Alice needs to classify her garden quadrilateral to determine if it is suitable for a specific species of flowers. She finds the sides equal in length and consecutive angles supplementary, which leads her to conclude the garden plot is a rhombus, meeting the criteria for her flowers.
Alice designs a garden plot in the shape of a quadrilateral. She knows that for a certain species of flower to grow optimally, her garden must have a specific shape: it needs to be a parallelogram with equal sides but not necessarily equal angles. In order to classify the quadrilateral of her garden, she begins by measuring the sides and finds that they are all of equal length. Then she measures the angles and finds that consecutive angles are supplementary, which means their measures add up to 180 degrees.
To determine if the quadrilateral meets the criteria for the species of flowers, she must classify her garden plot based on her measurements. Is Alice's garden a rectangle, a square, a rhombus, or a parallelogram with unequal angles?
Since the sides of the quadrilateral are all equal and the consecutive angles are supplementary, Alice can conclude that her garden plot is a rhombus, which is a type of parallelogram with all sides equal in length and opposite angles equal. Thus, it fulfills the requirements for her special species of flowers.
A rectangular room is 14 feet by 20 feet. The ceiling is 8 feet high. How do you find the length and width of the smaller and larger wall?
We need to visualize the box by using a diagram attached with this problem.
[tex] Length = 14 \; feet [/tex]
[tex] Width = 20 \; feet [/tex]
[tex] Height = 8 \; feet [/tex]
The blue is smaller rectangle and brown is the larger rectangle
Conclusion:
Length of smaller wall (in blue color) is 14 feet
Width of smaller wall (in blue color) is 8 feet
Length of Larger wall (in brown color) is 20 feet
Width of the Larger wall (in brown color) is 8 feet
10 POINTS AND BRAINLIEST FOR CORRECT ANSWER!
A rectangle is inscribed in a square so that each vertex of the rectangle is located on one side of the square, and the sides of the rectangle are parallel to the diagonals of the square. Suppose that one side of the rectangle is twice the length of the other and that the diagonal of the square is 12 meters long. Find the sides of the rectangle.
9514 1404 393
Answer:
The sides of the rectangle are 4 and 8 meters long.
Explanation:
Please consider the attached figure. Both the rectangle and the square are symmetrical about the x- and y-axes, so we only need to consider the corner of the rectangle in one quadrant.
If the rectangle is twice as long as wide, then the distance of the corner to one axis (we chose y) will be twice the distance to the other axis. The locus of points for which that is true is the line with slope 1/2. The corner of the rectangle will be on that line.
If the corner of the rectangle is also on the square, then it will be located at the point of intersection of the line with slope 1/2 and the line representing the edge of the square. That point of intersection is the point (4, 2) on this graph. That is, half the length of the rectangle is 4 m, and half the width is 2 m. This indicates the sides of the rectangle are 8 m and 4 m in length.
__
The diagonals of the square are 12 m long, so orienting the square the way we have makes the x- and y-intercepts 6 units from the origin in each quadrant.
Answer:
Step-by-step explanation:
four and eight, use soh cah toa
Suppose f and g are continuous functions such that g(3) = 6 and lim x → 3 [3f(x) + f(x)g(x)] = 54. find f(3).
When f and g are continuous functions such that g(3) = 6 and lim x → 3 [3f(x) + f(x)g(x)] = 54 the value of f(3) is 6.
Rewrite the given limit as: lim x→3 [3f(x) + f(x)g(x)] = lim x→3 [3f(x)] + lim x→3 [f(x)g(x)]
Substitute the limits using continuity: 54 = 3 lim x→3 f(x) + lim x→3 f(x) ⋅ lim x→3 g(x) 54 = 3f(3) + f(3) ⋅ 6 (since lim x→3 f(x) = f(3) and lim x→3 g(x) = 6)
Combine like terms: 54 = 9f(3)
Divide both sides by 9: f(3) = 6
Therefore, f(3) = 6.
Can you solve the measure of an angle is twenty-nine times the measure of a supplementary angle. what is the measure of each angle
Please help! The question is attached. And also I know the numbers on the triangle are blurry. The number on the long bottom of the triangle is 24, the one in the corner of the bottom of the triangle is 90 degrees, the side length is 18, and the diagonal angle is 26.
Tara and julia run a race. Julia takes 42 seconds to run the race. She is 7 seconds faster than Tara. How many seconds does Tara take?
Sara left home and drove East 12 miles to Bakersville for her friends birthday cake then she drove 10 miles south to a friends house how far apart is Sarah's friends house and Sarah's house
What is the x-coordinate for the minimum point in the function f(x) = 4 cos(2x − π) from x = 0 to x = 2π?
675,360.41 in expanded notation
The expanded notation of 675,360.41 is 6 * 100000 + 7* 10000 + 5 * 1000 + 3 * 100 + 6 * 10 + 0 * 1 + 4 * 0.1 + 1 * 0.01
How to rewrite the number?The number is given as:
Number = 675,360.41
Express the numbers using their place values
Number = 6 * 100000 + 7* 10000 + 5 * 1000 + 3 * 100 + 6 * 10 + 0 * 1 + 4 * 0.1 + 1 * 0.01
The above expression represents the expanded notation
Hence, the expanded notation of 675,360.41 is 6 * 100000 + 7* 10000 + 5 * 1000 + 3 * 100 + 6 * 10 + 0 * 1 + 4 * 0.1 + 1 * 0.01
Read more about expanded notation at:
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how many triangles have the following measurements? A=38, a=432, b=382
Using the Law of Sines, we determined that it is possible to form one triangle with the given measurements A=38°, a=432, and b=382. The calculation includes finding angle B and angle C, ensuring all triangle conditions are met.
To determine how many triangles can have the given measurements (A=38°, a=432, b=382), we need to check if these values satisfy the triangle inequalities and if they can form a possible triangle using the Law of Sines.
First, let's use the Law of Sines which states that:
sin(A)/a = sin(B)/b = sin(C)/c
Given:
A = 38° (angle)a = 432 (side opposite to angle A)b = 382 (side opposite to angle B)We can calculate angle B using:
sin(B) = (b × sin(A)) / a
sin(B) = (382 × sin(38°)) / 432 ≈ 0.556
Finding the arc sine of 0.556, we get:
B ≈ 33.8°
Now, we find angle C:
C = 180° - A - B ≈ 180° - 38° - 33.8° = 108.2°
Using the Law of Sines again to find side c:
c = (a × sin(C)) / sin(A)
c = (432 × sin(108.2°)) / sin(38°) ≈ 676.85
Thus, it's possible to form one such triangle with the given conditions.
What is the area of a sector with a central angle of 4pi/3 radians and a radius of 11cm
Use 3.14 for pi and round to the nearest hundredth
can anyone give an explanation and answer to this question,my sister needed help on this also :) Thank you again for taking your time to answer and read this <3
what is the circumference of a circular pond with a radius of 14 meters?
According to the Fundamental Theorem of Algebra, which polynomial function has exactly 11 roots?
A ) f(x) = (x - 1)(x + 1)^11
B ) f(x) = (x + 2)^3(x^2 -7x +3)^4
C ) f(x) = (x^5 + 7x + 14)^6
D ) f(x) = 11x^5 + 5x + 25
I originally chose A, but that was incorrect on my quiz.
Answer:
The correct answer is B
Step-by-step explanation:
What is a simpler form of the radical expression square root of 36g^6?
glacier is moving at a rate of 0.3 inches every hour. The table below represents this relationship.Glacial Movement
Distance Moved (inches)
Time
(hours)
0.3
1
0.6
2
0.9
3
x
4
What value of x completes the table?
1.2
1.5
3.6
13.3
Answer:
The correct option is 1.
Step-by-step explanation:
It is given that the glacier is moving at a rate of 0.3 inches every hour. It means the average rate of change is 0.3.
Let d is the total moved distance of glacier and t is number of hours. Then the total moved distance of glacier after t hours is defined as
[tex]d=0.3t[/tex]
At t=1,
[tex]d=0.3(1)=0.3[/tex]
At t=2,
[tex]d=0.3(2)=0.6[/tex]
At t=3,
[tex]d=0.3(3)=0.9[/tex]
At t=4,
[tex]d=0.3(4)=1.2[/tex]
Total moved distance of glacier after 4 hours is 1.2 inches.
The value of x is 1.2. Therefore the correct option is 1.
a car travels 450 miles in the same time that a motorcycle travels 390 miles. if the car’s speed is 10 miles per hour more than the motorcycle’s, find the speed of the car and the speed of the motorcycle.
the speed of the motorcycle is ___ mph.
the speed of the car is ___ mph
What is the value of x in the quadrilateral shown below?
A. 80°
B. 70°
C. 60°
a taxi company charges passengers $2.00 for a ride, no matter how long the ride is, and an additional $0.20 for each mile traveled. the rule c=0.20m + 2.00 describe the relationship between the number of miles m and the total cost of the ride c.
To make a profit, a company’s revenue must be greater than its operating costs. The company’s revenue is modeled by the expression 7.5x – 100, where x represents the number of items sold. The company’s operation costs are modeled by the expression 79.86 + 5.8x. How many items does the company need to sell to make a profit? The inequality that will determine the number of items that need to be sold to make a profit is ? The solution to the inequality is ? The company must sell at least? items to make a profit.
Using the profit concept, it is found that:
The inequality is: [tex]1.7x - 179.6 > 0[/tex]The solution is [tex]x > 105.6[/tex]The company must sell at least 106 items to make a profit.Profit is revenue subtracted by operations costs, that is:
[tex]P(x) = R(x) - C(x)[/tex]
In this problem, the functions are:
[tex]R(x) = 7.5x - 100[/tex]
[tex]C(s) = 79.6 + 5.8x[/tex]
Thus, the profit function is:
[tex]P(x) = R(x) - C(x)[/tex]
[tex]P(x) = 7.5x - 100 - 79.6 - 5.8x[/tex]
[tex]P(x) = 1.7x - 179.6[/tex]
It makes a profit if:
[tex]P(x) > 0[/tex]
Thus, the inequality is:
[tex]1.7x - 179.6 > 0[/tex]
The solution is:
[tex]1.7x > 179.6[/tex]
[tex]x > \frac{179.6}{1.7}[/tex]
[tex]x > 105.6[/tex]
Thus, the company must sell at least 106 items to make a profit.
A similar problem is given at https://brainly.com/question/24373628
If the radius of a circle is 18 yd, then the diameter of the circle is 9 yd
TRUE OR FALSE
Answer:
Step-by-step explanation: False.
Rylie's gross paycheck amount is $1305.60. She has 4% deducted from her paychecks for her 401(k). Her employer matches her deduction, up to 4%.
How mach is deducted from her paycheck for retirement plan?
A) $26.11
B) $52.22
C) $104.44
D) $522.24
The deduction from her paycheck is 52 dollars and 22 cents. Then the correct option is B.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
Rylie's gross paycheck amount is $1305.60. She has 4% deducted from her paychecks for her 401(k). Her employer matches her deduction, up to 4%.
So the deduction will be given as
[tex]\rm Deduction = \dfrac{4}{100} *1305.6\\\\Deduction = 0.04 * 1305.6\\\\Deduction = 52.224 \approx 52.22[/tex]
The deduction from her paycheck is 52 dollars and 22 cents. Then the correct option is B.
More about the percentage link is given below.
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Are the two expressions equivalent when x = 20?
8(12x + 4)
96x + 32
The solution of the two expressions for x = 20 will be equivalent.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the two expressions are 8(12x + 4) and 96x + 32. The expressions will be solved as,
8(12x + 4) = 8[12(20) + 4 ] = 1952
96x + 32 = 96 (20) + 32 = 1952
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What is the solution of the system?
{ 2x+y=15
{x−y=3
Enter your answer in the boxes.
(__ ,__ )
Hannah has $1000 in her savings account. During 1 month , she withdraws $25. Each successive month, she withdraws $10 more than the previous month . How much remains in her savings account after 10 months ?
Answer: A-$300 is correct
Find the value of x and the value
A: x=20,y=45
B:x=45,y=20
C:x=60,y=120
D:x=90,y=60
What's the difference between residential heating and cooling systems and commercial/industrial heating, cooling, or refrigerating facilities? A. The amount of energy the building or facility uses B. The location of the system—in a home or a business C. The number of people that occupy the building or facility D. The size of the building or facility
What is the measure of AC ? Enter your answer in the box. ° Circle with inscribed angle A B C. Angle A B C is 3 x minus 1.5 degrees. The intercepted arc A C is 3 x plus 9 degrees.
Use the Inscribed Angle theorem to get the measure of AC. The intercepted arc AC is [tex]21^{\circ}[/tex].
Given,
The inscribed angle [tex]\angle ABC[/tex] is [tex]3x-1.5[/tex].
And the Intercepted arc AC is [tex]3x+9[/tex].
What is the Inscribed Angle theorem?We know that, Inscribed Angle Theorem stated that the measure of an inscribed angle is half the measure of the intercepted arc.
So,
[tex]3x-1.5=\frac{1}{2} (3x+9)[/tex]
[tex]2 (3x-1.5)=3x+9[/tex]
[tex]6x-3.0=3x+9[/tex]
[tex]6x-3x=9+3[/tex]
[tex]3x=12\\x=4[/tex]
Since the intercepted arc AC is [tex]3x+9[/tex], putting the value of [tex]x=4[/tex] we get,
intercepted arc AC is [tex]21^{\circ}[/tex].
Hence the intercepted arc AC is [tex]21^{\circ}[/tex].
For more details on the Inscribed Angle theorem follow the link:
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What is the approximate area of the circle shown below 3.5cm
Answer:
D. 38.5 cm²
Step-by-step explanation:
The area of a circle is given by:
A = πr²
where r is the radius of the circle.
From the given figure,
Radius of the circle is r = 3.5 cm.
Therefore, the area of the circle is:
⇒A = 3.14 × (3.5 cm)² = 38.5 cm²
Thus, the correct option is D.
m ∠ U = (2x−5)° and m ∠W = (x+38)°What is m ∠W?
Question 1 options:
49°
180°
87°
90°
(HURRY!!! GET 24 PTS) The residential colony has a population of 5400 requires 60 liters of water is per person per day. For the effective utilization of rain water, a group of people decided for WATER HARVESTING. They constructed a water reservoir measuring 49mx27mx25m to collect the rain water. It this water reservoirs is full of water then for how many days it will last for the colony?
what he said hope it helped
Step-by-step explanation: