The perimeter of triangle XYZ is 24 units.
What is the area of triangle XYZ? Round to the nearest
tenth of a square unit.
Trigonometric area formula: Area=1/2absin(C)
o 14.7
square units
14.9 square units
15.0 square units
15.3 square units
Answers
To the nearest tenth, the area of triangle XYZ is approximately 14.7 units².
What is a triangle?A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon.
There are three sides and three angles in every triangle, some of which may be the same.
Triangles can be divided into three groups based on the lengths of their sides, and these groups are as follows: Scalene, Isosceles, and Equilateral.
So, the area of the triangle is:
We know that:
<YXZ = 102°
Length of XY = z = 3
Length of YZ = x = 11
Length of XZ = y = ?
The perimeter of the triangle:
x+y+z = 24 units
Length XZ = y:
11+y+3 = 24
14+y = 24
y = 24 - 14
Therefore, y = 0.
Area of triangle XYZ:
The formula for trigonometric area is area of XYZ = 12(yz)sin X.
Putting values of x, y, and z as follows:
Area of ∆ XYZ = ½×10×3×sin 102
= ½×30×0.9782
= 15 × 0.9782
= 14.673
Therefore, to the nearest tenth, the area of triangle XYZ is approximately 14.7 units².
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Correct question:
What is the area of triangle XYZ? Round to the nearest tenth of a square unit. Trigonometric area formula: Area 14.7 square units 14.9 square units 15.0 square units 15.3 square units
Related Questions
the answer to a multiplication problem is 3 /5 select to see if each statement is true or false
Answers
Part (A):
The value of 3/5 in the decimal form is 0.6 which is less than 1.
Thus, one of the factors of the should be less than 3/5 and other greater than 3/5.
Part (B):
For example take,
2 and 3/10.
The product of 2 and 3/10 is 3/5.
2 is greater than 3/5 and 3/10 is smaller than 3/5.
Which equation represents a circle? (x – 2)222+(y – 3)232=1 (x – 4)232+(y + k)212=1 x222+y222=1 x212+y232=1
Answers
Given:
Four different equations are given
Required:
To tell Which equation represents a circle?
Explanation:
The formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. If a circle is tangent to the x-axis this means it touches the x-axis at that point
[tex]\begin{gathered} \frac{x^2}{2^2}+\frac{y^2}{2^2}=1 \\ \\ x^2+y^2=2^2 \\ \\ so\text{ r =2} \end{gathered}[/tex]That is others are in the form of ellipse equation.
How do you find the general form of an ellipse?
The equation of an ellipse written in the form (x−h)2a2+(y−k)2b2=1. The center is (h,k) and the larger of a and b is the major radius and the smaller is the minor radius.
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]else three options resemble with ellipse equation
Required answer:
[tex]\frac{x^{2}}{2^{2}}+\frac{y^{2}}{2^{2}}=1[/tex]Patricia keeps apples in 3 bins and 2 crates in her store. Each bin can hold no more than 200 pounds. Each crate can hold no more than 50 pounds. Which number line represents all of the possible weights, in pounds, of apples Patricia can keep in her store?
Answers
Given:
The bins can hold no more than w(b) < 200 pounds.
The crate can hold no more than w(c) < 50 pounds.
The number of bins is n(b) = 3.
The number of crates is n(c) = 2.
The objective is to find the correct number line for the graph.
Explanation:
The maximum quantity of bins can be calculated as,
[tex]\begin{gathered} Q(b)The maximum quantity of crate can be calculated as,[tex]\begin{gathered} Q(c)To find the maximum store capacity:The maximum store capacity can be calculated as,
[tex]undefined[/tex]An electronics store purchases laptops for $425.00. They use a markup rate of 60%. How much do they sell the laptop to their customers?
Answers
Given that An electronics store purchases laptops for $425.00.
markup rate of 60%.
Selling price is:
[tex]\begin{gathered} SP=425+(0.60)425 \\ Sp=425+255 \\ SP=680 \end{gathered}[/tex]they sell the laptop to their customers at $680.
10. Use the Distributive Property to solve the equation 3(x - 6) + 6= 5x - 6.
Answers
3(x-6)+6 = 5x-6
Apply distributive property:
3x-18+6= 5x-6
Combine like terms
3x-12 = 5x-6
Move x terms to the right:
3x-5x = -6+12
-2x = 6
divide both sides by -2
x=-3
Write 5e slopes as a fraction or improper fraction using a slash
Answers
Given:
Given a graph of the function.
[tex]\begin{gathered} (x1,y1)=(0,3) \\ (x2,y2)=(-5,0) \end{gathered}[/tex]Required:
To find the slope.
Explanation:
The slope is
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ \\ =\frac{0-3}{-5-0} \\ \\ =\frac{-3}{-5} \\ \\ =\frac{3}{5} \end{gathered}[/tex]The y-intercept is at (0,3).
Final Answer:
The slope is : 3/5.
y-intercept : (0,3)
:) 4 inches of snow in 5 hoursHow much snow fell each hour?
Answers
The amount of snow fell in 5 hours is 4 inches.
To find snow fell in each hour, we divide 4 by 5.
Divide 4 by 5.
[tex]\frac{4}{5}=0.8[/tex]So 0.8 inches of snow fell each hour.
Answer: 0.8 inches
Using the cosine law to determine the measure of we could use _______:
Answers
Solution
- The Cosine law is given below as:
[tex]\begin{gathered} Given\text{ }\triangle ABC,\text{ with sides }a,b,c\text{ and angles }\angle A,\angle B,\angle C\text{ such that} \\ a\text{ is opposite }\angle A \\ b\text{ is opposite }\angle B \\ c\text{ is opposite }\angle C \\ \\ \text{ We have:} \\ a^2=b^2+c^2-2(bc)\cos\angle A \end{gathered}[/tex]- We can make [tex]\begin{gathered} a^2=b^2+c^2-2bc\cos\angle A \\ \text{ Subtract }b^2\text{ and }c^2\text{ from both sides} \\ \\ a^2-b^2-c^2=-2bc\cos\angle A \\ \\ \text{ Divide both sides by }-2bc \\ \cos\angle A=\frac{a^2-b^2-c^2}{-2bc} \\ \text{ } \\ \text{ Take the cos inverse of both sides} \\ \\ \therefore\angle A=\cos^{-1}(\frac{a^2-b^2-c^2}{-2bc}) \end{gathered}[/tex]
Final Answer
The answer is
[tex]\operatorname{\angle}A=\cos^{-1}(\frac{a^{2}-b^{2}-c^{2}}{-2bc})\text{ \lparen OPTION C\rparen}[/tex]How to slove these problems2 7/8 - 15/161 1/5 x 2 1/32 1/5 ./. 4
Answers
The Solution:
Given the following:
[tex]\begin{gathered} 2\frac{7}{8}-\frac{15}{16} \\ \\ 1\frac{1}{5}\times2\frac{1}{3} \\ \\ \frac{2\frac{1}{5}}{4} \end{gathered}[/tex]We are asked to evaluate each of them.
Step 1:
we shall convert each fraction into an improper fraction.
[tex]\frac{23}{8}-\frac{15}{16}[/tex][tex]\frac{46-15}{16}=\frac{31}{16}=1\frac{15}{16}[/tex][tex]\begin{gathered} 1\frac{1}{5}\times2\frac{1}{3} \\ \\ \frac{6}{5}\times\frac{7}{3}=\frac{2\times7}{5}=\frac{14}{5}=2\frac{4}{5} \end{gathered}[/tex][tex]\frac{2\frac{1}{5}}{4}=\frac{\frac{11}{5}}{4}=\frac{11}{5}\times\frac{1}{4}=\frac{11}{20}[/tex]I'm learning about Samples With the Mean Absolute Deviation but I have been having trouble with this type of math could you help me with my math?
Answers
Solution
For 3a)
[tex]\begin{gathered} \frac{30.1}{7.9}=\frac{3.81}{x} \\ \\ \Rightarrow x=\frac{7.9\times3.81}{30.1}=1 \end{gathered}[/tex]Sample W and Sample Z
Find the area A of the polygon with the given vertices. A(-5,-2) , B(4,-2), C(4,-7), D(-5,-7)A=
Answers
The area of the polygon is 45 square units.
From the question, we have
The given points make a rectangle with length AB and width AD.
Distance of AB = 4 - (-5) = 9
Distance of AD = -2 - (-7) = 5.
Area = length x width
Area = 9 x 5 =45 square units.
Area of Rectangle:
The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth. In contrast, the circumference of a rectangle is equal to the product of its four sides. Consequently, we can say that the area of a rectangle equals the space enclosed by its perimeter. The area of a square will, however, be equal to the square of side-length in the case of a square because all of its sides are equal.
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The pH of a fruit juice is 5.3 Find the hydronium ion concentration [H3O+] of the juice. Use the formula pH = -log[H30+]
Answers
Answer:
[tex]\lbrack H_3O^+\rbrack\text{ = }5.0\text{ }\times10^{-6\text{ }}moles\text{ per liter}[/tex]Explanation:
By definition, the pH of a solution is the negative logarithm to base 10 of the concentration of Hydroxonium or oxonium ion
Mathematically, we have this as:
[tex]pH=-log\lbrack H_3O^+\rbrack_{}[/tex]We can change the formula subject so we would have hydroxonium ion on the left
Mathematically, we have this as:
[tex]\lbrack H_3O^+\rbrack\text{ = ANTILOG (-pH)}[/tex]Finally, we have the calculation as follows:
[tex]\lbrack H_3O^+\rbrack\text{ = antilog(-5.3) = }0.000005011872[/tex]In the scientific form,we have this as:
[tex]5.0\text{ }\times10^{-6\text{ }}moles\text{ per liter}[/tex]
Which equation could be used to find how many soft drink refills Ryan ordered
Answers
Solution
We are given
Restaurant charge = $16.99
Soft drink refill charge each = $1.75
Ryan paid = C
Let x denotes the number of soft drink refill Ryan ordered, so we have
[tex]16.99+1.75x=C[/tex]Therefore, the answer is
[tex]1.75x+16.99=C[/tex]Amy and Fraser walk inside a circular lawn. Point O is the center of the lawn, as shown below:
Answers
Answer
Amy walks a distance equal to the diameter, and Frasier walks a distance equal to the radius of the lawn
Step-by-step explanation
Segment BC represents the diameter of the circle (a segment that connects two points on the circle and it passes through the center of the circle).
Segment OA represents the radius of the circle (a segment that connects the center of the circle and a point on the circle)
The following picture has the question that has me troubled can you show me how to get to the answer
Answers
Given that:
[tex]f(x)=\sqrt[]{x},x_0=8,dx=0.07[/tex]Find the change.
[tex]\begin{gathered} \nabla f=f(8+\text{0}.07)-f(8) \\ =f(8.07)-f(8) \\ =\sqrt[]{8.07}-\sqrt[]{8} \\ =0.0123474175 \end{gathered}[/tex]Find the estimate value.
[tex]\begin{gathered} df=\frac{1}{2\sqrt[]{8}}\cdot0.07 \\ =0.0123743687 \end{gathered}[/tex]Determine the approximate error.
[tex]\begin{gathered} |\nabla f-df|=|0.0123474175-0.0123743687| \\ =0.0000269512 \\ \approx0.00002 \end{gathered}[/tex]Option B is correct.
Solve in R Sin (x/4) = √2/2
Answers
Trigonometric Equations
Solve for x in R:
[tex]sin\text{ }\frac{x}{4}=\frac{\sqrt{2}}{2}[/tex]There are two angles whose sine is the given value: 45° and 135°. We need to express them in radians:
[tex]45^o=45\text{ }\frac{\pi}{180}=\frac{\pi}{4}[/tex][tex]135^o=135\frac{\pi}{180}=\frac{3\pi}{4}[/tex]Thus, we have two solutions:
[tex]\begin{gathered} \frac{x}{4}=\frac{\pi}{4} \\ x=\pi \\ And: \\ \frac{x}{4}=\frac{3\pi}{4} \\ x=3\pi \end{gathered}[/tex]Both solutions point to the same terminal angle, so we only have one solution in the first rotation of the angle:
x = π
Since it's required to find the solution for all the real numbers, we must account for all the possible angles in any number of rotations clockwise or counterclockwise as follows:
x = π + 2kπ
Where k is an integer number. For example, for k = 1, we have the already-found solution above x = 3π
Use the six steps in the "Blueprint for Problem Solving" to solve the following word problem. You may recognize the solution by just reading the problem. Use n as the variable for the number and write the equation used to describe the problem.When 8 is subtracted from three times a number, the result is 4. Find the number.Equation: ? The number is ? .
Answers
Let n be the number we don't know.
Three times this number can be express as:
[tex]3n[/tex]The sentence "When 8 is subtracted from three times a number" can be express (using the expression we found before) as:
[tex]3n-8[/tex]Finally we know that this is equal to 4, then we have the equation:
[tex]3n-8=4[/tex]Solving for n we have:
[tex]\begin{gathered} 3n-8=4 \\ 3n=8+4 \\ 3n=12 \\ n=\frac{12}{3} \\ n=4 \end{gathered}[/tex]Therefore the number we are looking for is 4.
Which best explains the transformation of TUV to form T'U'V
Answers
the figure T'U'V' is reflected on the x-axis, therefore is transformed by (x, - y)
answer: the first one
Trey made $2000 in taxable income last year. suppose the income tax rate is 10% for the first $9500 plus 14% for the amount over $9500. How much must trey pay in income tax for last year?
Answers
SInce he made $2000 , and this is less than the limit for the first bracket, Trey will need to pay just 10% on his gain:
10% of $2000 = 0.1 * 2000 = $200.
His tax is $200.
which one of these must be a correct congruence statement
Answers
Answer:
C. AB ≅ DE
Explanation:
If triangles ABC and DEF are similar, then the following holds:
[tex]\begin{gathered} \angle A\cong\angle D \\ \angle B\cong\angle E \\ \angle C\cong\angle F \end{gathered}[/tex]Likewise, the similar sides are:
[tex]\begin{gathered} AB\cong DE \\ AC\cong DF \\ BC\cong EF \end{gathered}[/tex]The correct choice is C.
through: (5, 5), slope = 10
Answers
Answer: The correct answer is y = 10x – 45
Step-by-step explanation:
When graphing a line with a slope of 10 from point (5,5), we find that the y-intercept (where the line crosses the y-axis) is -45
Use the slope-intercept form (y=mx+b), where m=slope (10) and b=the y-intercept (-45)
y = 10x - 45
The length of an arc of a circle is 5/3 pi feet. Find the measure of the angle that subtends (forms)the arc if the diameter is 18 feet.
Answers
EXPLANATION
We are given the following parameters:
Length of arc= 5/3pi
Diameter = 18 feet
Therefore, radius =18/2 = 9 feets
The formula for the length of the arc is given below.
[tex]\text{length of arc =}\frac{\theta}{360}\times2\pi r^{}[/tex]We will substitute the given parameters into the formula above to get the measure of the angle.
[tex]\begin{gathered} \frac{5}{3}\pi=\frac{\theta}{360}2\pi\times9^{} \\ \frac{5}{3}\pi=\frac{18\theta}{360}\pi \\ crossmultiply\text{ } \\ 3\times18\theta\pi=360\times5\pi \\ 54\theta\pi=1800\pi \\ \text{Divide both sides by 54}\pi \\ \theta=\frac{1800\pi}{54\pi} \\ \theta=33.3^0 \end{gathered}[/tex]Therefore, the measure of the angle is
[tex]\theta=33.3^0[/tex]7/5-6/5+3/2=17/10=1 7/10
Answers
Question:
Solution:
Let us denote by x the blank space in the given equation. Then, we get:
[tex]\frac{7}{5}-x+\frac{3}{2}=\frac{6}{5}[/tex]this is equivalent to:
[tex]\frac{7}{5}+\frac{3}{2}-x=\frac{6}{5}[/tex]this is equivalent to:
[tex]\frac{14+15}{10}-x=\frac{6}{5}[/tex]that is:
[tex]\frac{29}{10}-x=\frac{6}{5}[/tex]solving for x, we obtain:
[tex]\frac{29}{10}-\frac{6}{5}=x[/tex]that is:
[tex]x=\frac{29}{10}-\frac{6}{5}=\frac{29-12}{10}=\frac{17}{10}[/tex]so that, the blank space would be:
[tex]\frac{17}{10}[/tex]and the complete expression would be:
[tex]\frac{7}{5}-\frac{17}{10}+\frac{3}{2}=\frac{6}{5}[/tex]In the coordinate plane the vertices of angle RST are R(6,-1) S(1,-4) and T(-5,6). Prove that angle RST is a right triangle. State the coordinates of point P such that quadrilateral RSTP is a rectangle. Prove that your quadrilateral RSTP is a rectangle.
Answers
We are given coordinates of three points RST and are asked to prove that it forms a Right Triangle.
We kn
Calculate the density of the cube.240 grams4 cm3 cm5 cm
Answers
Answer:
4 g / cm^2
Explanation:
The density is defined is
[tex]p=\frac{M}{V}[/tex]where m is the mass of the object and V is its volume.
Now in our case, we see that the cube weighs M = 240 g and has a volume of
[tex]V=3\operatorname{cm}\times5\operatorname{cm}\times4\operatorname{cm}=60\operatorname{cm}^3[/tex]With the value of M and V in hand, we now calculate the density
[tex]p=\frac{240g}{60\operatorname{cm}^3}[/tex][tex]p=\frac{40g}{\operatorname{cm}^3}[/tex]which is our answer!
Find the reference angle for 342°. 1) 35°2) 5°3) 18°4) 162°
Answers
For an angle a in the fourth quadrant, the reference angle is given by:
360º - a
The angles in the fourth quadrant are those between 270º and 360º. So, 342º is in the fourth quadrant, and its reference angle is:
360º - 342º = 18º
Therefore, the third option is correct.
how many marriage licenses were issued in 2006 ? round answer to the nearest hundred
Answers
To solve the exercise we have to replace the value requested on the equation given to model the problem as above
[tex]y=3.4905(2006)^2-17674(2006)+21533000=124853.658[/tex]As we see and approximating the result to the options, we get that the correct answer is the second one (124900)
1. (4x3.5x2 + 3) + (2x3 - 5x²)
Answers
Then
4x3.5x2 = 28
28 + 3 = 31
31 + 2x3= 37
and so answer is
=37 - 5x^2
Suppose a jar contains 20 red marbles and 31 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
Answers
The probability that they are both are red is 0.15.
What is probability?Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true.
The jar contains 20 red marbles and 31 blue marbles. The total marble is 51.
Therefore, the probability will be:
= P(red) × P(red)
= 20/51 × 19/50
= 380 / 2550
= 0.15
The probability is 0.15.
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Fill in the table using function rule
Y=6x+2
Answers
Using our equation y = 6x + 2, we were able to write out values for our table of function.
Function TableA function table is a table that shows which coordinates should be plotted in the coordinate system, so that you can draw the graph of the function.
Since we have our equation, we can proceed to find what values of y we would have when x is in a certain condition.
Using from -2 to + 5, we can have a good table of function.
When x = -2
y = 6x + 2
y = 6(-2) + 2 = -10
When x = -1
y = 6(-1) + 2 = -4
When x = 0
y = 6(0) + 2 = 2
When x = 1
y = 6(1) + 2 = 8
When x = 2
y = 6(2) + 2 = 14
When x = 3
y = 6(3) + 2 = 20
When x = 4
y = 6(4) + 2 = 26
When x = 5
y = 6(5) + 2 = 32
Using the values above, we have a good function table and can proceed to plot a graph if needed.
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