Answer:
a = 3
b = 2
c = 0
d = -4
Step-by-step explanation:
Form 4 equations and solve simultaneously
28 = a(2)³ + b(2)² + c(2) + d
28 = 8a + 4b + 2c + d (1)
-5 = -a + b - c + d (2)
220 = 64a + 16b + 4c + d (3)
-20 = -8a + 4b - 2c + d (4)
(1) + (4)
28 = 8a + 4b + 2c + d
-20 = -8a + 4b - 2c + d
8 = 8b + 2d
d = 4 - 4b
Equation (2)
c = -a + b + d + 5
c = -a + b + 4 - 4b+ 5
c = -a - 3b + 9
28 = 8a + 4b + 2c + d (1)
28 = 8a + 4b + 2(-a - 3b + 9) + 4 - 4b
28 = 6a - 6b + 22
6a - 6b = 6
a - b = 1
a = b + 1
220 = 64a + 16b + 4c + d (3)
220 = 64(b + 1) + 16b + 4(-b - 1 - 3b + 9) + 4 - 4b
220 = 60b + 100
60b = 120
b = 2
a = 2 + 1
a = 3
c = -3 - 3(2) + 9
c = 0
d = 4 - 4(2)
d = -4
Step-by-step explanation:
Step 1: Solve using the first point
(2, 28)
[tex]28 = a(2)^3 + b(2)^2 + c(2) + d[/tex]
[tex]28 = 8a + 4b + 2c + d[/tex]
Step 2: Solve using the second point
(-1, -5)
[tex]-5 = a(-1)^3 + b(-1)^2 + c(-1) + d[/tex]
[tex]-5 = -a + b - c + d[/tex]
Step 3: Solve using the third point
(4, 220)
[tex]220 = a(4)^3 + b(4)^2 + c(4) + d[/tex]
[tex]220 = 64a + 16b + 4c + d[/tex]
Step 4: Solve using the fourth point
(-2, -20)
[tex]-20 = a(-2)^3 + b(-2)^2 + c(-2) + d[/tex]
[tex]-20 = -8a + 4b - 2c + d[/tex]
Step 5: Combine the first and fourth equations
[tex]28 - 20 = 8a - 8a + 4b + 4b + 2c - 2c + d + d[/tex]
[tex]8 = 8b + 2d[/tex]
[tex]8 - 8b = 8b - 8b + 2d[/tex]
[tex](8 -8b)/2 = 2d/2[/tex]
[tex]4 - 4b = d[/tex]
Step 6: Solve for c in the second equation
[tex]-5 + 5 = -a + b - c + d + 5[/tex]
[tex]0 + c = -a + b - c + c + d + 5[/tex]
[tex]c = -a + b + d + 5[/tex]
Step 7: Substitute d with the stuff we got in step 5
[tex]c = -a + b + (4 - 4b) + 5[/tex]
[tex]c = -a + b + 4 - 4b + 5[/tex]
[tex]c = -a - 3b + 9[/tex]
Step 8: Substitute d and c into the first equation
[tex]28 = 8a + 4b + 2(-a - 3b + 9) + (4 - 4b)[/tex]
[tex]28 = 8a + 4b - 2a - 6b + 18 + 4 - 4b[/tex]
[tex]28 - 22 = 6a - 6b + 22 - 22[/tex]
[tex]6 / 6 = (6a - 6b) / 6[/tex]
[tex]1 + b = a - b + b[/tex]
[tex]1 + b = a[/tex]
Step 9: Substitute a, b, and c into the third equation
[tex]220 = 64(1 + b) + 16b + 4(-(1 + b) - 3b + 9) + (4 - 4b)[/tex]
[tex]220 = 64 + 64b + 16b + 4(-1 - b - 3b + 9) + 4 - 4b[/tex]
[tex]220 - 100 = 60b + 100 - 100[/tex]
[tex]120 / 60 = 60b / 60[/tex]
[tex]2 = b[/tex]
Step 10: Find a using b = 2
[tex]a = b + 1[/tex]
[tex]a = (2) + 1[/tex]
[tex]a = 3[/tex]
Step 11: Find c using a = 3 and b = 2
[tex]c = -a - 3b + 9[/tex]
[tex]c = -(3) - 3(2) + 9[/tex]
[tex]c = -3 - 6 + 9[/tex]
[tex]c = 0[/tex]
Step 12: Find d using b = 2
[tex]d = 4 - 4b[/tex]
[tex]d = 4 - 4(2)[/tex]
[tex]d = 4 - 8[/tex]
[tex]d = -4[/tex]
Answer: [tex]a = 3, b = 2, c = 0,d = -4[/tex]
Find the volume of the cone whoever answers first gets brainiest!
Answer:
Exact Form: 6 π
Decimal Form: 18.8495559
Step-by-step explanation:
Answer: V= 1/3πr^2*h
Step-by-step explanation:
. A cone has a radius (r) and a height (h)
V= 1/3*base*h
and the base is πr^2
Nathan is buying a camera that regularly
costs $400.00. It is on sale for 25% off. If
the tax rate is 10%, what is the final cost
of the GoPro?
If a cross section was cut that was parallel to the base of a triangular prism below a shape with that cross section be ?
A. Square
B. Triangle
C. Parallelogram
D. Rectangle
57:43
Which scatterplot shows the strongest negative linear association?
Answer:
Its the third one i just took the test but it'd be helpful for others if you put the answer choices.
Step-by-step explanation:
Answer:
D or the graph pictures below
Step-by-step explanation:
edg2021
It can't be A or B because those are positive. D is strongest because it is clusters closest together and there is a more definitive line.
Select the correct answer from the drop-down menu.
Find the polynomial.
2(3y − 1)(y − 3) is the factored form of .
Answer:
6y² - 20y + 6
Step-by-step explanation:
Use FOIL method
(3y - 1)(y-3) = 3y*y + 3y*(-3) + (-1)*y + (-1)*(-3)
= 3y²- 9y - y + 3 {add the like terms}
= 3y² - 10y + 3
2(3y - 1)(y - 3) = 2 ( 3y² - 10y + 3)
= 2*3y² - 2*10y + 2*3
= 6y² - 20y + 6
multiply. write the result in scientific notation. (2.3x10^1)(7x10^6)
[tex] (2.3 \times 10^1) \times (7 \times 10^6)[/tex]
[tex](2.3 \times 7) \times (1 {0}^{1} \times {10}^{6} )[/tex]
[tex]16.1 \times {10}^{1 + 6} [/tex]
[tex]16.1 \times {10}^{7} [/tex]
The product of the given numbers is 1.61 × 10⁸.
What is meant by Scientific Notation?Scientific notation is a way of writing a large number or small number with many digits in a simpler form using the power of 10.
For example, 30,000 can be written as 3 × 10⁴.
Given that,
We have to multiply the numbers (2.3 x 10¹) (7 x 10⁶).
The numbers in scientific notation uses exponents.
So we have to use the product rule of exponents here.
(2.3 x 10¹) (7 x 10⁶) = (2.3 × 7) × (10¹ x 10⁶)
= 16.1 × (10¹ x 10⁶)
We have the product rule, xᵃ . xᵇ = xᵃ⁺ᵇ
So the product is,
(2.3 x 10¹) (7 x 10⁶) = 16.1 × (10¹⁺⁶)
= 16.1 × 10⁷
= 1.61 × 10⁸
Hence the product in scientific notation is 1.61 × 10⁸.
Learn more about Scientific Notation here :
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Select ALL the correct answers.
Select all the expressions that will include a remainder.
2112
251 - 4
31 + 4
(65x – 26) = -13%
-1512 + 45 + 96
31 – 8
-1212 + 281 + 48
3.12 - 71 + 12
(-78r2 + 12x) = 6x
HELP
Answer:
All the expressions that will include a remainder:
65x – 26 = -13%
3.12 - 71 + 12
(-78r2 + 12x) = 6x
Step-by-step explanation:
If you calculate all the answers, you only get a remainder with the following three:
65x – 26 = -13%
65x = 26 - 0.13
x = 25.87 / 65
x = 0.398
So this expressdion includes a remainder.
3.12 - 71 + 12
= -55.88
So this expressdion includes a remainder.
(-78r2 + 12x) = 6x
12x - 6x = 78r2
6x = 78r2
x = (78r2)/6
So this expressdion includes a remainder.
The mathematics department of a college has 6 male professors, 12 female professors, 10 male teaching assistants, and 9
female teaching assistants. If a person is selected at random from the group, find the probability that the selected person
is a teaching assistant or a female.
Answer: 19/37 or 21/37
Step-by-step explanation:
6 + 12+ 10+9= 37
There are 10 male teaching assistants and 9 female teaching assistants so in total there are 19 teachings assistants.
so the probability that a selected person is a teaching assistant is 19/37
or if they are female it will be 12 + 9 because there are 12 female professors and 9 female teaching assistants.
12+9= 21/37
Which equation represents the relationship shown in the table?
Answer:
y=x+1.5
Step-by-step explanation:
Y is always 1.5 more than x.
Find the volume of this cylinder. Give your answer to 1 decimal place when the radius is 11 cm and the length is 14 cm
Answer:
5324
Step-by-step explanation:
volume of cylinder=πr^2l=22/7×11^2×14=5324
Which of these groups of values plugged into the TVM Solver of a graphing calculator will return the amount of a 20-year loan with an APR of 19.2%, compounded monthly, that is paid off with monthly payments of $510? site:brainly.com
Answer:
my answer was B.
Step-by-step explanation:
I chose C and i got it wrong
HERE IS THE WHOLE THING FOR 50 PTS
START AT THE RED BOX AND NAVIGATE TO THE END BOX
THANK YOU SO MUCH
YOU'RE THE BRAINLIEST :)
Answer:
Step-by-step explanation:
there iss no photo :<
The change in the x-coordinates of any two points on a line in the xy-plane is
the______
A. rise
B. slope
C. angle
D. run
Answer:
D. run
Step-by-step explanation:
The slope is given by
m = (y2-y1)/ (x2-x1) = rise/ run
The change in the x coordinates is the run
The expression 10x + 25 can represent the area of the figure below. Which answer choice shows this expression when factored correctly?
Pls help!
Answer:
the correct answer would be 5(2x+5)
Step-by-step explanation:
Find the greatest common factor to divide the two numbers by. That would be 5.Divide the two numbers by 5 and then put the five outside some parenthesis. 5(2x+5). And then there you have it. That's the answer.what is 10 1/3 x 1/4? that is, what is ten and one third times one fourth?
answer
2 1/2
2 1/12
10 1/12
2 7/12
Answer:
[tex]2[/tex] [tex]\frac{7}{12}[/tex]
Step-by-step explanation:
1) Make the first term an improper fraction
10 1/3 = [tex]\frac{31}{3}[/tex]
2) Multiply
[tex]\frac{31}{3}[/tex] × [tex]\frac{1}{4\\ }[/tex]
When multiplying fractions, multiply the numerators together and the denominators together. This leaves you with....
[tex]\frac{31}{12}[/tex]
3) Convert back into a mixed fraction
[tex]\frac{31}{12}[/tex] = [tex]2[/tex] [tex]\frac{7}{12}[/tex]
I hope this helps!
Does the function model exponential growth or decay?
h(t) = 0.25 - 1.5t
A.) growth
B.) decay
Answer: it’s growth
Step-by-step explanation:
At A-1 Truck Dealership, a customer can order a red, turquoise, or green truck. The truck can have leather or cloth seats. A customer can also choose a black, tan, or grey interior color. From how many possible trucks can a customer choose? *
Answer:18 ways
Step-by-step explanation:
Given
There are three color available for truck i.e. red, turquoise and green
Truck can have leather or cloth seats
Also there are 3 color available for interior
So no of ways in which a customer can choose a truck is
[tex]=3\times 2\times 3[/tex]
[tex]=18\ ways[/tex]
What are m<1 and m<2?
Answer:
m<2 is 66 and m<1 is 114
Step-by-step explanation:
add the given angles together, that is the outaide angle. then subtract that from 180 and you get angle 2
A student spent 4/7 of an hour each evening reading a book about whales if it took the student 9 evenings to finish the book how many hours in all did the student spend reading
5 1/7 6 1/7 5 2/7
Answer:
5 1/7
Step-by-step explanation:
Look at the attachment
Suzy is shopping at a book sale. The table shows prices for paperbacks.
A two-column table with 3 rows. Column 1 is labeled Books (x) with entries 4, 6, 8. Column 2 is labeled Cost (y) with entries 6, 9, 12.
These points are graphed. Notice the pattern of the points. What is the rate?
The cost is $
for every 2 books.
Answer:
3 bucks
Step-by-step explanation:
The rate of change is 2 and the cost of two books is $3.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + C = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
Given, Suzy is shopping at a book sale. The table shows prices for paperbacks.
The points are, (4, 6), (6, 8), and (8, 12).
Slope(m) = (12 - 8)/(8 - 6).
Slope(m) = 4/2.
Slope(m) = 2.
Now, 4 books cost $6, hence 2 books cost $3.
learn more about lines and slopes here :
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What factors do 6 and 12 have in common?
Answer:
6x^2 im pretty sure thats whats its asking for
Step-by-step explanation:
The three friends drove to a park that had batting cages and pitching machines that tossed the balls to the batter automatically. Rameck took his place, ready to bat. "Keep your hands together," George shouted from the other side of the fence. "Bend your knees a little," Sampson offered. "I've watched the Yankees for years," Rameck said, ignoring both of them. "Baseball is easy!” The machine pitched the first ball. Rameck swung with a powerful twist. He missed. The second ball erupted from the machine. Rameck swung again. He missed it by a mile. A third ball came. He swung and missed that one, too. The balls kept coming. Rameck kept swinging. And missing. —We Beat the Street, Sampson Davis et al, Using the drop-down menus, identify the correct sequence of events. First: Second: Third:
Answer:
first B,second A, third C on edg
Step-by-step explanation:
Answer:
answer is D
Step-by-step explanation:
Which of the following rational function is graphed below?
Which expression is equivalent to x^−4 ?
See picture for answer and the work involved!
Answer:
I don't see any choices. But if I had to simplify, it would be 1/x^4
Since the exponent is a negative, you have to put the whole variable along with the exponent under 1.
Step-by-step explanation:
The angle 01 is located in Quadrant III, and cos(01) = -30/13
What is the value of sin(01)
Answer:
sin(01) = -32.70/13Step-by-step explanation:
Given cos(01) = -30/13 where angle 01 is located in quadrant III. In the third quadrant, both cos and sin are negative. only tan is positive.
To calculate sin(01), we will apply the trigonometry expression as shown below;
cos(01) = -30/13
According to SOH CAH TOA;
cos(01) = adjacent/hypotenuse = -30/13
sin(01) = opposite/ hypotenuse
To get the hypotenuse, we will use the pythagoras theorem
[tex]hyp^{2}=opp^{2}+adj^{2} \\opp^{2}= hyp^{2}-adj^{2}\\opp^{2}= 13^{2} -(-30^{2} )\\opp^{2} = 169+900\\opp^{2}=1069\\opp = \sqrt{1069} \\opp = 32.70\\[/tex]
sin(01) = 32.70/13
Since sin is also negaitve in the third quadrant, the value of
sin(01) = -32.70/13
[tex]01 = cos^{-1}- 30/13[/tex]
Aubrey is making cone-shaped hats for a birthday party. She mistakenly thinks that she will need about 104 square inches of paper for each hat.
Answer:
I dont know
Step-by-step explanation:
I dont know sorry
Answer:
70
Step-by-step explanation:
That’s the question?
Answer:
Domain: [0, 6]
Step-by-step explanation:
There's a rising slope between 0 and 6 and then it's decreasing for the rest.
I hope this helped and have a good rest of your day!
Translate the statement into an equation. Then solve the equation.
The sum of 8 and 3 times a number is 23.
3x - 8 = 23; 5
8+ 3x = 23,5
3x = 8+23; 10
(8 + 3)x = 23; 2
what is the simplify rational expression for 10b + 100
________
b + 10
Answer:
10 (b+10)
Step-by-step explanation:
10b + 100
Factor out a 10
10 *b + 10*10
10 (b+10)
Answer:
Step-by-step explanation:
10b + 100 = 10b +10*10
= 10(b + 10)
Someone please explain these questions
Answer: You find it by using slope
Step-by-step explanation
If the graph is rising from left to right, like climbing a hill, the slope is positive (on a graph, you could count up y units divided by right x units). If it is going down from left to right (like sliding down a hill), the slope is negative (on a graph you have to count down y units and right x units).
ex: y = 5x + 3 is an example of the Slope Intercept Form and represents the equation of a line with a slope of 5 and and a y-intercept of 3. y = −2x + 6 represents the equation of a line with a slope of −2 and and a y-intercept of 6.
