Solve the triangle.
B = 36°, a = 41, c = 17 (5 points)
Answer:
b = 29.0, A = 123.9°, C = 20.1°
9514 1404 393
Answer:
b = 29.0; A = 123.9°, C = 20.1°
Step-by-step explanation:
The given angle lies between the given sides, so the Law of Cosines is the appropriate relation.
b² = a² +c² -2ac·cos(B)
b² = 1681 +289 -1394cos(36°) ≈ 842.2303
b ≈ √842.2303 ≈ 29.021
__
The Law of Sines can be used to find angle C:
sin(C)/c = sin(B)/b
C = arcsin(c/b·sin(B)) = arcsin(17/29.021×sin(36°))
C ≈ 20.1°
A = 180° -36° -20.1° = 123.9°
The remaining side and angles are ...
b ≈ 29.0; A ≈ 129.9°; C ≈ 20.1°
_____
Additional comment
By choosing to find the smaller angle C first, we avoid having to deal with the ambiguity associated with the arcsine when the angle is greater than 90°.
There are 6 different cookies on a plate. James will choose 2 of these cookies to pack in his lunch. How many different pairs of 2 cookies can he choose from the 6?
Answer:
15
Step-by-step explanation:
He could choose 1 & 2, 1 & 3, 1 & 4, 1 & 5, 1 & 6, 2 & 3, 2 & 4, 2 & 5, 2 & 6, 3 & 4, 3 & 5, 3 & 6, 4 & 5, 4 & 6, 5 & 6
Find the integer solutions that
satisfy the inequality, 2 < x + 5<7.
Give your answer as an inequality.
Use the < or > signs to represent your
inequality
Given:
The compound inequality is:
[tex]2<x+5<7[/tex]
To find:
The integer solutions that satisfy the given inequality.
Solution:
We have,
[tex]2<x+5<7[/tex]
Subtracting 5 from each side, we get
[tex]2-5<x+5-5<7-5[/tex]
[tex]-3<x<2[/tex]
All the real numbers between -3 and 2 are in the solution set but -3 and 2 are not included in the solution set.
The integers between -3 and 2 are -2, -1, 0, 1.
Therefore, the integer solution of the given inequality are -2, -1, 0, 1. The answer as an inequality is [tex]-3<x<2[/tex].
What are the coordinates of the point that is 1/5
of the way from A(-7,-4) to
B(3,6)?
A. (-5,0)
B. (-5,-2)
C. (0,3)
O D. (1,4)
9514 1404 393
Answer:
B. (-5, -2)
Step-by-step explanation:
That point is ...
A + 1/5(B - A)
= (-7, -4) + 1/5(3 -(-7), 6 -(-4)) = (-7, -4) +1/5(10, 10)
= (-7, -4) +(2, 2) = (-5, -2)
The point (-5, -2) is 1/5 of the way from A to B.
Select the correct answer from each drop down menu. The GCF of the numbers in the expression (32+16) is( ) The numbers left inside the parentheses after factoring out the GCF are ( ) and ( )
Answer:
Eu não entendo inglês!!
In this picture, m∠XOZ = 70° and m∠YOZ = 37°. If m∠XOY = (5x + 16)°, what is the value of x?
Answer:
x = 3.4
Step-by-step explanation:
You have the value of xoz = 70, yoz = 37 and xoy = 5x+16
Set your formula up as
xoz = yoz + xoy
70 = 37 + 5x + 16
70 - 37 - 16 = 5x
17 = 5x
17 / 5 = x
3.4 = x
[tex]\huge\bold{Given :}[/tex]
m∠XOZ = 70°
m∠YOZ = 37°
m∠XOY = ( 5x + 16 )°
[tex]\huge\bold{To\:find :}[/tex]
The value of x°.
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]{\boxed{\mathcal{\red{The\:value\:of\: x° \:is\:3.4° .\:}}}}[/tex]✅
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
We know that,
[tex]\sf\pink{m∠XOZ\:=\:m∠YOZ\:+\:m∠XOY}[/tex]
➪ 70° = 37° + 5x° + 16°
➪ 5x° + 53° = 70°
➪ 5x° = 70° - 53°
➪ 5x° = 17°
➪ x° = [tex] \frac{17° }{5} [/tex]
➪ x° = 3.4°
[tex]\sf\red{Therefore, \:the\: value \:of \:x°\: is \:3.4°.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]
✒ 70° = 37° + 5 x 3.4° + 16°
✒ 70° = 37° + 17° + 16°
✒ 70° = 70°
✒ L. H. S. = R. H. S.
[tex]\boxed{Hence\:verified.}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{♡}}}}}[/tex]
Why is android sound louder then iPhone???
Answer ASAP
Cause my volume isn’t as loud as android and my speakers work fine and so does the volume?
Answer:
There are many outcomes or data that needs to be collected... like does the iPhone and android share the same speaker? or are your speaker grills blocked out by something? or is your iPhone old, because they do change the speaker each gen.
1. What are two possible first steps you could use when solving an equation like `6(x+4)=30?`
Answer:
Step-by-step explanation:
take 30 devide it by 6 then minose 4 off that and get x=1
Answer:
x = 1
Step-by-step explanation:
6(x + 4) = 30
Simplify.
6x + 24 = 30
Subtract 24 from each side.
6x + 24 - 24 = 30 - 24
Simplify.
6x = 6
Divide each side by 6.
6x ÷ 6 = 6 ÷ 6
Simplify.
x = 1
HELPPP!
Carl had two pieces of pizza. One piece had an angle measure of 60. The other one had an angle of 45. He put the two pieces together to make one large angle. What angle do the two pieces of pizza form?
Answer:
105°, obtuse angle
Step-by-step explanation:
60 + 45 = 105
please tell me? thx for ur help <3
Answer:
x = 63, y = 27
Step-by-step explanation:
x and 117 are adjacent angles and sum to 180°
x + 117 = 180 ( subtract 117 from 180 )
x = 63
x and y sum to 90°
x + y = 90
63 + y = 90 ( subtract 63 from both sides )
y = 27
Answer: x=63 y= 27
Step-by-step explanation:
180-117=63
x+y=90
63+y=90
90-63 = 27
hope this helps :)
There are nine counters in a bag numbered from one to nine. If a counter is drawn at random from the bag what is the probability that the number on the counter is not a multiple of three?
Step-by-step explanation:
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The probability is 1/3 that the number on the counter is not a multiple of three.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
We have to determine the probability that the number on the counter is not a multiple of three.
There are nine counters in a bag numbered from one to nine.
If a counter is drawn at random from the bag.
One to nine, there are three numbers are multiple of three that is (3, 6, 9)
Here favorable outcomes = 3
So the probability that the number on the counter is not a multiple of three as
⇒ 3/9
⇒ 1/3
Therefore, the probability is 1/3 that the number on the counter is not a multiple of three.
Learn more about the probability here:
brainly.com/question/11234923
#SPJ2
The elective courses for next year are gym, shop, art, consumer science, criminal justice, and computer science. Amber needs to choose 3 electives. How many ways can she choose her electives
Answer:
She can choose her electives in 20 ways.
Step-by-step explanation:
The order in which she chooses the courses is not important, which means that the combinations formula is used to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
How many ways can she choose her electives?
3 electives from a set of 6. So
[tex]C_{6,3} = \frac{6!}{3!(6-3)!} = 20[/tex]
She can choose her electives in 20 ways.
Choose the equation for the line that passes through (6, 5) and is parallel to the line x + 3y = 9.
Answer:
y = -1/3x + 7
Step-by-step explanation:
x + 3y = 9 ⇒ y = -1/3x + 3
Use point-slope form and substitute the values:
[tex]y-y_1=m(x-x_1)\\y-5=-\frac{1}{3}(x-6)\\y-5=-\frac{1}{3}x+2\\y=-\frac{1}{3}x+7[/tex]
On a particular game show, there are 8 covered buckets and 2 of them contain a ball.
To win the game, a contestant must select both buckets that contain a ball. Find the
probability that a contestant wins the game if he/she gets to select 4 of the buckets.
Answer:
0.2143 = 21.43% probability that a contestant wins the game if he/she gets to select 4 of the buckets.
Step-by-step explanation:
The buckets are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
8 covered buckets, so N = 8.
4 buckets are selected, so n = 4.
2 contain a ball, which means that k = 2.
Find the probability that a contestant wins the game if he/she gets to select 4 of the buckets.
This is P(X = 2). So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,8,4,2) = \frac{C_{2,2}*C_{6,2}}{C_{8,2}} = 0.2143[/tex]
0.2143 = 21.43% probability that a contestant wins the game if he/she gets to select 4 of the buckets.
Ezra had 46 green marbles. Then he bought 6 bags of blue marbles. There were 8 marbles in
each bag. How many marbles does Ezra have now?
marbles
Answer:
94 marbles
Step-by-step explanation:
46 green marbles + (6 bags x 8 pieces of marbles) = 94 marbles
Find the midpoint of the segment below and enter its coordinates as an ordered pair. If necessary, express the coordinates as fractions, using the slash mark (/) for the fraction bar.
(1,-1) (4,-6)
i need help with this one plz! (marking BRAINLIST) :)
Answer:
I gotchu man watch this
Step-by-step explanation:
in order to find x u gotta use tan or toh
opposite over hyp
anyway 17*tan(21)
6.525688596
or 6.53
Answer:
Step-by-step explanation:
tan θ = opposite / adjacent
tan 21 = x / 17
17 tan 21 = x
x = 6.52
What is the solution of the equation x² = 64?
4
+4
18
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = ±8}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
➺ [tex] {x}^{2} = 64[/tex]
➺ [tex] \: x = \sqrt{64} [/tex]
➺ [tex] \: x = \sqrt{8 \times 8} [/tex]
➺ [tex] \: x = \sqrt{ ({8})^{2} } [/tex]
➺ [tex] \: x = ±8[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
PLEASE HELP WILL GIVE BRAINLEIST
Step-by-step explanation:
You can prove it by pythegoras use unit and you will get
Ef=gh
And FG=EH
Lisa's shop sells 5 quarts of ice cream each day. How much is this in pints?
Answer:
10
Step-by-step explanation:
We know there are 5 quarts.
There are 2 pints for each quart.
This can be though of as a ratio of:
2 : 1
There are 5 quarts, which is 5 times bigger than the ratio of 1.
So this means we need to mutliply both sides of the ratio by 5, to make the quarts equivelent to 5:
2*5 : 1*5
=
10 : 5
So for every 5 quarts there are 10 pints.
Hope this helps!
Contains the point (5, 4) and is perpendicular to the y axis
Answer:
y = 4
Step-by-step explanation:
A horizontal line at
y = 4
is perpendicular to the y-axis and includes all values of x
I need help anyone please
Answer:
b = 19 inches
h = 5 inches
A = 95 inches^2
Step-by-step explanation:
The area is given by
A = bh where b is the base and h is the height
b = 19 inches
h = 5 inches
A = 19 inches * 5 inches = 95 inches^2
To prepare for a party, Mark buys a small bunch of balloons for $6.00 and gift bags that cost $5.15 each. He spends a total of
$72.95 on the balloons and a gift bag for each person invited to the party. Write and solve an equation to find x, the number of
people Mark invited to the party
Answer: [tex]72.95 =6.00+5.15x[/tex] , Required equation
The number of people Mark invited to the party = 13
Step-by-step explanation:
According to the question,
Total amount spent = (Price of bunch of ballons)+(cost per gift) x (Number of persons)
Given: Total amount spent =$72.95 , Price of bunch of ballons =$6.00 ,
cost per gift =$5.15
thus,
[tex]72.95 =6.00+5.15x[/tex] , Required equation
To solve , first
subtract 6 from both sides, we get
[tex]66.95=5.15x\\\\\Rightarrow\ x=\dfrac{66.95}{5.15}\\\\\Rightarrow\ x=13[/tex]
The number of people Mark invited to the party = 13
Use the Pythagorean Theorem to find the missing side
of right triangle RST in simplest radical form.
Answer:
9
Step-by-step explanation:
hip^2 = cat^2+cat^2
41^2= 40^2 + x^2
1681 = 1600 + x^2
1681-1600 = x^2
81 = x^2 /√
√81 = √x^2
9 = x
Select the correct answer.
The variable g varies directly as the cube root of h. If g=128 when h=8, which equation can be used to find other combinations of g and h?
[tex]g \sqrt[3]{h} = 256[/tex]
[tex]g = 64 \sqrt[3]{h} [/tex]
[tex]gh = 1024[/tex]
[tex]g = 16h[/tex]
the second equation is correct
Step-by-step explanation:
I got it right on the test
Question 6 of 10
How many solutions are there to the equation below?
12x + 32=124-7
A 1
B. iniintey many
co
SU
Answer:
1
Step-by-step explanation:
12x+32=117
12x=85
x=85/12
Which expression is equivalent to:1/m6
Answer:
A
Step-by-step explanation:
6 is a power. So both C and D are wrong because 6 is being treated as an ordinary integer.
So the answer must be either A or B.
B is not correct because to move an expression from the denominator to the numerator changes the sign in the base (which is m in this question).
A is correct. the power is changed from 6 in the denominator to -6 in the numerator. m is shifted to the numerator as well.
PLEASE ANYONE!! If the area of a triangle is 32 yd^2 and the base is 6.4 yds long, find the height
Answer:
10yd
Step-by-step explanation:
area= 1/2bh
area=32yd²
b= 6.4, ¹/2b=3.2
therefore, 32= 3.2h
h= 32/3.2
= 10yd
Please write an answer with NO FILES, NO LINKS, AND NO WRONG OR TRICK ANSWER!
Answer:
18 inches
Step-by-step explanation:
A=L·H
108 in²=L·6 in
L=[tex]\frac{108}{6}[/tex]
L=18 inches
Please helpppp me i
Answer:
y=-15/2 + 3x/4
Step-by-step explanation: