An equilateral triangle has a height of 10 feet. How long is one of its sides? (Note: In an equilateral triangle, all sides have the same length.)
Answers
Answer:
side length is [tex]\frac{20\sqrt{3} }{3}[/tex] feet
Step-by-step explanation:
An equilateral triangle has a height of 10 feet. the height of the triangle is the perpendicular bisector to the base
so it forms a two right angle triangle
the triangle formed is a 30-60-90 degree triangle
the diagram is attached below
Let x be the side if the equilateral triangle
sin(theta)=opposite by hypotenuse
[tex]sin(60)=\frac{10}{x}[/tex]
[tex]\frac{\sqrt{3}}{2} =\frac{10}{x}[/tex]
cross multiply
[tex]\sqrt{3} x=20[/tex]
[tex]x=\frac{20}{\sqrt{3} } =\frac{20\sqrt{3} }{3}[/tex]
The length of the side of an equilateral triangle with a height of 10 feet is approximately 11.54 feet. This is determined by applying the properties of a 30-60-90 triangle which is a half of an equilateral triangle.
Explanation:The problem is asking to solve for the side (s) of an equilateral triangle given the height (h). An equilateral triangle can be divided into two 30-60-90 right triangles. In such a triangle, the ratio between the hypotenuse (which is the side of the equilateral triangle) and the longer leg (which is half of the height) is 2:√3. Therefore, if the height is 10 feet, then the side length would be (2/√3)*h.
Step 1: Recognize that the triangle is a 30-60-90 triangle.
Step 2: Apply the ratio between the sides in a 30-60-90 triangle, 2:√3.
Step 3: Multiply the height by 2/√3 to get the length of one side which equals about 11.5 feet.
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Related Questions
An open box is to be constructed from a square piece of sheet metal by removing a square of side 2 feet from each corner and turning up the edges. If the box is to hold 32 cubic feet, what should be the dimensions of the sheet metal?
Answers
Answer:
length 8 feet and width 8 feet
Step-by-step explanation:
Lets x be the length and width of the sheet
An open box is to be constructed from a square piece of sheet metal by removing a square of side 2 feet from each corner
so height is 2 feet
length of the box is x-4 feet
width of the box is also x-4 feet
Volume of the box is length times width times height
[tex]V= (x-4)(x-4)2[/tex]
[tex]32=2 (x-4)^2[/tex]
divide both sides by 2
[tex]16=(x-4)^2[/tex]
take square root on both sides
[tex]4=x-4[/tex]
Add 4 on both sides
[tex]x=8[/tex]
So dimension of the sheet is
length 8 feet and width 8 feet
plz, help ASAP!!!!!!!!!!
the options are
reflection across the x-axis or y-axis
and then a translation 4 units down, up, right left
Answers
Answer:
Reflection over the x-axis and translation 4 units left
Step-by-step explanation:
Perform the following facility capacity problem. In planning the opening of your restaurant, you estimate that the restaurant's total area should allow each customer 20 square feet of dining space. Of the planned space, you hope to utilize one-third of the total space for the kitchen and storage. Seating capacity = 90 Area of dining room = a0 sq. ft. Area of kitchen and storage (to the nearest sq. ft.) = a1 sq. ft.
Answers
Answer:
Step-by-step explanation:
Total area = Dining space + Kitchen and Storage space
Dining space = 90 multiplied by 20 = 1800 square feet
Kitchen and Storage space = 1/3 of Total area
Total area = 1800 + 1/3 of Total area
(1-1/3) Total area = 1800
2/3 Total area = 1800
Total area = 3*1800/2 = 2700
Kitchen and Storage space = 2700*1/3 = 900 square feet
If a concrete column is 6 inches by 6 inches square and 8 ft. long, calculate its weight in Newtons, given a specific weight of 62.4 lb/ft3.
Answers
Step-by-step explanation:
Size of column = 6 inch x 6 inch x 8 ft
Size of column = 0.5 ft x 0.5 ft x 8 ft
Volume of column = 0.5 x 0.5 x 8 = 2 ft³
Specific weight of concrete = 62.4 lb/ft³
Mass = Volume x Specific weight
Mass = 2 x 62.4
Mass = 124.8 lb = 124.8 x 0.454 = 56.66 kg
Weight = 56.66 x 9.81 = 555.83 N
Weight of column is 555.83 N
When playing the 10 number game, we can use 1, 2, 3, 4, 5, 6, 7, 8, 9, 10(each number only one time), addition, multiplication, and parentheses. What is the largest number that we can create the 10-number game
Answers
A hockey player is offered two options for a contract: either a base salary of 50,000 and 1000 per goal, or a base salary of 40,000 and 1500 per hoal. How may goals must he score in order to make the same money as the other contract?
Answers
The hockey player must score 20 goals in order to make the same money as the first contract
Solution:
Given that, hockey player is offered two options for a contract
Let "x" be the number of goals made
Option 1 :A base salary of 50,000 and 1000 per goal
Therefore, money earned is given as:
Money earned = 50000 + 1000(number of goals)
Money earned = 50000 + 1000x ------- eqn 1
Option 2:Base salary of 40,000 and 1500 per goal
Therefore, money earned is given as:
Money earned = 40000 + 1500(number of goals)
Money earned = 40000 + 1500x --------- eqn 2
In order to make the same money as the other contract, eqn 1 must be equal to eqn 2
50000 + 1000x = 40000 + 1500x
1500x - 1000x = 50000 - 40000
500x = 10000
x = 20
Thus he must score 20 goals in order to make the same money as the first contract
Point N lies on the side AB in △ABC. Points K and M are midpoints of segments
BC
and
AN
respectively. Segments
CN
and
MK
intersect at point T. It is known that ∠CTK≅∠TMN and AB=7. Find the length of segment
CN
.
Answers
Answer:
CN = 7
Step-by-step explanation:
In the attached figure, we have drawn line CD parallel to AB with D a point on line MK. We know ΔMNT ~ ΔDCT by AA similarity, and because of the given angle congruence, both are isosceles with CD = CT. Likewise, we know ΔCDK is congruent to ΔBMK by AAS congruence, since BK = CK (given).
Then CD = BM (CPCTC). Drawing line NE creates isosceles ΔNEC ~ ΔTDC and makes CE = AB. Because ΔNEC is isosceles, CN = CE = AB = 7.
The length of segment CN is 7.
_____
If you assume CN is constant, regardless of the location of point N (which it is), then you can locate point N at B. That also collocates points T and K and makes ΔBMK both isosceles and similar to ΔBAC. Then CN=AB=7.
Billy and Ken, the school's cross-country stars, were each running at cross-country practice. Billy was going to run 3/4 of the training course, and Ken was going to run 1/2 of the course. However, during practice it started raining, so they could not finish their run. Billy had finished 1/3 of his run, while Ken had finished 1/2 of his run. Which cross-country star ran the furthest?
Answers
Final answer:
Billy and Ken both ran 1/4 of the training course before it started raining, making the distance they ran identical; neither ran further than the other.
Explanation:
Comparison of Distances Run by Billy and Ken
To determine which cross-country star, Billy or Ken, ran the furthest, we need to calculate the fractions of the total distance each one ran. Firstly, we'll look at Billy. Billy intended to run 3/4 of the course and finished 1/3 of his planned run. Therefore, the actual distance Billy ran is (3/4) × (1/3).
Now, for Ken. Ken planned to run 1/2 of the course and completed 1/2 of his intended distance. Hence, Ken's actual distance is (1/2) × (1/2). Calculating both distances:
Billy's distance: (3/4) × (1/3) = 1/4
Ken's distance: (1/2) × (1/2) = 1/4
Both Billy and Ken ran 1/4 of the total training course, hence they ran the same distance before it started raining. Therefore, neither ran further than the other.
Beth has 250 comic books in her collection She begins to sell 20 of them each week. Martin has 80 comic books in his collection. He
begins buying 15 new comic books each week
Select from the choices below, dragging and dropping to build an inequality that could be used to determine when Martin's comic book
collection exceeds Beth's
Answers
Answer:
The answer to your question is 250 - 20 < 80 + 15x
Step-by-step explanation:
Data
Beth has 250 books and sells 20 each week
Martin has 80 books and sells 15 each week
week = x
Process
1.- Write an equation for each situation
Beth 250 - 20x
Martin 80 + 15 x
2.- Write the inequality
250 - 20 < 80 + 15x
A countrys population in 1995 was 173 million in 1997 it was 178 million estamate the population in 2005 using the expontial growth formula round your awser to the nearest million
Answers
Answer: the population in 2005 is
199393207
Step-by-step explanation:
The formula for exponential growth which is expressed as
A = P(1 + r/n)^ nt
Where
A represents the population after t years.
n represents the periodic interval at which growth is recorded.
t represents the number of years.
P represents the initial population.
r represents rate of growth.
From the information given,
P = 173 million
A = 178 million
t = 1997 - 1995 = 2 years
n = 1
Therefore
178 × 10^6 = 173 × 10^6(1 + r/1)^2 × 1
178 × 10^6/173 × 10^6 = (1 + r)^2
1.0289 = (1 + r)^2
Taking square root of both sides, it becomes
√1.0289 = √(1 + r)^2
1 + r = 1.0143
r = 1.0143 - 1 = 0.0143
Therefore, in 2005,
t = 2005 - 1995 = 10
A = 173 × 10^6(1 + 0.0143)^10
A = 173 × 10^6(1.0143)^10
A = 199393207
A new drug on the market is known to cure 24% of patients with colon cancer. If a group of 15 patients is randomly selected, what is the probability of observing, at most, two patients who will be cured of colon cancer? 15 choose 2(0.24)2(0.76)13 15 choose 0(0.76)15 + 15 choose 1(0.24)1(0.76)14 + 15 choose 2(0.24)2(0.76)13 1 − 15 choose 2(0.24)2(0.76)13 15 choose 0 (0.76)15 1 − 15 choose 0 (0.76)15
Answers
Answer:
P = ₁₅C₀ (0.76)¹⁵ + ₁₅C₁ (0.24)¹ (0.76)¹⁴ + ₁₅C₂ (0.24)² (0.76)¹³
Step-by-step explanation:
Binomial probability:
P = nCr pʳ qⁿ⁻ʳ
where n is the number of trials,
r is the number of successes,
p is the probability of success,
and q is the probability of failure (1−p).
Here, n = 15, p = 0.24, and q = 0.76.
We want to find the probability when r is at most 2, which means r = 0, r = 1, and r = 2.
P = ₁₅C₀ (0.24)⁰ (0.76)¹⁵⁻⁰ + ₁₅C₁ (0.24)¹ (0.76)¹⁵⁻¹ + ₁₅C₂ (0.24)² (0.76)¹⁵⁻²
P = ₁₅C₀ (0.76)¹⁵ + ₁₅C₁ (0.24)¹ (0.76)¹⁴ + ₁₅C₂ (0.24)² (0.76)¹³
The correct answer is When P = ₁₅C₀ (0.76)¹⁵ + ₁₅C₁ (0.24)¹ (0.76)¹⁴ + ₁₅C₂ (0.24)² (0.76)¹³
The first step is Binomial probability:P = nCr pʳ qⁿ⁻ʳ
Also, that where n is the number of trials,After that r is the number of successes,p is the probability of success, and also that q is the probability of failure (1−p).So that Here, n = 15, p = 0.24, and q = 0.76.
The second step is We want to find the probability when r is at most 2, which were means that the r = 0, r = 1, and r = 2.When P = ₁₅C₀ (0.24)⁰ (0.76)¹⁵⁻⁰ + ₁₅C₁ (0.24)¹ (0.76)¹⁵⁻¹ + ₁₅C₂ (0.24)² (0.76)¹⁵⁻²After that P = ₁₅C₀ (0.76)¹⁵ + ₁₅C₁ (0.24)¹ (0.76)¹⁴ + ₁₅C₂ (0.24)² (0.76)¹³Learn more information:
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Hailey has five times as many stuffed animals as she does dolls her brother has 18 more video games and Hailey has stuffed animals if Hailey has $15 how many video games does her brother have
Answers
Answer:
Her brother has 33 video games
Step-by-step explanation:
You take 15 plus 18 because hailey has 15 stuffed animals and her brother has 18 more video games then she has animals so you add 15+ 18 to get your final answer of 33 video games
The number of video games Hailey brother is having will be equal to 93.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the information given in the question,
Stuffed animals = 5 × dolls (i)
Video games = 18 + stuffed animals (ii)
Total number of dolls Hailey has is 15
Then, put this in equation (i)
Stuffed animals = 5 × 15
= 75
Now, put 75 in equation (ii)
Video games = 18 + 75
= 93
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When a plane flies into the wind, it can travel 3000 ml in 6 h . When it flies with the wind, it can travel the same distance in 5 h. Find the rate of the plane in still air and the rate of the wind
Answers
Answer:
plane: 550 mphwind: 50 mphStep-by-step explanation:
If p and w represent the speeds of the plane and wind, respectively, the speed into the wind is ...
p - w = (3000 mi)/(6 h) = 500 mi/h
And, the speed with the wind is ...
p + w = (3000 mi)/(5 h) = 600 mi/h
Adding these two equations gives us ...
2p = 1100 mi/h
p = 550 mi/h . . . . . . . divide by 2
Then the wind speed is ...
w = 600 mi/h - p = (600 -550) mi/h
w = 50 mi/h
The rate of the plane in still air is 550 mi/h; the rate of the wind is 50 mi/h.
Answer:
Step-by-step explanation:
let speed of plane in still air =x
speed of wind=y
(x-y)6=3000
x-y=3000/6=500 ...(1)
(x+y)5=3000
x+y=3000/5=600 ...(2)
adding (1) and (2)
2x=1100
x=1100/2=550
550 +y=600
y=600-550=50
speed of plane in still air=550 m/hr
speed of wind=50 m/hr
Jackson has 1 3/8 kg of fertilizar. He used some to fertilizar a flower bed, and he only had 2/3 kg left. How much fertilizar was used in the flower bed
Answers
Answer:
17/24
Step-by-step explanation:
11/8 becomes 33/24
2/3 becomes 16/24
(33-16)/24 = 17/24
PLZ HELP ME ASAP!!!!!!
WHAT I CHOOSE IS IT THE RIGHT ANSWER????
Answers
Answer:
YES!!!
Step-by-step explanation:
Answer:
Your answer is going to be C
Step-by-step explanation:
So, when it is on the top, your X will always be first and you can see it is not in the negatives. When it is on the bottom Y is first and you can see it is in the negatives.
how many 7th grade students are expected to move by the end of the year? if 12 students actually moved, did more or fewer 7th grade students move than expected? justify your answer.
Answers
a. The number of 7th grade students expected to move by the end of the year is 8 students.
b. if 12 students actually moved, more 7th grade students move than expected.
how many 7th grade students are expected to move by the end of the year?
a.
Number of Students: 6th 250, 7th 200, 8th 150 Moves: 6th 2%, 7th 4%, 8th 8%
Number of 7th grade students expected to move by the end of the year = Moves × number of students
= 4% × 200
= 8 students
b.
if 12 students actually moved,
This means number of of 7th grade students expected to move by the end of the year are more.
Complete question:
How many 7th grade students are expected to move by the end of the year? If 12 students actually moved, did more or fewer 7th grade students move than expected? Justify your answer.
Number of Students: 6th 250, 7th 200, 8th 150 Moves: 6th 2%, 7th 4%, 8th 8%
Water flows out of a hose at a constant rate after 2 1/3 minutes 9 4/5 gallons of water had come out of the hose at what rate in gallons per minute is the water flowing out of the hose
Answers
Answer:
4 1/5 gallons per minute
Step-by-step explanation:
Divide gallons by minutes.
(9 4/5 gal)/(2 1/3 min) = (49/5 gal)/(7/3 min) = (49/5)(3/7) gal/min
= 21/5 gal/min = 4 1/5 gal/min
The Poe family bought a house for $240,000. If the value of the house increases at a rate of 4% per year, about how much will the house be worth in 20 years?
Answers
Answer:
about $525,900
Step-by-step explanation:
Each year, the value is multiplied by (1 +4%) = 1.04. After 20 years, it will have been multiplied by that value 20 times. That multiplier is 1.04^20 ≈ 2.19112314.
The value of the house in 20 years will be about ...
$240,000×2.19112314 ≈ $525,900 . . . . . rounded to hundreds
Answer: it would be worth $52587 in 20 years.
Step-by-step explanation:
If the value of the house increases at a rate of 4% per year, then the rate is exponential. We would apply the formula for exponential growth which is expressed as
A = P(1 + r/n)^ nt
Where
A represents the value of the house after t years.
n represents the period of increase.
t represents the number of years.
P represents the initial value of the house.
r represents rate of increase.
From the information given,
P = $24000
r = 4% = 4/100 = 0.04
n = 1 year
t = 20 years
Therefore
A = 24000(1 + 0.04/1)^1 × 20
A = 24000(1.04)^20
A = $52587
Find the root(s) of f (x) = (x + 5)3(x - 9)2(x + 1). -5 with multiplicity 3 5 with multiplicity 3 -9
Answers
Answer:
-5, multiplicity 3; +9, multiplicity 2; -1
Step-by-step explanation:
The roots of f(x) are those values of x that make the factors be zero. For a factor of x-a, the root is x=a, because a-a=0. If the factor appears n times, then the root has multiplicity n.
f(x) = (x+5)^3(x-9)^2(x+1) has roots ...
-5 with multiplicity 3+9 with multiplicity 2-1Answer:
a. -5 with multiplicity 3
d. 9 with multiplicity 2
f. -1 with multiplicity 1
Step-by-step explanation:
edge
After driving to a riverfront parking lot, Bob plans to run south along the river, turn around, and return to the parking lot, running north along the same path. After running 3.25 miles south, he decides to run for only 50 minutes more. If Bob runs at a constant rate of 8 minutes per mile, how many miles farther south can he run and still be able to return to the parking lot in 50 minutes?
(A) 1.5
(B) 2.25
(C) 3.0
(D) 3.25
(E) 4.75
Answers
Answer:A) 1.5
Step-by-step explanation: Bob runs at the rate of 8mins per mile
In 60mins his rate would be=60/8=7.5
Let a be the distance he further runs south
2s+3.25
Total distance covered in 50mins=Time=distance/speed=
50/60
50/60=2s +3.25/7.5
Cross multiply
60(2s+3.25)=50×7.5
120s+195=375
120s=375-195
S=180/120
S=1.5
I do not understand this question please help picture attached Which graph represents the function?
f(x)=x+2−−−−√3
Answers
the answer is (-2,0)
The ratio of the lengths of a triangle are 4:6:9 and its perimeter is 57cm. Find the length of the shortest side.
Answers
Answer:12cm
Step-by-step explanation:
The ratio are:
4:6:9
Perimeter=57cm
Let a be the unknown value.
The triangle has three sides: 4a, 6a, 9a
Perimeter=The sum of three sides
57=4a + 6a +9a
57=19a
Divide both side by 19
a=57/19
a=3
Therefore
4a:6a:9a
4×3:6×3:9×3
12:18:27
So the shortest side is 12cm
Final answer:
The shortest side of the triangle is found by setting up the sides as a proportion with a common multiplier and using the given perimeter to solve for it. Upon finding the multiplier, we multiply it by the smallest ratio to find the shortest side, which is 12 cm.
Explanation:
To solve for the length of the shortest side of the triangle, we should initially set up the ratio of the sides as 4x:6x:9x, where x is the common multiplier for each side of the triangle. Since the perimeter of the triangle is given as 57 cm, we can write the equation 4x + 6x + 9x = 57 to represent the sum of the sides of the triangle. This simplifies to 19x = 57, and by dividing both sides of the equation by 19, we find that x = 3. Therefore, the shortest side of the triangle, represented by 4x, will be 4 × 3 = 12 cm.
If the probability is 0.1 that a person will make a mistake on his or her state income tax return, find the probability that
(a) four totally unrelated persons each make a mistake;
(b) Mr. Jones and Ms. Clark both make mistakes, and Mr. Roberts and Ms. Williams do not make a mistake.
Assume the events are independent.
Answers
Answer: a) 0.0001, b) 0.0081.
Step-by-step explanation:
Since we have given that
Probability that a person will make a mistake on their state income tax return = 0.1
Probability that a person will not make any mistake = [tex]1-0.1=0.9[/tex]
Since the events are independent.
So, (a) four totally unrelated persons each make a mistake;
Our probability becomes,
[tex]P(A\cap B\cap C\cap D)=P(A)\times P(B)\times P(C)\times P(D)\\\\=0.1\times 0.1\times 0.1\times 0.1\\\\=0.0001[/tex]
(b) Mr. Jones and Ms. Clark both make mistakes, and Mr. Roberts and Ms. Williams do not make a mistake.
So, our probability becomes,
[tex]P(A\cap B\cap C'\cap D')=P(A)\times P(B)\times P(C')\times P(D')\\\\=0.1\times 0.1\times 0.9\times 0.9\\\\=0.0081[/tex]
Hence, a) 0.0001, b) 0.0081.
Final answer:
The probability that four unrelated persons each make a mistake on their tax returns is 0.0001. The probability that Mr. Jones and Ms. Clark both make mistakes, while Mr. Roberts and Ms. Williams do not, is 0.0081, calculated by multiplying the individual probabilities of each event.
Explanation:
The probability of independent events occurring simultaneously is calculated by multiplying the probabilities of each individual event. For part (a), we need to find the probability that four totally unrelated persons each make a mistake on their tax returns. Since the probability of one person making a mistake is 0.1, and the events are independent, we multiply this probability four times.
Probability (four unrelated persons each make a mistake) = 0.1x0.1x0.1x0.1 = 0.0001
For part (b), we are looking for the probability that Mr. Jones and Ms. Clark both make mistakes, while Mr. Roberts and Ms. Williams do not make mistakes. The probability of making a mistake is 0.1 and not making a mistake is 0.9 (which is 1 - 0.1).
Probability (Jones and Clark make mistakes, Roberts and Williams do not) = 0.1x0.1x0.9x0.9 = 0.0081
Carolina is twice as old as Raul. Ginny is the oldest and is three times Raul's age plus four. Their ages add up to be 52. How old will Ginny be on her next birthday?
Answers
Answer:
29
Step-by-step explanation:
Let c, r, g stand for the current ages of Carolina, Raul, and Ginny. Then we have the relations ...
c = 2r
g = 3r +4
c + r + g = 52
Substituting for c and g, we get ...
2r + r + (3r +4) = 52
6r = 48 . . . . . . . . . . . . . subtract 4
r = 8 . . . . . . . . . . . . . . . divide by 8
g = 3(8) +4 = 28 . . . . . .Ginny is presently 28
On Ginny's next birthday, she will be 29.
Answer: Ginny would be 29 years old on her next birthday.
Step-by-step explanation:
Let c represent Carolina's current age.
Let r represent Raul's current age.
Let g represent Ginny's current age.
Carolina is twice as old as Raul. It means that
c = 2r
Ginny is the oldest and is three times Raul's age plus four. It means that
g = 3r + 4
Their ages add up to be 52. It means that
c + r + g = 52 - - - - - - - - - - - - 1
Substituting
c = 2r and g = 3r + 4 into equation 1, it becomes
2r + r + 3r + 4 = 52
6r + 4 = 52
6r = 52 - 4 = 48
r = 48/6 = 8
c = 2r = 2 × 8
c = 16
g = 3r + 4 = 3 × 8 + 4
g = 24 + 4 = 28
On Ginny's next birthday, she would be 28 + 1 = 29 years old
Functions f(x) and g(x) are defined below.
Determine where f(x) = g(x) by graphing.
A.
x = -1
B.
x = 4
C.
x = -4
D.
x = -2
Answers
Answer:
C. x = -4
Step-by-step explanation:
Graphing calculators make solving a problem like this very easy. The two functions both have the value -1 at x = -4.
The solution to f(x) = g(x) is x = -4.
Ivan has 15 yd of green felt and 12 yd of blue felt to make 3 quilt if I have I even uses the same total numbers of each of yd for each quilt how many yd does she need To use for each quote
Answers
Answer:
9 yards of each quilt.
Step-by-step explanation:
Let the length of each quilt be 'x'.
Given:
Length of green felt = 15 yards
Length of blue felt = 12 yards
Total number of quilts = 3
Total length of all the quilts in terms of 'x' is given as:
[tex]Total\ length=x+x+x=3x ----(1)[/tex]
Total length is also equal to the sum of the lengths of green and blue felts. So,
[tex]Total\ length=15+12=27--- (2)[/tex]
Now, equating equations (1) and (2), we get:
[tex]3x=27\\\\x=\frac{27}{3}\\\\x=9 [/tex]
Therefore, the length of each quilt is 9 yards.
Kevin and his sister, katy,are trying to solve the system of equations . Keven thinks the new equation should be 3(6x-1)+2y=43 , while katy thinks it should be 3x+2(6x-1)=43.Who is correct and why
Answers
Answer:Kathy is correct
Step-by-step explanation: We need to solve both equations separately in order to determine with certainty which one is correct and which one is not.
Kevin thinks the new equation should be
3(6x-1) + 2y = 43
This can now be solved as follows;
18x - 3 + 2y = 43
Add 3 to both sides of the equation
18x - 3 + 3 + 2y = 43 + 3
18x + 2y = 46
2(9x + y) = 46 (factorize the left hand side of the equation by 2)
Divide both sides of the equation by 2
9x + y = 46
The variables remain unsolved
On the other hand, Kathy thinks the new equation should be
3x + 2(6x - 1) = 43
This can now be solved as follows;
3x + 12x - 2 = 43
Collect like terms (in this equation, x)
15x - 2 = 43
Add 2 to both sides of the equation
15x - 2 + 2 = 43 + 2
15x = 45
Divide both sides of the equation by 15
x = 3
In essence, Kathy's equation has a solution (x=3) while that of Kevin remains unsolved
Final answer:
Neither Kevin nor Katy's equations are correct in the context of solving a system of linear equations, as they do not logically combine the given equations correctly.
Explanation:
The question revolves around which sibling is correct in forming a new equation to solve a system of linear equations. To determine this, we need to see which sibling correctly used the properties of equality to combine or manipulate equations. Kevin's equation, 3(6x-1)+2y=43, is an attempt to modify an existing equation by distributing a 3. Katy's equation, 3x+2(6x-1)=43, seems to combine different parts of the given equations.
Upon closer inspection, neither Kevin nor Katy is entirely correct because their proposed equations do not logically follow from the given set. To solve for a system of equations, we would typically add, subtract, multiply, or divide entire equations by constants or variables to eliminate one variable, so we can solve for the other.
Jimmy Carter's family went apple picking they picked a total of 115 apples, the family are a total of eight apples each day after how many days they have 19 apples left
Answers
A homeowner wants to increase the size of a rectangular deck that now measures 14 feet by 22 feet. The building code allows for a deck to have a maximum area of 800 square feet. If the length and width are increased by the same number of feet, find the maximum number of whole feet each dimension can be increased.
Answers
Answer:
10.6 feet
Step-by-step explanation:
Length = 22ft
width= 14ft
Maximum area = 800 sq. ft
Let X be increase in the number of feet for the length and width.
The new length = (22 + x) ft
New width= (14 + x) ft
Area = (22+x)(14+x) ≤ 800
308 + 36x + x^2 ≤ 800
x^2 + 36x + 308 - 800 ≤ 0
x^2 + 36x - 492 ≤ 0
Solve using quadratic equation
x = (-b +/- √b^2 - 4ac) / 2a
a= 1, b = 36, c= 492
x = (-36 +/- √36^2 - 4*1*-492)/ 2*1
= (-36 +/- √1396 + 1968) / 2
= (-36 +/- √3264) / 2
= (-36 +/- 57.13) / 2
x = (-36 + 57.13)/2 or (-36 - 57.13)/2
x = 21.13/2 or -93.13/2
x = 10.6 or -31.0
x = 10.6 ft
The length and width must increase by 10.6 ft each
The number of whole feet by which the length and width of the deck can be increased would be calculated by setting up and solving an equation taking into account the original dimensions and maximum allowed area for the deck.
Explanation:The question is asking to find by how many whole feet the length and width of the rectangular deck can be increased, given a maximum area limit set by the building code. Let's suppose x is the number of feet by which both the length and width are to be increased. Given that the original area of the deck is 14 feet by 22 feet (which gives an area of 308 square feet), the new dimensions would be (14 + x) feet by (22 + x) feet.
According to the building code, the maximum area allowed for the deck is 800 square feet. We can write and solve the following equation to find x: (14 + x) * (22 + x) = 800.
Solving this equation would yield the maximum integral number of feet each dimension can be increased while still not exceeding the allowed 800 square feet.
Learn more about area calculation here:https://brainly.com/question/34380164
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Suppose a room is 5.2 m long by 4.3m wide and 2.9 m high and has an air conditioner that exchanges air at a rate of 1200 L/min. How long would it take the air conditioner to exchange the air in the room
Answers
Answer:
54 minutes
Step-by-step explanation:
From the question, we are given;
A room with dimensions 5.2 m by 4.3 m by 2.9 mThe exchange air rate is 1200 L/minWe are required to determine the time taken to exchange the air in the room;
First we are going to determine the volume of the room;
Volume of the room = length × width × height
= 5.2 m × 4.3 m × 2.9 m
= 64.844 m³
Then we should know, that 1 m³ = 1000 L
Therefore, we can convert the volume of the room into L
= 64.844 m³ × 1000 L
= 64,844 L
But, the rate is 1200 L/min
Thus, time = Volume ÷ rate
= 64,844 L ÷ 1200 L/min
= 54.0367 minutes
= 54 minutes
Therefore, it would take approximately 54 minutes