Answers
Hello,
[tex]\widehat{A}=180^o-24.4^o-103.6^o=52^o\\\\\dfrac{sin(24.4^o)}{37.3} =\dfrac{sin(103.6^o)}{c} \\\\\\c=87.760246\approx{87.8}\\\\\\\dfrac{sin(52^o)}{a} =\dfrac{sin(24.4^o)}{37.3} \\\\\\a=71.1510189...\approx{71.2}\\[/tex]
Related Questions
The half-life of a newly discovered radioactive element is 30 seconds. To the nearest tenth of a second, how long will it take for a sample of 9 grams to decay to 0.72 grams
Answers
Answer:
It will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.
Step-by-step explanation:
We can write a half-life function to model our function.
A half-life function has the form:
[tex]\displaystyle A=A_0\left(\frac{1}{2}\right)^{t/d}[/tex]
Where A₀ is the initial amount, t is the time that has passes (in this case seconds), d is the half-life, and A is the amount after t seconds.
Since the half-life of the element is 30 seconds, d = 30. Our initial sample has nine grams, so A₀ is 9. Substitute:
[tex]\displaystyle A=9\left(\frac{1}{2}\right)^{t/30}[/tex]
We want to find the time it will take for the element to decay to 0.72 grams. So, we can let A = 0.72 and solve for t:
[tex]\displaystyle 0.72=9\left(\frac{1}{2}\right)^{t/30}[/tex]
Divide both sides by 9:
[tex]\displaystyle 0.08=\left(\frac{1}{2}\right)^{t/30}[/tex]
We can take the natural log of both sides:
[tex]\displaystyle \ln(0.08)=\ln\left(\left(\frac{1}{2}\right)^{t/30}\right)[/tex]
By logarithm properties:
[tex]\displaystyle \ln(0.08)=\frac{t}{30}\ln(0.5)[/tex]
Solve for t:
[tex]\displaystyle t=\frac{30\ln(0.08)}{\ln(0.5)}\approx109.3\text{ seconds}[/tex]
So, it will take about 109.3 seconds for nine grams of the element to decay to 0.72 grams.
Plz do this, I’m so exhausted. Thxx
Answers
Answer:
12) B --> x < 8/3
13) B --> x ≤ 1/6
Step-by-step explanation:
12) Solving inequalities is just like solving normal equations where you and add, subtract, multiply and divide sides by the same value. Keep in mind dividing or multiplying by a negative flips the sign:
x - 10 < 6 - 5x
Add 5x to both sides to combine the x terms:
x - 10 < 6 - 5x
+5x +5x
6x - 10 < 6
Add 10 to both sides to isolate the x term:
6x - 10 < 6
+10 +10
6x < 16
Now, divide by 6 on both sides:
x < 8/3, this is B
13) Simplify 2 - 4:
2-3(2x + 1) ≤ 6x(-2)
Distribute:
2 - 6x - 3 ≤ -12x
Add 12x to both sides and combine like terms:
6x - 1 ≤ 0
Add 1 to both sides:
6x ≤ 1
Divide by 6:
x ≤ 1/6, this is B
X- 10 < 6-5x
So I brought over the five x to be on the side where the x is and then I placed the others on the other side so…
5x + x < 6 + 10
6x < 16
Then I divided both sides by 6
NO LINKS OR ANSWERING WHAT YOU DON'T KNOW?
1. Suppose y varies inversely with x, and y = 25 when x = 1/5. What is the value of y when x = 5?
a. 15
b. 5
c. 25
d. 1
2. Suppose y varies inversely with x, and y = a when x = a^2. What inverse variation equation related x and y?
a. y = a^2/x
b. y = a^3/x
c. y= a^3x
d. y = ax
3. Suppose y varies inversely with x, and y = 3 when x = 1/3. What is the inverse variation equation that relates x and y?
a. y = 1/x
b. y =x
c. y = 3x
d. y = 3/x
Answers
Answer:
1. D. 1
2. B. y=a³/x
3. A. y=1/x
Step-by-step explanation:
too long to give te explanations but they're there in the attachments
Write an expression for the sequence of operations described below.
divide s by u, add the result to t, then add v to what you have
Do not simplify any part of the expression
Answers
Step-by-step explanation:
s+u
Add t: You will need to introduce brackets
(s+u) + t
Add v: Introduce another v
((s/u) + t) + v
13. Given that
[tex] {x}^{2} + {y}^{2} + 10y + 16 = 0[/tex]
and
[tex] {(x - 3)}^{2} + {y}^{2} = 1[/tex] are two circles on the same plane. Find:
a) the coordinates of the center and the radius for each circle.
b) the equation of the straight line joining the center of both circles.
Answers
step by step explanation:
[tex]\mathfrak{x}^{2}+{y}^{2}+16=0[/tex]
=[x2+16=0x26]
=[2x{y}^2{16}~0]
=[4×{y}^0{16}]
=[32x{y}^x]
Given that Z1 = 1 + i and Z2 = 3 - 4i, find z1z2
Answers
Answer:
7-i
Step-by-step explanation:
It is asking for the product of the given complex numbers.
Z1Z2 means Z1 times Z2
(1+i)(3-4i)
You can do the whole foil thing here since we are multiplying a pair of binomials. But all you are doing when you do that is multiplying every term in the first ( ) to every term in the second ( ).
1(3)+1(-4i)+i(3)+i(-4i)
Simplify each term. That is, perform the multiplication in each term:
3-4i+3i-4i^2
Combine like terms and also replace i^2 with (-1):
3-1i-4(-1)
Multiplication identity property used:
3-i+4
Combine like terms:
7-i
Josephine left home traveling at 25 mph. One hour later her friend, Steve, leaves from the same place and travels the same road traveling at 50 mph. How many hours will it take Steve to catch up to Josephine?
Answers
Answer:
1 hour
Step-by-step explanation:
J = 50 mph by 2 hours
S = 50 mph by 1 hour
2-1 = 1
Pierre Martina is comparing the cost of credit to the cash price of an item. If Pierre makes a down payment of $70 and pays $34 a
month for 24 months, how much more will that amount be than the cash price of $695? (Input the amount as a positive value.)
Amount of difference
Answers
Answer:
$191
Step-by-step explanation:
Find how much she will be paying over the 24 months:
34(24)
= 816
Add the down payment to this:
816 + 70
= 886
Find the difference between this and 695:
886 - 695
= 191
So, the difference will be $191 more
5. Determine the total area of the figure below.
4 ft!
12 ft
10 ft
3 ft
9 ft
Answers
Explanation:
The triangles area is 24ft^2
The large rectangle is 120ft^2
The small rectangle is 27ft^2
24+120+27= 171ft^2
Amy needs to mail a gift card to a friend. She uses 47-cent stamps and 6-cent stamps to pay $2.42 in postage. How many of each stamp did Amy use?
Answers
Answer:
Answer:Amy used 4 41-cent stamps and 8 6-cent stamps.
Step-by-step explanation:
Let x represent the number of 41-cent stamps that Amy used. Let y represent the number of 6-cent stamps that Amy used.
41 cents = 41/100 = $0.41
6 cents = 6/100 = $0.06
She uses 41-cent stamps and 6-cent stamps to pay $2.12 in postage. It means that
0.41x + 0.06y = 2.12
Multiplying through by 100, it becomes
41x + 6y = 212
6y = 212 -41x
We would test for corresponding values of x and y that satisfies the equation and they must be whole numbers.
If x = 3,
6y = 212 - 41 × 3 = 89
y = 89/6 = 14.8333
If x = 4,
6y = 212 - 41 × 4 = 48
y = 48/6 = 8
Answer:Amy used 4 41-cent stamps and 8 6-cent stamps.
Step-by-step explanation:
Let x represent the number of 41-cent stamps that Amy used. Let y represent the number of 6-cent stamps that Amy used.
41 cents = 41/100 = $0.41
6 cents = 6/100 = $0.06
She uses 41-cent stamps and 6-cent stamps to pay $2.12 in postage. It means that
0.41x + 0.06y = 2.12
Multiplying through by 100, it becomes
41x + 6y = 212
6y = 212 -41x
We would test for corresponding values of x and y that satisfies the equation and they must be whole numbers.
If x = 3,
6y = 212 - 41 × 3 = 89
y = 89/6 = 14.8333
If x = 4,
6y = 212 - 41 × 4 = 48
y = 48/6 = 8
Together, the cost of 47x + 6y = 242 (242cents)
As x is more expensive, let’s look at that first.
If we bought 5 of the x stamps, that would cost 5x47=249. That is too much, so the most we can buy is 4 x stamps
4 of the x stamps cost 188.
We need to get to 242, so let’s look at the y stamps.
242 - 188 is 54. Each y stamp costs 6 cents, so how many can we buy?
54 / 6 = 9. And there we have our answer.
4 x stamps and 9 y stamps.
Four 47cent stamps and nine 6cent stamps.
Alex thinks of a number. he squares it, then takes away five .Next multiplies it by 4 ,takes away seven, divides it by three ,and finally adds six his answer is nine what number did he start with
Answers
Answer:
3
Step-by-step explanation:
start with the ending answer and go backwards
Answer:
3.
Step-by-step explanation:
.
Which option distinguishes what can be inferred in the following scenario?
Climatologists have recently observed a slow, steady increase in temperatures, which coincides with more frequent severe weather and higher sea levels.
1.The global climate is affected by human activity.
2.The global climate is undergoing significant changes.
3.The global climate is increasing concentrations of carbon dioxide.
4.The global climate is experiencing more severe weather because temperatures have increased.
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The global climate is undergoing significant changes.
Use the graph to find the y-intercept and axis of symmetry
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Answer: (a) and (d)
Step-by-step explanation:
From the graph, vertex is at
Graph is same about the point [tex]x=2[/tex] . Therefore, axis of symmetry is the line [tex]x=2[/tex]
Y intercept is the place where curve intersect the Y-axis that is [tex](0,2)[/tex]
Option (a) and (d) are correct.
find (f o g)(x)
f(x) = 5x+1, g(x)= *square root of x*
Answers
Step-by-step explanation:
Hey there!
Here;
f(x) = 5x + 1
g(x) = (√x)
Now;
fog(X) = f(g(x))
= f(√x)
= 5√x + 1
Therefore, fog(X) = 5√x + 1.
Hope it helps!
5. There are 8 sections of seats in an auditorium. Each section contains at least 150 seats but not more than 200 seats. Which of the following could be the number of seats in this auditorium? (A) 800 (B) 1,000 (C) 1,100 (D) 1,300 (E) 1,700
Answers
Answer:
1300
Step-by-step explanation:
Given that :
Number of sections = 8
Number of seats per section, x ;
150 ≤ x ≤ 200
The possible Number of seats in the auditorium :
Number of seats per section * number of sections
150 * 8 ≤ x ≤ 200 * 8
1200 ≤ x ≤ 1600
The possible Number of seats will lie within 1200 and 1600
From the options, only 1300 lie within this range
Identify the domain of the function shown in the graph.
Answers
What is the midpoint of the segment shown below?
Answers
Answer:
A
Step-by-step explanation:
Midpoints are found by averaging the coordinates.
Averaging " add all the numbers and divide by the number of numbers.
Here, there are only 2 numbers. So, you divide by 2.
(1,2) (1,-5)
[tex]\frac{1 +1}{2}[/tex] , [tex]\frac{2 + (-5)}{2}[/tex]
[tex]\frac{2}{2}[/tex] , [tex]\frac{-3}{2}[/tex]
(1, [tex]\frac{-3}{2}[/tex] )
Express the following composite numbers as products of prime factors 64
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Answer:
64 is a composite number, and it is 8 squared. 64 = 1 x 64, 2 x 32, 4 x 16, or 8 x 8. Factors of 64: 1, 2, 4, 8, 16, 32, 64. Prime factorization: 64 = 2 x 2 x 2 x 2 x 2 x 2, which can also be written 64 = 2⁶.
If there is an error in solving the equation below, then explain the error and in what step the error is in the equation. If no error, then just type “no error”
Answers
Answer:
To solve for x, you must multiply by the reciprocal.
In this case, multiply both sides by [tex]\frac{3}{2}[/tex] .
When doing this the result will be x = 3
Explain the difference between a rate, a ratio, and a proportion?
Answers
Answer:
A proportion is an equality of two ratios.
Example : [tex]\frac{1}{3}[/tex] = [tex]\frac{x}{9}[/tex]
We write proportions to help us find equivalent ratios and solve for unknown quantities.
A rate is the quotient of a ratio where the quantities have different units.
Example : [tex]\frac{distance}{time}[/tex]
A ratio is a comparison of two quantities.
Example : 1 : 3 or [tex]\frac{1}{3}[/tex]
Identify the transformation that occurs to create the graph of h(x).
H(x)=f(x+3)
Answers
Answer: The graph moved left 3 units.
(x, y) = (x - 3, y)
HELP ASAP I WILL GIVE BRAINLIST
Find the length of an arc of a circle with a 8-cm radius associated with a central angle of 240 degrees. Give your answer in exact and approximate form to the nearest hundredth. Show and explain your work
Answers
Answer:
33.51 cm
Step-by-step explanation:
240/360 = 2/3 (Arc length is 2/3 of the total circumference)
C = 2[tex]\pi[/tex]r ( Calculate the total circumference)
C = 2(8)[tex]\pi[/tex]
C = 50.265
2/3(50.265) (Take 2/3 of the circumference. times 2 divide by 3)
33.51
Use a calculator and leave the answer to C and then multiply and divide. You get a more precise answer.
The exact arc length is [tex]\frac{32\pi}{3}[/tex] radians.
The arc length in approximate form is 33.49 radians.
What is the formula for arc length?[tex]s = r\times \theta[/tex]
where r is the radius of the circle and [tex]\theta[/tex] is the central angle in radians.
How to convert angle from degrees to radians?Radians = Degrees ×[tex]\frac{\pi}{180^{\circ}}[/tex]
For given question,
We have been given a circle with a 8-cm radius associated with a central angle of 240 degrees.
[tex]r=8~cm,~\theta=240^{\circ}[/tex]
First we convert angle in radians.
[tex]\theta=240^{\circ}\\\\\theta=240^{\circ} \times \frac{\pi}{180^{\circ}}\\\\ \theta=\frac{4\pi}{3}[/tex]
Using the formula of the arc length,
[tex]s=8\times \frac{4\pi}{3} \\\\s=\frac{32\pi}{3}[/tex]
The exact answer of the arc length is [tex]s=\frac{32\pi}{3}[/tex]
Substitute the value of [tex]\pi = 3.14[/tex]
So, the arc length would be,
[tex]\Rightarrow s=\frac{32\times \pi}{3}\\\\\Rightarrow s=\frac{32\times 3.14}{3}\\\\\Rightarrow s=33.49[/tex]radians
Therefore, the exact arc length is [tex]\frac{32\pi}{3}[/tex] radians.
the arc length in approximate form is 33.49 radians.
Learn more about the arc length here:
https://brainly.com/question/16403495
#SPJ2
Please help! I feel like I'm drowning :(
Answers
Answer:
1d = -3
2b = 2
2c = 1
3a = 3
3d = 4
Step-by-step explanation:
Polynomial 1: [tex]x^2-8x+15[/tex]
Multiply the leading coefficient, 1, and the last term, 15. You get: 15.
Then, list out the factors of 15 and the addends of -8 until you get two of numbers that are the same:
Factors of 15: -5 * -3
Addends of -8: -5 + -3
Replace the -8x with -5x - 3x:
[tex]x^2-5x-3x+15[/tex]
Put parentheses around the first 2 terms & last 2 terms and factor like so:
[tex](x^2-5x)-(3x+15)[/tex]
[tex]x(x-5)-3(x-5)[/tex]
[tex](x-5)(x-3)[/tex]
Looking at the answer (ax + b)(cx + d), d would correspond with -3.
Polynomial 2: [tex]2x^3-8x^2-24x[/tex]
First factor out the x:
[tex]x(2x^{2}-8x-24)[/tex]
Divide the polynomial inside by 2 and place the 2 outside with the x:
[tex]2x(x^2-4x-12)[/tex]
Then find the factors of 1*-12 and the addends of -4 and see which two numbers match:
Factors of -12: -6 * 2
Addends of -4: -6 + 2
Replace the -8x with -6x + 2x:
[tex]2x(x^2-6x+2x-12)[/tex]
Put parentheses around the first 2 terms & last 2 terms and factor like so:
[tex]2x((x^2-6x)+(2x-12))[/tex]
[tex]2x(x(x-6)+2(x-6))[/tex]
[tex]2x((x+2)(x-6))[/tex]
[tex]2x(x+2)(x-6)[/tex]
Looking at the answer (2x)(ax + b)(cx + d), b & c would correspond with 2 & 1.
Polynomial 3: [tex]6x^2+14x+4[/tex]
Divide the polynomial by 2:
[tex](2)(3x^2+7x+2)[/tex]
Find the factors of 3*2 and the addends of 7 and see which two numbers match:
Factors of 6: 6 * 1
Addends of 7: 6 + 1
Replace the 7x with 6x + x:
[tex](2)(3x^2+6x+x+2)[/tex]
Put parentheses around the first 2 terms & last 2 terms and factor like so:
[tex](2)((3x^2+6x)+(x+2))[/tex]
[tex](2)(3x(x+2)+(x+2))[/tex]
[tex](2)((3x+1)(x+2))[/tex]
[tex](2)(3x+1)(x+2)[/tex]
Then multiply the 2 with the (x+2) and here's your final answer:
[tex](3x+1)(2x+4))[/tex]
Looking at the answer (ax + b)(cx + d), a & d correspond with 3 & 4.
Hope that helps (●'◡'●)
(This took a while to write, sorry about that)
The following is a scatterplot of the percent of children under age 18 who are not in school or in the labor force vs. the number of juvenile violent crime arrests for each of the 50 states. The least-squares regression line has been drawn in on the plot. We would like to predict what the number of juvenile violent crime arrests would be in a state if 25% of children are not in school or in the labor force. This is called
Answers
Answer:
Extrapolation
Step-by-step explanation:
From the linear regression plot created in the picture given, se could see that Tha percentage of student covered by the the plot is just above 16%. Therefore, to predict the percentage of the number of juvenile violent crime arrests would be in a state if 25% of children are not in school or in the labor force will require us to assume that the current trend continues into the future. Hence, we use the information and indications we have at present to make prediction into the future based on the assumption that we the current trend will remain relevant and applicable. This assumption into the future based on current trend is called EXTRAPOLATION.
f(x) =x-4/x+5
and g(x) = 2x-1
Find the composition f•g
Answers
Step-by-step explanation:
2x-1 - (4/(2x-1)) + 5
2x^2 -4x -2 -4 + 10x - 5
2x^2 +6x -11
How much do I need to subtract from 67/10 to make 6
Answers
Answer:
0.7
Step-by-step explanation:
67/10 is the same as 6.7 when you subtract the 0.7 you will remain with 6
You are certain to get a heart, diamond, club, or spade when selecting cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
Answers
Answer:
The probability of this event is represented by a value of 1.
Step-by-step explanation:
Probability of a certain event:
The probability of an event that is considered to be certain, that is, guaranteed to happen, is 100% = 1.
You are certain to get a heart, diamond, club, or spade when selecting cards from a shuffled deck.
This means that the probability of this event is represented by a value of 1.
What is the value of q?
2/5
2/14
Answers
Answer:
2√14 prob I'm not 100% sure
Hello friends!
Can anyone of you solve this?
so please solve
Answers
Step-by-step explanation:
each point should be at a 2. the center is 0,0
Given the number of hours spent amusing ourselves to death with screen time, how many Titanics could we have built in one year if all those hours had been spent building Titanics
Answers
Answer:
12
Step-by-step explanation:
