The most appropriate choice for tangent to a curve will be given by- 2x + 25y = 10 is the required equation of tangent.
What is tangent to a curve?
In geometry, a tangent line is a straight line that most closely resembles (or "clings to") a curve at a particular point. It could be thought of as the limiting role of straight lines that pass through the specified point and a nearby curve point as the second point gets closer to the first. If two curves share the same tangent at a given point, they are said to be tangent. Similar definitions apply to the tangent plane to an exterior at a point and two surfaces that are tangent at a point.
Equation of tangent to a curve at a point [tex](x_1, y_1)[/tex] is given by
[tex]y-y_1 = \frac{dy}{dx}|_{(x_1, y_1)}(x - x_1)[/tex]
Here,
f(x) = [tex]\frac{2}{x}[/tex]
f'(x) = [tex]\frac{d}{dx} (\frac{2}{x})[/tex]
= [tex]2(-1)x^{-1-1}\\-2x^{-2}[/tex]
[tex]f'(x)|_{(5, 0)} = -\frac{2}{5^2}[/tex]
[tex]= -\frac{2}{25}[/tex]
Equation of tangent
[tex]y - 0 = -\frac{2}{25}(x - 5)\\\\25y = -2x +10\\2x + 25y = 10[/tex]
To learn more about tangent to a curve
brainly.com/question/28199103
#SPJ13
Guenther drove 260 miles in 5 hours. He has 494 more miles to drive on his trip. If he continues at this same average speed, what will his driving time in hours be for the remainder of his trip?
The driving time in hours for the remainder of Guenther's trip would be = 9.5 hours.
What is average speed?Average speed of a moving object is defined as the average change in distance divided by change in time.
The first distance covered by Guenther = 260 miles.
The time it took to cover the first distance= 5 hours.
The remaining distance = 494 miles
The time it will take to cover the remaining distance= X hours
But if , 260 miles = 5 hours
494 miles = X hours
Make X the subject of formula;
X hours= 494 × 5 / 260
X hours = 2,470 / 260
X hours = 9.5 hours.
Learn more about speed here:
https://brainly.com/question/24739297
#SPJ1
175/500 as a percentage
Answer:
35%
Step-by-step explanation:
175/500
.35
35%
hope this helped
btw what did you just fail... lol ?
can anyone help me with this mixed number question pls.
7 2/3 + 2 1/5
Answer: The value of 7 2/3 + 2 1/5 is 9 13/15
Explaination: The lowest common multiple of 3 and 5 is 15. Therefore, 7 2/3 + 2 1/5 will be calculated thus:
= 7 2/3 + 2 1/5
= [7 + 2/3× 15] + [2 1/5 × 15]
= 7 10/15 + 2 3/15
= 9 13/15
In conclusion, the value of the fraction 7 2/3 + 2 1/5 is 9 13/15
Pls ayuda. Plsssss. Es para mañana
Becky made a box in the shape of the triangular prism shown. If she were to wrap this box, how many square inches of wrapping paper would she need? Select one: O 225 square inches O 240 square inches O 156 square inches O 216 square inches
Answer:
216 square inches
Explanation:
To find out how many square inches of wrapping paper she would need, calculate the total surface area of the triangular prism.
The triangular prism has five faces:
• Two equal triangles with base 6 in. and height 4 in.
,• Two rectangles (Rectangle 1) of dimension 5 in. by 12 in.
,• A rectangle of dimension 6 in. by 12 in.
Therefore:
[tex]\begin{gathered} \text{Surface Area}=2(\text{Area of Triangle)+2(Area of Rectangle 1)+Area of Rect. 2} \\ =2(\frac{1}{2}\times6\times4)+2(5\times12)+(6\times12) \\ =24+120+72 \\ =216\; in^2 \end{gathered}[/tex]She would need 216 square inches of wrapping paper.
Julie has a jewelry box shaped like a cube. If the volume is
216 cm³, what is the edge length of Julie's jewelry box?
A 14.7 cm
B 108 cm
C 6 cm
D 72 cm
Answer: C) 6cm
Step-by-step explanation:
6³= 6x6x6
6x6x6= 216
Answer:
Choice C: 6 cm
Step-by-step explanation:
The sides of a cube are all of equal length
If each side is a cm, then the volume = a x a x a = a³ cubic cm
So a = ∛V where V is the volume
Since we are given V = 216 cm³,
each side = ∛21 = 6 cm
What percent of 933 is 391.86?
the state of new hampshire has the approximate shape of a triange with base 90 mi and height 180 mi. estimate the area of new hampshire
Answer:
[tex]A = 8100mi^{2}[/tex]
Step-by-step explanation:
Are of a triangle: [tex]A = \frac{hb}{2}[/tex], where A is the area, h is height and b is base.
[tex]A = \frac{hb}{2}\\A = \frac{(180)(90)}{2}\\A = \frac{16200}{2}\\A = 8100mi^{2}[/tex]
The aproxiate area of NH is 8100mi^2
Abhasra made a trip to the town hall and back. On the trip there she drove 60 mph and on the return trip she went 75 mph . How long did the trip there take if the return trip took four hours ?
HELP ASAP PLEEASE!!
Answer:
Trip to town hall took 5 hours
Step-by-step explanation:
Distance traveled = Speed x Time
We know the return trip took 4 hours at 75 mph
So distance traveled from town hall to start = 75 x 4 = 300 miles
The distance from start to town hall is assumed to be the same.
So distance to town hall from start = 300 miles also
Time taken to travel 300 miles at 60 mph = 300/60 = 5 hours
find the circumference of circle with radius X CM
Answer:
To calculate the circumference of a circle, multiply the diameter of the circle with π (pi). The circumference can also be calculated by multiplying 2×radius with pi (π=3.14).
Step-by-step explanation:
brainiest please
Two neighbors are draining swimming pools. Mr. Zoetrope’s pool has 10,858 gallons and is
draining 150 gallons per minute. Mrs. Horner’s pool has 9,650 gallons and is draining 110
gallons per minute. Write and solve an equation to determine the number of minutes ( ) m the
two pools must drain to have the same amount of water
Step-by-step explanation:
I hope this answers your problem
Which inequality comparing two of the expressions is true when 0.1 ≤x≤0.4?
√x > x↑2
This is because, x↑2 is equal to -.4 and √x is equal to 0.1. This means x equals to 0.2
The solution is : The true inequality is √x > x³, Option C.
What is inequality?An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.
Here, we have,
Given 0.5≤ x ≤ 0.7
According to the range of x, we will check which option is true
Let x = 0.6
A. x/3 > √x
If x = 0.6
∴0.6/3 > √0.6 ⇒ 0.2 > 0.77 ⇒ Wrong inequality
B. x³ > 1/x
If x = 0.6
∴ 0.6³ > 1/0.6 ⇒ 0.216 > 1.667 ⇒ Wrong inequality
C. √x > x³
If x = 0.6
∴ √0.6 > 0.6³ ⇒ 0.77 > 0.216 ⇒ True inequality
D. (x/3) > (1/x)
If x = 0.6
∴ 0.6/3 > 1/0.6 ⇒ 0.2 > 1.667 ⇒ Wrong inequality
So, The true inequality is option C.
To learn more on inequality click:
brainly.com/question/24853349
#SPJ2
complete question:
Which inequality comparing two of the expressions below is true when 0.5
f(x)=y^5-2y^3+y find the zeros of this function
Answer: y=0 y=-1 y=1
Step-by-step explanation:
[tex]\displaystyle\\f(y)=y^5-2y^2+y\\\\y^5-2y^2+y=0\\\\y(y^4+2y^2+1)=0\\\\y((y^2)^2+2(y^2)(1)+1^2)=0\\\\y(y^2-1)^2=0\\\\y=0\\\\(y^2-1)^2=0\\\\y^2-1-0\\\\(y+1)(y-1)=0\\\\y+1=0\\\\y+1-1=0-1\\\\y=-1\\\\y-1=0\\\\y-1+1=0+1\\\\y=1[/tex]
Someone help pls tysm
Answer:
youd get 0.25 off and yes you would save 25 cents the difference would be 2.25 dollars instead of 2.50
Step-by-step explanation:
im so so sorry if im wrong so so sorry
a truck delivers 35 cases of books to the library. each case holds 12 books. the librarian plans to place 8 books on each shelf. what is the fewest number of shelves the librarian will need to hold all of the books delivered by the truck?
Answer:
52
Step-by-step explanation:
35×12÷8
35×12
8
(Cross out the common factor which is 8 and 12)
35×3 = 105
2 2
(find the largest integer less than or equal to 105 which is 52.)
2
the sat and act college entrance exams are taken by thousands of students each year. the mathematics portions of each of these exams produce scores that are ap- proximately normally distributed. in recent years, sat mathematics exam scores have averaged 480 with standard deviation 100. the average and standard deviation for act mathematics scores are 18 and 6, respectively.
a) 75.80 percentage of students will be scoring below 550 in a typical year.
b) 22.2 marks should be set by the engineering school setas a comparable standard on ACT math test.
Here we have been mentioned that in the recent years, sat maths exam scores have averaged 480 with standard deviation 100. the average and standard deviation for act mathematics scores are 18 and 6, respectively.
a) The percentage of the students scoring below 550 marks in a typical year is calculated as follows:
Let x be the SAT score
So, x follows normal distribution
Given above,
mean (μ) = 480
standard deviation (σ) = 100
we will find P ( x < 550)
We will use the excel function NORM.DIST to find the required probability
P(x < 550) = NORM.DIST[tex](550, 480, 100, TRUE)[/tex]
= 0.7580
= 75.80%
Hence the percentage of the students who are scoring below 550 in a typical year = 75.80%
b) We calculate the score to be set by the engineering school as a comparable standard on the ACT math test as follows:
Let Z be the ACT score
Z follows the normal distribution
Given above, μ = 18 and σ = 6
Let Z' be the ACT score comparable to the standard set for SAT
Then we need to find Z' such that P(Z < Z') = 75.80% = 0.758
From standard normal tables we get Y' such that
Z' = NORM.INV[tex](0.758, 18, 6)[/tex]
= 22.2
The ACT score that needs to be set by the college = 22.2 marks
To learn more about ACT click here:
https://brainly.com/question/15208083
#SPJ4
3 and 20
Drag each pair of numbers to show if their greatest common factor (GCF) is less than
5, equal to 5, or greater than 5.
12 and 30
GCF is less than 5.
DRAG AND
DROP ITEMS
HERE
25 and 30
E
[
15 and 20
6 and 33
GCF is equal to 5.
DRAG AND
DROP ITEMS
HERE
20 and 30
CLEAR CHECK
GCF is greater than 5.
DRAG AND
DROP ITEMS
HERE
A
The matching pairs of the greatest common factor (GCF) of the numbers is given as follows:
3 and 20: less than 5.12 and 30: greater than 5.25 and 30: equals to 5.15 and 20: equals to 5.6 and 33: less than 5.20 and 30: greater than 5.How to find the greatest common factor between two numbers?As the common word states, the greatest common factor between two numbers a and b is the greatest number by which both numbers a and b are divisible by.
Hence, the GCFs for the pairs in this problem are given as follows:
3 and 20 = 1, as 3 is prime(only divisible by 1 and by itself), hence less than 5.12 and 30 = 6, as 12/6 = 2 and 30/6 = 5, hence greater than 5.25 and 30 = 5, as 25/5 = 5 and 30/5 = 6, hence equals to 5.15 and 20 = 5, 15/5 = 5 and 20/5 = 4, hence equals to 5.6 and 33 = 3, as 6/3 = 2 and 33/3 = 11, hence the GCF of 3 is less than 5,20 and 30 = 10, as 20/10 = 2 and 30/10 = 3, hence the GCF of 10 is greater than 5.More can be learned about the greatest common factor at https://brainly.com/question/219464
#SPJ1
nine times the sum of a number and 4 equals 7.
Answer: the answer is 17
Step-by-step explanation:
Answer: The equation would be 9(x+4)=7
Divide both sides by the numeric factor on the left side, then solve.
Exact Form: x= −29/9
Mixed Number Form: x= −3 2/9
What is this slope of the line on the graph?
Answer:
Step-by-step explanation:
m = 5/7 is the slope of the line on the graph .
What is slope in plain ?
A line or a part of a line that connects two locations is said to have a slope, which is a measure of how steep it is.
The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises.
The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b.
point from given graph x = ( -7 , 0 ) and y = ( 0, 5 )
slope (m) =
m =
m = 5/7
Learn more about slope
brainly.com/question/3605446
here you go im late tho...
HELP ME OUT PLS MARKING BRAINLEIST
Answer:
243
Step-by-step explanation:
IM PRETTY SURE IT 243 PLS NOW BRAINLIST
113 disproves the conjecture that all number ending in 3 are divisible by 3
What is divisible rule ?Mathematicians use a set of precise rules called the "divisibility rules" to determine whether a given integer is divisible by a certain number or not. Examples of well-known divisibility tests range from 2 to 20. It enables us to calculate multiples and factors of numbers without having to use lengthy division. Applying the rules of divisibility, a person can determine if a number is divisible by another number or not.
Divisibility rule for 3 states that a number is completely divisible by 3 if the sum of its digits is divisible by 3.
243 is divisible by 3 as its sum is 2 + 4 + 3 = 9 and 9 easily get divided by 3
113 is not divisible by 3 as its sum is 5 and 5 can not divided by 3
therefore ,
113 disproves the conjecture that all number ending in 3 are divisible by 3
To learn more about divisibility rule visit :
brainly.com/question/21416852
#SPJ13
What number am I?
I am less than 10.
I am the only number
that gives a bigger
answer when you add
me to myself than when
you multiply me by
myself.
I am
Answer:
1
Step-by-step explanation:
We see that 1 + 1 = 2, while 1 * 1 = 1
So 1 gives a bigger answer when you add 1 to itself then when 1 is multiplied by itself
In the answer it is given that this is the only number for which this is correct, so there is not really a need to check for other options
but if you would want, you could just compute 2 till 9 and see that for example 2 + 2 = 4 and 2 *2 = 4, which are the same, so it is not a bigger number when added then when multiplied.
How many solutions exist for the following system if m1 ≠ m2?
y = m1x + b
y = m2x + b
answers:
an infinite number, none, one, the number of solutions cannot be determined.
Because the lines have different slopes, we conclude that there is only one intercept, and thus, the system of linear equations has only one solution.
How many solutions does the system of equations has?Remember that a system of equations has as many solutions as intercepts are when we graph both equations in the same coordinate axis.
Now, in this case, we have a system of linear equations:
y = m1*x + b
y = m2*x + b
Remember that linear equations are parallel only if the two lines have the same slope, in this case, we know that m1 ≠ m2, so the slopes are different.
Then the lines are not parallel, which means that intersect only one time, so we conclude that the system of equations has one solution.
Learn more about systems of equations:
https://brainly.com/question/13729904
#SPJ1
Complete the empty table from the provided information.
Translate the graph of f(x) up 2 units.
Write the equation of the resulting line in slope intercept form.
Tom is trying to write 3/47 as a decimal. he used long division and divided until he got the quotient 0.0638297872, at which point he stoped. since the decimal doesnt seem to terminate or repart, he concluded that 3/47 is not rational. do you agree or deagree? why?
Answer:
Disagree
Step-by-step explanation:
The decimal expansion may have a longer period than the division he carried out.
On Friday, Ariel received a $450 paycheck. On
Saturday, she spent $30 on gasoline and $15 on lunch.
What percent of her paycheck did Ariel spend on
Saturday?
Answer:
10%
Step-by-step explanation:
30+15=45
45 is 10% of 450 as 450/10= 45
5 -4y+y-3 how to you answer it?
Answer: -2[tex]Y^2[/tex]
Step-by-step explanation:
x+3x-y+y+2z+z
help please its my rsm homework
Answer:
the answer is 4x + 3z
Step-by-step explanation:
1x + 3x + -1y + 1y + 2z + 1z
1x + 3x = 4x
-1y + 1y = 0
2z + 1z = 3z
so the answer is 4x + 3z
Solve these 3 equations 1. (x - 8) (2x + 5) = 52. x² + 13x + 40 = 03. x² - 6x - 20 = 7
1. (x - 8) (2x + 5) = 5
2. x² + 13x + 40 = 0
3. x² - 6x - 20 = 7
Part 1
apply distributive property left side
2x^2+5x-16x-40=5
2x^2-11x-45=0
Apply the formula to solve quadratic equation
we have
a=2
b=-11
c=-45
substitute
[tex]\begin{gathered} x=\frac{11\pm\sqrt[\square]{(-11^2)-4(2)(-45)}}{4} \\ \\ x=\frac{11\pm\sqrt[\square]{481}}{4} \end{gathered}[/tex]the solutions are[tex]\begin{gathered} x1=\frac{11+_{}\sqrt[\square]{481}}{4} \\ \text{and} \\ x2=\frac{11-\sqrt[\square]{481}}{4} \end{gathered}[/tex]Part 2
x² + 13x + 40 = 0
we have
a=1
b=13
c=40
Apply the formula
[tex]\begin{gathered} x=\frac{-13\pm\sqrt[\square]{13^2-4(1)(40)}}{2} \\ \\ x=\frac{-13\pm\sqrt[\square]{9}}{2} \\ \\ x=\frac{-13\pm3}{2} \end{gathered}[/tex]so
x=-5 and x=-8Part 3
x² - 6x - 20 = 7
x² - 6x - 27=0
so
a=1
b=-6
c=-27
Apply the formula
[tex]\begin{gathered} x=\frac{6\pm\sqrt[\square]{(-6^2)-4(1)(-27)}}{2} \\ \\ x=\frac{6\pm\sqrt[\square]{144}}{2} \\ \\ x=\frac{6\pm12}{2} \end{gathered}[/tex]so
x=9 and x=-3Solve the formula Aa + By = C for B.
Answer: B = -(Aa)/y + C/y
By = -Aa + C
B = -(Aa)/y + C/y
hope this helps! <3
3(3x - 6) = 18 solve for x simplify your answer as much as possible