Final answer:
The lengths of the three sides of the triangular plot are 600 feet for the shortest side, 800 feet for the middle side, and 1000 feet for the longest side.
Explanation:
To find the lengths of the three sides of the triangular plot, let's define the shortest side as x. Therefore, according to the problem statement, the longest side would be 2x - 200 feet and the middle side would be (2x - 200) - 200 = 2x - 400 feet. The perimeter of the triangle is the sum of all its sides, which is given as 2400 feet.
The equation representing the perimeter of the triangle is:
x + (2x - 200) + (2x - 400) = 2400
Simplifying the equation, we get:
5x - 600 = 2400
Adding 600 to both sides:
5x = 3000
Dividing by 5 gives us:
x = 600
Thus, the shortest side is 600 feet, the longest side is 2(600) - 200 = 1000 feet, and the middle side is 1000 - 200 = 800 feet.
The lengths of the three sides of the triangular plot are 600 feet, 800 feet, and 1000 feet respectively.
what subset of real numbers does 26 belong to
Ravi is driving 440 miles to visit his grandma. if he drives at an average rate of 55miles per hour, how many hours will it take him to get 3/4 of the way there?
Answer:
Using formula:
[tex]\text{Time} = \frac{\text{Distance}}{\text{Speed}}[/tex]
As per the statement:
Ravi is driving 440 miles to visit his grandma. if he drives at an average rate of 55 miles per hour.
⇒Speed = 55 miles/hour and Distance = 440 miles.
We have to find how many hours will it take him to get 3/4 of the way there.
Distance to get 3/4 of the way there= [tex]\frac{3}{4} \cdot 440 = 3 \cdot 110 = 330[/tex] miles.
Substitute the given values we have;
[tex]\text{Time} = \frac{330}{55}[/tex]
Simplify:
Time = 6 hours.
Therefore, 6 hours will it take him to get 3/4 of the way there
Donte simplified the expression below.
4(1 + 3i) – (8 – 5i) = –4 + 8i
What mistake did Donte make?
A.He did not apply the distributive property correctly for 4(1 + 3i).
B.He did not distribute the subtraction sign correctly for 8 – 5i.
C.He added the real number and coefficient of i in 4(1 + 3i).
D.He added the two complex numbers instead of subtracted.
Solve –2x2 – 16x – 44 = 0
answer please using quadtratic equation ...?
Answer: x=-4 + or - i square root of 6
Katie cut out a rectangular piece of wrapping paper that was 2 times as long and 3 times as wide as the box that she was wrapping. the box was 5 inches long and 4 inch's wide. what is the perimeter of the wrapping paper that katie cut?
What percent of 20 is 40??
The gift shop at manatee mall was having a clearance sale. everything was marked down 30%. the original price of a manatee hat was $18. what is the clearance price?
Answer
Find out the what is the clearance price .
To prove
As given
The gift shop at manatee mall was having a clearance sale.
everything was marked down 30%.
The original price of a manatee hat was $18.
30% is written in the decimal form
[tex]= \frac{30}{100}[/tex]
= 0.30
Than
The clearance price = 18 - 0.30 × 18
= 18 - 5.4
= $12.6
Therefore the clearance price be $12.6 .
You have 10 fish, 5 drown, 3 come
back to life. How many fish do you have? ...?
The sum of two numbers is 26. When the second number is subtracted from the first number, the difference is 10. Find the two numbers.
Which ordered pairs are solutions to the inequality 2x + y > −4?
Select each correct answer.
A. (−3, 0)
B. (0, 1)
C. (−1, −1)
D. (5, −12)
E. (4, −12)
Using a new lawn mower, Abby can mow the lawn in 2 hours. Her sister Carla used an older lawn mower and takes 3 hours to mow the same lawn. How long will it take them if they work together?
Factor completely 3x3 + 12x2 + 18x.
x2 + 4x + 6
3(x3 + 4x2 + 6x)
3x(x2 + 4x + 6)
x(3x2 + 12x + 18)
Factor of [tex]3x^{3} + 12x^{2} + 18x[/tex] is [tex]3x ( x^{2} +4x + 6 )[/tex].
Here,
We have to find factor of [tex]3x^{3} + 12x^{2} + 18x[/tex].
What is Factor?
A number or algebraic expression that divides another number or expression evenly with no remainder.
Now,
Factor of [tex]3x^{3} + 12x^{2} + 18x[/tex] is,
⇒[tex]3x^{3} + 12x^{2} + 18x = 3x (x^{2} + 4x + 6x)[/tex]
Hence,
Factor of [tex]3x^{3} + 12x^{2} + 18x[/tex] is [tex]3x ( x^{2} +4x + 6 )[/tex].
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Identify the explanatory and response variables in the following situation:
There is a strong positive correlation between latitude above the equator and number of hours of daylight on June 21.
A. Explanatory: Latitude
Response: Average temperature
B. Explanatory: Daylight hours
Response: Latitude
C. Explanatory: Time of year
Response: Daylight hours
D. Explanatory: Latitude
Response: Daylight hours
Simplify √24
A 3√8
B 2√12
C 2√6
D 4√6
Bill started west on road U.S. 50, riding a bicycle at an average rate of 9 mph. Four hours later Charles started after Bill on a motor cycle and overtook him in 2 hours. What was Charles' rate?
Which equation could be used to solve for Charles' rate if it is represented by x?
A.2x = 36
B.2x = 54
C.6x = 54
Answer: 2x = 54
I got this question correct on my lesson.
To find Charles' rate, we can set up an equation using the formula Distance = Rate x Time. The correct equation to solve for Charles' rate x is 2x = 36.
Explanation:To solve this problem, we can use the equation Distance = Rate x Time. Let's assume that Charles' rate is represented by x. When Charles overtakes Bill, they have traveled the same distance. Bill has been riding for 4 hours at a rate of 9 mph, so his distance is 9 x 4 = 36 miles. Charles overtakes Bill in 2 hours, so his distance is x x 2. Setting the two distances equal to each other, we have 36 = 2x, which simplifies to 2x = 36. Therefore, the correct equation to solve for Charles' rate x is option A, 2x = 36.
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turn 4√5 into an entire radical (unsimplify), the process
To turn 4√5 into an entire radical, the expression is rewritten as a single radical expression, √80, by identifying that 4 is a perfect square (4²), and multiplying it by the number inside the original radical (5) to get the product under one radical sign.
To turn 4√5 into an entire radical, we need to rewrite it as a single radical expression, effectively reversing the process of simplifying radicals. Let's start by recognizing that 4 is a perfect square and can be written as 4². So, we have 4 (the square root of 5), which can be expressed as √(4² × 5).
Here are the steps to convert 4√5 into an entire radical:
Identify the square of the number outside the radical: 4² = 16.
Multiply the square by the number inside the radical: 16 × 5 = 80.
Write the product under a single radical sign: √80.
Now, the expression 4√5 has been turned into an entire radical, √80.
What is the solution to the equation? 3q 5 = -2q 20
a. q = 3
b. q = 5
c. q = 15
d. q = 25
4. In an A-frame house, the two congruent sides extend from the ground to form a 34° angle at the peak. What angle does each side form with the ground? (1 point)
156°
146°
73°
78°
True or False
5. All right triangles are isosceles. (1 point)
true
false
14. What does CPCTC represent and when would you use it? (4 points)
1) 2x + 35 = 180° so x= 180 - 35 / 2 =73°
the answer is 73°
2)
3) In geometry, "Corresponding parts of congruent triangles are congruent" (CPCTC) is a succinct statement of a theorem regarding congruent trigonometry, defined as triangles either of which is an isometry of the other. CPCTC states that if two or more triangles are congruent, then all of their corresponding angles and sides are congruent as well. CPCTC is useful in proving various theorems about triangles and other polygons.
If triangles ABC and DEF are congruent, denoted as
Final answer:
Each congruent side of the A-frame house forms a 73° angle with the ground, and the statement that all right triangles are isosceles is false. CPCTC is a geometric theorem that states corresponding parts of congruent triangles are congruent.
Explanation:
Angles in an A-frame house
The given A-frame house forms an isosceles triangle with a peak angle of 34°. Using the theorem that the sum of angles in a triangle is 180°, we can calculate the angles each side forms with the ground. Since the two congruent sides are equal, the angles they form with the ground are also equal. There are two steps to solve this:
Subtract the peak angle from 180° to find the sum of the two base angles: 180° - 34° = 146°.
Divide the sum of the base angles by 2 (since they are equal in an isosceles triangle): 146° / 2 = 73°.
Therefore, each side forms a 73° angle with the ground.
All right triangles are isosceles - True or False?
This statement is false. Not all right triangles are isosceles. A right triangle is defined as having one 90° angle, but it doesn't necessarily have two sides of equal length, which would make it isosceles.
What does CPCTC represent?
CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent. It is a theorem used in geometry to conclude that the corresponding parts (angles or sides) of two triangles are congruent, given that the triangles themselves are proven to be congruent based on certain criteria like side-angle-side (SAS) or angle-side-angle (ASA).
How many faces, edges, and vertices does a triangular pyramid have?
A. 3 faces, 4 edges, 4 vertices
B. 3 faces, 3 edges, 3 vertices
C. 4 faces, 6 edges, 3 vertices
D. 4 faces, 6 edges, 4 vertices
A student is training for the track team during the first three months of the year by running for 30 minutes every day while averaging 5 miles each day. Select the graph that correctly shows the total miles ran during the time of his training program.
Answer:
Graph 2 :)
Step-by-step explanation:
Jordan scores 6 points for every touchdown he makes. This season he has scored 18 touchdowns. Write a number sentence using the variable t to represent the number of points Joran scored this season.
Answer:
18 times 6= t
Step-by-step explanation:
Intr un oras sunt 235 de blocuri cu 8 etaje si cu 177 mai multe blocuri cu 4 etaje.Formuleaza intrebarea pentru a rezolva problema astfel
The Greens want to put an addition on their house 18 months from now. They will need to save $10,620 in order to achieve this goal. They set aside the same amount each month, and after a year discover they have saved $6,120. The Greens must adjust their plan in order to meet their goal, so they came up with the following optionsa.Only option A will allow them to meet their goal.b.Only option B will allow them to meet their goal.c.Both options A and B will allow them to meet their goal.d.Neither option A nor option B will allow them to meet their goal.
What is the approximate circumference of the circle shown below?
A.102.4 cm
B. 63.4 cm
C. 25.6 cm
D. 51.2 cm
Answer
Formula
[tex]Circumference\ of\ circle = 2\pi r[/tex]
where r is the radius of a circle.
As shown in the image
Diameter of the circle = 16 .3 cm
[tex]Radius\ of\ the\ circle = \frac{16.3}{2}[/tex]
= 8.15 cm
Put in the formula
[tex]Circumference\ of\ circle = 2\pi\times 8.15[/tex]
As
[tex]\pi = 3.14[/tex]
[tex]Circumference\ of\ circle = 2\times 3.14\times 8.15[/tex]
= 51.2 cm (approx)
Therefore the circumference of a circle is 51.2cm (approx) .
Option (D) is correct .
The circumference of the circle [tex]\boxed{51.2{\text{ cm}}}.[/tex] Option (D) is correct.
Further explanation:
The formula for the circumference of the circle can be expressed as follows,
[tex]\boxed{{\text{Circumference of circle}} = 2\pi r}[/tex]
The formula for the area of the circle can be expressed as follows,
[tex]\boxed{{\text{Area of circle}} = \pi {r^2}}[/tex]
Here, “r” represents the radius of the circle.
The relationship between the radius and the diameter can be given by,
[tex]\boxed{r =\dfrac{d}{2}}[/tex]
Here, “d” represents the diameter of the circle.
Given:
The options are as follows.
A.[tex]102.4{\text{ cm}}[/tex]
B.[tex]63.4{\text{ cm}}[/tex]
C.[tex]25.6{\text{ cm}}[/tex]
D.[tex]51.2{\text{ cm}}[/tex]
Explanation:
The diameter of the circle is [tex]16.3{\text{ cm}}.[/tex]
The radius of the circle can be obtained as follows,
[tex]\begin{aligned}{\text{Radius}}&= \frac{{16.3}}{2}\\&= 8.15\\\end{aligned}[/tex]
The radius of the circle is [tex]8.15{\text{ cm}}.[/tex]
The circumference of the circle can be obtained as follows,
[tex]\begin{aligned}{\text{Circumference of circle}}&= 2\times\frac{{22}}{7}\times 8.15\\&=\frac{{44}}{7}\times 8.15\\&= 51.2\\\end{aligned}[/tex]
The circumference of the circle [tex]\boxed{51.2{\text{ cm}}}[/tex].Option (D) is correct.
Option (A) is not correct as the circumference of the circleis .
Option (B) is not correct as the circumference of the circle is .
Option (C) is not correct as the circumference of the circle is .
Option (D) is correct as the circumference of the circle is .
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Circle
Keywords: Circle, circumference, radius, diameter, area of the circle, angle, sector, arc, approximate.
Complete these ordered pairs for this equation.
What is the value of p in the equation x2 = 12y?
What is √6/√5 in simplest radical form?
Hi i know this is late like by 2 years but for future people the answer is
[tex]\frac{\sqrt{30} }{\sqrt{5} }[/tex]
hope this helps other ppl
What assumption must be made about the sun rays if you use this method of determining the circumference of a large sphere?
Aditi has $50.00 in her wallet. She buys a shirt for $12.00 and also wants to buy some bracelets that are on sale for $0.60 each. The inequality below relates x, the number of bracelets she can buy, with her shirt purchase and the money in her wallet.
What is the greatest number of bracelets she could buy?
Answer:
The answer is 63.
Step-by-step explanation:
50-12=38 38/.6 is equal to 63.333 you can't buy .333 of a bracelet so she will be able to buy 63 and have little money left.
The greatest number of bracelets she could buy will be 63.
What is the definition of inequality?Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.
Given data;
The total amount of money in my wallet = $50.00
Cost of shirt = $12.00
Price of bracelet per piece = $0.60
Let x is the no of the bracelet;
The equation obtained as;
⇒The total amount of money in my wallet = Cost of the shirt + Price of the bracelet per piece × No of the bracelet
⇒50 = 12 + 0.60 x
⇒0.60 x = 50-12
⇒x = 38/0.60
⇒x= 63.333 ≈ 63 bracelet
Hence the greatest number of bracelets she could buy will be 63.
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look for the horizontal asymptote of
(sin x)/(1 + cos x).