Answers
A horizontal line with evenly spaced numerical increments is referred to as a number line.
[tex]$-1 \frac{3}{4}$[/tex] is located at point -1.
1.125 is located at point 1.
[tex]$\frac{14}{8}$[/tex] is located at point 1 < x < 2.
What is meant by number line?A number line is a diagram of a graduated straight line used to represent real numbers in introductory mathematics. It exists assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.
A horizontal line with evenly spaced numerical increments exists directed to as a number line. How the number on the line can be answered depends on the numbers present. The utilize of the number exists defied by the question that it corresponds to, such as when graphing a point.
[tex]$-1 \frac{3}{4}$[/tex] is located at point -1.
1.125 is located at point 1.
[tex]$\frac{14}{8}$[/tex] is located at point 1 < x < 2.
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1) -3 /4 is located at the point - 1
2).14/ 8 is located at point 1.
3) 1.125 is located at after 1.
What exactly is a number line?In basic mathematics, real numbers are represented by a number line, a representation of a graduated straight line. The presumption is that each point on a number line represents a real number, and that each real number represents a point.
There is something known as a number line, which is a horizontal line with uniformly spaced numerical increments. The numbers available determine how to respond to the number on the line. The number can be used in ways that defy the question it answers, such as when graphing a point.
1) -3 /4 is located at the point - 1
2).14/ 8 is located at point 1.
3) 1.125 is located at after 1.
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Related Questions
4
How many 3-cup servings are in 4 cups?
A. 1/2
B. 2/
C. 4
D. 12
Answers
State if the following are perfect square trinomials. Show work that proves your conclusion.
Answers
Solution:
A quadratic expression is said to be a perfect square trinomial if it has repeated factors.
Given the expression below:
[tex]x^2+7x+\frac{49}{4}[/tex]By factorization, we have
[tex]\begin{gathered} (x^2+\frac{7}{2}x)+(\frac{7}{2}x+\frac{49}{4}) \\ factor\text{ out the common term,} \\ x(x+\frac{7}{2})+\frac{7}{2}(x+\frac{7}{2}) \\ This\text{ gives} \\ (x+\frac{7}{2})(x+\frac{7}{2}) \\ \Rightarrow(x+\frac{7}{2})^2 \\ \end{gathered}[/tex]Since the above expression has a repeated factor of
[tex](x+\frac{7}{2})[/tex]We can conclude that the expression is a perfect square trinomial.
Using the graph determine which transformation is shown by the following figures
Answers
A reflection is a transformation representing a flip of a figure, they may be reflected in a point, line or plane. The image is congruent to the preimage.
Then, Figure A and Figure B are experiencing Reflection.
2. Figure B and Figure C= Rotation
Rotation describes the motion of a figure around a fixed point, a counterclockwise turn has a positive magnitude.
3. Figure C and Figure D=Translation
Translation is a type of transformation that moves each point in a figure the same distance in the same direction.
4. Figure D and Figure E= Dilation
The transformation that defines a proportional stretch or shrink of a figure on the coordinate plane based on a scale factor is Dilation.
Find the perimeter and area of the figure
Answers
The perimeter is 120m
The area of the figure is 432[tex]m^{2}[/tex]
How to find the area and perimeter of the figure?
Consider the triangle,
Side A = 15m
Side B = 15m
Side C= 18m
Perimeter = a + b+ c
= 15+ 15+ 18
= 48m
Height h = 12m
Base = b= 18m
Area = [tex]\frac{1}{2} bh[/tex]
[tex]=\frac{1}{2} *18*12[/tex]
= 108[tex]m^{2}[/tex]
Consider the square,
Side = a = 18m
Perimeter = 4a
Perimeter = 72m
Area = [tex]a^{2}[/tex]
=324 [tex]m^{2}[/tex]
Consider the figure,
The perimeter of the figure = Perimeter of the triangle + Perimeter of the square
= 48+ 72
= 120m
The area of the figure = 108 + 324
= 432[tex]m^{2}[/tex]
The perimeter is 120m
The area of the figure is 432[tex]m^{2}[/tex]
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This is algebra 2 ( function graphs) I’m usually okay with math but I been I of school recently for surgery and forgot a little bit I just need a refresher
Answers
The red function has the form of:
[tex]f(x)=\sqrt[]{-x+1}[/tex]In order to obtain the green function, we need to do a reflection over y-axis, then a translation one unit to the right, a translation 1 unit down, and finally a reflection over the x-axis, so:
[tex]\begin{gathered} g(x)=-(\sqrt[]{-(-x)+1-1}-1) \\ g(x)=-\sqrt[]{x}+1 \end{gathered}[/tex]A cat with 850 J of energy is stuck in a tree that is 15 meters off the ground. What is the mass of th. cat?
O 56.7 kg
O 12,750 kg
O 5.78 kg
O 147 kg
Answers
the school spirit club is stuffing bags for the pep rally. they have 450 bags to fill and 1000 pieces of candy to go in those bags. how many pieces of candy can go in each bag? round to the nearest hundredth if necessary
Answers
Given:
The number of bags = 450 bags
The number of candies = 1000
To find the number of candies per bag, divide 1000 by 450
so, the answer is;
[tex]\frac{1000}{450}=\frac{100}{45}=\frac{5\cdot20}{5\cdot9}=\frac{20}{9}=2.222[/tex]Rounding to the nearest hundredth
so, the answer is:
The number of pieces of candy that can go in each bag = 2.22
8) y= V1-5 A) Domain: x 20 Range: y 2-5 B) Domain: x > 0 Range: y'z 5 C) Domain: {All real numbers. } Range: {All real numbers. } D) Domain: x 25 Range: y 20
Answers
Domain:
we know that a root cannot have negative values inside so
[tex]\begin{gathered} \sqrt[]{x}\ge0 \\ x\ge0^2^{} \\ x\ge0 \end{gathered}[/tex]the domain is X >= 0
Range:
we solve the equation for y
[tex]\begin{gathered} y=\sqrt[]{x}-5 \\ y+5=\sqrt[]{x} \\ (y+5)^2=x \end{gathered}[/tex]and we replace the condition that x must be greater than or equal to 0
so
[tex](y+5)^2\ge0[/tex]now solve y
[tex]\begin{gathered} y+5\ge0^2 \\ y+5\ge0 \\ y\ge-5 \end{gathered}[/tex]so the range is Y >= -5
then the right option is A
The rate of growth dPdt of a population of bacteria is proportional to the square root of t with a constant coefficient of 9, where P is the population size and t is the time in days (0≤t≤10). The initial size of the population is 600. Approximate the population after 7 days. Round the answer to the nearest integer.
Answers
To solve this question we are going to need to define an equation with the data that the problem gives us
The first part (rate of growth) shows us a derivate, this is equal to 9 square root of t or:
[tex]\frac{dP(t)}{dt}=9\sqrt{t}[/tex]where P is the population size and t is the time in days
Now we need the population after 7 days, so we need the P(t) formula, which means that we need the integration
First, we send the dt to the other side to have something to integrate
[tex]\int dP(t)=\int9\sqrt{t}dt[/tex]Solving
[tex]\begin{gathered} P(t)=9(\frac{2}{3}t^{\frac{3}{2}})+C \\ \\ P(t)=6t^{\frac{3}{2}}+C \end{gathered}[/tex]We know that P(0)=600 so
[tex]P(0)=600=C[/tex][tex]P(t)=6t^{\frac{3}{2}}+600[/tex]Now we replace the t by 7
[tex]\begin{gathered} P(7)=6(7^{\frac{3}{2})}+600 \\ P(7)=711.121 \end{gathered}[/tex]Answer: 711
Compute the average rate of change of the function. Exercise A:
Answers
ANSWER
(a). Average Rate of Change = - 4
(b). Average Rate of Change =
[tex]12+6h+h^2^{}[/tex]EXPLANATION
(a).
Step 1: Given
[tex]h(x)=5-2x^2\text{ at interval \lbrack-2, 4\rbrack}[/tex]Step 2: Determine the Average Rate of Change
[tex]\text{Average rate of change = }\frac{h(b)\text{ - h(a)}}{b-a}[/tex]4. Joey has 468 stickers. Lorna has 215 stickers. How many more
stickers does Joey have than Lorna? Show how you figured it out.
Answers
After doing some mathematical operations, we know that Joey has 253 more stickers than Lorna.
What are mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value.The quantity of operands affects the operation's arity.The order of operations refers to the rules that define the sequence in which we should perform the operations necessary to solve an expression.Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction are all referred to as PEMDAS (from left to right).So, a number of more stickers Joey has:
The number of stickers Joey has is 468.The number of stickers Lorna has is 215.More stickers Joey has can be calculated as follows:
468 - 215 = 253Therefore, after doing some mathematical operations, we know that Joey has 253 more stickers than Lorna.
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is n divided by -1 always equal to -1
Answers
if n = a negative number is divided by a negative number the answer is positive.
So if (n) is -4 / -1 = 4
Two negatives = positive for multiplication and division
Answer:
Yes
Step-by-step explanation:
Any number divided by 1 equals itself. This rule tells us simply that if we have a number divided by 1, our answer will equal that number regardless of what that number is.
Hope this helps you
Tell me if I'm wrong
While on vacation in Washington DC the cab ride for the Dulles airport to the hotel is 15 miles. The total cost of the cab ride was $25.50. The cabbie charges $1.50 per mile for the entire trip A. Write an equation to that can be used to determine B. What is the flat rate of the cab ride? C. How much does it cost to travel 7 miles in a cab?
Answers
The total distance from Washington DC to Dulles airport is 15 miles
The total cost of the cab ride is $25. 50
The cabbie charges $1.50 per mile for the entire trip
Let T be the total cost of the entire trip
Let x represents the number of miles traveled
Let y be the flat rate of the cab ride
Total cost = flat rate + charge per trip x number of miles covered
Mathematically,
T = y + 1.5 * x
T = y + 1.5x
Where, 1.5 is the charge per trip.
The equation becomes
T = y + 1.5x
B
To calculate the flat rate of the cab ride?
The total cost = $25.50
Charges per mile = $1.5
Total number of miles = 15
Substitute the above values into the equation
25.50 = y + 1.5 x 15
25.50 = y + 22.5
Make y the subject of the formula
y = 25.50 - 22.5
Y = $3
The flat rate of the cab ride is $3
C
How much does it cos
The entire graph of the function h is shown in the figure below.
Write the domain and range of h as intervals or unions of intervals.
Answers
The domain of the function f is [-5. -2] U [ 1, 2].
The range of the function f is [-4, 3].
What is a function?A function is defined as a relation between a set of inputs having one output each.
The inputs are called the domain of the function.
The outputs are called the range of the function.
We have,
A graph of the function f.
We can see two curves on the graph.
One curve:
Domain = [1, 2]
Range = [-4, 0]
Another curve:
Domain = [-5, -2]
Range = [-3, 3]
We can combine both the curves domain and the range.
Domain = [-5. -2] U [ 1, 2 ]
Range = [-4, 3]
Thus,
The domain of the function f is [-5. -2] U [ 1, 2].
The range of the function f is [-4, 3].
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find the area of the indicated region under the standard normal curve. what is the area between z=0 and z=0.8 under the standard normal curve?
Answers
From the standard normal tables, we have the value of
P(z=0.8) =0.7881
P(z=0) = 0.5000
Therefore the area between z = 0 and z = 0.8 under the standard curve is,
P(z=0.8) - P(z=0) = 0.7881 - 0.5000
=0.2881
Thus, the answer is 0.2881
Need help asap extra points
Answers
The equation of line is y = 8/5x-26/5.
What is a line equation?
A line's equation is an algebraic way of expressing the collection of points that make up a line in a coordinate system.
Equation 8x-5y=4 is given.
-5y = 4-8x
y = 8/5x-4/5 and we are aware that the line's equation is y = mx+b
m = 8/5
Nowadays, coordinates are (2,-2)
Y=-2, X=2, and m=8/5
y = mx+c
-2 = 8/5(2)+c
c = -26/5
Consequently, the line's equation is
y = 8/5x-26/5
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write each of the following numbers line position as fraction with Demeter 100 as decimals and also as percentages
Answers
Answer:
Explanation:
To write the given numbers as fractions of 100, percentages, and decimals, we first need to estimate their values on the number line. Once, we have the values of the numbers, we can write the as a fraction of 100 as
[tex]\frac{Num}{100}[/tex]As percentages as
[tex]\frac{Num}{100}\times100[/tex]And as decimals as
[tex]Num\div100[/tex](a).
The estimate of the value of three numbers is 27, 45, 67.
Writing the above as fractions of 100 gives
[tex]\frac{27}{100},\frac{45}{100},\frac{67}{100}[/tex]As a percentage, these numbers are
[tex]\frac{27}{100}\times100,\frac{45}{100}\times100,\frac{67}{100}\times100[/tex][tex]\rightarrow27\%,45\%,67\%[/tex]To write the numbers as decimals we divide them by 100 to get
[tex]0.27,0.45,0.67[/tex](remember that dividing by 100 shifts the decimal point to the left by 2 digits)
(b).
The estimate of the values of the three numbers are 57, 74, and 89
Writing these numbers as fractions gives
[tex]\frac{57}{100},\frac{74}{100},\frac{89}{100}[/tex]As a percentage these numbers are
[tex]\frac{57}{100}\times100,\frac{74}{100}\times100,\frac{89}{100}\times100[/tex][tex]57\%,74\%,89\%[/tex]And as decimals
[tex]0.57,0.74,0.89[/tex](c).
The estimate of the value of the three numbers is 22, 36, 55.
Writing them as a fraction gives
[tex]\frac{22}{100},\frac{36}{100},\frac{55}{100}[/tex]As a per cent these numbers are written as
[tex]undefined[/tex]Josh is mountain climbing with Kendall and has just climbed a 6-meter vertical rock face. Kendall is standing 8 meters away from the bottom of the cliff, looking up at Josh. How far away are Josh and Kendall?
Answers
Josh and Kendall are 10m far away from each other.
Josh is mountain climbing with Kendall and has just climbed a 6-meter vertical rock face.
Kendall is standing 8 meters away from the bottom of the cliff
As he climbed a vertical rock face the, the angle formed between the rock and the ground is 90.
Josh climbed 6 meter vertical rock, so perpendicular is 6m
Kendall is standing 8 meters away from the bottom of the cliff, base = 8m
So, here pythagoras theorem is used here to find the distance between Josh and kendall
As per pythagoras theorem,
h² = b² + p²
= 8² + 6²
= 64 + 36
h² = 100
h = √100 = 10
Therefore the distance between Josh and Kendall is 10m.
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Write a similarity statement for the similar triangles.∆PQR ~ ∆____
Answers
As
[tex]FG\cong JK[/tex]we get that
[tex]\begin{gathered} \angle G\cong\angle J \\ \angle F\cong\angle K \end{gathered}[/tex]So the answer is AA postulate
Use square roots for the problem. Which equation(s) have -4 and 4 as solutions? Select all that apply
Answers
Given:
Different equations
To find:
the equation whose solutions have -4 and 4
To determine the equations with solutions -4 and 4, we will solve each of th given equation
[tex]\begin{gathered} a)\text{ x}^2\text{ = 8} \\ x\text{ = }\pm\sqrt{8}\text{ = }\pm\sqrt{4\times2} \\ x\text{ = }\pm\text{2}\sqrt{2}\text{ \lparen not a solution of -4 and 4\rparen} \end{gathered}[/tex][tex]\begin{gathered} b)\text{ x}^2\text{ + 16 = 0} \\ x^2=\text{ -16} \\ x\text{ = }\pm\sqrt{-16} \\ root\text{ of -16 gives a complex number. Hence, no solution of -4 and 4} \end{gathered}[/tex][tex]\begin{gathered} c)\text{ 2x}^2\text{ = 32} \\ divide\text{ both sides by 2:} \\ x^2\text{ = }\frac{32}{2} \\ x^2\text{ = 16} \\ x\text{ = }\pm\sqrt{16}\text{ = }\pm4 \\ x\text{ = 4 and -4} \end{gathered}[/tex][tex]\begin{gathered} d)\text{ -3x}^2\text{ = -48} \\ divide\text{ both sides by -1:} \\ division\text{ of same signs give positive sign} \\ 3x^2\text{ = 48} \\ x^2\text{ = 48/3} \\ x^2\text{ = 16} \\ x\text{ = }\pm\sqrt{16}\text{ = }\pm4 \\ x\text{ = 4 and - 4} \end{gathered}[/tex][tex]\begin{gathered} e)\text{ }6x^2\text{ + 56 = -40} \\ 6x^2\text{ = -40 - 56} \\ 6x^2\text{ = -96} \\ x^2\text{ = -96/6} \\ x^2\text{ = -16} \\ x\text{ = }\pm\sqrt{-16} \\ root\text{ of a negative number gives a complex number.} \\ Hence,\text{ no solution of -4 and 4} \end{gathered}[/tex][tex]\begin{gathered} f)\text{ 27 - 5x}^2\text{ = -53} \\ add\text{ 5x}^2\text{ }to\text{ both sides:} \\ 27\text{ - 5x}^2+\text{ 5x}^2\text{ = -53 + 5x}^2 \\ 27\text{ = -53 + 5x}^2 \\ \\ add\text{ 53 to btoh sides:} \\ 27\text{ + 53 = 5x}^2 \\ 80\text{ = 5x}^2 \\ divide\text{ both sides by 5:} \\ \frac{80}{5}=\text{ x}^2 \\ x^2\text{ = 16} \\ x\text{ = }\pm\sqrt{16}\text{ = }\pm4 \\ x\text{ = 4 and -4} \end{gathered}[/tex]Tammy drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 7 hours. When Tammy drove home, there was no traffic and the trip only took 5 hours. If her average rate was 18 miles per hour faster on the trip home, how far away does Tammy live from the mountains?
Answers
ANSWER
[tex]\begin{equation*} 315\text{ }miles \end{equation*}[/tex]EXPLANATION
Let her average rate on the trip to the mountains be x miles per hour.
This implies that her average rate on her way home was (x + 18) miles per hour.
The distance traveled can be found using the formula for speed(average rate):
[tex]\begin{gathered} speed=\frac{distance}{time} \\ \\ distance=speed*time \end{gathered}[/tex]Therefore, on her way to the mountains:
[tex]d=x*7[/tex]And on her way home:
[tex]d=(x+18)*5[/tex]Since the distance is the same for both trips, equate the two equations:
[tex]\begin{gathered} x*7=(x+18)*5 \\ \\ 7x=5x+90 \end{gathered}[/tex]Solve for x in the equation:
[tex]\begin{gathered} 7x-5x=90 \\ \\ 2x=90 \\ \\ x=\frac{90}{2} \\ \\ x=45\text{ mph} \end{gathered}[/tex]Substitute the value of x into the equation for distance to find the distance:
[tex]\begin{gathered} d=45*7 \\ \\ d=315\text{ }miles \end{gathered}[/tex]That is the distance from the mountains to where Tammy lives.
photo question graphing linear equations
Answers
We want to select the graph that represents the equation;
[tex]2x-5y=-10[/tex]Let's rewrite this equation as;
[tex]\begin{gathered} -5y=-2x-10 \\ divide\text{ both sides by -5, we obtain;} \\ y=\frac{2}{5}x+2 \end{gathered}[/tex]This equation has a slope of 2/5, an x-intercept of -5. and a y-intercept of 2, lets inspect the graphs to see which one matches it.
Going through the options, we see that the matching graph-the correct graph is Option A.
6. Suppose that y varies inversely with x. Use the information to find k, and then choose the equation of variation. x = 2 when y = 2.Ok = 1, y = 1xk = 4, y = 4x4= 4, y = 2 / 24= 1, y = 1/2
Answers
ANSWER:
k = 4, y = 4/x
STEP-BY-STEP EXPLANATION:
Since they are inverses they have the following form the equation
[tex]y=k\cdot\frac{1}{x}[/tex]now, x = 2 and y = 2, therefore, replacing and solving for k:
[tex]\begin{gathered} 2=k\cdot\frac{1}{2} \\ k=2\cdot2 \\ k=4 \end{gathered}[/tex]We replace and we would have the equation
[tex]\begin{gathered} y=4\cdot\frac{1}{x} \\ y=\frac{4}{x} \end{gathered}[/tex]The population of bobcats in northern Arizona since 2008 can be modeled using the function b(t) = –0.32t2 + 2.7t + 253
What does t represent?: the number of years since 2008
What is the domain for this function?:t values greater than or equal to 0
Which range values would not make sense for this function?:negative values
Would the graph be continuous or discrete, and why?:discrete, because number of bobcats cannot be broken into fractional parts (these are the answers to function notation EDGE 2022 algebra1)
Answers
A polynomial function is a function that only employs non-negative integer powers or only positive integer exponents of a variable in an equation such as the quadratic equation, cubic equation, etc. For instance, the exponent of the polynomial 2x+5 is 1.
Explain about the polynomial function?A polynomial equation in standard form before attempting to solve it. Factor it, then set each variable factor to zero after it has reached zero. The original equations' answers are the solutions to the derived equations. Factoring cannot always be used to solve polynomial equations.
The variable t in the formula b(t) stands for the number of years following 2008. This function's range of application is. More over 258.7 wouldn't make sense as a range. The function's graph is continuously drawn at all times.
Explanation:
Since 2008, the provided function b(t) displays the bobcat population in Northern Arizona. The number of years following 2008 is therefore represented by the variable t.
The domain of this function is because t stands for the number of years after 2008, which can be either positive or zero.(0,∞)
Provided that the given function is a quadratic function with a negative coefficient, it is a descending parabola. There is no meaning in the range above the vertex's y-coordinate.
Vertex function is (4.2,258.7)
This is polynomial function so the graph of the function always continuous
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15.4-32+(60/3*166)*8 divided by 4-(2*61)
Answers
The 15.4-32+(60/3*166)*8 divided by 4-(2*61) is -224.94.
As per the PEMDAS rule, firstly solving the parenthesis in the numeral : 15.4-32+(60/3*166)*8
Performing division in parenthesis
Number = 15.4 - 32 + (20×166) × 8
Performing multiplication in parenthesis
Number = 15.4 - 32 + 3320 × 8
Performing multiplication and subtraction
Number = - 16.6 + 26,560
Performing subtraction
Number = 26,543.4
Number = 4 - (2×61)
Performing multiplication in parenthesis
Number = 4 - 122
Performing subtraction
Number = - 118
Performing division now
Result = 26,543.4 ÷ -118
Result = -224.94
The number obtained on division will be -224.94.
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what products of 37 and 4
Answers
A product is the result of a multiplication between 2 numbers:
37 x 4 = 136
Select all the correct answers.Which vectors are unit vectors?1 一32l -一》《完,表》口 u={1, 1}1-(美)
Answers
The unit vector has a magnitude = 1
So, for the given vectors, we will find the magnitude of every vector
[tex]\begin{gathered} u=<\frac{\sqrt[]{3}}{2},-\frac{1}{2}> \\ |u|=\sqrt[]{(\frac{\sqrt[]{3}}{2})^2+(-\frac{1}{2})^2}=\sqrt[]{\frac{3}{4}+\frac{1}{4}}=\sqrt[]{\frac{4}{4}}=\sqrt[]{1}=1 \end{gathered}[/tex]So, it is a unit vector
[tex]\begin{gathered} u=<-\frac{2}{\sqrt[]{5}},\frac{1}{\sqrt[]{5}}> \\ |u|=\sqrt[]{(-\frac{2}{\sqrt[]{5}})^2+(\frac{1}{\sqrt[]{5}})^2}=\sqrt[]{\frac{4}{5}+\frac{1}{5}}=\sqrt[]{\frac{5}{5}}=1 \end{gathered}[/tex]So, it is a unit vector
[tex]\begin{gathered} u=<1,1> \\ |u|=\sqrt[]{1^2+1^2}=\sqrt[]{1+1}=\sqrt[]{2}=1.414 \end{gathered}[/tex]So, it is not a unit vector
[tex]\begin{gathered} u=<-\frac{5}{\sqrt[]{6}},\frac{1}{\sqrt[]{6}}> \\ |u|=\sqrt[]{(-\frac{5}{\sqrt[]{6}})^2+(\frac{1}{\sqrt[]{6}})^2}=\sqrt[]{\frac{25}{6}+\frac{1}{6}}=\sqrt[]{\frac{26}{6}}=2.08 \end{gathered}[/tex]So, it is not a unit vector
So, the correct options are: 1 and 2
Alan takes a taxi at the rate of $3 per mile. The taxi company charges an additional pickup fee of $5. How many miles, d, did Alan travel if the total fare was $29?
Answers
Answer:
8 miles
Step-by-step explanation:
You want to know the distance Alan traveled for $29 in a taxi that charges a fee of $5 plus $3 per mile.
Mileage chargeThe amount of the $29 that paid for mileage was $29 -5 = $24.
At $3 per mile, that will pay for ...
$24/($3/mile) = 8 miles
Alan traveled 8 miles for a total fare of $29.
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Select the y-intercept and another point that lies on the graph of the equation y = 3x − 2.
Answers
The y-intercept of the equation y = 3x − 2 is (0, -2).
y-intercept
In Mathematics, an intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx + c, where m is slope and c is the y-intercept.
Equation of a line
The standard form of equation of a line is ax + by + c = 0. Here a, b, are the coefficients, x, y are the variables, and c is the constant term. It is an equation of degree one, with variables x and y. The values of x and y represent the coordinates of the point on the line represented in the coordinate plane.
Given that lies on the graph of the equation y = 3x − 2.
We know that
In an equation of line
y = mx + c
m = slope of a line
c = y intercept
So therefore in given equation of line the y intercept is (0, -2).
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What is the quotient of the complex numbers below?A.10 - iB.2 - iC.2 + iD.10 + i
Answers
The given fraction is
[tex]\frac{7+i}{3-i}[/tex]We will multiply up and down by the conjugate of down (3 + i)
[tex]\begin{gathered} \frac{7+i}{3-i}\times\frac{3+i}{3+i}= \\ \\ \frac{(7+i)(3+i)}{(3-i)(3+i)}= \\ \\ \frac{(7)(3)+(7)(i)+(i)(3)+(i)(i)}{(3)(3)-(i)(i)}= \end{gathered}[/tex]Add the like terms
[tex]\begin{gathered} \frac{21+7i+3i+i^2}{9-i^2}= \\ \\ \frac{21+10i-1}{9-(-1)}= \\ \\ \frac{20+10i}{9+1}= \\ \\ \frac{20+10i}{10} \end{gathered}[/tex]Take 10 as a common factor from up
[tex]\begin{gathered} \frac{10(2+i)}{10}= \\ \\ 2+i \end{gathered}[/tex]The answer is C
