Given ABC below, with m B=25°, a = 9, and c = 16, find the area of the triangle.
Answers
It is given that the sides of the triangle are a =9 and c=16 . The angle is given mB=25 degree.
The area of triangle is determined as
[tex]A=\frac{1}{2}a\times c\times\sin B[/tex][tex]A=\frac{1}{2}\times9\times16\times\sin 25=72\sin 25^{\circ}[/tex][tex]A=30.428sq\mathrm{}\text{unit}[/tex]Thus the area of triangle is 30.428 sq.unit.
Related Questions
in a public opinion poll 624 people from a sample of 1100 indicated they would vote for specific candidate how many votes can the candidate expect to receive from a population of 40000
Answers
Hello!
In a sample of 1100 people, the specific candidate got 624 votes. So, we can write it as 624/1100.
And if the total of voters is 40,000, how many votes this specific candidate will receive? We can write it as x/40,000.
Now, let's equal both fractions look:
[tex]\begin{gathered} \frac{624}{1100}=\frac{x}{40000} \\ \\ 1100x=624\times40000 \\ 1100x=24960000 \\ x=\frac{24960000}{1100} \\ \\ x\cong22691 \end{gathered}[/tex]Answer:Approximately 22691 votes.
what are the three terms and 4x - 2y + 3
Answers
Solution
We have the following expression:
[tex]4x-2y+3[/tex]Here we have 3 terms:
[tex]4x,\text{ -2y and 3}[/tex]Variable terms:
[tex]4x,-2y[/tex]Constant term
[tex]3[/tex]Solve the following system of equation using substitution4x + 2y = 10x - y= 13What is the solution for y?
Answers
ANSWER
y = -7
EXPLANATION
To solve using the substitution method we have to clear x from one of the equations as a function of y. For example, for equation 2:
[tex]x=13+y[/tex]Then replace x in the first equation by this expression:
[tex]4(13+y)+2y=10[/tex]And solve for y:
[tex]\begin{gathered} 4\cdot13+4y+2y=10 \\ 52+6y=10 \\ 6y=10-52 \\ 6y=-42 \\ y=\frac{-42}{6} \\ y=-7 \end{gathered}[/tex]In the picture below, measure 1 is 5x-14 degrees and measure 3 is 2x+10 degrees. Find measure 2.
Answers
SOLUTION:
Step 1:
In this question, we have the following:
In the picture below, measure 1 is (5x-14) degrees and measure 3 is (2x+10) degrees.
Find the measure of 2.
Step 2:
From the diagram, we can see that angles 1 and 3 are vertically opposite and they are also equal.
Based on this fact, we can see that:
[tex]\begin{gathered} \angle\text{1 = }\angle3 \\ (\text{ 5 x- 14 ) = ( 2x + 10 )} \\ \text{collecting like terms, we have that:} \\ 5x\text{ - 2x = 10 + 14} \\ \text{3 x = 24} \end{gathered}[/tex]Divide both sides, we have that:
[tex]\begin{gathered} x\text{ =}\frac{24}{3} \\ \text{x = 8 } \end{gathered}[/tex]Then, we put x = 8 into the equation for Angle 1 , we have that:
[tex]\angle1=(5x-14)=5(8)-14=40-14=26^0[/tex][tex]\angle3=(2x+10)=2(8)+10=16+10=26^0[/tex]Hence, we can see that Angles 1 and 3 are equal.
Step 3:
From the diagram, we can see that:
we can see that angles 2 and 4 are vertically opposite and they are also equal.
Recall that angles 1 and 3 are also vertically opposite and they are also equal.
Therefore, we can see that:
[tex]\begin{gathered} \angle2\text{ = p} \\ \angle4\text{ = p} \\ \angle1\text{ = }26^0 \\ \angle3=26^0 \\ \text{Then, we have that:} \\ p+p+26^0+26^{\text{ 0 }}=360^0\text{ ( Sum of angles at a point)} \\ 2p+52^0=360^0 \\ 2p=360^0-52^0 \end{gathered}[/tex]Divide both sides by 2, we have that:
[tex]\begin{gathered} 2p=308^0 \\ p\text{ =}\frac{308^0}{2} \\ p=154^0 \end{gathered}[/tex]CONCLUSION:
[tex]\begin{gathered} \operatorname{Re}call\text{ that }\angle2\text{ = p} \\ \text{Then, we have that:} \\ \angle2=154^0 \end{gathered}[/tex]Solve the following system of linear equations using elimination. x-y=5 -x-y=-11
Answers
Elimination Method : In the elimination method you either add or subtract the equations to get an equation in one variable. When the coefficients of one variable are opposites you add the equations to eliminate a variable and when the coefficients of one variable are equal you subtract the equations to eliminate a variable.
The given system of equation :
x - y = 5 ( 1 )
- x - y = - 11 ( 2 )
Add the equation ( 1 ) & ( 2 )
x - y + ( -x - y ) = 5 + ( -11 )
x - y -x - y = 5 - 11
x - x - y - y = -6
0 - 2y = - 6
y = -6/( -2)
y = 3
Substitute the value of y = 3 in the equation ( 1)
x - y = 5
x - 3 = 5
x = 5 + 3
x = 8
Answer : x = 8, y = 3
Write the rate as a fraction in the simplest form $1680 for 8 weeks 236 miles on 12 gallons of gasoline
Answers
The question asked to write the rate as a fraction in simplest form
[tex]\text{ \$1,680 for 8 w}eeks[/tex]To write the above relation in a fraction, we will have
[tex]\begin{gathered} =\frac{1680}{8} \\ \end{gathered}[/tex]Dividing to the lowest term, we will have
[tex]\begin{gathered} =\frac{210}{1} \\ whichis\text{ \$210 for 1 we}ek \end{gathered}[/tex]The question asked to write the rate as a fraction in simplest form
[tex]236\text{ miles on 12 gallons of gasoline}[/tex]To write the above relation in a fraction, we will have
[tex]=\frac{236}{12}[/tex]To express as a fraction in its lowest terms will be
[tex]\begin{gathered} =\frac{59}{3} \\ \text{which represents 59 miles for 3 gallons} \end{gathered}[/tex]- 2/3 (x+12)+2/3 x=-5/4 x+2
Answers
We will have the following:
[tex]-\frac{2}{3}(x+12)+\frac{2}{3}x=-\frac{5}{4}x+2\Rightarrow-\frac{2}{3}x-8+\frac{2}{3}x=-\frac{5}{4}x+2[/tex][tex]\Rightarrow-\frac{2}{3}x+\frac{2}{3}x+\frac{5}{4}x=2+8\Rightarrow\frac{5}{4}x=10[/tex][tex]\Rightarrow5x=40\Rightarrow x=8[/tex]So, the value of x is 8.
Simplify [tex]{({4e}^{ - 8x})}^{0.5} [/tex]with no negative exponents. thanks!
Answers
Explanation
Given the following expression
[tex]\begin{gathered} \text{Simplify (4 }e^{-8x})^{\frac{1}{2}} \\ \text{This expression can be written as} \\ (4\cdot\text{ }e^{-8x})^{\frac{1}{2}} \\ \text{Splitting the expression, we can have the below expression} \\ (4)^{\frac{1}{2}}\cdot(^{}e^{-8x})^{\frac{1}{2}} \\ \text{According to the law of indicies} \\ x^{\frac{1}{2}}\text{ = }\sqrt[]{x} \\ \text{Hence, we have the following expression} \\ \sqrt[]{4\text{ }}\cdot\text{ (}e^{-8x\cdot\text{ }\frac{1}{2}}) \\ 2\cdot\text{ }e^{-4x} \\ 2e^{-4x} \\ \text{Therefore, the simplified form is 2}e^{-4x} \\ \frac{2}{e^{4x}} \end{gathered}[/tex]James is putting a frame around a rectangular photograph. The photograph is 12 inches long
and 10 inches wide, and the frame is the same width all the way around. What will be the
area of the framed photograph? (Hint: use "x" as your variable.)
Polynomial:________
=_________
=_________
=_________final answer in standard form.
PLEASSEEEEEE i need know this asap
Answers
Answer:
The area is 4x² + 44x + 120Step-by-step explanation:
GivenDimensions of rectangle are 12 in and 10 in,Width of the frame is x.To find The area of the framed photographSolutionDimensions of the framed photograph are:
12 + 2x and 10 + 2xArea of the framed photograph is:
A = lwA = (12 + 2x)(10 + 2x) = 12*10 + 12*2x + 10*2x + 2x*2x = 120 + 24x + 20x + 4x²= 4x² + 44x + 120can u find a b and c its parallelogramthank u
Answers
To answer this question, we need to remember two theorems of parallelograms:
1. If a quadrilateral is a parallelogram, the two sets of its opposite angles are congruent:
2. The consecutive angles of parallelograms are supplementary (they sum 180 degrees):
Then, with this information, we have that:
[tex]97\cong m\angle c\Rightarrow m\angle c=97[/tex]And also, we have that the diagonal forms two congruent triangles, and the sum of internal angles of a triangle is equal to 180, then, we have:
[tex]m\angle c+26+m\angle b=180\Rightarrow97+26+m\angle b=180\Rightarrow m\angle b=180-97-26[/tex]Then, we have:
[tex]m\angle b=180-123\Rightarrow m\angle b=57[/tex]Then, using that the consecutive angles of parallelograms are supplementary (they sum 180 degrees), we have:
[tex]97+m\angle a+m\angle b=180\Rightarrow97+m\angle a+57=180\Rightarrow m\angle a=180-97-57_{}[/tex]Thus, we have that the measure for angle a is:
[tex]m\angle a=180-154\Rightarrow m\angle a=26[/tex]In summary, we have that (all the measures in degrees):
m< a = 26
m< b = 57
m< c = 97
Hi, could you help me figure out why I got 8 points off in this problem?
Answers
In triangle PQR
Construction: Draw PX perpendicular to QR where x lies on QR
Since:
PX perpendicular to QR
In the 2 triangles PXQ and PXR
given
proved up
PX = PX ------- common side in the 2 triangles
Triangle PXQ congruent to triangle PXR by the AAS theorem of congruency
As a result of congruency
PQ = PR ------- proved
Earl Miller, a customer of J. Crew, will pay $400 for a new jacket. J. Crew has a 60% markup on selling price. What is the most that J. Crew can pay for this jacket?
Answers
If Earl Miller, a customer of J. Crew, will pay $400 for a new jacket. J. Crew has a 60% markup on selling price. The most that J. Crew can pay for this jacket is $160.
How to find the total payment?Given parameters:
Cost of new jacket = $400
Markup = 60%
Now let find the amount that was paid for the jacket using this formula
Amount = Cost of new jacket × ( 1- markup)
Let plug in the formula
Amount = $400 × ( 1 - .60 )
Amount = $400 × .40
Amount = $160
Therefore we can conclude that the amount of $160 was paid the most.
Least more about amount paid here: https://brainly.com/question/25898631
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9.5.35 Assigned Media An architect designs a rectangular flower garden such that the width is exactly two-thirds of the length. If 300 feet of antique picket fencing are to be used to enclose the garden, find the dimensions of the garden What is the length of the garden? The length of the garden is
Answers
Answer:
• The dimensions of the garden are 90 feet by 60 feet.
,• The length of the garden is 90 feet.
Explanation:
Let the length of the garden = l
The width is exactly two-thirds of the length, Width = (2/3)l
If 300 feet of antique picket fencing are to be used to enclose the garden, this means that the perimeter of the proposed garden is 300 feet.
[tex]\begin{gathered} \text{Perimeter}=2(\text{Length}+\text{Width)} \\ 300=2(l+\frac{2}{3}l) \end{gathered}[/tex]Next, solve the equation for the length, l:
[tex]\begin{gathered} \frac{300}{2}=l+\frac{2}{3}l \\ 150=\frac{5l}{3} \\ l=150\times\frac{3}{5} \\ l=90\text{ feet} \end{gathered}[/tex]The length of the garden is 90 feet.
Next, we determine the width.
[tex]\begin{gathered} \text{Width}=\frac{2}{3}l \\ =\frac{2}{3}\times90 \\ =2\times30 \\ =60\text{ feet} \end{gathered}[/tex]The dimensions of the garden are 90 feet by 60 feet.
What is the answer to this equation?
Answers
Answer:
D 7.5
Step-by-step explanation:
n + n-3 + 2n-4 = perimeter ≥ 37
4n-7≥37
4n≥30
n≥7.5
Passes through (8,8) with slope 11/6
Answers
Given:
point (8,8).
slope 11/6
The slope intercept form is,
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept.
we know that m=11/6 so subistute in the equation.
[tex]y=\frac{11}{6}x+b[/tex]Now, let us plug in the point in the equation to find the value of b that is the y-intercept.
[tex]undefined[/tex]Let the graph of f(x) be given below. Find the formula of f(x), a polynomial function, of least degree.
Answers
To detrmine the formula of the polynomial, we check for the roots on the graph:
when y = 0, x = -2
when y = 0, x = 4
We have two roots.
x = -2
x + 2 = 0
x = 4
x - 4 = 0
3rd factor is x = 0
Hence, we have two factors: x(x + 2) and (x - 4)
The polynomial function using the factors:
[tex]f(x)\text{ = ax(x + 2)(x - 4)}[/tex]Next, we find the value of a:
To get a , we pick a point on the graph. let the point be (0, -4)
substitute the point in the function above:
[tex]\begin{gathered} f(x)\text{ = y = -4, x = 0} \\ -4\text{ = a(0 + 2) (0 - 4)} \\ -4\text{ = a(2)(-4)} \\ -4\text{ = -8a} \\ a\text{ = -4/-8} \\ a\text{ = 1/2} \end{gathered}[/tex]The formula of the polynomial becomes:
[tex]f(x)\text{ = }\frac{1}{2}x(x\text{ }+2)(x-4)[/tex]a company loses $5,400 as the result of manufacturing defect. each of the 8 owners have agreed to pay an equal amount, x, to pay for the loss. How much each owner paid?
Answers
Explanation:
If 'x' is the amount each owner will pay, there are 8 owners and the total amount to pay is $5,400 the equation to solve is:
[tex]8x=5,400[/tex]Solving for x:
[tex]x=\frac{5,400}{8}=675[/tex]Answer:
Each owner has to pay $675
How to solve this problem? (the answer is 262 Hz). i want to know the step by step on how to solve the equation given. if it helps, i am a grade 10 student. (YES, this is a MATH problem)
Answers
The frequency of middle C = 262 Hz
Explanation:The formula for calculating the frequency, F hertz, of a note n seminotes above the concert pitch is:
[tex]F\text{ = 440(}\sqrt[12]{2})^n[/tex]This can be re-written as:
[tex]F=440(2^{\frac{n}{12}})[/tex]Middle C is 9 semitones below the concert pitch
That is, n = -9
To find the frequency of middle C, substitute n = -9 into the equation for F
[tex]\begin{gathered} F=440(2^{\frac{-9}{12}}) \\ F\text{ = 440(}0.5946) \\ F\text{ = }261.62\text{ Hz} \\ F\text{ = 262 Hz (to the nearest hertz)} \end{gathered}[/tex]The frequency of middle C = 262 Hz
Please I really need help. I just need the answer no steps
Answers
Explanation
The question wants us to obtain the margin of error
A margin of error tells you how many percentages points your results will differ from the real population value.
The formula to be used is
To do so, we will have to list out the parameters to be used
[tex]\begin{gathered} standard\text{ deviation=}\sigma=13.8 \\ sample\text{ size=n=18} \\ confidence\text{ level=}\gamma=80\text{ \%} \end{gathered}[/tex]The next step will be to find the z-score value for a confidence level of 80%.
From the statistical table, we have
[tex]Z_{\gamma}=1.28[/tex]So, we can input the given data obtained into the formula
So we will have
[tex]\begin{gathered} MOE=1.28\times\sqrt{\frac{13.8^2}{18}} \\ \\ MOE=1.28\times\frac{13.8}{\sqrt{18}} \\ \\ MOE=1.28\times3.2527 \\ \\ MOE=4.16344 \end{gathered}[/tex]So the margin of error (M.E.) = 4.163 (To 3 decimal places)
The measures of the angles of a triangle are shown in the figure below. Solve for x.
44°
61°
(8x+11)°
Answers
Explanation!!
- The measures of the angles of a triangle always equal 180 degrees.
So, we know: 44 + 61 + (8x+11) = 180!!
Now, just solve for x.
180 — 61 — 44 — 11 = 116
8x = 116
116/8 = 8
x=8
hope this helps!! <33
An elevator car starts on the second floor of a building 27 feet above the ground. The car rises 4.2 feet every second on its way up to the 15th floor. Assuming the car doesn’t slow down or make any stops , how long will it take the car to reach a height of 102 feet above the ground?
Answers
17.86 seconds
Explanation:The starting point of the elevator car = 27 feet above the ground
The endpoint point of the elevator car = 102 feet above the ground
The total distance traveled by the elevator car = 102 feet - 27 feet
The total distance traveled by the elevator car = 75 feet
Time taken by the elevator car to rise 4.2 feet = 1 second
Time taken by the elevator car to rise 75 feet = 75/4.2 seconds
Time taken by the elevator car to rise 75 feet = 17.86 seconds
Therefore, it takes the car 17.86 seconds to reach a height of 102 feet above the ground
the length of a rectangle is 11 yd more than twice the width and the area of the rectangle is 63 yd squared. find the dimensions of the rectangle.
Answers
the length of a rectangle is 11 yd more than twice the width and the area of the rectangle is 63 yd squared. find the dimensions of the rectangle.
Let
L ------> the lenght
W ----> the width
we know that
the area of rectangle is
A=L*W
A=63 yd2
63=L*W -------> equation 1
and
L=2W+11 ------> equation 2
substitute equation 2 in equation 1
63=(2W+11)*w
2W^2+11w-63=0
solve the quadratic equation using the formula
a=2
b=11
c=-63
substitute
[tex]w=\frac{-11\pm\sqrt[]{11^2-4(2)(-63)}}{2(2)}[/tex][tex]\begin{gathered} w=\frac{-11\pm\sqrt[]{625}}{4} \\ \\ w=\frac{-11\pm25}{4} \\ \end{gathered}[/tex]the solutions for W are
w=3.5 and w=-9 (is not a solution, because is negative)
so
Find the value of L
L=2W+11 -------> L=2(3.5)+11
L=18
therefore
the dimensions are
Length is 18 yardsWidth is 3.5 yardsWhat is the product of V3 and 7V30 in simplest radical form?
Answers
Determine the product of two expressions.
[tex]\begin{gathered} \sqrt[]{3}\times7\sqrt[]{30}=7\sqrt[]{30\cdot3} \\ =7\sqrt[]{3\cdot3\cdot10} \\ =7\cdot3\sqrt[]{10} \\ =21\sqrt[]{10} \end{gathered}[/tex]So answer is,
[tex]21\sqrt[]{10}[/tex]4. The temperature in Baguio is 18.6℃, while Manila the temperature is 31.5℃. How much warmer is it in Manila than Baguio?A. 12.6℃B. 12.7℃C. 12.9℃D. 13℃
Answers
Given:
The temperature in Baguio is 18.6℃.
The temperature in manila is 31.5℃.
To find:
The differene bin temperature etween imanila and aguio.
Explanation:
The difference between manila and Baguio's temperature s
[tex]31.5^{\circ}C-18.6^{\circ}C=12.9^{\circ}C[/tex]Thus, manila is 12.9 degrees Celcius warmer than Baguio.
Final answer:
anila is 12.9 degrees Celcius warmer than Baguio.
what is equivalent to 2^4 x 4^2?
Answers
Given an indices shown below
[tex]2^4\text{ }\times4^2^{}[/tex]Addition method of indices
The second power need to be split into the power of 2
[tex](2^4\text{ }\times2^2)2^2)[/tex]Hence the equivalent is Option B
A line passes through the point (-6,1) and has a slope of -5/2
Write an equation in slope - intercept form for this line .
Answers
Answer: [tex]y=-\frac{5}{2}x+16[/tex]
Step-by-step explanation:
The equation in point-slope form is [tex]y-1=-\frac{5}{2}(x+6)[/tex]. To find the equation in slope-intercept form, isolate [tex]y[/tex].
[tex]y-1=-\frac{5}{2}(x-6)\\\\y-1=-\frac{5}{2}x+15\\\\y=-\frac{5}{2}x+16[/tex]
Using the completing-the-square method, rewrite f(x) = x2 − 8x + 3 in vertex form. (2 points)
A) f(x) = (x − 8)2
B) f(x) = (x − 4)2 − 13
C) f(x) = (x − 4)2 + 3
D) f(x) = (x − 4)2 + 16
Answers
By using the completing the square method, f(x) = x² − 8x + 3 in vertex form is: B. f(x) = (x − 4)² − 13.
The vertex form of a quadratic equation.In this exercise, you're required to rewrite the given function in vertex form by using the completing the square method. Mathematically, the vertex form of a quadratic equation is given by this formula:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.
In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:
f(x) = x² − 8x + 3
f(x) = x² − 8x + (8/2)² - 13
f(x) = x² − 8x + (4)² - 13
f(x) = x² − 8x + 16 - 13
f(x) = (x² − 8x + 16) - 13
f(x) = (x − 4)² − 13
Read more on completing the square here: brainly.com/question/11398876
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The figure shows rectangle PQRS in the first quadrant of the coordinate plane?
Answers
The quadrants of a coordinate plane are:
Then, we can say that the rectangle PQRS is in the first quadrant.
The diameter of a circle has endpoints P(-12, -4) and Q(6, 12).
Answers
ANSWER
[tex](x+3)^{2}+(y-4)^{2}=145[/tex]EXPLANATION
The equation of a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h, k) = center of the circle
r = radius of the circle
The center of a circle is the midpoint of the endpoints of the diameter of the circle. Hence, to find the center of the circle, we have to find the midpoint of the diameter:
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]where (x1, y1) and (x2, y2) are the endpoints of the diameter.
Hence, the center of the circle is:
[tex]\begin{gathered} M=(\frac{-12+6}{2},\frac{-4+12}{2}) \\ M=(\frac{-6}{2},\frac{8}{2}) \\ M=(-3,4) \end{gathered}[/tex]To find the radius of the circle, we have to find the distance between any endpoint of the circle and the center of the circle.
To do this apply the formula for distance between two points:
[tex]r=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Therefore, the radius of the circle is:
[tex]\begin{gathered} r=\sqrt{(6-(-3))^2+(12-4)^2}=\sqrt{9^2+8^2} \\ r=\sqrt{81+64}=\sqrt{145} \end{gathered}[/tex]Hence, the equation of the circle is:
[tex]\begin{gathered} (x+3)^2+(y-4)^2=(\sqrt{145})^2 \\ (x+3)^2+(y-4)^2=145 \end{gathered}[/tex]I need a math wiz to explain this to me, are you a math wiz?
Answers
SOLUTION
The questions is outside scope