The equation that models the problem is given as follows:
s = 120/1.5.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
For this problem, the variables are given as follows:
y = 120 = total width of the wall.k = 1.5 = length of each stripe painted.x = s = number of stripes painted.Hence the equation used to obtain the number of stripes that Murphy will paint is given as follows:
1.5s = 120
s = 120/1.5
s = 80. (solution).
More can be learned about proportional relationships at https://brainly.com/question/10424180
#SPJ1
What is 5 in the expression 5x?
The numerical coefficient in the expression 5x is 5. 5x denotes a 5 times multiplier applied to the variable x.
CoefficientA phrase or a number that is multiplied by a variable is referred to as a coefficient. In most cases, the constant word comes before the variable term.
In a polynomial series or an equation, a coefficient is often a multiplicative factor.
ExpressionMathematical statements known as expressions are made up of two words, at least one of which must contain either variables, integers, or both. These expressions can either be expressed as numbers, variables, or as a product of numbers and variables. The mathematical operators used to separate the integers in these expressions are a mixture of numbers.
To know more about the mathematical expression on brainly : brainly.com/question/12976257
#SPJ4
a force of pounds is required to hold a spring stretched 0.5 feet beyond its natural length. how much work (in foot-pounds) is done in stretching the spring from its natural length to 1.1 feet beyond its natural length?
9.44ft-lbs work is done in stretching the spring from its natural length to 1.1 feet beyond its natural length.
when force is constant
Work = force x distance
i.e., w= fx
According to the question, force is not constant
Hence, For each infinitely small amount of work equals Force times the infinitely small change in the distance
dW= Fx dx
Total work W=[tex]\int\limits^0.9_0 {Force} \, dx[/tex] ----1
To stretch/compress a spring, we would need to apply a different amount of force, depending on the amount it is stretched/compressed
F=Kx ----2
where K is the spring constant
putting 2 in 1
W=[tex]\int\limits^0.9_0 {Kx} \, dx[/tex] ----3
According to ques F s 7 and x is 0.3
so, K= 7/0.3
K=23.3
Putting this value in 3
W=[tex]\int\limits^0.9_0 {23.3x} \, dx[/tex]
Putting constant out
W=23.3[tex]\int\limits^0.9_0\ {x} \, dx[/tex]
W=23.3 (x∧2)/
W=23.3(0.9∧2-0)
W=9.44
Therefore, 9.44 ft-lbs of work is done in stretching the spring from its natural length to 1.1 feet beyond its natural length.
To know more about work visit:
https://brainly.com/question/25573309
#SPJ4
Which segment represents a radius of the circle below?
Answer: Choose A my smart self just knew
a message in a bottle is floating on top of the ocean in a periodic manner. the time between periods of maximum heights is 24 seconds, and the average height of the bottle is 8 feet. the bottle moves in a manner such that the distance from the highest and lowest point is 4 feet. a cosine function can model the movement of the message in a bottle in relation to the height. part a: determine the amplitude and period of the function that could model the height of the message in a bottle as a function of time, t. (5 points) part b: assuming that at t
a) The amplitude and period of the function that could model the height of the message in a bottle as a function of time, t are 2 feet and 24 seconds.
b) At t = 0, h(t) = 8 feet , the equation of the function that could represent the situation is h(t) = 2 Cos( π/12( t + 6) + 8.
We have, In a bottle a message is floating on top of the ocean in a periodic manner. The time between periods of maximum heights = 24 sec.
Average height of bottle = 8 feet
The distance from the highest and lowest point = 4 feet
The height at any movement of time can be modelled as a cosine function,
h( t) = A cos(B(t - C)) + D
Where A --> amplitude of wave function
2π/B--> periodicity
C --> phase shift ( right / left)
D --> vertical shift
a) Amplitude, A in feet is defined as the maximum height that bottle reaches from mean sea level. It is calculated by the difference between hightest and lowest point and divided by 2. In this case, the distance from the highest and lowest point is 4 feet. So, amplitude is
A = 4/2 = 2 feet .
Time period, T in seconds is the time taken by bottle to complete one cycle. In this case, it is equal to time taken to reach at maximum height. That is equals to 24 seconds.
b) Period = 2π/ B = 24 seconds , so
B = 2π/24 => B = π/12
Using the part A results, the equation of movement is, h( t) = 2 cos(π/12( t - C) + D
At t = 0 , the message in a bottle is at its average height, i.e., 8 feet and moves upwards after. This implies at t = 0 ,
h(t) = 8 feet
=> 8 = 2 cos(π/12( 0 - C)) + 8
=> 2 cos(π/12( 0 - C) )= 0
=> cos(π/12(-C) )= 0
=> cos( πC/ 12) = 0
=> πC/12 = cos⁻¹ ( 0)
=> πC/12 = π/2
=> C = 12/2 = 6
plugging all known values in cosine function equation to get required equation, h(t) = 2 Cos( π/12( t + 6) + 8
Hence, the required equation is h(t) = 2 Cos( πt/12 + π/2) + 8.
To learn more about Cosine function, refer:
https://brainly.com/question/29100023
#SPJ4
Complete question :
A message in a bottle is floating on top of the ocean in a periodic manner. The time between periods of maximum heights is 24 seconds, and the average height of the bottle is 8 feet. The bottle moves in a manner such that the distance from the highest and lowest point is 4 feet. A cosine function can model the movement of the message in a bottle in relation to the height.
Part A: Determine the amplitude and period of the function that could model the height of the message in a bottle as a function of time, t. (5 points)
Part B: Assuming that at t = 0 the message in a bottle is at its average height and moves upwards after, what is the equation of the function that could represent the situation? (5 points)
From the line of scrimmage the quarterback gets the ball and back ups 5 yards so he can see the rest of the field unfortunately he has nowhere to go with the ball and falls back an additional 6 yards before being tackled which of the following numbers represents the yardage for that play ?
-11 number represents the yardage for play.
What is scrimmage?A series of plays that starts with the ball being positioned on the ground with its longest axis perpendicular to the goal line is known as scrimmage.
We know that
The quarterback backups to 5 yards (negative number).
He falls back another 6 yards more (negative number).
To know the total number of yards the quarterback felt back, we just need to sum these negative numbers.
-5-6=-11
-11 number represents the yardage for play.
Learn more about this Question here:
brainly.com/question/29051959
#SPJ1
Liliana is planning to exhibit paintings at her local library. She has 10 paintings already made, and she can make 4 new paintings in a day. If she knows that she wants to have more than 26 paintings for the exhibition, select the inequality that can help Liliana determine how many days she will need to paint, and then answer the question below.
Which of the following possible numbers of workdays will allow Liliana to prepare enough paintings for the exhibit?
Select all that are true.
4 days
10 days
5 days
8 days
The number of workdays that will allow Liliana to prepare enough paintings for the exhibit are 10 days, 5 days and 8 days (2nd - 4th option).
How many days would be enough to allow Liliana prepare for the exhibition?The first step is to determine the inequality sign that would be used in the inequality that represents the information in the question.
Here are inequality signs and what they mean:
> means greater than< means less than≥ means greater than or equal to ≤ less than or equal toThe form of the equation is:
number of painting already made + (new paintings per day x number of days) > 26
10 + (4 x n) > 26
10 + 4n > 26
4n > 26 - 10
4n > 16
n > 16 / 4
n > 4
To learn more about inequality, please check: https://brainly.com/question/5031619
#SPJ1
PLEASE HELP AND SHOW WORK PLEASEEE!!!!!
An odometer shows that a car has traveled 41,000 miles by January 1, 2020. The car travels 19,000 miles each year. Write an
equation that represents the number y of miles on the car's odometer x years after 2020.
y =
Answer:
The odometer shows that the car has traveled 41,000 miles by January 1, 2020, so we can use this as the starting point (x = 0) for our equation. We also know that the car travels 19,000 miles each year.
We can use this information to write an equation for the number of miles on the car's odometer x years after 2020.
The equation would be : y = 41,000 + (19,000 * x)
Where y represents the number of miles on the car's odometer and x represents the number of years after 2020.
The y is the number of miles at the odometer and x is the number of years passed from 2020.
This equation gives the number of miles on the car's odometer x years after 2020, whenever we have to know the number of miles on the odometer we just need to plug in the number of years passed in the equation.
Gabe goes to the mall. If d is the number of items he bought, the expression 13.09 d plus 28 gives the amount he spent in dollars at one store. Then he spent 22 dollars at another store. Find the expression which represents the amount Gabe spent at the mall. Then estimate how much Gabe spent if he bought 4 items.
The estimated amount he paid at the other store is $5.5.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, The amount(A₁) Gabe spent in dollars at one store is
A₁ = 13.09d + 28, where 'd' is the number of items he bought.
Then he spent 22 dollars at another store.
let, A₂ = 22 and he bought 4 items.
Therefore, The estimated amount he paid at the other store is,
= 22/4.
= $5.5
learn more about numerical expressions here :
https://brainly.com/question/29199574
#SPJ1
One fourth of blank is equal to 3
Answer: x=12
Step-by-step explanation:
The question: 1/4 of ___ = 3
Let's start solving it.
First, let's set ___ as x and rewrite the equation.
1/4 of x = 3
Now, when you say 1/4 of x, you mean that you multiply x by 1/4.
So the equation is:
1/4*x=3
Finally, multiply both sides by 4.
Answer: x = 12
You are really excited to have found a Puch Maxi Moped from the mid Eighties, and the spring weather is making you want to get out and ride it around. It doesn't run on straight gasoline, you have to mix the oil and gas together in a specific ratio of 2. 4 fl. Oz. Of oil for every gallon of gasoline
We should have to add 4.2 fl. oz. of oil to our 1.75 gallons of gas.
To figure out how much oil to add, we need to multiply the number of gallons of gas by the ratio of oil to gas. In this case, 1.75 gallons multiplied by 2.4 fl. oz. of oil per gallon of gas results in 4.2 fl. oz. of oil. 1.75×2.4= 4.2
Make sure to mix the oil and gasoline together thoroughly so it's evenly distributed throughout the fuel tank, otherwise our moped may not run properly. Once you've added the correct amount of oil, you can enjoy your ride, safe in the knowledge that you've got the perfect mixture for your Puch Maxi Moped.
Learn more about ratio:
https://brainly.com/question/13513438
#SPJ4
Correct question should be: You are really excited to have found a Puch Maxi Moped from the mid Eighties, and the spring weather is making you want to get out and ride it around. It doesn't run on straight gasoline, you have to mix the oil and gas together in a specific ratio of 2.4 fl. oz. of oil for every gallon of gasoline.
You have 1.75 gallon of gas. How much oil should you add?
What kind of slope is x =- 2?
x = - 2 is a vertical line with an undefined slope.
A slope is a measure of how steep a line is when graphed on a coordinate plane. It is the ratio of the change in y-coordinates (rise) to the change in x-coordinates (run) between two points on a line. It is represented by the letter m in the slope-intercept form of a linear equation, y = mx + b.
x = -2 is an equation of a vertical line, which means that for this line, the x-coordinate is always -2. A vertical line does not have a slope because it does not have a change in y-coordinate for a given change in x-coordinate. It is infinitely steep or undefined.
So, x = -2 is not a slope but an equation of a vertical line that has an undefined slope.
Learn more about slope here: https://brainly.com/question/3493733
#SPJ4
Which is the value of 2c²d if c = 0.5 and d = 3?
Answer: The value of 2c²d would be 2 * (0.5)² * 3 = 2 * (0.25) * 3 = 0.5 * 3 = 1.5
This is because you first square the value of c (0.5² = 0.25), then you multiply it by 2 (0.25 * 2 = 0.5) and then by d (0.5*3 = 1.5)
Step-by-step explanation:
[tex] \large \underline{ \tt \: \: Given \: : \: } \\ \: \: \: \: \boxed{ \red{\tt c : 0.5}} \\ \: \: \: \: \boxed{ \green{ \tt \: d : 3 \: \: \: }}[/tex]
[tex] \: [/tex]
put the value of c nd d in given eqⁿ ~
[tex] \: [/tex]
[tex] \large \tt \: 2 { \red{c}^{2}}\green{d}[/tex]
[tex] \: [/tex]
[tex]\large \tt \: 2 \times { \red{0.5}^{2}} \times \green{3}[/tex]
[tex] \: [/tex]
[tex]\large \tt \: 2 \times { \red{0.25}} \times \green{3}[/tex]
[tex] \: [/tex]
[tex] \large \tt \: 2 \times { \purple{0.75}}[/tex]
[tex] \: [/tex]
[tex] \underline{ \boxed{ \large \tt \purple{ \: \: 1.5 \: \: }}}[/tex]
[tex] \: [/tex]
hope it helps!:)
What is the extraneous root of the given rational function?
The extraneous roots of a given rational function occurs when we solve for a rational equations -, when we will multiply this results then the equation to clear the fractions and cancelling a 0/0 term , we will get the extraneous root.
Extraneous means external , these roots are there because when we solve an equation we cannot always get an equivalent equations when we simplify it.
Extraneous roots are used while solving a log equations. Extraneous roots occurs every time we apply functions to both sides of an equation that are not invertible. for example , | 2 x − 1 | = ( 2 x − 1) 2 , the two of this equations are totally same.
To learn more about roots
brainly.com/question/29755184
#SPJ4
y = | x| - 7…………………. Help
All the points on the graph represent the possible solution coordinates of the function y = |x| - 7.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression as -
y = |x| - 7
The given function is -
y = |x| - 7
Refer to the graph of the function attached. All the points on the graph represent the possible solution coordinates of the function {y}.
Therefore, all the points on the graph represent the possible solution coordinates of the function {y}.
To solve more questions on algebraic expressions, visit the link below -
brainly.com/question/1041084
#SPJ1
Can someone help me I'm confused?
20 POINTS
The length of MA with the endpoints at M(7, -2) and A(2, -6) is √41 units.
How to find the distance of MA?MA has the endpoints at M(7, -2) and A(2, -6). The distance of MA can be found as follows:
Using distance formula, the formula follows Pythagorean principle.
d = √(y₂ - y₁)² + (x₂ - x₁)²
x₁ = 7
x₂ = 2
y₁ = -2
y₂ = -6
Applying the formula,
distance of MA = √(-6 + 2)² + (2 - 7)²
distance of MA = √(-4)² + (-5)²
distance of MA = √ 16 + 25
distance of MA = √41
Therefore, distance of MA is √41 units.
learn more on endpoints here: https://brainly.com/question/12700142
#SPJ1
Which is the solution to this system of equations?
(0, 3) and (4,1)
(8,1)
Sy=√9-x
x+2y=6
(4,1) and (8, 1)
(0,3)
The solution to this system of equations is (8,1).
What is equation?An equation is an expression that uses mathematical symbols to represent a relationship between two or more things. Equations are often used to solve problems, describe patterns, and make predictions. Equations can involve numbers, variables, operations, and other mathematical elements.
The solution to this system of equations can be found by solving the two equations for x and y respectively. For the first equation, we can solve for y:
y = √9 - x
For the second equation, we can solve for x:
x = 6 - 2y
Substituting the value of y from the first equation into the second equation, we find that:
6 - 2√9 - x = 0
Solving for x yields the solution:
x = 8
Substituting the value of x into the first equation, we find that:
y = 1
Therefore, the solution to this system of equations is (8,1).
To know more about Equation click-
https://brainly.com/question/2972832
#SPJ1
Is Y =- 2x 5 linear?
The given equation y = -2x + 5 is a linear equation.
The given equation is:
y = -2x + 5
We observe the highest degree of x in a given equation to know whether it is a linear equation or not.
We know that if the highest degree of x in an equation is 1 then it is a linear equation else its a quadratic or non - linear equation.
In the given equation the highest degree of x is 1, hence it is a linear equation.
We can also check the same by graphing the equation.
If the graph of the given equation is a straight line then it is said to be a linear equation. The graph of this equation is also a straight line.
To know more about linear equations:
https://brainly.com/question/29111179
#SPJ4
Deondra is going to invest $90,000 and leave it in an account for 15 years. Assuming the interest is compounded monthly, what interest rate, to the nearest hundredth of a percent, would be required in order for Deondra to end up with $201,000?
The rate of interest be required in order for Deondra to end up with $201,000 is 14.88%
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Deondra is going to invest $90,000 and leave it in an account for 15 years.
We have o find the interest rate, to the nearest hundredth of a percent, would be required in order for Deondra to end up with $201,000
A=PRT
201000=90000×R×15
201000=1350000R
Divide both sides by 1350000
R=0.1488×100
R=14.88
Hence, the rate of interest be required in order for Deondra to end up with $201,000 is 14.88%
To learn more on Percentage click:
https://brainly.com/question/28269290
#SPJ1
Otto is almost finished with his new photography book, Noses of North America. The book is in the shape of a right triangle—to look like a nose. The base of the book measures 9 inches. Its height measures 12 inches. What is the area of the book?
Answer:
The area of the book is 108 square inches.
Step-by-step explanation:
This is calculated by multiplying the base (9 inches) by the height (12 inches). The area of a right triangle is equal to one-half of the base multiplied by the height.
Answer:
108 inches
Step-by-step explanation:
Multiply 12 by 9
) you roll 2 fair 6-sided dice, one red and one blue. what is the probability that the sum of the two values showing is 5?
The probability that the sum of the two values showing is 5 is 1/9 which is approximately 0.111 or 11.11%.
There are a total of 36 possible outcomes when rolling two fair 6-sided dice. Since the dice are fair, each outcome is equally likely. To find the probability of getting a sum of 5, we need to determine how many of the 36 possible outcomes will result in a sum of 5.
The possible outcomes that add up to 5 are (1,4), (2,3), (3,2) and (4,1). These are 4 possibilities, so the probability of getting a sum of 5 when rolling two fair 6-sided dice is 4/36 or 1/9 which is approximately 0.111 or 11.11%.
In general, the probability of getting a certain sum when rolling two fair dice is determined by the number of ways that the two dice can combine to give that sum.
Therefore, the probability that the sum of the two values showing is 5 is 1/9 which is approximately 0.111 or 11.11%.
Learn more about probability here: https://brainly.com/question/24756209
#SPJ4
5-2 skills practice medians and altitudes of triangles
in PQR, NQ = 6,RK =3 and PK =4
find each measure
1 . KM
2. KQ
3. LK
4. LR
5. NK
6. PM
The measures of KM, KQ, LK, LR, NK and PM are 2, 2, 4, 4, 6 and 2 respectively.
1) KM: Since N is the midpoint of QR, we know that QN = NR, so QN + NR = QN + QN = 2QN = 26 = 12. Therefore, KM = KR - QN = (PK+KQ) - QN = 4 - 6 = -2.
2) KQ: Since PK = 4 and KM = -2, we have KQ = PK + KM = 4 + (-2) = 2.
3) LK: The median of a triangle connects a vertex to the midpoint of the opposite side, and it's length is 2/3 the length of the hypotenuse of the right triangle formed by the median and the two segments from the vertex to the endpoints of the median.
In this case, LK = (2/3)(PQ) = (2/3)(4+2) = (2/3)*6 =4
4)LR: In this case, LR = LK = 4
5) NK: NK = QN = 6
6) PM: PM = PK - KQ = 4 - 2 = 2
Please note, that in order to be able to calculate all these lengths and measures, it is assumed that the triangle PQR is a valid triangle i.e, the sum of the lengths of any two sides of the triangle is greater than the length of the third side.
To learn more about triangles visit: brainly.com/question/2773823
#SPJ4
Question 1 (4 points)
(09.01 LC)
Choose the equation that represents the fraction one twelve . (4 points)
one whole partitioned into twelve parts with one part shaded
a
12 ÷ 1 = ________
b
12 ÷ 11 = ________
c
1 ÷ 12 = ________
d
11 ÷ 12 = ________
Question 2 (4 points)
(09.01 LC)
A cake is cut into 6 equal-sized pieces. Each piece is one sixth of the whole. Choose the equation that represents this fraction. (4 points)
a
5 ÷ 6 = ________
b
6 ÷ 5 = ________
c
1 ÷ 6 = ________
d
6 ÷ 1 = ________
Question 3 (4 points)
(09.01 LC)
Choose the division equation that represents the fraction shown. (4 points)
one fourteenth = ________
a
1 ÷ 14 = ________
b
14 ÷ 11 = ________
c
13 ÷ 14 = ________
d
14 ÷ 13 = ________
Question 4 (4 points)
(09.01 LC)
Choose the division equation that represents the fraction shown. (4 points)
one seventh = ________
a
6 ÷ 7 = ________
b
7 ÷ 6 = ________
c
7 ÷ 1 = ________
d
1 ÷ 7 = ________
Question 5 (4 points)
(09.01 LC)
Choose the equation that represents the fraction one eighth . (4 points)
one whole partitioned into eight parts with one part shaded
a
7 ÷ 8 = ________
b
1 ÷ 8 = ________
c
8 ÷ 7 = ________
d
8 ÷ 1 = ________
A construction manager needs 12 workers to complete a building project in 54 days. If the building project needs to be completed in 36 days how many more workers does the construction manager need to complete the project
The construction manager will need 6 more workers to complete the project
How to determine how many more workers the construction manager need to complete the project?To determine how many more workers are needed to complete the project in 36 days, the construction manager would need to determine the rate of work per worker and then calculate how many more workers are needed to achieve the desired rate.
If 12 workers to complete a building project in 54 days. Then 1 work will complete work in:
12 × 54 days = 648 days /worker
If the building project needs to be completed in 36 days, you need:
648 / 36 = 18 workers
Number of workers left = 18 - 12 = 6 workers
Learn more about rate on:
brainly.com/question/620388
#SPJ1
which is faster 4/5 mile every 1 and 1/3 minute or 3/4 mile every 1 and 1/8 minute
Answer:
4/5
Step-by-step explanation:
Which of the following methods can be used in solving quadratic equation of the form ax²+bx+c=0?
The two real solutions to this quadratic equation are -2 and 3/2.
The Quadratic Formula is the most popular method for solving quadratic equations of the form ax²+bx+c=0. It is derived from the quadratic equation which states that if a, b, and c are real numbers, and a is not equal to zero, then the roots of the quadratic equation ax²+bx+c=0 can be determined by the following equation:
x = (-b ± √(b² - 4ac))/(2a)
The quadratic formula can be used to solve for the two real solutions of any quadratic equation. It works by determining the discriminant, which is the number under the square root in the equation. The discriminant is calculated by subtracting 4ac from b². The ± symbol indicates that there are two solutions, one with the plus sign and one with the minus sign.
For example, if we have a quadratic equation 2x²+5x-3=0, the discriminant can be calculated as follows:
b² - 4ac = (5)² - 4(2)(-3) = 25 + 24 = 49
The two solutions can then be found using the formula:
x = (-5 ± √49)/(2(2))
x = (-5 ± 7)/(4)
x = -2 or 3/2
Therefore, the two real solutions to this quadratic equation are -2 and 3/2.
Learn more about quadratic equation here:
https://brainly.com/question/30098550
#SPJ4
Complete question:
Which of the following methods can be used in solving quadratic equation of the form ax²+bx+c=0?
A) Factoring
B) Completing the Square
C) Quadratic Formula
D) Graphing
−2=
\,\,\frac{t}{-3}
−3
t
The value of the unknown variable {t} is equal to 3/4.
What are functions?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.The set X is called the domain of the function and the set Y is called the codomain of the function.Functions whose domain are the non - negative integers, known as sequences, are often defined by recurrence relations.Given a function as [tex]${\displaystyle f\colon X\to Y}[/tex] its graph is, formally, the set -[tex]${\displaystyle G=\{(x,f(x))\mid x\in X\}.}[/tex]
Given is the equation as -
- 2 = (t/3) - 3t
The given equation is -
- 2 = (t/3) - 3t
Solving further , we get -
(t/3) - 3t = - 2
t/3 - 3t = - 2
t(1/3 - 3) = - 2
t(1 - 9)/3 = - 2
-8t/3 = -2
t = 2 x 3/8
t = 3/4
Therefore, the value of the unknown variable {t} is equal to 3/4.
To solve more questions on algebraic functions, visit the link below -
brainly.com/question/1041084
#SPJ1
what is the perimeter of a shape with the dimensions 3cm 2 cm 3cm 1cm
Answer: 9cm
Step-by-step explanation:
A rectangular window has a length of 12 ft and a width of x ft. Which expression represents the area of the window?
Answer: 12x ft
Step-by-step explanation:
12 times x
. .
ω
2. The area of a circle of radius 1 is π units squared. Use scaling to explain
why the area of a circle of radius r is πr^2units squared.
The area of the circle equation is shown below
How to prove the area of the circle equationFrom the question, we have the following parameters that can be used in our computation:
Area of radius 1 = π
The area of a circle is proportional to the square of its radius.
When the radius is multiplied by a scale factor of "r," the area is multiplied by the square of that factor: r^2.
So, the area of a circle of radius "r" is given by π * r^2 square units.
Read more about circle at
https://brainly.com/question/12823137
#SPJ1
What are the 3 different types of solutions for the quadratic formula?
3 different types of solutions for the quadratic formula are :
1. Factoring
2. Quadratic Formula
3. Completing the square
Quadratic formula/equation has a common formula
f(x) = a[tex]x^{2}[/tex] + bx + c
Where :
a is the coefficient of [tex]x^{2}[/tex]
b is the coefficient of x
c is the constant term
To solve that equation, we can use 3 solutions.
1. Factoring
This solution uses the factor of number and leaves 0 at the right side.
Common formula is ( x + a )( x + b ) = 0
Example :
[tex]x^{2}[/tex] + 6x + 8 = 0
(x + 4)(x + 2) = 0
x = -4 or x = -2
2. Quadratic Formula
The quadratic formula is
x = [tex]\frac{-b +- \sqrt[]{b^{2}-4ac } }{2a}[/tex]
Example :
[tex]x^{2}[/tex] + 6x + 8 = 0
x = [tex]\frac{-6 +- \sqrt{6^{2} -4(1)(8)} }{2(1)}[/tex]
x = [tex]\frac{-6 +- \sqrt{4} }{2}[/tex]
x = [tex]\frac{-6+2}{2}[/tex] or x = [tex]\frac{-6-2}{2}[/tex]
x = -2 or x = -4
3. Completing the square
Example :
[tex]x^{2}[/tex] - 6x + 5 = 0
[tex]x^{2}[/tex] - 6x = -5
because a = -1, add [tex](\frac{-6}{2}) ^{2}[/tex] or 9
[tex]x^{2}[/tex] - 6x + 9 = -5 + 9
[tex]x^{2}[/tex] - 6x + 9 = 4
[tex](x - 3 )^{2}[/tex] = 4
x-3 = ± 2
x -3 = 2 or x - 3 = -2
x = 5 or x = 1
Learn more about quadratic equation here
https://brainly.com/question/30098550
#SPJ4