Induction is the correct answer; when you use induction form general ideas and rules based on your experiences and observations. I hope this will help you! Have a wonderful day!
Answer:
d. induction
Step-by-step explanation:
When you use induction you form general ideas and rules based on your experiences and observations.
Veronica works each day and earns more money per hour the longer she works. Write a function to represent a starting pay of $20 with an increase each hour by 5%. Determine the range of the amount Veronica makes each hour if she can only work a total of 8 hours.
Answer:
20 ≤ f(x) ≤ 28.14
Step-by-step explanation:
Simplify the expression.
20*5^-2
Evaluate: 5P5
A:120
B: 1
C: 132
D: 126
(This is permutations btw)
[tex]_nP_k=\dfrac{n!}{(n-k)!}\\\\\\_5P_5=\dfrac{5!}{0!}=120[/tex]
Answer:
A. 120.
Step-by-step explanation:
5P5 = 5! / (5-5)!
= 5! / 0!
= 5!/1
= 5!
= 120.
Carmen y Carlos hacen pizzas para vender. La materia prima necesaria para hacer una pizza grande les cuesta $5.00 y para una pizza pequeña $3.00. Si disponen de $570.00 y quieren hacer 150 pizzas, ¿cuántas pizzas de cada tamaño podrán hacer?
Answer:
A large pizza costs $5 and a small pizza costs $3.
Let 'x' be the number of large pizzas and 'y' the number of small pizzas. We have that:
x + y = 150
5x + 3y = 570
Solving the system of equations:
x + y = 150 → 3x + 3y = 450 → 3y = 450 - 3x
5x + 3y = 570 → 5x + 450 - 3x = 570
2x = 120
x = 60
y = 150 - 60 = 90
Therefore. Carmen y Carlos will make 60 large pizzas and 90 small pizzas.
A system of linear inequalities is shown below: y − x > 0 x + 1 < 0 Which of the following graphs best represents the solution set to this system of linear inequalities? The first line is a dashed line which joins ordered pairs negative 1, 5 and negative 1, negative 4. The second line is a dashed line and joins ordered pairs negative 2, negative 2 and 4, 4. The portion common to the right of the first line and above the second line is shaded The first line is a dashed line which joins ordered pairs negative 1, 5 and negative 1, negative 4. The second line is a dashed line and joins ordered pairs negative 2, negative 2 and 2, 2. The portion common to the left of the first line and above the second line is shaded The first line is a dashed line which joins ordered pairs negative 1, 5 and negative 1, negative 4. The second line is a dashed line and joins ordered pairs negative 2, negative 2 and 2, 2. The portion common to the left of the first line, above the second line and below the x axis is shaded The first line is a dashed line which joins ordered pairs negative 1, 5 and negative 1, negative 4. The second line is a dashed line and joins ordered pairs negative 2, negative 2 and 3, 3. The portion common to the left of the first line and above the x axis is shaded
Answer:
The first line is a dashed line which joins ordered pairs negative 1, 5 and negative 1, negative 4. The second line is a dashed line and joins ordered pairs negative 2, negative 2 and 4, 4. The portion common to the right of the first line and above the second line is shaded
Step-by-step explanation:
we have
First inequality
x+1 > 0
x > -1
The solution of the first inequality is the shaded area at right of the dashed line x=-1 (vertical line)
Second inequality
y-x > 0
y> x
The solution of the second inequality is the shaded area above the dashed line y=x
therefore
The first line is a dashed line which joins ordered pairs negative 1, 5 and negative 1, negative 4. The second line is a dashed line and joins ordered pairs negative 2, negative 2 and 4, 4. The portion common to the right of the first line and above the second line is shaded
see the attached figure to better understand tye problem
What percent of 4600% is 2530
5500% of 4600% is 2530
Further explanationOrder of Operations in Mathematics follow this following rule :
ParenthesesExponentsMultiplication and DivisionAddition and SubtractionThis rule is known as the PEMDAS method.
In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.
Let us tackle the problem.
This problem is about Percentage.
Given:
What percent of 4600% is 2530?
We can translate above questions into mathematical equation as follows:
[tex]x\% \times 4600 \% = 2530[/tex]
[tex]x\% \times \frac{4600}{100} = 2530[/tex]
[tex]x\% \times 46 = 2530[/tex]
[tex]x\% = 2530 \div 46[/tex]
[tex]x\% = \frac{55}{1}[/tex]
To convert above fraction , we could multiply with 100% :
[tex]x\% = \frac{55}{1} \times 100\%[/tex]
[tex]x\% = \boxed{ 5500 \% }[/tex]
Conclusion:5500% of 4600% is 2530Another Example:
50% of 4600 is 2300
80% of 4600 is 3680
100% of 4600 is 4600
120% of 4600 is 5520
Learn moreInfinite Number of Solutions : https://brainly.com/question/5450548System of Equations : https://brainly.com/question/1995493System of Linear equations : https://brainly.com/question/3291576Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Percentage
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent
The 2530 is 55% of 46. This means that 2530 is 55% of 4600%, as 4600% is equivalent to 46 in decimal form.
To find what percent 2530 is of 4600%, we first need to understand that 4600% is equal to 46. Hence, we need to determine what percent of 46 is 2530.
Let x be the percentage we are trying to find. We can set up the equation:
x% of 46 = 2530
To solve for x, we divide both sides by 46:
x% = 2530 / 46
x% = 55
So, 2530 is 55% of 46.
To summarize, 2530 is 55% of 46. This means that 2530 is 55% of 4600%, as 4600% is equivalent to 46 in decimal form.
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The variable t in the formula d = rt stands for
Answer:
The distance formula d = rt, 'd' stands for distance, 'r' stands for rate and 't' stands for time.
It's a well known formula used in physics to solve problems that involves questions like "how fast", "how far", or "for how long".
In the formula d = rt, the variable t represents time. It's a consistent representation across situations whenever you are dealing with equations for motion, speed, or other physics contexts.
The variable t in the formula d = rt stands for time. This formula is used to calculate distance based on the rate of speed (r) and the time (t) traveled. To solve for time, you would rearrange the formula to t = d/r, which means time equals distance divided by rate.
In various physics and mathematical contexts, as shown in the reference information, the letter t consistently represents time. It could be the time an object takes to cover a certain distance at a given rate, or more complex scenarios involving non-Euclidean worlds or quantum mechanics. Nevertheless, whenever you see t in such equations, it is typically referring to time, unless otherwise specified.
Ethel surveyed a random sample of 100 students from her middle school to learn more about what type of school lunches are preferred. The table shows the result of the survey. Hamburgers Tacos Pizza Sample #1 13 43 44 Sample #2 20 41 38 Which of the following inferences can be made based on the data? Pizza is the most preferred lunch. Tacos and pizza are almost equally preferred. Hamburgers are two times more popular than tacos. Hamburgers are two times more popular than pizza.
-- Hamburgers got 33 total votes.
-- Tacos got 84 total votes.
-- Pizza got 82 total votes.
Tacos and pizza are almost equally preferred.
-- Tacos are out in front of pizza, but only by 2 votes.
-- Hamburgers are way behind, with less than half the votes of either tacos OR pizza.
It is found that Spaghetti and Pizza are preferred almost equally.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that Ethel surveyed a random sample of 100 students from his middle school to learn more about what type of school lunches are preferred based on his observation the table of the following is :
Hamburgers Spaghetti Pizza
Sample 1: 13 43 44
-----------------------------------------------------------------------
Sample 2: 20 41 39
-------------------------------------------------------------------------
Total: 33 84 83
Here, we see that the total number of spaghetti and Pizza chosen are almost equal as:
Total number of Spaghetti preferred=84.
Total number of Pizza preferred=83.
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PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!
Harry and Larry are having a barbecue dinner. The probability of Harry staining his shirt during the dinner is 1/5. The probability of Larry staining his shirt during the dinner is 15%.
Which of these events is more likely?
Choose 1 answer:
(Choice A)
Harry stains his shirt during the dinner.
(Choice B)
Larry stains his shirt during the dinner.
(Choice C)
Neither. Both events are equally likely.
Answer:
(Choice A)
Harry stains his shirt during the dinner.
Step-by-step explanation:
If Harry and Larry are having a barbecue dinner and the probability of Harry staining his shirt during the dinner is 1/5 and the probability of Larry staining his shirt during the dinner is 15%, Harry stains his shirt during the dinner is more likely.
Harry - 1/5 as a percent: 20%
Larry - 15% as a decimal: 0.15
Therefore 20% is more than 15 percent.
This makes the answer, Harry stains his shirt during the dinner.
Answer:
(Choice A)
Harry stains his shirt during the dinner.
Step-by-step explanation:
If Harry and Larry are having a barbecue dinner and the probability of Harry staining his shirt during the dinner is 1/5 and the probability of Larry staining his shirt during the dinner is 15%, Harry stains his shirt during the dinner is more likely.
Harry - 1/5 as a percent: 20%
Larry - 15% as a decimal: 0.15
Therefore 20% is more than 15 percent.
This makes the answer, Harry stains his shirt during the dinner.
Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36 miles but not more than 90 miles. The system of inequalities represents the number of hours he can walk, w, and the number of hours he can run, r, to reach his goal. 3w + 6r ≥ 36 3w + 6r ≤ 90 Which combination of hours can Keitaro walk and run in a month to reach his goal? 2 hours walking; 12 hours running 4 hours walking; 3 hours running 9 hours walking; 12 hours running 12 hours walking; 10 hours running
Answer:
Option 1 is correct. i.e 2 hours walking; 12 hours running
Step-by-step explanation:
We are given the equations
3w + 6r ≥ 36
3w + 6r ≤ 90
We will check which of the option satisfy the above equations.
1) 2 hours walking; 12 hours running
w = 2 and r =12
3w + 6r ≥ 36
3(2) + 6(12) ≥ 36
6+72 ≥ 36
78 ≥ 36
3w + 6r ≤ 90
3(2) + 6(12) ≤ 90
6+72 ≤ 90
78 ≤ 90
Both equations are satisfied. Option 1 is correct.
2) 4 hours walking; 3 hours running
w = 4 and r =3
3w + 6r ≥ 36
3(4) + 6(3) ≥ 36
12+18 ≥ 36
30 ≥ 36 (this equation doesn't hold as 30 < 36 and not < or equal to 36)
3w + 6r ≤ 90
3(4) + 6(3) ≤ 90
12+18 ≤ 90
30 ≤ 90
So, Option 2 is incorrect.
3) 9 hours running 12 hours walking
w = 9 and r =12
3w + 6r ≥ 36
3(9) + 6(12) ≥ 36
27+72 ≥ 36
99 ≥ 36
3w + 6r ≤ 90
3(9) + 6(12) ≤ 90
27+72 ≤ 90
99 ≤ 90 (this equation doesn't hold because 99 is greater than 90 and not less than 90)
Option 3 is incorrect.
4) 12 hours walking; 10 hours running
w = 12 and r =120
3w + 6r ≥ 36
3(12) + 6(10) ≥ 36
36+60 ≥ 36
96 ≥ 36
3w + 6r ≤ 90
3(12) + 6(10) ≤ 90
36+60 ≤ 90
99 ≤ 90 (this equation doesn't hold because 96 is greater than 90 and not less than 90)
Option 4 is incorrect.
13. For what value of b would the following system of equations have an infinite number of solutions? 9x + 12y = 21
6x + 8y = 7b Please explain and show steps :)
Answer:
b=2
Step-by-step explanation:
9x + 12y = 21
6x + 8y = 7b
To have an infinite number of solutions, the two equations must be equal
Take the first equation and divide by 3, since it is a factor of all the terms
9x/3 + 12y/3 = 21/3
3x+4y = 7
Then multiply by 2 to get the x term equal
2*3x + 2*4y = 2*7
6x +8y = 7*2
Comparing this to the second equation
6x + 8y = 7b
b must equal 2
Write an equation: After withdrawing $7 from a checking account, Carla’s balance was $89
The equation for the situation where Carla withdraws $7 and is left with an $89 balance is: B - $7 = $89. So Carla's initial balance was $96.
When writing an equation based on the statement that after withdrawing $7 from a checking account, Carla’s balance was $89, we are essentially working out what Carla's balance was before she made the withdrawal.
If we let the variable B represent Carla's initial balance, then after she withdraws $7, her new balance is B - $7.
Since it's given that her balance after the withdrawal is $89, we can write the following equation to represent the situation:
B - $7 = $89
To find the value of B, we would add $7 to both sides of the equation, which would give us:
B = $89 + $7
B = $96
So, Carla's initial balance before the withdrawal was $96.
which is the rationalized form of the expression the square root of x divided by the square root of x +the square root of 7
Answer:
I assume your goal is to rationalize the denominator -
So you need to multiply the denominator by its conjugate.
So we have:
[tex]\frac{\sqrt{x} }{\sqrt{x}-\sqrt{7} } *\frac{\sqrt{x} +\sqrt{7} }{\sqrt{x} +\sqrt{7}}[/tex]
->
[tex]\frac{x-\sqrt{7}\sqrt{x} }{x-7}[/tex]
gg
According to the Rational Root Theorem, which statement about f(x) = 66x4 – 2x3 + 11x2 + 35 is true? Any rational root of f(x) is a factor of 35 divided by a factor of 66. Any rational root of f(x) is a multiple of 35 divided by a multiple of 66. Any rational root of f(x) is a factor of 66 divided by a factor of 35. Any rational root of f(x) is a multiple of 66 divided by a multiple of 35.
Answer:
The correct option is Any rational root of f(x) is a factor of 35 divided by a factor of 66....
Step-by-step explanation:
According to the rational root theorem:
if [tex]a_{0}[/tex] and [tex]a_{n}[/tex] are non zero then each rational solution x will be:
x= +/- Factors of [tex]a_{0}[/tex] / Factors of [tex]a_{n}[/tex]
In the given polynomial we have:
66x4 – 2x3 + 11x2 + 35
[tex]a_{0}[/tex] = 35
[tex]a_{n}[/tex] = 66
Therefore,
x= +/- Factors of 35/ Factors of 66.
Thus the correct option is Any rational root of f(x) is a factor of 35 divided by a factor of 66....
Answer:
A
Step-by-step explanation:
trust bro
How to make s the subject in T=2(S+P)÷Z
Answer:
(TZ - 2P)/2 = S
Step-by-step explanation:
Multiply both sides by Z
T*Z = Z*2(S + P)/Z
TZ = 2*(S + P) Divide by 2
TZ/2 = 2(S + P)/2 Do the division
TZ/2 = S + P Subtract P from both sides
TZ/2 - P = S That's one answer. You could refine it.
Multiply P by 2 so that you can put TZ - 2P over a common denominator.
(TZ - 2P)/2 = S Is another answer.
I think the second one is probably the best one.
there are 63 students marching in a band, and they'are marching in 7 rows. how many students are in each row?
To find the number or rows, divide the total number of students by the number in each row.
63 / 7 = 9 rows.
Hello There!
If there are 63 students marching in the band and there is 7 rows, we can find out how many students are in each row by dividing 63 "number of students" by 7 "number of rows" and we will get an answer of 9.
Factor completely.
6x4 – 9x3 – 36x2 + 54x
3x(x2 + 6)(2x + 3)
6x(x2 – 6)(2x – 3)
3x(x2 – 6)(2x – 3)
6x(x2 + 6)(2x + 3)
Answer:
3x[x² - 6][2x - 3]
Step-by-step explanation:
Group each term carefully [two-by-two], and you will arrive at your answer.
To bill customers for water usage, one city converts the number of gallons used into units. This relationship is represented by the equation g = 748u, where g is the total number of gallons of water used and u is the number of units.
Determine which statements about the relationship are true. Choose two options.
Answer:
g is a dependent variable
u is an independent variable
Step-by-step explanation:
Given relationship is:
g=748u
Here two terms need to be defined
Independent Variable : The variable which can take any value. The independent variable is used to calculate the value of dependent variable
Dependent Variable: The dependent variable is determined by the independent variable.
Therefore,
The correct answer is:
g is a dependent variable
u is an independent variable ..
Kelly drinks 0.5 liters of coffee and 0.3 liters of yogurt drink at breakfast. How much did she drink in total in milliliters?
PLEASE ANSWER QUICK!!! Identify the equation of the circle that has its center at (-8, 15) and passes through the origin.
The equation of the circle is [tex](x+8)^{2} +(y -15)^{2} = 289[/tex].
What is the general equation for the circle?The general equation of the circle is [tex](x-h)^{2} +(y-k)^{2} = r^{2}[/tex].
Where, (h, k) is the center and r is the radius of the circle.
Let the equation of the circle be
[tex](x-h)^{2} +(y-k)^{2} =r^{2}..(i)[/tex]
According to the given question.
The center of the circle is (-8, 15).
⇒ (h, k) = (-8, 15)
And, the circle is passing through origin i.e. (0, 0).
Since, the center of the circle is (-8, 15).
So, the equation (i) can be written as
[tex](x-(-8))^{2} +(y - 15)^{2} = r^{2}[/tex]
Also, the circle is passing through (0, 0).
Therefore,
[tex](0+8)^{2} +(0-15)^{2} = r^{2}[/tex]
[tex]\implies 64+ 225 = r^{2} \\\implies 289 = r^{2} \\\implies r=\sqrt{289} \\\implies r = 17[/tex]
So, the radius of the circle is 17 unit and its center is (-8, 15).
Therefore, the equation of the circle is
[tex](x+8)^{2} +(y-15)^{2} = 289[/tex]
Hence, the equation of the circle is [tex](x+8)^{2} +(y -15)^{2} = 289[/tex].
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What are the zeros of f(x) = x2 - x - 30?
The zeros of f(x) = x^2 - x - 30 are x = 6 or -5
How to determine the zeros?The function is given as:
f(x) = x^2 - x - 30
Expand
f(x) = x^2 + 5x - 6x - 30
Factorize the function
f(x) = x(x + 5) - 6(x + 5)
Factor out x + 5
f(x) = (x - 6)(x + 5)
Set to 0
(x - 6)(x + 5) = 0
Solve for x
x = 6 or -5
Hence, the zeros of f(x) = x^2 - x - 30 are x = 6 or -5
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solve the equation -12=q-17
Answer:
q = 5
Step-by-step explanation:
Given
- 12 = q - 17 ( add 17 to both sides )
5 = q ⇒ q = 5
Answer:
q=5
Step-by-step explanation:
The equation is -12=q-17
In this equation we have to find the value of q.
So move the constant to the L.H.S
-17 will become +17 when it moves to the L.H.S
17-12=q
5=q
Thus the value of q is 5....
A group of 8 friends (5 girls and 3 boys) plans to watch a movie, but they have only 5 tickets. How many different combinations of 5 friends could
possibly receive the tickets?
A. 13
B. 40
C. 56
b. 64
[tex]_8C_5=\dfrac{8!}{5!3!}=\dfrac{6\cdot7\cdot8}{2\cdot 3}=56[/tex]
Madeline is standing 2x- 4 feet from the base of a tree. The height of the tree is 5x + 6 feet. Find the equation that shows
the straight-line distance from Madeline's feet to the top of the tree in terms of x.
Provide your answer below:
Answer:
c = sqrt( 29x^2 + 44x + 52)
Step-by-step explanation:
This is an application of the Pythagorean theorem
c = sqrt(a^2 + b^2)
a = 2x - 4
b = 5x + 6
c = sqrt( (2x - 4)^2 + (5x + 6)^2 ) Substitute and expand
c = sqrt( 4x^2 - 16x + 16 + 25x^2 + 60x + 36) Collect like terms
c = sqrt( 4x^2 + 25x^2 - 16x + 60x + 16+36) Combine the like term pairs.
c = sqrt( 29x^2 + 44x + 52)
This does not factor into anything very nice.
Answer:
Madeline is standing 2x - 4 feet from the base of a tree, and the height of the tree is 5x + 6
Now we want to know the distance from Madeline's feet to the top of the tree.
You could picture it as a triangle rectangle, where the cathetus is the distance between Madeline and the tree and the distance between the floor and the top of the tree, in this case the distance between Madeline's feet and the top of the tree is the hypotenuse of such triangle rectangle, and can be obtained using the Pythagorean theorem: "the square of the hypotenuse is equal to the sum of the square cathetus"
then:
[tex]H^2 = (2x - 4)^2 + (5x + 6)^2[/tex]
[tex]H^2 = (4x^2 -16x + 16) + (25x^2 + 60x +36)[/tex]
[tex]H^2 = (29x^2 + 44x + 52)[/tex]
[tex]H = \sqrt{ (29x^2 + 44x + 52)}[/tex]
this is the distance from Madeline's feet to the top of the tree in terms of x.
Given that the area of a triangle is given by the formula A =
1
2
bh, what is the value of A if b = 4 cm and h = 6 cm?
I will add brainlist from the last question its just that I have to wait till it appears!
THIS IS IXL QUESTION
Least to greatest:
-1 < -0.2 < 0.3When ordering decimals from least to greatest, it's crucial to understand place value. When ordering, I usually like to start with whole numbers and put them first and then I think about the numbers after the decimal.
A hamburger bun merchant can ship 8 large boxes or 10 small boxes of hamburger buns into a carton for shipping. In one shipment, he sent a total of 96 boxes of hamburger buns. If there are more large boxes than small boxes, how many cartons did he ship?
Answer:
11 cartons
Step-by-step explanation:
Number of large boxes that can be contained in a carton = 8
Number of small boxes that can be contained in a carton = 10
Total number of boxes sent in one shipment = 96
This shipment contains both large and small boxes. Let there be x cartons of large boxes and y cartons of small boxes in one shipment. So, we can say,
Total number of large boxes in one shipment = Number of boxes in one carton * Total number of cartons = 8x
Similarly,
Total number of small boxes in one shipment = 10y
Since, total number of boxes in one shipment is 96, we can set up the equation as:
8x + 10y = 96
This equation can have following possible solutions:
x =2, y = 8x = 7, y = 4x = 12, y = 0We are given in the statement that are more large boxes than the small boxes, the valid solutions are:
x = 7, y = 4x = 12, y = 0Assuming that he sent both large and small boxes, the only valid solution will be:
x = 7, y = 4This means, the merchant sent 7 cartons of large boxes i.e. 56 large boxes and 4 cartons of small boxes i.e. 40 small boxes. So in total he sent 11 cartons.
Answer:
11 boxes total 4 small 7 large
Step-by-step explanation:
1 small box *10 = 10 96-10 = 86 (NO MULTIPLE OF 8)
2 small boxes*10=20 96-29=76 ( no multiple of 8)
3 small boxes *10=30 96-30= 66(no multiple of 8)
4 small boxes*10 = 40 96-40 = 56 (YES multiple of 8) 56/8 = 7 (7 large boxes)
4 large boxes and 7 large boxes
Solve the radical equation.
Answer:
there are no extraneous solutions to the equation
Step-by-step explanation:
Given
[tex]\sqrt{8x+9}[/tex] = x + 2 ( square both sides )
8x + 9 = (x + 2)² ← expand
8x + 9 = x² + 4x + 4 ( subtract 8x + 9 from both sides )
0 = x² - 4x - 5 ← in standard form
0 = (x - 5)(x + 1) ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 1 = 0 ⇒ x = - 1
As a check
Substitute these values into the equation and if both sides are equal then they are the solutions.
x = 5 : [tex]\sqrt{8(5)+9}[/tex] = [tex]\sqrt{49}[/tex] = 7
right side = 5 + 2 = 7
left side = right side ⇒ x = 5 is a solution
x = - 1 : [tex]\sqrt{8(-1)+9}[/tex] = [tex]\sqrt{1}[/tex] = 1
right side = - 1 + 2 = 1
left side = right side ⇒ x = - 1 is a solution
There are no extraneous solutions
Answer:
There are no extraneous solutions
Step-by-step explanation:
sqrt(8x+9) = x+2
Square each side
(sqrt(8x+9))^2 = (x+2)^2
8x+9 = (x+2)^2
FOIL
8x+9 = x^2 +2x+2x+4
Combine like term
8x+9 = x^2 +4x+4
Subtract 8x from each side
8x-8x+9 = x^2 +4x-8x+4
9 = x^2 -4x+4
Subtract 9 from each side
0 = x^2 -4x-5
Factor
0=(x-5) (x+1)
Using the zero product property\
x-5 =0 x+1=0
x=5 x=-1
Check the solutions
x=5
sqrt(8*5+9) = 5+2
sqrt(40+9) = 5+2
sqrt(49) =7
7=7
x=-1
sqrt(8*(-1)+9) = -1+2
sqrt(-8+9) = -1+2
sqrt(1) =1
1=1
Both solutions are true solutions
If sin0=-1/2 and 0 is in quadrant III then tan0=
Answer:
tan O = √3/ 3.
Step-by-step explanation:
The tangent is positive in quadrant 3.
The adjacent side has length √((2^2 - (-1)^2)
= -√3.
So tan O = -1 / -√3
= 1 / √3
= √3/ 3.
To determine tan(θ) for an angle θ where sin(θ) = -1/2 and θ is in quadrant III, we perform the following steps:
1. **Understand the given information:** When sin(θ) = -1/2, it means the opposite side to angle θ in a right triangle is -1 and the hypotenuse is 2. Since θ lies in the third quadrant, both sine and cosine values are negative, implying that the adjacent side length must also be negative.
2. **Use the Pythagorean theorem:** For a right triangle:
\[ \text{hypotenuse}^2 = \text{opposite}^2 + \text{adjacent}^2 \]
Substituting hypotenuse and opposite side values:
\[ 2^2 = (-1)^2 + \text{adjacent}^2 \]
Simplify and solve for the adjacent side:
\[ 4 = 1 + \text{adjacent}^2 \]
\[ 3 = \text{adjacent}^2 \]
\[ \text{adjacent} = \sqrt{3} \] or \[ \text{adjacent} = -\sqrt{3} \]
Since the angle is in the third quadrant where cosine is also negative, we must take the negative square root:
\[ \text{adjacent} = -\sqrt{3} \]
3. **Calculate tan(θ):** By definition,
\[ \tan(θ) = \frac{\text{opposite}}{\text{adjacent}} \]
Substitute the known side lengths:
\[ \tan(θ) = \frac{-1}{-\sqrt{3}} \]
4. **Simplify the expression:**
\[ \tan(θ) = \frac{1}{\sqrt{3}} \]
To rationalize the denominator:
\[ \tan(θ) = \frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} \]
\[ \tan(θ) = \frac{\sqrt{3}}{3} \]
Thus, if sin(θ) = -1/2 and θ is in quadrant III, then tan(θ) = √3/3. Note that in the context of trigonometry, it is often assumed that the angle and the ratios are dimensionless, so a negative 'opposite' simply reflects the direction along the coordinate axis rather than a literal negative length.
According to the definition of theoretical probability, the probability of an
event occurring is the number of favorable outcomes divided by the number
of unfavorable outcomes.
True or False
Answer: True
Step-by-step explanation: that is the correct definition on theoretical probability! :D
. Probability is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes, not unfavorable outcomesThe statement about theoretical probability in the question is false.
The provided statement about theoretical probability is false. According to the definition of theoretical probability, the probability of an event occurring is in fact the number of favorable outcomes divided by the total number of possible outcomes, not the unfavorable outcomes. To calculate the theoretical probability of an event A, one must count the number of outcomes that are favorable for event A (those that result in the event occurring) and divide by the total number of all possible outcomes.
Example:
If a die is rolled, the probability of rolling a three (a favorable outcome) is 1 in 6 (the total number of possible outcomes), as there is one three on a die and six possible outcomes in total.
Therefore, the correct way to express probability is:
Probability = (number of favorable outcomes) / (total number of possible outcomes)