cheeseburgers on Wednesday. There were 57 fewer fewer cheeseburgers sold than hamburgers. How many hamburgers were sold on Wednesday
Answers
693-57 = 636
636/2 = 318
cheeseburgers sold = 318
hamburgers sold = 318 + 57 = 375
To determine the number of hamburgers sold on a specific day, an equation is set up and solved to find the value of hamburgers. In this scenario, 375 hamburgers were sold on Wednesday.
The question is asking how many hamburgers were sold on a specific Wednesday given the total combined sales of hamburgers and cheeseburgers and that fewer cheeseburgers were sold than hamburgers. To find the number of hamburgers sold, we can set up a system of equations. Let's define H as the number of hamburgers and C as the number of cheeseburgers. From the information provided, we have the following equations:
H + C = 693 (Total sales of both types of burgers)C = H - 57 (There were 57 fewer cheeseburgers sold than hamburgers)Substituting the second equation into the first gives us:
H + (H - 57) = 693
2H - 57 = 693
Adding 57 to both sides, we get:
2H = 693 + 57
2H = 750
Now divide both sides by 2:
H = 375
Therefore, 375 hamburgers were sold on Wednesday.
What are the next two numbers in the pattern 3.1, 3.11, 3.11, 33.11
Answers
If the measures of the angles of a triangle are in the ratio of 19:13:4, then the expressions 19x, 13x, and 4xrepresent the measures of these angles. Find these angle measures.
Answers
You do 19x + 13x + 4x = 26x
180 divided by 26x = x = 6.92307...
plug in x then round to tenth
6.9 x 19 = 131.1 degrees
6.9 x 13 = 89.7 degrees
6.9 x 4 = 27.6 degrees
19x + 13x + 4x = 180
36x = 180
x = 180/36
x = 5
19x = 19(5) = 95 <== heres one
13x = 13(5) = 65 <== and another
4x = 4(5) = 20 <==and another
19:13:4 = 95:65:20
What is the number of square units in the area of the triangle whose vertices are points (2,0), (6,0), (8,5)
Answers
you can pretty much just count how many units for the base, and height.
Answer: 10 square units.
Step-by-step explanation:
The area of triangle with vertices [tex](x_1,y_1),(x_2,y_2)\text{ and }(x_3,y_3)[/tex] is given by :-
[tex]A=\dfrac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)][/tex]
Given : The vertices of triangle : (2,0), (6,0), (8,5)
Then , the area of the triangle will be :_
[tex]A=\dfrac{1}{2}[(2)((0)-(5))+(6)((5)-(0))+(8)((0)-(0))\\\\\Rightarrow A=\dfrac{1}{2}[20]\\\\\Rightarrow A=10\text{ square units}[/tex]
Hence, the number of square units in the area of the triangle whose vertices are points (2,0), (6,0), (8,5) = 10
In a study conducted for the state department of education, 30% of the teachers who left teaching did so because they were laid off. assume that we randomly select 16 teachers who have recently left their profession. find the probability that at least 7 of them were laid off.
Answers
p = 30% = 0.3 is the probability that a teacher was laid off.
q = 1 -p = 0.7 is the probability that a teacher was not laid off.
n = 16 is the sample size.
r = 7 is the expected number of teachers who were laid off
The probability that 7 out of 16 teachers were laid off is
₁₆C₇ p⁷q⁽¹⁶⁻⁷⁾ = 11440*(0.3⁷)*(0.7⁹) = 0.101 =10.1%
Answer:
The probability is 0.101 or 10.1%