Answer:
Step-by-step explanation:
Absolute minimum is where, in the infinite domain of f(x), the least value the function is the absolute minimum.
However, the local minimum is only a specific interval on the domain of f(x) where the lowest value is, but only in that interval.
So, usually, this comes up when you're dealing with 1st and 2nd derivatives. The first derivative tells you where local max and mins are, where the 2nd derivative tells you if the concavity is up or down.
An absolute minimum is the lowest point on the entire domain of a function, while a local minimum is the lowest point in a specific interval or neighborhood around a point on the graph.
Explanation:
An absolute minimum and a local minimum are both points on a graph where the function reaches its lowest value, but there are key differences between them.
An absolute minimum is the lowest point on the entire domain of the function. In other words, it is the smallest function value among all the points.
On the other hand, a local minimum is the lowest point in a specific interval or neighborhood around a particular point on the graph. It is possible for a function to have multiple local minima.
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The price of a share of stock increases 45.69 over 3 days. What was the average rate of change in its price in dollars per day?
Answer:
The answer would be 15.23$
Step-by-step explanation:
If you take the over all growth, 45.69, and divide that by the 3 days, you get your average of 15.23 per day
if f(x)=sqrt x+12 and g(x)= 2 sqrt x what is the value of (f – g)(144)?.
Answer:
the answer is 0
Step-by-step explanation:
Please help me out.....................
Simplify the expression.
sec x/tan x
Answer:
Option b
Step-by-step explanation:
We know that, by definition:
[tex]secx = \frac{1}{cosx}[/tex]
We also know that:
[tex]tanx = \frac{sinx}{cosx}[/tex]
Applying these identities we can simplify the given expression
[tex]\frac{secx}{tanx} = \frac{\frac{1}{cosx}}{\frac{sinx}{cosx}}\\\\\frac{secx}{tanx} = \frac{cosx}{sinxcosx}\\\\\frac{secx}{tanx} = \frac{1}{sinx}[/tex]
We know that, by definition:
[tex]\frac{1}{sinx} = cscx[/tex]
Final answer:
To simplify sec x/tan x, we use trigonometric identities to show that sec x/tan x equals csc x, which is the cosecant of x.
Explanation:
To simplify the expression sec x/tan x, we need to recall the trigonometric identities for secant (sec) and tangent (tan). We know that sec x is equal to 1/cos x and tan x is equal to sin x/cos x. When we divide sec x by tan x, we are essentially dividing 1/cos x by sin x/cos x. This simplifies to:
sec x/tan x = (1/cos x) / (sin x/cos x)Multiply the numerator by the reciprocal of the denominator: (1/cos x) * (cos x/sin x)The cos x terms cancel out, leaving us with: 1/sin xThe expression 1/sin x is the definition of cosecant (csc x), thus:sec x/tan x = csc xTo summarize, the simplified form of the expression sec x/tan x is csc x.
A bakery has 63 donuts and 36 muffins for sale. What is the ratio of muffins to donuts?
The ratio of muffins to donuts in the bakery is 4:7, calculated by dividing the number of muffins (36) by the number of donuts (63).
To find the ratio of muffins to donuts, we divide the number of muffins by the number of donuts.
Given:
- Number of donuts: 63
- Number of muffins: 36
Ratio of muffins to donuts:
[tex]\[ \text{Ratio} = \frac{\text{Number of muffins}}{\text{Number of donuts}} \][/tex]
[tex]\[ \text{Ratio} = \frac{36}{63} \][/tex]
We can simplify this ratio by finding the greatest common divisor (GCD) of 36 and 63, which is 9.
[tex]\[ \text{Ratio} = \frac{\frac{36}{9}}{\frac{63}{9}} \][/tex]
[tex]\[ \text{Ratio} = \frac{4}{7} \][/tex]
So, the ratio of muffins to donuts is 4:7 .
The ratio of muffins to donuts is [tex]\( \frac{4}{7} \)[/tex].
To find the ratio of muffins to donuts, we divide the number of muffins by the number of donuts:
[tex]\[ \text{Ratio of muffins to donuts} = \frac{\text{Number of muffins}}{\text{Number of donuts}} \][/tex]
Given that the bakery has 63 donuts and 36 muffins, we can substitute these values into the formula:
[tex]\[ \text{Ratio of muffins to donuts} = \frac{36}{63} \][/tex]
Now, we can simplify this fraction:
[tex]\[ \frac{36}{63} = \frac{4 \times 9}{7 \times 9} = \frac{4}{7} \][/tex]
So, the ratio of muffins to donuts is [tex]\( \frac{4}{7} \)[/tex].
(9Q) Solve the log.
Answer:
D
Step-by-step explanation:
Bert and Ernie are missing each other and their friend Big Bird They want to meet at Big Bird's nest which is halfway from their apartments. The distance from Bert's apartment to Big Bird's nest (5x + 4) ismiles away while Ernie's apartment to Big Bird's nest is (15x-30) miles away How far are Bert and Ernie's apartments from Big Bird's nest?
Answer:
The distance between Bert and Ernie's apartments from Big Bird's nest
is 21 miles
Step-by-step explanation:
* Lets change the story problem to an equation to solve the problem
- The information i the story problem is
# The Big Bird's nest is halfway from there apartments
# The distance between Bert's apartment and Big Bird's nest is (5x + 4)
# The distance between Ernie's apartment and Big Bird's nest is (15x - 30)
* Now lets solve
∵ The Big Bird's nest is halfway from there apartments
∴ The distance between Bert's apartment and Big Bird's nest = The
distance between Ernie's apartment and Big Bird's nest
∴ 5x + 4 = 15x - 30
- Collect the variable terms in one side and the numerical terms
in th other side
∴ 15x - 5x = 30 + 4 ⇒ add
∴ 10x = 34
∴ x = 34 ÷ 10 = 3.4
* Now lets find the distance between Bert and Ernie's apartments
from the Big Bird's nest
- We can use any relation to find the distance
∵ The distance = 5x + 4
∵ x = 3.4
∴ The distance = 5(3.4) + 4 = 17 + 4 = 21 miles
You can check the answer by using second equation
∵ The distance = 15x - 30
∵ x = 3.4
∴ The distance = 15(3.4) - 30 = 51 - 30 = 21 miles
Answer:
The distance between Bert and Ernie's apartments from Big Bird's nest
is 21 miles
Step-by-step explanation:
* Lets change the story problem to an equation to solve the problem
- The information i the story problem is
# The Big Bird's nest is halfway from there apartments
# The distance between Bert's apartment and Big Bird's nest is (5x + 4)
# The distance between Ernie's apartment and Big Bird's nest is (15x - 30)
* Now lets solve
∵ The Big Bird's nest is halfway from there apartments
∴ The distance between Bert's apartment and Big Bird's nest = The
distance between Ernie's apartment and Big Bird's nest
∴ 5x + 4 = 15x - 30
- Collect the variable terms in one side and the numerical terms
in th other side
∴ 15x - 5x = 30 + 4 ⇒ add
∴ 10x = 34
∴ x = 34 ÷ 10 = 3.4
* Now lets find the distance between Bert and Ernie's apartments
from the Big Bird's nest
- We can use any relation to find the distance
∵ The distance = 5x + 4
∵ x = 3.4
∴ The distance = 5(3.4) + 4 = 17 + 4 = 21 miles
You can check the answer by using second equation
∵ The distance = 15x - 30
∵ x = 3.4
∴ The distance = 15(3.4) - 30 = 51 - 30 = 21 miles
Of 500 students going on a class trip 350 are student band members and 65 are athletes 25 band members and student athletes what is the probability that one of the students on the trip is an athlete or a band memeber?
Answer:
0.78
Step-by-step explanation:
There are 500 students in total. Thus,
350 students are band members;65 students are athlets;25 students are both band members and athlets;350-25=325 students are only band members. not athlets;65-25=40 students are only athlets, not band members.The probability that one of the students on the trip is an athlete or a band memeber is
[tex]Pr=\dfrac{325+40+25}{500}=\dfrac{390}{500}=0.78.[/tex]
Joelle's parents have combined all the candy from her and her three siblings Halloween bags so that the candy can be split evenly amongst the children. Altogether, the kids accumulated 256 pieces. How many pieces does each child receive?
There are 64 pieces that each child receive.
What is Division?It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken.
Here, Joelle's parents have combined all the candy = 256 candy
Total number of Children = 4
Equal division of candy in 4 children = Total Candy/No. of children
= 256 / 4
= 64
Thus, there are 64 pieces that each child receive.
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Final answer:
Each of the four children, including Joelle, will receive 64 pieces of candy after dividing the total of 256 pieces evenly among them.
Explanation:
To find out how many pieces of candy each child receives, we need to divide the total number of pieces by the number of children. Joelle and her three siblings make a group of four children in total. They have accumulated 256 pieces of candy. To divide this evenly, we do the following calculation:
Divide the total number of candies (256) by the number of children (4).
The division gives us the result 64 pieces of candy for each child.
Therefore, each child, including Joelle, will receive 64 pieces of candy.
Gray and Brenda and Jack went bowling together. Bryant's score was 55. Jacks score was exactly double bryant's. Brenda has 13 fewer points than Jack. What was Brenda's score?
Bryant's score is 55 (given)
Jack's score is twice the score of Bryant, so it's
[tex]55\cdot 2 = 110[/tex]
Brenda's score is 13 less than Jack, so it's
[tex]110-13 = 97[/tex]
Each month, Kaisorn deposits $50.00 onto her public transportation card. It costs her $2.50 per trip to ride the subway. Thom deposits $40.00 on his public transportation card. It costs him $2.00 per trip to ride the subway. If x represents the number of trips and y represents the amount remaining in each account, which system of equations represents their transportation costs? 50 − 2.5x = y 40 − 2x = y 50 + 2.5x = y 40 + 2x = y 50 − 2.5y = x 40 − 2y = x 50 + 2.5y = x 40 + 2y = x
Answer:
For Kaisorn: [tex]y=50-2.50x[/tex]
For Thom: [tex]y=40-2x[/tex]
Step-by-step explanation:
Each month, Kaisorn deposits $50.00 onto her public transportation card.
It costs her $2.50 per trip to ride the subway. Means 2.50x
Thom deposits $40.00 on his public transportation card. It costs him $2.00 per trip to ride the subway. Means 2x
Let x represents the number of trips
Let y represents the amount remaining in each account.
Then the system of equations represents their transportation costs are :
For Kaisorn: [tex]y=50-2.50x[/tex]
For Thom: [tex]y=40-2x[/tex]
On Monday Paula has $20 is her bank account. She spends $25 and then spends another $10. How much money does she need to add into her account (deposit) to return to the original amount she started with on Monday?
Answer:
15
Step-by-step explanation:
10 + 25= 35 and 35-20 = 15
please give branlest
Answer:
Step-by-step explanation: She Needs To Deposit $35 Dollars To Return To The Orginal Ammount She Started With On Monday.
Find the measure of the line segment GE. Assume that lines which appear tangent are tangent.
Answer:
The measure of the line segment GE is [tex]18\ units[/tex]
Step-by-step explanation:
we know that
The Intersecting Secant-Tangent Theorem states that, the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment
so
In this problem
[tex]GE*GF=GH^{2}[/tex]
substitute the values
[tex](8+x)(8)=12^{2}[/tex]
solve for x
[tex]8x+64=144[/tex]
[tex]8x=144-64[/tex]
[tex]8x=80[/tex]
[tex]x=10[/tex]
Find the measure of the line segment GE
[tex]GE=8+10=18\ units[/tex]
If a = 5 centimeters, w = 10 centimeters, and h = 6 centimeters, what is the area of the decorative paper he will require?
Final answer:
The area of decorative paper needed, given the dimensions of length and width, is calculated as 50 square centimeters.
Explanation:
To answer the question about the area of decorative paper required, we need to use the formula for the area of a rectangle which is length times width. However, the given dimensions of a = 5 centimeters, w = 10 centimeters, and h = 6 centimeters seem to describe a box or a prism rather than a flat piece of paper. If the decorative paper is meant to cover the side of the box, then the relevant dimensions are likely length and width, not including the height. Assuming the decorative paper is to cover a flat surface, the formula for the area is A = length × width. Therefore, the required area of decorative paper is A = 5 cm × 10 cm = 50 square centimeters.
Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph.
y=-1 tan 1/10 x+4
Answer:
Reflection across x-axis, horizontal stretch by a factor of 10
and vertical translation up 4 units ⇒ answer (c)
Step-by-step explanation:
* The basic function of tanФ is
# y = tanФ
1- If y = -tanФ ⇒ reflect y over the x-axis
2- If y = tan(-Ф) ⇒ reflect y over the y-axis
3- If y = tan(Ф - k) ⇒ shift y right k units
4- If y = tan(Ф + k) ⇒ shift y left k units
5- If y = tanФ + k ⇒ shift y up k units
6- If y = tanФ - k ⇒ shift y down k units
7- If y = k tanФ ⇒ multiply y-values by k
(k > 1 stretch, 0 < k < 1 compressed vertical)
The scale factor is k
8- If y = tan(kФ) ⇒ divide x-values by k
(k > 1 compressed, 0 < k < 1 stretch horizontal)
The scale factor is 1/k
* Lets solve the problem
∵ y = -tan(1/10)x + 4
* We will use rules number 1 , 5 and 8
∴ Reflect y over the x-axis, shift y up k units and stretch
horizontal by scale factor is 1/k (0 < k < 1)
∴ Reflection across x-axis, horizontal stretch by a factor of 10
and vertical translation up 4 units
Find the coordinates of the midpoint of a line segment with end points (-3,4) and (7,9)
Answer: (2, 6.5)
Step-by-step explanation:
[tex]Midpoint_{x,y}=\bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)\\\\\\.\qquad \qquad \quad=\bigg(\dfrac{-3+7}{2},\dfrac{4+9}{2}\bigg)\\\\\\.\qquad \qquad \quad=\bigg(\dfrac{4}{2},\dfrac{13}{2}\bigg)\\\\\\.\qquad \qquad \quad=\large\boxed{(2,6.5)}[/tex]
Item 16 Simplify the expression. 5+8(3+x)
First, to simplify the expression 5 + 8(3 + x), distribute the 8 to everything inside the parentheses to get 5 + 24 + 8x. Then, combine the numerical terms to get the answer 29 + 8x.
Explanation:The expression you are asked to simplify is 5 + 8(3 + x). To do this, you'll need to use the distributive property, which allows you to multiply a number outside a set of parentheses by every term inside the parentheses.
Start with the expression: 5 + 8(3 + x)
Before adding, you'll need to multiply eight by every term inside the parentheses, three, and x:
5 + 8*3 + 8*x
That changes your expression to:
5 + 24 + 8x
Now, you need to combine like terms (add together the numbers that are not attached to variable x):
5 + 24 = 29
So, the simplified version of the expression is:
29 + 8x
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Which of the following statements is true? a. sin 18° = cos 72° b. sin 55° = cos 55° c. sin 72° = cos 18° d. Both a and c. Please select the best answer from the choices provided A B C D
D
generally,
[tex] \sin( \alpha ) = \cos(90 - \alpha )[/tex]
you can visualize this by drawing a right triangle with acute angles a and 90-a
Answer:
D. Both a and c are true.
Step-by-step explanation:
a . sin 18 = cos (90 - 18) = cos 72 so a is True.
b. this is not true.
c. sin 72 = cos(90 - 72) = cos 18, so c is true.
Solve the equation. Round to the nearest hundredth. Show work.
[tex]6e^{2x} - 5e^{x} = 6[/tex]
Answer:
The value of x = 0.41
Step-by-step explanation:
∵ [tex]6e^{2x}-5e^{x}=6[/tex]
Let [tex]e^{x}=y[/tex]
∴ [tex]e^{2x}=y^{2}[/tex]
∴ 6y² - 5y = 6
∴ 6y² - 5y - 6 = 0 ⇒ factorize
∴ (3y + 2)(2y - 3) = 0
∴ 3y + 2 = 0 ⇒ 3y = -2 ⇒ y = -2/3
∴ 2y - 3 = 0 ⇒ 2y = 3 ⇒ y = 3/2
∵ [tex]y=e^{x}[/tex]
∴ [tex]e^{x}=\frac{-2}{3}[/tex] ⇒ refused
([tex]e^{ax}[/tex] never gives -ve values)
∵ [tex]e^{x}=3/2[/tex] ⇒ insert ln in both sides
∵ [tex]lne^{ax}=axlne=ax[/tex] ⇒ ln(e) = 1
∴ [tex]xlne=ln(3/2)[/tex]
∴ x = ln(3/2) = 0.41
There are 36 gold cards and 36 silver cards in a deck. The gold cards are numbered 1,3,5,... 71 and the silver cards are numbered 2.4.6,... 72. The cards are throughly shuffled and one card is randomly selected.
A. Find the probability of selecting a gold card or a card with a multiple of 12 on it. Show your work
B. Find the probability of selecting a silver card or a card with a multiple of 9 on it. Show your work.
A) multiples of 12 up to 72 ( 72 total cards)
12, 24, 36, 48, 60, 72 = 6 cards.
36 are gold.
Total gold cards and multiple of 12 = 36 + 6 =42
Probability of getting one of them is 42/72, which reduces to 7/12
B) 36 silver cards
Multiples of 9: 9, 18, 27, 36, 45, 54,63 = 7 cards
Silver cards are even and there is 3 even cards that are also multiples of 9, so subtract 3 from 7 to get 4.
Total silver cards and multiples of 9 = 36 + 4 = 40
Probability = 40/72 which reduces to 5/9
Answer:
Step-by-step explanation:
A.
Because there is no overlap between good card and card with a multiple of 12,
P(gold card or a card with a multiple of 12)
= P(gold card) + P(a card with a multiple of 12)
P(gold card)
= no. of gold cards / total no. of cards
= 36 / (36 + 36)
= 36 / 72
= 1/2
P(a card with a multiple of 12)
= no. of cards with multiples of 12 / total no. of cards
= (12, 24, 36, 48, 60, 72) / 72
= 6/72
= 1/12
P(gold card or a card with a multiple of 12)
= 1/2 + 1/12
= 7/12
B. There ARE overlaps between a silver card and a card with a multiple of 9,
P(silver card or a card with a multiple of 9)
= P(silver card) + P(a card with a multiple of 9) - P(silver card AND a multiple of 9)
P(silver card)
= no. of silver cards / total no. of cards
= 36 / (36 + 36)
= 36 / 72
= 1/2
P(a card with a multiple of 9)
= no. of cards with multiples of 9 / total no. of cards
= (9, 18, 27, 36, 45, 54, 63, 72) / 72
= 8/72
= 1/9
P(silver card AND a multiple of 9)
= no. of silver cards AND a multiple of 9 / total no. of cards
= (18, 36, 54, 72) / 72
= 4/72
= 1/18
P(silver card or a card with a multiple of 9)
= 1/2 + 1/9 - 1/18
= 10/18
= 5/9
Please help me out........ :)
Answer:
x = 5
Step-by-step explanation:
For the parallelogram to be a square we use the property
The diagonals of a square are congruent, hence
12x - 23 = 4x + 17 ( subtract 4x from both sides )
8x - 23 = 17 ( add 23 to both sides )
8x = 40 ( divide both sides by 8 )
x = 5
How do you do this problem?
Answer:
Step-by-step explanation:
Part A
If it is compounded quarterly, the interest of 1.5 must be cut into a quarter of its present size. 1.5 //4 = 0.375 % per quarter.
In addition, the number of times that payment will be received is
4 quarters * 5 years = 20 quarters.
i = principle (1 + 0.375/100) ^20
i = principle (1 + 0.00375)^20
The principle = 4000 dollars.
i = 4000 * (1.00375)^20
i = 4000 * 1.07773
i = 4310.93
So she's tied up 4000 dollars to make 300 dollars.
Part B
I can't really give you an answer to this because I don't know if the 7% is compounded and over what period of time if it is, or if they mean 7% annually. There's a lot of variation in this question. Most people don't take money out of the market, so if it compounded, the formula would be
New Principle = starting amount (1.07)^4
New Principle = 4000 * 1.07^4
New Principle = 5243.18 so she would make about 4 times as much as the 300 she makes if she puts the money in a bond.
=============
If the interest is simple interest
Gain would be 0.07 * 4000 = 280 dollars.
Over four years = 4*280 = 1120 dollars.
You are going to have to ask your teacher what is intended by this question.
In the trapezium, a = 7cm , b = 10.4cm h = 6.7cmwork out the area of the trapezium
What is the trigonometric function's period?
Question 3 options:
pi
2 pi
3 pi
4 pi
➷ Find the difference from one peak ( highest point) to the next
In this case, it is 2 pi
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
2 pi
Step-by-step explanation:
. A soccer team played 32 games. If they won 25% of them, how many games did the team win?V
Answer:
[tex]8\ games[/tex]
Step-by-step explanation:
Let
x----->number of games won by the football team
we know that
[tex]25\%=25/100=0.25[/tex]
so
[tex]x=0.25(32)=8\ games[/tex]
Solve for x for 0 ≤ x < 2 π .
cotxcosx - cotx = 0
0
Pi/2
Pi
3Pi/2
2Pi
[tex]\bf cot(x)cos(x)-cot(x)=0\implies cot(x)[cos(x)-1]=0 \\\\[-0.35em] ~\dotfill\\\\ cot(x)=0\implies \cfrac{cos(x)}{sin(x)}=0\implies cos(x)=0\\\\\\ x=cos^{-1}(0)\implies \boxed{x= \begin{cases} \frac{\pi }{2}\\\\ \frac{3\pi }{2} \end{cases}} \\\\[-0.35em] ~\dotfill\\\\ cos(x)-1=0\implies cos(x)=1\implies x=cos^{-1}(1)\implies \boxed{x=0}[/tex]
Answer:
x = π/2, 3π/2
Step-by-step explanation:
cot(x)cos(x) - cot(x) = 0
Factor out cot(x)
cot(x)[cos(x) -1] = 0
Solve each part separately
cot(x) = 0 cos(x) - 1 = 0
x = π/2, 3π/2 cos(x) = 1
x = 0
There are three possible solutions:
x = 0, π/2, 3π/2
However, the function is undefined for x = 0.
∴ x = π/2, 3π/2
Twenty is fourteen more than 3 times a number. What is the number?
Answer:
2
Step-by-step explanation:
Let's disect the problem. Three times a particular number plus fourteen equals 20. Let's make an equation, and replace the number with x.
3x + 14 = 20The "3x" represents the 3 times the number,the 14 represents the 14 added to make 20.Let's solve the equation!We'll first minus 14 from each side to balance the equation, but with the intention of isolating the variable, x.
3x = 6We have almost successfully isolated the variable. To isolate the variable, we can divide by three on each side.
x = 2The number is 2.Given f(x)=7x^9 , find f^1(x). Then state whether f^1f(x) is a function.
a : y=(x/7)^1/9 ; f^1(x) is a function.
b : y=(x/7)^9 ; f^1(x) is not a function
c : y=(x/7)^1/9 ; f^1(x) is not a function
d : y=(x/7)^9 ; f^1(x) is a function
Answer:
A
Step-by-step explanation:
Edge 2021
The inverse function of f(x) = 7x^9 is found to be f^{-1}(x) = (x/7)^{1/9}. By substituting f(x) into its inverse, we can verify that f^{-1}(f(x)) = x, which shows that the composition is indeed a function. Therefore, the correct answer is option a.
The student has asked to find the inverse function of f(x) = 7x^9 and determine if the composition of the original function and its inverse is a function. The inverse function, denoted as f^{-1}(x), undoes the action of the original function. To find the inverse, we replace f(x) with y, switch the roles of x and y, and then solve for y:
Start with y = 7x^9.Switch x and y to get x = 7y^9.Divide both sides by 7 to get x/7 = y^9.Take the ninth root of both sides to solve for y, yielding y = (x/7)^{1/9}.This gives us option a: y = (x/7)^{1/9}. To check if f^{-1}(f(x)) is a function, we substitute f(x) into the inverse, resulting in f^{-1}(7x^9) = (7x^9/7)^{1/9} = x, which is indeed a function. Therefore, f^{-1}(x) is a function, and option a is correct.
he point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y – 4 = 1/4 (x – 8). What is the slope-intercept form of the equation for this line?
Answer:
[tex]y=\frac{1}{4}x+2[/tex]
Step-by-step explanation:
The point-slope form of the equation of a line that passes that through points (8, 4) and (0, 2) is given as;
[tex]y-4=\frac{1}{4}(x-8)[/tex]
To find the slope-intercept form of this line, we need to expand the point-slope form.
[tex]y-4=\frac{1}{4}x-2[/tex]
We now solve for y to obtain;
[tex]y=\frac{1}{4}x-2+4[/tex]
We simplify to obtain:
[tex]y=\frac{1}{4}x+2[/tex]
This equation is now in the form;
[tex]y=mx+c[/tex]
This is what we refer to as the slope-intercept form.
Help with this question, please! I need help!
Answer:
$357Step-by-step explanation:
We have a rectangle measuring 25 feet × 9 feet. Remove from the rectangle two regular hexagons with a side length equal to 2 feet.
The formula of an area of a rectangle:
[tex]A_r=lw[/tex]
l - length, w - width.
Substitute l = 25 ft and w = 9 ft:
[tex]A_r=(25)(9)=225\ ft^2[/tex]
The formula of an area of a regular hexagon:
[tex]A_h=6\cdot\dfrac{a^2\sqrt3}{4}[/tex]
a - side
Substitute a = 2 ft:
[tex]A_h=6\cdot\dfrac{2^2\sqrt6}{4}=6\sqrt3\ ft^2[/tex]
The area of the wall:
[tex]A=A_r-2A_h[/tex]
Substitute:
[tex]A=225-2(6\sqrt3)=225-12\sqrt3\approx225-20.785=204.215\ ft^2[/tex]
Paiting the wall costs $1.75 per ft². Calculate:
[tex](\$1.75)(204.215)\approx\$357[/tex]