Which is the equation of the graph?
y = -2/3|x|
y = 3/2|x|
y = -3/2|x|
y = 2/3|x|
Answers
Answer:
y= -2/3|x| is the right answer
Step-by-step explanation:
If you substitute x and y values from the graph, this equation turns true.
For example take the value (6; -4) and (-6; -4) from the graph and substitute in the funxtion:
a) -4 = -2/3 |6|
-4 = -4
b) -4 = -2/3 |-6|
-4 = -2/3* 6
-4 = -4
Related Questions
Please answer the question!! Thanks!!
Answers
The value of (g/f)(x) is 7x/ 6(x+1) , and the domain is all Real numbers except -1 which is (-∞,∞)-{-1} .
In the question ,
it is given that
the function f(x) = 6/x
and the function g(x) = 7/(x+1)
the function (g/f)(x) means g(x) / f(x)
so , (g/f)(x) = [tex]\frac{\frac{7}{x+1} }{\frac{6}{x} }[/tex]
= 7/(x+1) * x/6
= 7*x / 6(x+1)
= 7x/ 6(x+1)
For Domain 6(x+1) ≠ 0
6(x+1) ≠ 0
which means 6 ≠ 0 and x+1 ≠ 0
x ≠ -1
so domain is all Real numbers except -1 .
that is (-∞,∞)-{-1}
Therefore , The value of (g/f)(x) is 7x/ 6(x+1) , and the domain is all Real numbers except -1 in interval notation is (-∞,∞)-{-1} .
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(A) which data set appears to show no relationship between it's to variable choose one( Data set in figure 1, data set figure 2, data set figure 3, data set figure 4)(B) answer for B choose one( data set figure 1, figure2, figure 3, figure 4(C) choose one ( data set figure 1, figure 2, figure 3, figure 4)(D) choose (Figure 1, figure 2, figure 3, figure 4)
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EXPLANATION :
a. Data set that shows NO relationship between two variables.
The data will be scattered without having a linear or definite shape.
From the options, it is Figure 2
b. Data set that shows a negative linear relationship between two variables.
Negative linear relationship implies a downward direction in a shape of a line.
From the options, it is Figure 1
c. Data set that shows a positive linear relationship between two variables.
Positive linear relationship implies an upward direction in a shape of a line.
From the options, it is Figure 4
d. Data set that shows a nonlinear relationship between two variables.
There is a definite shape but it is not in a shape of a line.
From the options, it is Figure 3
Below, the two-way table is given for aclass of students.FreshmenSophomoreJuniorsSeniorsTotal62463Male 42Female 3TotalIf a student is selected at random, find theprobability the student is a female given that it'sa junior. Round to the nearest whole percent.[?]%
Answers
Given the table, we want to calculate the probability of choosing a female student, given that it is a junior. Since we are conditioned that the student is a junior, we can forget all the table data excep for the column that says "junior"
For this column, we have that 2 students are male and 6 are female. That is, we have a total of 8 students.
Now, we want to calculate the probability. To do so, we simply divide the total number of possibilites such that the event "choosing a female" is true by the total number of people.
Since we have 6 female students, we have 6 possibilites of choosing a female. So the probability would be
[tex]\frac{6}{8}=\frac{2\cdot3}{2\cdot4}=\frac{3}{4}=0.75[/tex]To express it as a percentage, we simply multiply it by 100. So we get
[tex]0.75\cdot100=75[/tex]Pamela is 5 years older than Jiri . The sum of their ages is 45 . What is Jiri's age ?
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Jiri's age is 20
Let Pamela's ae be P and Jiri's age be J
From the equation;
P = J + 5 ...............(i)
This is as Pamela is 5 years older
Adding their ages, we have 45
P + J = 45 ........................(ii)
Substitute i into ii
J + 5 + J = 45
2J + 5 = 45
2J = 45-5
2J = 40
J = 40/2
J = 20
Assume the sales price is $15 per unit, variable cost is $6 per unit, and fixed cost is $5,000. If the variable cost decreases to $3 per unit, how many fewer units will have to be sold to earn a target profit of $4,000?
Answers
Assume the sales price is $15 per unit, variable cost is $6 per unit, and fixed cost is $5,000. If the variable cost decreases to $3 per unit. The number of units is 250 units.
How to find the units sold?Using this formula to find the units sold
Number of units = [Fixed cost / ( Sales - variable cost)] - [Fixed cost / ( Sales - decrease in variable cost)
Let plug in the formula
Number of units = [$9,000 / ($15- $6)] - ($9,000 / ($15-$3)
Number of units = ($9,000 /$9) - ($9,000 / $12)
Number of units = 1,000- 750
Number of units = 250 units
Note:
(Fixed cost + target profit = $5,000+$4,000 = $9,000)
Therefore 250 units was sold.
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2y=12x-10 and y=6x+12 Do the lines intersect, coincide, or are they parallel?
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Dividing the first equation by 2 we get:
[tex]\begin{gathered} \frac{2y}{2}=\frac{12x-10}{2}, \\ y=6x-5. \end{gathered}[/tex]Therefore, both lines have the same slope, then they must be parallel or the same line. Now, since they have different y-intercept, we get that they must be different lines.
Answer: The given lines are only parallel.
Fine the value of x and y
Answers
Answer:
x = 62 and y = 28
Step-by-step explanation:
Solving for x:
[tex]47+15 = 62\\180-62 = 118\\180 - 118 = 62 \\x = 62[/tex]
Solving for y:
[tex]62 + 90 =152\\180-152=28\\y = 28[/tex]
Find the coordinates of the new vertices of the image that has been dilated by a factor of 5 in orderS(-5,2) -->SY(-4,5) -->YR(-1,1) -->RA(-4,-2) -->A
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S( -5, 2) ----------------> S'(-25, 10)
Y(-4, 5) ------------------> Y'(-20, 25)
R(-1, 1) --------------------> R' (-5, 5)
A(-4, -2) -----------------> A' (-20, -10)
Helppppppppppppppppppppppp
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Since the x-coordinate is the one that changed, this is a horizontal reflection over the y-axis.
If you put this on a graph, you'll see the two points are opposite each other, with respect to the y-axis.
Q 6 7 8 6.5CHOOSE ONE 6 7 OR 86 7 OR 8
Answers
(6) We must solve the following integral:
[tex]I=\int_1^{e^7}dx\cdot\frac{(ln\text{ }x)^3}{x}.[/tex]1) We make the following change of variables:
[tex]\begin{gathered} u=\ln(u)\Rightarrow du=\frac{dx}{x}, \\ u_2=\ln(e^7)=7, \\ u_1=\ln(1)=0. \end{gathered}[/tex]With this change of variables, the integral is:
[tex]I=\int_0^7du\cdot u^3.[/tex]2) The result of the integral in terms of u is:
[tex]I=\frac{1}{4}*u^4|_0^7=\frac{1}{4}*(7^4-0^4)=\frac{2401}{4}=600.25[/tex]Answer600.25
For the function f(x) = –x^2+x– 7find f(1)
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Given:
[tex]f\mleft(x\mright)=-x^2+x-7[/tex]To find f(1):
Put x=1, we get
[tex]\begin{gathered} f(1)=-(1)^2+1-7 \\ =-1+1-7 \\ =-7 \end{gathered}[/tex]Hence, the value of f(1) is -7.
image below for question
Answers
The equation is y = (1/4)x.
Given :
The equation must be in the form y = mx.
so we need to find the m(slope) value.
Finding m:
To find m the equation must pass through a point , from the graph take any point because the graph is in the proportional relationship so any ratio will be same,therefore (4,1) be a point.
substitute (4,1) in y = mx we get,
1 = m*4
divide by 4 on both sides
m*4/4 = 1/4
m = 1/4
substitute m value in y = mx
y = (1/4)x ≈ x - 4y = 0.
Therefore the equation is y = (1/4)x.
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Dan wants to put a fence around his rectangular garden. His garden measures 35 feet by 44 feet. The garden has a path around it that is 3 feet wide. How much fencing material does Dan need to enclose the garden and path?
Answers
Garden measures:
Width(w) : 35 feet
Length(L) : 44 feet
Then, add the measures of the path
35+3 = 38
44+3 =47
Apply the perimeter formula:
P = 2w+ 2L
Replace:
P = 2(35)+2(44) = 70+88=158
Dan needs 158 feet of fencing material to enclose the garden and path.
Juan bought 4.5 lbs of steak for $7.98 per lb sales tax is 6% what was the total amount Juan paid for steak
Answers
Juan bought 4.5 lbs for $7.98 per lb
This implies that 1 lb is sold at the rate of $7.98
1 lb -------- $7.98
4.5lb ------ $x
Introduce cross multiplication
1 * x = 7.98 x 4.5
x = $35.91
Therefore, 4.5lbs is sold at the rate of $35.91
The tax sales is 6%
Total amount = original price + 6% of original price
Total amount = 35.91 + 6/100 x 35.91
= 35.91 + 0.06 x 35.91
= 35.91 + 2.1546
= $38.0646
The total amount Juan paid is $38.0646
Given a series discount of 25/25 what is the net cost equivalent?
Answers
We need to find the net cost equivalent after two consecutive discounts of 25%.
After the first discount, the percentage of the list price the client should pay is given by:
[tex]100\%-25\%=75\%[/tex]After the second discount, the percentage of the list price the client should pay is:
[tex]\begin{gathered} 75\%\cdot(100\%-25\%) \\ \\ =75\%\cdot75\% \\ \\ =\frac{75}{100}\cdot\frac{75}{100} \\ \\ =\frac{5625}{100}\cdot\frac{1}{100} \\ \\ =56.25\% \end{gathered}[/tex]Therefore, the net cost equivalent is 56.25%.
log8x^3expand log fully using the properties of logs.
Answers
The answer is: log(8) + 3log(x)
[tex]\begin{gathered} \log (8\cdot x^3)=log(8)+log(x^3) \\ =\text{ log(8) + 3log(x) } \end{gathered}[/tex]The ratio of the side lengths of a quadrilateral is 5:2:4:7, and its perimeter is 90 meters. What is the length of the longest side?
Answers
Answer:
35 meters.
Explanation:
The ratio of the side lengths of the quadrilateral are:
[tex]\begin{gathered} 5\colon2\colon4\colon7 \\ 5+2+4+7=18 \end{gathered}[/tex]The perimeter of the figure is 90 meters. Therefore, the length of the longest side will be:
[tex]\begin{gathered} =\frac{7}{18}\times90 \\ =7\times5 \\ =35m \end{gathered}[/tex]The length of the longest side is 35 meters.
help meeeeeeeeeeeeeeee pleasee
Answers
Answer:
16.1 seconds
Step-by-step explanation:
h = 16t²
h = 4144
4144 = 16t²
÷16 ÷16
----------------
259 = t²
√259 = √t²
16.1 ≈ t
I hope this helps!
if 3/4 is the dividend and -2/5 is the divisor then what is the quotient ?
Answers
Answer:
[tex]\dfrac{-15}{8}[/tex]
Step-by-step explanation:
Fraction division:[tex]\sf \dfrac{3}{4} \ \div \dfrac{-2}{5}[/tex]
Use KCF method.
Keep the first fraction.Change division to multiplicationFlip the second fraction.[tex]\sf \dfrac{3}{4} \ \div \dfrac{-2}{5}=\dfrac{3}{4}*\dfrac{-5}{2}[/tex]
[tex]\sf = \dfrac{3*(-5)}{4*2}\\\\ =\dfrac{-15}{8}[/tex]
Write the rate as a unit rate 339 calories in a 3-ounce serving The unit rate is ? ( I don’t need a detailed explanation just the answer please )
Answers
It is given that 339 calories in 3 ounce serving.
So in one ounce serving there will be:
[tex]\frac{339}{3}=113\text{ calorie/ounce}[/tex]So the unit rate is 113 calories/ounce.
Peter has half of his investments in stock paying a 6% dividend and the other half in a stock paying 14 % interest. If his total annualinterest is $500, how much does he have invested?
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Assume that Peter will invest $x
Then he will invest 1/2 x with a rate of 6% and 1/2 x with a rate of 14%
Since the rule of the interest is
[tex]I=\text{PRT}[/tex]P is the amount of investment
R is the rate in decimal
T is the time
For the first account
[tex]\begin{gathered} P=\frac{1}{2}x \\ R=\frac{6}{100}=0.06 \\ T=1 \end{gathered}[/tex]For the second account
[tex]\begin{gathered} P=\frac{1}{2}x \\ R=\frac{14}{100}=0.14 \\ T=1 \end{gathered}[/tex]Then the interest of each account is
[tex]\begin{gathered} I_1=(\frac{1}{2}x)(0.06)(1) \\ I_1=0.03x \end{gathered}[/tex][tex]\begin{gathered} I_2=(\frac{1}{2}x)(0.14)(1) \\ I_2=0.07x \end{gathered}[/tex]Since the total interest is $500, then add I1 and I2, equate the sum by 500
[tex]\begin{gathered} I_1+I_2=500 \\ 0.03x+0.07x=500 \\ 0.10x=500 \end{gathered}[/tex]Divide each side by 0.10
[tex]\begin{gathered} \frac{0.10x}{0.10}=\frac{500}{0.10} \\ x=5000 \end{gathered}[/tex]Then he invested in each account 5000/2 = $2500
He invested a total of $5000
A line is parallel to the equation 3y-x=-12 and this line also passes through the point (18,2). What is the equation of this line?
Answers
Given;
[tex]3y-x=-12[/tex]Recall that the equation of a straight line is given as;
[tex]\begin{gathered} y=mx+c\text{ } \\ \text{Where m= slope of the line} \\ 3y=x-12 \\ y=\frac{1}{3}x-4 \\ \text{Thus, m=}\frac{1}{3} \end{gathered}[/tex]The slope of two parallel lines is equal.
Thus, the slope of the second line is also 1/3;
Then, the equation is;
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{Where x}_1=18_{} \\ \text{and y}_1=2 \\ y-2=\frac{1}{3}(x-18) \\ 3(y-2)=x-18 \\ 3y-6=x-18 \\ 3y-x=6-18 \\ 3y-x=-12 \end{gathered}[/tex]The equation of the line is also 3y - x = -12
What is the third term needed to complete the square of the equation below?
Answers
EXPLANATION
The third needed term would be the following:
Dividing both sides by 4:
[tex]x^2+\frac{3}{4}x=0[/tex]Multiplying the second term by 1/2 and the squared power:
[tex](\frac{1}{2}*\frac{3}{4})^2=\frac{9}{64}[/tex]Adding 9/64 to both sides:
[tex]x^2+\frac{3}{4}x+\frac{9}{64}=\frac{9}{64}[/tex]Finally, we can conclude the third term is 9/64.
The function f(x) = -3x - 4 was replaced with f(x + k) resulting in the function g(x) = -3x - 13. What is the value of k? A. -9 B. -3 C. 3 D. 9
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then we need to solve the second equation for k
[tex]3k=-4+13=9[/tex]then the answer is C.
[tex]k=3[/tex]Read image for instructions How many students in the survey were in the age category of 18 to 22?
Answers
Answer:
82
Step-by-step explanation:
78+4
Determine whether the two polygrams are similar. If so write the similarities ratio in the similarity statement for questions 1 please
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Given rectangles ABCD and WXYZ, you need to determine whether they are similar.
By definition, two figures are similar if the lengths of their corresponding side are in proportion and if the measures of their corresponding angles are equal.
You know that all the interior angles of a rectangle measure 90 degrees. Therefore, you know that the corresponding angles of the given rectangles are congruent.
In order to determine if their corresponding sides are in proportion, you can set up this equation:
[tex]\frac{64}{96}=\frac{30}{50}[/tex]Reducing the fractions, you get:
[tex]\frac{2}{3}=\frac{3}{5}\text{ (False)}[/tex]Therefore, the lengths of the corresponding sides are not in proportion.
Hence, the answer is: The rectangles are not similar.
how to factor 3x^2-9x-84
Answers
To solve a question like this, you will need to factorise the first term of the expression out.
So, our expression becomes
[tex]3(x^2\text{ }-3x-28)\text{ }[/tex]
Now, you will need to find the factors of 28 whose sum will give you -3
Always remember to express it in terms of x.
The answer to that is -7x and +4x. Thus we can rewrite the expression as;
[tex]\begin{gathered} 3(x^2-7x+4x-28) \\ 3\left\lbrace x(x-7)+4(x-7)\right\rbrace \text{ }\Longrightarrow\text{ By factorizing the terms of the expression } \\ 3\left\lbrace x(x-7)+4(x-7)\right\rbrace \text{ }\Longrightarrow\text{which can further be factorized as} \\ 3(x-4)(x-7) \end{gathered}[/tex]In summary 3x^2-9x-84 can be factorized as
[tex]3(x-4)(x-7)[/tex]Which set of coordinates satisfies the equations x - 2y = -1 and 2x + 3y = 12?6541-6-5-4-3-2- 1123456-1-2-3-4-5-6
Answers
Given data:
The given equations are x - 2y = -1 and 2x + 3y = 12.
The given point of intersection is the solution of the equation which is (3, 2).
Thus, the solution of the given equations is (3, 2).
What is the diameter of the circle (write only the numeric answer no units)
Answers
The circumference is 15.996 cm
Explanation:Given the area of the circle as
[tex]200.96cm^2[/tex]This means:
[tex]\begin{gathered} \pi r^2=200.96 \\ r^2=\frac{200.96}{\pi}=63.97 \\ \\ r=\sqrt{63.967}=7.998 \end{gathered}[/tex]Now that the radius has been obtained, the diameter of a circle is twice the radius, therefore
[tex]\begin{gathered} c=2\times7.998 \\ =15.996cm \end{gathered}[/tex]12/9 = v/3 what is v
Answers
In order to solve the equation for v we just have to remember one simple rule: what we do in one side of the equal "=" is what we must do on the other side.
We have that
[tex]\frac{12}{9}=\frac{v}{3}[/tex]We want to find a way to let v alone on the right side of the equation. If can multiply both sides of the equation by 3:
[tex]\begin{gathered} \frac{12}{9}=\frac{v}{3} \\ \downarrow \\ \frac{12}{9}\cdot3=\frac{v}{3}\cdot3 \\ \end{gathered}[/tex]For the right side, since 1/3 = 1:
[tex]\frac{v}{3}\cdot3=v\cdot1=v[/tex]Then:
[tex]\frac{12}{9}\cdot3=v[/tex]Since 12 · 3 = 36, then
[tex]\frac{36}{9}=v[/tex]Since 36/9 = 4, then:
[tex]4=v[/tex]Answer- v = 4