Answer:
A definition and a theorem can be used as a reason in a two-column proof. A two column proof is assembled into statement and reason columns, where each statement should have verified reason.
Step-by-step explanation:
Answer:
Definitions and algebraic properties
Step-by-step explanation:
From September 1991 to September 1994 the enrollment at a particular school declined by 20 percent. If the number of students enrolled at that school in September 1994 was 720, what was the enrollment in September 1991
Answer:
900
Step-by-step explanation:
Given that :
Enrollment declined by 20% from between September 1991 to September 1994
This means there was a reduction in enrollment ;
Enrollment in September 1994 = 720
Enrollment in September 1991 = x
Hence,
Enrollment in 1994 = (1 - decline rate ) * enrollment in 1991
720 = (1 - 20%) * x
720 = (1 - 0.2) * x
720 = 0.8x
720 / 0.8 = 0.8x/0.8
900 = x
Hence, Enrollment in September 1991 = 900 enrollments
What is the slope of a roof on a house that has a vertical height of 2.4 feet from the ceiling of the top floor to the top of the pitch and a length of 8.2 feet from the center of the edge of the house?
Answer:
Step-by-step explanation:
It is unclear from the phrasing what dimension 8.2 ft represents.
If 8.2 ft is the direct distance from the edge of the roof to the top of the pitch, then the horizontal distance from the edge to the top is √(8.2²-2.4²) ≅ 7.84 ft, and the slope is 2.4/7.84 ≅ 0.31
If 8.2 ft is the horizontal distance from the edge of the root to the top of the pitch, then the slope is 2.4/8.2 ≅ 0.29
The slope of a roof on a house is 0.2926 and the angle of elevation is 16.31°.
What is slope of a line?
The slope or gradient of a line is a number that describes both the direction X and Y and the steepness of the line. It is the ratio of the vertical change to the horizontal change between any two distinct points on a line.
For the given situation,
The diagram below shows the house with the roof.
The vertical height of roof on a house, rise = 2.4 feet
The horizontal length of a roof on a house, run = 8.2 feet
The slope of a roof can be found as
[tex]Slope = \frac{rise}{run}[/tex]
⇒ [tex]slope = (\frac{2.4}{8.2} )[/tex]
⇒ [tex]slope = 0.2926[/tex]
The angle of the slope of a roof can be found as
[tex]tan \alpha =\frac{vertical height}{horizontal length}[/tex]
⇒ [tex]\alpha =tan^{-1} (\frac{2.4}{8.2} )[/tex]
⇒ [tex]\alpha =tan^{-1} (0.2926)[/tex]
⇒ [tex]\alpha =16.31[/tex]
Hence we can conclude that the slope of a roof on a house is 0.2926 and the angle of elevation is 16.31°.
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Simplify this expression.
6 + 8 ÷ 2
3
7
10
12
A sound technician analyzes the audio feedback by placing a microphone at certain distances from a speaker. If the microphone is connected to the speaker, then the microphone senses 606060 decibels (\text{dB})(dB)left parenthesis, start text, d, B, end text, right parenthesis at a distance of 000 meters (\text{m})(m)left parenthesis, start text, m, end text, right parenthesis from the speaker with the decibel level decreasing by half of itself for every additional meter from the speaker. If the microphone is not connected to the speaker, then the microphone senses 30 \, \text{dB}30dB30, start text, d, B, end text at a distance of 0 \, \text{m}0m0, start text, m, end text from the speaker with the decibel level decreasing by 888 for every additional meter from the speaker. Three meters from the speaker, what is the difference between the decibel level when it is connected to the speaker versus when it is not connected to the speaker?
At three meters, the difference in the decibel level if and if not connected to the speaker is 1.5 dB
The reason for arriving at the above value is as follows:
The known parameters:
The audio sensed by the microphone when connected to the speaker are;
0 meters = 60 decibels
The level of the decibel decrease by half for each additional meter;
Therefore, when the microphone is connected to the speaker, we have;
[tex]\begin{array}{|c|cc|}\mathbf{Distance \ (m)}&&\mathbf{Sound \ (dB)}\\0&&60\\1&&30\\2&&15\\3&&7.5\end{array}\right][/tex]
If the microphone is not connected to the speaker, we have;
0 meters = 30 decibels
The level of the decibel decreasing by 8 dB for every additional meter from the speaker, therefore, when the microphone is not connected to the speaker we have;
[tex]\begin{array}{|c|cc|}\mathbf{Distance \ (m)}&&\mathbf{Sound \ (dB)}\\0&&30\\1&&22\\2&&14\\3&&6\end{array}\right][/tex]
At three meters from the speaker, the difference in the decibel level when it is connected and when it is not connected to the speaker is therefore;
Decibel level at 3 meters when connected, s₁ = 7.5 dB
Decibel level at 3 meters when not connected, s₂ = 6 dB
The difference in the decibel level = s₂ - s₁ = 7.5 dB - 6 dB = 1.5 dB
The difference in the decibel level when connected to the speaker and when not connected to the speaker is 1.5 dB
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The graph of the function f(x)= x2 − 4x + 6 is shown here. What is its axis of symmetry? A. x = 0 B. x = 2 C. x = 6 D. x = -2
9514 1404 393
Answer:
B. x = 2
Step-by-step explanation:
The graph is symmetrical about the vertical line through its vertex. The x-value of that vertex is 2, so the line of symmetry is ...
x = 2
Venn diagrams: unions, intersections, and complements
Attached is the photo reference
Answer:
(a) {5}
(b) {1, 2, 5, 6}
(c) {1, 2, 5, 6}
Express as index form
log 2 64 = 6
Answer:
hsv s deutsche ki bhar ke dekhte hai mera gham na
Which expressions are equivalent to 6 + 12x?
A.
5(1 + 2x) + 1 + 2x
B.
7(1 + 2x) + 2x - 1
C.
3(2 + 6x) + 2x
D.
7(1 + 2x) - 2x - 1
E.
3(2 + 4x)
Answer:
A. 5(1 + 2x) + 1 + 2x
D. 7(1 + 2x) - 2x - 1
E. 3(2 + 4x)
what is the probability that the 2 cards you will draw will be blackjacks?
Answer:
Need more explation of the question
Step-by-step explanation:
-3x^5y^7/6xy^8
PLEASE HELP
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Answer:
-x^4/(2y)
Step-by-step explanation:
Perhaps you want to simplify ...
[tex]-\dfrac{3x^5y^7}{6xy^8}=-\dfrac{3}{6}x^{5-1}y^{7-8}=-\dfrac{x^4y^{-1}}{2}=\boxed{-\dfrac{x^4}{2y}}[/tex]
__
The applicable rules of exponents are ...
(a^b)/(a^c) = a^(b-c)
a^-b = 1/a^b
_____
Comment on notation
When writing a fraction in plain text, any denominator that includes an arithmetic operation must be enclosed in parentheses. Your given expression is properly written as ...
-3x^5y/(6xy^8)
Without the parentheses, the product xy^8 is in the numerator. This is demanded by the order of operations, which requires you evaluate your expression as (-3x^5y^7/6)·xy^8
find all the missing measurement
Answer:
Hello,
|FD|=15
Step-by-step explanation:
Since the triangles are similar, the bissects are also.
k*35=21 ==> k=21/35
k*25=|FD|
|FD|=(21/35)*25=15
"The fitted regression line will always run through the mean of the observed data. In other words, the point (x with bar on top, y with bar on top) will always lie on the estimated (fitted) regression line. Is it true or false?"
The diagram shows a wooden prism of height 5cm.
The cross section of the prism is a sector of a circle with sector angle 25º.
The radius of the sector is 15 cm.
Calculate the total surface area of the prism.
Answer:
280.8997
Step-by-step explanation:
cross section = 2*15*5+2*(25/360)*15*15*pi+5*(25/360)*2*pi*15
= 280.8997
Total surface area of prism is 280.890cm²
What is surface area?A solid object's surface area is a measurement of the overall space that the object's surface takes up, and it is always expressed in square units.
The term "surface area" is sometimes used to refer to "total surface area".
Find the sector angle in radians
α = 25× (π/180)
α = (25π)/(180) rad
Find the area of the prism:
A = 2×15×5 + 15×15×α + 5×15×α
A = 150 + 15×15×(25π)/(180) + 5×15×(25π)/(180)
A = 280.890cm²
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A recipe calls for 4 cups of flour and 6 cups of sugar. How many cups of sugar per cup of flour does the recipe require?
Answer:
3 cups of sugar per 2 cups of flour
Step-by-step explanation:
just flip and simplify the fraction
4/6 = 6/4 = 3/2
Which key correctly represents the information below? A. 11 | 2 = 12 B. 1 | 2 = 12 C. 11 | 2 = 112 D. 11 | 2 = 13
Answer:
The answer is (B) 1/2=12
If we decrease a dimension on a figure, how is the figure’s area affected?
The area decreases.
The area increases.
The area becomes 0.
The area remains the same.
Nghiệm riêng của phương trình
y′′−y′=x2+x
có dạng
Answer:
i don't understand the question
01:15:51 Differential equation of the family of circles touching the y-axis at origin is
Step-by-step explanation:
Correct option is
B
x
2
−y
2
+2xy
dx
dy
=0
The system of circles touching Y axis at origin will have centres on X axis. Let (a,0) be the centre of a circle. Then the radius of the circle should be a units, since the circle should touch Y axis at origin.
Equation of a circle with centre at (a,0) and radius a
(x─a)²+(y─0)²=a²
That is,
x²+y²─2ax=0 ─────► (1)
The above equation represents the family of circles touching Y axis at origin. Here 'a' is an arbitrary constant.
In order to find the differential equation of system of circles touching Y axis at origin, eliminate the the arbitrary constant from equation(1)
Differentiating equation(1) with respect to x,
2x+2ydy/dx─2a=0
or
2a=2(x+ydy/dx)
Replacing '2a' of equation(1) with the above expression, you get
x²+y²─2(x+ydy/dx)(x)=0
That is,
─x²+y²─2xydy/dx=0
or
x²─y²+2xydy/dx=0
Which of the following is the function for the graph below and shows the end behavior of the function as x>-00?
Answer:
A
Step-by-step explanation:
I just used a graphing calculator.
Just type in all the functions and pick the graph and function pair that match the picture.
I hope this helps!
pls ❤ and mark brainliest pls!
Assuming you want x to approach negative infinity, you have the correct answer. It is choice A.
=====================================================
Explanation:
The root x = -2 leads to the factor x+2. That means the answer is between A and B.
As x approaches negative infinity, i.e. as we move to the left, we're going down the red curve and y = f(x) is going to approach negative infinity as well.
In terms of symbols, we'd write [tex]x \to -\infty, \ f(x) \to -\infty[/tex]
Informally, we could say "it falls to the left" as a way to describe this left end behavior.
Jenny has borrowed K2500from a bank at 9.25% p.a. invested for 185 days. How much will she pay back to the bank?
Answer:
115.625
PRT/100
An oil company is going to issue new ID codes to its employees. Each code will have one letter, followed by one digit, followed by three letters. The letters w, x, y, and z will not be used. So, there are 22 letters and 10 digits that will be used. Assume that the letters can be repeated. How many employee ID codes can be generated?
Answer:
2342560 combos
Step-by-step explanation:
so its 1 letter*1number*1 letter*1 letter*1 letter, or 22x10x22x22x22 which should equate to 2342560 possible ID codes, hope this helps :)
A ball was bounced 3 times between 3:15p and 3:18p, thrown 10 times between 3:20p and 3:30p and bounced 7 times between 4:15p and 4:20p. What is the rate per hour of ball bouncing based on a 2 hour data collection time period.
Answer:
strange phrasing of a question
If one assumes that the "observation" was from 3:00 pm - 5:00 pm (2 hours)
and the ball was ONLY "bounced" 10 times (3+7)
we can can say that the rate was 10 bounces/2 hours or 5 b.p.h. (bounces per hour)
Step-by-step explanation:
a) Express the prime number 31 as the difference of two squares? 31 =
Answer:
31 = 16²-15²
Step-by-step explanation:
16² = 256
15² = 225
256 - 225 = 31
Someone please help me with this
Answer:
Step-by-step explanation:
Which of the following functions best describes this graph? y=(x+2)(x+7)
Answer:
hope. It helps. What. I Understood
match the polynomial with its correct name
Answer
Attach a file for us to see the problem
Step-by-step explanation:
y = 95°, find the measure of x
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Answer:
x = 100°
y = 95°
Step-by-step explanation:
It is probably easier to find y first. Opposite angles of an inscribed quadrilateral are supplementary, so ...
y = 180° -85° = 95°
The measure of an arc is double the measure of the inscribed angle subtending it. The arc subtended by angle y is ...
90° +x = 2y
x = 190° -90° = 100°
_____
Additional comment
The rule cited above regarding opposite angles of an inscribed quadrilateral comes from the theorem regarding inscribed angles. In the given diagram, the diagonal from the bottom vertex to the top one is a chord that divides the circle into two arcs. Their sum is 360°. The inscribed angle theorem tells you ...
2y +2(85°) = 360°
y + 85° = 180° . . . . . . . divide by 2; opposite angles are supplementary
In this diagram,which equation could prove to be true in order to conclude that the lines are parallel?
Answer:
b/a = c/d (first option)
Step-by-step explanation:
Two lines:
f(x) = a*x +b
g(x) = m*x + s
are parallel if m = a, and s ≠ b.
So the lines must have the same slope and different y-intercept.
For the graphed lines is obvious that the y-intercepts are different, so let's look at the slopes.
Remember that if a line passes through the points (x₁, y₁) and (x₂, y₂), then the slope can be written as:
slope = (y₂ - y₁)/(x₂ - x₁)
So now let's look to our lines.
The top one, passes through (-a, 0) and (0, b)
Then its slope is:
a₁ = (b - 0)/(0 - (-a)) = b/a
The bottom line passes through the points (0, -c) and (d, 0)
Then the slope will be:
m₁ = (0 - (-c))/(d - 0) = c/d
Then the lines will be only parallel if the slopes are equal, which means that we must have
b/a = c/d
The correct option is the first one.
look at the image for the question
Answer:
112 ft^2
Step-by-step explanation:
The volume of the rectangular prism is
V = l*w*h where l is the length, w is the width and h is the height
V = 4*4*7
V = 112 ft^2
Can anyone help me?
Answer:
y is not a function of x
Step-by-step explanation:
This fails the vertical line test. This means that not all inputs have exactly one output. This makes this not a function.
