The expression 2x+(x-7)^2 is equivalent to x^2+bx+49 for all values of x.
what is the value of b?
A. 12
B. -12
C. 14
D. -14
Answers
The expression [tex]2x+(x-7)^2[/tex] is equivalent to [tex]x^2+bx+49[/tex].
Then Value of b is - 12.
Option(B) is correct answer.
What is an expression?An expression is a mathematical phrase combining numbers and/or variables using mathematical operations. Both sides of an equation are expressions.
According to the question,
The expression [tex]2x+(x-7)^2[/tex] is equivalent to [tex]x^2+bx+49[/tex].
[tex]2x+(x-7)^{2}=x^{2} +bx+49[/tex]
⇒ [tex]2x+(x-7)^{2}=x^{2} +bx+49[/tex]
⇒[tex]2x+x^{2} -14x+49=x^{2} +bx+49[/tex]
⇒ [tex]x^{2} -12x+49=x^{2} +bx+49[/tex]
⇒[tex]-12x=bx[/tex]
⇒ [tex]b=-12[/tex]
∴ [tex]b=-12[/tex]
Hence, the expression [tex]2x+(x-7)^2[/tex] is equivalent to [tex]x^2+bx+49[/tex].
Then Value of b is - 12.
Option(B) is correct answer.
Learn more about expression here
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Related Questions
What is the solution to the linear equation? 2/5 + p = 4/5 + 3/5p
Answers
Answer:
p=1
Step-by-step explanation:
2/5 + p = 4/5 + 3/5p
Multiply each side by 5 to clear the fractions
5(2/5 + p) = 5(4/5 + 3/5p)
2 +5p = 4 + 3p
Subtract 3p from each side
2+5p-3p = 4+3p-3p
2+2p = 4
Subtract 2 from each side
2+2p -2 = 4-2
2p =2
Divide by 2
2p/2 = 2/2
p=1
[tex]\huge\mathbb{\fcolorbox{red}{lavenderblush}{✰Answer}}[/tex]
[tex]\sf{\dfrac{2}{5}+p=\dfrac{4}{5}+\dfrac{3p}{5} }[/tex] [tex]\sf{ \dfrac{2}{5}+p=\dfrac{4+3p}{5} }[/tex] [tex]\sf{5(\dfrac{2}{5}+p)=4+3p }[/tex] [tex]\sf{ 2+5p=4+3p }[/tex] [tex]\sf{5p-3p=4-2 }[/tex] [tex]\sf{ 2p=2 }[/tex] [tex]\sf{p=\dfrac{2}{2} }[/tex] [tex]\bold{p=1 }[/tex]How many minutes will it take to bake 24 tortillas
Answers
Answer:
72 mins
Step-by-step explanation:
12 mins = 4 tortillas
1 tortilla = 3 mins
3x24=72
72 mins
Answer:
72 minutes
1 hour and 12 minutes
Step-by-step explanation:
[tex]\frac{4}{12}: \frac{24}{y}[/tex]
4 × y = 12 × 24
4y = 288
4y ÷ 4 = 288 ÷ 4
y = 72
what is lighter than a feather but the strongest man can't hold for 5 minutes
Answers
Answer:
obviously our breathe is lighter than a feather but the strongest man can't hold for 5 minutes.
Answer:
breathe
Step-by-step explanation:
breathe. air is light but even the strongest man can't hold for 5 minutes
PLS ANSWER ASAP DUE 9:35
Answers
Answer:
c) 72
hope this helps!
please give brainiest<3
Answer:
72
Step-by-step explanation:
Substitution:
4^3 + 4 x 6 - 16
64+24-16=72
can someone pls help for brainlest
Answers
Answer:
12.56 in ^2
Step-by-step explanation:
First find the area of a circle with radius 4
A = pi r^2
A = (3.14) 4^2
A =50.24
Since it is 1/4 of a circle, multiply by 1/4
1/4 ( 50.24)
12.56
Answer:
Quarter circle's area is 12.56 inches².
Step-by-step explanation:
Concept:- Firstly, we need to find the area of circle and Since, it is quarter of circle we need to multiply the area of circle by 1/4. and we get answer
✯ Solution ✯Finding area of circle
Using Formula
Area of circle = π × r ²
Where,
r ,is the radius of circleAnd we have given
Radius, r of circle is 4 in.Value of π is 3.14Substitute the value into the formula
Area of circle = 3.14 × ( 4 in. )/²
now,
Area of circle = 3.14 × 16 in ².
multiply , we get
Area of circle is 50.24 nches ²
As have to find the quarter circle's area ,
and we know that quarter is the one fourth of the circle .
Quarter circle's area = Area of circle × 1/4
Multiply , we get
Quarter circle's area = 50.24 × 1/4
Therefore, quarter circle's area is 12.56 inches².
Graph the system below and write its solution.
2x+y=4
1
y =
2*-1
Note that you can also answer "No solution" or "Infinitely many" solutions.
.
Solution:
?
No
solution
Infinitely
many
(0,0)
0
5
?
Answers
Answer:
2x+y=4
2times-1 is -2
2x+-2=4
2x=4
x=2
Mrs. Archer is doing a painting project with her art class. She uses a large jug with 28.5 ounces of blue paint to fill 6 smaller bottles. If she divides the paint evenly, how much paint will be in each bottle?
Answers
Answer:
4.75
Step-by-step explanation:
Divide 28.5 evenly with 6 because thee are 6 bottles. Then you receive 4.75
Hope this helps
please help me answer this!!
Answers
Answer:
(x, y) = (10, 290)
Step-by-step explanation:
From the table
Total fees = fixed + variable
Fixed:
When number of times Ahmed mowed, x = 0
y = 40
When x = 2, y = 65
Rate of change = y2 - y1
= 65 - 40
= 25
y = 40 + 25x
Where,
y = total fees charged
40 = fixed fee
25x = variable fee
Total amount Ahmed will make for mowing 10 times
when x = 10
y = 40 + 25x
y = 40 + 25(10)
= 40 + 250
= 290
y = 290
(x, y) = (10, 290)
pleaseeee helpppp meee!!
Answers
Answer:
15 players on each team
Step-by-step explanation:
- 2 players from EACH team is subtracted= 2(players)x6(teams) = 12 players in total off the field
- now there are only 78 players on the field
(78+12)/6= 15
-Adding the amount of players on the feild and the players that were sent for equitment is 90. Then dividing 90 by the amount of teams there are, 6
Can anyone help me on this I would appreciate it
Answers
Answer:
14
Step-by-step explanation:
Triangle=180
180-90 (RA) = 90
90-41= 39
(2x+11)=39
2x=28
x=14
PLEASE HELP!! This is timed, but I don't recall ever learning this info T-T
I'll mark brainliest!!
Answers
Answer:
c
Step-by-step explanation:
i hope it helped ᘳ◕ᴥ◕ᘰ
A bag of cereal contains 12 blue marsh mellows, 16 red marshmellows , and 8 orange marsh mellows.If a marshmellow is picked from the bag at random, what is the probability that it is a red marsh mellow? Answers have been rounded to the tenths place.
Answers
Answer:
0.4 (decimal)
4/9 (fraction)
Step-by-step explanation:
Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.
For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.
Probability a red marshmallow is picked = number of red marshmallows in the bag / sum of marshmallows in the bag
sum of marshmallows in the bag = 12 + 16 + 8 = 36
Probability a red marshmallow is picked = 16/36
To transform to the simplest form. divide both the numerator and the denominator by 4
= 4/9
to convert to decimal, divide 4 by 9 = 0.4444
0.4 to the nearest tenth
the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero
1250 people visit a certain website every day. At this rate, how many visitors will the site receive in a week?
Answers
Answer:
8750 people
Step-by-step explanation:
1250 * 7 (7 days in a week)
8750 people
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Select the correct answer.
How would you write this expression as a sum or difference?
[tex]log_{3} (^{5\sqrt{x}} X y )[/tex]
Answers
Answer:
[tex]\log_{3} ({5\sqrt{x}} * y ) = \log_{3}({5) + \log_{3}(\sqrt{x}) +\log_{3}( y )[/tex]
Step-by-step explanation:
Given
[tex]\log_{3} ({5\sqrt{x}} * y )[/tex]
Required
Write as sum or difference
Using addition law of logarithm, the equation becomes:
[tex]\log_{3} ({5\sqrt{x}} * y ) = \log_{3}({5\sqrt{x}) +\log_{3}( y )[/tex]
Expand
[tex]\log_{3} ({5\sqrt{x}} * y ) = \log_{3}({5 * \sqrt{x}) +\log_{3}( y )[/tex]
Apply addition law
[tex]\log_{3} ({5\sqrt{x}} * y ) = \log_{3}({5) + \log_{3}(\sqrt{x}) +\log_{3}( y )[/tex]
What is the value of c?
30°
с
Answers
Answer:
c = 60°
Step-by-step explanation:
Since the measures are among a 90° angle, we need to subtract 30° from 90° which equals 60°
c = 60°
What is the value of X in the figure below? In this diagram ∆ABD is similar to ∆CAD.
Answers
Answer:
F. 45/4Step-by-step explanation:
Corresponding sides have same ratio:
AB/AC = BD/ADFind AB:
AB = [tex]\sqrt{20^2-15^2} = 5\sqrt{7}[/tex]Find AD:
AD = √15²-x²Now the ratio:
5√7/15 = (20 - x)/√(15²-x²)√7 *√(225-x²)= 3(20 - x)7(225 - x²) = 9(20 -x)²7*225 - 7x² = 9(400 - 40x + x²)1575 - 7x² = 3600 - 360x + 9x²16x² - 360x + 2025 = 0(4x)² - 2*4x*45 + 45² = 0(4x - 45)² = 04x - 45 = 04x = 45x = 45/4Correct choice is F
Acircle with radius of 2 cm sits inside a llcm x 12 cm
rectangle.
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
Answers
Answer:
119.4
Step-by-step explanation:
The Area of the Rectangle : 132 cm
Area of the Circle : 12.6 cm
Shade= MINUS - 132 cm - 12.5 cm = 119.4!
Happy To Help! :)
What is the slope of a line passing through the points (3,9) and (5,10)?
Answers
Answer:
1 / 2 or 0.5
Step-by-step explanation:
use the formula ; m = y2 - y1 / x2 - x1
where y2 = 10
y1 = 9
x2 = 5
x1 = 3
Select ALL the functions whose graphs include the point (16, 4).
Answers
Answer:
D
Step-by-step explanation:
x=16
y=4
4=16-12
4=4
Answer:
D
Step-by-step explanation:
write the expression in expanded form
3h^3(k+3)^2
Answers
Answer:
3h³k² + 18h³k + 27h³
Step-by-step explanation:
Given
3h³(k + 3)² ← expand factor using FOIL
= 3h³(k² + 6k + 9) ← distribute parenthesis
= 3h³k² + 18h³k + 27h³
lol it looks easy but everytime i submit my answer it ends up wrong sooo help pls
Answers
Answer:
(y+8)(y+2)
Step-by-step explanation:
y^2 + 10y + 16
What two numbers multiply to 16 and add to 10
8*2 = 16
8+2 =10
(y+8)(y+2)
y^2+8y+2y+16
y(y+8)+2(y+8)
(y+8)(y+2)
Find the equation of the line that is perpendicular to the line
y = x-9 and passes through the point (7,9).
Answers
Answer:
[tex]y=-x+16[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)Perpendicular lines always have slopes that are negative reciprocals (ex. 3 and -1/3, 5/6 and -6/5, etc.)1) Determine the slope (m)
y=x-9
Rewrite the equation
y=1x-9
Now, we can identify clearly that the slope of the line is 1. The negative reciprocal of 1 is -1, so therefore, the slope of a perpendicular line would be -1. Plug this into [tex]y=mx+b[/tex]:
[tex]y=-1x+b\\y=-x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=-x+b[/tex]
Plug in the given point (7,9) and solve for b
[tex]9=-7+b[/tex]
Add 7 to both sides to isolate b
[tex]9+7=-7+b+7\\16=b[/tex]
Therefore, the y-intercept is 16. Plug this back into [tex]y=-x+b[/tex]:
[tex]y=-x+16[/tex]
I hope this helps!
Math question. Genius, please answer correctly.
Answers
Answer:
16-31 20, 18,25,28,31,23,19,27,22,25,20 11
32-47 33,42,36,41,47 5
48-65 65,52,61,50 4
Step-by-step explanation:
45
24
K K
AM
51
이
15
17
15
이
8
15
O
8
17
음
Answers
Hope this help!!!
Have a nice day!!!!
WORTH 25 POINTS!!!!
match the following
Answers
Answer:
Step-by-step explanation:
Domain of a function is defined by the set of x-values (input values) and Range is the set of y-values (output values) of the function.
1). The range and domain of P = {(x, y)| y = 3}
Domain: Set of all real numbers
Range: {y: y=3}
2). The domain set of C = {(2, 5), (2, 6), (2, 7)}
Domain: {2}
3). The range set of E = {(3, 3), (4, 4), (5, 5), (6, 6)}
Range: {3, 4, 5, 6}
4). The range and domain set of F = {(x, y)| x + y = 10}
Domain = Range = {All real numbers}
what is the solution to x^2 + 6x + 7
Answers
Answer:
x2+6x+7
Step-by-step explanation:
there are no like terms
i think you are missing something in your question (like the equal sign?)
reply in comment so i can help:)
a right triangle has legs of lengths 7 and 2, what is the length of the hypotenuse to the nearest tenth
Answers
Answer:
hypotenuse = 7.3
Step-by-step explanation:
here 7 and 2 are the legs og the right triangle .we should find hypotenuse.
let the legs of the right triangle be a nd b respectively . And c be hypotenuse
using pythagoras theorem to find hypotenuse
a^2 + b^2 = c^2
7^2 + 2^2 = c^2
49 + 4 = c^2
53 = c^2
[tex]\sqrt{53}[/tex] = c
7.28 = c
7.3 =c
Answer:
7.3
Step-by-step explanation:
[tex]7^{2} + 2^{2} = x^{2} \\ 53 = x^{2}\\\sqrt{53} = \sqrt{x^{2}} \\x = 7.3[/tex]
Find mZB.
Round to the nearest degree.
11
B В
7.
15
Answers
Answer:
m∠B = 111º
Step-by-step explanation:
use law of cosines
c² = a² + b² - 2ab*cosC
---------------------------------
15² = 7² + 11² - 2(7)(11)cosB
225 = 49 + 121 - 154cosB
225 = 170 - 154cosB
Subtract 170 form both sides
55 = -154cosB
Divide both sides by -154
-0.3571428571 = cosB
m∠B = arccos -0.3571428571
use calculator
m∠B = 110.924832425009406
Rounded
m∠B = 111º
A group of friends wants to go to the amusement park. They have $363 to spend on
parking and admission. Parking is $5.50, and tickets cost $35.75 per person,
including tax. How many people can go to the amusement park?
Answers
Answer:
10 people can go to the amusement park
Step-by-step explanation:
363 - 5.50 = 357.5
357.5 / 35.75 = 10
True or False: in a table of a proportional relationship, the ratio or y/x is constant.
Answers
Answer:
true
Step-by-step explanation:
It is True that in a table of a proportional relationship, the ratio or y/x is constant.
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
It is given that, y∝x
In order to eradicate the proportional sign introduces the constant as,
y=kx
k=y/x
k is the constant value.
Thus, it is True that in a table of a proportional relationship, the ratio or y/x is constant.
Learn more about the proportional here:
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