Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
tan A = [tex]\frac{sinA}{cosA}[/tex] , cot A = [tex]\frac{cosA}{sinA}[/tex]
Consider the left side
(1 + cotA + tanA)(sinA - cosA)
each term in the second factor is multiplied by each term in the first factor.
1(sinA - cosA) + cotA(sinA - cosA) + tanA(sinA - cosA)
= sinA - cosA + cosA - [tex]\frac{cos^2A}{sinA}[/tex] + [tex]\frac{sin^2A}{cosA}[/tex] - sinA ( collect like terms )
= [tex]\frac{sin^2A}{cosA}[/tex] - [tex]\frac{cos^2A}{sinA}[/tex]
= ( sinA × [tex]\frac{sinA}{cosA}[/tex] ) - ([tex]\frac{cosA}{sinA}[/tex] × cosA )
= sinAtanA - cotAcosA
= right side ⇒ proven
If x – 9 is a factor of x2 – 5x – 36, what is the other factor? x – 4 x 4 x – 6 x 6
Answer:
(x+4)
Step-by-step explanation:
Solve by factoring. Think about what numbers multiply to be -36 (the last term) BUT also subtract/add up to be -5, which is the middle term. The answer to this is 4 and -9. Therefore, the two factors are (x-9)(x+4)
Answer:
b (x+4)
Step-by-step explanation:
edge
What is the scale factor from small triangle to the larger triangle
Answer:
scale factor = 3
Step-by-step explanation:
The scale factor is the ratio of corresponding sides, larger to smaller.
scale factor = [tex]\frac{BC}{TB}[/tex] = [tex]\frac{12}{4}[/tex] = 3
A computer manufacturer estimates that its cheapest screens will last less than 2.8 years. A random sample of 61 of these screens has a mean life of 2.4 years. The population is normally distributed with a population standard deviation of 0.88 years. At α=0.02, what type of test is this and can you reject the organization’s claim using the test statistic?
Answer:
The test is left - tailed
We cannot reject the organization's claim ( its cheapest screens will truly last less than 2.8 years)
Step-by-step explanation:
Sample size, n = 61
Sample mean, [tex]\bar{X} = 2.4[/tex]
Standard deviation, [tex]\sigma = 0.88[/tex]
Significance level, α=0.02
Null hypothesis, [tex]H_{o} : \mu = 2.8[/tex]
Alternative hypothesis, [tex]H_{a} : \mu < 2.8[/tex]
It is clearly seen from the alternative hypothesis, that it is a left tailed test. It is not tailed towards the two directions.
Calculate the test statistic:
[tex]Z = \frac{\bar{X} - \mu}{\sigma/\sqrt{n} } \\Z = \frac{2.4 - 2.8}{0.88/\sqrt{61} }\\Z = - 3.55[/tex]
Calculate the P-value:
P(Z < -3.35) = 0.0002
Since (p-value = 0.0002) < (α=0.02), the null hypothesis is rejected.
It can therefore be concluded that the mean of the cheapest screen is less than 2.8 years. i.e. the cheapest screen will last less than 2.8 years
Answer:
The null and alternative hypotheses:
H0: u = 2.8
H1: u < 2.8
This is a left - tailed test.
For test statistics, use the formula:
[tex] Z = \frac{x' - u}{\sigma/ \sqrt{n}} [/tex]
Where,
Mean, u = 2.8
Sample mean,x' = 2.4
Sample size, n = 61
Standard deviation [tex] \sigma [/tex] = 0.88
Significance level = 0.02
[tex] Z = \frac{2.4 - 0.02}{0.88/ \sqrt{61}} =-3.55[/tex]
Test statistics, Z = -3.55
Pvalue:
Pvalue of Z = -3.55 using standard normal table,
NORMSTID(-3.55) = 0.00019
Pvalue = 0.0002
Critical value:
Since this is a left tailed test, the critical value at 0.02 level of significance is:
[tex] Z_\alpha = Z_0_._0_2 = -2.05 [/tex]
Decision: If pvalue is less than level of significance reject null hypothesis H0.
Conclusion:
Since pvalue, 0.00019 is less than level of significance, 0.02, reject null hypothesis, H0.
We conclude that the mean life of the cheapest screen is less than 2.8 years
Workers in an office of 90 staff where asked there favourite type of takeaway. The results are summarised in the table. Work out the size of each angle to draw a pie chart.
Step-by-step explanation:
just draw out according to a graph chart or pie chart
Subtract 2y²+5y +8 from 6y- 2y+3.
Answer:
The answer to this problem would be :
-2y^2-y-5
Find the x intercept. y = x + 3 / x - 2
Answer:
(-3, 0).
Step-by-step explanation:
At the x intercept y = 0 so
(x + 3) / (x - 2) = 0
x + 3 = 0
x = -3.
x-intercept is at (-3,0).
Tanya has ten bills in her wallet. If she has one more $5 bill than $10 bills, and two more $1 bills than $5 bills, how many of each does she have?
Please tell me the steps will choose brainliest
Answer:
5 Ones dollar bills
3 five dollar bills
2 ten dollar bills
Step-by-step explanation:
Which scenario is modeled in the diagram below? Percents Total 75% 25% 100% 25% 25% 25% 25% $55.15 $55.15 $55.15 $55.15 Kaia saved $55.15 on a new guitar because it was 75 percent off. She paid $220.60 for the guitar. Kaia saved $165.45 on a new guitar because it was 75 percent off. She paid $220.60 for the guitar. Kaia saved $55.15 on a new guitar because it was 75 percent off. The price of the guitar before the discount was $220.60. Kaia saved $165.45 on a new guitar because it was 75 percent off. The price of the guitar before the discount was $220.60.
Answer:
the answer is d
Step-by-step explanation:
i did whhat the other person said and got it right
Answer:
D
Step-by-step explanation:
18) A TV screen has a length of 15 inches.
The diagonal of the TV is 25 inches. What
is the width of the TV?
A) 400 inches
B) 40 inches
C) 20 inches D) 29.2 inches
Answer: 20 inches
Step-by-step explanation:
From the question, a television screen has a length of 15 inches while the diagonal of the TV is 25 inches. To calculate the width, we will use the hypoteneous rule.
Hypotenuse² = length² + width²
25² = 15² + width²
width² = 25² - 15²
width² = 625 - 225
width² = 400
width = ✓400
width = 20
The width of the TV is 20 inches.
What is the value of this discriminant?
Answer:
The answer is A.
Step-by-step explanation:
The formula of discriminant is D = b² - 4ac using ax² + bx + c. In this question, a is 1, b is -4 and c is 4. Then substitute the values into the formula :
D = b² - 4ac
D = (-4)² - 4(1)(4)
= 16 - 16
= 0
If f(x) = 49- x and g(x) = 7-, which is the rule of the function (8-3)(x)?
a
-x2 - X+ 56
b. x? - 7x2 - 49x + 343
7+X
d. x2 + x +42
C.
Please select the best answer from the choices provided
A. B. C. D.
Answer:
B ) x³ -7 x² -49 x +343
(f .g) (x) = x³ -7 x² -49 x +343
Step-by-step explanation:
Explanation:-
Given f(x) = 49 - x² and g(x) = 7-x
(f .g) (x) = f(x) .g(x)
(f .g) (x) = ( 49 - x² ) (7-x)
= 49 ((7-x))- x²(7-x)
= 343 -49 x -7 x² + x³
(f .g) (x) = x³ -7 x² -49 x +343
Conclusion:-
(f .g) (x) = x³ -7 x² -49 x +343
After reading 7/9 of a book , 40 pages are left .How many pages are there in the book
Answer:
180 pages
Step-by-step explanation:
Answer: 180 pages
Step-by-step explanation:
Let the equation be
x - 7/9x = 40
9x - 7x = 360
x = 360 / 2 = 180
The book has total 180 pages
Means he has read (180 - 40) = 140 pages
Based on this work, what is the solution to the system?
(-4, -4)
(0, 0)
no solution
infinitely many solutions
Answer:
no solution
Step-by-step explanation:
Based on the information provided, the solution to the system is (-4, -4). Option A is the correct answer.
In a system of equations, the solution represents the values of the variables that satisfy all the equations simultaneously. In this case, we are given the solution points (-4, -4) and (0, 0). Option A is the correct answer.
If the given points satisfy both equations in the system, then it is the solution to the system. By substituting the values of x and y from the given points into the equations, we can check if they hold true.
Let's assume the system of equations is represented as follows:
Equation 1: x + y = -8
Equation 2: 2x + 2y = -16
Substituting (-4, -4) into the equations:
Equation 1: -4 + (-4) = -8 (True)
Equation 2: 2(-4) + 2(-4) = -16 (True)
Since both equations are true for the point (-4, -4), it is the solution to the system. Therefore, the solution to the system is (-4, -4).
Learn more about Solution System here:
https://brainly.com/question/30285644
#SPJ2
The complete question is, "Based on this work, what is the solution to the system?
a. (-4, -4)
b. (0, 0)
c. no solution
d. infinitely many solutions"
what is the value of y in the equation 6.4x + 2.8y = 44.4, when x = 3?
Answer
y=45
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
6.4 × 3 =19.2
44.4 - 19.2 =2.8y
25.2=2.8y
25.2/2.8=y
y=9
Pls help me w this question
Answer:
The answer is (3, 18)
Step-by-step explanation:
This is because if you go to 3 on the x axis and up to 18 on the y axis, you have a point there.
Merryvale Orchards sold 85 bags of oranges yesterday. Each bag contained 32 oranges. Round each number to the nearest ten to estimate the number of oranges sold
Answer:
2720 oranges were sold
I will mark you brainliest!!!! What is the first step in adding these equations to eliminate y?
Answer:
I believe D
Step-by-step explanation:
If you multiplied -3 times 3 that would make -9
you can then add 9 + -9 and cross y off
2y + 4(y + 1) = blank y + blank
[tex]2y + 4(y + 1)[/tex]
Expand the brackets.
[tex]2y + 4y + 4[/tex]
Add the like terms.
[tex]6y + 4[/tex]
6y+4Answer:
6 y + 4
Step-by-step explanation:
=> 2y+4(y+1)
=> 2y+4y+4
=> 6y+4
2x^2+14x-36 factored. please and thanks
Answer:
2 (x - 2) (x + 9)
Step-by-step explanation:
Mark brainliest please
what is a slope of the line?
Answer
0
Step-by-step explanation:
A horizontal line has a slope of 0 always
Please help! Correct answer only! This assignment is due today.
A student has to choose an elective class for the last semester of high school. His counselor suggested 8 electives, 5 of which were dance classes.
If the student randomly chose to read about 4 of the electives, what is the probability that all of them are dance classes?
Write your answer as a decimal rounded to four decimal places.
Answer:
Probability ≈ 0.0714
Step-by-step explanation:
Consider permutation and combination;
[tex]Total Combinations - 8C4,\\8C4 = 8! / 4! * ( 8 - 4 )!,\\8 * 7 * 6 * 5 / 4!,\\\\Total Combinations = 70,\\\\Combinations of Dance Classes - 5C4,\\5C4 = 5! / 4! * ( 5 - 4 )!,\\5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1,\\\\Dance Classes = 5,\\\\Probability - 5 / 70 = 0.0714,\\Conclusion; Probability = ( About ) 0.0714[/tex]
An adult ticket costs $5.25 and a child ticket costs $3.05. If $498.60 were collected for 100 tickets, how many child tickets were sold?
Answer:
work is shown and pictured
zero has _________ reciprocal
Answer:
No
Step-by-step explanation:
No real number when multiplied with zero makes one.
Answer:
Zero has no reciprocal
Step-by-step explanation:
The reciprocal of a number is what you get when you flip the numerator and the denominator of a number. For instance, with the number 5, it can be rewritten as 5/1. The reciprocal of this would therefore be 1/5. For 0, it can also be rewritten as 0/1. However, if you take the reciprocal of this, you get 1/0, which is undefined. Therefore, zero has no reciprocal. Hope this helps!
How old am I if 2 times my age increased by 244 is 400?
Answer:
78
Step-by-step explanation:
400-244=156
156/2=78
Answer:
78 years old
Step-by-step explanation:
400 − 2 x = 244
400 − 244 = 2 x
156 = 2 x
so the answer would be 78 years old...
Hope that was helpful.Thank you!!!
What are the domain and range of f(x) = |x + 6|?
Answer:
The domain is (-∞,∞)
The range is [0,∞)
Step-by-step explanation:
The graph will be a V shape facing upwards with a vertex of (-6,0)
Answer:
Domain = (-∞,∞)
Range = [0,∞)
Step-by-step explanation:
a circular pool has a radius of 40 feet. what is the area of the pool?
Answer:
5026.55
Step-by-step explanation:
A=πr2=π·402≈5026.54825ft²
g(x) = 1/3 * (2/9)^x. Does the function model growth or decay?
Answer:
It Decays
Step-by-step explanation:
Why because Kahn Acadmey said so
20 PTS What is the sixth term of the sequence shown in the table? Term Value 1 –46,656 2 7,776 3 –1,296 4 216 5 6 {SEE IMAGE}
Answer:
a₆ = 6
Step-by-step explanation:
There is a common ratio r between consecutive terms in the sequence, that is
r = [tex]\frac{216}{-1296}[/tex] = [tex]\frac{-1296}{7776}[/tex] = [tex]\frac{7776}{-46656}[/tex] = - [tex]\frac{1}{6}[/tex]
This indicates the sequence is geometric.
To obtain any term in the sequence, multiply the previous term by r, thus
a₅ = 216 × - [tex]\frac{1}{6}[/tex] = - 36
a₆ = - 36 × - [tex]\frac{1}{6}[/tex] = 6
Answer:
It's 6
Step-by-step explanation:
Got it right!
1 –46,656
2 7,776
3 –1,296
4 216
5 36
6 6
divided by 6 every time
A geometric sequence has the explicit formula an = (-2) x 3^n- 1. What is the 4th term?
Answer:
-54
Step-by-step explanation:
Please write this sequence in the following form: a(n) = (-2)*3^(n- 1)
Then a(1) = -2*3^0 = -2
a(2) = -2*3^(2 - 1) = -6
a(3) = -2*3^(3 - 1) = -2*9 = -18
a(4) = -2*3^(4-1) = -2*27 = -54
Corey and David both have lots of video games. The number of games Corey has can be represented by x . Ricky has 3 times as many games as Corey. The total number of games is 64 . What is x, the total number of games Corey has?
Answer:
21.3333333
Step-by-step explanation:
64/3=x
64/3=21.3333333
Sorry if its wrong.
