Answers
Answer:
b ≈ 9.5, c ≈ 14.7
Step-by-step explanation:
Using the Sine rule in Δ ABC, that is
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] , substitute values
[tex]\frac{7}{sin23}[/tex] = [tex]\frac{b}{sin32}[/tex] ( cross- multiply )
b × sin23° = 7 × sin32° ( divide both sides by sin23° )
b = [tex]\frac{7sin32}{sin23}[/tex] ≈ 9.5 ( to the nearest tenth )
Also
[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex]
[tex]\frac{7}{sin23}[/tex] = [tex]\frac{c}{sin125}[/tex] ( cross- multiply )
c × sin23° = 7 × sin125° ( divide both sides by sin23° )
c = [tex]\frac{7sin125}{sin23}[/tex] ≈ 14.7 ( to the nearest tenth )
Related Questions
Which expression is equivalent to 73 ⋅ 7−5? 72 77 1 over 7 to the 2nd power 1 over 7 to the 7th power
Answers
Answer:
1/7^2
Step-by-step explanation:
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
a^-b = 1/a^b
__
Then your expression simplifies to ...
[tex]7^3\cdot 7^{-5}=7^{3-5}=7^{-2}=\boxed{\dfrac{1}{7^2}}[/tex]
Answer:
The answer is 1/7^2
Step-by-step explanation:
I took the test lol
For what values of K does the equation (2k+1)x^2 +2x= 10x - 6 have two real and equal roots.
Answers
Answer:
Step-by-step explanation:For what values of does the equation (2 + 1) have two 2
+ 2 = 10 − 6
real and equal roots?
A quadratic equation that has 2 roots that are equal means that the discriminant of the equation is 0. The value of k that makes the equation have 2 real and equal roots is [tex]k = \frac{5}{6}[/tex]
Given that:
[tex](2k + 1)x^2 + 2x = 10x - 6[/tex]
Rewrite as:
[tex](2k + 1)x^2 + 2x - 10x + 6 = 0[/tex]
[tex](2k + 1)x^2 - 8x + 6 = 0[/tex]
A quadratic equation is represented as:
[tex]ax^2 + bx + c = 0[/tex]
By comparison:
[tex]a=2k+1\\ b =-8\\\ c =6[/tex]
If an equation has 2 real and equal roots, then:
[tex]b^2 = 4ac[/tex]
So, we have:
[tex](-8)^2 = 4 \times (2k + 1) \times 6[/tex]
[tex]64 = 4 \times (2k + 1) \times 6[/tex]
Divide by 4
[tex]16 = (2k + 1) \times 6[/tex]
Divide by 6
[tex]\frac{16}{6} = (2k + 1)[/tex]
[tex]\frac{8}{3} = 2k + 1[/tex]
Subtract 2 from both sides
[tex]2k = \frac{8}{3} -1[/tex]
Take LCM
[tex]2k = \frac{8-3}{3}[/tex]
[tex]2k = \frac{5}{3}[/tex]
Divide by 2
[tex]k = \frac{5}{6}[/tex]
Hence, the value of k that makes the equation have 2 real and equal roots is [tex]k = \frac{5}{6}[/tex]
Read more about real and equal roots at:
https://brainly.com/question/2535040
Convert 50 yards into meters.
A. 45.87 meters
C. 72.45 meters
B. 50 meters
D. 60 meters
Answers
Convert 50 yards into meters.
A. 45.87 meters
C. 72.45 meters
B. 50 meters
D. 60 meters
It's actually 45.72 but A is the closest :)
Answer:
Hey there!
One yard is about 0.9144 m.
Thus, 50 yards would be about 45.87 meters.
Let me know if this helps :)
Please answer this correctly without making mistakes
Answers
Answer:
so first convert to fraction so
9 3/4 = 39/4
so it was spread among 3
so this is division so you do 39/4 divided by 3
so you keep switch flip
which is 39/4 *1/3
answer is 13/4
Answer:
3 1/4 bagsStep-by-step explanation:
[tex]9\frac{3}{4}= \frac{(4 \times 9)+3}{4}= \frac{39}{4} \\\\\frac{39}{4} = 3 \:vegetable \: beds\\x \:\:\:= 1 \: vegetable \:bed\\\\3x = \frac{39}{4} \\\\\frac{3x}{3} = \frac{\frac{39}{4} }{3} \\\\x = \frac{13}{4} \\\\x = 3\frac{1}{4}[/tex]
g If two events are mutually exclusive, what is the probability that both occur at the same time? a. 1.00 b. 0.00 c. Cannot be determined from the information given. d. 0.50
Answers
The correct answer is B. 0.00
Explanation:
In statistics, two events are mutually exclusive if only one event can occur at one time. For example, if you have a deck of cards with Hearts and Spades, every time you choose a card you will have either Hearts or Spades but not both at the same time as there is not any card that combines Hearts and Spades in the same card. This means it is statistically impossible for two mutually exclusive events to occur at the same time, which means the probability is 0.00.
Tanθ - cosecθ secθ (1-2 cos²θ) = cotθ
Answers
Answer:
I thinksomething is wrong.
I'm getting another proving it's-tan thita.
I hope this is the one you are searching for..
solve the equation: 14<2x−1≤20
Answers
Answer:
7.5 < x≤10.5
Step-by-step explanation:
14<2x−1≤20
Add 1 to all sides
14+1<2x−1+1≤20+1
15<2x≤21
Divide each side by 2
15/2 <2x/2 ≤21/2
7.5 < x≤10.5
Steps to solve:
14 < 2x - 1 <= 20
~Add 1 to everything
15 < 2x <= 21
~Divide 2 to everything
7.5 < x <= 10.5
Best of Luck!
Given: f(x) = x + 2 and g(x) = x2 +3, find the following:
28) f(-3)
29) f(g(2))
30) g(f(x))
31) f-1(x)
Answers
Answer:
28) -1
29) 9
30) x^2+4x+7
31) x-2
Step-by-step explanation:
Given:
f(x) = x + 2
g(x) = x^2 +3
Find:
28) f(-3)
29) f(g(2))
30) g(f(x))
31) f-1(x)
Solution:
Put the function argument values into the expression and do the arithmetic.
28) f(-3) = (-3) +2 = -1
__
29) f(g(2)) = f((2)^2 +3) = f(7) = (7) +2 = 9
__
30) g(f(x)) = g(x+2) = (x+2)^2 +3 = x^2 +4x +7
__
31) The meaning of y = f^-1(x) is x = f(y).
x = f(y) = y+2
y = x -2
f^-1(x) = x -2
The minute hand of a watch has a length of 1.4 cm. Find the; (a) distance moved by the tip of the minute hand from 8.13 am to 8.49 am. (b) angle swept by the minute hand if the tip moves 8.8 mm (c)time it will bee when the minute hand sweeps the angle calculated in (b), if the minute hand started moving at 8.39 am
Answers
Answer:
A). The distance covered= 5.2752 cm
B). Angle swept = 36°
C). The time = 8:45 am
Step-by-step explanation:
The watch is assumed to be a circle while the minute hand is assumed to be the radius
Radius = 1.4cm
A). From 8:13 to 8:49= 36 minutes
Recall, there is 60 minutes in a round watch.
The distance covered= 2πr*36/60
The distance covered= 2*3.14*1.4*0.6
The distance covered= 5.2752 cm
B). If distance covered is 8.8 mm
8.8 mm = 0.88cm
0.88= 2*3.14*1.4*(x/360)
0.88/(8.792)=x/360
0.1= x/360
0.1= x/360
36°= x
Angle swept = 36°
C). The time it will be if the watch started from 8:39 am and moved 36°
36/360= y/60
0.1= y/60
0.1*60= y
6 minutes= y
The time with be 8:39+6 minutes
The time = 8:45 am
Let f(x) = 8x3 + 16x2 − 15 and g(x) = 2x + 1. Find f of x over g of x
Answers
[tex]\dfrac{f(x)}{g(x)}=\dfrac{8x^3+16x^2-15}{2x+1}[/tex]
ASAP HELP WILL MARK BRAINLIEST
Answers
Answer:
c(x)=(3/4)^x
(3/4)^-2= 16/9
(3/4)^-1 =4/3
(3/4)^0=1
(3/4)^1 = 3/4
(3/4)^2= 9/16
If you only have a
1
6
cup measuring cup and a recipe calls for
15
1
6
cups of flour, how many 1/6 cups would you need to use?
Answers
Hi! I'm happy to help!
To solve this problem, we need to divide the recipe amount in 1/6 amounts. So, we will do a fraction division problem like this:
15[tex]\frac{1}{6}[/tex]÷[tex]\frac{1}{6}[/tex]
This problem is hard to do with mixed numbers, so we need to turn 15[tex]\frac{1}{6}[/tex] into an improper fraction. To do that we need to multiply 15 by 6, because that is our denominator, then add the extra [tex]\frac{1}{6}[/tex].
(15×6)+1
90+1
91
So, our improper fraction would be[tex]\frac{91}{6}[/tex], now, let's solve.
[tex]\frac{91}{6}[/tex]÷[tex]\frac{1}{6}[/tex]
It is difficult to do division problems on their own, so we can change this into an easier problem. We can do the inverse operation and turn this into multiplication. We do this by changing it to multiplication (obviously), then flip the second fraction.
[tex]\frac{91}{6}[/tex]×[tex]\frac{6}{1}[/tex]
Now, we just multiply the top by the top, and bottom by the bottom.
[tex]\frac{546}{6}[/tex]
We could end it here, but we want a whole number, so, we simplify the number by dividing both the top and bottom by 6.
[tex]\frac{91}{1}[/tex]
Anything over 1, is just a whole number
91.
Therefore, the recipe should require 91 uses of the 1/6 cup.
I hope this was helpful, keep learning! :D
What is f(0) given f(x) = 5(x + 2)2 – 10?
Answers
Answer:
10
Step-by-step explanation:
f(o) is given when x= 0 in f(x)
f(0) = 5 ( 0 + 2 ) 2 - 10
= 20 - 10
= 10
Answer:
[tex] \boxed{ \bold{ \huge{ \sf{f{(0) = 10}}}}}[/tex]
Step-by-step explanation:
Given, f ( x ) = 5 ( x + 2 )² - 10
Let's find f ( 0 ) :
[tex] \sf{f(0) = 5( {0 + 2)}^{2} - 10}[/tex]
Add the numbers
⇒[tex] \sf{f(0) = 5( {2)}^{2} - 10}[/tex]
Evaluate the power
⇒[tex] \sf{f(0) = 5 \times 4 - 10}[/tex]
Multiply the numbers
⇒[tex] \sf{ 20 - 10}[/tex]
Subtract 10 from 20
⇒[tex] \sf{10}[/tex]
Hope I helped !
Best regards !!
The sum of two numbers is twenty-four. The second number is equal to twice the first number. Call the first number m and the second number n.
Answers
Answer:
Step-by-step explanation:
Hello, please consider the following.
m and n are the two numbers.
m + n = 24, right?
n = 2 m
We replace n in the first equation, it comes
m + 2m =24
3m = 24 = 3*8
So, m = 8 and n = 16
Thank you
The first number is 8 and second number is 16.
What is equation?Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
Given that the sum of two numbers is twenty-four
The second number is equal to twice the first number
Let x and y are the two numbers.
According to the question,
m + n = 24,
n = 2m
Substitute the value of n in the first equation,
m + 2m =24
3m = 24
m = 24/3
m = 8
Substitute the value of m in the n = 2m
So, n = 2(8)
n = 16
Hence, the first number is 8 and second number is 16.
Learn more about equation here:
brainly.com/question/10413253
#SPJ5
Please help. I’ll mark you as brainliest if correct
Answers
Answer:
32 20 17 -57 13
-24 15 -31 31 -28
27 10 -7 18 22
Step-by-step explanation:
Write the equation of the line that passes through the points (- 4, - 3) and (3, - 5) . Put your answer in fully reduced slope intercept form, unless it is a vertical or horizontal line
Help:(
Answers
Answer:
y = (-2/7)x - (29/7)
Step-by-step explanation:
2/5(10c -35) (the 35 is negative)
Answers
Answer:
The simplified form is 2 (c - 7).
Step-by-step explanation:
The expression to be solved is:
[tex]f (c)=\frac{2}{5} (10c -35)[/tex]
Simplify the expression as follows:
[tex]f (c)=\frac{2}{5} (10c -35)[/tex]
[tex]=[\frac{2}{5}\times 10c]-[\frac{2}{5}\times 35]\\\\=[2\times 2c]-[2\times 7]\\\\=4c-14\\\\=2(c-7)[/tex]
Thus, the simplified form is 2 (c - 7).
Chloe wants to wrap a present in a box for Sarah. The top and bottom of the box is 8 in. by 3 in., the sides are both 3 in by 2 in. and the front and back are 8 in by 2 in. How much wrapping
paper will Chloe need to wrap the present?
Answers
Answer:
92 inches squared
Step-by-step explanation:
T/P = 8 * 3
L/R = 3 * 2
F/B = 8 * 2
Solving for surface area!
2(24) + 2(6) + 2(16) = 92
The town administrators separate the 84 houses in a neighborhood into equal
groups to do safety inspections. Which of the following groupings is not
possible?
F. Three groups of 26 houses H. Six groups of 14 houses
G. Four groups of 21 houses I. Seven groups of 12 houses
Answers
Answer:
Step-by-step explanation:
F: 3×26 = 78 ≠ 84
G: 4×21 = 84
H: 6×14 = 84
I: 7×12 = 84
how to do divide
[tex]3 + 255255[/tex]
Answers
Answer:
Step-by-step explanation:
Just add 3 to the last 5. The right most figure before the decimal is the units figure. So add 3 to the units digit. The answer is 244258
The driveway needs to be resurfaced. what is the BEST estimate of the area of the driveway?
Answers
Answer:
125π ft²
Step-by-step explanation:
1/4π(30)² - 1/4π(20)² = 125π
PLEASE HELP QUICK!!!!!!! Find the length of a rectangle that has one side of length 8 and area 32
Answers
Answer:
4
Step-by-step explanation:
Length of one side=8
Area=32
Length of another side=x
8 into x = 32
X=32/8
=4
Please help me solve it .
Answers
9514 1404 393
Answer:
ii)
36 -16 = 206 -5 = 130 -11 = 19iii)
15 -6 = 95 +2 = 720 -4 = 16Step-by-step explanation:
Straightforward addition and subtraction. You could do this in 2nd grade. Work from lower right to upper left.
ii) 30 -11 = 19; 6 -5 = 1 . . . . bottom two rows
20 -1 = 19; 16 -5 = 11 . . . . right two columns
36 -16 = 20 . . . . top row
Check
36 -6 = 30 . . . . left column
Then the solution by row is ...
36 -16 = 206 -5 = 130 -11 = 19__
iii) Same deal, working from lower right.
20 -4 = 16 . . . . bottom row
9 +7 = 16 . . . . right column
6 -2 = 4 . . . . middle column
5 +2 = 7 . . . . middle row
15 -6 = 9 . . . . top row
15 +5 = 20 . . . . left column
The solution by row is ...
15 -6 = 95 +2 = 720 -4 = 16Twice one number added to another number is 18. if the 2nd number is equaled to 12 less than 4 times the 1st number, find the two numbers
2x + y= ? ; y= ?x - ?
Answers
Answer:
8
Step-by-step explanation:
Math Word Problem: Twice one number added to another number is 18. Four times the first number minus the other number is 12. Find the number.?
Let the two numbers be x and y
As per statement twice one number added to another number is 18.
2x + y = 18
y = 18 - 2x…Eq..1
Four times the first number minus the other number is 12.
4x - y = 12…Eq..2
Now substituting the value of y from Eq..1 to Eq..2
4x - y = 12
4x - (18 - 2x) = 12
4x - 18 + 2x = 12
4x + 2x = 12 + 18
6x = 30
x = 30 / 6
x = 5
Thus one number is 5. Now calculating the other number by putting the value of x in Eq. 1
y = 18 - 2x
y = 18 - 2×5
y = 18 - 10
y = 8
Other number is 8
Answer the two numbers are 5 and 8
Let us check the correctness of answer by putting the value of x and y in Eq. 1
y = 18 - 2x
8 = 18 - 2 × 5
8 = 18 - 10
8 = 8
Means answer is correct
y = 4x - 12
2x + y = 18
2x + (4x - 12) = 18
6x - 12 = 18
6x = 30
x = 5
y = 4x - 12
y = 4(5) - 12
y = 20 - 12
y = 8
Therefore the first number is 5 and the second number is 8.
Actual time in seconds recorded when statistics students participated in an experiment t test their ability to determine when one minute 60 seconds has passed are shown below.Find the mean median mode of the listed numbers. 53 52 72 61 68 58 47 47
Answers
Answer:
53 52 72 61 68 58 47 47 (arrange it)
47 47 52 53 58 61 68 71 (done!)
Mode: 47 (appear twice)
Median: (53+58)/2 = 55.5
Mean = 47+47+52+53+58+61+68+71/ 8
=457/8
=57.12
Q-The general solution of inequality cos 2 x≤- sin x is
Answers
Answer:
x∈[2nπ−5π/6, 2nπ−π/6]∪{(4n+1)π/2}, n ϵ I
Step-by-step explanation:
1−2sin2 x≤−sin x ⇒ (2sin x+1)(sin x−1)≥0
sin x≤−1/2 or sin x≥1
−5π/6+2nπ≤x≤−π/6+2nπ or , n ϵ I x=(4n+1)π/2, n ϵ I⇒ -5π6+2nπ≤x≤-π6+2nπ or , n ϵ I x=4n+1π2, n ϵ I (as sin x = 1 is valid only)
In general⇒ In general x∈[2nπ−5π/6, 2nπ−π/6]∪{(4n+1)π/2}, n ϵ I
Find TAN
Instructions: Find the value of the trigonometric ratio. Make
sure to simplify the fraction if needed.
Answers
please mark this answer as brainlist
Four couples are at a party. Four of the eight people are randomly selected to win a prize. No person can win more than one prize. What is the probability that both of the members of at least one couple win prizes? Express your answer as common fraction.
Answers
Answer:
27/35
Step-by-step explanation:
We use combination to solve for this
C(n, r), =nCr = n!/r!(n - r)!
From the question, we are told that:
Four couples are at a party. Four of the eight people are randomly selected to win a prize.
Four couples = 8 people.
= 8C4 = 8!/4! (8 - 4)!
= 70
No person can win more than one prize. ( No person can win more than one prize of the 4 people selected)
This can happen in 4 ways
[4C1 × 3C2 ] × 4=
[4!/1! ×( 4 - 1)!] × [3!/2! ×(3-2)!] × 4 ways
= 4 × 3 × 4 ways
= 48
The probability that both of the members of at least one couple win prizes
48 + 4C2/ 8C4
4C2 = 4!/2!(4 - 2) !
= 6
8C4 = 8C4 = 8!/4! (8 - 4)!
= 70
48 + 6/ 70
= 54/70
= 27/35
Therefore, the probability that both of the members of at least one couple win prizes is 27/35.
The probability that both of the members of at least one couple win prizes is 27/35 and this can be determined by using the given data.
Given :
Four couples are at a party. Four of the eight people are randomly selected to win a prize. No person can win more than one prize.The following steps can be used in order to determine the probability that both of the members of at least one couple win prizes:
Step 1 - The concept of probability is used in order to determine the probability that both of the members of at least one couple win prizes.
Step 2 - According to the given data, the total number of people is 8.
Step 3 - So, the probability that both of the members of at least one couple win prizes is:
[tex]\rm P =\dfrac{ \;^4C_1\times \;^3C_2\times 4 + \;^4C_2}{\;^8C_4}[/tex]
Step 4 - Simplify the above expression.
[tex]\rm P =\dfrac{48+ 6}{70}[/tex]
[tex]\rm P = \dfrac{27}{35}[/tex]
So, the probability that both of the members of at least one couple win prizes is 27/35.
For more information, refer to the link given below:
https://brainly.com/question/795909
i will rate you brainliest
Answers
Answer:
D. Factoring trinomials
Step-by-step explanation:
The factoring trinomials method is the best way to factor the expression, since it is in the standard trinomial form ax² + bx + c
In this method, you can factor the expression by finding 2 factors of c that add up to b.
The expression is not in the simplest form, and difference of squares cannot be used because there are no perfect squares. Prime factorization is also not used for factoring expressions with variables.
So, D is the right answer.
Apply Simpson's rule to approximate the value of integration 1 to 4 e^x In x dx with n = 3.
Answers
[tex]Here, h=41,0.25,y=1+x21
[/tex]
[tex]x y101.020.25 0.9413 0.250.94140.750.64510.5
[/tex]
[tex]By Simpson's Rule:
[/tex]
[tex]∫011+x2dx=4×31
[/tex]
[tex][(1+0.5)+4(0.941+0.941+0.64)+2(0.8)]
[/tex]
[tex]=121[9.424]=0.785
[/tex]