For each triangle shown below, determine whether you would use the Law of Sines or Law of Cosines to find angle x, and explain how you know which Law to use. Then find angle x to the nearest tenth.
NOTE: The perimeter of ABC-31
Answers
Given:
The figure of a triangle.
The perimeter of the triangle ABC is 31.
To find:
The value of x in the given triangle.
Solution:
Three sides of the triangle ABC are AB, BC, AC are their measures are [tex]3b-4,2b+1,b+10[/tex] respectively.
The perimeter of the triangle ABC is 31.
[tex]AB+BC+AC=31[/tex]
[tex](3b-4)+(2b+1)+(b+10)=31[/tex]
[tex]6b+7=31[/tex]
Subtract 7 from both sides.
[tex]6b=31-7[/tex]
[tex]6b=24[/tex]
[tex]b=\dfrac{24}{6}[/tex]
[tex]b=4[/tex]
Now, the measures of the sides are:
[tex]AB=3b-4[/tex]
[tex]AB=3(4)-4[/tex]
[tex]AB=12-4[/tex]
[tex]AB=8[/tex]
[tex]BC=2b+1[/tex]
[tex]BC=2(4)+1[/tex]
[tex]BC=8+1[/tex]
[tex]BC=9[/tex]
And,
[tex]AC=b+10[/tex]
[tex]AC=4+10[/tex]
[tex]AC=14[/tex]
Using the law of cosines, we get
[tex]\cos A=\dfrac{b^2+c^2-a^2}{2bc}[/tex]
[tex]\cos A=\dfrac{(AC)^2+(AB)^2-(BC)^2}{2(AC)(AB)}[/tex]
[tex]\cos A=\dfrac{(14)^2+(8)^2-(9)^2}{2(14)(8)}[/tex]
[tex]\cos A=\dfrac{179}{224}[/tex]
Using calculator, we get
[tex]\cos A=0.7991[/tex]
[tex]A=\cos ^{-1}(0.7991)[/tex]
[tex]x=36.9558^\circ[/tex]
[tex]x\approx 37.0^\circ[/tex]
Therefore, the value of x is 37.0 degrees.
Related Questions
Intercept Form
Point (-3,4)
Slope 5
m= b=
Answers
Answer:
y = 5x + 19
Step-by-step explanation:
y = 5x + b
4 = 5(-3) + b
4 = -15 + b
19 = b
the 28th term of an ap is -5,find the common difference if the first term is 31
Answers
Answer:
The common difference is -4/3.
Step-by-step explanation:
Recall that the direct formula for an arithmetic sequence is given by:
[tex]\displaystyle x_n=a+d(n-1)[/tex]
Where n is the nth term, a is the initial term, and d is the common difference.
We are given that the first term a is 31.
We also know that the 28th term is -5. Hence, x₂₈ = -5. Substitute:
[tex]\displaystyle x_{28}=-5=(31)+d(28-1)[/tex]
Solve for d. Simplify:
[tex]-5=31+27d[/tex]
Thus:
[tex]\displaystyle 27d=-36[/tex]
Divide both sides by 27. Hence, the common difference is:
[tex]\displaystyle d=-\frac{36}{27}=-\frac{4}{3}[/tex]
Answer:
-4/3
Step-by-step explanation:
This question is equivalent to:
Find the slope of a line going through points (28,-5) and (1,31).
*Arithmetic sequences are linear. The common difference is the slope.
Any ways to find the slope line the points up and subtract vertically. Then put 2nd difference over 1st difference.
(28,-5)
(1,31)
---------subtracting
27, -36
So the slope or the common difference of this line or arithmetic sequence is -36/27. This reduces to -4/3.
Find an equation for the line below.
Answers
Answer:
y= -1/4x+ 3.75
Step-by-step explanation:
please help answer these!!!!
Jimmy’s family moved to a tropical climate. For the year that followed, he recorded the number of days that had a temperature above 400C each month. His data contained -
14, 14, 10, 12, 11, 13, 11, 11, 14, 10, 13 and 8
1) Find the mean for his data set of days that had a temperature above 400C.
2) Find the median for his data set of days that had a temperature above 400C.
3) Find the mode for his data set of days that had a temperature above 400C.
4) If, instead, there are 5 more days per month that had a temperature above 400C, what will be the mean for the data?
5) If, instead, there are 2 more days per month that had a temperature above 400C, what will be the mode for the data?
Answers
Answer:
1) 11.75
2) 11.5
3) 11 and 14
4) 16.75
5) 13, and 16
Step-by-step explanation:
The given data is 14, 14, 10, 12, 11, 13, 11, 11, 14, 10, 13, 8
1) The mean, [tex]\overline x[/tex] = (14+14+10+12+11+13+11+11+14+10+13+8)/12 = 11.75
2) The data arranged in increasing order is presented as follows;
8, 10, 10, 11, 11, 11, 12, 13, 13, 14, 14, 14
The count of he data points = 12
The median = The data at the (n + 1)/2 = (12 + 1)/2 = 6.5th position = 11 + (12 11)/2 = 11.5
The median = 11.5
3) The mode of the data set are 11 and 14
4) Where there are 5 more days per month that had a temperature above 40°C, we get;
The mean, [tex]\overline x_1[/tex] = (14+14+10+12+11+13+11+11+14+10+13+8+5×12 )/12 = 16.75 = [tex]\overline x[/tex] + 5
5) Given that there are 2 more days per month that had a temperature above 40°C, we get the days per month with temperatures above 40°C as follows;
8 + 2, 10 + 2, 10 + 2, 11 + 2, 11 + 2, 11 + 2, 12 + 2, 13 + 2, 13 + 2, 14 + 2, 14 + 2, 14 + 2
10, 12, 12, 13, 13, 13, 14, 15, 15, 16, 16, 16
Therefore, the mode are 13, and 16
Find the value of sin H rounded to the nearest hundredth, if necessary
Answers
Answer:
7/25 or .28
Step-by-step explanation:
sin=opp/hyp
7/25
suppose you start with a single bacterium of streptococcus at hour 0 , and it has a generation time of 60 minutes. how many bacteria will you have at the end of hour 24
Answers
Answer:
60x24
Step-by-step explanation:
60x24=1224
Sam made $147 for 7 hours of work at the same rate how much would he make for 9 hours of work
Answers
so your answer will be $189 for 9 hours of work
hope this helps!
Which expression can be used to find the difference of the polynomials?
(10m – 6) – (7m – 4)
Answers
Answer:
3m -2
Step-by-step explanation:
(10m – 6) – (7m – 4)
Distribute the minus sign
(10m – 6) – 7m + 4
Combine like terms
3m -2
Martin was selling tickets for a basketball game in a high school. He sold 1,250 tickets and the total amount collected for the game was $2,750. The student tickets cost $2 each, and adult tickets cost $3 each. How many student and adult tickets were sold?
Answers
Answer:
x = number of students tickets = 1,000
y = number of adults tickets = 250
Step-by-step explanation:
Let
x = number of students tickets
y = number of adults tickets
x + y = 1,250 (1)
2x + 3y = 2,750 (2)
Multiply (1) by 2
x + y = 1,250 (1) * 2
2x + 2y = 2,500 (3)
2x + 3y = 2,750 (2)
Subtract (3) from (2) to eliminate x
3y - 2y = 2,750 - 2,500
y = 250
Substitute y = 250 into (1)
x + y = 1,250
x + 250 = 1,250
x = 1,250 - 250
x = 1,000
x = number of students tickets = 1,000
y = number of adults tickets = 250
To indirectly measure the distance across a lake, Nachelle makes use of a couple landmarks at points D and E. She measures CF, FD, and FG as marked. Find the distance across the lake (DE), rounding your answer to the nearest hundredth of a meter
Answers
Answer:
207.68 m
Step-by-step explanation:
From the diagram,
ΔDEC is similar to ΔFGC
Therefore,
(DE)/(FG) = (DC)/(FC).............. Equation 1
make line DE the subject of the equation
DE = [(DC)(FG)/(FC)]................ Equation 2
From the diagram,
Given: DC = 190 m, FG = 142.1 m, FC = 130 m
Substitute these values into equation 2
DE = (190×142.1/130)
DE = 207.68 m
Hence the distance across the lake is 207.68 m
Applying the similarity theorem, the distance across the lake to the nearest hundredth is: DE = 207.68 m
Recall:
The corresponding side lengths of two triangles that are similar are always proportional to each other.Thus:
ΔCDE and ΔCFG are similar to each other
FG = 142.1 m
FC = 130 m
DF = 60 m
DC = 130 + 60 = 190 m
Therefore:
DE/FG = DC/FC
SubstituteDE/142.1 = 190/130
Cross multiply[tex]DE = \frac{190 \times 142.1}{130} \\\\\mathbf{DE = 207.68 $ m}[/tex] (nearest hundredth).
Therefore, applying the similarity theorem, the distance across the lake to the nearest hundredth is: DE = 207.68 m
Learn more about similar triangles here: https://brainly.com/question/11899908
I need help bad? What’s the answer
Answers
Answer:
76°,60°
Step-by-step explanation:
sum of angles of a triangle=180
x+64+x+80+44=180
2x+188=180
2x=180-188=-8
x=-8/2=-4
so angles are -4+60=60°
and -4+80=76°
A chocolate factory uses 16 of a bag of cocoa butter in each packet of chocolate. The factory used 13 of a bag of cocoa butter today. How many packets of chocolates did the factory make?
Answers
Answer:
13/16 of a packetStep-by-step explanation:
Solve using ratios:
1 packet ⇒ 16 bagsx packets ⇒ 13 bagsFind x:
x*16 = 1*13x = 13/16Tell whether the angles are adjacent or vertical. Then find the value of x.
The angles are angles
The value of x is
Answers
Answer:
If two angles have common side and they shares common vertex, they are called adjacent angles.
When two lines crosses each other, the opposite angles are called vertical angles as they share same vertex.
Two angles shown in diagram are adjacent as they are on common side.
Both the angles are on a straight line, hence
Subtracting 109 from both sides
Both angles shown in diagram are opposite to each other, hence vertical angles.
As they are opposite to each other, they both are equal.
Subtracting x from both sides
Subtracting 1 from both sides
Both angles are having a common side means they are adjacent angles.
As they are on straight line, both angles will add up to 180 °.
Subtracting 96 from both sides
Dividing from 6 in both sides
Hope it will help :)
If f(x) = 5x + 40, what is f(x) when x = –5?
answer
1. -9
2. -8
3. 7
4. 15
Answers
Answer:
option 4
Step-by-step explanation:
f(x) = 5x + 40
f(x = - 5) = 5 ( - 5) + 40
= - 25 + 40
= 15
f(x) = 5x + 40
f(-5) = 5(-5) + 40
= 15
Ans: 15
what's this problem please
Answers
Answer:
Option A : 135°Step-by-step explanation:
If the table and ground are to be parallel then,
45° + x = 180° [Co-interior angles]
=> x = 180 - 45
=> x = 135° (Ans) (Option A)
pls help i need this answer
Answers
Fraction form 1/16
I think,sorry if it’s wrong
The probability that Caroline wins a raffle is given by the expression
m/n.
Write down an expression, in the form of a combined single fraction, for the probability that Caroline does not win.
Answers
Answer: [tex]\frac{n-m}{n}[/tex]
This is the same as writing (n-m)/n
Don't forget about the parenthesis if you go with the second option.
==================================================
Explanation:
The probability that she wins is m/n, where m,n are placeholders for positive whole numbers.
For instance, m = 2 and n = 5 leads to m/n = 2/5. This would mean that out of n = 5 chances, she wins m = 2 times.
The probability of her not winning is 1 - (m/n). We subtract the probability of winning from 1 to get the probability of losing.
We could leave the answer like this, but your teacher says that the answer must be "in the form of a combined single fraction".
Doing a bit of algebra would have these steps
[tex]1 - \frac{m}{n}\\\\\frac{n}{n} - \frac{m}{n}\\\\\frac{n-m}{n}\\\\[/tex]
and now the expression is one single fraction.
What is the explicit formula for this sequence?
7, 2, -3, -8...
Answers
Answer:
The explicit formula of that sequence is T - 5
Step-by-step explanation:
Let T represent each term in the sequence. So now try replacing T with each term in the sequence. Like this ;
7 - 5 = 2
2 - 5 = -3
-3 - 5 = -8
hope this helps
Find sin A, round to the nearest hundredth.
Answers
Answer:
.92
Step-by-step explanation:
sin A = opp side/ hypotenuse
We can use the Pythagorean theorem to find the hypotenuse
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
3^2 +7^2 = AC ^2
9+49 = AC ^2
58 = AC^2
Taking the square root
sqrt(58) = hypotenuse
sin A = 7/sqrt(58)
sin A =.91914503
sin A = .92
Drag each expression to the correct category.
Apply the produc rules to determine the sign of each expression.
Answers
[tex]( - \frac{4}{9} )( \frac{7}{4} ) = \: \: negative [/tex]
[tex]( - 2 \frac{3}{4} )( - 1 \frac{1}{5} ) = \: \: positive[/tex]
[tex](3)( - 3)( - 3)( - 3)( - 3) = \: \: positive[/tex]
[tex]( - \frac{1}{6} )( - 2)( - \frac{3}{5} )( - 9) = \: \: positive[/tex]
[tex]( - \frac{4}{7} )( - \frac{3}{5} )( - 9) = \: \: negative[/tex]
[tex]( - \frac{10}{7} )( \frac{8}{3} ) = \: \: negative[/tex]
Can somebody answer this????
Answers
Answer:
x=46
Step-by-step explanation:
Isosceles triangle which means that the bottom two angles are equal. 180 degrees minus 88=92. Since there are two angles you divide 92/2 which gets 46.
Answer:
D
Step-by-step explanation:
two sides are equal.
so opposite angles are also equal.
x+x+88=180
2x=180-88=92
x=92/2=46°
What is the answer to this question
Answers
Answer:
4 is the answer to this question
Describe what a vaccine is made of and how it helps prevent infection.
Answers
Answer:
Vaccines are made of mixtures that contain either parts of pathogens or whole pathogens that prepare the body's defenses to fight against the pathogens.
hope it helps.
stay safe healthy and happy...Answer:Vaccines are made of mixtures that contain either parts of pathogens or whole pathogens that prepare the body's defenses to fight against the pathogens.
Step-by-step explanation:
find the x-intercept and y-intercept from the following linear equation: -7x+4y=56
Answers
Answer:
x-intercept = (-8,0) y-intercept = (0,14)
Step-by-step explanation:
-7x + 4y = 56
4y = 7x + 56
y = 7/4x + 14
y-intercept = 14
0 = 7/4x + 14
-7/4x = 14
x = -8
What is the difference of the fractions? 3StartFraction 13 over 15 EndFraction – 1Four-fifths 2One-fifteenth 2Five-fifteenths 2Seven-tenths 2Nine-tenths
Answers
Answer:
2One-fifteenth
Step-by-step explanation:
[tex]3\frac{13}{15} - 1\frac{4}{5}[/tex]
[tex]2\frac{13 - 12}{15}[/tex]
2 [tex]\frac{1}{15}[/tex]
Whoever finishes this gets "brainliest".
just for fun
35a^7--11a^7
Answers
Answer:
a=0
Step-by-step explanation:
Factor:
a^7 (35-11)
Set it equal to zero and solve:
a^7=0
a=0
I don't even know where to start on this circle.
Answers
Answer:
[tex]b=80[/tex]°
Step-by-step explanation:
The central angles theorem states that the measure of an angle whose vertex is the center of the circle is equivalent to the arc surrounding it. One can apply this here by stating that the measure of the arc surrounding the (90) degree angle is (90) degrees.
The total degree measure of a circle is (360). Thus one can form an equation and solve it to find the measure of the arc surrounding the angle (b). Call the arc surrounding angle (b); ([tex]b_1[/tex]).
[tex](b_1)+(90)+(110)=360[/tex]
Simplify,
[tex]b_1+200=360[/tex]
Inverse operations,
[tex]b_1+200=360[/tex]
[tex]b_1=160[/tex]
The peripheral angles theorem states that if the vertex of an angle formed between a tangent and a chord, is on the circumference (outer edge) of a circle, then the measure of the angle is equal to half of the measure of the surrouding arc. Please note that a chord is a line segment in a circle that intersects the circle in two points. A tangent is a line segment that intersects a circle at one point. One can apply this here by stating the following,
[tex]b=\frac{b_1}{2}[/tex]
Substitute,
[tex]b=\frac{160}{2}[/tex]
Solve,
[tex]b=80[/tex]
estimate the solution to the following system of equations by graphing.
3x+5y=14
6x-4y=9
A. ( 4/3,5/2)
B. ( 7/3, -7/2 )
C. ( -5/2, -7/2)
D. (5/2, 4/3)
Answers
Answer:
(101/42, 19/14)
Step-by-step explanation:
Given the following equations
3x+5y=14 ..... 1 * 2
6x-4y=9 ... 2 * 1
__________________
6x+10y=28
6x-4y=9
Subtract
10y+4y = 28 - 9
14y = 19
y = 19/14
Get the value of x
Since 3x+5y = 14
3x+5(19/14) = 14
3x + 95/14 = 14
3x = 14 - 95/14
3x = 101/14
42x = 101
x = 101/42
Hence the solution is (101/42, 19/14)
I you borrow 500 for 4 years at an annual interest rate of 6% HOW MUCH WILL YOU PAY altogether
Answers
Answer:
620
amount= p+i , to find interest .I=500*4*6/100 =120 amount=500+120=620
Michele was making tuna salad for a party. The recipe for 10 servings called for 8 oz of mayonnaise. A total of 240 people were expected to be at the brunch. How much mayonnaise would Michele need?
Answers
1. Divide 240 by 10 = 24
2. Multiply 24 • 8 = 192
Michele will need 192 oz. of mayonnaise.
Answer:
192 oz
Step-by-step explanation:
Hi there!
1) Create a proportion
[tex]\frac{8 (oz)}{10(servings)} =\frac{x(mayo)}{240(servings)} \\\frac{8}{10} =\frac{x}{240}[/tex]
2) Solve for x
[tex]\frac{8}{10} =\frac{x}{240}[/tex]
Multiply both sides by 240
[tex]\frac{8}{10} *240=x\\192=x[/tex]
Therefore, Michele would need 192 oz of mayonnaise.
I hope this helps!
