Answer: A= 8
B= False
C= False
D= True
Step-by-step explanation:
COME ON ITS 1 QUESTION FOR 50 POINTS!
If you have a cubic polynomial of the form y = ax^3 + bx^2 + cx + d and lets say it passes through the points (2,28), (-1, -5), (4, 220), and (-2, -20) what would the coefficients a, b, c, and d equal? So confused, I'd greatly appreciate help! Thank you!
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]
HELP ME PLZ ASAP!!!!!
Answer:
x=30, A=132
Step-by-step explanation:
These 2 angels are alternate interior angles so they are equal
5x-18=3x+42
Solve.
2x=60
x=30
Now substitute x into angle A
A=150-18
A=132
Answer:
The variable X should be 30.
Step-by-step explanation:
∠132=5(30)-18° = ∠132=3(30)+42°
find the surface area of this cube
Answer: 150
Step-by-step explanation: Area = 6a^ this is the formula for surface area
The substitute Area = 6 * 25
then multiply Area = 150
hope this helps mark me brainlist if it did hope you have a great day
Answer:
150 cm²
Step-by-step explanation:
bottom: 25cm
top: 25cm
right: 25cm
left: 25cm
front: 25cm
back: 25cm
25+25+25+25+25+25=150cm²
x ≥ 63.4
x ≤ 96.6
x ≤ 63.4
x ≥96.6
Answer:
x ≤ 63.4
Step-by-step explanation:
.25x+4.15 ≤20
Subtract 4.15 from each side
.25x +4.15 -4.15 ≤ 20-4.15
.25x ≤ 15.85
Divide each side by 15.85
.25x/.25 ≤ 15.85/.25
x ≤ 63.4
I need help uwuwuwuwuwuauauuwuwuauaua
The answer is B
35+50+35+20=140
175-140= 35
5. The length of a rectangle is 5 inches greater than the width.
Question
Answer
a. Write an expression for the width of the rectangle.
b. Write an expression for the length of the rectangle.
multiply
Answer:
see below
Step-by-step explanation:
Let w = width
L = length = w+5
The area is l*w
A = (w+5)*w
A = w^2 +5w
My teacher will give me a f if I don’t do this can somebody help me
Answer:
good luck
have a good day - be safe - and healthy too
find the value of 4^7/4^9
A.-16
B.1/16
C.1/8
D.8
Answer:
B. 1/16
Step-by-step explanation:
[tex] \frac{ {4}^{7} }{ {4}^{9} } = {4}^{7} \div {4}^{9} = {4}^{(7 - 9)} \\ = {4}^{ - 2} = \frac{1}{ {4}^{2} } = \frac{1}{4 \times 4} = \frac{1}{16} [/tex]
The answer is 1/16, option B
Answer:
[tex]\tt{} \frac{1}{16} [/tex]
Step-by-step explanation:
[tex]\tt{} \frac{ {4 }^{7} }{ {4}^{9} }[/tex]
[tex] \tt{} \frac{1}{ {4}^{(9 - 7)} } \\ \\ \tt{} \frac{1}{ {4}^{2} } \: \: \: \: \: \: \: \: \: [/tex]
[tex] \tt{} \frac{1}{4 \times 4} \\ \\ \tt{} \frac{1}{16} \: \: \: \: \: \: [/tex]
Below are two truths and one lie, choose the lie.
Answer:
The horizontal asymptote is x-axis
Step-by-step explanation:
The horizontal asymptote is the y axis not x axis
Which equation best represents the data given in the table ?
Answer:
B
Step-by-step explanation:
The equation that satisfies the above table is y = 8[tex](\frac{1}{2})^{x}[/tex]
Given,
Table between x and y .
Here,
To get the equation between x and y first justify the data given in the table.
So,
When,
x = -3 , y = 64
x = -2 , y = 32 .
In the equation y = 8[tex](\frac{1}{2})^{x}[/tex] substitute the values of x and check for y .
Put x = -3 ,
y = 8[tex](1/2)^{-3}[/tex]
y = 8 * 8
y = 64
Thus it satisfies the value given in the table .
So the correct equation will be Option B .
Know more about equations,
https://brainly.com/question/14686792
#SPJ2
What is the maximum of f(x) = sin(x)?
- 2π
-1
01
2π
Answer:
1
Step-by-step explanation:
The maximum value of sin(x) is 1.
When x = 90 degrees sinx = 1.
Lines A and B are parallel lines cut by a transversal. Find the value of x.
Answer:12.33333333333
Step-by-step explanation:
8x - 2 = 14x - 76
74 = 6x
12.333 = x
The required value of the x is 13 in the measures of the angle.
Given that,
Line A and B are parallel lines and intersect by a transversal line.
A line can be defined by the shortest distance between two points is called a line.
What are parallel lines?Parallel lines are defined as the line on which the corresponding points are equidistant throughout the line
Here,
If a pair of parallel lines intersect by the transversal line then their corresponding angles are equal in measure,
Thus,
8x + 2 = 14x - 76
6x = 78
x = 78 / 6
x = 13
Thus, the required value of the x is 13 in the measures of the angle.
Learn more about lines here:
brainly.com/question/2696693
#SPJ2
!!15p!!
Which statement explains how to calculate the mean of a set of data?
A
Subtract the smallest from the largest value.
B. Add the largest and the smallest values and divide by 2.
C. Find the sum of all the values and then divide by the number of values.
D. Organize the data from least to greatest and find the value in the middle.
E Organize the data from least to greatest and identify which value is repeated the most often.
Answer:
C
Step-by-step explanation:
Mean is just another name for average. To find the mean of a data set, add all the values together and divide by the number of values in the set. The result is your mean!
Solve this for me please
is there a picture to this??
The radius of the earth is 3959 miles. A meteor with a diameter of 750 miles strikes the earth in an unpopulated area. What percent of the earths surface is affected by the meteor strike? Is it a 36% be 0.9% C9% or D3.6%
Answer:
B. 0.9%
Step-by-step explanation:
If the diameter of the meteor is 750 miles, then its radius is 750/2 = 375 miles
The radius of the earth is 3959 miles
Assuming that both bodies are spherical, their surface are:
meteor's surface: π*r² = π*375² = 441786.467 miles²
Earth's surface: π*3959² = 49240321.1 miles²
If 49240321.1 miles² represents 100% then 441786.467 miles² represents:
49240321.1 miles² / 100% = 441786.467 miles² / x%
x = 441786.467/49240321.1*100
x = 0.9%
Answer:
B) 0.9%
Step-by-step explanation:
10 points need help asap
Answer:
D
Step-by-step explanation:
Mark placed a pool in his backyard, which is enclosed by a triangular fence. The radius of the pool is 20.5 feet.
Answer:
A. 3,864 ft²
B. 1,319.585 ft²
C. 2,544.415 ft²
Step-by-step explanation:
Area of triangle:
½ × 92 × 84
3864 ft²
Area of circle:
pi × r²
3.14 × 20.5²
1319.585 ft²
Difference:
3864 - 1319.585
2544.415 ft²
Solve 5(g-2)+g=6(g-4
Answer:
g = -13
Step-by-step explanation:
5(g-2)+g=6(g-4)
5g - 10 + g = 6g - 24
5g + g - 6g = -24 + 10
6g - 6g = -13
g = -13
A line passes through the points (4, -1) and (2,3). What is the slope of the line?
Answer:
-2
Step-by-step explanation:
image attached!
Will give brainliest answer
Answer
Step-by-step explanation:
To find the area of a shape multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.
please mark me as brainliest.
Answer:
[tex]7 units^2[/tex]
Step-by-step explanation:
You can split this irregular shape into a square and a trapezoid.
The formula for a square is:
[tex]A=lw[/tex]
The formula for a right trapezoid:
[tex]A=\frac{1}{2} (h)(a+b)[/tex]
Area of square:
[tex]A=(2)(2)\\A=4[/tex]
Area of right trapezoid:
[tex]A=\frac{1}{2} (2)(1+2)\\A=3[/tex]
Add up the individual areas to find the overall:
4 + 3 = 7
this box holds cereal. how many cubic inches of cereal can it hold the size of the box is 6 in,2 in,12 in
PLEASE HELP!!!
How many cubes with side lengths of 1/2 cm does it take to fill the prism?
Answer:
I think the answer is 3. Im not fully sure/
Step-by-step explanation:
A friend bought 2 boxes of pencils and 8 notebooks for school, and it cost him $11. He went back to the store the same day to buy supplies for his younger brother. He spent $11.25 on 3 boxes of pencils and 5 notenooks. How much would 9 notebooks cost?
Answer:
9 notebooks would cost $6.75
Step-by-step explanation:
How I solved this problem was by taking the data and writing it out first.
During one trip, he got 2 boxes of pencils and 8 notebooks for $11.00
During the second trip, he got 3 boxes of pencils and 5 notebooks for $11.25
This led me to believe that the boxes were definitely more expensive than the notebooks, as there were many notebooks bought during the first trip, yet that trip was cheaper than the second. So, by the process of elimination, I started off the value of the notebooks to be $0.50, and the boxes of pencils to be $3.00, and I continued to experiment with values until I found two values that would work in both scenarios, the values being $2.50 for a box of pencils, and $0.75 for a notebook. (I know there's likely an easier way of doing this, but I haven't done a problem like this in a while, and this method works just fine. It's just a bit more time consuming.)
1st Case: 2(2.50) + 8(0.75) = 11
2 times 2.50 equals 5, and 8 times 0.75 equals 6. 5 added to 6 gives you a sum of 11.
2nd Case: 3(2.50) + 5(0.75) = 11.25
3 times 2.50 equals 7.50, and 5 times 0.75 equals 3.75. 7.50 added to 3.75 gives you a sum of 11.25
Now that it is known how much each notebook costs ($0.75), you would take that value and multiply it by 9, since you're wanting to know how many 9 would cost, and this gives you a product of $6.75.
I hope this helps :)
Answer:
it would cost £6.75
Step-by-step explanation:
Event A: stops on red
Event B: stops on yellow
Find P(A or B)
A.) 1/4
B.) 1/8
C.) 1/2
D.) 1/16
Answer:it is 1/2
Hopefully this helps
Answer:
Event A: stops on red
Event B: stops on yellow
Find P(A or B)
1/2
Both perpendicular lines and parallel lines must
A
never meet.
В
meet at right angles.
C
exist on the same plane.
D
be curved in the same place.
Answer:
A.) Never meet.
Step-by-step explanation:
It’s A they never meet
Which descriptions are true of the function shown in the table? Check all that apply.
quadratic
linear
exponential
y = 3x + 3.2
y = 3x2
y = 3.2x
Answer:B & F
Step-by-step explanation:
On edge
How to solve a system of equation using a graph?
Answer:
The solution of such a system is the ordered pair that is a solution to both equations. To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect.
Step-by-step explanation:
Help I will mark BRAINLIEST if correct please help
Answer:
[tex](-\frac{1}{4}, \frac{5}{8} )[/tex]
Step-by-step explanation:
If you label the points on the axes, it will show that point K is actually on [tex]\frac{5}{8}[/tex] not [tex]\frac{3}{4}[/tex]
Help please !!! Meg correctly solves 4680 divided by 40. Enter numbers in the boxes to show the equations she could use to solve the problem.
(4000 divide )+ (600 divide
+ (80 divide)
What is 4680 divided by 40
Enter the answer in the box.
Answer:
117
Step-by-step explanation:
Here, we have to find the result when 4680 is divided by 40.
Meg wants to simplify the process of division here.
We know that 4680 can be written as 4000 + 600 + 80.
So,
[tex]4680 \div 40 = (4000 \div 40) + (600\div 40) + (80\div 40)\\\\\Rightarrow 100 + 15 + 2\\\Rightarrow 117[/tex]
This method makes division very easy if we have to find results of division for large numbers. This example is an illustration of the same.
Please refer to image attached for results.
Hence, Meg gets the result as 117.
Find the area. Will mark brainliest.
Step-by-step explanation:
Area of the parallelogram=bh
b=20cm
h=12cm
Area=12*20=240cm²