A veterinary clinic plans to build four identical dog kennels along the side of its building using 210 feet of fencing. (See the picture.) What should be the dimensions of each kennel to maximize the enclosed area? (Note: No fencing is needed along the side of the building.)
Final answer:
To maximize the enclosed area, each kennel should be in the shape of a square with dimensions of 52.5 feet by 52.5 feet.
Explanation:
To maximize the enclosed area, each kennel should be in the shape of a square. Let's assume that each side of the square kennel has a length of x feet.
Each kennel has four sides, so the total length of fencing required for all four kennels is 4x feet.
Given that there are 210 feet of fencing available, we can set up the equation 4x = 210 and solve for x to find the length of each side of the square kennel.
Dividing both sides of the equation by 4, we get x = 52.5 feet.
Therefore, each kennel should have dimensions of 52.5 feet by 52.5 feet to maximize the enclosed area.
Stefan is measuring the angles of a triangle. He measures the first angle and gets a measure of 80° What does he know about the other two angles? A) They are each 50°. B) Their measures should add up to be 100°. C) Their measures should add up to be 280°. D) He doesn't know anything about the other two angles.
The answer is (B) Their measures should add up to be 100°.
Step-by-step explanation:We know that the sum of all angles of a triangle is equal to 180 degrees. Stefan has calculated the first angle and it came out to be 80 degrees. So the other two angles must be equal to 100 in order to complete the total measurement of triangle angles which is 180.
PLEASE HELP WILL GIVE BRAINLIEST ******* Lucy made tables of values to approximate the solution to a system of equations.
Answer:(1.6,1.3)
Step-by-step explanation:
joey's little sister must take four steps for every three steps joey takes. suppose one step of joey's covers one foot. how many feet would his sister
Joey's sister takes 0.75 foot for each step she takes since she takes four steps for every three of Joey's, and Joey's step is 1 foot.
The question revolves around a ratio of steps taken by Joey and his sister. Since Joey's one step covers one foot and his sister takes four steps for his three, we need to determine how many feet his sister covers for each of Joey's steps. Let's use a ratio to figure this out.
First, we establish the ratio of steps: for every 3 steps Joey takes, his sister takes 4. If Joey's 3 steps equal 3 feet (because 1 step = 1 foot), we then find the length of his sister's step compared to his. We divide the 3 feet by Joey's 3 steps to find that each step Joey takes is 1 foot long. Then, we calculate his sister's step length in feet by dividing the 3 feet by 4 (since she takes 4 steps to his 3), which equals 0.75 foot per step for his sister.
So, for each of Joey's steps being 1 foot, his sister's step would be 0.75 foot. Therefore, Joey's sister covers 0.75 foot for each step she takes.
Which of the following equations will produce the graph shown?
A. x^2= 8y
B. x-1/8y^2= 0
C. y=1/2x^2
D. x^2= -8y
Answer:
Step-by-step explanation:
Give two examples of items that weigh less than 1 ounce and two examples of items that weigh more than 1 ton.
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What would be the slope of the line perpendicular to the line 4x + 2y = 12?
Final answer:
The slope of the line perpendicular to the line 4x + 2y = 12 is the negative reciprocal of the original line's slope, which in this case is 0.5 or 1/2.
Explanation:
The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. To find the slope of the line perpendicular to the line 4x + 2y = 12, we first need to rewrite the given equation in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
First, we solve for y:
4x + 2y = 12
2y = -4x + 12
y = -2x + 6
From the equation y = -2x + 6, we can see that the slope (m) is -2. The slope of the perpendicular line will be the negative reciprocal of -2, which is ½ or 0.5. Therefore, the slope of the line perpendicular to the line 4x + 2y = 12 is ½.
Nivea lost her cell phone somewhere in her 7500 square foot house. Her mother tells her there is a 16% chance that the phone is in the game room.
a. Find the probability (as a fraction) that the phone is in the game room.
b. what is the area of the game room?
With 128,134,140,146,152,whats the next number If the pattern continues?
I need help please ASAP and I will mark branlist
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Let us take as a given that x is normally distributed with a mean of 8.5 and a standard deviation of 2, what is p(x ≤ 6)? note: round your answer, if necessary, to two places after the decimal. please express your answer with two places after the decimal.
an im mperative sentence A. asks a question B. make a request C. make a statement D. show emotion.
You decide to make a beanbag in the shape of a sphere with a diameter of 120 millimeters. You will need to find the volume to know how many beans to put in the bag. What is the volume?
Explain how you would solve a triangles given two sides and the included angle?
To solve a triangle given two sides and included angle, use the law of cosines. This law is expressed as a² = b² + c² - 2bc cos(A), where a, b, c are the lengths of the sides, and A is the included angle.
Explanation:To solve a triangle given two sides and the included angle, you would use the Law of Cosines. This law is used when you're given two sides and the included angle in a triangle (often abbreviated as SAS). The law states,
a² = b² + c² - 2bc cos(A)
where a, b, and c are the lengths of the sides of the triangle, and A is the included angle. So, in this case, if you're given sides b and c and included angle A, you would substitute these values into the formula to find side a.
For instance, if side b is 3 units, side c is 4 units, and angle A is 60 degrees, we would substitute these values into our formula like so: a² = 3² + 4² - 2(3)(4) cos(60).
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The correct way to solve a triangles given two sides and the included angle is by the sine and cosine rule.
Solving triangles using the sine and cosine ruleFor angle placed in between two sides of a triangle, we can use the cosine rule to determine the unknown angle
According to the cosine formula, we will have:
[tex]a^2=b^2+c^2-2bc \ cos\theta[/tex]
where a, and c are the sides of the triangle and theta is the central angle.
Also, the remaining angles can be determined using the law of cosines as shown:
a/sinA = b/sinB = c/sinC
Hence the correct way to solve a triangles given two sides and the included angle is by the sine and cosine rule.
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Javier's family bought 3 juices at Bagel Mania. Which of these could NOT be the amount of money Javier's family spent of juices
Juices ___ small $0.75
Large $1.25
A. $2.25
B. $2.75
C. $3.25
D $3.50
A vehicle travels a distance of 5t4 − 10t2 + 6 miles in t + 2 minutes.
The vehicle's speed is __________miles/minute.
Answer:
Speed of the vehicle=[tex]\frac{5t^{4}-10t^{2}+6}{t+2}miles/min[/tex]
Step-by-step explanation:
Given that,
Distance traveled by the vehicle = 5t⁴ - 10t² + 6 miles
time = t + 2 minutes
We need to find the speed of vehicle. Use the formula of speed is:
[tex]Speed=\frac{Dstance}{Tme}[/tex]
[tex]Speed=\frac{5t^{4}-10t^{2}+6}{t+2}[/tex]
So, speed of the vehicle=[tex]\frac{5t^{4}-10t^{2}+6}{t+2}[/tex]
That's the final answer.
Answer:
The speed is 5t^3 - 10t^2 + 10t - 20 + 46/(t+2) miles per minute.
Help please!!!!!!!!!!!!!
Yi and Sue play a game. They start with the number $42000$. Yi divides by a prime number, then passes the quotient to Sue. Then Sue divides this quotient by a prime number and passes the result back to Yi, and they continue taking turns in this way.
For example, Yi could start by dividing $42000$ by $3$. In this case, he would pass Sue the number $14000$. Then Sue could divide by $7$ and pass Yi the number $2000$, and so on.
The players are not allowed to produce a quotient that isn't an integer. Eventually, someone is forced to produce a quotient of $1$, and that player loses. For example, if a player receives the number $3$, then the only prime number (s)he can possibly divide by is $3$, and this forces that player to lose.
Who must win this game, and why? Explain your reasoning in complete sentences. (Don't just show one example of how the game could go. Instead, explain why the same player must always win, no matter what strategy either player tries to use!)
A science teacher needs up to 15 female and male students for a competition. The science teacher needs at least 6 male volunteers. Let x represent the number of male volunteers and y represent the number of female volunteers. Which inequalities model the situation? Select each correct answer.
a. x+y≤15
b. y≥0
c. x+y<15
d. x>6
e. x≥6
What is 1/4 written as a percent
Do the table and the equation represent the same function?
y = 115 + 32(x)
0 115
2 179
4 243
6 307
8 371
After plugging the x-values from the table into the equation y = 115 + 32(x) and finding matching results with the y-values in the table, it is clear that the table and equation represent the same function.
To determine if the table and the equation y = 115 + 32(x) represent the same function, we can plug the x-values from the table into the equation and see if the resulting y-values match those provided in the table.
For x = 0: y = 115 + 32(0) = 115, which matches the table.For x = 2: y = 115 + 32(2) = 115 + 64 = 179, which matches the table.For x = 4: y = 115 + 32(4) = 115 + 128 = 243, which matches the table.For x = 6: y = 115 + 32(6) = 115 + 192 = 307, which matches the table.For x = 8: y = 115 + 32(8) = 115 + 256 = 371, which matches the table.Since the y-values for all listed x-values in the table correspond exactly to those calculated using the equation, it is evident that the table and the equation do indeed represent the same function.
The place value of the 3 in 27.4359 is _____.
The place value of the '3' in 27.4359 is in the tenths place, and therefore its value is 0.3. The position of the '3' relative to the decimal point determines its place value.
Explanation:The place value of the '3' in 27.4359 is determined by its position relative to the decimal point. In this example, the '3' is located in the first space to the right of the decimal point, which represents the tenths place.
So, the value of the '3' in this decimal is three-tenths, or 0.3. Looking at other numbers for comparison, consider 0.00347. Here, the '3' is three places to the right of the decimal, but the place value would be significantly lower, as it is in the thousandths place.
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whats a square root?
In parallelogram RSTU, SW=4 cm, WT=6 cm, RS=5 cm, And ST=7 cm what is the length of line segment WU
The length of line segment WU is 4 cm.
Hence, 4 cm is correct.
What is Line segment?Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.
Now, As given that, RSTU is an parallelogram.
RT and SU are its two diagonals.
They intersect each other at point W.
Properties of parallelogram is that they bisect each other.
i.e SW = WU and RW = WT
As given that, SW = 4 cm.
So, WU = SW = 4 cm
Therefore, the length of line segment WU is 4 cm.
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Is Sylvia buys 5 shirts for $75 a unit rate?
I believe you are finding the total cost of 5 shirts given the unit rate. To compute for the total cost, you have to multiply the unit rate to the number of shirts bought:
5 shirts x $75 unit rate = $375
Therefore, Sylvia will spend $375 to buy 5 shirts.
The minimum size of a photo book ordered through a website is 6 pages. The website charges $1.70 per page for the first 6 pages. Any additional pages increase the cost of the photo book by $0.90 per page. If x represents the number of additional pages in a photo book order, which equation can be used to find the total cost, in dollars, of a photo book ordered through the website?
A number z is fewer than 34.
Final answer:
The letter 'z' in mathematics can refer to various concepts including complex numbers with arguments measured in degrees, z-scores in statistics indicating deviation from the mean, and as a variable within equations and inequalities.
Explanation:
The concept of 'z' seems to refer to multiple mathematical contexts, including complex numbers, z-scores in statistics, and equations involving z. Specific examples from the information provided include:
Complex numbers where z's argument could be positive or negative, and use of degrees in the context of a circle's 360 degrees showing that -30 and 330 degrees represent the same angle.
The z-score, which measures how many standard deviations a data point is from the mean in statistics, such as z = -4 indicating a data point four standard deviations to the left of the mean.
Equations where z is a variable representing a number, which could be within a certain range or satisfying a given condition.
Understanding these uses of z in the mathematical context allows for precise interpretation of equations, probabilities, and analyses of data sets.
The inequality that represents the statement "A number z is fewer than 34." is: z < 3/4.
How to express the inequality?
The inequality that represents the word sentence "A number z is fewer than 3/4" is z < 3/4.
To explain this, we can compare z to 3/4. If z is smaller than 3/4, we can use the less than symbol (<) to represent this relationship.
So, the inequality is z < 3/4.
For example, if z is 1/2, which is smaller than 3/4, the inequality holds true: 1/2 < 3/4.
Complete question is:
Write the word sentences as an inequality.
A number z is fewer than 3/4.
An inequality that represent this word sentences is?
a rectangle has an area of 156 square inches and a perimeter of 50 in what are the width and the length of the rectangle
Final answer:
To find the length and width of the rectangle with an area of 156 square inches and a perimeter of 50 inches, we can set up and solve a system of equations based on the area and perimeter formulas. After solving, we determine that the length is 13 inches and the width is 12 inches.
Explanation:
The student has asked to find the length and width of a rectangle given that it has an area of 156 square inches and a perimeter of 50 inches. To solve this problem, we need to use the formulas for the area and perimeter of a rectangle.
Area and Perimeter Formulas
Area formula: A = length × width
Perimeter formula: P = 2(length + width)
Let's denote the length as 'l' and the width as 'w'. The area of the rectangle is 156, so we can write:
l × w = 156
The perimeter of the rectangle is 50, so we can write the perimeter formula as:
2(l + w) = 50
This simplifies to:
l + w = 25
Now, we have two equations:
l × w = 156
l + w = 25
We can solve this system of equations by expressing one variable in terms of another. Let's express 'w' in terms of 'l' from the second equation:
w = 25 - l
Now, substitute 'w' in the area equation:
l × (25 - l) = 156
This is a quadratic equation that can be solved to find the values of 'l'. Once we have 'l', we can find 'w' using the second equation.
After solving, we find that the length is 13 inches and the width is 12 inches. Therefore, the rectangle's dimensions are 13 inches by 12 inches.