Answers
a. Absolute value function the reference beam is g(x) = |8x/5|.
b. g(x) = +8x/5 ; x < 5 and g(x) = -8x/5 > 5.
What is defined as the absolute value function?An absolute value function is one that has an algebraic expression enclosed in absolute value symbols. Remember that a number's absolute value is its distance from 0 just on number line.For the given function;
Part a: The reference beam is passing from the points;
(x₁, y₁) = (5, 8)
(x₂, y₂) = (0, 0)
Then the slope of the line is -
m = (y₂ - y₁)/(x₂ - x₁)
Put the values ;
m = (0 - 8)/(0 - 5)
m = 8/5
The equation of the line is;
y - y₁ = m(x - x₁)
Put the values;
y - 0 = 8/5(x - 0)
y = 8x/5
Or in absolute modulus function for the path of reference beam; y = |8x/5|.
Part b: absolute function in terms of piecewise function;
g(x) = +8x/5 ; x < 5 as the slope is increasing.
and g(x) = -8x/5 > 5.; as the slope is decreasing.
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Related Questions
Determine the momentum of a system that consists of two objects. One object, m1, has a mass of 6 kg and a velocity of 13 m/s in the direction of the positive x-axis and a second object, m2, has a mass of 14 kg and a velocity 7 m/s in the direction of the negative x-axis.
Answers
Answer:
The solution to the question will be explained better using the image below
Concept:
The formula to calculate momentum is given below as
[tex]\begin{gathered} momentum=mass\times velocity \\ m=mv \end{gathered}[/tex]The first momentum will be
[tex]\begin{gathered} m_1=m_1v_1 \\ m_1=6\times13 \\ m_1=78kg\text{ m/s} \end{gathered}[/tex]The second momentum will be
[tex]\begin{gathered} m_2=m_2v_2 \\ m_2=14kg\times7 \\ m_2=98kg\text{ m/s} \end{gathered}[/tex]Since they are moving in different directions,
We will substract both momentums
[tex]\begin{gathered} momentum=m_1v_1-m_2v_2 \\ momentum=78-98 \\ momentum=-20kg\text{ m/s} \end{gathered}[/tex]Hence,
The momentum of a system that consists of two objects should be 20 kg m/s in the direction of the negative x-axis
Fats, sugars, and proteins are important food molecules. What do these types of molecules have in common?
Answers
The fact that Fats, sugars, and proteins molecules have in common is that all of these are macronutrients.
What are macronutrients?The many categories of macronutrients include proteins, lipids—also known as fats—carbohydrates, or sugars. These are the three primary nutrients that the body uses to function. This indicates that they are chemical substances that your cells use as a source of chemical energy and that you require in quite significant quantities. These nutrients also produce energy or calories. They are broken down into smaller components during digestion. Energy is derived from carbohydrates (glucose). After being broken down into fatty acids, fats are used for energy. Although it can be used as fuel, protein's primary function is in the synthesis of hormones, muscle, and other proteins.To know more about macronutrients visit:
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Answer:
They all have carbon atoms.
Step-by-step explanation:
Solve ×^2-4×-5=?
Your Genius If You Answered This Correctly
Answers
Answer:
(x+1)(x-5)
Step-by-step explanation:
Solve the proportion. 7 42 = 1 w w=
Answers
When the given proportion is solved the value of w is calculated to be 6.
What is proportion?
A proportion can be commonly understood as two ratios that have been set equal to each other; a proportion is an equation that can be solved.
When it is said that proportion is two ratios that are equal to each other, it means in the sense of two fractions being equal to each other.
for example 5/10 = 1/2, 5:10 = 1: 2
7:42 = 1 : w
[tex]\frac{7}{42} = \frac{1}{w} \\[/tex]
[tex]\frac{1}6{} = \frac{1}{w}[/tex]w = 1 x 6
w = 6
When the given proportion is solved the value of w is calculated to be 6
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Triangle MNP is dilated by a factor of 2 with a center of dilation at (0,0).
What are the new coordinates of point N?
A
(1, -1)
B
(-4, 4)
C
(4, 0)
D
(4, -4)
Answers
The new coordinates of the point N after the given dilation transformation is; (-2, 6)
What is the Dilation of the triangle?
From the attached image, we see the given triangle MNP. We see that it's coordinates are;
M(-1, -2)
N(0, 2)
O(2, -2)
Now, when we talk about dilation in transformation, we are simply referring to a transformation that produces an image that is the same shape as the original, but is a different size.
Thus, triangle MNP will be dilated according to the rule (x,y), where point P is the center of dilation.
Given the coordinate N = (0, 2)
The rule of dilation with scale factor k =2 and point P is the center of dilation is given by:
(x, y) = (2x - 2), (2x + 2)
Thus;
N = (0, 2) → N'(2(0) - 2), (2(2) + 2)
= N'(-2, 6)
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Two buses are driving along parallel freeways that are 5mi apart, one heading east and the other heading west. Assuming that each bus drives a constant 55mph, find the rate at which the distance between the buses is changing when they are 13mi apart, heading toward each other.
Answers
The rate at which the distance between the buses is changing when they are 13mi apart, heading toward each other is 101.54 km per hour.
How to calculate the rate?Let l = distance further away at which they'll meet. This will be illustrated as:
l = ✓13² - ✓5²
= ✓169 - 25
= ✓144
= 13m
Assuming that each bus drives a constant 55mph. The passes towards each other will be:
= -(55 + 55)
= -110m/h
Therefore, h² + l² = b².
Differentiate
2hdh/dt + 2ldl/dt = 2bdb/dt
= 2 × 5 × 0+ 2 × 12 (-110)
= 3 × 13db/dt
= -101.54 m/h
The rate is 101.54 m/h.
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1. no association 2. negative association 3. positive association 4. nonlinear association
Answers
From the graph it can be observed that line fits curve and line has positive slope as increase in hours cause increase in miles.
The line with postive slope represent the positive relation between the variables. So there is postive association between miles and time spent for running.
Answer: positive association
For the rhombus below, solve for y
Answers
Notice that this set of angles is congruent
herefore,
[tex]y-60=56[/tex]Solving for y ,
[tex]\begin{gathered} y=56+60 \\ \rightarrow y=116 \end{gathered}[/tex]nswer: 116
In order to make a specific shade of green paint, a painter mixes 1/2 of a gallon of blue paint with 4/5 of a gallon of yellow paint. How many gallons of yellow paint are needed to mix with 3 gallons of blue paint?
Answers
To make a specific shade of green paint, 4.8 gallons of yellow paint is needed to mix with 3 gallons of blue paint.
In the question ,
it is given that
to make a specific shade of green paint , the painter mixes 1/2 gallon of blue paint and 4/5 gallon of yellow paint .
so , the ratio of yellow paint to blue paint [tex]=\frac{\frac{4}{5} }{\frac{1}{2} }[/tex]
writing in the simplified form , we get
= 4/5 × 2/1
= 8/5
So, for the given specific shade of green , the ratio of yellow : blue paint will remain same ,
let the amount of yellow paint used to mix with 3 gallons of blue paint be x gallons .
[tex]\frac{8}{5} =\frac{x}{3}[/tex]
On simplifying
x = 24/5
x = 4.8
so yellow paint required is 4.8 gallons
Therefore , to make a specific shade of green paint , 4.8 gallons of yellow paint is needed to mix with 3 gallons of blue paint.
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The points H(3,-1), I(-6, -1), and J(3,-9) form a triangle. find the
perimeter of the triangle?
Answers
The perimeter of the given triangle having vertices H(3,-1); I(-6,-1) and J(3,-9) is 29.04.
The points which form a triangle are:
H(3,-1) ; I(-6,-1) and J(3,-9)
Perimeter of the given triangle with vertices H(3,-1); I(-6,-1) and J(3,-9) is required:
To find the length we have to find the distance between the points.
Using distance formula i.e.
[tex]\sqrt{ [ (x2 - x1)^2 + (y2 - y1)^2 ][/tex]
Let the length of the sides be A1, A2 , A3
On applying the distance formula to H(3,-1) and I(-6,-1) ;
We get,
A1 = [tex]\sqrt{[ (-6-3)^2 + (-1+1)^2 ][/tex]
= [tex]\sqrt{ [ (-9)^2 + (0)^2 ][/tex]
= [tex]\sqrt[ 81 + 0 ]}[/tex][tex]\sqrt{[ 81 + 0 ][/tex]
= [tex]\sqrt{81}[/tex]
= 9
On applying the distance formula to I(-6,-1) and J(3,-9);
We get,
A2 = [tex]\sqrt{ [ (3+6)^2 + (-9+1)^2 ][/tex]
= [tex]\sqrt{[ (9)^2 + (-8)^2 ][/tex]
= [tex]\sqrt{[ 81 + 64 ][/tex]
= [tex]\sqrt{145}[/tex]
= 12.04
On applying the distance formula to J(3,-9) and H(3,-1);
We get,
A3 = [tex]\sqrt{[ (3-3)^2 + (-9+1)^2 ][/tex]
= [tex]\sqrt{[ (0)^2 + (-8)^2 ][/tex]
= [tex]\sqrt{ [ 0 + 64 ][/tex]
=[tex]\sqrt{64}[/tex]
= 8
Hence,
The perimeter is 9 + 12.04 + 8 = 29.04
The perimeter of the triangle having vertices H(3,-1); I(-6,-1) and J(3,-9) is 29.04.
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The graph shows your distance from home while out on a walk. The next day, you jog the same route twice at a constant speed. The entire jog takes 1 hour. Compare your walk to your jog
Answers
Using proportions, it is found that your walk and jogging rates are given as follows:
Walking: 3.75 miles per hour.Jogging: 5 miles per hour.What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations.
One example of application, in the context of this problem, is for the relation between velocity, distance and time, as velocity is distance divided by time, that is:
v = d/t.
From the graph, the walk takes 40 minutes = 2/3 of an hour, and you walk 1.25 x 2 = 2.50 miles, as you walk 1.25 miles and then you come back home, hence the rate is given as follows:
v = 2.50/(2/3) = 3 x 2.50/2 = 3.75 miles per hour.
For the jog, you jog the same distance twice in one hour, hence you jog 5 miles in one hour, and the rate is given as follows:
v = 5/1 = 5 miles per hour.
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If this trapezoid is
translation
moved through the
(x+3, y-2), what will the
coordinates of D' be?
D' = ([?], [ ])
Answers
The coordinates of D' are (4,0)
A Trapezoid is regarded as a quadrilateral that has only one pair of opposite sides that are said to be parallel.
The coordinates of the given trapezoid are:
A = (-6,2)
B = (-5,4)
C = (-2,4)
D = (1,2)
It is given that the trapezoid is moved to the points of (x+3, y-2) on the graph.
Now, consider A = (-6,2)
A' = (-6+3, 2-2)
A' = (-3,0)
Consider B = (-5,4)
B' = (-5+3, 4-2)
B' = (-2,2)
Consider C = (-2,4)
C' = (-2+3, 4-2)
C' = (1,2)
Consider D = (1,2)
D' = (1+3, 2-2)
D' = (4,0)
Therefore, D' has the coordinates (4,0)
Refer to the full question given in the following image.
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The following are the temperatures in °C for the first 12 days of January: 4.5 , − 3 , − 2 , 2 , 2.5 , 3 , − 1 , 4 , − 2.5 , 7 , − 4 , 3.5 What is the median temperature for those 12 days? Give your answer as a decimal.
Answers
Answer:
First you will put the numbers in order least to greatest. So, it would be -4.5, -4, -3.5, -2, -1, 0, 1.5, 2, 2.5, 4, 6. 0 is the median because it in in the middle here’s how. You cross out -4.5 and 6 then 4 and -4 then -3.5 and 2.5 then 2 and -2 then -1 and 1.5 and you’re left with just the 0
Step-by-step explanation:
Which age group of this set of numbers has twice as many people as another age group?
A) 76-85
B) 15-25
C) 36-45
D) 46-55
Answers
Answer:I believe it is 15-25
Step-by-step explanation:
[tex]\rm\int_0^1 \frac{( {x}^ \varphi - 1 {)}^{2} }{ log {}^{2} (x) } dx\\[/tex]
Answers
I assume the natural logarithm, and not the base-10 log. Parameterize the integral as
[tex]\displaystyle I(a) = \int_0^1 \frac{(x^a - 1)^2}{\log^2(x)} \, dx[/tex]
Differentiate twice with respect to [tex]a[/tex].
[tex]\displaystyle I'(a) = 2 \int_0^1 \frac{x^{2a} -x^a}{\log(x)} \, dx[/tex]
[tex]\displaystyle I''(a) = 2 \int_0^1 (x^{2a} - x^a) \, dx[/tex]
Evaluate the last integral, then solve for [tex]I(a)[/tex] with the fundamental theorem of calculus, noting that [tex]I(0)=I'(0)=0[/tex].
[tex]\displaystyle I''(a) = 2\left(\frac1{2a+1} - \frac1{a+1}\right)[/tex]
[tex]\displaystyle I'(a) = 2 \int_0^a \left(\frac1{2t+1} - \frac1{t+1}\right) \, dt \\\\ ~~~~ = \log(2a+1) - 2 \log(a+1)[/tex]
[tex]\displaystyle I(a) = \int_0^a (\log(2t+1) - 2\log(t+1)) \, dt \\\\ ~~~~ = (2a+1) \log(2a+1) - 2(a+1) \log(a + 1)[/tex]
Let [tex]a=\phi[/tex] to recover the original integral.
[tex]\displaystyle I(a) = (2\phi+1) \log(2\phi+1) - 2(\phi+1) \log(\phi + 1)[/tex]
Using various properties of the golden ratio [tex]\phi[/tex], namely
[tex]\phi = 1 + \dfrac1\phi \implies \phi^2 = \phi + 1 \implies \phi^3 = \phi^2 + \phi[/tex]
[tex]2\phi+1 = \phi\left(2+\dfrac1\phi\right) = \phi(1 + \phi)[/tex]
[tex]\phi=\dfrac{1+\sqrt5}2 \implies \phi^3 = 2 + \sqrt5[/tex]
we can simplify the result to
[tex]\displaystyle I(\phi) = \int_0^1 \frac{(x^\phi-1)^2}{\log^2(x)} \, dx = \boxed{\sqrt5\,\log(\phi)}[/tex]
Increase 270 by 20%
please help asap
Answers
Answer:
324
Step-by-step explanation:
20%-> 0.2
0.2(270)= 54
270+54=324
Answer:The answer is 324
Step-by-step explanation:20% of 270 is 54 so add 54 and 270 because you increase by 20 to get the answer
I need help......................................................................
Answers
Answer: The answer is D.
Step-by-step explanation: Because I use a graphing calculator
2. Complete the table for the equation, and graph the equation. (4pts)
2x - y = - 3
Answers
I attached a photo to answer you question. Hope this helps!
Which of the following is an equivalent expression of 15x2 +12x + 8?
27x3 + 8
15x2(12x + 8)
12x + 15x2 + 8
8(15x2 + 12x)
Answers
The option that is an equivalent expression of 15x² +12x + 8 is C. 12x + 15x² + 8.
What is an equivalent expression?Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same values for the variable, two algebraic expressions that are equivalent have the same values.
If two systems of equations have the same solution, they are equivalents. In algebra, 2(2x - 3y + 6) is equal to 4x -6y + 12 as an example of an equivalent expression.
In this case, it should be noted that 15x² +12x + 8 is the same as 12x + 15x² + 8. Therefore, the correct option is C.
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Let g (x) be the reflection across the y-axis of the function f (x) = 5x + 8. Identify the rule for g (x). g(x) = 5x + 8g (x) = -5x+8g (x) = -5x -8g (x) = 5x - 8
Answers
Given a function f(x), we can write the function g(x), where g(x) is the reflection over teh y-axis of f(x) by:
[tex]g(x)=f(-x)[/tex]In this case, the function given is:
[tex]f(x)=5x+8[/tex]Thus the reflection over the y-axis is:
[tex]g(x)=f(-x)=5(-x)+8[/tex]Now simplify:
[tex]g(x)=-5x+8[/tex]hus the answer is:
g (x) = -5x+8 (second option)
a stack of 20 identical boxes. The stack is 180cm tall, Julia then removes 3 boxes from the top. How tall is the stack now
Answers
A stack of 20 identical boxes are 180 cm tall, then after removing 3 boxes from the top it is 153 cm tall.
As given in the question,
Number of identical boxes in a stack=20
Stack of 20 identical boxes are 180 cm tall
Height of 1 box=180/20
=9cm
Julia removes 3 boxes from the top
Height of 3 identical boxes=9 × 3
=27 cm
Height of stack after removing 3 boxes from the top
=Original height - height of 3 boxes
=180 -27
=153cm
Therefore, a stack of 20 identical boxes are 180 cm tall, then after removing 3 boxes from the top it is 153 cm tall.
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Which shows the integers in order from least to greatest?
a.20, 6, -2, -13
b. -2, 6, -13, 20
c..-13, -2, 6, 20
d.20, -13, 6, - 2
Answers
The integers that are in order from least to greatest will be C. -13, -2, 6, 20.
What is an integer?It should be noted that an integer simply means a natural number or a whole number that given. It should be noted that they can either be positive or negative.
In this case, the numbers will be illustrated as thus:
The smallest number is -13.
The biggest number is 20.
Therefore, the arrangement is -13, -2, 6, 20.
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Find the value of x.
Answers
Answer:
x = 8
Step-by-step explanation:
You want to know the value of x in an expression for an angle measure at parallel lines.
Angles at a transversalWhere at transversal crosses parallel lines, all acute angles created are congruent, all obtuse angles created are congruent, and the acute angles are supplementary to the obtuse angles.
The angle marked 83° is acute. The angle marked (12x+1)° is obtuse, so these angles are supplementary:
83° +(12x +1)° = 180°
12x +84 = 180 . . . . . . . divide by ° and simplify
12x = 96 . . . . . . . . . . subtract 84
x = 8 . . . . . . . . . . . . divide by 12
The value of x is 8.
A hang glider dropped his cell phone from a height of 450 feet. How many seconds did it take for the cell phone to reach the ground? Use radical equations and round to the nearest tenth.
Answers
The cell phone will takes about 4.7 seconds to reach the ground.
What are equations of motion?There are three equation of motions that can be used when motion of the object is under constant acceleration and on a straight path.
They are listed below as:
[tex]v = u + at\\\\s = ut + \dfrac{1}{2} at^2\\\\v^2 = u^2 + 2as[/tex]
where u = initial velocity of the considered object
v = final velocity of the object
a = acceleration of the object
s = distance traveled by the object in 't' time.
Given that hang glider dropped his cell phone from a height of 450 feet:
Acceleration is rate of change of velocity.
[tex]s = ut + \dfrac{1}{2} at^2[/tex]
Height = h = 450 feet
Gravitational Acceleration = g = 9.8 feet/s²
Initial Velocity = u = 0 m/s
h = 1/2at²
h = √2h/g
h = √2 x 450/ 9.8
h = 9.58 s.
Therefore, the cell phone will take 9.58 seconds to reach the ground.
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test score hours studying 2 3 4 test score 44 66 88 test score ratio hours studying 22 1 ? ?
Answers
The test score ratio for studying 2 : 2 : 1 hours is represented as
44 : 44 : 22
What is a ratio?The comparison of two similar quantities or the relationship between them is known as a ratio. Using ratio symbols or words, ratios can be expressed in three different ways while maintaining their meaning.
To put it another way, ratios can be expressed by putting a fraction bar, the word "to," or the ratio symbol ":" between the two values being compared.
If 2 hours of studying = 44 marks
If 3 hours of studying = 66 marks
If 4 hours of studying = 88 marks
Then total sum of hours of studying = 9 hours
9 hours of studying = Sum of all marks
= 44 + 66 + 88
= 198
1 hour of studying = 198/9
= 22 marks
So, the test score ratio for studying 2 : 2 : 1 hours is represented as
44 : 44 : 22
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i need help with the 2 problems in this picture.
Answers
Answer:
5 degree Celsius
Explanation:
Using the formula for conversion included in the image attached, we have:
[tex]\begin{gathered} \frac{5(F-32)}{9}=C \\ F^{\circ}=41 \\ \frac{5(41-32)}{9}=C \\ \frac{5(9)}{9}=C \\ 5^=C^{\circ} \\ \\ \therefore41^{\circ}F=5^{\circ}C \end{gathered}[/tex]Therefore, 41 degrees Fahrenheit is equivalent to 5 degrees Celsius
The balance sheet for Tempest, Inc., is shown here in market value terms. There are 19,000 shares of stock outstanding.
Answers
Based on the number of shares outstanding and the market value, the price the stock is currently selling for is $31.40
How to find the selling price of the stock?To find the selling price of the stock the formula is:
= Equity value of stock / Number of stock outstanding
The number of stock outstanding is 19,000 shares. The equity value of the stock is $596,600.
The selling price of the stock today then is:
= Equity value of stock / Number of stock outstanding
= 569,600 / 19,000
= $31.40
Full question is:
What is the stock selling for today?
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B ВaAbСLet c=12, and a=4.020. What is tan(A) in radians? Round to 3 decimal places.
Answers
Answer
Tan (A) = 0.109 radians
Explanation:
The figure given is a right angles triangle
Given that AB = c is the hypotenus
AC = b = adjacent
BC = a = opposite
Tan A can be calculated using SOH CAH TOA
Tan A = opposite / adjacent
Tan A = BC / AC
BC = a = 4.020
We need to find b uisng pythagoras theorem
[tex]\begin{gathered} c^2=a^2+b^2 \\ 12^2=4.020^2+b^2 \\ 144=16.1604+b^2 \\ \text{Collect the like terms} \\ b^2\text{ = 144 - 16.1604} \\ b^2\text{ = 127.8396} \\ b\text{ = }\sqrt[]{127.8396} \\ b\text{ = 11.307} \end{gathered}[/tex]b = 11.307
Tan A = 4.020 / 11.307
Tan A = 0.3555
A = tan ^-1 (0.3555)
A = 19.570 degrees
Convert degrees to radian
since 1 pi = 180 degrees
x pi = 19.570
Cross multiply
19.570 * 1 = x * 180
x = 19.570 / 180
x = 0.109
Therefore, tan (A) is 0.109 radians
7 lorries can carry 987 cartons of books. How many cartons of books can each lorry carry
Answers
Answer:
141 each
Step-by-step explanation:
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