David loves his dog Thor and he wants to create a rectangular enclosure that has an area of 1600ft² for the dog to stay in while no one is home. David has a total of 120 feet of fencing available and he wants to use the wall of his garage as one of the sides of the enclosure. What are the dimensions of the enclosure?
Make a Sketch of the rectangular enclosure and label the sides using variable(s).
Write and solve an equation(s) that model this situation.
What are the dimensions of the rectangular enclosure?
Answers
Answer:
80 feet by 20 feet
Step-by-step explanation:
Area of the rectangular enclosure = 1600ft²
Area, lw=1600
w=1600/l
Perimeter, 2w+l=120 feet
Substituting w=1600/l into the perimeter
2(1600/l)+l=120
3200/l+l=120
[tex]\dfrac{3200+l^2}{l}=120\\ 3200+l^2=120l\\l^2-120l+3200=0\\l^2-40l-80l+3200=0\\l(l-40)-80(l-40)=0\\(l-40)(l-80)=0\\l-40=0\:or\:l-80=0\\l=40\:or\:l=80[/tex]
When l=40, w=1600/40=40 feet
When l=80, w=1600/80=20 feet
Since the enclosure is rectangular, the acceptable dimensions are:
Length =80 feet
Width =20 feet
Related Questions
Expand and combine like terms.
(x+3)(x+4)
Answers
Answer:
x^2 +7x+12
Step-by-step explanation:
(x+3)(x+4)
FOIL
first x*x= x^2
outer: 4x
inner:3x
Last 3*4=12
Add together
x^2+3x+4x+12
Combine like terms
x^2 +7x+12
What is the domain of the function represented by this graph?
the graph of a quadratic function y = x^2 – 4 with a minimum value at the point (0,-4)
A.
x ≥ 4
B.
x ≤ 0
C.
-2 ≤ x ≤ 2
D.
all real numbers
Answers
Answer: D
Step-by-step explanation:
all real numbers
The domain of the function should be all real numbers.
What are real numbers?Real numbers refer to the numbers that involved both rational and irrational numbers. Rational numbers like integers, fractions, etc while on the other hand, irrational numbers like the square roots numbers, etc.
Therefore, we can conclude that the domain of the function should be all real numbers.
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HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
how are we supposed to help with that
Step-by-step explanation:
use your snip tool on your computer and connect them
Answer:
Use the numbers that they gave you..
Step-by-step explanation:
It's not that hard
Makena made 11 quarts of punch. How many gallons of punch did she make
Answers
Answer:
2 3/4 gallons
Step-by-step explanation:
We know that there are 4 quarts in a gallon
11 quarts * 1 gallon/ 4 quarts
11/4 gallons
Changing to a mixed number
2 3/4 gallons
6x+ 35=-7y slope intercept form
Answers
Answer:
y = -6/7x -5
Step-by-step explanation:
6x+ 35=-7y
Divide each side by -7
6x/(-7)+ 35/-7=-7y/-7
-6/7x -5 = y
Flipping the sides
y = -6/7x -5
This is slope intercept form
y = mx+b where m is the slope and b is the y intercept
Bonnie is making a dipping sauce . She mixes 150 milliliters of soy sauce with 100 milliliters of vinegar.
How much soy sauce does Bonnie mix with every 1 milliliter of vinegar?
How much vinegar does Bonnie mix with every 1 milliliter of soy sauce?
For the vinegar into soy sauce it has to a fraction that’s what I’m confused on.
Answers
Answer:
1.5 or 3/2
Step-by-step explanation:
Answer: Bonnie uses 1.5 millimeters of soy sauce with every 1 millimeter of vinegar.
Bonnie uses 2/3 millimeter of vinegar for every 1 millimeter of soy sauce.
Step-by-step explanation:
What is the value of x?
10
8
Answers
Answer:
x=6
Step-by-step explanation:
E2020
The value of x will be 6 for the given triangle.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle, the hypotenuse square is equal to the square of the sum of the other two sides.
According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Given that in the right-angle triangle, the hypotenuse is 10, the base is 8 and the perpendicular is x.
The value of x will be calculated as:-
x² = 10² - 8²
x² = 100 - 64
x² = 64
x = √36
x = 6
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What are all kinds of triangle
Answers
A triangle is a three-sided two-dimensional shape that can be classified based on side lengths and angle measurements. There are various types of triangles, including equilateral, isosceles, scalene, acute, right, obtuse, equiangular, and right-angled isosceles triangles.
Explanation:A triangle is a three-sided two-dimensional shape. It is a polygon, which is a closed figure with straight sides. Triangles can be classified based on their side lengths, such as equilateral (all sides are equal), isosceles (two sides are equal), and scalene (no sides are equal). They can also be classified based on their angle measurements, such as acute (all angles are less than 90 degrees), right (one angle is 90 degrees), and obtuse (one angle is greater than 90 degrees). Additionally, there are special types of triangles like equiangular triangles (all angles are equal) and right-angled isosceles triangles (one angle is 90 degrees and two sides are equal).
Evaluate the expression. a+b/c when a=to 24 b =36 and c =4
Answers
Answer:
(a + b)/c = 15
a + (b/c) = 33
Step-by-step explanation:
Evaluate the expression. a+b/c when a=to 24 b =36 and c =4
if you meant Evaluate (a + b)/c
then
(24 + 36) /4 = 60/4 = 15
or if you meant Evaluate a + (b/c) then
a + (b/c) = 24 + (36/4) = 24 + 9 =33
In a class of students, the following data table summarizes how many students play an instrument or a sport. What is the probability that a student chosen randomly from the class plays a sport and an instrument?
Answers
Answer:
This picture doesn't have anything to do with instruments or sports. If the picture is right, the answer is 18/27 or about 68%.
Step-by-step explanation:
You calculate the total number of people in the class. It comes up to 27. Then you calculate how many of them is female. Then you divide.
Is x = 0 a valid potential solution to the equation log(x + 7) + log(x − 3) = 17? Question 9 options: A) No, because it isn't possible to take the logarithm of zero: log(0). B) No, because when x = 0, the second term is log(− 3), and it's impossible to take the logarithm of a negative number. C) Yes, logarithms are valid for any integer. D) No, because 17 isn't divisible by 7 or 3.
Answers
Answer:
its B
Step-by-step explanation:
No, x = 0 is not a valid solution for log(x + 7) + log(x − 3) = 17 .
Given,
log(x + 7) + log(x − 3) = 17
Here,
Substitute the value of x in the equation,
log(7) + log(-3) = 17
So,
log(-3) is not a valid number and thus its value does not exist .
Thus the equation can not be equated to 17 .
Hence option B is correct .
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A rectangle has an area of (x - 17x + 72) square units. Since the area of a rectangle is determined using the formula, A =
kw, what could be the length and width of the rectangle?
length = (x - 8) units and width = (x - 9) units
length = (x + 9) units and width = (x + 8) units
length = (x-6) units and width= (x - 12) units
length = (x + 12) units and width = (x + 6) units
Answers
Answer:
Step-by-step explanation:
x² - 17x + 72 = 0
Sum = -17
Product = 72
Factor = 8 , 9
x² - 17x + 72 = 0
x² - 8x -9x + (-8)*(-9) = 0
x(x - 8) -9(x -8) = 0
(x - 8 ) (x - 9) = 0
Length = (x - 8) units
Width = (x - 9) units
1. What has left tons of “space junk” in orbit around the earth?
robots sent on space missions
years of space exploration
lack of recycling
missiles in outer space
2. Countries around the world have agreed to limit the time their space tools stay in orbit to 25 years. As explained in the passage, what problem does this solution address?
the increasing amount of space junk in orbit around the earth
space agencies exploring space
Chinese efforts to blow up a satellite
objects moving around the planet at very high speed
3. Trash has become a problem in outer space too.
What evidence from the text best supports this statement?
The Chinese tried to blow up one of its satellites with a missile in 2007.
In England, a metal harpoon is being tested that can be fired into space, gripping space trash and pulling it back into the earth’s atmosphere to burn up.
The Germans have been planning a space mission with robots to collect some space trash and bring it back to Earth.
According to BBC News, there are more than 22,000 pieces of junk in space around the earth.
4. Why have countries agreed to build space tools that must fall safely into the earth’s atmosphere?
so that the tools can remove pollution from the atmosphere after returning from space
so that the tools burn up in the atmosphere and don’t become space junk
so that the tools pollute the atmosphere instead of outer space
so that the tools can analyze the different gases that make up the atmosphere after returning from space
5. What was the passage mostly about?
different missions scientists are trying in space
the effects that tiny pieces of space junk could have on the earth
the problem of space junk and scientists’ attempts to solve this problem
the problem of trash on planet Earth
6. Read the following sentences: “In our opinion the problem is very challenging and it's quite urgent as well,'’ said Marco Castronuovo, an Italian Space Agency researcher who is working to solve the problem. One reason that it’s urgent is that countries are sending more and more objects into space. Many of these objects are tools that help people use their cell phones or computers.”
What does the word urgent most nearly mean?
easy to solve
unnecessary
needs immediate attention
minor
7. Choose the answer that best completes the sentence below.
Years of space exploration have left tons of “space junk,” _______ many scientists are trying to find a way to clean up outer space.
so
instead
because
similarly
8. What did the 2009 collision of a United States satellite and a Russian satellite cause?
(please use complete sentences)
9. What have the Germans done to help clean up space junk?
(use complete sentences)
10. Different countries have explored or are exploring different methods to clean up space junk. Explain why some methods may be more effective than others. Use evidence from the text to support your answer.
Don't Guess the answers i will give you the link to read the passage that goes along with the questions!
Answers
Answer:
1-B
2-A
3-D
4-B
5-C
6-C
7-A
8- The collision resulted in significant debris in low Earth orbit.
9-
10-
Step-by-step explanation:
What is the size of the sample space?
Answers
Could you be more specific?
Answer:
the answer is 36
Step-by-step explanation: i took the test
Find the slope of (-2,1),(-5,5)
Answers
Answer: m = - 4/3
Step-by-step explanation:
The formula to find slope is m = y2 - y1 / x2 - x1.
So for this problem I did 1 - 5 / -2 - (-5) which equals -4/3
The fanumber of lowers is 14:6. total
The ratio of white flowers to the total
number of flowers is 4:6.
DRAG AND
Answers
Container 1: 18 flowers (6 pink + 12 white)
Container 2: 9 flowers (3 pink + 6 white)
Container 3: 15 flowers (10 white + 5 pink)
Container 1:
4 out of 6 flowers are pink, meaning 2 are white.To maintain the ratio, scale up the total number of flowers by a factor of 3 (6 / 2).Therefore, you need 18 flowers in Container 1 (6 pink + 12 white).Container 2:
1/3 of the flowers are pink, so 2/3 are white.Let x be the total number of flowers.Pink flowers: 1/3 * xWhite flowers: 2/3 * xSince the total number of flowers is x, we have 1/3 * x + 2/3 * x = x.Solving for x, we get x = 9 flowers (3 pink + 6 white).Container 3:
The ratio of white flowers to the total number of flowers is 4:6, meaning 2 parts are white and 3 parts are total.Let y be the total number of flowers.White flowers: 2/3 * yTotal flowers: ySince the total number of flowers is y, we have 2/3 * y = y.Solving for y, we get y = 15 flowers (10 white + 5 pink).A spinner has five equal sectors colored red, yellow, green, blue, orange. What is the
probability of landing on a yellow first and then on a blue sector after two consecutive
spins?
Answers
Answer: 5/25
5/50
Step-by-step explanation: If each part has 5 sections then it equals to 25 so you have a 5 out of 25 chance of getting it, The second time I added 25 twice since it says your spinning it twice, but you still only have 5 sections so you would have 5 out of 50
The calculated probability is 4 percent.
The student's question involves calculating the probability of two independent events occurring in sequence. Since each sector on the spinner is equal, the probability of landing on yellow for the first spin is 1 out of 5 or 0.2. Similarly, the probability of landing on blue for the second spin is also 1 out of 5 or 0.2.
Since these are independent events, their probabilities are multiplied to find the combined probability. Therefore, the probability of landing on yellow first and then on blue for the second spin is 0.2 * 0.2 = 0.04. This means there is a 4 percent chance of this outcome occurring.
The orginal price of a toy was $15 if the price is reduced by 20% what is the new price of the toy
Answers
Answer:
$12
Step-by-step explanation:
You have to find what is 20% of 15 which is 3, and then subtract 3 from from 15, which is 12. Real simple!
Cookies are on sale! Today each cookie costs $0.75 less than the normal price. Right now if you buy 7 of them it will only cost you $2.80
Answers
Please help me with this problem
Answers
Answer:
Step-by-step explanation:
x - 2 is a factor. Therefore, P(2) = 0
P(x) = x³ - 4x² + 3x + c
P(2) = 0
2³ - 4*(2)² + 3*2 + c = 0
8 - 4*4 +6 +c = 0
8 - 16 + 6 + c = 0
-2 + c = 0
c = 2
SAT verbal scores are normally
distributed with a mean of 450
and a standard deviation of 120.
Determine what percent of the
scores lie between 450 and 570.
Answers
Answer:
The percentage of the scores lying between 450 and 750 is 49.4%
Step-by-step explanation:
In this question, we are simply asked to calculate the percentage of the scores lying between a particular range.
The first thing to do here is to calculate the z score of both scores
Mathematically, z score = (x - mean)/SD
for score 450, we have ; z = (450-450)/120 = 0/120 = 0
For score 750, we have z = (750-450)/120 =
2.5
Now, we move on to calculate the probability before turning it into a percentage.
The supposed probability we are to calculate is as follows;
P(450 < x < 750) or P(0 < z < 2.5)
Using standard score table, P = 0.49379
The percentage is thus 49.4%
Solve for x to the nearest hundredth
3^x=38
Answers
Answer:
The value of x is 3.31 to the nearest hundredthStep-by-step explanation:
Given the equation [tex]3^{x} = 38[/tex], to calculate the value of x the following steps must be carried out;
Step 1;
Take the natural logarithm of both sides
[tex]ln3^{x}=ln38\\ xln3 = ln38[/tex]
Step 2;
Divide both sides by ln3
[tex]xln3/ln3=ln38/ln3\\x=ln38/ln3\\x=3.31[/tex]
The value of x is 3.31 to the nearest hundredth
Tom saves 35% of his salary . Jerry spends 3/5 of his salary and saves rthe rest of his salary work out who saves the most money each month you must show your working.
Answers
Final answer:
Jerry saves more money each month than Tom. Tom saves 35% of his salary, whereas Jerry spends 3/5 and saves the remainder, which is 2/5 of his salary. Assuming equal salaries, Jerry's savings are greater.
Explanation:
The question is asking us to compare how much Tom and Jerry save from their salaries. Let's assume each of them earns the same amount of salary, say for example $1000 (this figure is just for simplicity and can represent any currency or amount).
Tom saves 35% of his $1000 salary, which is 0.35 * $1000 = $350.
Jerry spends 3/5 of his salary, which is 3/5 * $1000 = $600. Therefore, he saves 2/5 of his salary because 1 - 3/5 = 2/5. So Jerry saves 2/5 * $1000 = $400.
Comparing the two, Jerry saves more each month since $400 (Jerry's savings) is greater than $350 (Tom's savings).
There are 25 people in a classroom. Each person shakes each other person's hand once
and only once. How many handshakes were there altogether?
Answers
Answer:
13
Step-by-step explanation:
13 because there pretend there is 24 people then it would be 12 but then there is one left over so 13 because somebody would have to shake hands with that person
Find the slope of the line that passes through (68, -3) and (69, 76)
Answers
Answer:
79
Step-by-step explanation:
Hope this helps!
Determine the solution to the system of equations below.
x - 3y = 1
3x-5y = 11
Answers
Final answer:
To solve the system of equations, use the method of substitution. Solve one equation for one variable and substitute the value in the other equation. Simplify and solve for the variable, then find the value of the other variable. The solution to the system is x = 7 and y = 2.
Explanation:
To determine the solution to the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.
Step 1: Solve one equation for one variable
From the first equation, we can isolate x: x = 1 + 3y
Step 2: Substitute the value of the variable in the other equation
Substitute x = 1 + 3y into the second equation: 3(1 + 3y) - 5y = 11
Step 3: Simplify and solve for y
Expand the equation and simplify: 3 + 9y - 5y = 11
Combine like terms: 9y - 5y = 11 - 3
Simplify: 4y = 8
Solve for y: y = 2
Step 4: Find the value of the other variable
Substitute the value of y into the first equation: x - 3(2) = 1
Simplify and solve for x: x - 6 = 1
x = 7
Therefore, the solution to the system of equations is x = 7 and y = 2.
how many cups are in three pints
Answers
Answer:
6 us cups
Step-by-step explanation:
1 pint is equal to 2 cups
Answer:
12
Step-by-step explanation:
There are 4 pints in a gallon and 4 cups in each pint
Which of the following is NOT in the solution set of the inequality -2g+3>-5g+5
Group of answer choices
-6
0
-2
3
Answers
the answer is 20 is not a solution
I think of a number, multiply by 2, subtract 6 and then divide by 4. If the answer is -8, what is the original number?
Answers
Answer:
-13
Step-by-step explanation:
you just start from -8 and work backwards.
so it's -8 multiply 4 to get -32, then add 6 to get -26, then divide 2 to get -13.
when you check from the beginning with -13, then it fits and the answer is -8!
The graph of f "(x) is continuous and decreasing with an x-intercept at x = 0. Which of the following statements is true?
The graph of f has a relative maximum at x = 0.
The graph of f has a relative minimum at x = 0.
The graph of f has an inflection point at x = 0.
The graph of f has an x-intercept at x = 0.
Thank you in advance!
Answers
Answer:
The graph of f has an inflection point at x = 0.
Step-by-step explanation:
An inflection point occurs when the second derivative changes signs. Since f"(x) is decreasing and has an x-intercept at 0, it changes signs from + to -, so there is an inflection point at x = 0.
The statements "The graph of f has an inflection point at x = 0." is true
X-interceptThe meaning of X-INTERCEPT is the x-coordinate of a point where a line, curve, or surface intersects the x-axis.
How to solve this problem?F''(x) tells you whether the function is concave up, down, or where it's inflection points are.F"(x)>0 tells you it's concave up.F"(x)<0 tells you it's concave down.F"(x)=0 tells you there's a possible point of inflection at xSince this function is continuous and decreasing, we can assume that before it intercepts x at 0, it is concave up and after it intercepts, it continues to decrease which makes it concave down. Since F"(x)=0 & there is a change in sign, the statement 'The graph of f has an inflection point at x = 0." is true.From above reasons we can say that the statement "The graph of f has an x-intercept at x = 0." is true
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