Answer:
x=5 and x=15
Step-by-step explanation:
3x^2-60x+225=0
3x^2-60x+225/3=0/3
x^2-20x+75=0
x^2-5x-15x+75=0
x(x-5)-15(x-5)=0
(x-5)(x-15)=0
x-5=0 x-15=0
x=5 x=15
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!
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]
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
|5−4r|=17
Can someone answer this question for me?? I will mark you brainliest if you get the correct answer!!
Answer:
R=-3 which is the same thing as 11/2
Step-by-step explanation:
Answer:
r=−3,11/2
Step-by-step explanation:
thats what I got
Writing What is the diameter of a circle with a circumference of 11.277 ft? Use pencil and paper.
The diameter is
ft.
I hope this helps you
What is the mode of 4, 9, 9, 9, 4, 6, 6, 6, 9?
Answer:
9
Step-by-step explanation:
That's the most common number there
Answer:
9
Step-by-step explanation:
The mode of a set of data values is the value that appears most often.
in this set, 9 appears 4 times -> 9 is mode
X = ________ ft. (No guessing please)
Answer:
x=12
Step-by-step explanation:
12(x+8)= 8(30)
Distribute
12x+ 96= 240
Subtract 96 on both sides
12x= 144
Divide 12 on both sides
x=12
Explain how to use a graph of the function f(x) to
find f(3).
Answer:
For f(3), the input is 3 and you are looking for the output. To determine the function's value when x = 3, go to the value of 3 on the x-axis and then locate the graph for that value of x. Determine the value of y from the y-axis at that location on the graph.
Step-by-step explanation:
up there
Frank will paint a wall that measures 10 feet by 14 feet what is the area of the wall that frank will paint
Answer:
140 ft squared
Step-by-step explanation:
Answer:
140 ft
Step-by-step explanation:
10 × 14 = 140 so the answer is 140 ft
(Question) Write to Explain; Shauna evaluated the expression 9 - 6 + (12/3) *2 and got the answer 4 is she correct? Why or why not?
And if this helps I'll add the screenshot I took of it.
Why is she not correct or Why is she correct.
the answer is, no.. she is not correct.
she solved the equation/question incorrectly.
why? Shauna subtracted 9 - 12/3 = 5
she multiplied 5 and 2 = 10
then subtracted by 6.
so she got 4.
but, this how you do it.
subtract 9 and 6, equaling 3.
12/3 x 2= 8
add 8 and 3, which equals 11.
the correct answer is 11!
2/3 divided by 1 1/2
Answer: 0.4
Step-by-step explanation:
The length of a rectangle is six times its width.
If the perimeter of the rectangle is 112 ft, find its area.
Answer:
Area = 48*8=384 sq. in
Step-by-step explanation:
Perimeter = 112
Length 6x
Width =x cm
Perimeter = 2(6x+x)
Perimeter = 14x
112 = 14x x=
8 in Width
Length = 6*8=48 in
Area = 48*8=384 sq. in
Did this kinda fast but I hope it helped XD
Length of the rectangle = 48ft
Width of the rectangle = 8ft
Area of rectangle = 384 ft²
What is rectangle?Rectangle is a shape with four straight sides and four angles of 90 degrees (right angles). Two of the sides are longer than the other two.
Given,
Length of a rectangle is six times its width
Let width is x then length is 6x
Perimeter of rectangle = 112 ft
Perimeter of rectangle = 2(Length + Width)
2(Length + Width) = 112
2(x + 6x) = 112
7x = 56
x = 8
Width = 8 ft
Length = 6 × 8 = 48 ft
Area of rectangle = length × width
= 48 × 8
= 384 ft²
Hence, 8ft is width and 48ft is length of the rectangle. 384 ft² is the area of rectangle.
Learn more about rectangle here:
https://brainly.com/question/29123947
#SPJ2
Please Answer ASAP!
Subtracting a number is the same as adding its opposite. Use this understanding to complete each of the equations below.
Enter numbers to evaluate ‐13−23.
‐13−23= ‐13 + ___
= ___
Enter numbers to evaluate ‐13−(‐23).
‐13−(‐23)= ‐13 + ____
= _____
Step-by-step explanation:
-13 - 23 = -13 + (-23)
= -36
-13 - (-23) = -13 + 23
= 10
Answer:
Step-by-step explanation:
-13 - 23 = -13 + (-23)
= -36
-13 - (-23) = -13 + 23
=10
A continental breakfast has a choice of toast, muffin, or a bagel AND a choice of coffee, milk or apple juice. How many possible outcomes are there?
There are an unknown number of possible outcomes. To figure this out all we need to do is multiply the amount of options per category to get the number of possible combinations.
In this case, there are 3 choices of food items and 3 choices of drinks.
Therefore, we need to multiply 3 by 3 to get the combinations.
3 times 3 equals 9
In conclusion, there are 9 possible combinations to be made from the choices presented.
Answer:
there are 12 possible outcomes
Step-by-step explanation:
PLEASE HELP AGAIN, SORRY I SUCK AT MATH.
Answer:
C. 24 degrees
Step-by-step explanation:
All triangle must be 180 degrees in total. So you have to add all the known degrees together to find the missing degree.
120+36=156
Then subtract the sum of the known angles from 180 to find the degree of the unknown angle
180-156=24
Answer: C
Step-by-step explanation:
I'll explain why.
The sum of the angles in a triangle must be equal to 180º. We already know 2 of the 3 angles, therefore, we can make an equation to find x.
The sum of the angles (x+36+120) must be equal to 180 (=180)
x+36+120=180
Combine like terms
x+156=180
Subtract 156 to isolate x
x=180-156
x=24
What is the area of the trapezoid?
Answer:
The answer is 36 squared centimeters
In July 2008, a wildfire near Yosemite
National Park burned about 53 square
miles of forest. If one square mile equals
640 acres, about how many acres of
forest were burned?
help please, what is the the perimeter of the figure to the nearest hundredth.
Answer:
100
Step-by-step explanation:
A school newspaper took a survey of 100 students. The results of the survey showed that 43 students are
fans of the Buffalo Bills, 27 students are fans of the New York Jets, and 48 students do not like either
team. How many of the students surveyed are fans of both th
math question down below screen shot
Answer:
the screen shoy isnt showing up
Step-by-step explanation:
Solve for K: 40 + K = 56
K=
Answer:
k=16
Step-by-step explanation:
To solve this, we can isolate k.
40+k=56.
We can do this by subracting 40 from both sides.
40+k-40=k
56-40=16
k=16
First isolate or get k by itself by subtracting 40 from both sides.
That leaves us with k = 16.
To check our answer, substitute 16 back into the equation.
So we have 40 + (16) = 56 or 56 = 56.
Anyone know the answer to this ?
Answer:
Triangle HBN ~ triangle LYR
=> HN/LR = HB/LY
=> (3x - 7)/(x + 11) = 28/21
=> 21(3x - 7) = 28(x + 11)
=> 63x -147 = 28x + 308
=> 35x = 455
=> x = 455/35 = 13
There is no answer to select. But I still believe there is no mistake in my calculation.
Hope this helps!
:)
I need an answer quick!!!!
Answer:
investment 2 $400 Simple Interest Rate
Step-by-step explanation:
If f(x)=x-1/3 and g(x) = 3x+1, what is(fºg)(x)?
Answer:
(fog)(x)=18x+1029x+1. (gof)(x)=27x+87x−8. Explanation: Given: f(x)=3x−12x+5 and g(x)=7x+33x−1. Solution for (fog)(x).
Step-by-step explanation:
Answer:(fog)(x)=18x+1029x+1. (gof)(x)=27x+87x−8. Explanation: Given: f(x)=3x−12x+5 and g(x)=7x+33x−1. Solution for (fog)(x).
Step-by-step explanation:
(09.01 LC))
For f(x) = x2 and g(x)=(x-3)2, in which direction and by how many units should f(x) be
shifted to obtain g(x)? (5 points)
Answer:
3 units to the right
Step-by-step explanation:
Given f(x) then f(x + a) represents a horizontal translation of f(x)
• If a > 0 then a shift of a units to the left
• If a < 0 then a shift of a units to the right
Thus
g(x) = (x - 3)² is f(x) shifted to the right by 3 units
Evaluate (if possible) the six trigonometri
trigonometric functions of the real number t. (If an answer is undefined, enter UNDEFINED.)
t= 4π/3
Answer:
undefined
Step-by-step explanation:
can someone help me please?
Answer:
(10,11)
(8,7)
(6,3)
(4,-1)
(2,-5)
(0,-9)
(-2,-13)
(-4,-17)
Answer: the image of how its supposed to be graphed is listed down below! hope this helped!
Step-by-step explanation:
The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x). So, the graph of a function if a special case of the graph of an equation.
Which statement best describes the function represented by the graph?
Answer:
Step-by-step explanation:
You read a graph from left to right, just like you would read words on a page in a book. At the left-most "side" of this graph, we are way up at positive infinity. As we move from left to right, the graph begins to drop in y values. A drop in y values indicates a decreasing graph. So it's decreasing, we have that part. As the graph grows up into y values that increase forever, it will also grow in the x direction to negative infinity. As the graph decreases in y values from left to right, the x values increase into positive infinity. So your choice is the second one: The function is decreasing on the interval (-∞, ∞).
Answer:
It's B
Step-by-step explanation:
WILL MARK BRAINLIEST!!! OWO
Answer:
G equilateral
Step-by-step explanation:
scalene = all the sides of the triangle are not equal
isosceles = two sides of the triangle is equal
Answer should be equilateral = All the sides of the triangle is equal.
F H J are not describing any triangle.
Answer:G equilateral
Step-by-step explanation:
^///^
A functiom is graphed on the coordinate plane.
What is the value of the function when x=4?
Answer: The answer is 2. Go open of the x line 2 then it lines up with the y.
Answer:
I thought it was 1
Step-by-step explanation:
Find the missing angle.
Answer:
127
Step-by-step explanation:
Answer:
x= 127 degrees
Step-by-step explanation:
use the vertical angles theorem to say that x=90*+37*. So, x=127 degrees.
Please i need help my homework is really hard
.
Answer:
f' (n)=9
Step-by-step explanation:
is this what you were looking for?
