9.
Graph the data in the table. Which kind of function best models the data? Write an equation to model the data.
A. quadratic; y = 2.5x2
B. exponential; y = 2.5x
C. quadratic; y = –2.5x2
D. linear; y = 2.5x
Answers
Answer:
A. quadratic; y = 2.5x2
Step-by-step explanation:
Answer:
Option (1)
Step-by-step explanation:
x -2 -1 0 1 2
y 10 2.5 0 2.5 3.0
Ist difference,
= -2.5
= 2.5
= 7.5
2nd difference,
= 5
= 5
= 5
Since 2nd difference is common, given table represents a quadratic equation.
Let the equation is,
y = ax²+ bx + c
For a point (0, 0) passing through the quadratic equation,
0 = c
Therefore, quadratic equation is y = ax² + bx
Since ordered pair (-1, 2.5) passes through the graph of the function,
2.5 = a(-1)² + b(-1)
a - b = 2.5 ------(1)
For another point (1, 2.5)
2.5 = a(1)² + b(1)
a + b = 2.5 ------(2)
By adding equations (1) and (2),
2a = 5
a = 2.5
and from equation (2)→ y = 0
Therefore, equation of the quadratic function given in the table is y = 2.5x²
Option (1) is the answer.
Related Questions
A box of crayons has one each of red, orange, yellow, green, blue, purple, black, and brown. What is the probability of randomly selecting the black crayon and then randomly selecting the purple crayon if you do replace the first crayon before selecting the second crayon?
Answers
P ( selecting purple crayon) 1/8
P ( B,P)= 1/8 x 1/8 = 1/64
The probability is 1/64 and you can draw a tree diagram to visualise the two events.
For there is always light, if only we’re brave enough to see it.
If only we’re brave enough to be it.
Answers
Answer:
sun is the answer to absolutely
If the length of rectangle is x + 4 and the width is 3x - 5 what is the perimeter?
Answers
Answer:
8x-2
Step-by-step explanation:
l = x+4
w = 3x-5
The perimeter is
P =2(l+w)
= 2(x+4+3x-5)
Combine like terms
= 2(4x-1)
Distribute
= 8x-2
Answer:
[tex]8x-2[/tex]
Step-by-step explanation:
The perimeter of a rectangle is 2L + 2W, where L represents the length and W represents the width. In this scenario, L is equal to x + 4 and W is equal to 3x - 5. We can setup an equation:
[tex]2(x+4)+2(3x-5)[/tex]
We can then multiply x - 4 by 2 to get [tex]2x+8[/tex]
We can then multiply 3x - 5 by 2 to get [tex]6x-10[/tex]
Adding them together, we get the answer as [tex]8x-2[/tex]
4.
The table shows the estimated number of deer living in a forest over a five-year period. Are the data best represented by a linear, exponential, or quadratic model? Write an equation to model the data.
A. quadratic; y = 0.62x2 + 89
B. exponential; y = 89 • 0.62x
C. linear; y = 0.62x + 89
D. quadratic; y = 89x2 + 0.62
Answers
Answer:
B. exponential; y = 89 • 0.62x
Step-by-step explanation:
Answer:
exponential; y = 89 • 0.62^x
...............................................................................................................................................
Answer:
Option B exponential y = 89 · 0.62x
Step-by-step explanation:
The table shows the estimated number of deer living in a forest over a five year period.
Year Number of deers
0 89
1 55
2 34
3 21
4 13
Now we have to find the model representing this situation. Difference in number of deer, in the forest.
We can see there is a common ratio between each successive term r = = 0.618
r = = 0.618
so it can be represented by an exponential model.
Option B is the answer.
...............................................................................................................................................
math class 10
the compound amount of rupees 4000 for 3 years is 5500 rupees find the compound interest
Answers
Answer:
11%
Step-by-step explanation:
Compound Interest Formula: initial ( 1 + interest rate )^time = final amount
Let compound interest be x
4000(1+x)^3 = 5500
Divide both sides by 4000
4000(1+x)^3 / 4000 = 5500/4000
Cube root both sides
[tex]\sqrt[3]{(1+x)^3} =\sqrt[3]{11/8}[/tex]
1 + x = 2.22398 / 2
1 + x = 1.11199
Minus both sides by 1
1 + x = 1.11199
-1 -1
x = .11199 = 11%
What is the value of the exponential expression below?
Answers
The answer is 4
What is the value of m in the diagram?
Answers
Answer:
81
Step-by-step explanation:
The angles shown are formed on a straight line
Angles formed on a straight line add up to 180
So m + m + 18 = 180
We've just created an equation that we can use to solve for m
So we can now solve for m
m + m + 18 = 180
Combine like terms
2m + 18 = 180
Subtract 18 from both sides
2m + 18 - 18 = 180 - 18
2m = 162
Divide both sides by 2
2m/2 = 162/2
m = 81
Find the area of the triangle (white)
Answers
Step-by-step explanation:
something is missing here.
it is not clear, what exactly is 27 km. only the side of the orange triangle ? or the whole distance to the 90 degree angle ?
but in both cases that is not enough. we need some information about the split ratio of the orange side and the white side. it some angles in the graphic.
otherwise I can simply keep the given sides with their lengths but freely move the line between the orange and white triangles. there are infinite many solutions.
is it meant to be an isoceles triangle (2 equal sides) ? it certainly does not look like it, but that would be the only case where the given information can lead to a solution.
under that assumption the baseline of the white triangle is also 27 km.
the first side is 9km.
the second side we get via Pythagoras :
27² = 9² + x²
729 = 81 + x²
648 = x²
x = 25.46 km
now, since this is a right-angled triangle we can (especially to calculate the area) also consider the two sides enclosing the 90 degree angle as baseline and height.
the area of a triangle is baseline×height/2
area = 9×25.46/2 = 114.55 km²
77 yd
36 yd
What is the length of the hypotenuse?
C =
yards
Answers
Answer:
c = 85 yd
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is
c² = 77² + 36² = 5929 + 1296 = 7225 ( take square root of both sides )
c = [tex]\sqrt{7225}[/tex] = 85
Answer:
[tex]85yd[/tex]
Step-by-step explanation:
According to PYTHAGORAS Theorem,
[tex] {c}^{2} = {77}^{2} + {36}^{2} \\ {c}^{2} = 5929 + 1296 \\ {c}^{2} = 7225 \\ c = \sqrt{7225} \\ c= 85yd[/tex]
What is the interquartile range of this data set? 1,5,12,14,29,45,48,61,72,84,96
Answers
Answer:
60
Step-by-step explanation:
Q1 = 12
Q3 = 72
the interquartile range = Q3-Q1 = 72-12 =60
If AC = 4x-60 and BD = 30-x, find BD (GIVING BRAINLIEST)
The figure given is a rectangle
Answers
Answer:
12
Step-by-step explanation:
AC = BD (as the diagonal of the rectangle)
4x-60=30-x
4x+x = 30+60
5x = 90
x = 90/5
x = 18
=> BD = 30-18 = 12
Which graph represents the function f (x) = StartFraction 2 Over x minus 1 EndFraction + 4?
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = negative 4.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = negative 4.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = 4.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 4.
Answers
Answer:
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 4
Step-by-step explanation:
The given function is presented as follows;
[tex]f(x) = \dfrac{2}{x - 1} + 4[/tex]
From the given function, we have;
When x = 1, the denominator of the fraction, [tex]\dfrac{2}{x - 1}[/tex], which is (x - 1) = 0, and the function becomes, [tex]\dfrac{2}{1 - 1} + 4 = \dfrac{2}{0} + 4 = \infty + 4 = \infty[/tex] therefore, the function in undefined at x = 1, and the line x = 1 is a vertical asymptote
Also we have that in the given function, as x increases, the fraction [tex]\dfrac{2}{x - 1}[/tex] tends to 0, therefore as x increases, we have;
[tex]\lim_ {x \to \infty} \dfrac{2}{(x - 1)} \to 0, and \ \dfrac{2}{(x - 1)} + 4 \to 4[/tex]
Therefore, as x increases, f(x) → 4, and 4 is a horizontal asymptote of the function, forming a curve that opens up and to the right in quadrant 1
When -∞ < x < 1, we also have that as x becomes more negative, f(x) → 4. When x = 0, [tex]\dfrac{2}{0 - 1} + 4 = 2[/tex]. When x approaches 1 from the left, f(x) tends to -∞, forming a curve that opens down and to the left
Therefore, the correct option is on a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 4.
Answer:
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 4
Step-by-step explanation:
The given function is presented as follows;
From the given function, we have;
When x = 1, the denominator of the fraction, , which is (x - 1) = 0, and the function becomes, therefore, the function in undefined at x = 1, and the line x = 1 is a vertical asymptote
Also we have that in the given function, as x increases, the fraction tends to 0, therefore as x increases, we have;
Therefore, as x increases, f(x) → 4, and 4 is a horizontal asymptote of the function, forming a curve that opens up and to the right in quadrant 1
When -∞ < x < 1, we also have that as x becomes more negative, f(x) → 4. When x = 0, . When x approaches 1 from the left, f(x) tends to -∞, forming a curve that opens down and to the left
Therefore, the correct option is on a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 4.
HELP ME ASAP PLEASEEEEEEEEEEEEEEEEEEEEEEEE
Answers
Answer:
y = 3x ..... 1:3
y=9x ...... 1:9
Step-by-step explanation:
Solve for . Round to the nearest tenth of a degree, if necessary.
3.9
2.2
Answer: 2 =
Submit Answer
attempt 1 out of 2
PLSSS HELp
Answers
Answer:
x = 60.6
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp /adj
tan x = 3.9/ 2.2
Taking the inverse tan of each side
tan ^-1 (tan x )= tan ^-1(3.9/ 2.2)
x=60.57254
To the nearest tenth
x = 60.6
insert 3 rational no. between 4/13 and 1/13
Answers
Answer:
2/13,3/13,4/13....
hope it helps
Answer:
Step-by-step explanation:
4/13=40/130
1/13=10/130
numbers between 10/130 and 40/130 are 11/130,12/130,13,130 ,...,39/130.
we can select any three out of these.
Determine the sum of the first 33 terms of the following series:
−52+(−46)+(−40)+...
Answers
Answer:
1320
Step-by-step explanation:
Use the formula for sum of series, s(a) = n/2(2a + (n-1)d)
The terms increase by 6, so d is 6
a is the first term, -56
n is the terms you want to find, 33
Plug in the numbers, 33/2 (2(-56)+(32)6)
Simplify into 33(80)/2 and you get 1320
what is the equation of the axis of symmetry do the quadratic function f(x) = -(x+4) (x-1)
Answers
9514 1404 393
Answer:
x = -3/2
Step-by-step explanation:
The zeros of the function are the values of x that make the factors zero:
x = -4, x = 1
The axis of symmetry is the vertical line halfway between these zeros.
x = (-4 +1)/2 = -3/2
The equation of the axis of symmetry is x = -3/2.
Classify this triangle
A) Acute scalene triangle
B) Obtuse isosceles triangle
C) Right isosceles triangle
D) Right scalene triangle
Answers
Answer C Right Isosceles Triangle
Step-by-step explanation:
Do it
Answer: C
Step-by-step explanation:
It has a 90 degree angle, right triangle, and both legs in the triangle seem to be the same size, so it's also isosceles.
Joanna bakes a cake in the shape of a
cylinder. The cake is 10 inches in
diameter and 4.5 inches tall. She
wants to put frosting on the entire
cake that is not resting on the tray.
How many square inches of frosting
will she need? im confused on how to do the work. please answer quickly
Answers
Answer:
total surface area = 298.45105 m2
lateral surface area = 141.37155 m2
top surface area = 78.53975 m2
bottom surface area = 78.53975 m2
Step-by-step explanation:
Joanna will need approximately 298.3 square inches of frosting to cover the entire cake.
To calculate the amount of frosting Joanna will need for the entire cake, we first need to find the surface area of the cylindrical cake.
The formula for the surface area of a cylinder is given by:
Surface Area = 2πr² + 2πrh
Where r is the radius of the base and h is the height of the cylinder.
Given that the diameter of the cake is 10 inches, we can find the radius by dividing it by 2: r = 10/2 = 5 inches.
Plugging in the values, we have:
Surface Area = 2π(5)² + 2π(5)(4.5)
Simplifying the equation:
Surface Area = 2π(25) + 2π(22.5)
Surface Area = 50π + 45π
Surface Area = 95π
To find the actual numerical value, we can approximate π as 3.14:
Surface Area ≈ 95 * 3.14
Surface Area ≈ 298.3 square inches
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The cost of carpeting a sqaure yard is $9.10. How much does it cost to carpet 12.5 square yards?
Answers
Answer:
113.75$
Step-by-step explanation:
I. When a square yard = 9.10
so 1 * 9.1 = 9.1
if 12.5 square yard
then 12.5 * 9.1 = 113.75$
Will give brainliest plz answer quick
Answers
Answer:
65
Step-by-step explanation:
Exterior angle = Sum of 2 interior angles
x + 31 = x + x - 34
x + 31 = 2x - 34
x - 2x = - 34 - 31
- x = - 65
x = 65
Step-by-step explanation:
A triangle's angles add up to 180°, and a straight line is 180 degrees, so 180 - x + 31 is the interior angle that isn't labeled.
[tex]x+x-34+180-x-31=180[/tex]
[tex]x=180-115[/tex]
[tex]x=65[/tex]
which of the following equations is an example of direct variation?
Answers
Answer:
C
Step-by-step explanation:
[tex] \frac{x}{3} [/tex]
A fair spinner has 10 equal sections: 3 red, 3 blue and 4 green.
It is spun twice.
What is the probability of getting 2 different colours?
Answers
Answer:
11/30
Step-by-step explanation:
7 is subtracted from the product of 6
Answers
Answer:
product =7×6=42
subtract 42-7=35
7 - 2 x 3
Step-by-step explanation:
7 is subtracted from the product of 6
7 - 2 x 3
29 A student has N425. He bought seven ex-
ercise books and he was given N5 as
change. What is the average cost of one
exercise book?
A N60.71 B N50 C N60
DN50.71 E
N75
Answers
He was given N5 change which means he spent a total of N420
Therefore,he used N420 to buy 7 books,the average cost of one book= 420/7=60.Thanks
kx - c = 9 solve for x
Answers
Answer:
x = [tex]\frac{9+c}{k}[/tex]
Step-by-step explanation:
Given
kx - c = 9 ( add c to both sides )
kx = 9 + c ( isolate x by dividing both sides by k )
x = [tex]\frac{9+c}{k}[/tex]
therefore your answer would be x = 9/k + c/k
Find the volume of each figure. Round your answers to the nearest tenth, if necessary
Answers
Answer:
437.9
Step-by-step explanation:
Volume is pi*r^2*h=pi*(49)*9=437.9
highest common factor of 28,40,12 and 24
Answers
Answer:
4
Step-by-step explanation:
We want to find the highest common factor
Breaking them into factors
28 = 4*7 = 2*2*7
40 = 4*10 = 2*2*2*5
12 = 4*3 = 2*2*3
24 = 3*8 = 3*2*2*2
The factor that appears in all is 2*2
2*2 =4
Answer:
4
Step-by-step explanation:
28÷4=7
40÷4=10
12÷4=3
24÷4=6
7, 10, 3 and 6 cannot be divided by any same number.
John walked from town A to Town B at a uniform speed of 4km/hr.When he reached town B ,he was turned back immediately and he walked back to town A along the same road at a uniform speed of 6km/hr.What is his average speed for the whole trip?
Answers
Answer:
His average speed for the whole trip is 5km/hr
Step-by-step explanation:
Answer:
4.8 km/hr
Step-by-step explanation:
Assume that the distance is 24 km (evenly divisible by 4 & 6)
then the A-B time would be 24/4 or 6 hrs.
on the return the time would be 24/6 or 4 hrs.
total time 10 hrs total distance 48 km....
48/10 = 4.8 km/hr
A faraway planet is populated by creatures called Jolos. All Jolos are either
green or purple and either one-headed or two-headed.
Balan, who lives on this planet, does a survey and finds that her colony of 140
contains 30 green, one-headed Jolos; 45 purple, two-headed Jolos; and 75
one-headed Jolos.
One-headed Two-headed Total
Green 30
Purple
45
Total
75
140
How many green Jolos are there in Balan's colony?
Answers
Answer:
30 green jolos
Step-by-step explanation:
in the problem itself it states this "Balan, who lives on this planet, does a survey and finds that her colony of 140 contains 30 green, one-headed Jolos 45 purple, two-headed Jolos; and 75 one-headed Jolos.".
There are green Jolos are there in Balan's colony are 30 green jolos.
We have given that,
A faraway planet is populated by creatures called Jolos. All Jolos are either green or purple and either one-headed or two-headed.
Balan, who lives on this planet, does a survey and finds that her colony of 140.
What is the probability?
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
contains 30 green, one-headed Jolos; 45 purple, two-headed Jolos; and 75 one-headed Jolos.One-headed Two-headed Total
Green Purple
30 45
Total 75 140
In the problem itself, states this Balan, who lives on this planet, does a survey and finds that her colony of 140 contains 30 green, one-headed Jolos 45 purple, two-headed Jolos; and 75 one-headed Jools.
Therefore there are green Jolos are there in Balan's colony are 30 green jolos.
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