Answers
Answer:
a = p * q
b = p * s + q * r
c = r * s
Step-by-step explanation:
In the trinomial ax² + bx + c
a is the coefficient of x²
b is the coefficient of x
c is the numerical term
∵ The trinomial is ax² + bx + c
∵ Its factors are (px + r) and (qx + s)
∴ ax² + bx + c = (px + r)(qx + s)
∵ (px + r)(qx + s) = (px)(qx) + (px)(s) + r(qx) + (r)(s)
∴ (px + r)(qx + s) = pqx² + (psx + qrx) + rs
∴ ax² + bx + c = pqx² + (ps + qr)x + rs
→ By comparing the two sides
∵ ax² = pqx² ⇒ divide both sides by x²
∴ a = pq
∵ bx = (ps + qr)x ⇒ Divide both sides by x
∴ b = ps + qr
∴ c = rs
∴ a = p * q
∴ b = p * s + q * r
∴ c = r * s
Related Questions
How many solutions does the equation have?
x^4 + 7x^2 – 144 = 0
Answers
Answer:
The equation has no real solutions. It has 2 imaginary, or complex solutions.
Step-by-step explanation:
Tony bought 255 1-inch nails and 5 boxes of 2-inch nails. Each box of 2-inch nails had equal amounts of nails in them. He bought a total of 620 nails. Find the number of nails in each box of 2-inch nails.
Answers
Answer:
73 nails
Step-by-step explanation:
Number of 1 inch = 255
Boxes of 2 - inch = 5
Each box of 2 _inch has equal amount of nails
Total number of nails = 620
Number of nails in each box of 2_inch nails:
Let Number of nails in each box = b
Number of 1_inch + 5 * number of 2_inch = 620
255 + 5b = 620
5b = 620 - 255
5b = 365
5b / 5 = 365 / 5
b = 73
Hence, there are 73 nails in each box of 2_inch nails
HELP! Quickly! I need this ASAP
Answers
Answer:
y=10x+5
Step-by-step explanation:
y1-y2/x1-x2
5-15/0-1
-10/-1
10
The slope is 10
when the x is zero, y is 5 therefore 5 is the Y-intercept
y=10x+5
~PumpkinSpice1♥
PLEASE HELP
In Exercises 1 and 2, identify the slope of the line. Then identify a point the line
passes through.
1. y - 2 - 4(x - 5)
2. y - 7 - -3(x + 6)
Answers
Answer:
1. Slope = 1/4
Point = ( 1, 1 )
2. Slope = -3
Point = ( 3, -20 )
Step-by-step explanation:
HELP
The length of a rectangle is
[tex]18x ^{2} + 6x - 4[/tex]
and the width of the rectangle is
[tex]3x {}^{2} - 9x + 10[/tex]
what expression would represent the perimeter of the rectangle?
Answers
Answer:
21x^2+3x+12
Step-by-step explanation:
When Leroy went to bed, the temperature was – 2°F. He needed his electric blanket to keep warm! By morning, the temperature had risen 9°F. What was the temperature in the morning?
Answers
Answer:
it would be 7
Step-by-step explanation:
the equation would be ( if you read the problem) -2+9 and that is equal to 7
the pyramid shown has a rectangular base and faces that are isosceles triangles find the total surface area to the nearest tenth
Answers
Answer:
I think is C.
Step-by-step explanation:
I'm so sorry if wrong!
How many liters each of a 45% acid solution and a 70% acid solution must be used to produce 50 liters of a 65% acid solution? (Round to two decimal places if necessary.)
Answers
Answer:
The number of liters of the 45% acid solution = 10 liters
The number of liters of the 70% acid solution is = 40 liters
Step-by-step explanation:
How many liters each of a 45% acid solution and a 70% acid solution must be used to produce 50 liters of a 65% acid solution? (Round to two decimal places if necessary.)
Let x be the number of liters of the 45% acid solution
The number of liters of the 70% acid solution is y
x + y = 50
x = 50 - y
Also
How many liters each of a 45% acid solution and a 70% acid solution must be used to produce 50 liters of a 65% acid solution?
We have:
45% × x + 70% × y = 65% × 50
0.45x + 0.70y = 0.65 × 50
0.45x + 0.70y = 32.5
We substitute x = 50 - y in the equation
0.45(50 - y) + 0.70y = 32.5
= 22.5 - 0.45y + 0.70y = 32.5
= - 0.45y + 0.70y = 32.5 - 22.5
= 0.25y = 10
Divide both sides by 0.25
= y = 10/0.25
y = 40 liters
x = 50 - y
x = 50 - 40
x = 10 liters
Hence,
The number of liters of the 45% acid solution = 10 liters
The number of liters of the 70% acid solution is = 40 liters
Il signor Rossi percepisce uno stipendio mensile di2000 euro. L’azienda dove lavora, in seguito a un periodi di utili superiori al previsto, aumenta gli stipendi del 6%.Successivamente, a causa di un periodo di crisi, gli stipendi vengono diminuiti del 6%. Dopo l’aumento e la diminuzione, a quanto ammonterà lo stipendio del signor Rossi? E qual e in percentuale la variazione di stipendio rispetto allo stipendio iniziale?
RISPOSTA: 1992,8 euro; -0,36%
Answers
Answer:
Mr. Rossi receives a monthly salary of 2000 euros. The company where he works, following a period of profits higher than expected, increases salaries by 6%. Subsequently, due to a period of crisis, salaries are reduced by 6%. After the increase and decrease, how much will Mr. Rossi's salary be? And what is the percentage change in salary compared to the initial salary?
Step-by-step explanation:
I translated it from Italian to English for you.
Select all the pairs that could be reasonable approximations for the diameter and circumference of a circle. Explain your reasoning.
5 meters and 22 meters.
19 inches and 60 inches.
33 centimeters and 80 centimeters.
Answers
Answer:
19 inches and 60 inches
Step-by-step explanation:
The offense of a high school football team gained 8 yards on first down and then lost 5 yards on second down. What expression represents the total amount of yards gained by the offense?
Answers
The answer would be 8 + (-5).
What is the y intercept of y= -3x-2
Answers
(0,-2) or just -2 is the correct y intercept you can find this by graphing it:)
Answer:
-2
Step-by-step explanation:
we always know that the y intercept is after the x part. for example, if it was
y = 5x + 3 the y intercept would be 3. in this equation, it's negative 2 because of the subtraction sign
help please!!!!!!!!!!!!!!!!!
Answers
Answer:
the answer is 9.5
Step-by-step explanation:
Answer:
I think it's C. 9.5
Hope this Helps!
sandra colored 1/3 of her picture black, as shown. what percent of her picture did she color white
Answers
The painting as a whole = 1. 1 - 1/3 (the amount that is black) = 2/3. Thus, 2/3 is white.
The difference 3 1/2 minus 1 1/2 must be
between and
Answers
Answer:
2
Step-by-step explanation:
3 1/2 - 1 1/2 = 2
PLS GIVE BRAINLIEST
The length of x 200 feet
Answers
Answer:
If the length of x is less than 200, then add <.
If the length of x is more than 200, then add >.
If the length of x is 200, then add =.
Step-by-step explanation:
I need help quick please
Answers
What is the probability of rolling at least one six on a pair of fair
dice?
Answers
It is a 67% percent chance.
What is the slope-intercept equation for the line below?
(5, 4)
(0, 2)
Answers
Answer:
=
2/5x +2
Step-by-step explanation:
let me know if im wrong
hope it helps :)
Answer:
A. y=2/5x +2
step-by-step explanation:
hope this helped :-)
ABCD is a rhombus. Solve for x, if m AFB
(16x + 6)
B
F
D
C
Answers
Mary is buying hair clips online. The online store charges a fee for each hairclip and a shipping fee. On Monday, Mary placed an order for 8 hairclips, and her total came to $33.75. On Friday, she placed an order for 11 hair clips, and her order came to $44.25. Find the price of each hair clip and the price of shipping.
Answers
4x19(clips total)= 76
78-76=2
2/2=1
so $1 for shipping for each order and $4 a clip
7 – Зу = 20
y = 5х – 4
QUICK! how do i do this i need the x and y this is the Systems of equations with substitution
Answers
Answer:
x=1/15 y = -4 1/3
Step-by-step explanation:
First combine like terms.
-3y = 13
y= -13/3
y= -4 1/3
Substitute for y in next equation
-4 1/3 = 5x - 4
5x = 4 1/3 - 4
5x = 4 1/3 - 4
5x = 1/3
x = 1/3 divided by 5
Since fractions can't be divided, multiply by the inverse
x = 1/3 times 1/5 = 1/15
steph,andra,emily,and becca are planning a road trip from their hometown to san antonio
hometown:8,6
san antonio:-6,-7
a. if the girls take turns driving and each girl drives the same distance,at what point should they stop from emily to begin her turn as the third driver?
b.at what point does emily's turn to drive end?
Answers
Answer:
a. Emily should begin her turn as the third driver at point (1, -0.5).
b. Emily's turn to drive end at point (-2.5, -3.75).
Step-by-step explanation:
Let assume that the group of girls travels from their hometown to San Antonio in a straight line. We know that each location is, respectively:
Hometown
[tex]H(x,y) = (8,6)[/tex]
San Antonio
[tex]T(x,y) = (-6,-7)[/tex]
Then, we can determine the end of each girl's turn to drive by the following vectorial expression based on the vectorial equation of the line:
Steph
[tex]S(x,y) = H(x,y) + \frac{1}{4}\cdot [T(x,y)-H(x,y)][/tex] (1)
[tex]S(x,y) = (8,6) + \frac{1}{4}\cdot [(-6,-7)-(8,6)][/tex]
[tex]S(x,y) = (8,6) +\frac{1}{4}\cdot (-14,-13)[/tex]
[tex]S(x,y) = (4.5,2.75)[/tex]
Andra
[tex]A(x,y) = H(x,y) + \frac{2}{4}\cdot [T(x,y)-H(x,y)][/tex] (2)
[tex]A(x,y) = (8,6) + \frac{2}{4}\cdot [(-6,-7)-(8,6)][/tex]
[tex]A(x,y) = (8,6)+\frac{2}{4}\cdot (-14,-13)[/tex]
[tex]A(x,y) =(1, -0.5)[/tex]
Emily
[tex]E(x,y) = H(x,y) + \frac{3}{4}\cdot [T(x,y)-H(x,y)][/tex] (3)
[tex]E(x,y) = (8,6) + \frac{3}{4}\cdot [(-6,-7)-(8,6)][/tex]
[tex]E(x,y) = (8,6)+\frac{3}{4}\cdot (-14,-13)[/tex]
[tex]E(x,y) = (-2.5, -3.75)[/tex]
a. If the girls take turns driving and each girl drives the same distance, at what point should they stop from Emily to begin her turn as the third driver?
Emily's beginning point is the Andra's stop point, that is, [tex]A(x,y) =(1, -0.5)[/tex].
Emily should begin her turn as the third driver at point (1, -0.5).
b. At what point does Emily's turn to drive end?
Emily's turn to drive end at point (-2.5, -3.75).
Mrs. Bell can grade 12 papers in 20 minutes. At this
rate, how many papers can she grade in one hour?
Answers
Answer:
36
Step-by-step explanation:
1. Fill in the chart
Words
Expression
The Value of the Expression
a. 50 times the sum of 64 and 36
50 x 64 + 36 )
5000
b. Divide the difference between
1,200 and 700 by 5
(1,200 - 700): 5
100
C. The sum of 3 fifteens and 17
fifteens
45 + 255
d. 15 times the sum of 14 and 6
e.
10 x (250 +45)
f.
(560 + 440) x 14
Answers
Answer:
See answers in bold
Step-by-step explanation:
Words Expression
The Value of the Expression
a. 50 times the sum of 64 and 36 ... 50 x (64+36) = 50x (100) = 5000
50 x 64 + 36 )
5000
b. Divide the difference between 1,200 and 700 by 5 ...(1200-700) / 5 = 500/5 = 100
(1,200 - 700): 5
100
C. The sum of 3 fifteens and 17 fifteens ... [tex]\frac{3}{15}[/tex] + [tex]\frac{17}{15}[/tex] = [tex]\frac{20}{15}[/tex] = [tex]\frac{4}{3}[/tex]
45 + 255
d. 15 times the sum of 14 and 6 ... 15 x (14 + 6) = 15 (20) = 300
e.
10 x (250 +45) ...10 times the sum of 250 and 45
f.
(560 + 440) x 14... 14 times the sum of 560 and 440
Hope this helps
pls answer QUICK PLSSSS
Answers
Step-by-step explanation:
1) 13.57
+2.93
With this, we subtract from the back Meaning we add starting from back to forward;
13.57
+2.93
16.50
We have that because when you add 7 and 3 you get 10 so we write the 0 there and add the remaining 1 to the 5 making it 6 and then 6 plus 9 will give you 15 then we write the 5 then we add the remaining 1 to the 3 making it 4 then we add the 4 to the 2 making it 6 after this there is no remainder so we just write the 1.
Find the slope and y-intercept for the table.
slope:
y-intercept:
Answers
Answer:
slope: 3
y-intercept: 3?
Step-by-step explanation:
Y-intercept is 2
Will give brainliest if correct.
Answers
Your answer should come to:
y = -2/3x + 3
HELPP
Lacey was looking at some data on World Cup soccer matches. She noticed a negative linear relationship
between the number of fans attending a match and the number of total goals scored in that match. Here is
computer output from a least-squares regression analysis for using attendance (in thousands of fans) to predict
the total number of goals scored:
Predictor
Coef
SE Coef
T
P
Constant
3.260
0.145
22.535
0.000
Attendance (thousands)
-0.009
0.003
-3.330
0.001
Use this model to predict the total number of goals scored in a match with 90 thousand fans in attendance.
You may round your answer to the nearest whole number of goals.
goals
Answers
Answer:
the answer is 2
Step-by-step explanation:
this was a question on my test on khan academy :D
Estimate by rounding both numbers to tens and then divide.
61 ÷ 29 is approximately
Answers
Answer:
2
Step-by-step explanation:
Round: 61 → 60Round: 29 → 30Divide: 60 ÷ 30 = 2I hope this helps!