Answer:
x² -3/4x +1/4 = 0
Step-by-step explanation:
Consider the two equations in factored and expanded forms:
(x -p²)(x -q²) = x² -(p²+q²)x +p²q² = 0 ⇒ p²+q² = 1, p²q² = 16
and
(x -1/p)(x -1/q) = x² -(1/p+1/q)x +1/(pq) = 0
Consider the squares of the sum and product of roots:
constant term: (1/(pq))² = 1/(p²q²) = 1/16 ⇒ 1/(pq) = √(1/16) = 1/4
x-term: (1/p +1/q)² = (p +q)²/(pq)² = (p² +q² +2pq)/(p²q²)
= (p² +q²)/(p²q²) +2/(pq)
= 1/16 +2/√16 = 9/16 ⇒ (1/p +1/q) = √(9/16) = 3/4
Then the equation with roots 1/p and 1/q is ...
x² -3/4x +1/4 = 0
...................................
Answer:
tha.nks for the p.oints buddy!
Select all the expressions that equal:
-7 - (- 12)
below:
Answer:
c and e
Step-by-step explanation:
[tex]-7-(-12) = -7 +12 = 12 +(-7)[/tex]
Plz help ToT I'm horrible at math
Answer:
192
Step-by-step explanation:
multiply by each side to find the answer. 4x2 is 8 and 8 x 24 is 192. Which ever order you multiply the numbers in you will always get 192. Hope this helps ^^
to convert 25 hours to minutes would you use the ratio 1/60
Answer:
Yes
Step-by-step explanation:
1 hour = 60 min
25 hours = 60 x 25 min
Help PLEASE!!! I really need it I really do please anyone
Answer:
5. alternate interior angles
7. angle addition postulate
Please help me
I such at geometry
Find the slope of the line that passes through (10, 8) and (1, 9).
Answer:
m = 1/9
Step-by-step explanation:
Given:
x = 10
y = 8
x1 = 1
y1 = 9
Solution:
y - y1 = m ( x - x1 )
9 - 8 = m ( 10 - 1 )
1 = 9m
m = 1/9
4 1/2 x 5 Multiply and answer with a mixed number in the simplest form.
Answer:
[tex]22\frac{1}{2}[/tex]
Step-by-step explanation:
(4.5)(5) = 22.5
[tex]22.5 = 22\frac{1}{2}[/tex]
Can someone plz help Me?
Answer:
The answer is A!
Step-by-step explanation:
please help me asap, pleaseee :/
ty ty :D
7x+8y=32
Just do pemdas
Answer:
7x+8y=32
Step-by-step explanation:
Hi there!
We are given the following equation:
[tex]y=-\frac{7x}{8} +4[/tex]
And we want to convert it into standard form
Standard form is ax+by=c, where a, b, and c are integer coefficients, a and b cannot be zero, and a cannot be negative
a is the coefficient in front of x and b is the coefficient in front of y
Since we have the term with x ([tex]-\frac{7x}{8}[/tex]) on the right side, and we want it on the left side with the term with y, we can move it to the other side, by adding [tex]\frac{7x}{8}[/tex] to both sides.
[tex]y=-\frac{7x}{8} +4[/tex]
+[tex]\frac{7x}{8}[/tex] +[tex]\frac{7x}{8}[/tex]
_________________
[tex]\frac{7x}{8} + y =4[/tex]
Now we have the terms of x and y on both sides, but remember; we want the coefficients to be integers (whole numbers).
We'll need to clear the fraction of [tex]\frac{7x}{8}[/tex]. To do that, we can multiply both sides by 8.
[tex]8(\frac{7x}{8} + y) =8(4)[/tex]
Now doing the distributive property:
[tex]8(\frac{7x}{8}) + 8(y) =8(4)[/tex]
Multiply each term by 8.
7x + 8y = 32
Hope this helps!
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Answer:
Answer: 4
Step-by-step explanation:
Find the slope of each line.
1)
Answer:
7/1 or 7
Step-by-step explanation:
because you rise (vertically) seven and run (horizontally) 1, so 7/1 but simplified it's just 7 so either is valid.
WILL GIVE BRAINLIEST
HELP ASAP!! WILL ADD 5 STAR RATING !!!
ANY AND ALL LINKS OR WRONG ANSWERS WILL BE REPORTED !!!!
Is the sequence {4, 7, 10, 13, 16, ...} a function? Explain.
a
Yes, because each input is a natural number with multiple output numbers in the sequence
b
Yes, because each input is a natural number with a single output number in the sequence
c
No, because there are no input values paired with a single output number in the sequence
d
No, because there are multiple input values paired with a single output number in the sequence
Step-by-step explanation:
tricky, as the sequence does not define the input values.
by we can assume that the corresponding input values are 1, 2, 3, 4, 5, ... as it is usual for a sequence.
in that sense, b is the correct answer.
The sequence is a function because each input is a natural number with a single output number in the sequence.
What is arithmetic progression?The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence.
Given the sequence {4, 7, 10, 13, 16, ...},
Given that each term has a common difference, this is an arithmetic sequence. In this instance, the next item in the sequence is obtained by multiplying the previous term by 3.
a₂ - a₁ = 7 - 4 = 3
a₃ - a₂ = 10 - 7 = 3
the difference in output is the same for all the numbers in sequence.
Hence the sequence is the function of the Arithmetic Sequence.
Learn more about arithmetic progression;
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Cost to store is $32, Markup 3%, what's the selling price, what is answer?
Answer:
the answer to this question is $32.96
What would be the equation of the midline of this graph?
Answer:
Step-by-step explanation:
Vertices of the quadrilateral ABCD are,
A → (-5, 2)
B → (-3, 4)
C → (-2, 4)
D → (-1, 2)
By reflecting the given quadrilateral ABCD across x-axis to form the image quadrilateral A'B'C'D',
Rule for the reflection of a point across x-axis is,
(x, y) → (x , -y)
Coordinates of the image point A' will be,
A(-5, 2) → A'(-5, -2)
From the picture attached, point E is obtained by translation of point A'.
Rule for the translation of a point by h units right and k units up,
A'(x+h, y+k) → E(x', y')
By this rule,
A'(-5 + h, -2 + k) → E(1, -1)
By comparing coordinates of A' and E,
-5 + h = 1
h = 6
-2 + k = -1
k = 1
That means
Rule for the translation will be,
[(x + 6), (y + 1)]
In a litter of 7 kittens, each kitten weighs less than 3.5 ounces. Find and graph all the possible combined weights of the kittens.
Answer:
Step-by-step explanation:
24.5 just multiply hope that helpss
Factor
y=x² + 4x + 3
Answer:
[tex]y=(x+3)(x+1)[/tex]
Step-by-step explanation:
[tex]y=x^2+4x+3[/tex] <-- Given
[tex]y=x^2+x+3x+3[/tex] <-- Expand middle term
[tex]y=x(x+1)+3(x+1)[/tex] <-- Factor into two parts
[tex]y=(x+3)(x+1)[/tex] <-- Combine like terms
Jill takes 2 hours to paint a room, Jim takes 3 hours to paint a room. How long (in minutes) will it take both of them to paint a room
Answer:
72 minutes
Step-by-step explanation:
The sum of the rates of work in rooms per hour is ...
Jill's rate + Jim's rate
= (1/2 room/hour) +(1/3 room/hour) = (3/6 +2/6 room/hour) = 5/6 room/hour
__
Then the combined rate in hours per room is ...
1/(5/6 room/hour) = 6/5 hours/room = (6/5 hours/room)(60 minutes/hour)
= 72 minutes per room
Jill and Jim can paint the room in 72 minutes when they work together.
xsquare- 2x -4 = 0 using completing Square method
Answer:
........................
Darrian creates caricatures for an initial fee of $5 then charges $2 each minute it takes him to complete the drawing.Write an equation to match the situation.
Answer:
2x+5
Step-by-step explanation:
Equation y = 3x + 5 correctly represents the situation.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
Darrian creates caricatures for an initial fee of $5 then charges $2 each minute.
Let x be the number of each extra minutes.
And y be the total fees.
So, the equation;
The total fee = Charges of x minutes + initial fee.
y = 3x + 5
Therefore, the equation is y = 3x + 5.
To learn more about the equation;
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Consider the equation 5/3v +4 + 1/3v = 8. What is the resulting equation after the first step in the equation?
Answer:
See below
Step-by-step explanation:
[tex]\frac{5}{3}v+4+\frac{1}{3}v=8[/tex]
[tex]2v+4=8[/tex] <-- Resulting equation after first step
[tex]2v=4[/tex]
[tex]v=2[/tex] <-- Actual solution
please answer this, click file, thank you
Answer:
the answer is 34°
Step-by-step explanation:
a straight line = 180°
just do 180 - 146 = 34
A package weighs P pounds P being a whole number. to ship this package by express costs one dollar and sixty five cents for the first five pounds and twelve cents for each additional pound. the total shipping cost is three dollars and forty five cents. how many pounds of the package weigh?
I give brainliest to first answer
is y=2/3x+2 proportional
I need help please? ????????
Answer:
ummmmm i really don't get it but I think its 17/66
Step-by-step explanation:
multiply in to each fraction
Help stuck on this question
Solve for x help me please *****
Answer:
it's so blury pls fix the picture so I can solve it NOW
The map shows two walking trails in a park. Both paths end at the picnic area, located at C(6, 1). Trail A starts at A(−6, 6), and Trail B starts at B(−10, −11). If each unit on the map represents 0.5 mile, how many miles longer is Trail B than Trail A?
Answer:
12 miles
Step-by-step explanation:
because of slope
Please help- not a test. 15pts.
The orthocenter of ΔABC lies at vertex A. What can you conclude about the line segments BA and AC? Explain.
Answer:
You can conclude that the line segments BA and AC are perpendicular to each other.
Step-by-step explanation:
That is because in this case, the triangle presented would be a right triangle. In right triangles, the orthocenter is the vertex of the triangle where two of the segments intersect perpendicularly, forming a 90 degree angle. As the orthocenter is where the altitudes intersect (altitudes are 90 degrees), we are able to conclude that BA and AC are perpendicular to each other.
Answer:
CE
AE
segment addition postulate
Given: ABC is a triangle.
To prove: BC + AC > BA
Proof: In triangle ABC, we can draw a perpendicular line segment from vertex C to segment AB. The intersection of AB and the perpendicular is called E. We know that BE is the shortest distance from B to CE and AE is the shortest distance from A to CE because of the shortest distance theorem.
Therefore, and .
Now, add the inequalities, we get
.
Then, because Segment addition postulate (states that given 2 points E and F, a third point D lies on the line segment EF if and only if the distances between the points satisfy the equation ED + DF = EF)
Therefore, by substitution.
Step-by-step explanation: