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Use triangle XYZ to answer the questions
Use special right triangles to help find the length of segment XY. What is the exact base of triangle XYZ?
What is the exact area of triangle XYZ? Leave your answer in RADICAL terms
What is the area of triangle XYZ to the nearest tenth of a Square feet
Answers
The trigonometric function gives the ratio of different sides of a right-angle triangle. The area of the triangle is 55.4256 ft².
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
For the given triangle the length of AB and BC can be written as,
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Sin(30^o) = \dfrac{AB}{AC}\\\\\\AB = Sin(30^o) \times 16 \\\\\\AB=8\rm\ ft[/tex]
[tex]Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Cos(30^o) = \dfrac{BC}{AC}\\\\\\BC = Cos(30^o) \times AC\\\\\\BC = 13.8564\rm\ ft[/tex]
Now, the area of the triangle is,
Area of triangle = 0.5× 8 × 13.8564 = 55.4256 ft²
Hence, the area of the triangle is 55.4256 ft².
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Related Questions
what is pemdas? algebra 1
Answers
Answer:
p=Parentheses
e=Exponents
m=Multiplication
d=Division
a=Addition
s=Subtraction
its an order of solving a equation
Please help to prove parallelogram.
Answers
The question requests proof that WV = VR. See the definition of Mathematical proof and the explanation for the proof below.
What is a mathematical proof?Mathematical proof refers to the steps of logical arguments which are given to show that a mathematical statement is true or correct.
What is the proof that WV = VR?Note that SR ║ QT;Reason: This is given. The image is a parallelogram.
Hence, ∠PSR = ∠WVPReason: Alternate angles formed by two parallel lines crossing each otherHence, SV = PVReason: This is given by the annotation on the imageTherefore: ΔSVR ≅ PVWReason: They are formed by two parallel lines crossing each other.
Therefore if ΔSVR ≅ PVW;
Then WV = VR.
QED.
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Pls answer this for. I need it now ASAP, thanks
create a feature writing article on the topic "Parallel lines: Nature's beauty". Including an explanation/proof why the lines are parallel and insights
Answers
The angle between two parallel lines is zero, we can prove it by putting the value of tanθ as 0.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
As we know, parallel lines in geometry are co-planar straight lines that do not cross at any point. Parallel planes are planes that never meet in the same three-dimensional space. Curves that do not touch or contact each other and maintain a constant minimum distance are known as parallel curves.
We know that the angle between two parallel lines is zero degrees.
[tex]\rm tan\theta = \dfrac{m_1-m_2}{1+m_1m_2}[/tex]
tanθ = 0
m1 = m2
Thus, the angle between two parallel lines is zero we can prove it by putting the value of tanθ as 0.
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Given that the expression x³_ ax² + bx+c leaves the same remainder when divided by x + 1 or x-2, find 'a' in terms of 'b'.
Answers
Answer:
Hi,
a=b+3
Step-by-step explanation:
[tex]\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=-1&&-1&a+1&-a-b-1\\---&---&---&---&---\\&1&-a-1&a+b+1&c-a-b-1\\\end{array}[/tex]
[tex]\begin{array}{c||c|c|c|c}&x^3&x^2&x&1\\---&---&---&---&---\\&1&-a&b&c\\x=2&&2&4-2a&2b+8-4a\\---&---&---&---&---\\&1&2-a&b+4-2a&c+2b+8-4a\\\end{array}[/tex]
Thus:
c+2b+8-4a=c-a-b-1
3b-3a=-9
a=b+3
Use the long division method to find the result when 2 x 3 + 3 x 2 + 17 x + 8 2x 3 +3x 2 +17x+8 is divided by 2 x + 1 2x+1.
Answers
The following table shows the total number of quizzes taken in high school. how many quizzes are taken per week?
Answers
If a doctor prescribes 75 milligrams of a specific drug to her patient how many milligrams of the drug will remain in the patients bloodstream after 6 hours if the drug decays at a rate of 20 percent per hour
Answers
After 6 hours the drug remains is 19.66 mg if the drug decays at a rate of 20 percent per hour.
What is exponential decay?During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.
We have:
If a doctor prescribes 75 milligrams of a specific drug to her patient how many milligrams of the drug will remain in the patients' bloodstream.
We know the exponential decay can be given as:
D = a(1 - r)ⁿ
a is the starting value and n is the number of hours.
D = 75(1 - 0.20)⁶
D = 19.66 milligrams
Thus, the after 6 hours the drug remains is 19.66 mg if the drug decays at a rate of 20 percent per hour.
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grapes cost $1.68 a pound. If you buy 2.5 pounds,how much will it cost?
Answers
Answer:
Step-by-step explanation:
we know that
Solve for x
so
therefore
The number of pounds of apples is 4.5 and the number of pounds of grapes is 2.5
You have 6 different colored balloons. In how many distinct ways can the balloons be ordered?
Select one:
a.
720
b.
365
c.
5040
d.
120
Answers
Answer: a. 720
Step-by-step explanation:
You have 6 different sticks to choose from for the first stick. Then there are 5 for the second (6 - 1 = 5), then 4 for the third (5 - 1 = 4), etc all the way to the last stick.
Mathematically, this can be shown with 6!. In other words, 6 factorial.
6 * 5 * 4 * 3 * 2 * 1 = 720
The answer to our question is:
a. 720
Use the Pythagorean Theorem to find the m
14.1
X
X=
14.7
Answers
Answer:
x = 4.2
Step-by-step explanation:
14.1² + x² = 14.7²
198.81 + x² = 216.09
216.09 - 198.81 = 17.28
√17.28 = 4.15
x = 4.15
Round to nearest tenth
x = 4.2
Please help me solve this composite shape step by step
Answers
Answer:
73 cm²
Step-by-step explanation:
Areas and volumes of composite figures are found by dividing the figure into shapes you have formulas for. Sometimes that will be a sum of shapes, and sometimes it will involve the difference of shapes.
__
setupThis shape can be decomposed into two rectangles by extending the horizontal line. (This is the dashed line shown in the attachment.)
The width of the top rectangle will be the sum of the lengths of the labeled horizontal segments:
4 cm + 5 cm + 3 cm = 12 cm
The height of the top rectangle, and the dimensions of the bottom rectangle (square) are shown in the given figure.
The area of each rectangle is the product of its width and height.
A = WH
__
solutiontop rectangle area = WH = (12 cm)(4 cm) = 48 cm²
bottom rectangle area = WH = (5 cm)(5 cm) = 25 cm²
Area = top rectangle area + bottom rectangle area = (48 cm²) +(25 cm²)
Area = 73 cm²
The area of this composite shape is 73 cm².
_____
Additional comment
The figure will fit into a rectangle that is 9 cm high by 12 cm wide. From that rectangle, a rectangle 5 cm high and 4 cm wide is removed from the lower left, and a rectangle 5 cm high and 3 cm wide is removed from the lower right. Figuring the area this way, we find it to be ...
figure area = bounding rectangle area - removed areas
= (9 cm)(12 cm) -(5 cm)(4 cm) -(5 cm)(3 cm) = 108 cm² -20 cm² -15 cm²
= 73 cm²
Find the median of the following data : 9, 15, 17, 18,6, 20, 8, 5, 18, 18, 10, 5, 14, 12, 10, 7
Answers
Answer:
The median of the data is 12.
Step-by-step explanation:
The median is really just another word for the average. To find that, you add all of the numbers and divide that sum by the number of numbers there are.
9+15+17+18+6+20+8+5+18+18+10+5+14+12+10+7=192
There are 16 numbers in this data set. So, we will divide the sum by 16.
192÷16=12
I hope this helps!! :)
The midterm score of 45 is the decide
Answers
The midterm score of 45 is the 3rd decile, meaning that 42% of the Senior High School students scored below this test.
What is a decile?Deciles are a type of percentile that divides data into groups of 10%. That is, each decile comprises 10% of the dataset.
To determine the decile, sort the data from lowest to highest. Now, divide the result by ten. This number reflects the no. of observed values within each decile.
Sorting the data from lowest to highest, we have:
37, 43, 45, 61, 63, 74, 75, 76, 82, 87, 89, 98, 99, 100= 14/10
= 1.4
Thus, each decile contains only a 1.4 score.
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Tomás bought a new car for $41,000. If the value of the car depreciates by 17% each year, determine the value
of his car in 9 years.
Answers
This is a means of reducing the cost of a goods or an asset over time. The value of the car after 9 years is approximately $888
DepreciationThis is a means of reducing the cost of a goods or an asset over time.
Mathematically, the cost of goods after a particular year is expressed as:
P(t) = P0e^-rt
Given
P0 = $41000rate r = 17% = 0.17time t = 9 yearsSubstitute
P(17) = 41000r^0.17(9)
P(17) = 4100(0.21653)
P(17) = 887.79
Hence the value of the car after 9 years is approximately $888
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A pie has a diameter of 9 inches. each slice of the pie has a central angle of 45 degrees. What is the area of each slice of pie?
Answers
Area of sector
Ø/360×πr²45/360×π(4.5)²1/8×π(20.25)7.95in²option B
Answer:
b
Step-by-step explanation:
The area of a sector is (the angle) over 360 multiplied by pi (radius) squared
This would be 45/360 pi (4.5) squared, resulting in option b.
Which polygon has 11 sides
Answers
Answer:
Hendecagon
Step-by-step explanation:
a hendecagon has 11 sides
Answer:
Hendecagon
Step-by-step explanation:
It has 11 sides, 11 corners, and 11 angles inside the shape that equal to 1620 degrees
What is the area of the trapezoid shown? The figure is not drawn to scale.
284.31 in.²
303.75 in.²
568.62 in.²
607.5 in.2
Answers
The area of the trapezoid is 284.31 square inches
How to determine the area?The area of a trapezoid is:
Area = 0.5 * (Sum of parallel sides) * height
Using the given figure, we have:
Area = 0.5 * (17 + 31.6) * 11.7
Evaluate
Area = 284.31
Hence, the area of the trapezoid is 284.31 square inches
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Which function has a vertex at (2, 6)?
f(x) = 2x21 - 6
f(x) = 2|x2| +6
f(x) = 2x + 2+ 6
f(x) = 2x + 2 - 6
Answers
The function f(x) = 2|x – 2| + 6 has a vertex at (2, 6) option second is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function that has vertex at (2, 6)
The options are:
f(x) = 2|x – 2| – 6
f(x) = 2|x – 2| + 6
f(x) = 2|x + 2| + 6
f(x) = 2|x + 2| – 6
As we know the vertex form of a quadratic function is given by:
f(x) = a(x - h)² + k
Similarly, mod function can be expressed as:
m(x) = a|x - h| + k
Here (h, k) is the vertex of a function.
In the function:
f(x) = 2|x – 2| + 6
The vertex of the function is (2, 6)
Thus, the function f(x) = 2|x – 2| + 6 has a vertex at (2, 6) option second is correct.
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I need help on this urgently please thank you
Answers
Answer:
g(x) = -√(x+6)
Step-by-step explanation:
The inverse of the function y = f(x) can be found by solving for y the relation x = f(y).
__
solve for yx = f(y)
x = y^2 -6
x +6 = y^2 . . . . . . add 6
-√(x +6) = y . . . . . negative square root
The negative root produces y ≤ 0, equivalent to x ≤ 0 for f(x).
The inverse of f is g(x) = -√(x +6).
_____
Additional comment
The graph of a function and its inverse are mirror images of each other across the line y=x. This is shown in the attachment for the f(x) and g(x) in this problem.
a
ОЈ
6(3+2d) = 54
I need that answer
Answers
Answer:
d = 3
Step-by-step explanation:
6*3=18
2d*6=12d
54-18 = 12d
36/12 = 12d/12
d = 3
Answer:
d = 3
Step-by-step explanation:
6 ( 3 + 2d ) = 54
First, solve the brackets.
18 + 12d = 54
Take 18 to the right side.
12d = 54 - 18
12d = 36
Divide both sides by 12.
d = 3
Write an equation that represents the line.
Answers
Step-by-step explanation:
a general line equation is
y = ax + b
"a" being the slope is the line, "b" being the y-intercept (the y value when x = 0).
we see from the 2 marked points (by we could choose any points on the line) that
y changes by 2 units, when x changes by 3 units.
so the slope is 2/3.
we use one point (1, 2) to solve for b
2 = 2/3 × 1 + b = 2/3 + b
6/3 = 2/3 + b
4/3 = b
and the full equation is
y = 2/3 x + 4/3
Helpppppp asappppp pls
Show your work
I’ll give brainliest!!!!!!
Answers
Answer: 3360 ft squared
Step-by-step explanation:
Short side : 30 x 14 = 420
Long side 30 x 3 x 14 = 1260
420 + 420 + 1260 + 1260 = 3360
pls give brainliest
have a nice day
Choose the triangle that seems to be congruent to △AEC.
△BFC
△ABD
△EFD
Answers
Explanation: There’s no thinking in this, because you can use your eyes to look for the answer. Not all questions will have this type of question. But they do seem pretty similar to me.
What is the rotation that translates AWXY to AW'X'Y'? Be sure to give the degre
measure AND direction of rotation.
Please help !!!
Answers
The rotation that that translates AWXY to AW'X'Y' is a 45° anticlockwise rotation. See the attached image for details.
What is a rotation in math?Rotation in math refers to the change in the angle of a geometric shape around a central axis on a point on the geometric plane such that it's original coordinates are modified but it's size or shape.
Hence, it is correct to state that The rotation that that translates AWXY to AW'X'Y' is a 45° anticlockwise rotation.
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which function is increasing on the interval (-∞, ∞)
Answers
Differentiating each function, we have for all x, unless otherwise indicated,
[tex]h(x) = 2^x - 1 \implies h'(x) = \ln(2) \, 2^x > 0[/tex]
[tex]g(x) = -4 (2^x) \implies g'(x) = -4 \ln(2) \, 2^x < 0[/tex]
[tex]f(x) = -3x+7 \implies f'(x) = -3 < 0[/tex]
[tex]j(x) = x^2 + 8x + 1 \implies j'(x) = 2x + 8 > 0 \text{ only when } x > -4[/tex]
and only h(x) has a strictly positive derivative. (A)
Help please thanksssssssssss
Answers
Answer:
what is your from my from is province philippines
In the discussion board, post the coordinates of the center point and the radius of a circle.
Answers
Step-by-step explanation:
coordinates of center is 0,0 there are no hints given to find radius
12.A circle has a radius of 3.8 feet. Which measurement is closest to the circumference of
the circle in feet?
A. 23.8 ft
B. 45.3 ft
C. 47.7 ft
D. 11.9 ft
Answers
Circumference = 2 x radius x PI
Circumference = 2 x 3.8 x 3.14
Circumference = 23.86
answer: the closest one is A. 23.8 FT.
Which inequality represents the number line: Number line with points marked for eighteen, nineteen, twenty, twenty one, twenty two, twenty three. The twenty two point is marked with an open circle pointing left. x < 22 x ≤ 22 x ≥ 22 x > 22
Answers
The inequality which represents this is x ≥ 22 , Option C is the right answer.
What is an Inequality ?When two algebraic expressions are equated using an inequality operator, <, > etc then the expression formed is called Inequality.
IT is given in the question that
There is a number line , with points marked for eighteen, nineteen, twenty, twenty one, twenty two, twenty three.
The twenty two point is marked with an open circle pointing left
The inequality which represents this is
x ≥ 22 , Option C is the right answer.
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which expression is not equivalent to -1.5(-6m+8n).
Answers
Answer:
D
Step-by-step explanation:
-1.5(-6m+8n) = 9m-12n
3(3m -4n) = 9m - 12n
9m -12n = 9m -12n
-6(-1.5m +2n) = 9m - 12n
-2(-4.5m+ 4n) = 9m - 8n
Answer: D. -2(-4.5m + 4n)
Step-by-step explanation:
First, let us simplify -1.5(-6m+8n).
Given:
-1.5(-6m + 8n)
Distribute:
9m - 12n
[A] ✗
9 /3 = 3 and 12 / 3 = 4
This means that 3(3m - 4n) = 9m - 12n = -1.5(-6m+8n)
Option A is not our answer.
[B] ✗
Using this simplified version we did above, option B is not our answer as 9m - 12n = 9m - 12n and 9m - 12n = -1.5(-6m+8n).
[C] ✗
We will distribute option C to see if we reach the same expression. Seeing below, we do, so option C is not our answer.
-6(-1.5m + 2n)
9m - 12n
[D] ✓
Since none of the other options are correct, the answer to your question D because it is not equivalent.
Answer:
D. -2(-4.5m + 4n)