Rachel says that Graph R has a greater constant of variation that Graph S. Which statement explains whether Rachel is correct?
Answers
For this case we have that by definition the constant of variation of a line is given by the slope m, of said line.
Where:
[tex]m = \frac {(y_ {2} -y_ {1})} {(x_ {2} -x_ {1})}[/tex]
To find the slope of a line it is necessary to find two points through which the line passes.
To solve the given problem, we find the slopes of the lines shown in the graphics R and S:
Graphic R:
It is observed that the line passes through the following points:
[tex](x_ {1}, y_ {1}) = (0,0)\\(x_ {2}, y_ {2}) = (2,1)[/tex]
Substituting in the formula of the slope we have:
[tex]m_ {R} = \frac {(y_ {2} -y_ {1})} {(x_ {2} -x_ {1})}[/tex]
[tex]m_ {R} = \frac {1-0} {2-0}[/tex]
[tex]m_ {R} = \frac {1} {2}[/tex]
Thus, the slope of the line of the graph R is given by: [tex]m_ {R} = \frac {1} {2}[/tex]
Graphic S:
It is observed that the line passes through the following points:
[tex](x_ {1}, y_ {1}) = (0,0)\\(x_ {2}, y_ {2}) = (1,2)[/tex]
Substituting in the formula of the slope we have:
[tex]m_ {S} = \frac {(y_ {2} -y_ {1})} {(x_ {2} -x_ {1})}[/tex]
[tex]m_ {S} = \frac {2-0} {1-0}[/tex]
[tex]m_ {S} = \frac {2} {1}[/tex]
[tex]m_ {S} = 2[/tex]
Thus, the slope of the line of the graph R is given by: [tex]m_ {S} = 2[/tex]
[tex]m_ {S}> m_ {R}[/tex]
then, the graph S has a variation constant greater than the graph R.
Answer:
The graph S has a variation constant greater than the graph R.
Rachel's idea is wrong
Answer:
It’s D
Step-by-step explanation:
Related Questions
dr. Trekcir has $875 to invest. he invests some of it in account#1 paying 8% annual interest and the rest of it in account#2 paying 4% annual interest. After 1 year total interest is $49.00. find hou much is invested in each account
Answers
0.08n + 0.04(875-n) = 49
Multiply both sides by 100:
8n + 3500 - 4n = 4900
Simplify:
4n+3500=4900
Isolate n:
4n = 1400
n = 350
8% invested: 350
4% invested: 525
A standard dartboard has a diameter of 18 in. What is its area to the nearest square inch?
Answers
In this exercise is given that the diameter of a standard cardboard is 18 inches or a radius of 9 inches and it is asked to find its area. Therefore, to find the area of the circle you should substitute the value of the radius into the previous mention formula.
[tex]A= \pi r^{2}[/tex]
[tex]A= \pi (9 in)^{2} [/tex]
[tex]A= \pi (81 in^{2})[/tex]
[tex]A=254.47 in^{2} [/tex]
The area of the standard dartboard is 254.47 square inches or 254 square inches.
solve the system using substitution method
3x+y=6
2x-4y=10
Answers
[tex]\boxed{\left\{\begin{array}{ccc}x=\dfrac{17}{7}\\\\y=-\dfrac{9}{7}\end{array}\right}[/tex]
Multiply 4 to the first equation:
[tex]\begin{cases}&12x + 4y = 24 \\&2x - 4y = 10\end{cases}[/tex]
ADD Equation 1 to Equation 2 and find x:
[tex]\begin{aligned}&14x =34 \\&x= 34/14 \\& x = 17/7\end{aligned} [/tex]
Substitute x = 17/7 and find y:
[tex]\begin{aligned}&3x + y = 6 \\&3 (17/7) + y = 6 \\& 51/7 + y = 6 \\&y = -9/7\end{aligned} [/tex]
Answer: x = 17/7, y = -9/7
The area of the parallelogram is 65 square miles. Find its base and height.
Answers
(base 5) (height 13)
Base = 13
Height = 5
Or:
Base = 5
Height = 13
Hope this helped☺☺
The elevation is 12,000 feet. the altimeter reading in an airplane is 17.00 in hg. this pressure is equal to
Answers
There are 29.92inHg in 1 atm
thus
17 inHg×(1 atm/29.92inHg)
=17/29.92
=0.5682 atm
Answer: 0.5682 atm
what is the solution to the equation 3sqrt(5x-4)=3sqrt(7x+8)
Answers
However this is an extraneous solution since it would make the number under the sqrt a negative number.
Answer:
The answer is: 'no solution'
Step-by-step explanation:
The given equation is: [tex]3\sqrt{5x-4}=3\sqrt{7x+8}[/tex]
Dividing both sides of the equation by 3, we will get.....
[tex]\sqrt{5x-4}=\sqrt{7x+8}[/tex]
Taking square on both sides.....
[tex](\sqrt{5x-4})^2=(\sqrt{7x+8})^2\\ \\ 5x-4=7x+8\\ \\ 5x-7x=8+4\\ \\ -2x=12\\ \\ x=\frac{12}{-2}=-6[/tex]
Plugging this [tex]x=-6[/tex] back to the given equation......
[tex]3\sqrt{5(-6)-4}=3\sqrt{7(-6)+8}\\ \\ 3\sqrt{-34}=3\sqrt{-34}[/tex]
As we are getting a negative number inside the square root, so the equation becomes imaginary. Thus [tex]x=-6[/tex] is a restricted value.
Hence, there is 'no solution' for this equation.
Iris is building a model of the Washington Monument. Her model measures 15 in. tall and is 1.5 in. wide at the base. The actual width measurement at the base of the Washington Monument is about 55 ft. About how tall is the Washington Monument?
Answers
=>tall/wide
The model 15in/1.5in
The actual x/55ft
Convert everything into the same units so 55ft to inches
There are 12in in 1ft
55ft * 12in/1ft
The ft cross out leaving in
55*12in= 660 in
So
15in/1.5in = x/660in
Now solve for x my multiplying both side by 660in
660in *15in/1.5in=x
x= 6600in tall
Answer: 550
Step-by-step explanation:Solve the proportion: 15 in./1.5 in. = h/55 ft. The value of h is 550 ft. The Washington Monument is about 550 ft tall.
A technique used to rewrite a quadratic function in standard form to vertex form is
Answers
[tex]f(x)=a(x-h)^{2}+k, [/tex]
where (h,k) is the vertex of parabola. In some literatures, the standard form of the quadratic equation is written as
[tex]f(x)=a x^{2} +bx+c[/tex]
Therefore, in order to avoid the confusion, the first equation is taken as a vertex form. When the standard form is converted into the vertex form, the process is called completing the square.
Answer:
completing the square.
Step-by-step explanation:
trust me
Find the area of the figure
Answers
The parallelogram, you can just do base * height. The base is 11 yards, and the height is 4 yards. 11 * 4 = 44 square yards.
Now for the trapezoid. If you split it up into a rectangle and a triangle, it becomes much more easier to solve. The rectangle and triangles can be made by splitting the figure down the center. This makes a rectangle with a length of 7 yards and a height of 8, and a triangle with a base of 7 yards and a height of 8 as well.
Solve for the area of both shapes.
The rectangle: Multiply length * height: 7 * 8 = 56 square yards
The triangle: Multiply base * height, and then divide by 2: 7 * 8 = 56
56 / 2 = 28 square yards
Now add the areas together.
28 + 56 + 44 = 128 square yards
Hope this helped!
1. Find area of the trapezium.
2. Find area of the parallelogram.
3. Add the 2 areas together.
Step 1: Find the area of the trapezium:
Formula : area = 1/2 (a + b) h
Area = 1/2(7 + 14) (8) = 84 yd²
Step 2: Find the area of the parallelogram:
Formula : area = base x height
Area = 11 x 4 = 44 yd²
Step 3: Find the total area:
Total Area = 84 + 44 = 128 yd²
Answer: 128 yd²
if an object is propelled upward from a height of s feet at an initial velocity of v feet per second h=-16t^2+96t+8 after how many seconds is the height 116 feet?
Answers
This graph shows how much Marie earns babysitting compared with the number of hours she works select the correct statement about the graph
Answers
The graph reflects that she is getting paid 10 dollars an hour
If you plot the points, you will see she makes 5 dollars every half hour
Answer:
Option D is the answer.
Step-by-step explanation:
This graph represents a linear function representing earnings of Marie at y axis and hours of working at x axis. To get the change in Marie's earnings for every 5 hours we will find the slope of the given line.
Slope of the line will define the rate of change in earning of Marie with respect to the time.
End points of the line at time t = 0 and t = 5 hours are (0, 0) and (5, 50).
Therefore slope = [tex]\frac{y-y'}{x-x'}=\frac{50-0}{5-0}=\frac{50}{5}=10[/tex]
So for each hour she works her earnings go up by $10.
Option D is the correct option.
Ted researched the price of airline tickets and discovered a correlation between the price of a ticket and the number of miles traveled. After recording his data on a scatter plot, he determined the equation for the line of best fit is y = 300 + 0.45x. What does 0.45 represent in the equation? A) the lowest ticket price B) the number of miles traveled C) the expected change in the price of multiple tickets Eliminate D) the expected change in price of the ticket for each mile traveled
Answers
Because it is a coloration between the two
Because it is a coloration between the two
Suppose that 44% of all Americans approve of the job the President is doing. The most recent Gallup poll consisted of a random sample of 1,400 American adults.
a. What is the mean of the sampling distribution?
b. What is the standard deviation of the sampling distribution (don't forget to justify the use of the formula)?
c. Describe the normal approximation for this sampling distribution (don't forget to justify this) You can simply write as N (mean, standard deviation)
d. What is the probability that the Gallup poll will come up with a proportion within three percentage points of the true 44%
Answers
b) SD = √ (n×p×q) n 1400 p is 0.44 and q = 1-p=1-0.44=0.56
A table is going to be painted. How much less surface area of the table will be painted if the underside remains unpainted. The length is 22 in, the width is 20 in, and the height is 1 in
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If the volume is 56 1/4 cubic feet and the length is 7 1/2ft and the width is 3 3/4ft what is the height?
Answers
You have been averaging 55 sales per day. Per our new policy, everyone needs to increase his or her sales per day by 10% in the next month. Rounding up, by next month you will need to be up to __________ sales.
Answers
The next month sales should be 1,815.
Given that,
You have been averaging 55 sales per day. increase his or her sales per day by 10% in the next monthBased on the above information, the calculation is as follows:
[tex]= 55 \times 1.10 \times 30 days[/tex]
= 1,815
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Final answer:
To meet the new policy of a 10% increase in sales, you would multiply your current average sales by the increase percentage and round up to the nearest whole number. Starting from 55 sales, a 10% increase results in an additional 5.5 sales, which when rounded up equals 6. Therefore, you need to achieve 61 sales per day.
Explanation:
If you have been averaging 55 sales per day and need to increase your sales by 10%, you will first need to calculate the increase. To calculate a 10% increase, you multiply your current average sales (55) by the percentage increase (10%), expressed as a decimal (0.10). The increase in sales can be found by the formula:
Increase = Current Sales × Percentage Increase
For your sales:
Increase = 55 × 0.10 = 5.5 sales
Since you need to round up, the increase will be 6 sales when considering whole units, as you cannot sell half a unit.
Therefore, the new target sales per day will be:
New Sales Target = Current Sales + Increase
New Sales Target = 55 + 6 = 61 sales
By next month, you will need to be up to 61 sales per day after rounding up.
Find the derivative of f(x) = (1 + 5x2)(x − x2) in two ways. use the product rule. f '(x) = perform the multiplication first. f '(x) = do your answers agree? yes no
Answers
Answer:
The answers agree.
[tex]f^{\prime}(x) = - 20x^{3} + 15x^{2} - 2x + 1[/tex]
Step-by-step explanation:
The product rule is:
[tex]f(x) = g(x)h(x)[/tex]
[tex]f^{\prime}(x) = g^{\prime}(x)h(x) + g(x)h^{\prime}(x)[/tex]
In this problem, we have that:
[tex]f(x) = (1 + 5x^{2})(x - x^{2})[/tex]
So
[tex]g(x) = 1 + 5x^{2}[/tex]
[tex]g^{\prime}(x) = 10x[/tex]
[tex]h(x) = x - x^{2}[/tex]
[tex]h^{\prime}(x) = 1 - 2x[/tex].
[tex]f^{\prime}(x) = g^{\prime}(x)h(x) + g(x)h^{\prime}(x)[/tex]
[tex]f^{\prime}(x) = (10x)*(x - x^{2}) + (1 + 5x^{2})(1-2x)[/tex]
[tex]f^{\prime}(x) = 10x^{2} - 10x^{3} + 1 - 2x + 5x^{2} - 10x^{3}[/tex]
[tex]f^{\prime}(x) = - 20x^{3} + 15x^{2} - 2x + 1[/tex]
Multiplication first:
[tex]f(x) = (1 + 5x^{2})(x - x^{2})[/tex]
[tex]f(x) = x - x^{2} + 5x^{3} - 5x^{4}[/tex]
[tex]f(x) = -5x^{4} + 5x^{3} - x^{2} + x[/tex]
[tex]f^{\prime}(x) = -20x^{3} + 15x^{2} - 2x + 1[/tex]
Comparing the results, we can see that the derivatives obtained using the two methods are indeed the same. The answer is yes.
What's the function about?The derivative of f(x) = (1 + 5x2)(x − x2) can be found using the product rule and by performing the multiplication first.
Using the product rule:
The product rule states that the derivative of f(x)g(x) is f′(x)g(x)+f(x)g′(x).
In this case, f(x) = 1 + 5x2 and g(x) = x − x2. So the derivative of f(x)g(x) is:
f′(x)g(x)+f(x)g′(x)
=(10x+10x3)(x−x2)+(1+5x2)(2x−2x3)
=10x2−10x3+10x3−10x4+2x−2x3+1+10x2−10x3
=−10x4+12x2+2x
Performing the multiplication first:
We can first multiply out the expression (1 + 5x2)(x − x2) to get:
x2−5x4+x3−5x3+x−x2
=−5x4+12x2+x
Then, we can take the derivative of this expression to get the same derivative as we found using the product rule:
f′(x)=−10x4+12x2+2x
Therefore, the derivative of f(x) = (1 + 5x2)(x − x2) is -10x4+12x2+2x, regardless of whether we use the product rule or perform the multiplication first.
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hey can you please help me posted picture of question
Answers
[tex]x= \frac{-b+- \sqrt{ b^{2} -4ac} }{2a} [/tex]
b =coefficient of x term = -2
a = coefficient of squared term = 1
c = constant term = 10
Using the values in the above formula we get:
[tex]x= \frac{2+- \sqrt{4-4(1)(10)} }{2(1)} \\ \\ x= \frac{2+- \sqrt{-36} }{2} \\ \\ x= \frac{2+-6i}{2} \\ \\ x=1+3i, x=1-3i [/tex]
So the correct answer to this question is option A
The perimeter of the base of a regular quadrilateral prism is 60 cm, the area of a lateral face is 105 cm2. Find: the volume of the prism
Answers
s = P/4
s = (60 cm)/4 = 15 cm
The area of one lateral face is the product of side length and height.
A = s×h
105 cm² = (15 cm)×h
Then the height of the prism is
h = (105 cm²)/(15 cm) = 7 cm
The area of the base is then
B = s²
B = (15 cm)² = 225 cm²
The volume of the prism is the product of its base area and height.
V = Bh
V = (225 cm²)×(7 cm) = 1575 cm³
The volume is 1575 cm³.
What is the value of x in the equation –6 + x = –2?
8
4
–4
–8
Answers
If the radius of a cone is doubled and the height is tripled, what happens to the volume?
Answers
What percent of the scores were between 71 and 96
Answers
Determine whether the two figures are similar. If so, give the similarity ratio of the smaller figure to the larger figure. The figures are not drawn to scale
A. yes; 1:1:2
B. yes; 1:1:4
C. yes; 1:2:4
D. no
Answers
smaller figure
ha=8.7
ra=1.6
larger figure
hb=10.44
rb=1.92
ha/hb=8.7/10.44----> 0.83
ra/rb=1.6/1.92-------> 0.83
ratio smaller figure to the larger figure
1.6/1.92-------> divided by 1.6 both members
[1.6/1.6]/[1.92/1.6]-------> 1/1.2
the ratio ha/hb is equal to the ratio ra/rb
so
the smaller figure and the larger figure are similar
and the ratio smaller figure to the larger figure is equal to----> 1/1.2
the answer is
the option
yes 1/1.2
A rectangular storage area is to be constructed along the side of a tall building. a security fence is required along the remaining 3 sides of the area. what is the maximum area that can be enclosed with 800 m of fencing? (a = lw)
Answers
A = lw = l(800 -l)/2
This is the equation of a downward-opening parabola with zeros at l=0 and l=800. The zeros are symmetrical about the axis of symmetry of the parabola, which axis goes through the vertex. That is, the vertex is located at
l = (0 +800)/2 = 400
The maximum aea that can be enclosed is 400 m long by 200 m wide, so is
(400 m)×(200 m) = 80,000 m²
To find the maximum area enclosed with 800 m of fencing, the dimensions of the rectangular storage area need to be determined. The perimeter equation is derived to eliminate a variable, allowing the area to be expressed in terms of the remaining variable. Using this approach, the dimensions that maximize the area can be found.
Explanation:To find the maximum area that can be enclosed with 800 m of fencing, we need to determine the dimensions that will result in the largest possible area. Let's assume the length of the rectangular storage area is L and the width is W.
Since there are 3 sides already covered by the security fence, the perimeter of the rectangular storage area will be: 2L + W = 800 m.
To find the maximum area, we need to eliminate one variable from the equation above. We can do this by expressing W in terms of L and substituting it back into the area formula A = LW.
By applying this approach, we can find the dimensions of the rectangular storage area that will enclose the maximum area with 800 m of fencing.
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write an expression that represents the difference between t and 8
Answers
Short answer: t - 8
Why?
When we are finding the difference between two numbers, we are subtracting. So, the difference between t and 8 would be t - 8.
Hope this helped you! ♥
N a class, 20% of the students are male and 80% female. among male students, 40% wears eyeglasses; among female students, 30% wear eye glasses. if we select a student from the class at random, what is the probability that the student wears eyeglasses
Answers
The height of an object from a distance
Answers
x = distance from tower
tan(19.9) = y/x
tan(21.8) = y/(x-50) ( x is 50 feet closer so subtract 50 from x)
find the tan of the angles:
tan19.9 = 0.362
tan21.8 = 0.400
replace those values in the equations:
0.362 = y /x
0.400 = y / (x-50)
rewrite to solve for height:
0.362x = y
0.400(x-50) = y distribute the 0.400 and rewrite as 0.400x-20 =y
now solve:
0.362x = 0.400x-20
add 20 to each side:
0.362x +20 = 0.400x
subtract 0.362x from each side:
20 = 0.038x
divide both sides by 0.038
x = 20 / 0.038 = 526.3 feet
now that x is known replace x in the original equation and solve for y:
tan19.9 = y /x
0.362 = y / 526.3
y = 0.362 x 526.3
y = 190.5
the height of the tower is 190.5 feet
Oil-rich countries in the middle east cover about 4% of earth’s total land area but possess about 48% of the world’s known oil reserves. what is the main reason for the high concentration of reserves in this part of the world?
Answers
Geological processes are things such as erosion, tectonic plate shifts, e.t.c.
Bruce bought a map that cost $7.35 he used a $10 bill to pay for his map what is the change
Answers
You can get this by subtracting the 7.35 from the 10.
10 - 7.35 = 2.65
sq root of x +11 =15
Answers
You can solve for x by subtracting 11 from 15 to get 4. Once you've got 4, you can power 4 by 2 (4²) to get 16 as your answer
x=16
So the value of x is 16
I hope this helps!
I take it you want to find x.
Square both sides.
(sqrt(x + 11))^2 = (15)^2
x + 11 = 225 Subtract 11 from both sides.
x = 225 - 11
x = 214
Edit
This answer is edited to reflect which interpretation is correct. If you give out Brainlys (and you should) give it to Brick123. We all need them.
Sqrt(x) + 11 = 15 Subtract 11 from both sides.
sqrt(x) = 15 - 11
sqrt(x) = 4 Square both sides.
(sqrt(x)^2 = 4^2
x = 16