Answers
Answer:
A) Gradient = -3
B) 3y - x = 7
Step-by-step explanation:
The curve has the equation;
y = x³ - 6x² + 9x + 1
We are given the pints it passes through as;
A(2,3) and P(3, 1)
A) to find the gradient, we will find the derivative of the given equation.
Thus;
Gradient = y' = 3x² - 12x + 9
At point A, x = 2. Thus;
Gradient = 3(2²) - 12(2) + 9
Gradient = 12 - 24 + 9
Gradient = -3
B) since the gradient of the tangent = -3, it means the gradient of the normal will be; -1/-3 = 1/3
Thus, equation of the normal to the curve at point A will be;
(y - 3) = ⅓(x - 2)
Multiply both sides by 3 to get;
3y - 9 = x - 2
3y - x = 9 - 2
3y - x = 7
Related Questions
4 yards to 30 inches write each ratio in simplest form
Answers
Answer:
24:5
Step-by-step explanation:
4 yards is 3 feet, so 4*3=12. There are 12 inches in a foot, so 12*12=144. 144:30= 72:15 = 24:5
Given that 6x – 4y= 29
Find x when y = 4
Give your answer as an improper fraction in its simplest form.
x=
Answers
Answer:
substitute the y equation to the other equation.
6x - 4(4) = 29
6x - 16 = 29
6x = 29 + 16
6x = 45
x = 15/2
Mr. Spencer wants to rent a car.He has two deals:
Deal A: rent Tesla with initial fee of$75 and
$25 fee each day
Deal B: rent Porsche with no initial fee and $50 each day
Help Mr.Spencer to select a better deal.
Answers
Answer:
The answer is depending on how long he us going to rent the car. If Spencer wants to rent the car for less than 150 days, the Porsche is cheaper for that. However, if Spencer wants to rent a car for more than 150 days, the Tesla is the cheaper option.
Step-by-step explanation:
You can write both Deals in slope inter form.
Tesla: y = 25x+75
Porsche: y=50x
Remember: slope inter form is y = mb + b
"mx" being the change in y over the change in 1 or (y1-y2/x1-x2)
"b" in the formula represents the y-axis
Write another expression equivalent to 2(x + 3) please answer i will make you brainliest
Answers
Answer:
2x + 6
Step-by-step explanation:
distribution
plz mark branliest
Find the measure ZBCD in the
following parallelogram.
Answers
Answer:
I think the answer is 2
x=1
Step-by-step explanation:
2x=2x
divide
x=1
plug it in
1×2
Mark was working on the long jump competition, and he was able to jump 9 3/4 feet. Chris jumped 7/8 as far as Mark. write and solve the equation that will help you fight how far Chris jumped. explain the steps you took to solve problem. THIS URGENT PLEASE HELP!!
Answers
Answer:
10 5/8
Step-by-step explanation:
9 3/4 + 7/8 = 9 6/8+7/8=
10 5/8
The distance jumped by Chris in total would be as follows:
[tex]10\frac{5}{8}[/tex]
Find the distance
Distance is denoted as the space that one covers from a particular place to the other.
Given that,
The distance jumped by Mark [tex]= 9\frac{3}{4}[/tex] feet
The distance jumped by Chris [tex]= \frac{7}{8} + 9\frac{3}{4}[/tex]
So,
The total distance covered by Chris would be:
[tex]= \frac{7}{8} + 9\frac{3}{4}[/tex]
[tex]= \frac{7}{8} + \frac{39}{4}[/tex]
[tex]=[/tex] [tex]\frac{(7 + 78)}{8}[/tex]
[tex]= \frac{85}{8}[/tex]
[tex]=[/tex] [tex]10\frac{5}{8}[/tex]
Thus, [tex]10\frac{5}{8}[/tex] is the correct answer.
Learn more about "Fraction" here:
brainly.com/question/1301963
56 = n - 33.
N = __?
Answers
n = 89
whew
A person who weighs 65 pounds on earth will weigh 169 pounds on the planet Jupiter. How much will a person weigh on Jupiter who weighs 45 pounds on earth?
ANSWER ASAP
Answers
Answer:
117
Step-by-step explanation:
science
Answer:
117 pounds
Step-by-step explanation:169 pounds divided by 65 pounds is 2.6
So that means that we would need to multiply 45 by 2.6. So 45 multiplied by 2.6 is 117 pounds.
please help asap with work!!!! thank you
Answers
Answer:
answer is C
Step-by-step explanation:
midpoint = ((x¹ + x²)÷2 , (y² +y²)÷2)
example:
((-4+2)÷2 , (-15+-1)÷2)
= ((-2÷2) , (-16÷2))
=(-1 , -8)
Dr. Ballard refers to Earth as a ‘living breathing creature’- do you think he meant for us to take this literally?
Answers
Answer:
I don't think so.
Step-by-step explanation: I think he just wanted us not to take advantage of earth and treat earth like a living creature
I’m gonna mark brainliest plz answer
Answers
Answer:
1) 6
2) 8/125
3) 5
4) 4/5
Step-by-step explanation:
1) 2x2x2x2x2x2 = 64 then 2^6 = 64
2) (2/5)^3 =8/125
3) 3x(3^4) = 3^5
4) sq rt 16/25 = 4/5
A manufacturing machine has a 10% defect rate. If 3 items are chosen at random, what is the probability that at least one will have a defect
Answers
Answer:
0.271 = 27.1% probability that at least one will have a defect
Step-by-step explanation:
For each item, there are only two possible outcomes. Either they have a defect, or they do not. Items are independent. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A manufacturing machine has a 10% defect rate.
This means that [tex]p = 0.1[/tex]
3 items are chosen at random
This means that [tex]n = 3[/tex]
What is the probability that at least one will have a defect?
This is
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.1)^{0}.(0.9)^{3} = 0.729[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.729 = 0.271[/tex]
0.271 = 27.1% probability that at least one will have a defect
PLSSS HELP ASP TYSMMM
Answers
Answer:
For what I can’t see the page or equation?
Step-by-step explanation:
If f(x)= 1/2x-10+3, which inequality can be used to find the domain of f(x)?
Answers
Answer:
x ≠ 5
Step-by-step explanation:
Assuming you mean f(x) = (1/(2x-10))+3
Please be careful with how ambigiuous your question can appear with the / sign.
The domain is the set of values that can be used as an input.
In this case the only input we have that could cause problem is if the denominator of the fraction is 0, because then we divide by 0 which is not allowed.
This gives us 2x-10 ≠ 0
2x ≠ 10
x ≠ 5
The domain of the function is given by the inequality ( 1/2 )x - 10 ≥ 0 and the value of x ≥ 20
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = [ √ ( 1/2 )x - 10 ] + 3
Now , the expression (1/2)x - 10 inside the square root must be greater than or equal to 0, as the square root of a negative number is not defined in the real number system.
(1/2)x - 10 ≥ 0
To solve this inequality, we can isolate x:
(1/2)x ≥ 10
x ≥ 20
Hence , the domain of the function f(x) is x ≥ 20.
To learn more about domain and range click :
https://brainly.com/question/28135761
#SPJ7
The complete question is attached below :
If f(x)= 1/2x-10+3, which inequality can be used to find the domain of f(x)?
Find the value of 0.7 x 0.08
Answers
Answer:
0.056
Step-by-step explanation:
I used my calculator, not much work to show :)
Answer:
The answer for 0.7 x 0.08 is 0.056.
Explantion:
I am smart like that.
I am built different.
HELP PLS ASAP!!!
these figures are congruent. What series of transformations moves quadrilateral FGHI onto quadrilateral F’G’H’I’?
Answers
Answer:
D
Step-by-step explanation:
It must first translate 1 unit to the left because quadrilateral F'G'H'I is one unit away from to y axis. It can then translate across the y-axis.
Answer:
ITS B!
Step-by-step explanation:
Ape x!
Graphing plobem 8th grade. First anserw gets brainest
Answers
Answer: -5 is equal to x
Step-by-step explanation:
This is since you just make y = 0 to solve, so
0=x+5
= -5=x
Answer:
x=-8 and y=2 / x=-5 and x=5
Step-by-step explanation:
put x as 0 to find y
y=1÷4x+2
y=1÷4×0+2
y=0+2
y=2
put y as 0 to find x
y=1÷4x+2
0=1÷4x+2
-2+0=1÷4x
-2=1÷4x
1÷4x=-2
1x=-2×4
x=-8
y=x+5
0=x+5
x=-5
y=0+5
y=5
At The Fencing Center, 60% of the fencers use the foil as their main weapon. We randomly survey 21 fencers at The Fencing Center. We are interested in the numbers that do not use the foil as their main weapon.
Part (a) In words, define the Random Variable X.
the number of fencers that do not use the foil as their main weaponthe different types of weapons the number of fencers at The Fencing Centerthe number of fencers that do use the foil as their main weapon
Part (b) List the values that X may take on.
X = 0, 1, 2, . . ., 60X = 1, 2, 3, . . ., 21 X = 0, 1, 2, . . ., 21X = 1, 2, 3, . . ., 60
Part (c) Give the distribution of X.
X ~
,
Part (d) How many fencers are expected to not use the foil as their main weapon? (Round your answer to the nearest whole number.)
fencers
Part (e) Find the probability that eleven do not use the foil as their main weapon. (Round your answer to four decimal places.)
Part (f) Based on numerical values, would you be surprised if all 21 did not use foil as their main weapon?
Yes. The probability of all 21 fencers not using the foil as their main weapon is small (less than 1%).No. The probability of all 21 fencers not using the foil as their main weapon is large (more than 10%).
Answers
Answer:
A.) the number of fencers that do not use the foil as their main weapon
B.) X : 0, 1, 2, 3,..., 21
C.) X ~ p(X) ; 21 ~ 0.4
D.) 21 ~ 0.4
E.) 0.0895
F.) Yes. The probability of all 21 fencers not using the foil as their main weapon is small (less than 1%)
Step-by-step explanation:
A.) since it is reported that 60% of fencers use the foil as their main weapon ;
The random variable (x) : number of fencers that do not use foil as their main weapon ;
( 100% - 60%) = (1 - 0.6) = 0.4
B.) values that X may take on :
Sample size = 21 ;
X : 0, 1, 2,..., 21
The distribution of X
X ~ B ; X ~ p(X) ; 21 ~ 0.4
Part (d) How many fencers are expected to not use the foil as their main weapon?
X * p(x)
21 * 0.4
= 8.4
= 8 (nearest whole number)
Part (e) Find the probability that eleven do not use the foil as their main weapon.
P(x = 11)
Using the binomial probability relation :
P(x =x) = nCx * p^x * (1 - p)^(n - x)
P(x = 11) = 21C11 * 0.4^11 * 0.6^10
P(x = 11) = 0.0895
Part (f) Based on numerical values, would you be surprised if all 21 did not use foil as their main weapon?
P(x = 21) = 21C21 * 0.4^21 * 0.6^0
P(x = 21) = < 0.00001 ( approximately 0)
Hence, based on this very low value which is almost equal to 0 ; it will be surprising if all 21 do not use foil as their main weapon
NEED ASAP
According to the results in the chart, what is the experimental probability of getting a number greater than 3 on the die? 3 over 12 6 over 12 9 over 12 8 over 12
Answers
Answer:
3 over 12
Step-by-step explanation:
3 over 12
Answer: 3/12
Step-by-step explanation:
Mr. McMurry wants to get a gym membership. Planet fitness charges $25 a month. Everyday Fitn
charges membership fee of $30 and charges $10 a month. How many months would it take for E
options To be equal?
Equation
Solution
Answers
Answer:
pp
Step-by-step explanation:
If the kidneys filter 20% of medication
Answers
Answer:
Estimated glomerular filtration rate is the best test to measure ... stage of kidney disease and helps the doctor plan your treatment. If ... If your GFR number is low, your kidneys are not working as well as ... 20–29, 116.
Step-by-step explanation:
you have to study
7
Jackson is creating a rectangular board game that includes a diagonal line from two of the corners of the game. How long is the diagonal if the board game is 10 inches
long by 8 inches wide? Explain your reasoning. Round your answer to the nearest tenth of an inch.
Helppp
Answers
Answer:
diagonal = = 12.8 inches (to the nearest tenth of an inch)
Step-by-step explanation:
As shown in the diagram attached to this solution:
Let the Length of the rectangular board = a
Let the width = b
Let the diagonal = d
where:
a = 10 inches
b = 8 inches
d = ?
Triangle ABC in the diagram is a right-angled triangle, therefore, applying Pythagoras theorem:
(hypotenuse)² = (Adjacent)² + (Opposite)²
d² = 10² + 8²
d² = 100 + 64
d² = 164
∴ d = √(164)
d = 12.806 inches
d = 12.8 inches (to the nearest tenth of an inch)
N:B Rounding off to the nearest tenth of an inch is the same as rounding off to 1 decimal place.
What is 150 increase by 10%
Answers
Answer:
500 hope this helps
Step-by-step explanation:
490 as a product of its prime factors
Answers
Answer:
2×5×7²
Step-by-step explanation:
You will start by using the factor tree.
490
^
2 245
^
5 49
^
7 7
How do you find the y-intercept of a line given two ordered pairs?
Answers
Answer:
Using the "slope-intercept" form of the line's equation (y = mx + b), you solve for b (which is the y-intercept you're looking for). Substitute the known slope for m, and substitute the known point's coordinates for x and y, respectively, in the slope-intercept equation.
Step-by-step explanation:
goog
Help please with this
Look at picture
Complementary angles
Answers
Answer:
70°
Step-by-step explanation:
80° - x + 80° = 90° { being complementary angles }
160° - x = 90°
x = 180° - 90°
x = 70°
Hope it will help :)
Help asap!!!!!!!!!!!!!
Answers
your laptop is useless if you don't have braon
Divide using long division.
(x3 + 3x2 + x - 4) + (x - 1)
Answers
Answer:
2x+3x2 +x3 −5
Step-by-step explanation:
Hope this helps
Answer:
x^2 - 2x + 2
step-step explanation:
which of these show equivalent fractions? A. 1/4=4/8 B. 1/2=2/4 C. 3/5 = 5/10 D. 2/3 = 3/6
Answers
Fifty tickets were sold for the lottery. Jackson bought five tickets. What are the chances he will win?
Answers
Answer:
1/10 chances or 5/50.....
