Step-by-step explanation:
Perimeter of rectangle = 2( l+b)
Ie, P = 2( L+B )
In substituting,
322 = 2( L + 74)
Ie, 322 = 2L + 148
Re - arrange
Hence,
2L = 322 - 148
2L = 174
Thus, L = 174/2
L = 87M
"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?"
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
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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Someone please help me with this
Answer:
Step-by-step explanation:
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.
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
The graph of y=x√ is translated 5 units to the left and 7 units up. What is the equation of the graph that results from this translation?
Answer:
[tex]y = \sqrt{x - 5} + 7[/tex]
Consider this polynomial, where a is an unknown real number.
correctly/incorrectly
and why
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Answer:
incorrectly; used 1 in the division instead of -1incorrectly; evaluated higher powers of -1 incorrectlyStep-by-step explanation:
The result each should have obtained is ...
a +10 = 17
a = 7
Braulio's mistake was in using 1 as his divisor instead of -1. His bottom row should have been 1, 4, a-4, 1-a, a +10.
Zahra's mistake was improperly evaluating higher powers of -1. Her evaluation should have been 1 -5 +a +3 +11 = a +10.
A math class is having a discussion on how to determine if the expressions 4 x minus x + 5 and 8 minus 3 x minus 3 are equivalent. The class has suggested four different methods. Which describes the correct method? Both expressions should be evaluated by substituting one value for x. If the final values of the expressions are both positive after the substitution, then the two expressions must be equivalent. Both expressions should be evaluated by substituting with one value for x. If the final values of the expressions are the same, then the two expressions must be equivalent. Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are positive, then the two expressions must be equivalent. Both expressions should be evaluated by substituting any two values for x. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.
Answer:
Both expressions should be evaluated by substituting with one value for x. If the final values of the expressions are the same, then the two expressions must be equivalent.
Step-by-step explanation:
its B
Option (D) both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent is the correct answer.
What is a word problem?
A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
The expressions are [tex]4x-x+5 , 8-3x-3[/tex]
If the expressions are equivalent then,
⇒ [tex]4x-x+5 = 8-3x-3[/tex]
⇒ [tex]3x+5=-3x+5[/tex]
In both the sides the x has different values.
So, Both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent.
Hence we can conclude that option (D) both expressions should be evaluated with two different values. If for each substituted value, the final values of the expressions are the same, then the two expressions must be equivalent is the correct answer.
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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:
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:
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 :)
please help me i have a couple mins
Answer:
x + 3
Step-by-step explanation:
Because he bought an unknown number of soccer balls that is where we use the variable, x. And we know that he bought 3 baseballs, and we add them both to get the total number of things bought. Hope this helped and you could give brainliest :)
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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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
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.
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
Hello! Please help thanks
Answer:
A. [tex]\frac{5}{13}[/tex]
Step-by-step explanation:
Hi there!
We are given right triangle PQR, with PR=5, RQ=12, and PQ=13
We want to find the value of sin(Q)
Let's first recall that sine is [tex]\frac{opposite}{hypotenuse}[/tex]
In reference to angle Q, PR is the opposite side, RQ is the adjacent side, and PQ is the hypotenuse
So that means that sin(Q) would be [tex]\frac{PR}{PQ}[/tex]
Substituting the values of PR and PQ gives sin(Q) as [tex]\frac{5}{13}[/tex], which is A
Hope this helps!
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
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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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
Nghiệm riêng của phương trình
y′′−y′=x2+x
có dạng
Answer:
i don't understand the question
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
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.
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
Megan and Suzanne each have a plant. They track the growth of their plants for four weeks.
Whose plant grew at a faster rate, and what was the rate?
Suzanne’s at 2 inches per week
Suzanne’s at 1.5 inches per week
Megan’s at 3 inches per week
Megan’s at 2.5 inches per week
Megan’s plant grew at a faster rate, Growing at a rate of 3 inches per week.
What is the slope?The y-rate axis of change with respect to the x-axis is known as the slope.
y = mx + b, where slope = m and y-intercept = b, is the slope-intercept form equation of a line.
We are aware that a slope's graph or rate of change will be steeper the higher its absolute value.
Given, Megan and Suzanne each have a plant. They track the growth of their plants for four weeks.
From the given options, Megan's plant which is growing at a rate of 3 inches per week has a faster growth rate.
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Express as index form
log 2 64 = 6
Answer:
hsv s deutsche ki bhar ke dekhte hai mera gham na
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
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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
