Answers
The points for the ordered pairs of the linear function has been plotted in the graph shown in the image attached below.
How to Graph a Linear Function?A linear function is a straight line graph consisting of domain elements (x-values) and their corresponding range elements (y-values).
Given the function, y = 1/2x + 1 having the following domain elements (x-values):
D: {-8, -4, 0, 2, 6}
Find the corresponding y-value to each of the x-values by substitution
When x = -8, then:
y = 1/2(-8) + 1
y = -4 + 1
y = -3
(-8, -3)
When x = -4, then:
y = 1/2(-4) + 1
y = -2 + 1
y = -1
(-4, -1)
When x = 0, then:
y = 1/2(0) + 1
y = 0 + 1
y = 1
(0, 1)
When x = 2, then:
y = 1/2(2) + 1
y = 1 + 1
y = 2
(2, 2)
When x = 6, then:
y = 1/2(6) + 1
y = 3 + 1
y = 4
(6, 4)
Thus, the points for the ordered pairs of the linear function has been plotted in the graph shown in the image attached below.
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Related Questions
Solve each equation. 2 e ³x=16
Answers
The solution of the exponential equation 2e³x = 16 is x = 0.398.
What are defined as the exponential equation?Exponential equations are those in which the variables appear as exponents.
Exponential equations, for example, take the form a∧x = b∧y.Should use property of equality of the exponential functions to solve exponential calculations with the same base.If b is not a positive number, then b∧x = b∧y if but only if x = y. Throughout other words, is if bases are exactly the same, the exponents must also be the same as well.If the bases are not the same, accomplish the exponential equations using logarithms.Now, for the stated equation 2 e³x=16;
Divide both side by 2
=> e³x = 8
=> x = 8/ e³
As, we are aware of the exponential function 'e' that is the value of e = 2.72...
Substitute the value of the exponent 'e' in the obtained expression.
=> x = 8/ (2.72)³
=> x = 8/20.132
=> x = 0.398
Therefore, the obtained value of x for the given exponential function is 0.398.
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What are the solutions for |3(x+4)|+8=23
a) x=1 and x= -9
b) x=1
c) x=9
d) x= -1 and x= 9
Question 4
Looking at your answer for the question above, we’re there any extraneous answers?
a) Yes
b) No
Answers
q3: -9, 1
q4: No
The reason there are multiple answers for this question is because of the absolute value sign. to solve this you can isolate the absolute value onto one side and solve for the positive and negative possibilities.
step 1: isolate the absolute value
|3(x+4)|+8=23 ----> |3(x+4)|=15
step 2: remove the absolute value sign the remember that now it has two answer possibilities where 15 can be both negative and positive and still be right. Then just solve just like you would a normal equation.
3(x+4)= +-15 ----> x+4= +-5
x = -9, 1
What is 33% written as a fraction?
thirty-three over one thousand
3 over ten
8 over twenty-five
thirty-three over one hundred
Answers
Answer: 33/100
A mountain grows by 2 centimeters every year. At this rate in how many years will the mountain grow by 1.3 meters?
Answers
well, let's keep in mind that a meter has 100 centimeters, thus 1.3 meters will be 1.3 * 100 cm, namely 130 cm.
[tex]\begin{array}{ccll} cm&year\\ \cline{1-2} 2 & 1\\ 130& x \end{array} \implies \cfrac{2}{130}~~=~~\cfrac{1}{x}\implies \cfrac{1}{65}=\cfrac{1}{x}\implies x=65[/tex]
X-2/5 + 1/2x-3=1 pls solve this
Answers
Answer:
44/15
Step-by-step explanation:
[tex]x-\frac{2}{5}+\frac{1}{2}x-3=1 \\ \\ \frac{3}{2}x-\frac{17}{5}=1 \\ \\ \frac{3}{2}x=\frac{22}{5} \\ \\ x=\frac{44}{15}[/tex]
Suppose you invest a dollars to earn an annual interest rate of r percent (as a decimal). After t years, the value of the investment with interest compounded yearly is A(t)=a(1+r) t . The value with interest compounded continuously is A(t)=a . e rt
b. Suppose you can earn interest at some rate between 0 \% and 5 \% . Use your. knowledge of the exponential function to explain why continuous compounding does not give you much of an investment advantage.
Answers
$1.051271 is the exponential function to explain why continuous compounding does not give you much of an investment advantage.
With an example, what is compound interest?
When you add the interest you have already earned back into your principal balance, you are earning compound interest, which increases your profits. Consider that you have $1,000 in a savings account earning 5% interest annually. If you made $50 in the first year, your new balance would be $1,050.Simple Interest: A = P(1+rt)
P: the principal, the amount invested
A: the new balance
t: the time
r: the rate, (in decimal form)
Ex 1 - If $1000 is invested now with simple interest of 8% per year. Find the new amount after two years.
P = $1000, t = 2 years, r = 0.08.
A = 1000(1+0.08(2)) = 1000(1.16) = 1160
B) Suppose you invest $1 at 5% compounded yearly.
Suppose you invest $1 at 5% compounded continuously.
The 1st case gives you $1*(1.05)1 = $1.05
The 2nd case gives you $1*e0.05 = $1.05127
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Part 2: What the answers to the worksheet
Answers
The rule is reflection in y=x (x, y)→(y, x) and reflection in y=-x (x, y)→(-y, -x).
Given that, a rotation and reflection composition is equivalent to other compositions.
What are rotation and reflection?Reflection is flipping an object across a line without changing its size or shape. Rotation is rotating an object about a fixed point without changing its size or shape.
Rotation rule:
Rotation of a point through 180°, about the origin when a point A (x, y) is rotated about the origin O through 180° in the anticlockwise or clockwise direction, it takes a new position A' (-x, -y).
Reflection rule:
A vertical reflection reflects a graph vertically across the x-axis, while a horizontal reflection reflects a graph horizontally across the y-axis.
Therefore, the rule is reflection in y=x (x, y)→(y, x) and reflection in y=-x (x, y)→(-y, -x).
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Find each real root. ³√-27
Answers
A package of a 8 count AA batteries cost 6.40. A package of 20 count AA batteries cost 15.80. Which statement about the unit prices is true?
Answers
Calculation: We are trying to find the unit rate: To identify it, we can start off initially by acknowledging that an 8 count package costs $6.40. Dividing this by 8 will give us our unit rate for the cost of one AA battery.
$6.40 / 8 batteries = $0.80 per battery
In a package of 8 count batteries, each battery costs $0.80.
We can apply the same process for the unit rate of a package of 20 count batteries. This would look like:
$15.80 / 20 batteries = $0.79 per battery
In a package of 20 batteries, each battery is $0.79.
Explanation: Seeing both of the unit rates, we know that $0.79 is less than $0.80. Because of this, it costs a cent more to get a single battery from an 8 count set of batteries than it would to get a singular battery from a 20 count set of batteries.
Final answer: It costs one more cent per battery for an 8 count battery than a 20 count battery. The statement about the unit prices that is true is the 20-count batteries have a lower price than the 8-count batteries.
Missing answer choices are listed in the image provided. D is the correct answer.
Can anyone help me calculate the value of y
Answers
Based on the fact that this is an equilateral triangle, the value of y can be found to be 5.
What is the value of y?The figure given is an equilateral triangle which means that the lengths of all the sides are equal.
As DC is equal to 20, it means that all the other sides should be 20 as well.
This means that the value of y is:
20 = 15 + y
y = 20 - 15
y = 5
In conclusion, y is 5.
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A scout leader is going to pair a new member with one of the fifteen troop members. five of the boys love to go camping ten like to fish three enjoy archery twelve like to go hiking and one boy enjoys carving.what is the probability the new boy will be paired with a boy who does not love camping
Answers
The probability of the new boy being paired up with a boy who does not love camping is 2/3 or 66.66%
Total no. of troop members = 15
No. of boys who love camping = 5
No. of boys who love fishing = 10
No. of boys who love archery = 3
No. of boys who love hiking = 12
The boy who enjoys carving = 1
Boys who do not like camping = 1 - 5/15 = 10/15 = 2/3*100 = 66.66%
So, the probability that the new boy will be paired up with a boy who does not love camping is 66.66% or 2/3.
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a) how much £60 is worth in euros (€).
b) how much €98.60 is worth in pounds (£).
Exchange rate
£1 = €1.16
Answers
In the foreign exchange market, if a Pound is equal to 1.59 USD, one Euro is equal to 1.46 USD. So roughly speaking, one Pound is equal to 1.09 Euro.
given,
a ) £1 = €1.16
= £60 x 1.16 = 69.60
b) 0.87 pound = 1 euro
€98.60 ,
therefore , 98.60/0.87 = 113.33
Euro is the term used to specify the currency of European Union countries.Pound or British pound is the currency of Great Britain. There is one more term which refers to this currency. It is Pound Sterling. This is the financial term used to represent the currency Great Britain.The name “the euro” was chosen in 1995 by a European Council meeting in Madrid. The symbol € is based on the Greek letter epsilon (Є), with the first letter in the word “Europe” and with 2 parallel lines signifying stability. The ISO code for the euro is EUR.Convert Euro to British Pound
EUR GBP
1,000 EUR 876.24 GBP
5,000 EUR 4,381.2 GBP
10,000 EUR 8,762.4 GBP
50,000 EUR 43,812 GBP
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The lines represented by y=-5x+10and5y=x+15 are
Answers
The lines represented by y = -5x + 10 and 5y = x + 15 are; Perpendicular
How to interpret slopes of lines?
We are given the equation of two lines as;
Line 1; y = -5x + 10
Line 2; 5y = x + 15
Now, the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, for the equation in line 1, we know that;
slope = -5 while the y-intercept is 10
For line 2, the equation can be rewritten as;
y = ¹/₅x + 3
Slope = 1/5
y-intercept = 3
Now, we know that when two lines are perpendicular, it means that their slopes are negative reciprocals of each other.
Slopes of lines 1 and 2 are negative reciprocals of each other and thus they are perpendicular.
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5x - 2x + 5 = 2x + 26
solving for x when d is on both sides
Answers
answer :
so this is the answer of the value of x
The solution of the linear equation is x = 21.
How to solve the linear equation for x?
Here we have the linear equation:
5x - 2x + 5 = 2x + 26
To solve this for x, move all the terms with x to the left side and all the others to the right side:
5x - 2x - 2x = 26 - 5
5x - 4x = 21
x = 21
The solution of the linear equation is x = 21.
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What value of x makes the equation -5x - (-6 - 4x) = -2(3x - 4) true?
Answers
Answer: [tex]x=\Large\boxed{\frac{2}{5} }[/tex]
Step-by-step explanation:
Given equation
[tex]-5x-(-6-4x)=-2(3x-4)[/tex]
Expand the parenthesis
[tex]-5x+6+4x=-2\times3x-2\times(-4)[/tex]
[tex]-5x+6+4x=-6x+8[/tex]
Combine like terms
[tex]-x+6=-6x+8[/tex]
Add 6x on both sides
[tex]-x+6+6x=-6x+8+6x[/tex]
[tex]5x+6=8[/tex]
Subtract 6 on both sides
[tex]5x+6-6=8-6[/tex]
[tex]5x=2[/tex]
Divide 5 on both sides
[tex]5x/5=2/5[/tex]
[tex]x=\Large\boxed{\frac{2}{5} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Write each logarithmic expression as a single logarithm.
log 3+4 log x
Answers
The single logarithm of log 3 + 4 log x is = log (3x^4).
What is a logarithmic function?
A logarithmic function in mathematics is defined as the function which is the inverse of the exponential function. It is denoted by using the word log. For example log 10 = 1
Write the given logarithmic expression in a single logarithm. log 3 + 4 log x
Given logarithmic expression is log 3 + 4 log x
Applying given properties of logarithmic function;
log a + log b = log (ab)
2 log a = log a²
Now, log 3 + 4 log x = log 3 + log x^4
= log (3x^4)
Hence, the single logarithm of log 3 + 4 log x is = log (3x^4).
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If the total price for two cars at a dealership is $ 108 , 000 $108,000, where one car’s price is $ 9000 $9000 less than twice the other, what is the price of the cheaper vehicle?
Answers
The price of the cheaper vehicle is $39,000
Calculating CostFrom the question, we are to determine the price of the cheaper vehicle
Let the cost of one of the cars b $x
and the cost of the other car be $y
From the given information,
The total price for two cars at a dealership is $108,000
That is
x + y = 108000 ----------- (1)
and
one car’s price is $9000 less than twice the other
x = 2y - 9000 ----------- (2)
Put equation (2) into equation (1)
x + y = 108000
2y - 9000 + y = 108000
2y + y - 9000 = 108000
2y + y = 108000 + 9000
3y = 117000
y = 117000/3
y = 39000
∴ The price of one of the vehicles is $39,000
Substitute this value into equation (2)
x = 2y - 9000
x = 2(39000) - 9000
x = 78000 - 9000
x = 69000
The price of the other vehicle is $69,000
Hence, the price of the cheaper vehicle is $39,000
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Write an equation in slope-intercept form of the line
Answers
The linear equation in the slope-intercept form is:
y = (-1/3)*x + 4
How to write the linear equation?Remember that if a line passes through two points (a, b) and (c, d), then the slope is given by:
slope = (d - b)/(c - a)
By looking at the graph, we can see that the points (0,4) and (3, 3), then the slope will be:
s = (3 - 4)/(3 - 0) = -1/3
And we can see that the y-intercept is y = 4 (because the line passes through the point (0,4))
Then the linear equation in the slope-intercept form is:
y = (-1/3)*x + 4
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Please help me please help me please help me please
Answers
Explanation: 180° is half which is clearly how it’s turned.
Name a line that passes through point D
Answers
Answer:
BC
Step-by-step explanation:
its easy d will keep going as shown the arrow so when its pass c it will be in between makinn it BC (i cant explain well but thats the answer)
Identify the percentage of growth or decay for the exponential function: y = 18(0.75) x
Answers
The percentage of decay for the exponential function: y = 18(0.75) x is 25%.
How to illustrate the information?This equation represents exponential decay. Whenever the base is less than 1, the function represents decay. When the base is greater than 1, the function represents growth. In this case, the base is 0.75 which is less than 1, representing decay.
The formula for exponential decay is y=a(1-r)x.
r is the decay rate, expressed as a decimal.
In this case, r = 1 - 0.75 = 0.25 which represents 25%.
Therefore, the percentage of decay for the exponential function: y = 18(0.75) x is 25%.
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The average temperature in the mountains is 61° in April. The average temperature in that same spot is −2° in December. Determine how much warmer this location is in April than in December, and determine which temperature is the farthest away from 0°.
61 + |−2| = 63°, −2° is the farthest from 0°
61 − |−2| = 59°, −2° is the farthest from 0°
61 + |−2| = 63°, 61° is the farthest from 0°
61 − |−2| = 59°, 61° is the farthest from 0°
Answers
The location is 63° warmer in April than in December. The correct option is the third option 61 + |−2| = 63°, 61° is the farthest from 0°
From the question, we are to determine how much warmer the location is in April than in December
From the given information,
Average temperature in April = 61°
and
Average temperature in December = -2°
To determine how much warmer the location is, we will add the absolute values of the temperatures
That is,
61 + |-2|
= 61 + 2
= 63°
61° the temperature that is farthest from 0
Hence, the location is 63° warmer in April than in December. The correct option is the third option 61 + |−2| = 63°, 61° is the farthest from 0°
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Write a description of a line. How are lines labeled?
Answers
1. A line can be described as a one-dimensional figure without thickness or width.
2. Lines are labeled with two points (A ↔ B). Lines can be marked using lowercase letters (for example, line k).
What is a line?
A line is a one-dimensional figure with a length only. A line does not have width or thickness.
A line can have line segments with two endpoints. A line cannot be measured, but its segments are measurable.
There are different types of lines, including:
Curved lineStraight lineVertical lineHorizontal lineParallel linesIntersecting lineTransversal linePerpendicular lineCurly and spiral lines.Thus, lines are one-dimensional with lengths and no widths or thicknesses.
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Determine if each statement is true or false. Justify your answer.
(log x)² = log x²
Answers
The given logarithmic representation i.e., (log x)² = log x² is true only for x = 1 and 100 and for rest it is not valid.
Given that, (log x)² = log x², let's proceed to simplify this in order to reach at the conclusion part.
(log x)² = log x²
(log x)² = 2log x
(log x)² - 2log x = 0
log x(log x - 2) = 0
⇒log x = 0 or log x - 2 = 0
Now, put log x = 0
⇒ x = 1
Now, put log x - 2 = 0
log x = 2
log x = 10²
x = 100
Hence, we got two values for x one is 1 and other is 100. Now, putting one by one in (log x)² = log x² in order to reach at the conclusion.
Put x = 1 in (log x)² = log x², we get
(log 1)² = log 1²
0 = 0²
0 = 0
⇒ true for x = 1
Now, put x = 100 in (log x)² = log x² , we get
(log 100)² = log 100²
2² = 2log 100
4 = 2 x 2
4 = 4
⇒ true for x = 100
So, (log x)² = log x² is true only when x = 1 and 100 for rest it is false.
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Macario works part time at a clothing store in the mall. He is paid $9 per hour plus 12% commission on the items he sells in the store. Write an equation in slope-intercept form to represent Macario's hourly wage y.
Answers
The equation in the form of slope-intercept for Macario's hourly wage is y=9x+0.12s
What is a slope-intercept function?
A slope-intercept equation comprises the total amount paid as wages to Macario which includes the hourly rate of $9 multiplied by the number of hours spent working plus the 12% of total sales achieved by Macario, in essence, if we assume that the number of hours spent working is x and that total sale is s, the slope-intercept form that represents Macario's hourly wage y is shown thus:
y=9x+0.12s
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i need help asap please help me
Answers
Answer: yo wassup picture isn't straight cant see
Step-by-step explanation:
math (find the area in square feet)
Answers
Answer: 50
Step-by-step explanation:
8x4 =32
6x3=18
32+18=50
For each annual rate of change, find the corresponding growth or decay factor. -55 %
Answers
The decay factor for the annual rate of change of - 55 % is 0.45.
A quantity must vary by a specific percentage each time period in order for growth or decay to be exponential.
With the function displayed to the right, you may represent exponential growth or decay.
A(x) = a( 1 + r)ˣ
Where A is the amount after x time periods, a is the initial amount, x is the number of time periods, and r is the rate of change.
Now, we have the annual rate of change as:
r = - 55 % = - 55 / 100 = - 0.55
From the function A(x) = a( 1 + r)ˣ , the corresponding factor is 1 + r.
So, let B = 1 + r
B = 1 + r
B = 1 + (- 0.55)
B = 1 - 0.55
B = 0.45
Now, the value of B is less than 1 therefore, the corresponding decay factor is 0.45.
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find the vertex y= -2x^2
Answers
The vertex of the function where the equation of the function is given as y = -2x^2 is (0, 0)
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the vertex of the function?The equation of the function is given as
y = -2x^2
A quadratic function is represented as
y = a(x - h)^2 + k
Where the vertex is
vertex = (h, k)
This means that the equation y = -2x^2 can be rewritten as
y = -2(x - 0)^2 + 0
When the equations are compared, we have
vertex = (h, k) = (0, 0)
Hence, the vertex of the function where the equation of the function is given as y = -2x^2 is (0, 0)
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Solve. Check for extraneous solutions. √x²+3 =x+1
Answers
x = 1 is not an extraneous solution.
✓(x² + 3) = x + 1
Taking square on both the sides of the equation, we get
(✓(x² + 3))² = (x + 1)²
x² + 3 = (x + 1)²
Using the identity (a+b)²= a² + b² + 2ab on the right hand side of the equation, we get
x² + 3 = x² + (1)² + 2(x)(1)
x² + 3 = x² + 1 + 2x
2x = 2
x = 1
Confirming the value is extraneous solution or not
Putting the root x = 1 in the original equation ✓(x² + 3) = x + 1, we get
✓(1² + 3) = 1 + 1
✓4 = 2
2 = 2
⇒ LHS = RHS
∴ x = 1 is not an extraneous solution.
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