The constant of proportionality (K ) we will write
Perimeter = 3 ( side) where K = 3
Perimeter of any polygon is defined as the sum of all sides of polygon.
Given polygon is a triangle. A triangle is any polygon which has three sides.
And as the sides of a polygon increases the perimeter also increases.
One can say that perimeter and side of a polygon has a direct relationship.
That is when we write it mathematically we write it like:
Perimeter ( P ) ∝ Sides of polygon
However given is an equilateral triangle
this means that all sides of the triangle are equal
so let us consider the side of the triangle as "s"
Thus we get that perimeter will be 3 times s
which when mathematically written will be:
Perimeter ∝ ( side)
to remove the constant of proportionality (K ) we will write
Perimeter = 3 ( side) where K = 3
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If you have a garden that is 5m x 8m and there are 120 pepper plants, what is the population density of the pepper plants?
Three pepper plants are present per population density.
How do you calculate population density?You must divide the population by the area's size to determine the population density. Population Density is therefore equal to the number of people divided by the land area.
Since we are working with plants here, the formula is as follows:
Population Density = Plants Per Unit Area
Given,
There are 120 plants.
Area of Land = 5 x 8
= 40 m^2
Just enter the values into the formula now.
Number of People = 120/40
= 3
Consequently, the number of pepper plants per square foot is 3.
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Simply the expression below.
10-8.3
If you solve an equation by graphing each side as a separate line, which of the following corresponds to the solution of the equation? a. there is only a solution if the lines are identical c. the y–coordinate of the intersection point b. both the x–coordinate and the y–coordinate of the intersection point d. the x–coordinate of the intersection point Please select the best answer from the choices provided A B C D
Answer:
d. the x–coordinate of the intersection point
Step-by-step explanation:
The solution of the system with two lines is the x-coordinate of their intersection point.
a. there is only a solution if the lines are identical
No, it gives infinitely many solutions.b. both the x–coordinate and the y–coordinate of the intersection point,
No, only the x-coordinate is consideredc. the y–coordinate of the intersection point
No, only the x-coordinate is consideredd. the x–coordinate of the intersection point
Yes, correctconsider the population p of deer in salt lake county as a function of time t, where t is the number of years after 1990. what values are in the range of this function?
The range of the function is for the population of the deer in the salt lake if found as [P, ∞).
What is defined as the range of the function?A function's range is the set of outputs it produces when applied to its entire set of outputs. The range is the collection of objects that actually come from the machine when individuals feed it all the inputs with in function machine metaphor.The number of deer is proportional to t, the number of years since 1990.
As a result, time t becomes the independent variable as well as the number of deer becomes the dependent variable; the number of deer DEPENDS upon the year.
A function's range is the set of values that the dependent variable can take.
The values in the range in this example represent the number of deer throughout salt lake in specific years.
Let 'P' be the population of the deer in salt lake.
Range: [P, ∞)
Then, the range of the function is for the population of the deer in the salt lake if found as [P, ∞).
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Using a map, Sasha measures the distance between the city in which she lives and her vacation destination to be 450 miles. She assumes that she may be off by 30 miles in her estimation.
What equation can Sasha use to determine the minimum and maximum distance her city is from her vacation destination?
Drag numbers or symbols to the boxes to correctly complete the equation.
The equation that Sasha can use to determine the minimum and maximum distance her city is from her vacation destination is 450 + 30 and 450 - 30.
What is an equation?It should be noted that an equation is simply used to illustrate the relationship between the variables that are illustrated or given in the data.
It should be noted that for the minimum distance, she has to subtract 30 miles from the vacation destination.
The minimum value will be:
= 450 - 30
= 420. miles.
For the maximum distance, she has to add 30 miles from the vacation destination.
The maximum distance will be:
= 450 + 30
= 480 miles.
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Valeria is a physical therapist who specializes in pediatric leg injuries. Her patients differ in age and type of injury. Knee pain Ankle pain
0-12 years old 1 4
13-19 years old 4 3
What is the probability that a randomly selected patient is 0-12 years old given that the patient suffers from ankle pain?
The probability that a randomly selected patient is 0-12 years old given that the patient suffers from ankle pain is 4/7.
What is the probability?
Probability is used to determine the likelihood that a random event would happen. The odds that the random event happens has a probability value that lies between 0 and 1. The more likely it is that the event would occur, the closer to one, the probability value would be.
The probability that a randomly selected patient is 0-12 years old given that the patient suffers from ankle pain = number of 0 - 12 that suffer from ankle pain / total number of people that suffer from ankle pain
= 4 / (4 + 3) = 4 / 7
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the difference of the product of 4 times a number and 2/3 is 34 / 3
Answer: x=3
Step-by-step explanation:
[tex]\displaystyle\\4x-\frac{2}{3}=\frac{34}{3}\\[/tex]
Multiply both parts of the equation by 3:
[tex]4x(3)-2=34\\12x-2=34\\12x-2+2=34+2\\12x=36[/tex]
Divide both parts of the equation by 12:
[tex]x=3[/tex]
The unknown number from the equation is 3.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, the difference of the product of 4 times a number and 2/3 is 34/3.
Let the unknown number be x.
4x-2/3 =34/3
(12x-2)/3=34/3
12x-2=34
12x=36
x=3
Therefore, the unknown number is 3.
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Write an equation of the line passing through point P(0, 0) that is perpendicular to the line y=-9x-1.
Graph the equations of the lines to check that they are perpendicular.
Answer: [tex]y=\frac{1}{9}x[/tex]
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes, so the slope of the line we want to find is 1/9.
Since the y-intercept is 0, the equation is [tex]y=\frac{1}{9}x[/tex].
You can graph the lines on a website like Desmos.
Acoording to the school survery, 20% of the students at rockwood junior high school speak spanish. There are 25 students at the school who speak spanish. How many students were surveyed?
The percentage is that indicating the hundredth total number of students surveyed such that 20% of them are 25 will be 125.
What is the percentage?
The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
Let's suppose the total number of students that are surveyed was x.
It is known that x% of y is given as, (x/100)y.
Therefore,20% of x is (20/100)x = 0.2x
The 20% of the total students is 25.
So, 0.2x = 25
x = 25/0.2 = 125
Hence "The percentage is that indicating the hundredth total number of students surveyed such that 20% of them are 25 will be 125".
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you are choosing between two different cell phone plans. the first plan charges a rate of 23 cents per minute. the second plan charges a monthly fee of $34.95 plus 10 cents per minute.
You will need to use at least 267 minutes in a month in order for the second plan to be preferable.
Given the following:
First plan=23 cent per minute
Second plan=$34.95 plus 10 cents per minute
Calculate the number of mins to use in a month to make second plan preferable:
We first change $34.95 to cents:
1 usd=100 cents
$34.95=($34.95*100 cents)/$1
=3495 cents
Second plan will now be 3495 plus 10 cents per minute
Now, calculate the number of mins to use:
Let x represents the number of mins, now 23 cent per minute will be:
23(x)>3495 plus 10 cents per minute
23x>3495+10x
23x-10x>3495
13x=3495
x=3495/13
x>268.85 mins
Therefore, one will need to use at least 267 minutes in a month in order for the second plan to be preferable.
The question is incomplete, complete question is given below:
You are choosing between two different cell phone plans. The first plan charges a rate of 23 cents per minute. The second plan charges a monthly fee of $34.95 plus 10 cents per minute. How many minutes would you have to use in a month in order for the second plan to be preferable?
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Two equations are written to express how far a car can go when driving on different roads. On Road 1, the car can go 60 miles in 2 hours. On Road 2, the car can go 90 miles in 4 hours. Write an equation where y is the distance in miles and x is the time in hours to represent the motion of the faster car.
Answer:
y=30 x=22.5 =25 = 55
Step-by-step explanation:
Answer:
Step-by-step explanation:
y=30x
Find a quadratic function to model the values in the table.
The quadratic function to model the values in the table will be,
y = 3x² + 3x - 3
Option 1 is true.
What is Quadratic equation?
An algebraic equation of the second degree in x is called Quadratic equation.
Given that;
The values of x and y are,
x = -1, 0, 3
y = -3, -3, 33
Let a quadratic function is,
y = ax² + bx + c ... (i)
Then, It satisfy all the values given in table.
So, Substitute point (x, y) = (-1, -3) in equation (i) we get;
- 3 = a - b + c ... (ii)
And, Substitute point (x, y) = (0, -3) in equation (i) we get;
-3 = c .. (iii)
And, Substitute point (x, y) = (3, 33) in equation (i) we get;
33 = 9a + 3b + c ... (iv)
Now, Substitute c = -3 from (iii) in equations (ii) and (iv) we get;
From (ii);
- 3 = a - b - 3
a - b = 0 ... (v)
From (iv);
33 = 9a + 3b - 3
Divide by 3;
11 = 3a + b - 1
3a + b = 12 .... (vi)
Solve equations (v) nd (vi) we get;
a = 3 and b = 3
Thus, Substitute the values a = 3, b = 3 and c = -3 in quadratic equation we get;
y = ax² + bx + c
y = 3x² + 3x - 3
So, The quadratic function to model the values in the table will be,
y = 3x² + 3x - 3
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A small business that makes candles uses a proportional amount of essential oil and wax. For 208 ounces of wax, they use 8 ounces of essential oil.
How many ounces of essential oil is needed for 728 ounces of wax?
12.5 ounces
28 ounces
42 ounces
91 ounces
Answer:
B, 28.
Step-by-step explanation:
728 divided by 208, which is 3.5. then you multiply 3.5 & 8 to get 28.
The answer above me has the answer.
Step-by-step explanation: He is 101% confident its it and I back it up because got it right (he should've been 102% confident tho)
Charmaine has b decks of cards. Each deck has 52 cards in it. Using b, write an expression for the total number of cards Charmaine has
Answer:
Step-by-step explanation:
52 + b = 52b or 52(b = 52b ( means x
Vincent earned 24$ for 3 hours worked. Later he earned 72$ for 9 hours of work. How much money does he earn per hour
in her garden pam plants the seed 2 1/4 in below the ground. After one month the tomato plant has grown a total of 10 1/2 in. How many inches is the plant above the ground.?
The plant is 8 inches above the ground
How to calculate the height of the plant above the ground ?The height of the seed below the ground is 2 1/4
9/4
After one month, the tomatoes has grown 10 1/2
10 1/2
= 21/2
The height of the plant above the ground is
21/2 - 9/4
= 8
Hence the height of the plant above the ground is 8 inches
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Juanita used the steps shown below to correctly solve an equation. A step is missing.
-3(c-6) + 4c = 5(2c + 9)
?
c+ 18 = 10c +45
c-27 = 10 c
-27= 9c
-3 = c
O-3c-6 + 4c = 10c + 9; associative property of addition
O-3c+ 18+ 4c = 10c + 45; associative property of addition
O-3c-6 + 4c = 10c + 9; distributive property
O-3c + 18+ 4c = 10c +45; distributive property
Answer: Option (D) property of distribution
Step-by-step explanation:
got it right on test
Help please !! due at 8pm tonight
Answer:
y=-3x+7
Step-by-step explanation:
:]
Answer:
Y=-3x+7
Step-by-step explanation:
Use rise/run
If m/FEG is 3x - 11 and m/CBH is x + 27, what is the value of x?
Answer:
x= 19
Step-by-step explanation:
I believe you would put both expressions equal to each other. So,
3x-11= x+27
3x-x=27+11
2x=38
x= 38/2
x=19
Let f(x) = (6x³ - 7)³ and g(x) = 6x³ - 7.
Given that f(x) = (h° g)(x), find h(x).
0080
Clear all
Enter the correct answer.
+?
DONE
When the result of one function is utilized as the input for another, this is known as a composite function. If f(x) = (6x³ - 7)³ and g(x) = 6x³ - 7 then the value of h(x) = x³.
What is meant by composition functions?A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function exists essentially applied to the output of another function.
Function composition is an operation used in mathematics that takes two functions, f and g, and creates a function, h = g ° f, such that h(x) = g. The function g is applied in this operation on the outcome of applying the function f to x.
Let the two functions be f(x) = (6x³ - 7)³ and g(x) = 6x³ - 7.
f(x) = (h° g)(x)
⇒ f(x) = (h(g(x))
If f(x) = (h° g)(x) (6x³ - 7)³ = (h(g(x)) then h(x) = x³.
The complete question is:
Let f(x) = (6x³ - 7)³ and g(x) = 6x³ - 7. Given that f(x) = (h° g)(x), find h(x).
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Answer:
h(x) = x³
Step-by-step explanation:
Given:
[tex]f(x)=(6x^3-7)^3[/tex]
[tex]g(x)=6x^3-7[/tex]
[tex]f(x)=(h \circ g)(x)[/tex]
The relationship between f(x) and g(x) is that function f is function g cubed:
[tex]f(x)=(g(x))^3[/tex]
(h o g)(x) means we replace the x-variable of function h(x) with function g(x). So:
[tex](h \circ g)(x)=h(g(x))[/tex]
If (h o g)(x) equals f(x), then h(x) must be h(x) = x³.
Check by replacing the x-variable of function h(x) with the function g(x) and comparing it to f(x):
[tex]\begin{aligned}(h \circ g)(x)&=h(g(x))\\&=(g(x))^3\\&=(6x^3-7)^3\\&=f(x)\end{aligned}[/tex]
Hence proving that h(x) = x³.
Kim buys 6 pounds of apples.
What is the weight of the apples in kilograms?
Round to the nearest tenth, if necessary.
Answer: 2.7 kg
1 kilogram (kg) = 2.204623 pounds (lb)
[tex]\frac{6 lb}{1}[/tex] × [tex]\frac{1 kg }{2.204623 lb}[/tex] = 2.721553753 kg
You place 1 kg over 2.204623 lb since they are equal. In the above equation, the pounds (lb) cancel out since one is in the numerator (the number on top of the fraction) and one is in the denominator (the number on the bottom of the fraction). You multiply 6 by the 1 in the numerator and multiply the 1 in the denominator by 2.204623. This turns the equation into:
[tex]\frac{6 kg}{2.204623}[/tex] =2.721553753 kg
You divide 6 by 2.204623 to get 2.721553753
To round to the tenths place, you include only the first number to the right of the decimal, which is 7. Since the number to the right of the 7 is less than five, it stays 7. If it were five or bigger, 7 would turn into 8.
The answer: 2.7 kg
50 POINTS
Does the point (1, 3) fall on the graph of the line that goes through (-2, 8) and (3, -1)? Show me how you know without graphing. Show your work algebraically (That is, don't draw me a graph... show me using numbers, variables, and/or symbols).
can someone explain please :)
Step-by-step explanation:
1.First work out the equation of the line.
1.1 work out gradient
[tex]y = ( \frac{ - 1 - 8}{3 - ( - 2)} )x + c[/tex]
[tex]y = - \frac{9}{5} x + c[/tex]
1.2 substitute in x and y value of one of the two given point. ill use (3;-1).
[tex] - 1 = - \frac{9}{5} (3) + c[/tex]
[tex]c = \frac{22}{5} [/tex]
therefore equation is
[tex]y = - \frac{9}{5} x + \frac{22}{5} [/tex]
2. Now sub in x value of the point you want to test and see if y value correlates.
[tex]y = - \frac{9}{5} (1) + \frac{22}{5} [/tex]
[tex]y = \frac{13}{5} [/tex]
3. We can conclude that point (3;1) does not fall on the graph
109% as a mixed or whole number
Answer:
1 9/100Step-by-step explanation:
In order to convert 109/100 to mixed number, you follow these steps :
Divide the numerator by the denominator
109 ÷ 100 = 1 with a remainder of 9
Write down the whole number 1 and then write down the remainder as new numerator (9) above the denominator (100), As below :
1
9
100
Answer:
109/100 or 1.09
Do number 6 please thank you!
PLEASE HELP I HAVE 3 MINUTES, THANK YOU!!
Answer:
-4 + -10
Step-by-step explanation:
Even with an addition sign, it still adds up to the same amount.
Hope this helps!
(Btw, if u get this right, pls do brainliest, I really need it! Thanks!)
The function 1500x+y=35000 represents the altitude in feet, y, of a passenger airplane after x minutes of its descent.
PART A: Which graph represents the passenger airplane’s altitude?
By identifying the y and x-intercepts of the linear equation, we conclude that the correct graph is the third one
Which graph represents the altitude?We know that the relation between altitude and time is given by the linear equation:
1,500x + y = 35,000
If we isolate y, we get:
y = -1,500x + 35,000
Notice that when x = 0, we have:
y = -1,500*0 + 35,000
y = 35,000
So the y-intercept is 35,000
And the plane reaches the ground when:
0 = -1,500*x + 35,000
1,500*x = 35,000
x = 35,000/1,500 = 23.3
So it intercepts the x-axis at x = 23.3
With that in mind, we can see that the correct graph is the third one.
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6. Match each polynomial function with its leading coefficient.
A. P(x) = (x + 2)(2x - 3)(4x + 7)
B. P(x) =
(x-2)(2x - 3)(4x + 7)
C. P(x) = 5(x-2)(2x - 3)(4x + 7)
D. P(x) = -(x-2)(2x - 3)(4x + 7)
E. P(x) = (x + 2)(2x - 3)(4x + 7)
(From Unit 2, Lesson 6.)
1.40
2.8
3.4
4.2
5.-8
The perfect match leading coefficient for the given polynomial will be as below:-
A. P(x) = (x + 2)(2x - 3)(4x + 7) => 2. 8
B. P(x) = (x-2)(2x - 3)(4x + 7) => 3. 4
C. P(x) = 5(x-2)(2x - 3)(4x + 7) => 1. 40
D. P(x) = -(x-2)(2x - 3)(4x + 7) => 5. - 8
E. P(x) = (x + 2)(2x - 3)(4x + 7) => 4. 2
Leading Coefficient:
The leading coefficient of the polynomial is means the coefficient of the variable having the highest power in the polynomial.
Given,
Here we have the following list of polynomials,
A. P(x) = (x + 2)(2x - 3)(4x + 7)
B. P(x) = (x-2)(2x - 3)(4x + 7)
C. P(x) = 5(x-2)(2x - 3)(4x + 7)
D. P(x) = -(x-2)(2x - 3)(4x + 7)
E. P(x) = (x + 2)(2x - 3)(4x + 7)
Now, we need to find the matching leading coefficients for this polynomials.
In the given polynomials, we have to calculate the highest power variable in each polynomial with the coefficient. That coefficient is known as the leading coefficients.
First, we have to take the expression A, then we get,
A. P(x) = (x + 2) (2x - 3) (4x +7)
Here we have to multiply the x term alone to get the leading coefficient,
P(x) = (x)(2x) (4x)
Thus will results the leading coefficient as P(x) = 8x³
Similarly, for expression B,
P(x) = 1/2(x - 2) (2x - 3) (4x + 7)
P(x) = 1/2(x) (2x)(4x)
P(x) = 1/2 8x³
P(x) = 4x³
For expression C,
P(x)= 5(x - 2) (2x - 3) (4x + 7):
P(x) = 5(x)(2x)(4x)
P(x)= 40x³
For expression D,
P(x) = -(x - 2) (2x - 3) (4x + 7):
P(x) = -(x)(2x)(4x)
P(x) = -8x³
Finally, for the expression E,
P(x) = 1/4(X + 2) (2x - 3) (4x + 7):
P(x) = 1/4(x)(2x(4x)
P(x) = 2x³
Therefore, the corresponding leading coefficients are 8, 4, 40, -8, and 2 respectively.
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how to solve a problem like this? (the bottom problem)
A parking garage in the city charges $2.75 for the first hour and $1.25 for each additional hour, x. Write and solve an inequality to find the maximum time of additional hours that Tony can park his car at the garage if he wants to pay less than $8. and i have another question
.The inequality is given by:
[tex]2.75+1.25t<8[/tex]Subtract 2.75 from both sides of the inequality:
[tex]\begin{gathered} 2.75-2.75+1.25t\lt8-2.75 \\ 1.25t\lt5.25 \\ \text{ Divide both sides by }1.25 \\ \frac{1.25t}{1.25}\lt\frac{5.25}{1.25} \\ t\lt4.2 \end{gathered}[/tex]Therefore, the maximum time of additional hour is 4
Answer:
4 hours
Step-by-step explanation:
→ Write inequality
2.75 + 1.25x < 8
→ Minus 2.75 from both sides
1.25x < 5.25
→ Divide both sides by 1.25
x < 4
Select the correct answer. dudley is biking. he wants to cover 40 miles. if he travels 30 miles every 2 hours, what is the equation of a line that models y, the number of miles he has left to travel, after biking x hours? a. y = -15x â€" 40 b. y = -30x 40 c. y = -15x 40 d. y = 30x â€" 40
The equation will be y = -15x + 40
Equations help us to understand a particular problem better, they give us possible insights into the situation. Equation Formation is an important aspect of Mathematics. We can form equations on the basis of the information given and then analyze it.
Given:
The biker, Dudley wants to travel 40 miles.
It is given that he travels 30 miles every 2 hours.
Obtaining Equation,
Distance traveled in 2 hours = 30 miles
Then, distance traveled in x hours = [tex]\frac{30}{2}*x = 15x[/tex]
So, the remaining distance to cover = 40 - 15x
or y = 15x - 40
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