50 points!!
The first few steps in deriving the quadratic formula are
shown.
Which best explains why
62
is not added to the left
40?
-C-ax? +bx
side of the equation in the last step shown in the table?
Use the subtraction property of
equality
Factor out a
-ax² + x
O The term
b?
is added to the right side of the
40²
b?
b
2a
Find half of the b value and square
it to determine the constant of the
perfect square trinomial
4a?
equation, so it needs to be subtracted from the left
side of the equation to balance the sides of the
equation.
ba
-C-
4a
a
4a
The distributive property needs to be applied to
determine the value to add to the left side of the
equation to balance the sides of the equation.
O The term
b2
40²
needs to be converted so it has a
common denominator before adding it to the left side
of the equation to balance the equation.
© The square root of the term needs to be found before
Answers
Answer:
The distributive property needs to be applied to determine the value to add to the left side of the equation to balance the sides of the equation
Step-by-step explanation:
There is a factor of a outside of the parentheses on the right has side
We are really adding a( b^2/4a^2) to the right side
Simplifying we are adding b^2 /4a
This is what we need to add to the left side to be fair and equal.
We used the distributive property to determine what we were actually adding to the right side.
Related Questions
Which inequality represents the compound in
equality x > 3 and x < 5
Answers
Answer:love
Step-by-step explanation:
Inequalities and Absolute Value Equations.
x > 3 and x < 5
Inequality Form:3<x<5
Interval Notation:
(3,5)
An inequality is a mathematical statement that compares algebraic expressions using greater than (>), less than (<), and other inequality symbols
What are the 5 inequalities?The 5 inequality symbols are less than (<), greater than (>), less than or equal (≤), greater than or equal (≥), and the not equal symbol (≠).
Which of the following is an example of compound inequality?Think about the example of the compound inequality: x < 5 and x ≥ −1. The graph of each individual inequality is shown in color. Since the word and joins the two inequalities, the solution is the overlap of the two solutions. This is where both of these statements are true at the same time.
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X + 2 (x + 1) + 1 in the simplest form
Answers
Answer:
3x + 3
Step-by-step explanation:
First, the 2 must be distributed. This leaves us with x + 2x + 2 + 1. x and 2x are like terms, as are 2 and 1. They can be combined, giving us 3x + 3. 3x + 3 cannot be simplified any further, so it is the final answer.
Question: X + 2 (x + 1) + 1 in the simplest form
Answer: 3x+3
A spinner with 8 equal-size sections labeled as shown is spun 200 times. What is the sample
space for this experiment?
Answers
Answer:
hiiooioudzzxuxojxoufxodyzufxufxyfxuoxudr tztdxhxfuoxir d and
Check all of the correct names for the object pictured below.
A. UT
B. TU
C. UT
D. TU
E. TU
DE UT
Answers
+
y.com/student/dashboard/home
D
Solving Systems of Linear Equations Algebraically - Qutz - Level H
Question 7
Solve.
3
b=0
a + b = 21
a = 20
a = 12
a = 20
a = 37
b = 11
0 = 371
%
b = 9
b = 15
b = -16
ET
6:26
Answers
Write - 32/12 as a mixed number in reduced form.
Answers
-2 2/3 = -2.6 = -8/3
Answer: -2 2/3 or -8/3
Step-by-step explanation:
Hope this help
Juan's work for solving by completing the square is below. In which step (if any) does Juan make a mistake?
(SEE PICTURE FOR STEPS)
Step 4
Step 1
Juan does not make a mistake.
Step 3
Answers
The solution is : x = 19 is the extraneous solution Li Juan obtained.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Here, we have,
The given equation is 13 - 2w = w + 6.
We need to solve the equation by squaring both sides of the equation.
Now, 13 - 2w = w + 6 squaring both sides of the equation.
That is, (13-2w)²= 169 - 52w + 4w²
(w+6)²= w²+ 12w + 36
Setting them equal, we get
169 - 52w + 4w² = w² + 12w + 36
⇒3w²- 64w + 133 = 0
Now, using the quadratic formula, we get
x = (64±√(64² - 4×3×133))/6
⇒x = (64±√2500)/6.
⇒x = (64±√50)/6.
⇒x = 19 or 14/6 = 7/3.
Solving the original equation, we get
7 = 3w⇒w = 7/3
Therefore, x = 19 is the extraneous solution Li Juan obtained.
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complete question:
Li Juan solves the equation below by first squaring both sides of the equation.
13 - 2w = w + 6
What extraneous solution does Li Juan obtain?
Find the position vector of a particle that has the given acceleration and the specified initial velocity and position.a (t) = 8t i + sin t j + cos 2t k, v(0) = i, r(0) = jr(t) = ?(b) On your own using a computer, graph the path of the particle.
Answers
Answer:
remember that:
a*i + b*j + c*k can be written as a vector: (a, b, c)
We know the acceleration of the particle, and we want to find the velocity of the particle, so we just need to integrate two times.
a(t) = (8*t, sin(t), cos(2*t))
integrating that, we get:
V(t) = ( (1/2)*8*t^2, -cos(t), sin(2*t)/2) + v0
where v0 is the vector that defines the velocity at t = 0
in the question you wrote:
V(0) = i
so i suppose that this is:
V(0) = (1, 0, 0)
Then the velocity equation gives:
V(t) = ( (1/2)*8*t^2, -cos(t), sin(2*t)/2) + (1, 0, 0)
V(t) = (4*t^2 + 1, -cos(t), sin(2*t)/2)
Now to get the position equation, we integrate it again
r(t) = ((4/3)*t^3 + t, -sin(t), -cos(2*t)/4) + r0
where r0 is the initial position, in the question you wrote:
r(0) = j
so we get:
r(0) = (0, 1, 0)
replacing that we get:
r(t) = ((4/3)*t^3 + t, -sin(t), -cos(2*t)/4) + (0, 1, 0)
r(t) = ((4/3)*t^3 + t, -sin(t) + 1, -cos(2*t)/4)
Writing this in the same notation than in the question, we get:
r(t) = [(4/3)*t^3 + t}*i + [-sin(t) + 1]*j + [-cos(2*t)/4]*k
b) Now we want to graph this:
The image isn't really good but can be used to understand the motion of the particle.
Help ASAP please!!
For a proof by induction of the math statement below,
identify the correct step for proving the theorem is true
for n=k+1
2+4+6+...+2n=n(n+1)
Answers
Answer:
2+4+6+...+2k+2(k+1) = k(k+1) + (k+1)(k+1)
Step-by-step explanation:
Proved case for n
2+4+6+...+2n = n(n+1) ................(1)
for n = k + 1, we replace n by k and add n = k+1 on both sides (
2+4+6+...+2k+2(k+1) = k(k+1) + 2(k+1))
rearrange by factoring the right-hand-side
2+4+6+...+2k+2(k+1) = (k+1)(k+2)
which if we substitute n=k+1, we get back
2+4+6+...+2(n-1) + 2(n) = n(n+1) ...............(2)
This means that equation (1) is applicable to case n+1, and the proof by induction is completed.
please help me solve this
Answers
Answer:
x=5, y=16
Step-by-step explanation:
y=x^2-9
y=2x+6
solve by substitution
2x+6= x^2 -9
2x+6 = (x+3) (x-3)
2 (x+3) = (x+3) (x-3)
divide both sides by x+3
2= x-3
add 3 to both sides
x=5
y= 2(5) +6
y= 16
Answer:
(-3, 0), (5, 16)Step-by-step explanation:
y = x² - 9y = 2x + 6Solve by substitution:
x² - 9 = 2x + 6x² - 2x - 15 = 0x² - 2x + 1 = 16 (x - 1)² = 4²x - 1 = ± 4x = 1 ± 4x = 5 ⇒ y = 2*5 + 6 = 16x = - 3 ⇒ y = 2*(-3) + 6 = 0g At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship B is sailing north at 25 knots. How fast (in knots) is the distance between the ships changing at 4 PM
Answers
Answer:
[tex]\triangle d=47.69 Knots[/tex]
Step-by-step explanation:
Distance of Ship A from B [tex]d_1=10 West[/tex]
Speed of Ship A [tex]V_a=17 knots West[/tex]
Speed of Ship A [tex]V_b=25 knots North[/tex]
Generally the equation for Rate of distance change is mathematically given by
[tex]\triangle d=\frac{1}{2\sqrt{(17t+10)^2+(25t)^2}}*\triangle t[17t+10^2+25t^2][/tex]
[tex]\triangle d=\frac{578+340+1250}{2\sqrt{(17t+10)^2+(25t)^2}}[/tex]
Therefore with
t=>4PM
We substitute
[tex]\triangle d=\frac{882(4)+420+648(4)}{2\sqrt(21(4)+10^2)+(18(4))^2}[/tex]
[tex]\triangle d=47.69 Knots[/tex]
High School Dropouts
Number of Dropouts
1990
2000
Male
Female
MAMD.M.D.3: Which of the
following is true about the graph?
Answers
Answer:
There are more females dropping than males each year and that there are more females than males
How is the product of a complex number and a real number represented on the coordinate plane?
A. When 2+3i is multiplied by 3, the result is 6+9i. Graphically, this shows that the product is a scalar of the complex number.
B. When 2+3i is multiplied by 3, the result is 6+9i. Graphically, this shows that the product is a countercockwise rotation of 90 degrees of the complex number.
C. When 2+3i is multiplied by 3, the result is 6+9i. Graphically, this shows that the product is a clockwise rotation of 90 degrees of the complex number.
D. When 2+3i is multiplied by 3, the result is 6+9i. Graphically, this shows the product is a counterclockwise rotation of 90 degrees and a scalar of the complex number.
Please help I don't know which one.
Answers
Answer:
A
Step-by-step explanation: When you multiply a coordinate in the complex plane it doesn't just magically rotate. It works the exact same way a normal coordinate would. Therefore, the answer is A
When 2 + 3i is multiplied by 3, the result is 6 + 9i. Graphically, this shows that the product is a scalar of the complex number.
The correct answer is an option (A)
What is a complex number?"It is number of the form [tex]x+iy[/tex] where the first part (x) is called real part and the second part ([tex]iy[/tex]) is called as imaginary part and [tex]i=\sqrt{-1}[/tex]"
What are real numbers?"It is a combination of rational and irrational numbers, including positive and negative whole numbers, integers, decimals, fractions"
For given example,
The product of a complex number and a real number.
Let, [tex]u[/tex] be any real number and [tex]x+iy[/tex] be any complex number.
The product of 'u' and 'x + iy' is,
[tex]\Rightarrow u\times(x+iy)=(u\times x)+i(u\times y)\\\\\Rightarrow u(x+iy)=ux+i(uy)[/tex]
Let [tex]2+3i[/tex] be a complex number.
For [tex]u=4[/tex],
[tex]\Rightarrow 4\times(2+3i)=8+12i[/tex]
Let [tex]u=-2[/tex],
[tex]\Rightarrow -2\times(2+3i)=-4-6i[/tex]
We can observe that, the product is a scalar of the complex number.
Therefore, when 2+3i is multiplied by 3, the result is 6+9i. Graphically, this shows that the product is a scalar of the complex number.
The correct answer is an option (A)
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13. Find the area of the parallelogram.
Answers
Answer:
Step-by-step explanation:
make it 1 triangle and trapezium
1) 1/2 x 7 x 8 = 28 in2
Answer:
56 in^2
Step-by-step explanation:
A = b* h
A = (8) * (7)
A = 56
A = 56 in ^2
Hope this helps!
please help. having trouble with this question.
Answers
Answer:
Step-by-step explanation:
The problem told you what all the variables represent, so all we have to do it fill them in accordingly and solve:
[tex]V=6440e^{(.068)(8)}[/tex] and
[tex]V=6440e^{.544}[/tex] and
V = 6440(1.7228846) so
V = $11,095.38
What is the smallest counting number that is divisible by 2, 4, 5, 6, and 12? express each number and your final answer as a product of primes. What do you notice?
Answers
Answer:
60
[tex]2^{2} * 3 * 5[/tex]
Step-by-step explanation:
It costs a total of R138.90 to purchase 10 loaves of bread and 12 litres of cooidrinks in a store. If the store raises the price of bread by 20% and the price of cooldrinks by 10%, the total price of these items becomes R159.54. Find the original price of three loaves of bread and two litres of cooldrinks.
Answers
9514 1404 393
Answer:
R32.15
Step-by-step explanation:
Let x and y represent the original price of a loaf of bread and a liter of drink, respectively. The two relations given by the problem statement are ...
10x +12y = 138.90
10(1.2x) +12(1.1y) = 159.54
Multiplying the first equation by 1.2 and subtracting the second gives ...
1.2(10x +12y) -(10(1.2x) +12(1.1y)) = 1.2(138.90) -(159.54)
1.2y = 7.14 . . . . collect terms
y = 5.95 . . . . . divide by 1.2
The value of x can be found from the first equation.
10x + 12(5.95) = 138.90
10x = 67.50 . . . . . . . . . . . subtract 71.40
x = 6.75 . . . . divide by 10
Then the value of 3x+2y is ...
3(6.75) +2(5.95) = 32.15
The original price of 3 loaves and 2 liters is R31.15.
Solve the inequality for s:
5s + 2 > 7
Answer:
Answers
Answer:
S>1
Step-by-step explanation:
5s + 2 > 7
Subtract 2 from both sides
5s>5
Divide 5 from both sides
S>1
Solution of the inequality is s>1.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to one another.
Adding the same amount to each side, taking the same amount away from each side, multiplying or dividing each side by the same positive integer, and other operations can be used to solve the inequality.
The inequality sign must be reversed if either side is multiplied or divided by a negative number.
5s+2 > 7
Subtracting 2 on both side,
5s > 5
s>1
Therefore, the solution set of inequality is s>1.
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Solve for x. Resuelve la x. 5 (4 + 2x) < 40
Answers
Step 1: Simplify both sides of the inequality.
10x+20<40
Step 2: Subtract 20 from both sides.
10x+20−20<40−20
10x<20
Step 3: Divide both sides by 10.
[tex]\frac{10x}{10}[/tex] < [tex]\frac{20}{10}[/tex]
x<2
select an expression that is equivalent to 4√x2/3
A x14x14
B x94x94
C x16x16
D x83x83
Answers
Answer:
here is your answer
Step-by-step explanation:
here is your answer
Determine the value of x.
Answers
Answer:
x=10
Giving brainiest would be appreciated! :D
If function f has zeros at -3 and 4, which graph could represent function f?
Answers
Answer:
A
Step-by-step explanation:
f has zero means that f(x)=0
if f(x)=0 we have to look intersection point or points in the graph on the x-axis.
for A
y=0
x=-3, x=4
for B
y=0
x=-4, x=3
for C
y=0
x=-4, x=-3
for D
y=0
x=3, x=4
How many Egyptian numerals (total) are needed to represent the following problem?
Answers
Which graph represents the function f(x)=|x|-4?
Answers
See the graph in the attached image.
Keenan is throwing an Independence Day party he wants to buy sparklers each pack of 12 smugglers cost $3.99 kina needs 120 sparklers that each gas can have two how much will Keenan spend on sparklers?
Answers
Answer:
$478.8
Step-by-step explanation:
1 sparkler costs= $3.99
120 sparklers cost= $3.99 x 120 = $478.8
plsss help !!
Jack and Grace went to the store to buy flowers. Jack bought 3 carnations and 5 roses for a total cost of $22.50. Grace bought 3 carnations and 2 roses for a total cost of $13.50. what does one carnation and one rose cost?
Answers
Answer:
carnation $2.50; rose $3.00
Step-by-step explanation:
Let c = price of 1 carnation.
Let r = price of 1 rose.
3c + 5r = 22.5
3c + 2r = 13.50
Subtract the se3cond equation from the first equation.
3r = 9
r = 3
Now substitute r = 3 in the first equation and solve for c.
3c + 5r = 22.5
3c + 5(3) = 22.5
3c = 7.5
c = 2.5
Answer: carnation $2.50; rose $3.00
In one season, a basketball player missed 15% of her free throws. How many free throws did she attempt if she made 102 free throws? Write the exact answer. Do not
round
Answers
Answer:
120 free throws
Step-by-step explanation:
If she misses 15% of her free throws, that means she makes 85% of them.
Find how many she attempted by dividing 102 by 0.85:
102/0.85
= 120
So, she attempted 120 free throws
The number of free throws that were attempted is 120 free throws.
Since the basketball player missed 15% of her free throws, This means that the percentage scored will be:
= 100% - 15% = 85%
Therefore, 85% of x = 102
0.85x = 102
x = 102/0.85.
x = 120
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Help me i think it’s c
Answers
Answer: Graph B
=====================================================
Explanation:
Point A appears to be at (2.5, -1)
If we shift 6 units to the left, then we subtract 6 from the x coordinate. So the new x coordinate is now 2.5-6 = -3.5
If we shift 4 units up, then we add 4 to the y coordinate to go from -1 to -1+4 = 3
Overall, the point A(2.5, -1) moves to A'(-3.5, 3)
Graph B is the answer because of this. The other points B and C will follow the same pattern as point A does.
Find mzmon???????????
Answers
Answer:
angle MON = 57 degree
Step-by-step explanation:
Angle LOM + Angle MON =90 degree (being perpendicular)
3x- 15+5x -23 = 90
8x -38 = 90
8x = 90 + 38
8x = 128
x = 128/8
x = 16
Angle MON
5x - 23
5*16 - 23
80 - 23
57 degree
Angle LOM
3x - 15
3*16 - 15
48 - 15
33 degree
8 subtracted by 1/3 + 2/3 equals?
Answers
Answer:
8-1/3=7 2/3+2/3=8 1/3
Step-by-step explanation:
