Answer:
We know that the polynomial:
x²- 6y²- xy - 5x - 5y + 6
is rewritten as:
(x+ay+b)(x+cy-2)
First, lets expand the above expression:
x^2 + x*(cy) + x*(-2) + (ay)*x + (ay)*(cy) + (ay)*(-2) + b*x + b*(cy) - 2*b
Now we can simplify this to get:
x² + c*(xy) - 2*x + a*(xy) + ac*y² - 2a*y + b*x + bc*y - 2b
now let's group together the terms with the same variables:
x² + (c + a)*(xy) + (b - 2)*x + (bc - 2a)*y + ac*y² - 2b
And that must be equal to:
x²- 6y²- xy - 5x - 5y + 6
notice that equations are equal if and only if all the correspondent factors are equal.
notice that in both cases, the factor that multiplies the x² term is 1.
for the y² term we will have:
a*c = -6
for the xy term we will have
c + a = -1
for the x term we will have
b - 2 = - 5
for the y term we will have
bc - 2a = -5
for the constant term, we will have:
-2b = 6
Then we have a lot of equations, rewriting these we have:
a*c = -6
c + a = -1
b - 2 = -5
bc - 2a = -5
-2b = 6
From the fourth equation, b - 2 = -5
we can get:
b = -5 + 2 = -3
b = -3
notice that for the last equation:
-2b = 6
b = 6/-2 = -3
we have the same solution
Then we can replace the value of b in the above equations to get:
a*c = -6
c + a = -1
-3*c - 2a = -5
Now, we need to isolate one of the variables in one of the equations.
For example, we can isolate c in the second one to get:
c = -1 - a
now we can replace that in other equation, for example the third one:
-3*(-1 - a) - 2a = -5
now we can solve that for a.
3 + 3a - 2a = -5
3 + (3 - 2)a = -5
3 + a = -5
a = -5 - 3 = -8
a = -8
now we can use the equation "c = -1 - a" to find the value of c:
c = -1 -(-8) = -1 + 8 = 7
c = 7
then we have:
b = -3
a = -8
c = 7
then:
a + b*c = -8 + (-3)*7 = -8 - 21 = -29
what is x: |3x-1| = 4
Step-by-step explanation:
here's the answer to your question
Chloe was given a gift of a conical bird feeder that has a volume of 785.4 cubic centimeters. What is the area of the lid she will need to cover the bird feeder?
Answer:
392.7 cubic centimeters. Hope that helps :)
Step-by-step explanation:
FOR EASY BRAINLIEST ANSWER THIS QUESTION:
Two cars leave from the same place and travel in the same directionOne car travels one an one third times as fast as the other. After 3 hours, they are 45 miles apart. What is the speed of each car?
Answer:
22.5 m/h and 7.5 m/h
Step-by-step explanation:
Let's said that x is the speed of the faster car. That means the slower one must have the speed of x/3.
x/3 * 3 + 45 = x * 3
x + 45 = 3x
45 = 3x - x
45 = 2x
x = 22.5
x/3 = 7.5
Solve using the laws of cosine
Answer:
13°
Step-by-step explanation:
Cosine formula: a² = b² + c² - 2(b)(c)cos(a)
8² = 21² + 14² - 2(21)(14)cos(x)
64 = 441 + 196 - 588cos(x)
Bring constants to one side
64 = 441 + 196 - 588cos(x)
-441 -441 -196
-196
-573 = -588cos(x)
Divide by the coefficient
-573/-588 = -588cos(x)/-588
cos(x) = 573/588
To find x you need to use arcsin or cos^-1
x = arccos(573/588) = 12.969°
Answer:
[tex]\displaystyle 13° = m∠X[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{x^2 + y^2 - z^2}{2xy} = cos∠Z \\ \frac{x^2 - y^2 + z^2}{2xz} = cos∠Y \\ \frac{-x^2 + y^2 + z^2}{2yz} = cos∠X \\ \\ \frac{-8^2 + 14^2 + 21^2}{2[14][21]} = cos∠X → \frac{-64 + 196 + 441}{588} = cos∠X → 0,9744897959... = cos∠X \\ \\ 12,969468847...° = cos^{-1}\:0,9744897959... \\ \\ 13° ≈ 12,969468847...°[/tex]
As you can see, the inverse function MUST be used towards the end of your result, or elce you will throw it off!
I am joyous to assist you at any time.
What conclusion can be derived by comparing the central tendencies of the two data sets?
A: (7, 6, 3, 1, 6, 2, 4, 6, 3, 5;
B: {2, 2, 2, 3, 4, 5, 2, 8, 7, 6}
Ming drew the model to represent the equation 24+12=_x(8+4). What is the missing value in Ming's equation 3 4 12 24
Answer:
3 is the missing value
Step-by-step explanation:
Given
[tex]24 + 12 = \_ * (8 + 4)[/tex]
Required
Complete the blank
The model is not given; but the question can still be solved.
We have:
[tex]24 + 12 = \_ * (8 + 4)[/tex]
Add 8 to 4
[tex]24 + 12 = \_ * 12[/tex]
Add 24 to 12
[tex]36= \_ * 12[/tex]
Divide both sides by 12
[tex]3= \_[/tex]
Rewrite as:
[tex]\_ = 3[/tex]
Hence, the blank will be completed with 3
Answer:
a
Step-by-step explanation:
edg 2021
Prime numbers between 1 and 11
Answer:
2, 3, 5, 7, 11
Step-by-step explanation:
jajwjendnna1ll4tllsqk2nenqn
Answer:
2, 3, 5, 7, 11
Step-by-step explanation:
just list all the numbers that are only divisible by itself and 1
1 is just not a prime number
not 4 because it has factors 2x2 as well
not 6 because it has factors 3x2
not 8 because it has factors 4x2
not 9 because it has factors 3x3
I need help with this one, its too hard for me
Answer:
<C + <D = < DEK
<D = 40
Step-by-step explanation:
The exterior angle is equal to the sum of the opposite interior angles
<C + <D = < DEK
60 + <D = 100
<D = 100 -60
<D = 40
Answer:
[tex]m\angle C+m\angle D=m\angle DEK[/tex][tex]60+m\angle D=100[/tex]
[tex]m\angle D=100-60[/tex]
[tex]m\angle D=40[/tex]--------------------------
Hope it helps...
Points for late night math helpers! Thank you guys :)
Find the distance between (-5,5) and (2,-2)
Answer:
The distance is 7[tex]\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{The formula for \underline{distance between} is: }\mathsf{\sqrt{(x_2-x_1)^2 + (y_2 - y_1)^2}}[/tex]
[tex]\large\textsf{Whereas }\mathsf{x_2}\large\textsf{ is }\mathsf{2}\large\textsf{ and }\mathsf{x_1}\large\textsf{ is }\mathsf{ -5}\\\\\large\textsf{And also }\mathsf{y_2}\large\textsf{ is }\mathsf{ -2}\large\textsf{ and }\mathsf{ y_1}\large\textsf{ is }\mathsf{5}[/tex]
[tex]\mathsf{\sqrt{(2 - -5)^2+ (-2 + 5)^2}}\\\mathsf{2 - -5}\\\mathsf{= 2 + 5}\\\mathsf{= \bf 7}\\\\\mathsf{-2 + 5}\\\mathsf{= \bf -7}\\\\\mathsf{= \sqrt{(7)^2+ (-7)^2}}\\\\\mathsf{7^2}\\\mathsf{= 7\times7}\\\mathsf{= \bf 49}\\\\\mathsf{(-7)^2}\\\mathsf{= -7\times-7}\\\mathsf{= \bf 49}\\\\\mathsf{= \sqrt{49 +49}}\\\\\mathsf{49+49}\\\mathsf{=\bf 98}[/tex]
[tex]\mathsf{= \sqrt{98}}\\\mathsf{= 7\sqrt{2}}[/tex]
[tex]\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf 7\sqrt{2}}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
What is the midline equation of the function h(x) = -4 sin (x- pi/4)
Answer:
[tex]y = \boxed0[/tex]
Step-by-step explanation:
we are given a sin function
[tex] \displaystyle h(x) = - 4 \sin(x -\pi /4) [/tex]
we want to figure out the midline of the function graphically The midline of a sinusoidal function is the horizontal line that passes exactly in the midline of its extreme value however since we a function recall that,
[tex] \displaystyle f(x) = a \sin(bx -c) + d[/tex]
where the midline is
[tex]y = d[/tex]to figure out the midline rewrite the function
[tex] \displaystyle h(x) = - 4 \sin(x -\pi /4) + 0[/tex]
therefore the midline is
[tex]y = \boxed0[/tex]
Label five places in the photo that have a slope.
Step-by-step explanation
The orange machine, the very end of the shovel part. That line is a slope. The middle part of the scooper could also be a slope. The very beginng part of the scooper is also a slope. The bottom part of the scooper is also a slope. The bottom part at the end of the scooper could also be slope.
Complete this item.
For the following figure, can you conclude that / | | m? Select true or false.
Answer:
true
Step-by-step explanation:
:)
Jasmine wants to use her savings of $1,128 to buy video games and movies. The total price of the movies she bought was $72. The video games cost $43 each. Choose the inequality that would be used to solve for the maximum number of video games Jasmine can buy with her savings. A 43 + 72x ≤ 1,128 B43 + 72x ≥ 1,128 C43x + 72 ≥ 1,128 D 43x + 72 ≤ 1,128
Answer:
D
Step-by-Step Explanation:
You can mark out B and C because the amount of money they spend has to be less or equal to the amount of money they have.
A is wrong because we already know the total price for the movies. We know the price of the games are $43 each. X is the amount of game she can afford to get.
So in conclusion, D is the correct answer.
Add parentheses to the expression so that its value is 70:
4 + 8 × 6 - 2
4 + (8 × 6) - 2
4 + 8 × (6 - 2)
no parentheses are needed
(4 + 8) × 6 - 2
Answer:
(4 + 8) * 6 - 2
Step-by-step explanation:
P - Parenthesis
E - Exponent
D - Division
M = Multiplication
A - Addition
S - subtraction
(4 + 8) * 6 - 2 = 12 *6 - 2
= 72 - 2
= 70
Answer:
d.) ( 4 + 8 ) × 6 - 2
Step-by-step explanation:
( 4 + 8 ) × 6 - 2
Add 4 and 8.
12 × 6 -2Multiply; 12 by 6.
72 - 2Subtract 2 from 72.
70.a recipe for a cake calls for 5 1/10 cups of sugar Anjali accidentally puts in 5 3/4 cups how much extra did she put
Answer:
2/15
Step-by-step explanation:
I think not 100% on this but not so sure-
Subtract 5 1/10 from 5 3/4
5 3/4 - 5 1/10
• Subtract the whole numbers (5 and 5)
5 - 5 = 0
• LCM of the denominators (4 and 10)
= 13/20
She put an extra 13/20
E(5,3) and F (2,-1) are two vertices of a square EFGH and H is in the x-axis .Find the coordinates of H and G. Please need answer quick with accurate explanation.
Answer:
coordinates of H = (1, 0)
Coordinates of G = ( - 3.6, -2) or (5.6, -2)
Step-by-step explanation:
E(5,3) and F (2,-1) are two vertices of a square EFGH and H is in the x-axis.
Let the coordinates of H is (x, 0) and G is (a, b).
The length of side EF is
[tex]EF = \sqrt{(5 -2)^2 + (3 +1)^2} = 5[/tex]
So,
[tex]EH = \sqrt{(5 -x)^2 + (3 -0)^2} = 5\\\\(5 -x)^2+ 9 = 25\\\\5 - x = 4\\\\x = 1[/tex]
And
[tex]GH = \sqrt{(a -x)^2+ b^2} = 5\\\\(a -1)^2+ b^2 = 25\\\\a^2 + b^2 + 1 - 2 a = 25\\\\a^2 + b^2 - 2a = 24 .... (1)[/tex]
Now
[tex]FG = \sqrt{(a -2)^2+ (b +1)^2} = 5\\\\(a -2)^2+ (b+1)^2 = 25\\\\a^2 + b^2 + 2b - 2 a = 20\\ ..... (2)[/tex]
Solving (1) and (2)
b = - 2 ,
[tex]a = \frac{2 \pm\sqrt{4 + 80}}{2}\\\\a = \frac{2 \pm 9.2}{2}\\\\a = - 3.6, 5.6[/tex]
Find the area of the circle.
Use 3.14 for n. Do not round your answer.
Hint: A = tir2
3 in.
Area = [?] inches?
Enter the number that
belongs in the green box.
Enter
Pls someone help
Answer:
28.26
Step-by-step explanation:
A = (3.14)(3)^2
A = 3.14 * 9
A = 28.26
Answer:
28.26
Step-by-step explanation:
The area of a circle is
A = pi r^2 where r is the radius
A = 3.14 ( 3)^2
A = 3.14 *9
28.26
Choose ALL of the ordered pairs that are solutions to the equation.
5y = 2x - 7
a) (6, 0)
b) ( 7, 21)
c) (8, 18)
d) ( -3, 4)
b) ( 7, 21)
Step-by-step explanation:
5(7)=2(21)-7
35=42-7
35=35
Answer:
None of them
Step-by-step explanation:
a: 5*0=2*6-7 False
b: 5*21=2*7-7 False
c: 5*18=2*8-7 False
d: 5*4=2*-3-7 False
Sophia has 3 forths
of a turkey sub sandwich. She cut the sandwich into 2 equal portions to share with her friend. How much of the sandwich will each girl get?
Answer:
Each girl will get 3/8 of a sub
Step-by-step explanation:
3/4 ÷ 2
Copy dot flip
3/4 * 1/2
3/8
Each girl will get 3/8 of a sub
Roy spent 3/8 of his money on 10 identical files and 10 identical board games. He then spent 1/10 of the remainder on 6 identical staplers. A board game cost 5 times as much as a file. A stapler cost $1.50 more than a file. (a) How much did Roy spend on a file? (b) How much did Roy spend on a board game?
Question seems incomplete as the initial amount Roy has isn't given. Kindly provide Roy's initial amount
Answer:
Step-by-step explanation:
ASAPPPPPP PLEASE HELP MEEEEEEEEEEEEEEEEEEEE
Answer:
4 weeks per level
Step-by-step explanation:
notice the pint (1,4)
the next is (2, 8)
meaning that in 4 weeks she completes 1 level and in 8 weeks she completes 2 levels.
Mark dropped an object from a bridge 400 feet above ground level
i think the question is incomplete.Then what happened???? And what to find???
What is the y-intercept of this quadratic function f(x) = x2 + 2x + 3
Hi there!
[tex]\large\boxed{0, 3}[/tex]
Find the y-intercept by substituting in 0 for x:
f(0) = 0² + 2(0) + 3
Simplify:
f(0) = 3
Answer:
0,3
hope this helped !!!
Step-by-step explanation:
Can someone help me with number 18 and explain how to do it please.
Answer:
its 380
(TRUST ME)
Step-by-step explanation:
how many units is 12x+16
Answer:
I think the answer is 1/2
Step-by-step explanation:
because
12x=6
x=6/12
•°•x=1/2
Idenify the domain for the function, f(x).
(Negative infinity, infinity)
(Negative infinity, 0) Union (0, infinity)
(Negative infinity, 2) Union (0, 2) Union (0, infinity)
(negative infinity, negative 2) Union (negative 2, 0), union (0, infinity)
Answer:
[tex]Domain = (-\infty,\infty)[/tex]
Step-by-step explanation:
The function is not given; So, I will answer this question using
[tex]f(x) = 1.6x - 2[/tex]
Required
The domain
In [tex]f(x) = 1.6x - 2[/tex],
- there is no fraction where x is in the denominator
- there is no root where x is in the radicand
This means that, there is no restriction on x.
Hence, the domain is:
[tex]Domain = (-\infty,\infty)[/tex]
Answer:
A. (negative infinity, infinity)
Step-by-step explanation:
Three tennis balls that fit in cylindrical tennis ball cane. If each ball is 14 inches in diameter, what is the volume of air left between the balls and the cane
Given:
Diameter of the tennis ball = 14 inches.
Three tennis balls are fit in a cylindrical tennis ball cane.
To find:
The volume of air left between the balls and the cane.
Solution:
Diameter of the tennis ball = 14 inches.
Radius of the tennis ball = 7 inches
Radius of tennis ball is equal to radius of cane. So,
Radius of the cane = 7 inches
Height of cane is:
[tex]3\times 14=42[/tex] inches
Volume of a ball is:
[tex]V_1=\dfrac{4}{3}\pi r^3[/tex]
Where, r is the radius of the ball.
So, the volume of 3 ball is:
[tex]V_2=3\times V_1[/tex]
[tex]V_2=3\times \dfrac{4}{3}\times \dfrac{22}{7}\times (7)^3[/tex]
[tex]V_2=4312[/tex]
Volume of the cane is:
[tex]V_3=\pi r^2h[/tex]
Where, r is the radius of the cane and h is the height of the cane.
[tex]V_3=\dfrac{22}{7}\times (7)^2\times 42[/tex]
[tex]V_3=6468[/tex]
Now, the volume of air left between the balls and the cane is:
[tex]V=V_3-V_2[/tex]
[tex]V=6468-4312[/tex]
[tex]V=2156[/tex]
Therefore, the volume of air left between the balls and the cane is 2156 cubic inches.
A line passes through the points (0,0) and (4,4). What is the equation of the line?
Answer:
y = x
Step-by-step explanation:
So what we're going to want to do here is use the slope formula and the general equation y = mx + b.
Let's start.
The slope formula is y2-y1/x2-x1. So, put our points in here. 4-0/4-0. Slope: 1.
Okay, we have that. Now, a line that passes through the origin (0,0) is not going to have a y-intercept because it hits the y-axis at 0. So, that cancels out the b.
With our slope 1, the answer is just y = x. Very simple equation.
Hope this helped!
Evan tosses a ball from the roof of a building. The path of the ball can be modelled
by the following equations where h represents the height of the ball in meters and
t represents the time in seconds. Each equation below represents the EXACT same
path. Using the information you can obtain from these equations, answer the
following questions.
nu = -4(t + 1)(t-5)
h2 = -4/t - 2)2 + 36
hz = -4t? + 16 + 20
Draw a detailed SKETCH representing the path of the ball. Be sure to include titles
for your axes, appropriate scales, and critical points such as initial value, vertex and
roots of the parabola.
Answer:
Please find attached sketch of the path of the ball, having plot area and plot points, created with MS Excel
Step-by-step explanation:
Question;
The equation representing the path of the ball obtained from a similar question posted online are;
h₁ = -4·(t + 1)·(t - 5), h₂ = -4·(t - 2)² + 36, h₃ = -4··t² + 16·t + 20
The above equations represent the same path
The equation, h₁ = -4·(t + 1)·(t - 5), gives the roots of the height function, h(t), used in determining the height of the ball after time t
At (t + 1) = 0 (t = -1) or at (t - 5) = 0 (t = 5), the ball is at ground level
The ball reaches the ground, is at ground level at t = 1, and at t = 5 seconds after being tossed, where h(t) = 0
The equation of the path of the ball in vertex form, y = a·(x - 2)² + k, is h₂ = -4·(t - 2)² + 36, where, by comparison, we have;
The vertex of the ball = The maximum height reached by the ball = (h, k) = (2, 36)
The coefficient of the quadratic term, t², is negative, therefore, the shape of the parabola is upside down, ∩, shape
The sketch of the path of the ball created with MS Excel, used in plotting the vertex, the initial value and the root points of the parabola, through which the ball passes and joining of the points with a 'smooth' curve is attached
