Answers
Answer:
f(x) = 8.917x³ + 2x² + 0.083x - 7
Step-by-step explanation:
f(x)= y
Let the coefficients of x³, x², x be a, b, c and the constant be d
y= ax³ + bx² + cx + d
When y = -65, x = -2
-65= a(-2)³ + b(-2)² + c(-2) + d
-65= -8a + 4b - 2c + d ...eq. 1
When y = -14, x = -1
-14= a(-1)³ + b(-1)² + c(-1) + d
-14= -a + b - c + d ...eq. 2
When y = -7, x = 0
-7= a(0)³ + b(0)² + c(0) + d
-7 = d ...eq.3
When y = 4, x = 1
4= a(1)³ + b(1)² + c(1) + d
4= a + b + c + d ...eq. 4
when y = 78, x = 2
78 = a(2)³ + b(2)² + c(2) + d
78= 8a + 4b + 2c + d ...eq. 5
From eq. 3, d is - 7
putting d as - 7 in equations 1, 2, 4 and 5
In eq. 1,
-65= -8a + 4b - 2c - 7
-58= -8a + 4b - 2c ...eq. 6
In eq. 2
-14= -a + b - c - 7
-7= -a + b - c ...eq. 7
In eq. 4,
4= a + b + c - 7
11= a + b + c ...eq. 8
In eq. 5
78= 8a + 4b + 2c - 7
85= 8a + 4b + 2c ...eq.9
Subtracting eq. 9 from eq. 6
-143 = -16a - 4c... eq 10
subtracting eq. 8 from eq 7
-18= -2a - 2c
9= a + c
a = 9 - c ...eq 11
putting a as 9 - c in eq. 10
-143 = -16(9 - c) - 4c
-143 = -144 + 16c - 4c
1= 12c
c = 1/12 or 0.083
putting c as 1/12 in eq. 11
a = 9 - 1/12
a = 107/12 or 8.917
Putting a as 107/12 and c as 1/12 in eq. 8
11= 107/12 + b + 1/12
multiplying through by 13
132 = 107 + 12b + 1
132 - 108 = 12b
24= 12b
b = 24/12
= 2
Therefore, a= 8.917, b= 2, c= 0.083 and d = -7
f(x) = 8.917x³ + 2x² + 0.083x - 7
Related Questions
what is the area of 146km 6.3km and 5.4km
Answers
Answer:
Step-by-step explanation:
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Answer:
Step-by-step explanation:
(f+g)(x)
f(x)= x-3, g(x)= 2x+8
Answers
Answer: 13x4+g
Step-by-step explanation:
How can one determine the number of x-intercepts of the graph of a quadratic function without graphing the function?
Answers
Answer:
The easiest method is to find the x-intercepts of the quadratic function by substituting y=0 in the function and solving it to find the possible values of x. The number of all possible values of x is the number of x-intercepts of the graph.
what is the value of y so that the equation is true y^2 = -81
Answers
Step-by-step explanation:
to make the equation true the value of y must be.
-1×9²-1×81-81hope it helps.
stay safe healthy and happy.
Answer:
y=-/+9
Step-by-step explanation:
y^2=81
find the square root
y=positive/negative 9
Simplify: (ab + bc) (ab - bc)
Answers
[tex] \: \: \: \: [/tex]
[tex] = {a}^{2} \: {b}^{2} - {b}^{2} \: {c}^{2} [/tex]
Step-by-step explanation:
[tex](ab + bc)(ab - bc)[/tex]
use ( a + b ) ( a + b ) = a² - b² to simply the product[tex](ab {)}^{2} - (bc {)}^{2} [/tex]
to raise a product to a power ,raise each factor to that power[tex] = {a}^{2} {b}^{2} - {b}^{2} {c}^{2} [/tex]
hope it helpsWhat is the slope of the line (-5,-7) and (4,-1)
Answers
Answer:
2/3
Step-by-step explanation:
slope = change in y / change in x = (-7-(-1))/(-5-4) = (-6)/(-9) = 2/3
Laurie wants to join the basketball team. Her parents ask her to figure out how much it will cost. Laurie knows that she has to pay an activities fee of $42 plus a fixed amount for each tournament. Write a formula that describes how much it will cost to join the team. Let's let:
c=cost for each tournament
n=number of tournaments the team plays
t=total amount to join the team
Answers
The Formula:
t = cn + 42
Three-fourths of the 8th graders at Kingston
Middle School went on the class trip. If 252
students went on the trip, how many 8th
graders are there?
Answers
sAnswer:189 students
Step-by-step explanation:
a family buys 6 airline tickets online. the family buys travel insurance that costs 18 per ticket. the total cost is 1,044
Answers
Answer:
936
Step-by-step explanation:
Therefore you multiply 6 by 18 = 6×18= 108
1,044 - 108 = 936
So therefore the total is 936
Which of the following have a sum of 0? (Pick 2) *
1:The football team gained 10 yards on the first play, gained 10 yards on the second play, and lost 10 yards on the third play. What was the overall change in yardage?
2: While playing the integer game, Sam pulled the following cards: 8, 4, 5, -6, -8, -3. What is the sum of Sam's hand?
3: -15 - 8 + 12 + 11
4: 6 + (-5) - 7 + (-4) + (-4)
Answers
Answer:
The answer is number 3.
Step-by-step explanation:
-15 - 8 = -23
12 + 11 = 23
When you subtract -23 from 23 you have a sum of 0
Therefore the answer is 0
Determine the value of cos 45 X 29
Answers
Answer:
20.50609665
around 20.506
PHOTO ATTACHED PLESE HELPPPP!!!!!!!!!!!!!!
Answers
Answer:
[tex]5x^2 + 3x - 2[/tex]
This answer is correct because I simplified using like terms.
Step-by-step explanation:
Subtracting Polynomials
They key to subtract, multiply, add, and divide polynomials is by using like terms. Like terms are values with the same bases. For example :
[tex]ax^2[/tex] and [tex]2ax^2[/tex] are like terms because they have the base [tex]ax[/tex]
Step 1: Move like terms together
First, let's remove all parenthesis:
[tex](3x^2 + 9x-6)-(2x^2-4x^2+6x-4)\\\\= 3x^2+9x-6-2x^2+4x^2-6x+4[/tex]
Now let's move all like terms together:
[tex]3x^2+9x-6-2x^2+4x^2-6x+4= \\3x^2-2x^2+4x^2+9x-6x-6+4[/tex]
Step 2: Simplify
Now we can add and subtract the like terms like we do in any other problem
[tex]3x^2-2x^2+4x^2+9x-6x-6+4 = \\5x^2+3x-2[/tex]
Step 3: Explaining your answer
Just say: "This answer is correct because I simplified using like terms"
-Chetan K
Find the volume of the following figure. Use 3.14 for pi. best answer gets brainliest also 100 points
Answers
Answer: 301.44 cubic inches.
Step-by-step explanation:
The formula for the volume of a cone is [tex]V = \pi r^2 \frac{h}{3}[/tex], so by plugging in the radius (6) and height (8), and using 3.14 as pi, you can get 301.44 as the total volume.
Since it is volume, it is in inches cubed, Therefore, the final answer is 301.44 cubic inches.
I hope this helps! :)
YOU’RE GETTING A BRAINLIST IF YOU ANSWER THESE:
If you and I meet halfway between the fountain and the restrooms what are the coordinates of our meeting place?
If my cat and your dog meet halfway between the ball field and the swings what are the coordinates of their meeting place?
Now to the nearest yard how far are you and I to our pets after arriving to our meeting place?
Answers
Answer:
(0.5,-0.5)(0.5,0.5)2 yardsy= 3/4x + 3 Find the y and x intercept
Answers
[tex]y - intercept = 3[/tex]
[tex]x - intercept = - 4[/tex]
what is the surface area of a polyhedron with measurements 4cm x 4cm x 7cm?
Answers
Check the picture below.
so let's add all sides and that'd be the area of the rectangular prism.
[tex]\stackrel{\textit{top and bottom}}{2(4\cdot 7)}+\stackrel{\textit{left and right}}{2(4\cdot 4)}+\stackrel{\textit{front and back}}{2(4\cdot 7)}\implies 56+32+56\implies 144[/tex]
Jaime is three years younger than his brother Keegan. In five years, the sum of their ages will be thirty-nine.
How old are they now?
Answers
Answer:
Keegan is 16 and Jamie is 13.
Step by Step Explanation:
So if we were to take the number 39 and divide it by 2, we would get 19.5. Since Jaime is 3 years younger, we would subtract 3 from one of the 19's. Then we would add 1.5 to both of the numbers since that 3 we subtracted has to go somewhere in that 39, and we come up with the numbers 21 and 18. Since it is asking how old they are NOW and not in the future, we subtract 5 from both numbers to account for the 5 years, and we end up with the years 16 and 13.
Math:
39÷2 = 19.5
19.5 19.5
-3
___________
16.5 19.5
+1.5 +1.5
___________
18 21
-5 -5
13 16
: West Gorham High School is to be located at the population center of gravity of three communities: Westbrook, population 16,000; Scarborough, population 22,000; and Gorham, population 36,500. Westbrook is located at 43.6769˚N, 70.3717˚W; Scarborough is located at 43.5781˚N, 70.3222˚W; and Gorham is located at 43.6795˚N, 70.4447˚W.
a. Where should West Gorham High School be located?
b. If only two pieces of adequate land are available for sale: Baker’s Field at 43.6784˚N, 70.3827˚W; or L onesome Acres at 43.5119˚N, 70.3856˚W, using rectilinear distances, which is closer to the site located in part (a)?
Answers
Answer:
(a) 43.6490°N, 70.3928°W
(b) Baker's Field
Step-by-step explanation:
The locations are all within a 7-mile square, so we will make the assumption of a flat Earth with parallel longitude lines. Then the "central" location will be the weighted average of the latitude and longitude coordinates.
(a)Total population is 16000 +22000 +36500 = 74,500. For purposes of the arithmetic, we will subtract 43 from latitude and 70 from longitude, then multiply each fraction by 10. Similarly, we will divide each population by 1000.
The weighted average location is found from ...
(16/74.5)(6.769, 3.717) +(22/74.5)(5.781, 3.222) +(36.5/74.5)(6.795, 4.447)
= (1.4537, 0.7983) +(1.7071, 0.9515) +(3.3291, 2.1787) = (6.490, 3.928)
The center of gravity is about 43.6490°N, 70.3928°W.
__
(b)The coordinate differences from the center of gravity are (in (°lat, °long)) ...
Baker's Field: (0.0294, -0.0101)
Lonesome Acres: (-0.1371, -.0072)
Clearly, Baker's field is closer to the site of part (a).
_____
Additional comment
Distance calculations could be refined further by considering that a degree of longitude at this latitude represents about 0.72 times the distance of a degree of latitude. In this problem, the location of Lonesome Acres has a latitude difference that is several times any of the other coordinate differences, so it is clearly much farther away from the desired location.
The calculations done here are a sort of first-level approximation. The least-significant digits in the coordinates represent a distance of less than 50 feet. If you really want accuracy to that level, then the (approximately) spherical shape of the Earth needs to be accounted for. As a second-level approximation, some reference point needs to be identified, and coordinates in miles (or feet) need to be expressed in relation to that reference. The best accuracy would be obtained using spherical trigonometry to identify the distances.
We expect any school that is constructed to be somewhat larger than 50 feet in any direction, so accuracy to the 4th decimal place in these locations is probably not required--except to satisfy some answer-checker.
Can someone help me?help me please
Answers
Answer:
10 tomatoes (bottom fruit) - 9 kiwis (top fruit) = 1 tomato
10-9=1
Step-by-step explanation:
Which side lengths form a right triangle?
Choose all answers that apply
(Choice A)
A
3
,
27
,
6
3,
27
,63, comma, square root of, 27, end square root, comma, 6
(Choice B)
B
8
,
15
,
17
8,15,178, comma, 15, comma, 17
(Choice C)
C
Answers
Answer:
4, 7.5, 8.54,7.5,8.5
Step-by-step explanation:
We can use the Pythagorean Theorem to see if the side lengths will form a right triangle.
The equation for the Pythagorean Theorem is
a^2 + b^2 = c^2a
2
+b
2
=c
2
a, squared, plus, b, squared, equals, c, squared
where aaa and bbb are the lengths of the two legs of the triangle, and ccc is the length of the hypotenuse.
[How can I tell which side is the hypotenuse?]
Hint #22 / 5
Let's check each set of numbers:
\begin{aligned} a^2 + b^2 &= c^2 \\\\ 4^2 +\sqrt8^2 &\stackrel{\large?}{=} 24^2 \\\\ 16 + 8&\stackrel{\large?}{=} 576\\\\ 24&\neq 576\\\\ \end{aligned}
a
2
+b
2
4
2
+
8
2
16+8
24
=c
2
=
?
24
2
=
?
576
=576
The side lengths 4, \sqrt8, 244,
8
,244, comma, square root of, 8, end square root, comma, 24 do not form a right triangle.
Hint #33 / 5
\begin{aligned} a^2 + b^2 &= c^2 \\\\ 5^2 + 5^2 &\stackrel{\large?}{=} 5^2 \\\\ 25+ 25&\stackrel{\large?}{=} 25\\\\ 50&\neq 25\\\\ \end{aligned}
a
2
+b
2
5
2
+5
2
25+25
50
=c
2
=
?
5
2
=
?
25
=25
The side lengths 5, 5, 55,5,55, comma, 5, comma, 5 do not form a right triangle.
Hint #44 / 5
\begin{aligned} a^2 + b^2 &= c^2 \\\\ 4^2 + 7.5^2 &\stackrel{\large?}{=} 8.5^2 \\\\ 16+ 56.25&\stackrel{\large?}{=} 72.25\\\\ 72.25&\stackrel{\checkmark}{=} 72.25\\\\ \end{aligned}
a
2
+b
2
4
2
+7.5
2
16+56.25
72.25
=c
2
=
?
8.5
2
=
?
72.25
=
✓
72.25
Answer:
4, 7.5, 8.5
Step-by-step explanation:
I had this question on Khan, and it was right (:
What is the diameter of a circle with the equation x2 + y2 - 8x + 2y - 8 = 0?
5 units
6 units
9 units
10 units
Answers
Answer:
Diameter is 10 units
Step-by-step explanation:
Convert standard form to general form by completing the square:
[tex]x^2+y^2-8x+2y-8=0[/tex]
[tex]x^2-8x+y^2+2y-8=0[/tex]
[tex]x^2-8x+y^2+2y=8[/tex]
[tex]x^2-8x+16+y^2+2y+1=8+16+1[/tex]
[tex](x-4)^2+(y+1)^2=25[/tex]
[tex](x-4)^2+(y+1)^2=5^2[/tex]
So, since the radius of the circle is 5 units, then the diameter is twice the radius, which is 10 units.
Answer:
50
Step-by-step explanation:
x2 + y2 - 8x + 2y - 8 = 0
first we find the radius with the equation.
write the equation in standard form.
x2 + y2 - 8x + 2y - 8 = 0
(x-4)^2 + (y+1)^2 = 25
(x-h)² + (y-k)² = r²
this means 25 is the radius and the diameter is two times the radius so,
25 x 2 = 50
Enter the number that belongs in the green box
Answers
Answer:
72°
Step-by-step explanation:
The diagonals of a parallelogram intersect at a point that forms the center of symmetry of the parallelogram.
Camry has 612 photos she needs to put
into albums. If each album holds 36
pictures, how many albums will it take
to hold all the photos?
Answers
Answer:
36 = 1
612 =?
(612×1)
----------
36
=17
How to solve 12 2/3 23
Answers
Answer: I dont understand the question
Step-by-step explanation:
I need help on this question as soon as possible. If anybody can give me the correct answer I’ll give brainly. I just need help. This is my 2nd question and there is 11 questions
Answers
Answer:
The solution of the system is (6, 9).
Step-by-step explanation:
Solve one of the variables and substitute the answer for the other variable.
Select one of the problems and solve for x.
3x+y=27
Subtract y from both sides.
3x+-y=27
Divide both sides by three.
x=1/3(-y + 27)
Multiply 1/3 by -y + 27.
x = -1/3y + 9
Replace -y/3 + 9 for x in the other problem 3x-2y=0.
3(-1/3y + 9) - 2y = 0
Multiply 3 by -y/3 + 9.
−y+27−2y=0
Add -y to -2y.
−3y+27=0
Subtract 27 from both sides of the problem.
−3y=−27
Divide both sides by −3.
y=9
Replace 9 for y in x=−1/3y+9.
x=−1/3*9+9
Multiply −1/3 times 9.
x=-3+9
Add 9 to -3.
x = 6.
x = 6, y = 9.
Subtract 38¢ from $5.60. Include the dollar sign and no spaces in your answer.
Answers
Answer:
5.22
Step-by-step explanation:
Answer:
its easy, just subtract 50 - 38 = 22 so its $5.60
(your welcome and math makes me notalisgica :) )
Step-by-step explanation:
What is correct answer For this problem
The table shows how the length of a fish changes over time.
Which equation represents the relationship between x, the time in years, and y, the length in centimeters?
Question options:
x = 4.5y
x = 9y
y = 4.5x
y = 9x
Answers
Answer:
C. y=4.5x
Step-by-step explanation:
divide y by x
The graph shows the relationship between time
and the number of soda bottles a machine can
make. Use the points (2,48) and (7,168) to find
the number of soda bottles the machine can make
each minute.
Answers
Answer:
24
Step-by-step explanation:
The number of soda bottles the machine can make each minute is the unit rate, slope. To find slope using those two points, use the formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Identify the points: (2,48) (7,168)
[tex]y_2=168[/tex]
[tex]y_1=48[/tex]
[tex]x_2=7[/tex]
[tex]x_1=2[/tex]
Plug these into the formula then solve:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\frac{168-48}{7-2}[/tex]
[tex]=\frac{120}{5}[/tex]
[tex]=24[/tex]
The slope is 24, and therefore the unit rate. Hence, the machine can make 24 soda bottles each minute.
Simple way
Where you see the point at 48 and 2, it means [tex]\frac{48}{2}[/tex]. So divide
48 ÷ 2 = 24.
9 x 6 and explenation will win a brainliest
Answers
Answer:
54
Step-by-step explanation:
9 = 3 x 3
6 = 3 x 2
9 x 6
= 3 x 3 x 3 x 2
= 54
Answer:
54
Step-by-step explanation:
9+9+9+9+9+9 = 54
Hope that helps. Can i have the brainliest :)
Arthur is saving money to buy a used car in 8 months. The car costs $2,180. Arthur plans to start with an initial deposit and then deposit 25% more than the previous month until he has enough money to buy the car. What is the minimum initial deposit Arthur must make? Round to the nearest whole dollar.
Answers
The minimum initial deposit Arthur must make is $ 4.24.
Since Arthur is saving money to buy a used car in 8 months, and the car costs $ 2,180, and Arthur plans to start with an initial deposit and then deposit 25% more than the previous month until he has enough money to buy the car, to determine what is the minimum initial deposit Arthur must make the following calculation should be performed:
X x 1.25 x 1.56 x 1.95 x 2.44 x 3.05 x 3.81 x 4.76 = 2180 514.10X = 2180 X = 2180 / 514.10 X = 4.24
Therefore, the minimum initial deposit Arthur must make is $ 4.24.
Learn more about maths in https://brainly.com/question/25749130
