Answer:
16.39 square units.
Step-by-step explanation:
The parametric equations x = sin t and y = 3 cos t describe a curve in the xy-plane known as an ellipse.
To see this, we can use the Pythagorean identity for sine and cosine:
sin^2 t + cos^2 t = 1
Multiplying both sides by 9, we get:
9 sin^2 t + 9 cos^2 t = 9
Substituting x = sin t and y = 3 cos t, we get:
9 x^2 + y^2/3 = 9
This is the equation of an ellipse centered at the origin with semi-axes a = 3 and b = sqrt(3), where a is the length of the horizontal semi-axis and b is the length of the vertical semi-axis.
The area of an ellipse is given by the formula:
Area = pi * a * b
Substituting the values of a and b, we get:
Area = pi * 3 * sqrt(3) ≈ 16.39
Therefore, the area of the ellipse described by the parametric equations x = sin t and y = 3 cos t is approximately 16.39 square units.
HELP!!!!!!!!!!!!!!!!!
What did I do wrong on 6,7, and 8??
Once there is an answer… Please no one else answer!
The transformation in words for picture 6 is a rotation of 90° counterclockwise or 90° counterclockwise rotation.
The algebraic rule for the above transformation is (x, y) → (-y, x).
The transformation in words for picture 7 is a reflection across the line x = -3.
The algebraic rule for the above transformation is [tex]Ref_{x=-3} \triangle ABC[/tex].
The transformation in words for picture 8 is a reflection across the x-axis.
The algebraic rule for the above transformation is (x, y) → (x, -y).
What is a rotation?In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).
By applying a rotation of 90° counterclockwise to the vertices of quadrilateral RSTUVW, the coordinates of W of the image is as follows:
(x, y) → (-y, x)
Ordered pair W = (-1, 3) → Ordered pair R' = (-(3), -1) = (-3, -1).
What is a reflection?In Mathematics and Geometry, a reflection over the x-axis is modeled by this transformation rule (x, y) → (x, -y). Therefore, a reflection over the x-axis would maintain the same x-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.
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1. A group of armed forces personnel were surveyed. The branch of
service was recorded in the chart below.
27%
12%
Branch of Service
Army
Navy
What percent of the whole group are in the Navy?
A
26%
Marine Corps
Air Force
Coast Guard
Number of Members
165
135
60
130
10
The percent of the whole group are in the Navy is 27%.
How to calculate the percentagePercent is a term used to express a fraction or a ratio out of 100. It is represented by the symbol "%". For example, if there are 20 red balls out of a total of 100 balls, we can say that the percentage of red balls is 20%.
To calculate the percentage, we can use the following formula:
Percentage = (Part / Whole) x 100
where "Part" is the value we want to express as a percentage, and "Whole" is the total value.
The percent of the whole group are in the Navy is:
= 135/500 × 100
= 27%.
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Answer:
27%
Step-by-step explanation:
135 of the 500 total members are in the Navy. Meaning that 135 out of 500 is 27%
Is this quadrilateral a parallelogram?
Answer:
Yes it is a parallelogram because opposite sides of this quadrilateral are equal.
I really need help with this to find x value and need reasons
Answer:
x = 45 degrees
Step-by-step explanation:
All angles in a triangle will add up to 180 degrees. So far we have 57 degree of 180. We also see a supplementary angle, with one side being 102 degrees, so the other is 78 degrees, because it must add up to 180. We see that the arrows in the bases show that the corners are even, so now we know two corners: one with 57 degrees and the other with 78.
Now, follow this equation to find x:
57 + 78 + x = 180
135 + x = 180
-135 -135
x = 45
Find the slope of the line that contains these points.
(1, -3) (2, -5)
use slope equation -5 - (-3)/(2-1) then solve
The committee spends $462 on costumes for 24 people. Each costume costs the same amount of money.
How much did each costume cost, in dollars?
Answer:
Step-by-step explanation: 462 Divided by 24 = 19.25$
Proof: 19.25 x 24 = 462
Answer: 19.25$
Write an equation that you can use to solve for x.
Three lines intersect at the same point. Two of the lines intersect at a 90 degree angle. The third line divides one of the right angles into two adjacent angles. One of the adjacent angles is labeled 63 degrees and the other adjacent angle is labeled x degrees
Answer:
Ok so we know it has to equal=180 right?
90+90=180
180/4
45
5 pts
It's time to remodel your home! You'd like to replace the tile in your kitchen. The room is 12'x20' with
8' ceilings. The tile costs $4.75 per square foot. How much will it cost?
If the room is 12'x20' with 8' ceilings and the tile costs $4.75 per square foot, the total cost is $1140.
To calculate the cost of replacing the tile in the kitchen, we need to first calculate the total area of the floor.
Area of the floor = Length x Width = 12 ft x 20 ft = 240 sq ft
Since we know the cost per square foot of tile, we can now multiply the total area of the floor by the cost per square foot to find the total cost:
Total cost = Area of the floor x Cost per square foot
Total cost = 240 sq ft x $4.75/sq ft
Total cost = $1140
Therefore, it will cost $1140 to replace the tile in the kitchen, assuming there are no additional costs such as labor or materials for removing the old tile.
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A graph has weight (ounces) on the x-axis, and cost (dollars) on the y-axis. A line labeled gold starts at (0, O) and has a positive slope. A line marked platinum starts at (0, 0) and has a greater positive slope than gold.
Gold costs ---------------- platinum per ounce because the ----------- of the graph for gold is
- ----------that of the chart for platinum.
The --------of the graph tells you the unit rate in
Gold costs less than platinum per ounce because the slope of the graph for gold is less steeper than that of the chart for platinum. The slope of the graph tells you the unit rate in dollars.
What is a steeper slope?In Mathematics, a steeper slope simply means that the slope of a line is bigger than the slope of another line. This ultimately implies that, a graph with a steeper slope has a greater (faster) rate of change in comparison with another graph.
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
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I’m in 4th period and it’s almost over with in 3 minutes please help!!
-3x-24 ≤-36
Answer:
-3x - 24 < -36
-3x < -12
x > 4
01. Resuelve: (4x² + 8x +12) + (5x² − 3x + 6) =
02. Evalúa: 5-21 + (-3) (2) =
03. Evalúa la expresión: (-3) (-2) (-1) (4) =
04. 18+ 3x = 27, el valor de x es:
05. Evalúa: 3² + 4 (3)² =
1. Por lo tanto, la suma de las dos expresiones es 9x² + 5x + 18.
2. Por lo tanto, el resultado de la expresión es -22.
3. Por lo tanto, el resultado de la expresión es 24.
4. Por lo tanto, el valor de x es 3.
5. Por lo tanto, el resultado de la expresión es 45.
¿Cuál es la expresión?1. Para sumar las dos expresiones, simplemente sumamos los términos semejantes:
(4x² + 8x +12) + (5x² − 3x + 6) = 9x² + 5x + 18
Por lo tanto, la suma de las dos expresiones es 9x² + 5x + 18.
2. Evaluando la expresión numérica:
5 - 21 + (-3) (2) = 5 - 21 + (-6)
Luego, sumamos los términos:
= -16 - 6 = -22
Por lo tanto, el resultado de la expresión es -22.
3. Evaluando la expresión numérica:
(-3) (-2) (-1) (4) = 24
Por lo tanto, el resultado de la expresión es 24.
4. Para encontrar el valor de x, debemos despejarlo de la ecuación:
18 + 3x = 27
Restando 18 de ambos lados, obtenemos:
3x = 9
Dividiendo ambos lados por 3, obtenemos:
x = 3
Por lo tanto, el valor de x es 3.
5. Evaluando la expresión numérica:
3² + 4 (3)² = 3² + 4 (9)
Primero elevamos al cuadrado 3, luego multiplicamos 4 por 9 y sumamos ambos términos:
= 9 + 36
Por lo tanto, el resultado de la expresión es 45.
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Jenny mixed 4 kg of mixed nuts containing 16% peanuts with 12 kg of mixed nuts containing 40% peanuts. What percent of the new mixture if peanuts?
A. 34%
B. 17%
C. 13%
The new mixture contains 34% peanuts.
How to calculate percent of the new mixture if peanutsUsing a weighted average approach.
Let x be the percentage of peanuts in the new mixture. Then we can set up the following equation:
(0.16)(4) + (0.40)(12) = x(4 + 12)
simplifying the equation, we get:
0.64 + 4.8 = 16x
5.44 = 16x
x = 0.34 or 34%
Therefore, the new mixture contains 34% peanuts.
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Answer please and thank you
Answer:
Step-by-step explanation
The answer is 72. 2 x 36 equals 72.
find the values of variables, then find the lengths of the sides of each quadrilateral
The variables are as follows:
x = 4
y = 4.8
The lengths of the sides of the kites are 4.5 and 6.8 units.
How to find the side of a kite?A kite is a quadrilateral with 2 pairs of consecutive congruent sides. The diagonals are perpendicular in a kite.
The non vertex angles are congruent.
Therefore,
x + 0.5 = 2x - 3.5
2x - x = 0.5 + 3.5
x = 4
y + 2 = 2y - 2.8
2y - y = 2 + 2.8
y = 4.8
Hence,
length of one pair = 4 + 0.5 = 4.5 units
length of the other pair = 4.8 + 2 = 6.8 units
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Factor Special Polynomials:
Factor each of the following expressions, please
Answer:
2) [tex](3x+2)^{2}[/tex]
3) [tex](2x+5)(2x-5)[/tex]
4) [tex](x^{2} +8)(x^{2} -8)[/tex]
Step-by-step explanation:
A method I was taught was the snowflake method whenever there were numbers in front of [tex]x^{2}[/tex] (ex [tex]4x^{2} and 9x^{2}[/tex]) picture shown below (you can search up some videos if you would like)
The snowflake method is really efficient and helps factor polynomials faster
For 3 and 4, you basically have to find the square root of the number without the [tex]x^{2}[/tex] and make sure (for example 25) one parenthesis had -5 and the other had +5. Number 4 had [tex]x^{4}[/tex], [tex]x^{2}*x^{2}[/tex] is [tex]x^{4}[/tex] so you would include that in the equation. To double check, use foil.
this. please look at photo fir ref
The coordinates of point H' include the following: H' (0, -1).
What is a translation?In Mathematics, the translation a geometric figure or graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image while the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.
By translating the pre-image of this trapezoid vertically downward by 2 units and horizontally right by 3 units, the coordinates of the image include the following:
(x, y) → (x + 3, y - 2)
E(-1, 4) → (-1 + 3, 4 - 2) = E' (2, 2).
H (-3, 1) → (-3 + 3, 1 - 2) = H' (0, -1).
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An American football field is 120 yards long, including the end zones. How long is that in inches?
The length of an American football field including end zones is 21600 inches.
How many inches is a 120-yard football field?To convert yards to inches, we multiply by 36, since there are 36 inches in one yard.
Therefore, a football field that is 120 yards long is equivalent to 120 x 36: = 4320 feet. To convert feet to inches, we multiply by 12, since there are 12 inches in one foot.
Therefore, a 120-yard football field is equivalent to 4320 x 12 = 51,840 inches. However, we must also take into account the two end zones, which are each 10 yards long, or 360 inches. Thus, the total length of an American football field including the end zones is 120 x 36 x 12 + 2 x 360 = 21,600 inches.
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PLSSS HELPP
This figure represents the base of a fish tank that is 8 inches high.
What is the volume of the fish tank?
Responses
378 in³
378 in³
408 in³
408 in³
480 in³
480 in³
768 in³
The volume of the fish tank is 408in³
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
The volume of regular object is given as;
V = base area × height
base area = 13 × 6
= 78in²
The area of the cut out section = 1/2(a+b) h
= 1/2 × (3+6) × 6
= 9× 3 = 27in²
The actual area of the base shown = 78-27
= 51 in²
therefore the volume of the tank will be
V = 51 × 8
= 408in³
therefore the volume of the tank is 408in³
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1) You're traveling to Spain this
summer. You'll have $200 to spend on
memorabilia items. How much euros
do you have to spend on memorabilia
items? Note: $1=0.84 E
Using the conversion factor we know that we will spend 180.69€ on memorabilia items.
What is the conversion factor?A conversion factor is a number that is used to multiply or divide one set of units into another.
If a conversion is required, it must be done using the correct conversion factor to get an identical value.
A fraction that is equal to "1" is a conversion factor.
The numerator and denominator are the same amounts, but they are expressed in different units. It is used to change a number's unit of measurement.
By multiplying the initial number by the fraction that is equal to "1," you can change the units without changing the original number's value.
So, in the given situation:
$200 = euros?
We know that:
$1 = 0.90€
Then,
$200 = 180.69€
Therefore, using the conversion factor we know that we will spend 180.69€ on memorabilia items.
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Chairs need to be set up for the audience members. You want to use. the fewest number of chairs and still meet these three additional condions.
• There are 23 rows of chairs.
• There are the same number of chairs in esch row.
• There are an even number of chairs in cads rom.
Based on the number of students expected to attend, design a plan to set up the chairs. State how many total chairs there are, and explain why your plan meets these conditions.
There must be 46 chairs in each row and total number of chairs are 1058
To meet the given conditions, we need to find a number that has the following properties:
It should be divisible by 2, as there are an even number of chairs in each row.
It should be divisible by 23, as there are 23 rows of chairs.
It should be the same number in each row.
The smallest number that satisfies these conditions is 46, which is the least common multiple of 2 and 23.
So, we need to set up 46 chairs in each row.
The total number of chairs required will be:
Total number of chairs = 23 rows x 46 chairs per row = 1058 chairs
Hence, the total number of chairs are 1058
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Find the missing measurements in the triangle.
Angles should be to the nearest degree.
Side lengths should be rounded to the nearest tenth.
Answer: angle b= 63
Ac= 23.6
Ab=26.4
Step-by-step explanation:
angle b= 63
Ac= 23.6
Ab=26.4
Angle B is 63 degrees, the length of AC is approximately 22.23 units, and the length of AB is approximately 26.42 units.
What is right angle triangle?
A triangle in which one of its angles measures 90 degrees is called a right-angled triangle .
The side opposite the right angle is called the hypotenuse while the other two sides are called the legs or the adjacent and opposite sides.
According to given figure angle C is a right angle, we know that the sum of angles A and B must be 90 degrees.
So, angle B = 90 - angle A = 90 - 27 = 63 degrees.
To find the length of AC, we can use trigonometry. Since we know the length of the opposite side (BC) and the angle opposite the side we want to find (angle A), we can use the tangent function:
tan A = opposite / adjacent
tan 27 = BC / AC
AC = BC / tan 27
AC = 12 / tan 27
AC ≈ 22.23
Now,
[tex]AB^2 = AC^2 + BC^2 \\ AB^2 = 22.23^2 + 12^2 \\ AB^2 ≈ 697.57 \\ AB ≈ 26.42[/tex]
Therefore, Angle B is 63 degrees, the length of AC is approximately 22.23 units, and the length of AB is approximately 26.42 units.
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Please help !!
i only need help with the second problem which is:
5. For 0≤x≤ 6, express g(x) in terms of x. Do not include +C in your final answer.
Your help is very appreciated !!
From the calculation, g increases on the interval [-3, 6) and for 0 ≤ x ≤ 6, g(x) = 6 - 1/2(x-2)^2.
What is the interval that g increases?To determine where g is increasing, we need to find where its derivative, g'(x), is positive. We can find g'(x) by differentiating g(x) with respect to x:
g'(x) = f(x)
Since f(x) is a piecewise-defined function, we need to consider each interval separately.
For -3 ≤ x < 0, f(x) = 3, so g'(x) = 3, which is positive.For 0 ≤ x ≤ 6, f(x) = -x + 3, which is a decreasing function, so g'(x) is also decreasing. However, since f(x) is always non-negative on this interval, g'(x) is non-negative as well.For 6 < x ≤ 9, f(x) = -3, so g'(x) = -3, which is negative.Therefore, g is increasing on the interval [-3, 6).
To justify this, note that g'(x) = 0 at x = 0 and x = 6, where g has local maxima. This means that g is increasing on the intervals (-3, 0) and (0, 6) and decreasing on (6, 9]. Since g is continuous, it cannot have any jumps, so it must be increasing or decreasing on each of these intervals. Since g(-3) = 0 and g(6) = 9, we know that g is increasing on the interval [-3, 6).
We can evaluate g(x) on the interval [0, 6] by integrating f(x) with respect to t from -2 to x:
g(x) = ∫_{-2}^{x} f(t) dt
On the interval [-3, 0), f(t) = 3, so we have:
g(x) = ∫_{-2}^{0} 3 dt + ∫_{0}^{x} (-t + 3) dt
Simplifying the integrals, we get:
g(x) = 6 - 1/2(x-2)^2, for 0 ≤ x ≤ 6
(Note that we can drop the "+C" since it's being evaluated at the limits of integration.)
Therefore, for 0 ≤ x ≤ 6, g(x) = 6 - 1/2(x-2)^2.
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Is anyone good at “describe linear and nonlinear function” please help ASAP!
Answer:
A
If u plug it into desmos u get a straight line
**HELP**
Intersecting Line Plots
⭐️VIEW PHOTO⭐️
A line plot for the data is shown in the image attached below.
What is a line plot?In Mathematics and Statistics, a line plot can be defined as a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.
In this scenario and exercise, we would use an online graphing calculator to graphically represent the given data set on a line plot as shown in the image attached below.
In conclusion, we can reasonably infer and logically deduce that the mode of the data set is equal to 3.5 or 3 1/2 because it has the highest frequency of 5.
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Make x the subject of y=3+2^x+1
Answer:
y=3+2 to the power of x +1
Step-by-step explanation:
Gabriella is 53 5/6
inches tall. Sheila is 1 1/3
inches shorter than Gabriella and Jane is 1 1/4
inches shorter than Sheila. How tall is Jane?
Find m∠MQN. help me on this one.
Answer:
Vertically opposite angles are always same.
Straight angle=180°
Angle MQN=70°
pls help thank u i dont no what im doing
Answer:5,4
Step-by-step explanation:
simplify the following equation
Answer:
the required answer is √5-√6
Identify the line that appears tangent to circle O and includes point B.
Answer:
D. Line O
Step-by-step explanation:
We can simply tell which one it is by looking at the picture. A tangent line is a line that intersects at one point only. Line L doesn't even touch the circle. Line M and N touch the circle in more than one place. If we look at O, we can see that it is "scraping" the edge of the circle, which is what pretty much every tangent line looks like.
Therefore, the answer is D.