Answer:
∠A1 = 27.4°, ∠A2 = 56.6°, ∠C1 =104.6°, ∠C2=75.4°, a1 = 79.9 and a2 = 144.9
Step-by-step explanation:
From Sine rule
[tex]\frac{a}{sinA}=\frac{b}{sinB} = \frac{c}{sinC}[/tex]
∴ b / sinB = c / sinC
From the question,
b = 129, c = 168 and ∠B = 48°
∴ 129 / sin48° = 168 / sinC
Then, sinC = (168×sin48)/129
sinC = 0.9678
C = sin⁻¹(0.9678)
C = 75.42
∠C2=75.4°
and
∴∠C1 = 180° - 75.4°
∠C1 =104.6°
For ∠A
∠A1 = 180° - (104.6°+48°) [sum of angles in a triangle]
∠A1 = 27.4°
and
∠A2 = 180° - (75.4° + 48°)
∠A2 = 180° - (123.4°)
∠A2 = 56.6°
For side a
a1/sinA1 = b/sinB
a1/ sin27.4° = 129/sin48
a1 = (129×sin27.4°)/sin48
a1 = 79.8845
a1 = 79.9
and
a2/sinA2 = b / sinB
a2/ sin56.6° = 129/sin48
a2 = (129×sin56.6°)/sin48
a2 = 144.9184
a2 = 144.9
Hence,
∠A1 = 27.4°, ∠A2 = 56.6°, ∠C1 =104.6°, ∠C2=75.4°, a1 = 79.9 and a2 = 144.9
PLS HELP
Evaluate the piecewise function at the indicated values from the domain
==========================================================
Explanation:
Piecewise functions are admittedly a bit confusing at first if you aren't familiar with them.
However, they aren't too bad. Effectively we have two functions going on depending on what the input is.
If the input x is less than 0, then we go for the top row and say [tex]f(x) = x^2[/tex]
OR
If the input x is greater than 0, then we go for the bottom row to say [tex]f(x) = \sqrt[3]{x}[/tex]
-------------------------------
In this case, the input is x = -8. So we go for the first row since this x value satisfies x < 0.
We would then say:
[tex]f(x) = x^2\\\\f(-8) = (-8)^2\\\\f(-8) = 64\\\\[/tex]
Which points us to choice A as the final answer.
Answer:
f(-8) = 64
Step-by-step explanation:
Input -8 into one of the formulas (either will work) and the answer should be 64. therefore, if x is -8, f(-8) would equal 64.
Henry bought 2 kilograms of chicken for a family dinner. After dinner, only 61.5 grams were left. How much chicken was eaten, in kilograms?
Answer:
1.9385 kg
Step-by-step explanation:
Given :
Total kilogram of chicken = 2 kilograms
Amount left after dinner = 61.5 gram
Recall :
1000 grams = 1 kilogram
Hence,
61.5 grams = x kg
x = (61. 5 / 1000) = 0.0615 kg
Hence,
Amount eaten = Total chicken - amount left
Amount eaten = (2 - 0.0615) kg
Amount eaten = 1.9385 kg
Which graph has the solutions -1 and 4?
a.
On a coordinate plane, a parabola opens up and goes through (negative 4.2, 0) and (0, negative 1).
c.
On a coordinate plane, a parabola opens up and goes through (negative 4, 0) and (1, 0).
b.
On a coordinate plane, a parabola opens up and goes through (0, negative 3) and (4.5, 0).
d.
On a coordinate plane, a parabola opens up and goes through (0, negative 1) and (4, 0).
Please select the best answer from the choices provided
A
B
C
D
Answer:
graph d
in graph d, the line intersects the x axis twice at (-1,0) and (4,0), so those two are the solutions of the graph
A group of friends will go on a weekend camping trip and split the cost of gas
equally. The cost that each person will pay for gas is inversely proportional to the
number of people who go on the trip. If four friends go on the trip, each person pays
$23 for gas. Write an equation that describes the relationship between cost (c) that
each person pays for gas, and the number of people on the trip (n).
C = 92/n
C= n/0.17
C = 5.75n
C = 5.75/n
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Answer:
(a) C = 92/n
Step-by-step explanation:
The "inversely proportional" relation is represented by the equation ...
C = k/n
The value of k can be found from the given values of C and n.
23 = k/4
23×4 = k = 92
Then the relationship is ...
C = 92/n
I don’t understand the last 2
Nice job on getting the correct answer 144 for the first box. For anyone curious, this is found by multiplying the side lengths of the square. So 12*12 = 144.
======================================
All four sides are decreased by 5 meters. So we go from 12 meter sides to 12-5 = 7 meter sides.
The area of the square is found in the same way as earlier: We multiply the side by itself
area = side*side = 7*7 = 49 square meters
So you'll type 49 into the second box
=======================================
To find the amount of decrease, you subtract the two area values:
144 - 49 = 95 goes in the third box
This indicates that the area has decreased by 95 m^2
a film lasts 45 minutes what fraction of the film is left after 15 minutes and 25 minutes ?
Answer: i) [tex]\frac{1}{3}[/tex]
ii) [tex]\frac{5}{9}[/tex]
Step-by-step explanation:
Total length of film = 45 mins
Fraction of time left after 15 mins = [tex]\frac{15}{45}[/tex]
= [tex]\frac{1}{3}[/tex]
Fraction of time left after 25 mins = [tex]\frac{25}{45}[/tex]
= [tex]\frac{5}{9}[/tex]
Do this please helpppp
Answer:
y = [tex]\frac{20}{9}[/tex]
Step-by-step explanation:
Since the figures are similar then the corresponding sides are in proportion, that is
[tex]\frac{JH}{PQ}[/tex] = [tex]\frac{FM}{ST}[/tex] , substitute values
[tex]\frac{6}{4}[/tex] = [tex]\frac{7}{3y-2}[/tex] ( cross- multiply )
6(3y - 2) = 28
18y - 12 = 28 ( add 12 to both sides )
18y = 40 ( divide both sides by 18 )
y = [tex]\frac{40}{18}[/tex] = [tex]\frac{20}{9}[/tex]
Answer:
20/9
Step-by-step explanation:
since the 2 are similar,
JH/PQ = FM/ST
6/4 = 7/(3y-2)
6(3y-2) = 7*4
18y-12=28
18y = 40
y = 40/18 = 20/9 = 2 2/9
I need help ASAP thank you guys
Answer:
The fraction is undefined when x=-2
Step-by-step explanation:
The fraction will be undefined when the denominator is zero
x+2 = 0
x+2-2 = 0-2
x = -2
The fraction is undefined when x=-2
Answer:
as to me 5
Step-by-step explanation:
ask someone else to say that I am not sure if you have any questions or need any further information please contact me at the end of the world
Write a quadratic function f whose zeros are 4 and 1
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Answer:
f(x) = (x -4)(x -1)
Step-by-step explanation:
If 'a' is a zero of the function, then (x -a) is a factor. The two zeros mean the factored form of the quadratic is ...
f(x) = (x -4)(x -1)
__
The expanded form will be ...
f(x) = x² -5x +4
Can you please help me
Answer:
Step-by-step explanation:
⅝ - 5/9 = 5/72
Can someone help me solve this and explain how to solve if possible please?
what are the answers to the questions below?
Answer:
You have to follow PEMDAS or parenthesis, exponents, multiplication, division, addition, and subtraction. It's an order to solve equations. I listed the steps and the answers for you below :) I have throughly checked them so they should be correct! yw :D
Step-by-step explanation:
1. 5x + 4x - 6x = 24
9x - 6x = 24
3x = 24
24/3 = 8
x = 8
2. 8y + 5 - 4y + 1 = 46
8y - 4y = 4y
5 + 1 = 6
4y + 6 = 46
4y = 46 - 6
4y = 40
40/4 = 10
y = 10
3. 33 = 5 ( x + 8 ) + 3
33 = 5x + 40 + 3 (because we distributed)
33 = 5x + 43
5x + 43 = 33 (just rewriting it to make it easier)
5x = 33 - 43
5x = -10
-10/5 = -2
so x = - 2
4. 2m + 3 ( m - 8 ) = 1
2m + 3m - 24 = 1
we got 3m - 24 because we distributed the 3
5m - 24 = 1
5m = 25
25/5 = 5
m = 5
5. p + p - 2p + 4p = - 48
2p - 2p + 4p = - 48
4p = - 48
- 48 / 4 = - 12
p = - 12
6. 2 ( y + 5 ) + 3y = 25
2y + 10 + 3y = 25
5y + 10 = 25
5y = 25 - 10
5y = 15
15/5 = 3
y = 3
7. 1/4 h + 3/4 h + 1/2 h + 2 = 5
1/4 h + 3/4 h + 1/2 = 3/2 h
3/2 h + 2 = 5
3/2 h = 5 - 2
3/2 h = 3
h = 2
8. 60 = 4 ( k + 3 ) + 2 ( k - 3 )
60 = 4k + 12 + 2k - 6
4k + 12 + 2k - 6 = 60
6k + 6 = 60
6k = 60 - 6
6k = 54
k = 9
9. - 2 ( d + 1.4 ) - 1.8 = 20.6
-2d + - 2.8 - 1.8 = 20.6
-2d - 2.8 = 22.4
-2d = 25.2
d = - 12.6
10. 8 - 2 ( w + 4 ) = 10
8 + - 2 w + - 8 = 10
-2w + 9 + - 8 = 10
-2w = 10
10 / -2 = -5
w = -5
Four students each ran 100 m in a 400-m relay race. The team’s total was 49.44 seconds. Find the average time of each runner.
the average time of each runner is 12.36
Answer:
12.36 seconds
Step-by-step explanation:
Total time = 49.44 seconds
Students = 4
Average = 49.44/4 = 12.36 seconds
Answered by GAUTHMATH
12 workers take 4 hours to complete a job. How long would it take 15 workers to complete the job?
Answer:
3.75
Step-by-step explanation:
Which of the following points would fall on the line produced by the point-slope form equation y - 10 = 3(x - 11) when graphed?
Answer:
(-5,-37)
(-4,-34)
(-3,-31)
(-2,-28)
(-1,-25)
(0,-22)
(1,-19)
(2,-16)
(3,-13)
(4,-10)
(5,-7)
(6,-4)
Step-by-step explanation:
y - 10 = 3(x - 11)
y - 10 = 3x - 33
y = 3x -22
For the z test, the critical region for rejection of H0 _________. Group of answer choices depends on N is determined only by alpha and N allows us to accept the null hypothesis is determined only by alpha
Answer:
allows us to accept the null hypothesis
Explanation:
The z test(in a normal distribution) score for the critical region determines whether we reject the null hypothesis(H0) or accept the null hypothesis(reject or fail to reject the null hypothesis). If we fail to reject the null hypothesis, then we have accepted the alternative hypothesis (H1). The critical region rejection for z test is calculated using alpha and z score, if z score is greater or less than alpha(positive or negative), we reject the null hypothesis.
7
Abdul's gas tank is
1
3
full. After he buys 12 gallons of gas, it is
full. How many gallons can Abdul's tank hold?
9
Answer:
27
Step-by-step explanation:
Let T be the capacity of the tank.
Since the tank was 1/3 full and ends up 7/9 full.
[tex]\frac{7}{9}[/tex]T - [tex]\frac{1}{3}[/tex]T = 12
Simplifying the left side of the equation, tells us how much 12 gallons fills.
[tex]\frac{4}{9}[/tex]T = 12
Now we solve for T:
T = 12*9/4
T = 27
17 Geometry question: Use an algebraic equation to find the measurement of each angle that is represented in terms of X
Answer:
2x + 30° = 40°
4x + 30° = 50°
Step-by-step explanation:
2x + 30° and 4x + 30° are complementary angles.
Complementary angles sum up to give 90°.
Therefore,
2x + 30° + 4x + 30° = 90°
Add like terms
6x + 60 = 90
6x = 90 - 60
6x = 30
6x/6 = 30/6
x = 5
✔️2x + 30°
Plug in the value of x
2(5) + 30
10 + 30
= 40°
✔️4x + 30°
4(5) + 30°
20 + 30
= 50°
State if the scenario involves a permutation or a combination. Then find the number of possibilities.
The batting order for nine players on a 12 person team.
Permutation/Combination:
Answer:
Step-by-step explanation:
combination
is answer of this question
Solve d – 0.31 ≥ 1.87 Question 1 options: A) d ≤ 2.18 B) d = 2.18 C) d ≥ 1.56 D) d ≥ 2.18
Answer:
D) d ≥ 2.18
Step-by-step explanation:
d – 0.31 ≥ 1.87
d >_ 1.87 + 0.31
d >_ 2.18
In a study of 806 randomly selected medical malpracticeâ lawsuits, it was found that 513 of them were dropped or dismissed. Use a 0.01 significance level to test the claim that most medical malpractice lawsuits are dropped or dismissed. What is the hypothesis test to beâ conducted?
Solution :
[tex]$H_0: p = 0.5$[/tex]
[tex]$H_a: p > 0.5$[/tex]
Alpha, α = 0.01
The sample proportion is :
[tex]$p'=\frac{x}{n}$[/tex]
[tex]$=\frac{513}{806}$[/tex]
= 0.636
Test statistics, [tex]$z=\frac{p'-p}{\sqrt{\frac{pq}{n}}}$[/tex]
[tex]$z=\frac{0.636-0.5}{\sqrt{\frac{0.5\times 0.5}{806}}}$[/tex]
[tex]$z=\frac{0.136}{0.0176}$[/tex]
z = 7.727
The p value = 0.00001
Here we observe that p value is less than α, and so we reject the hypothesis [tex]H_0[/tex].
Therefore, there is sufficient evidence,
Select the statement that best justifies the conclusion based on the given information.
If a(b + c) = d, then ab + ac = d.
associative
commutative
distributive
closure
Answer:
distributive
Step-by-step explanation:
a(b + c)=ab + ac
it's distributive one
a company has decreased the weight of its boxes of macaroni by 8 %. if the new weight of the box is 13.1ounces, what was the original weight of the box?
Answer:
실례합니다 ?
Step-by-step explanation:
이것이 무엇을 의미하는 질문입니까?
회사는 마카로니 상자의 무게를 8% 줄였습니다. 상자의 새 무게가 13.1온스인 경우 상자의 원래 무게는 얼마였습니까? 오른쪽 ?
Answer:
x*0.92 = 13.1
x = 14.24
Step-by-step explanation:
Round 254 212 610 to the nearest million
Answer:
254,000,00
I hope this helps
lim(x-0) (sinx-1/x-1)
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Answer:
as written: the limit does not existsin(x-1)/(x-1) has a limit of sin(1) ≈ 0.841 at x=0Step-by-step explanation:
The expression written is interpreted according to the order of operations as ...
sin(x) -(1/x) -1
As x approaches 0 from the left, this approaches +∞. As x approaches 0 from the right, this approaches -∞. These values are different, so the limit does not exist.
__
Maybe you intend ...
sin(x -1)/(x -1)
This can be evaluated directly at x=0 to give sin(-1)/-1 = sin(1). The argument is interpreted to be radians, so sin(1) ≈ 0.84147098...
The limit is about 0.841 at x=0.
a) __m=10km 25m =___km
b) __m=__km__m=1.5 km
Example :
a) 7250m= 7km 250m = 7.250km
Please help me
Answer:
a) 10,025 m = 10km 25m = 10.025 km
b) 1,500 m = 1 km 500 m = 1.5 km
Answer:
a) 10025m = 10km 25m = 10.025km
b) 1500m = 1km 500m = 1.5km
Step-by-step explanation:
Concept:
Here, we need to know the idea of unit conversion.
Unit conversion is the conversion between different units of measurement for the same quantity.
1 km = 1000 m
Solve:
a)
10km 25m = 10×1000 + 25 = 10025 m10km 25m = 10 + 25/1000 = 10.025 kmb)
1.5km = 1 + 0.5 × 1000 = 1km 500m1.5km = 1.5 × 1000 = 1500mHope this helps!! :)
Please let me know if you have any questions
a car completes a journey in 8hours it covers half the distance at 40kms per hours and the rest at 60 km per hour. what is the total distance of the journey?
Answer:
384 kmph
Step-by-step explanation:
I need to know the answer please
Focusing on the center point of f(x) (0,0), we can see that it has moved to the left 4 units and up 3 units.
g(x) = [tex](\sqrt[3]{x + 4}) + 3[/tex]
Option C
Hope this helps!
$26,876 is invested, part at 9% and the rest at 5%. If the interest earned from the amount invested at 9% exceeds the interest earned from the amount invested at 5% by $720.78, how much is invested at each rate? (Round to two decimal places if necessary.)
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Answer:
$14,747 at 9%$12,129 at 5%Step-by-step explanation:
Let x represent the amount invested at 9%. Then the difference in interest amounts is ...
(9%)x -(5%)(26876 -x) = 720.78 . . . . . assuming a 1-year investment
0.14x -1343.80 = 720.78 . . . . . . . . . simplify
0.14x = 2064.58 . . . . . . . . . . . . . . add 1343.80
x = 14,747 . . . . . . . . . . . . . . . . divide by 0.14
$14,747 is invested at 9%; $12,129 is invested at 5%.
The probability that you will make the hockey team is 2/3
The probability that you will make the swimming team is 3/4.
If the probability that you make
both teams is 1/2
what is the probability that you at least make one of the teams?
Answer:
p = [tex]\frac{11}{12}[/tex]
Step-by-step explanation:
Probability that you make the hockey team only: 2/3 * (1-3/4) = 1/6
Probability that you make the swimming team only: 3/4 * (1-2/3) = 1/4
Probability that you make the both team: 1/2
the probability that you at least make one of the teams: 1/6 + 1/4 + 1/2 = 11/12
