The value of [tex]c[/tex] such that the line [tex]y = 2\cdot x + 3[/tex] is tangent to the parabola [tex]y = c\cdot x^{2}[/tex] is [tex]-\frac{1}{3}[/tex].
If [tex]y = 2\cdot x + 3[/tex] is a line tangent to the parabola [tex]y = c\cdot x^{2}[/tex], then we must observe the following condition, that is, the slope of the line is equal to the first derivative of the parabola:
[tex]2\cdot c \cdot x = 2[/tex] (1)
Then, we have the following system of equations:
[tex]y = 2\cdot x + 3[/tex] (1)
[tex]y = c\cdot x^{2}[/tex] (2)
[tex]c\cdot x = 1[/tex] (3)
Whose solution is shown below:
By (3):
[tex]c =\frac{1}{x}[/tex]
(3) in (2):
[tex]y = x[/tex] (4)
(4) in (1):
[tex]y = -3[/tex]
[tex]x = -3[/tex]
[tex]c = -\frac{1}{3}[/tex]
The value of [tex]c[/tex] such that the line [tex]y = 2\cdot x + 3[/tex] is tangent to the parabola [tex]y = c\cdot x^{2}[/tex] is [tex]-\frac{1}{3}[/tex].
We kindly invite to check this question on tangent lines: https://brainly.com/question/13424370
5x + 8 + 3x + 4 = -40 +4
Answer:
x=-6
Step-by-step explanation:
Answer:
[tex]x=-6[/tex]
Step-by-step explanation:
[tex]5x+8+3x+4=-40+4[/tex]
⇒ Subtract 4 from both sides:
[tex]5x+8+3x+4-4=-40+4-4[/tex]
[tex]5x+8+3x=-40[/tex]
⇒ Combine like terms:
[tex]5x+3x=8x[/tex]
[tex]8x+8=-40[/tex]
⇒ Subtract 8 from both sides:
[tex]8x+8-8=-40-8[/tex]
[tex]8x=-48[/tex]
⇒ Divide both sides by 8:
[tex]\frac{8x}{8}=\frac{-48}{8}[/tex]
[tex]x=-6[/tex]
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What is the y-intercept of the line shown below? Enter your answer as a coordinate pair.
Answer:
The x intercept is (-2,0)
the y intercept is (0,4)
Can someone help me with 8-grade math homework, please
Answer:
so y=7.25x+9.99 where y is the total money they spend, and the x is the total number of they want to bought jersey which is 20,
So here it's equation:
y=7.25(20)+9.99
y= 145+9.99
y=154.99, therefore the total is 154.99
and the second one is find and explain the mistake
the y values is the mistake when you equate the number of x to the equation given so the true answer of that table if you use the equation is:
X Y
2 0
3 -2
4 -4
5 -6
Write the equation of the line in slope-intercept form that passes through the given points.
(-1, 8) and (5,-2)
Answer:
y = -5/3x + 19/3
Step-by-step explanation:
y2 - y1 / x2 - x1
-2 - 8 / 5 - (-1)
-10/6
= -5/3
y = -5/3x + b
8 = -5/3(-1) + b
8 = 5/3 + b
19/3
20 < 5 (F – 32) < -15
solve the compound inequalities
Answer:
no solution
Step-by-step explanation:
20 < 5(F - 32) < -15
-15 can never be greater than 20, thus the answer is no solution
Mr. Reyes broke his bicycle. He asked Renato to fix it. Renato charged 350 php for the
new parts of the bicycle and 150 php per hour for labor to repair the bicycle. If Renato
spent 4 hours repairing Mr. Reyes’ bike, what is the total amount he needs to pay?
a. What is asked?
b. What are the given numbers?
c. What are the operations needed?
d. Write the number sentence.
e. Solve. Show your solution.
Answer:
950 phpStep-by-step explanation:
a. What is asked?
Find the total amount for repair of the bike.b. What are the given numbers?
350 php for parts and 150 php per hour for labor. Total 4 hours repair duration.c. What are the operations needed?
Multiplication and additiond. Write the number sentence.
Find the labor charge by multiplying the rate by the number of hours and add to the cost of parts.e. Solve. Show your solution.
350 + 150*4 = 350 + 600= 950 phpA group of students left school at 8:00 am on a field trip to a science museum 90 miles away. Which best the average speed of the bus if they arrived at 10:00
Answer:
45 mph
Step-by-step explanation:
90 / 2 = 45 mph
HELP ME ASAP!!!!!!
See pic attached
Step-by-step explanation:
a ) 9 × 2 = 18 → 18 + 3 = 21
o/p = 21
b) 17 - 3 = 14 → 14/2 = 7
i/p = 7
hope this answer helps you dear!
There are 35 boys in 6th grade. The number of girls in 6th grade is 40. Emma says that means the ratio of the number of boys in 6th grade to the number of girls in 6th grade is 3:4. Is Emma correct? If not, what is the correct answer?theses are the answers you chose froma: correct ratiob:7:8c: 5;8d: 8:7
Answer:
No, Emma is not correct.
Step-by-step explanation:
because if we put 35 and 42 in rational form we can write it to its simple form by dividing it
35 / 7 = 5
42 / 7 = 6
after dividing we get the answer as 5:6.
Hope it helps ☺️
1/5d=-3 help I'm confused
Answer:
d=-15
Step-by-step explanation:
1/5d= -3
d= -3×5
d= -15
Hope this helps you. Have a nice day. Please mark as brainliest. It helps a lot. ^_^
express 23/15-7/10 as a percentage
Answer:
83.3%
Step-by-step explanation:
PLZZZ HELPPPP ILL MARK BRAINLIEST TO FIRST AND CORRECT ANSWER THAT HAS WORK AND A THX TO SECOND AND CORRECT ANSWER.
Answer:
well I think it is none of these because the square root would be 9^2
Step-by-step explanation:
Answer:
9^2
Step-by-step explanation
if the are is 81 then you have to think for th numbers like if the are was 20
it would be 5x4=20cm sorry i can't type in anything special ti won'y let me
b^(3) * b^(4) write without exponents
Answer:
(b×b×b)×(b×b×b×b)
Step-by-step explanation:
Writing the equation out is the only way to remove the exponents.
please help me someone
It costs 4.99 for 2lbs of bacon and 6.99 for 5lbs of bacon.which is a better buy?
Answer:
The 5lbs is a better buy
Step-by-step explanation:
Find the price per pound:
4.99/2= $2.49
6.99/5= $1.39
3) if the cost of 1 pen is Rs.10, find the cost of 5 pen
Answer: 5 pens cost Rs.50
Explanation: Since 1 pen costs Rs.10, you will need to multiply the number of pens (1) and the cost of that number of pens (Rs.10) by the amount of pens you must find the cost for (5). Since 10 times 5 is 50, that means that 50 is the cost of 5 pens.
I hope this helps!
factor [tex]x^{2} + 2x[/tex]
Answer:
the answer is x(x+2)
what the slope of a line
Answer:
The slope of a line is a number that measures its "steepness", usually denoted by the letter m. It is the change in y for a unit change in x along the line.
Hope it helps.
4) Ashley's Bikes rents bikes for S13 plus $5
per hour. Mary paid $38 to rent a bike.
For how many
hours did she rent the bike?
Answer:
6 hours.
Step-by-step explanation:
1st hour - 13
2nd hour - add 5 = 18
3rd hour - 23
4th hour - 28
5th hour - 33
6th hour - 38 (which is the end total)
Can someone pls help me out
___________
[tex] \: [/tex]
[tex]\boxed{ \rm{answer \: by \: { \boxed{ \rm{☆HayabusaBrainly}}}}}[/tex]
This is Question no picture, soo iam work in question before^^
Step by step :x² = 12² + 10²
x² = 144 + 100
x² = 244
x = 15,6m✔
solve for r to find the missing term in geometric sequence
—
hi can someone please answer my question. thank you ❤️
Step-by-step explanation:
given :
120, 60, 30, _, _, _
find r!
solution :
r = 60/120 = ½.
=> 120,60,30, 15, 15/2 , 15/4 , ...
Step-by-step explanation:
Calcute the ratio :
r = Un/Un-1
r = 60/120
r = ½
Calculate 4th term :
Un = ar^n-1
U4 = 120 × ½^4-1
U4 = 120 × ½³
U4 = 120 × 0.125
U4 = 15
Calculate 5th term :
Un = ar^n-1
U5 = 120 × ½^5-1
U5 = 120 × ½⁴
U5 = 120 × 0.0625
U5 = 7.5
Calculate 6th term :
Un = ar^n-1
U6 = 120 × ½^6-1
U6 = 120 × ½⁵
U6 = 120 × 0.03125
U6 = 3.75
80°
50°
Зc +2°
C=.
Can i get a step by step or a video on this?
Answer:
C= 19.333333(Its infinite)
Solve for x.
9(x + 1) = 25 + x
x = 2
x = 3
x = 4
x = 5
Answer:
x = 2
Give me the brainlest, please?
Step-by-step explanation:
Answer: x=2
Step-by-step explanation:
9(x+1)=25+x (Distribute the 9)
9x+9=25+x (Work both sides to isolate the variable)
-9 -9
9x=16+x
-x -x
8x=16
/8 /8
x=2
Caroline wears a suit to work everyday. Caroline has 6 suits, 3 overcoats, and 4 pairs of shoes. How many different outfits can Caroline create? *
please answer, it’s a test
Answer:
A
Step-by-step explanation:
The inverse of 2x would be 1/2 x and the inverse of +6 would be -6.
What can divided 62 and 30
A number that multiplies a variable in a term is a_____.
A. factor
B. coefficient
C. term
D. variable
Answer:
coefficient
Step-by-step explanation:
Answer: Answer:
Step-by-step explanation:
Help me pls and thx and have a nice day
Answer: the answer should be the last one
Step-by-step explanation:
8+7+5+7+9
Mathematics middle school
Answer:
36
Step-by-step explanation:
hope this helps
8+7+5+7+9
15+5+7+9
20+7+9
27+9
36
= 8+7+5+7+9
= 15+5+7+9
= 20+7+9
= 27+9
= 36
The answer is 36.HELPPPP PLEASEEEE!!!!
Answer:
B
Step-by-step explanation: