Based on the information, it can be inferred that Gustave gives 2,100 steps for every mile he walks.
How to calculate the number of steps Gustave takes in a mile?To calculate the number of steps Gustave takes in a mile, we must take into account the information available about the ratio of steps to the distance he covers. In this case, we know that for every 3 miles, Gustave takes 6,300 steps.
To find how many steps he takes in a mile we must divide the number of steps into the number of miles he walked as shown below:
6,300 / 3 = 2,100According to the above, Gustave takes 2,100 steps for every mile he walks.
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Find the length of the segment indicated.
Answer:
11.281
Step-by-step explanation:
For this question, since we see a right angle triangle, we know that we can use Pythagoras' Theorem to solve for this question.
By Pythagoras' Theorem,
[tex] {c}^{2} = {a}^{2} + {b}^{2} \\ {x}^{2} = {4.6}^{2} + {10.3}^{2} \\ \\ {x}^{2} = 127.25 \\ x = \sqrt{127.25} \\ = 11.281 \: or \: \frac{ \sqrt{509} }{2} [/tex]
please help me, 20 points
The area of the shaded region is 502.4 ft^2
The area of a circle is the space occupied by a circle in a two-dimensional plane. Alternatively, the space taken up inside the boundary/circumference of a circle is called the area of the circle. The formula for the area of a circle is A = πr2, where r is the radius of the circle. The unit of area is the square unit, such as m2, cm2, in2, etc. Area of a circle = πr2 or πd2/4 in square units, where (Pi) π = 22/7 or 3.14. Pi (π) is the ratio of the circumference to the diameter of any circle. It is a special mathematical constant.
It is given that inner diameter is 36 ft and width of the ring is 4 ft
We need to find the area of the shaded region
diameter of outer ring= d1=36+4+4 = 44 ft ,
diameter of inner ring= d2=36 ft,
r1=d1/2= 44/2 = 22 ft , r2=d2/2 = 36/2 = 18 ft
Area of shaded region = Area of Outer circle - Area of inner circle
= π r1^2 - π r2^2
= π ( 22^2 - 18^2 )
= 3.14 * 160
= 502.4 ft^2
Hence the area of the shaded region is 502.4 ft^2
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The area of the shaded region is 502.4 sq. ft.
An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The word "area" refers to a free space.
According to the question,
Diameter of inner circle = 36 ft.
Radius of inner circle = 36/2 ft. =18 ft.
As the width of the ring is 4 ft. , the diameter of the outer circle = 36+4+4= 44 ft.
Radius of outer circle = 22 ft.
Area of the shaded region = Area of outer circle - Area of inner circle
= π(22)(22) - π(18)(18)
= π(484 - 324)
= 3.14 * 160
= 502.4 sq. ft.
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David drives from his home to the airport to catch a flight. He drives 35 miles in the first hour, but realizes that he will be 1 hour late if he continues at this speed. He increases his speed by 15 miles per hour for the rest of the way to the airport and arrives 30 minutes early. How many miles is the airport from his home
The distance between David's home and the airport is 210 miles.
Distance traveled after 1 hour
let the distance traveled after first 1 hour = y
distance/speed = time
after 1 hour his speed = (35 + 15) = 50 mph
total time after 1 hour and 30 mins = 1.5 hr
y/50 + 1.5 = y/35
multiply through by350
7y + 525 = 10y
3y = 525
y = 525/3
y = 175 miles
In the first 1 hour, at 35 mph, distance covered = 35 miles
Distance from his home to airport = 175 miles + 35 miles = 210 miles
Thus, the distance between David's home and the airport is 210 miles.
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PLEASE HELP! Solve each of the following by using the general quadratic formula.
Using the quadratic formula, the solutions are:
a) [tex]x = \frac{3 \pm \sqrt{41}}{4}[/tex]
b) [tex]x = 1 \pm 2i[/tex]
What is a quadratic function?A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]
In which:
[tex]\Delta = b^2 - 4ac[/tex]
Item a:
The coefficients are a = 2, b = -3, c = -4, hence:
[tex]\Delta = (-3)^2 - 4(2)(-4) = 41[/tex][tex]x_1 = \frac{3 + \sqrt{41}}{4}[/tex][tex]x_2 = \frac{3 - \sqrt{41}}{4}[/tex]Item b:
The coefficients are a = 1, b = 2, c = 2, hence:
[tex]\Delta = (2)^2 - 4(1)(2) = -4[/tex][tex]x_1 = \frac{2 + \sqrt{-4}}{2} = 1 + 2i[/tex][tex]x_2 = \frac{2 - \sqrt{-4}}{2} = 1 - 2i[/tex]More can be learned about quadratic equations at https://brainly.com/question/24737967
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3x-2y=10 find the y intercept and the x intercept
Answer:
(0, -5) (10/3, 0)
Step-by-step explanation:
First, convert the given equation into the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
3x - 2y = 10
2y = 3x - 10
y = 3/2x - 5
The y-intercept is -5.
Next, to find the x-intercept, let y = 0 and solve for x. X-intercept is the point where the graph intersects the x-axis, so the y-coordinate of x-intercepts are always 0.
3x - 2*0 = 10
3x - 0 = 10
3x = 10
x = 10/3
X-INTERCEPT
Plug y=0 into the equation and solve the resulting equation 3x=10 for x.
The x-intercept:
[tex]\left(\frac{10}{3},0\right)\approx \left(3.33333333333333,0\right)[/tex]
Y-INTERCEPT
Plug x=0 into the equation and solve the resulting equation −2y=10 for y.
The y-intercept:
[tex]\left(0, -5\right)[/tex]
A teacher has 14 senior students, 7 junior students, 4 sophmore, 5 freshmen, what is the proabability that she chooses a senior?
Answer:
7/15
Step-by-step explanation:
To find the probability the student is a senior
P( senior) = number of seniors / total students
= 14 / ( 14+7+4+5)
= 14/30
= 7/15
Answer:
14/30 or 7/15
Step-by-step explanation:
probability = no. of senior students / total no. of students
probability = 14 / (14+7+4+5)
probability = 14/30
This can be simplified to 7/15.
Hope this helps!
Which of these is a zero of the polynomials p(y) = 3y^3 - 16 y - 8? * - 8 0 2 - 2
The zero of polynomials is -2. The polynomials is p(y) = [tex]3y^{3} - 16 y - 8[/tex].
According to the question,
The polynomials is p(y) = [tex]3y^{3} - 16 y - 8[/tex]. In order to find the zero of polynomials only if we substitute the value and polynomials become zero.
p(-2) = [tex]3(-2)^{3} - 16 (-2) - 8[/tex]
= 3(8) + 32 -8
= 0
Hence, the zero of polynomials is -2. The polynomials is p(y) = [tex]3y^{3} - 16 y - 8[/tex].
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the graph below could be the graph of which exponential function?
The graph above could be a graph of this exponential function: A. F(x) = 3.(1.2)^x.
How to interpret the graph?Mathematically, the standard form of an exponential function is given by:
F(x) = ab^x
Where:
a is the initial value of an exponential function.b is the growth rate.As a general rule, f(x) is an increasing function when b is greater than 1 (b > 1) and f(x) is a decreasing function when b is less than 1 (b < 1)
By critically observing the given graph, we can deduce that the initial value (a) is 3 and it's an increasing function (b > 1).
F(x) = 3.(1.2)^x
Thus, the graph above could be a graph of this exponential function F(x) = 3.(1.2)^x.
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You select one red marble from the full bag in exercise 20. what is the probability that the next marble you select will be green without replacement of the first marble?
P(blue) = 1/3
Step-by-step explanation:
Probability for any event A is given by
p(A) = no of times of happening of event A/ total no of occurrence of all the events given under the situation.
A bag contains 5 blue marbles, 6 red marbles, and 4 green marbles
So, total no of occurrences of all the events given under the situation
one can either pick blue, red, or 4 green marbles
Total no. of occurrence of all the event = 5 + 6 + 4 = 15
Now, no occurrence of selecting blue.
since there are 5 blue marbles, there is a chance of selecting blue as 5.
no occurrence of selecting blue = 5
Therefore,
P(blue) = no of occurrence of selecting blue /total no of occurrence of picking any color ball
P(blue) = 5/15 = 1/3.
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Jamie and owen joined a monthly walking challenge at their youth center. jamie has already walked 120 minutes and plans to walk 20 minutes per day. owen plans to walk 30 minutes per day. let x represent the number of days and y represent the total number of minutes walked during the challenge. which system of equations can be used to find the number of days it will take for owen and jamie to have walked the same number of minutes? a system of equations. y equals 20 x plus 120. y equals 30 x. a system of equations. y equals 20 x. y equals 30 x plus 120. a system of equations. y equals 120 x plus 20. y equals 30 x. a system of equations. y equals 120 x. y equals 30 x plus 20.
Answer:
The system of equation y=120+20x and y=30x
Step-by-step explanation:
Let the number of days be x and y be the total number minutes
Jamie has walked 120 mins. She will walk at a rate of 20 mins per day.
y=120+20x
Owen walks 30 mins a day. So
y = 30x
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Determine whether the triangles can be proved similar. If they are similar, write a similarity statement. If they are not similar, explain why.
a baby's t-shirt requires 4/5 feet of fabric. How many t-shirts can be made out of 56 feet of fabric
The complete question:
A baby's t-shirt requires 4/5 yards of fabric. How many t-shirts can be made from 48 yards? A book is on sale at a 30% discount. If the sales price is $28, what was the original price?
Charles is going to buy 3 computer tables for $390. If he pays the same rate, how much would it cost for 8 computer tables?
If your cell phone bill was $67.82 and you were charged a 7.5% late fee, how much will your total bill be?
Mrs. Margulis paid $125 to have her hair colored and cut. If she tips her hairdresser 15%, what is her total bill?
Macy's is having a one-day 35% off special. If Sara bought $124.50 worth of items, what would the final bill total be after applying the discount of 35%?
Sara's total bill exists the cost of the items bought smaller the amount of the 35% is $143.75.
what would the final bill total be after applying the discount of 35%?
The number of t-shirts that can be created from 48 yards exists at 60 yards.
The original price of the book exists $40.
The cost of 8 computer tables exists $1040.
My total bill would be $72.91.
Mrs. Margulis's total bill is $143.75
My total bill after involving the discount of 35% would be $80.93.
If one t-shirt requires 4/5 yards. The number of t-shirts that can be created with 48 yards can be specified by dividing 48 yards by 4/5 yards
48 yards ÷ 4/5 yards
48 x 5 / 4 = 60 shirts
The cost of the book existed decreased by 30%. This indicates that the sales price exists 70%(100 - 30%) of the original price.
Let p denote the original price. This equation can be utilized to describe the information in the question:
70% [tex]*[/tex] p = $28
0.7p = $28
p = $28 / 0.7
p = $40
To define the cost of 8 computer tables, the cost of one computer table contains to be decided first.
Cost of one computer table = cost of three tables / 3
$390 / 3 = $130
The cost of 8 computer tables = Cost of one computer table [tex]*[/tex] 8
$130 x 8 = $1040
The total bill exists as the sum of the cell phone bill and the late phone charge
$67.82 + ( 7.5% [tex]*[/tex] $67.82)
$67.82 + (0.075 [tex]*[/tex] $67.82 )
$67.82 + 5.09
= $72.91
Mrs. Margulis's total bill exists the sum of the amount she paid and the cost of her tip.
$125 + ( 15% [tex]*[/tex] $125)
$125 + (0.15 [tex]*[/tex] $125)
$125 + $18.75
= $143.75
Sara's total bill exists the cost of the items bought smaller the amount of the 35%
$124.50 - (35% [tex]*[/tex] $124.50)
$124.50 - (0.35 [tex]*[/tex] $124.50)
$124.50 - $43.58
= $80.93
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Kim's softball team was playing in the championship game. When there were 444 innings left, the team was losing by a score of 171717 to 666 runs. In the last 444 innings, her team scored the same number of runs per inning, and the other team did not score any more runs. Kim's team won with the most runs.
Write an inequality to determine the number of runs per inning, ppp, Kim's team could have scored.
Find the minimum whole number of runs per inning Kim's team could have scored.
The inequality to determine the number of runs per inning, p Kim's team could have scored is; 4r + 6 > 17
How to write an Inequality?
Let r represent the number of runs per inning. Thus for 4 innings, we have 4r.
The team already has 6 runs. Now add the additional runs to this to get;
4r + 6
The team wants to score more than the other team, this means they need more than 17 and so the inequality required is;
4r + 6 > 17
Subtract 6 from each side to get;
4r + 6 - 6 > 17 - 6
4r > 11
Divide both sides by 4 to get:
r > 2.75
Approximating to a whole number gives;
r > 3
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Answer:
6+4p> 17
3
Step-by-step explanation:
The sum of a positive number and 56 times its reciprocal is equal to its cube. What is the number?
Answer:
2×sqrt(2) = 2.828427125...
Step-by-step explanation:
x = "a positive number"
x + 56/x = x³
x² + 56 = x⁴
x⁴ - x² - 56 = 0
(x² + 7)(x² - 8) = 0
this is true only for
x² = -7
or
x² = 8
x² = -7 would mean that x is an imaginary number. so, that is not a valid solution here.
x² = 8 means
x = sqrt(8) = sqrt(4×2) = 2×sqrt(2) = 2.828427125...
Can someone help with this problem please.
A sheet of paper, 12 inches by 18 inches, is folded so that 2 opposite corners touch, as shown in the figures below. What is the area, in square inches, of the shaded triangle formed as the result of the overlap. (Please look at the picture!)
The area of the shaded triangle formed as the result of the overlap is = 62.35 inches ²
Calculation of the equilateral triangleAfter folding the rectangle with length of 12 inches and width of 18 inches, an equilateral triangle was formed.
An equilateral triangle is a type of triangle where by all the three sides are equal.
To determine the value of one of the sides, CB or CD is used because the folding didn't affect these sides.
Using the formula for the area of an equilateral triangle,
A = √¾ a²
a= 12 inches
A = √¾ ×12²
A = 62.35 inches ²
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Answer:
Its 78!!!!
Solution:
1/2(12 * 18 - 5 * 12) = 78
Given the following results from a spinner game after spinning 20 times.
What is the experimental probability of landing on red?
The experimental probability of landing on red is 7/20 or 0.35 or 35%
How to determine the experimental probability of landing on red?The complete question is added as an attachment
From the question, we have the following outcomes:
Red = 7
Green = 5
Blue = 5
Yellow = 3
The total number of spins is
Total = Red + Green + Blue + Yellow
This gives
Total = 7 + 5 + 5 + 3
Evaluate the sum
Total = 20
The experimental probability of landing on red is the calculated as:
P(Red) = Red/Total
Substitute the known values in the above equation
P(Red) = 7/20
Evaluate
P(Red) = 0.35
Express as percentage
P(Red) = 35%
Hence, the experimental probability of landing on red is 7/20 or 0.35 or 35%
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Find the equation of the line described.
5. Perpendicular to y = 3x + 5; passing through the point (-6,-4)
Answer: [tex]y+4=-\frac{1}{3}(x+6)[/tex]
Step-by-step explanation:
The slope of the given line is 3, so the slope of the line we want to find is -1/3.
Substituting into point-slope form, we get the equation of the line to be
[tex]y+4=-\frac{1}{3}(x+6)[/tex].
What is the explicit formula for this sequence?
-9,-3,3,9,15
Answer: A
Step-by-step explanation:
Normally in choice questions, I would choose to substitute the values into the formulas but I think it is better if I explain to you.
In a sequence, if the numbers increase by d each time and the first number in the sequence is [tex]a_{1}[/tex], then the explicit formula is [tex]a_{1}[/tex] + (n - 1)d when n is the order of the number in the sequence, like n = 1 for the first number, n = 2 for the second number and so on. Using this, we get that the answer to this problem is [tex]a_{n}[/tex] = -9 + (n - 1)6 so the answer is A
Are the triangles similar? If so, state the similarity and the postulate or theorem that justifies your answer.
Answer: The triangles are not similar.
Step-by-step explanation:
Two figures are similar simply if they have the same shape, but not necessarily the same size. In a more mathematical sense, similar figures have the same angle measures and proportionate side lengths.
For reference, side lengths are proportionate when the ratios between corresponding/matching sides are the same.
Since we do not have any angles, we will try using the SSS Similarity Theorem, which states that if all three sides of both triangles are in proportion, then the triangles are similar. We will first list all the side lengths and match corresponding ones.
[tex]\triangle ABC \rightarrow 18,20,32\\ \triangle UVT \rightarrow 14,15,24[/tex]
Since we matched corresponding sides, we can now check whether they have the same ratio).
[tex]\frac{18}{14}=\frac{20}{15}=\frac{32}{24}[/tex]
[tex]\frac{9}{7}=\frac{4}{3}=\frac{4}{3}[/tex]
Not all of the side lengths have the same ratio, so these triangles aren't similar. you must multiply 14 by 9/7 to get to 18, but you need to multiply the other two sides by 4/3 to get to their
[tex] \color{red} \sf Solve \: for \: x : \\ \sf \: \: 4x + 2 = -8?[/tex]
Thank uh !
Answer:
[tex]\huge\boxed{\sf x = -2.5}[/tex]
Step-by-step explanation:
Given equation:4x + 2 = -8
Subtract 2 to both sides
4x = -8 - 2
4x = -10
Divide 4 to both sides
x = -10/4
x = -2.5[tex]\rule[225]{225}{2}[/tex]
Answer:
x = -5/2x = -2.5Step-by-step explanation:
4x + 2 = - 8
Subtract 2 from both sides,
4x = - 8 - 2Subtract 2 from - 8 = - 10,
4x= -10Divide both sides by 4,
4x/4 = -10/4x = - 5/ 2 or x = - 2.5____________________
Evaluate each expression for the given values of the variables: 4|a|+8-a, if a =-2
The value of expression is 18.
modulus of functionA modulus function is a function that determines a number or variable's absolute value. A function with absolute values is another name for it. This function's result is always positive. let's suppose if you want to find modulus of -2 then you will get 2 as the answer.
now according to question
4|a|+8-a at a=-2
here a is negative that means modulus will give us positive value.
put a =-2 in the expression and get the answer. modulus of -2 will give us +2
so
=4(2)+8-(-2)
=8+8-(-2)
=8+8+2
=18
hence the answer is 18.
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Problem: A piece of farmland is a watering plot of land in a circular pattern. A sewer line needs to be installed from a new housing project to a processing plant The city does not want the sewer line to cross the farm land. Can a direct line be installed?
● Let 1 unit = 100 feet.
● The entry to the sewer plant is at (2,3)
● The sewage exit from the housing project is at (12,6)
● The sprinkler system extends 200 ft and the center of the land is at (8,3)
Questions: (1) Will the sewer line cross the farmland? If so then at what points?
(2) If the farmer wants to maximize the farming area and does not want to cross the sewer line, what is the longest sprinkler system that could be installed?
The entry and exit points of (2, 3), and (12, 6), and 200 ft. extension of the sprinkler system gives;
(1) The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)
(2) The longest installable sprinkler system is approximately 172.4 feet
How can the points where the line crosses the farmland be found?1. The slope of the sewer line is found as follows;
m = (6 - 3)/(12 - 2) = 3/10 = 0.3The equation of the sewer line can be expressed in point and slope form as follows;
(y - 3) = 0.3×(x - 2)y = 0.3•x - 0.6 + 3
y = 0.3•x + 2.4
The equation of the circumference of the sprinkler can be expressed as follows;
(x - 8)² + (y - 3)² = 2²Therefore;
(x - 8)² + (0.3•x + 2.4 - 3)² = 2²
Solving gives;
x= 6.53, or x = 8.48
y = 0.3×6.53 + 2.4 = 4.36
y = 0.3×8.48 + 2.4 = 4.9
Therefore;
The sewer line crosses the farmland at (6.53, 4.36), and (8.48, 4.9)2. When the farmland does not cross the sewer line, we have;
sewer line is tangent to circumference of farmland
Slope of radial line from center of the land is therefore;
m1 = -1/0.3
Equation of the radial line to the point the sewer line is tangent to the circumference is therefore;
y - 3 = (-1/0.3)×(x - 8)
Which gives;
y = (-1/0.3)×(x - 8) + 3
The x-coordinate is therefore;
0.3•x + 2.4 = (-1/0.3)×(x - 8) + 3
x ≈ 7.5y = 0.3 × 7.5 + 2.4 ≈ 4.65The longest sprinkler system is therefore;
d = √((7.5 - 8)² + (4.65 - 3)²) ≈ 1.724
Which gives;
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A math club is researching a golf tournament fund-raiser. it will cost $1,000 to host the tournament. if it rains, the club will lose the investment. if it is sunny, it is expected that the club will collect $4,500 from the participants. if the chance of rain is 20%, what is the expected value for the tournament?
The expected value of tournament is $2600.
According to the statement
we have given that the tournament will cost $1000 and if it is sunny, it is expected that the club will collect $4,500 from the participants. And we have to find the expected value of a tournament.
So, we know that the
Cost of hosting the tournament : $1,000
If it rains, the club will lose the investment: $ -1,000
If it is sunny, the club will collect $4,500 ;
From all this the profit they will get
profit: 4,500 - 1000 = 3,500
And
There is a chance of 20% then
The club will loss the investment is
-1000*20 = -200
And
Effect on their profit if there is a rain then
3500*80 = 2800
then
The expected value of tournament is 2800-200=2600.
So,The expected value of tournament is $2600.
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Answer:
C
Step-by-step explanation:
on edge
a. Are the area of a square and the length of its side directly proportional quantities. Explain.
b. Are the perimeter and side length of a square directly proportional quantities. Explain.
**Will mark brainliest for the correct answer with explanation**
**Will report wrong answers**
A square is a plane shape that has an equal length of sides. The required answers to the questions are;
i. Yes, the area of a square and its length of sides are directly proportional.
ii. Yes, the perimeter and length of the side of a square are directly proportional.
A square is a plane shape that has an equal length of sides, with four internal right angles. The area of a square can be determined as:
Area = length x length
= [tex](length)^{2}[/tex]
This implies that the value of area of a given square depends on the value of its length. So that the area and length of sides of a square are directly proportional.
If the value of its length increases, then the value of its area increases, viz-a-viz. Then the area and length of the sides of a square are directly proportional.
The perimeter of a square is the sum of the length of its individual sides. Thus, the perimeter of a square can be determined by:
perimeter = 4 x length
Thus the value of the length determines the value of its perimeter. If the length of its sides increases, so is that of the perimeter. Therefore, the length and perimeter of a square are directly proportional.
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A dindercal container close at boat and have a radius 7cm and hight 6cm find total surface area of the container what is the volume of this container
A) The total surface area of the given cylindrical container is 571.76 cm² and B) The volume of the given cylindrical container is 923.62 cm³.
What are the formulae for the total surface and volume of the cylinder?Consider a cylinder with height 'h', and radius 'r'.
The total surface area of the cylinder(TSA) = 2πr (r + h) square units
and
The volume of the cylinder V = πr²h cubic units.
Calculation:It is given that,
A cylindrical container closed on both ends has a radius r = 7 cm and a height h = 6 cm.
So,
TSA = 2πr (r + h)
= 2× π × 7 × (7 + 6)
= 14 × π × 13
= 571.76 cm²
and
Volume = πr²h
= π × 7² × 6
= π × 49 × 6
= 923.62 cm³
Therefore, the total surface area and volume of the cylindrical container are 571.76 cm² and 923.62 cm³ respectively.
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What is the area of the trapezoid below?
Answer:
50 in²
Step-by-step explanation:
→ Find the area of the square
5 × 5 = 25
→ Find the area of the triangle
( 0.5 × 5 × 5 ) = 12.5
→ Double the answer as there is 2 triangles
12.5 × 2 = 25
→ Add the areas together
25 + 25 = 50 in²
What is the slope of line m?
The slope of the line passing through the coordinates 8(0, 0) and (-2 , 1) is -1/2
Slope of a lineThe formula for calculating the slope of a line is expressed as
slope = y2-y1/x2-x1
Given the coordinate points (0, 0) and (-2 , 1), the slope is expressed as:
Slope = 1-0/-2-0
Slope = 1/-2
Slope = -1/2
Hence the slope of the line passing through the coordinates 8(0, 0) and (-2 , 1) is -1/2
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The slope of the line m is - 1 / 2.
How to find the slope of a line?The slope a line can be found as follows:
slope = m = y₂ - y₁ / x₂ - x₁
using (0, 0)(2, -1)
hence,
slope = - 1 - 0 / 2 - 0
slope = - 1 / 2
hence,
slope = - 1 / 2
Therefore, the slope of the line m is - 1 / 2.
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In the diagram below, ABC ~ DEC. What is the value of x?
A. 2
B. 3.5
C. 2.5
D. 3
Answer:
x = 3
Step-by-step explanation:
Please refer to the attached photo. (Apologies for the terrible drawing.)
Since we know triangles ABC and DEC are similar, we can use the ratio method to find x.
[tex] \frac{ec}{bc} = \frac{ed}{ba} \\ \frac{25}{5} = \frac{18 - x}{x} \\ \frac{18 - x}{x} = 5 \\ 18 - x = 5x \\ 18 = 5x + x \\ 6x = 18 \\ x = \frac{18}{6} \\ = 3[/tex]
please help with this
Answer:
a) x = 1, x = -7
b) (-3, -48)
c) x = -3
d) upwards
Step-by-step explanation:
Given quadratic equation:
[tex]y=3(x-1)(x+7)[/tex]
Part (a)Intercept form of a quadratic equation:
[tex]y=a(x-p)(x-q)[/tex]
where:
p and q are the x-interceptsa is some constantComparing the formula with the given equation:
⇒ p = 1
⇒ q = -7
Therefore, the x-intercepts of the given equation are x = 1 and x = -7.
Part (b)The midpoint between the two x-intercepts is the x-coordinate of the vertex.
[tex]\implies \textsf{Midpoint}=\dfrac{x_2+x_1}{2}=\dfrac{1+(-7)}{2}=-3[/tex]
Therefore, the x coordinate of the vertex is -3.
To find the y-coordinate of the vertex, substitute this into the given equation:
[tex]\implies y=3(-3-1)(-3+7)=-48[/tex]
Therefore, the coordinates of the vertex are (-3, -48).
Part (c)The x-coordinate of the vertex is the axis of symmetry.
Therefore, the axis of symmetry is x = -3.
Part (d)If the leading coefficient of a quadratic equation is positive, the parabola opens upwards.
If the leading coefficient of a quadratic equation is negative, the parabola opens downwards.
From inspection of the given equation, the leading coefficient is 3.
Therefore, the parabola opens upwards.
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the height of a can of coke is 11cm and the radius is 6 cm. the manufacturer of coke want to double the volume of the can but keep the radius as it is , calculate the height of the can?
Answer:
22 cm.
Step-by-step explanation:
Volume = πr^2 h = π 6^2 * 11
So to double the volume
Height will be 2*11 = 22 cm.