Answers
For this exercise you need to use the following formula:
[tex]\theta=\frac{S}{r}[/tex]Where θ is the Central angle in radians, "S" is the arc length and "r" is the radius of the circle.
In this case, you can identify that:
[tex]\begin{gathered} S=8\pi cm \\ r=8\operatorname{cm} \end{gathered}[/tex]Knowing these values, you can substitute them into the formula and then evaluate, in order to find the measure of the Central angle in radians. This is:
[tex]\begin{gathered} \theta=\frac{8\pi cm}{8\operatorname{cm}} \\ \\ \theta\approx\pi radians \end{gathered}[/tex]The answer is:
[tex]\pi radians[/tex]Related Questions
You are scuba diving at 120 feet below sea level. You begin to ascend at a rate of 4 feet per second.a. Where will you be 10 seconds after you begin your ascension? b. How long will it take to reach the surface?
Answers
The ascension can be modeled using the function:
[tex]d(t)=d_0-r\cdot t[/tex]Where d is the number of feet below the sea level at time t (in seconds), d₀ is the initial "depth", and r is the ascension rate.
From the problem, we identify:
[tex]\begin{gathered} r=4\text{ feet per second} \\ d_0=120\text{ feet} \end{gathered}[/tex]Then:
[tex]d(t)=120-4t[/tex]a)
After 10 seconds, we have t = 10:
[tex]\begin{gathered} d(10)=120-4\cdot10=120-40 \\ \\ \Rightarrow d(10)=80\text{ feet} \end{gathered}[/tex]After 10 seconds, we will be 80 feet below sea level.
b)
To find how long will it take to reach the surface, we need to solve the equation d(t) = 0.
[tex]\begin{gathered} d(t)=0 \\ 120-4t=0 \\ 4t=120 \\ \\ \therefore t=30\text{ seconds} \end{gathered}[/tex]We will reach the surface after 30 seconds.
Evaluate the expression when x= -1/4 and y= 31. 2xyI don't understand his question.
Answers
The expression is 2xy
we will substitute x and y by the given values
x = -1/4 and y = 3
[tex]2xy=2\times(\frac{-1}{4})\times(3)[/tex]We put the values of y in the expression
Now we will calculate the value
[tex]2xy=\frac{2\times-1\times3}{4}[/tex]We will multiply the numbers in the numerator
[tex]2xy=\frac{-6}{4}[/tex]We will simplify the fraction by divide up and down by 2
[tex]\begin{gathered} 2xy=\frac{-\frac{6}{2}}{\frac{4}{2}}=\frac{-3}{2} \\ 2xy=-\frac{3}{2} \end{gathered}[/tex]IF G and R denote the grade and the radian measure of an angle, then prove that G/200 = R/pie
Answers
Solution:
Given;
IF G and R denote the grade and the radian measure of an angle, i.e.
Where
[tex][/tex]The ratio of the lengths of corresponding sides of two similar triangles is 5:8. The smaller triangle has an area of 87.5cm^2. What is the area of the larger triangle
Answers
Question:
Solution:
Remember the following theorem: the ratio of the areas of two
similar triangles is equal to the ratio of the squares of their corresponding sides. Then, here A1 and A2 are areas of two similar triangles, and S1 and S2 are their corresponding sides respectively :
S1 : S2 = 5 : 8
then
[tex]\frac{S1}{S2}=\frac{5}{8}[/tex]now, A1 = 87.5. Thus, according to the theorem, we get the following equation:
[tex](\frac{5}{8})^2=\frac{87.5}{A2}[/tex]this is equivalent to:
[tex]\frac{25}{64}=\text{ }\frac{87.5}{A2}[/tex]by cross-multiplication, this is equivalent to:
[tex](A2)(25)\text{ = (64)(87.5)}[/tex]solving for A2, we get:
[tex]A2\text{ =}\frac{(64)(87.5)}{25}=224[/tex]so that, we can conclude that the correct answer is:
The area of the larger triangle is
[tex]224cm^2[/tex]
Growing up, Mrs. Reeder's favorite book was THE ADVENTURES of TOM SAWYER.Now that she is a teacher, she buys 25 copies to read with her class. If each book coast $7.19, how much does Mrs. Reeder spend?
Answers
According to the given data we have the following:
Total copies she buys= 25 copies
book cost=$7.19
Therefore, in order to calculate the amount of money that Mrs. Reeder spend we would have to make the following calculation:
Amount of money that Mrs. Reeder spend= quantity of copies * book cost
Amount of money that Mrs. Reeder spend=25 copies*$7.19
Amount of money that Mrs. Reeder spend=$180
The amount of money that Mrs. Reeder spend was $180
With aging body fat increases in muscle mass declines the graph to the right shows the percent body fat in a group of adult women and men as they age from 25 to 75 years age is represented along the X-axis and percent body fat is represented along the Y-axis use interval notation to give the domain and range for the graph of the function for women
Answers
Step 1
The domain and range of a function is the set of all possible inputs and outputs of a function respectively. The domain is found along the x-axis, the range on the other hand is found along the y-axis.
Find the domain of the graph of the function of women using interval notation.
[tex]\text{Domain:\lbrack}25,75\rbrack[/tex]Step 2
Find the range of the graph of the function of women using interval notation.
[tex]\text{Range:}\lbrack32,40\rbrack[/tex]Therefore, the domain and range in interval notation for the women respectively are;
[tex]\begin{gathered} \text{Domain:\lbrack}25,75\rbrack \\ \text{Range:}\lbrack32,40\rbrack \end{gathered}[/tex]Someone please help me with this
Answers
Polynomial equations are those created using exponents, coefficients, and variables. It may have several exponents, with the higher one being referred to as the equation's degree.
How are polynomial equations solved?Polynomial equation illustration
Write 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.
6h²(5 + 9h)(5 - 9h)
6h²(9h + 5)(5 - 9h)
6h²(9h + 5)(-9h + 5)
Distribute6h²(9h + 5)(-9h + 5)
54(-9h +5)h³ + 30(-9h + 5)h²
(-486h)4 + 270h³+30(-9h+5)h²
(-486h)4 + 270h³-270h³+150h²
(-486h)4 + 150h²
Solution(-486h)4 + 150h²
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Labron James made 255/310 baskets. What percent of the baskets did he make?
Answers
82.26%
Explanations:The ratio of baskets made by Lebron James = 255/310
To find the percentage equivalent of the ratio, multiply it by 100%
Percentage of the baskets made by Lebron James = 255/310 x 100%
Percentage of the baskets made by Lebron James = 82.26%
1. It is h before closing time at the grocery store. It takes about h for Jane to find 1 item on her shopping list. How many items can she find before the store closes? (a) Create a model or write an equation for the situation. (b) Find the solution. Explain what you did. (c) State the solution as a full sentence.
Answers
GIVEN
The time left before the store closes is 3/4 h while the time taken to find one item is 1/8 h.
QUESTION A
Let the number of items that can be gotten before the store closes be N.
The number of items can be calculated using the formula:
[tex]N=\text{ number of hours left}\div\text{ number of hours used to find one item}[/tex]Therefore, the equation to get the number of items will be:
[tex]N=\frac{3}{4}\div\frac{1}{8}[/tex]QUESTION B
The solution can be obtained by division.
Apply the fraction rule:
[tex]\frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]Hence, the solution will be:
[tex]\begin{gathered} \frac{3}{4}\div\frac{1}{8}=\frac{3}{4}\times\frac{8}{1} \\ \Rightarrow\frac{3\times\:2}{1\times\:1}=6 \end{gathered}[/tex]The answer is 6.
QUESTION C
Jane can find 6 items before the store closes.
Consider the following expression:-27 x (-18)By the laws of signs, this is equivalent to27 x 18 this is equivalent to:27 x 18= 486we can conclude thatthe correct answer is:486I feel like that’s wrong, it’s not algebra can anyone help
Answers
The answer is actually CORRECT.
The correct procedure is when two negatives multiply each other, the answer is always a positive.
Therefore;
[tex]\begin{gathered} -27\times(-18)=27\times18 \\ 27\times18=486 \end{gathered}[/tex]We can conclude that the correct answer is 486
If the area of the rectangle to be drawn is 12 square units, where should points C and D be located, if they lie vertically below A and B, to make this rectangle?
Answers
Answer:
C(2,-2), D(-1,-2)
Explanation:
The area of a rectangle is calculated using the formula:
[tex]A=L\times W[/tex]• From the graph, AB = 3 units.
,• Given that the area = 12 square units
[tex]\begin{gathered} 12=3\times L \\ L=\frac{12}{3}=4 \end{gathered}[/tex]This means that the distance from B to C and A to D must be 4 units each.
Count 4 units vertically downwards from A and B.
The coordinates of C and D are:
• C(2,-2)
,• D(-1,-2)
The first option is correct.
The measures of the angles of a triangle are shown in the figure below. Solve for x. (2x+6)° 42°
Answers
A triangle is a shape that has a total angle of 180°.
How to solve the triangle?It's important to note that a triangle is a shape that has three sides and the total sum is equal to 180°.
In this case, we have 2x + 6 and 42°. The other angle isn't given and this can't be solved further
The sides will have been illustrated as:
= a + b + c = 180
The expression given will then be allocated for each side to solve it further.
Note that an overview was given as the information is incomplete.
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What value of Y makes this equation true?6y/-2 = 8 (-4/2)
Answers
Step 1
Given;
[tex]\frac{6y}{-2}=8(-\frac{4}{2})[/tex]Required; To find the value of y that makes the equation true
Step 2
Find the value of y
[tex]\begin{gathered} \text{Simplify} \\ -3y=4(-4) \end{gathered}[/tex][tex]\begin{gathered} \text{expand} \\ -3y=-16 \end{gathered}[/tex][tex]\begin{gathered} \text{Divide both sides by -3} \\ \frac{-3y}{-3}=\frac{-16}{-3} \end{gathered}[/tex][tex]\begin{gathered} \text{Simplify} \\ y=\frac{16}{3} \end{gathered}[/tex]Hence, the value of y that makes the equation true is 16/3
A certain species of deer is to be introduced into a forest, and wildlife experts estimate the population will grow to P(t) = (944)3 t/3, where t represents the number ofyears from the time of introduction.What is the tripling-time for this population of deer?
Answers
Ok, so
Here we have the function:
[tex]P(t)=944(3)^{\frac{t}{3}}[/tex]Now we want to find the tripling-time for this population of deer.
If we make t=0, we will find the initial population of deer. This is:
[tex]P(0)=944(3)^{\frac{0}{3}}=944[/tex]Now, we want to find the time "t" such that this population is the triple.
This is:
[tex]\begin{gathered} 944(3)=944(3)^{\frac{t}{3}} \\ 2832=944(3)^{\frac{t}{3}} \\ \frac{2832}{944}=3^{\frac{t}{3}} \\ 3=3^{\frac{t}{3}} \end{gathered}[/tex]We got this exponential equation:
[tex]3=3^{\frac{t}{3}}[/tex]As the base is the same, we could equal the exponents:
[tex]\begin{gathered} 1=\frac{t}{3} \\ t=3 \end{gathered}[/tex]Therefore, tripling-time for this population of deer are 3 years.
(c) Given that q= 8d^2, find the other two real roots.
Answers
Polynomials
Given the equation:
[tex]x^5-3x^4+mx^3+nx^2+px+q=0[/tex]Where all the coefficients are real numbers, and it has 3 real roots of the form:
[tex]x_1=\log _2a,x_2=\log _2b,x_3=\log _2c[/tex]It has two imaginary roots of the form: di and -di. Recall both roots must be conjugated.
a) Knowing the sum of the roots must be equal to the inverse negative of the coefficient of the fourth-degree term:
[tex]\begin{gathered} \log _2a+\log _2b+\log _2c+di-di=3 \\ \text{Simplifying:} \\ \log _2a+\log _2b+\log _2c=3 \\ \text{Apply log property:} \\ \log _2(abc)=3 \\ abc=2^3 \\ abc=8 \end{gathered}[/tex]b) It's additionally given the values of a, b, and c are consecutive terms of a geometric sequence. Assume that sequence has first term a1 and common ratio r, thus:
[tex]a=a_1,b=a_1\cdot r,c=a_1\cdot r^2[/tex]Using the relationship found in a):
[tex]\begin{gathered} a_1\cdot a_1\cdot r\cdot a_1\cdot r^2=8 \\ \text{Simplifying:} \\ (a_1\cdot r)^3=8 \\ a_1\cdot r=2 \end{gathered}[/tex]As said above, the real roots are:
[tex]x_1=\log _2a,x_2=\log _2b,x_3=\log _2c[/tex]Since b = a1*r, then b = 2, thus:
[tex]x_2=\log _22=1[/tex]One of the real roots has been found to be 1. We still don't know the others.
c) We know the product of the roots of a polynomial equals the inverse negative of the independent term, thus:
[tex]\log _2a_1\cdot2\cdot\log _2(a_1\cdot r^2)\cdot(di)\cdot(-di)=-q[/tex]Since q = 8 d^2:
[tex]\begin{gathered} \log _2a_1\cdot2\cdot\log _2(a_1\cdot r^2)\cdot(di)\cdot(-di)=-8d^2 \\ \text{Operate:} \\ 2\log _2a_1\cdot\log _2(a_1\cdot r^2)\cdot(-d^2i^2)=-8d^2 \\ \log _2a_1\cdot\log _2(a_1\cdot r^2)=-8 \end{gathered}[/tex]From the relationships obtained in a) and b):
[tex]a_1=\frac{2}{r}[/tex]Substituting:
[tex]\begin{gathered} \log _2(\frac{2}{r})\cdot\log _2(2r)=-8 \\ By\text{ property of logs:} \\ (\log _22-\log _2r)\cdot(\log _22+\log _2r)=-8 \end{gathered}[/tex]Simplifying:
[tex]\begin{gathered} (1-\log _2r)\cdot(1+\log _2r)=-8 \\ (1-\log ^2_2r)=-8 \\ \text{Solving:} \\ \log ^2_2r=9 \end{gathered}[/tex]We'll take the positive root only:
[tex]\begin{gathered} \log _2r=3 \\ r=8 \end{gathered}[/tex]Thus:
[tex]a_1=\frac{2}{8}=\frac{1}{4}[/tex]The other roots are:
[tex]\begin{gathered} x_1=\log _2\frac{1}{4}=-2 \\ x_3=\log _216=4 \end{gathered}[/tex]Real roots: -2, 1, 4
work out sues total pay
Answers
Sue's total pay for the year given the salary, bonus and share of profit is £38,110.
What is the total pay?Sue's total pay for the year is a function of the salary, the share of the profit that she earns and the bonus.
Salary for the year = monthly salary x number of months in a year
£1410 x 12 = £16,920
The next step is to determine the profit last year
Profit = total revenue - total cost
£549,000 - £473,500 = £75,500
Now determine the share of profit that Sue would earn.
Share of profit = 26% x £75,500
0.26 x £75,500 = £19,630
Now determine the total bonus she would earn : 4 x £390 = £1560
Total salary = £1560 + £19,630 + £16,920 = £38,110
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how long does it take the snail to crawl 86 inches enter answer in decimal number
Answers
To get the equation of the line graph, first, we have to find its slope. The slope of a line that passes through points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]From the picture, the line passes through the points (0,0) and (10, 1), then its slope is:
[tex]m=\frac{1-0}{10-0}=\frac{1}{10}_{}[/tex]The slope-intercept form of a line is:
y = mx + b
where m is the slope and b is the y-intercept.
From the graph, the line intersects the y-axis at y = 0, this means that b = into
the equation. Therefore, the equation is:
y = 1/10x
where x is distance (in inches) and y is time (in minutes).
To find how long it takes the snail to crawl 86 inches, we have to replace x = 86 into te equation as follows:
[tex]\begin{gathered} y=\frac{1}{10}\cdot86 \\ y=8.6 \end{gathered}[/tex]The snail takes 8.6 minutes to crawl 86 inches
&A(n)is formed when two rays have a common endpoint.Oline segmentangle
Answers
When two rays are with a common endpoint, an angle is formed and the common endpoint is called the vertex of the angle
Question 2 of 10The one-to-one functions g and h are defined as follows.g={(-8, 6), (-6, 7), (-1, 1), (0, -8)}h(x)=3x-8Find the following.g-¹(-8)=h-¹(x) =(hoh− ¹)(-5) =
Answers
Answer: We have to find three unknown asked quantities, before we could do that we must find the g(x) from the coordinate points:
[tex]\begin{gathered} g=\left\{\left(-8,6\right),(-6,7),(-1,1),(0,-8)\right\}\Rightarrow(x,y) \\ \\ \text{ Is a tabular function} \\ \end{gathered}[/tex]The answers are as follows:
[tex]\begin{gathered} g^{-1}(-8)=0\text{ }\Rightarrow\text{ Because: }(0,-8) \\ \\ \\ h^{-1}(x)=\frac{x}{3}+\frac{8}{3} \\ \\ \\ \text{ Because:} \\ \\ h(x)=3x-8\Rightarrow\text{ switch }x\text{ and x} \\ \\ x=3h-8 \\ \\ \\ \\ \text{ Solve for }h \\ \\ \\ h=h^{-1}(x)=\frac{x}{3}+\frac{8}{3} \end{gathered}[/tex]The last answer is:
[tex]\begin{gathered} (h\text{ }\circ\text{ }h^{-1})(-5) \\ \\ \text{ Can also be written as:} \\ \\ h[h^{-1}(x)]\text{ evaluated at -5} \\ \\ h(x)=3x-8 \\ \\ h^{-1}(x)=\frac{x}{3}+\frac{8}{3} \\ \\ \\ \therefore\Rightarrow \\ \\ \\ h[h^{-1}(x)]=3[\frac{x}{3}+\frac{8}{3}]-8=x+8-8=x \\ \\ \\ \\ h[h^{-1}(x)]=x \\ \\ \\ \\ h[h^{-1}(-5)]=-5 \end{gathered}[/tex]The function f(x) = 6x represents the number of lightbulbs f(x) that are needed for x chandeliers. How many lightbulbs are needed for 7 chandeliers? Show your work
Answers
There are a total of 42 lightbulbs needed for 7 chandeliers
How to determine the number of lightbulbs needed?From the question, the equation of the function is given as
f(x) = 6x
Where
x represents the number of chandeliersf(x) represents the number of lightbulbs
For 7 chandeliers, we have
x = 7
Substitute x = 7 in f(x) = 6x
So, we have
f(7) = 6 x 7
Evaluate the product
f(7) = 42
Hence, the number of lightbulbs needed for 7 chandeliers is 42
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The number of lightbulbs needed for 7 chandeliers would be; 42
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
From the given problem, the equation of the function is;
f(x) = 6x
Where
x be the number of chandeliers and f(x) represents the number of lightbulbs.
For 7 chandeliers, x = 7
Now Substitute x = 7 in f(x) = 6x
Therefore, f(7) = 6 x 7
Evaluate the product;
f(7) = 42
Hence, the number of lightbulbs needed for 7 chandeliers would be; 42
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Kuta Sotware - Infinite Algebra 2 Solving Inequalities Solve each inequality and graphite 10 > Kuin Software - Infinite Algebra 2 Graphing Linear Inequalities Sketch the graph of each linear inequality. Name Samante 1) yz-2x-2 Y-2-2 2). ys - !
Answers
Could you please send a picture of the inequality you are asked to solve?
I'll be closing the session now if you cannot do it. Please ask your question again, and send the image in the question itself to avoid this problem of your uploaded images and messages not getting to me.
Thank you, and please re-submit your question request.
H = -16t^2 + 36t + 56 Where H is the height of the ball after t seconds have passed.
Answers
we have the equation
H = -16t^2 + 36t + 56
This equation represents a vertical parabola open downward, which means, the vertex is a maximum
The time t when the ball reaches its maximum value corresponds to the x-coordinate of the vertex
so
Convert the given equation into vertex form
H=a(t-h)^2+k
where
(h,k) is the vertex
step 1
Complete the square
H = -16t^2 + 36t + 56
Factor -16
H=-16(t^2-36/16t)+56
H=-16(t^2-36/16t+81/64)+56+81/4
Rewrite as perfect squares
H=-16(t-9/8)^2+76.25
the vertex is (9/8,76.25)
therefore
the time is 9/8 sec or 1.125 seconds when the ball reaches its maximum
In a competition of 837 people, Jenny scored at the 77th percentile.
In what place did she finish?
Answers
Answer:
Jenny scored 644th place.
Step-by-step explanation:
To find out what place she finished, you need to write it out first like this:
77% of 837.
Now, to make the equation possible to solve, we can take the 77 and make it a decimal: 0.77.
The term "of" means multiplication.
So, in turn, we have the equation:
0.77 x 837 = 644.49
And, if you round it, your answer would be:
Jenny scored 644th place.
Answer:
See below
Step-by-step explanation:
77th percentile means she scored better than 77 per cent of the test takers...
So Jenny's place was .23 * 837 = ~ 193 rd Out of 837 people
What is the value of 0 put a comma and space between answer sin61°=cos=0; cos17°=sin0;
Answers
For
[tex]\begin{gathered} \sin 61=\cos \theta \\ \theta=\cos ^{-1}(\sin 61) \\ \end{gathered}[/tex]For
[tex]\begin{gathered} \cos 17=\sin \theta \\ \theta=\sin ^{-1}(\cos 17) \\ \end{gathered}[/tex]In an electrical circuit, the voltage across a resistor is directly proportional to the current running through the resistor. If a current of 14 amps produces 280 volts across a resistor, how many volts would a current of 5.5 amps produce across an identical resistor?
Answers
A current of 5.5 amps produce across an identical resistor will produce 110Volts across an identical resistor
What is a current?From above,
Current 1 (I₁) = 14 amps
P.d (V₁) = 280 V
By Ohm's law which states that that for a linear circuit the current flowing through it is proportional to the potential difference across it so the greater the potential difference across any two points the bigger will be the current flowing through it.
V₁ = I₁R
= 280 = 14R
= 20Ω = R
Current 2 (I₂) = 3.5 A
Resistance (R) = 20 Ω
Assuming the resistance stays the same,
Using Ohm's law,
V₂ = I₂R
= 5.5*20
= 110 Volts
110Volts would be produced across an identical resistor
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A triangular pryamid is shown in the diagram. What is the volume of the triangular pyramid?
Answers
Given the following question:
[tex]\begin{gathered} V=\frac{1}{3}BH \\ B=\text{ Base Area} \\ A=\frac{1}{2}BH \\ B=7.8 \\ H=4 \\ A=\frac{1}{2}7.8(4) \\ 7.8\times4=31.2 \\ 31.2\div2=15.6 \\ A=15.6 \\ V=\frac{1}{3}BH \\ B=15.6 \\ H=4 \\ \frac{1}{3}15.6(4) \\ 15.6(4)=62.4 \\ 62.4\div3=20.8 \\ V=20.8 \end{gathered}[/tex]Volume is equal to 20.8 cubic centimeters.
A sector of a circle has a central angle of 60∘ . Find the area of the sector if the radius of the circle is 9 cm.
Answers
Step-by-step explanation:
area of a sector is theta ÷360 ×πr²
-1/2 (2/5y - 2) (1/10y-4)
Answers
we multiply the first parenthesis by its coefficient
[tex]\begin{gathered} ((-\frac{1}{2}\times\frac{2}{5}y)+(-\frac{1}{2}\times-2))(\frac{1}{10}y-4) \\ \\ (-\frac{2}{10}y+\frac{2}{2})(\frac{1}{10}y-4) \\ \\ (-\frac{1}{5}y+1)(\frac{1}{10}y-4) \end{gathered}[/tex]now multiply each value and add the solutions
[tex]\begin{gathered} (-\frac{1}{5}y\times\frac{1}{10}y)+(-\frac{1}{5}y\times-4)+(1\times\frac{1}{10}y)+(1\times-4) \\ \\ (-\frac{1}{50}y^2)+(\frac{4}{5}y)+(\frac{1}{10}y)+(-4) \\ \\ -\frac{1}{50}y^2+(\frac{4}{5}y+\frac{1}{10}y)-4 \\ \\ -\frac{1}{50}y^2+\frac{9}{10}y-4 \end{gathered}[/tex]What is the independent and dependent variable for k(d) =2d^2 - d +32
Answers
Given:
[tex]k(d)=2d^2-d+32[/tex]Required:
To find the independent and dependent variable.
Explanation:
In the given equation,
The dependent variable = k(d)
The independent variable = d
Final Answer:
The dependent variable = k(d)
The independent variable = d
Given f(x) and g(x) = f(k⋅x), use the graph to determine the value of k.A.) - 2B.) -1/2C.) 1/2D.) 2
Answers
In order to solve this problem we have to remember that the equation of any line takes the form
[tex]y(x)=mx+b[/tex]Therefore,
[tex]y(kx)=\text{mkx}+b[/tex]In other words, multiplying k by x is just multiplying the slope m by a factor of k.
The slope of g(x) is
[tex]m=2[/tex]and the slope of f(x) is
[tex]m=1[/tex]We see than the slope of g(x) is 2 times the slope of f(x); therefore, k = 2 which is choice D.
