Answer:
[tex]\left\{x\in \mathbb {Z}\ : \ x \le 0 \right\}[/tex]
Step-by-step explanation:
Set-Builder Notation: A shorthand used to describe sets, often sets with an infinite number of elements.
The set {...,-3, -2, -1, 0} is the set of all negative integers and 0, so you can use such set-builder notation:
[tex]\left\{x\in \mathbb {Z}\ : \ x \le 0 \right\}[/tex]
Note: Here [tex]\mathbb{Z}[/tex] represents the set of all integers.
Final answer:
The set {... -3, -2, -1, 0} can be represented in set builder notation as {x ∈ ℤ | -3 ≤ x < 1 }, which describes all integers x that are greater than or equal to -3 and less than 1.
Explanation:
To express the set that includes the numbers -3, -2, -1, and 0 using set builder notation, we start by recognizing that these numbers can be described by a pattern or rule, which is that they are all the integer numbers greater than or equal to -3 and less than 1. We can then write this using set builder notation as:
{x ∈ ℤ | -3 ≤ x < 1 }
In this notation, the variable 'x' represents the elements of the set and ∈ stands for 'element of.' ℤ is the symbol for integers. The vertical bar or colon (|) stands for 'such that.' Our notation reads as 'the set of all integers x such that -3 is less than or equal to x and x is less than 1.'
How do u solve this?
Answer:
[tex]\large\boxed{\left\{\begin{array}{ccc}f(1)=5\\f(n)=f(n-1)\cdot(-2)\end{array}\right}[/tex]
Step-by-step explanation:
[tex]f(n)=5\cdot(-2)^{n-1}\\\\f(1)\to\text{put n = 1 to the equation of}\ f(n):\\\\f(1)=5\cdcot(-2)^{1-1}=5\cdot(-2)^0=5\cdot1=5\\\\\text{calculate the common ratio:}\ \dfrac{f(n+1)}{f(n)}\\\\f(n+1)=5\cdot(-2)^{(n+1)-1}=5\cdot(-2)^{n+1-1}=5\cdot(-2)^n\\\\r=\dfrac{f(n+1)}{f(n)}=\dfrac{5\!\!\!\!\diagup^1\cdot(-2)^n}{5\!\!\!\!\diagup_1\cdot(-2)^{n-1}}\qquad\text{use}\ \dfrac{a^m}{a^n}=a^{m-n}\\\\r=(-2)^{n-(n-1)}=(-2)^{n-n+1}=(-2)^1=-2\\\\\text{Therefore}\\\\f(n)=f(n-1)\cdiot(-2)[/tex]
which equation has the solutions x=5+-2(sqrt)7/3
Answer:
the solution is the last one.
Step-by-step explanation:
We know that for a second grade equation of the type:
ax^2 + bx + c = 0
The solution will be given by the quadratic formula, which states that:
x1 = [-b + sqrt(b^2 - 4ac)]/2a
x2 = [-b - sqrt(b^2 - 4ac)]/2a
So, according to the solution, we have:
x1 = [-5 + 2sqrt(7)]/3
Then:
2a = 3
-b = 5
b^2 - 4ac = 28
Solving each equation:
a = 2/3
b= -5
c = 9/8
None of the alternatives equals the values obtained before. So we can say that the expression is simplified.
Now we knoe what the first and second equation are wrong because b is not equal to -5.
So we have the other two alternatives, where b=-10. This gives us an idea that maybe, the equation is simplified by two. If that's the case:
then:
2a = 6
b= -10
b^2 - 4ac = 112
Then b=-10, a = 3 and c=-1
So the solution is the last one.
Final answer:
The correct quadratic equation with the solutions x = 5 ± 2√7 / 3 is 3x² - 10x - 1 = 0, determined by matching the given solution to the quadratic formula.
Explanation:
The student is asking which of the given quadratic equations has the solutions x = 5 ± 2√7 / 3. The correct equation that yields these solutions must be in the form ax² + bx + c = 0, where a, b, and c are constants.
To determine the right equation, we can work backwards from the given solutions using the quadratic formula:
x = ∛( -b ± √(b² - 4ac) ) / 2a
Comparing the solutions to the standard form obtained by the quadratic formula, we need to match the coefficients such that:
a equals the denominator (3) after the ± symbol,b is opposite in sign to the middle term (5),The discriminant b² - 4ac results in 4×7.After testing each equation, we find that:
33x² - 5x + 7 = 0 (Incorrect)3x² - 5x - 1 = 0 (Incorrect)3x² - 10x + 6 = 0 (Incorrect)3x² - 10x - 1 = 0 (Correct)The discriminant for the last equation is (10)² - 4×3×(-1) = 100 + 12 = 112, which is 4×7, confirming that x = 5 ± 2√7 / 3 are indeed the solutions.
simplify (-6^1/3)^(-2)=
For this case we must simplify the following expression:
([tex](-6 ^ {\frac {1} {3}}) ^ {- 2}[/tex]
So, by definition of power properties we have:
[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
Then, rewriting the expression:
[tex]\frac {1} {(- 6 ^ {\frac {1} {3}}) ^ 2} =\\\frac {1} {(- 6 ^ {\frac {1} {3}}) * (- 6 ^ {\frac {1} {3}})} =\\\frac {1} {(6 ^ {\frac {1} {3}}) * (6 ^ {\frac {1} {3}})} =\\\frac {1} {6 ^ {\frac {2} {3}}}[/tex]
ANswer:
[tex]\frac {1} {6 ^ {\frac {2} {3}}}[/tex]
Help please I need help
Answer:
x = 4Step-by-step explanation:
Look at the picture.
ΔABC and ΔACD are similar. Therefore the corresponding sides are in proportion:
[tex]\dfrac{AB}{AC}=\dfrac{AC}{AD}[/tex]
We have:
[tex]AB=2+6=8,\ AC=x,\ AD=2[/tex]
Substitute:
[tex]\dfrac{8}{x}=\dfrac{x}{2}[/tex] cross multiply
[tex]x^2=(8)(2)\\\\x^2=16\to x=\sqrt{16}\\\\x=4[/tex]
Bob and Dave go to PizzaScoff. Starting with 35 pizzas, Bob eats 6 4/5 pizzas and Dave eats 8 1/3 pizzas. How many are left?
Answer:
19.87 Pizzas are left
Step-by-step explanation:
To solve, just take 35 the number of starting pizzas and then subtract the number pizzas both of them consumed. So, 35 - 6.8 given 4/5 converts to 0.8 this leaves use with Bob's pizza consumption only at 28.2 pizza's left. Next, we are going to take 28.2 - 8.33 given 1/3 is .3333 repeating this then gives us the answer with having 19.87 pizzas left - although if it asks how many whole pizzas you would say 28 given you can't have .87 of a pizza.
A fraction is a way to describe a part of a whole. The amount of pizza left is 19 13/15.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
Given the total number of pizzas is 35. Also given, Bob eats 6 4/5 pizzas and Dave eats 8 1/3 pizzas. Therefore, the amount of pizza both together eat are,
Amount of pizza Bob and Dave eat = 6 4/5 + 8 1/3
= 34/5 + 25/3
= 102/15 + 125/15
= (102+125)/15
= 227/15
Amount of pizza left = 35 - 227/15
= (525 - 227)/15
= 298/15
= 19 13/15
Hence, the amount of pizza left is 19 13/15.
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If cosine of x equals 1 over 2, what is sin(x) and tan(x)? Explain your steps in simple complete sentences
Answer:
[tex]sin(x) =\±\frac{\sqrt{2}}{2}[/tex]
[tex]tan(x) =\±\sqrt{2}[/tex]
Step-by-step explanation:
By definition we know that:
[tex]sin ^ 2 (x) = 1-cos ^ 2 (x)\\\\tan (x) = \frac{sin(x)}{cos (x)}[/tex]
in this case we know that
[tex]cos(x) =\frac{1}{2}[/tex]
So how:
[tex]sin ^ 2(x) = 1-cos ^ 2(x)[/tex]
Substitute the values of cosine in the function
[tex]sin ^ 2 (x) = 1-\frac{1}{2}[/tex]
[tex]sin ^ 2 (x) = \frac{1}{2}[/tex]
[tex]sin(x) =\±\sqrt{\frac{1}{2}}[/tex]
[tex]sin(x) =\±\frac{\sqrt{2}}{2}[/tex]
Then how:
[tex]tan(x) = \frac{sin(x)}{cos (x)}[/tex]
Substitute the values of sine and cosine in the function
[tex]tan(x) = \±\frac{\frac{\sqrt{2}}{2}}{\frac{1}{2}}=\sqrt{2}[/tex]
If f(x) =x^2-2x and g(x) =6 x+4 for which value of x does (f+g) (x)=0
-4
-2
2
4
Answer:
-2Step-by-step explanation:
[tex](f+g)(x)+f(x)+g(x)\\\\f(x)=x^2-2x\\\\g(x)=6x+4\\\\\text{Substitute:}\\\\(f+g)(x)=(x^2-2x)+(6x+4)=x^2-2x+6x+4\\\\\text{combine like terms}\\\\(f+g)(x)=x^2+(-2x+6x)+4=x^2+4x+4\\\\(f+g)(x)=0\Rightarrow x^2+4x+4=0\\\\x^2+2x+2x+4=0\\\\x(x+2)+2(x+2)=0\\\\(x+2)(x+2)+0\\\\(x+2)^2=0\iff x+2=0\qquad\text{subtract 2 from both sides}\\\\x=-2[/tex]
Simplify (9/100)^3/2 in rational form.
27\1000 is your rational form.
To simplify (9/100)^3/2, cube 9/100 to get 729/1000000 and then take the square root, which simplifies to 3/100 in rational form.
Explanation:To simplify (9/100)^3/2 in rational form, we first understand that the exponent 3/2 can be broken down into two steps: first cubing the number, then taking the square root. Cubing 9/100 gives us (9^3)/(100^3), or 729/1000000. Then, taking the square root of this result and multiplying by the convenient factor of 1 in the form of 100/100, we simplify to 3/100, which is the result in rational form.
Place is highest to lowest 3/4 84% 1/3 0.82
ANSWER
84%,0.82,¾,⅓
EXPLANATION
Convert everything to decimals.
[tex] \frac{3}{4} = 0.75[/tex]
[tex] 84\% = 0.84[/tex]
[tex] \frac{1}{3} = 0.333....[/tex]
The last one is already in decimals.
[tex]0.82[/tex]
We can now see clearly, that
[tex]0.84 \: > \: 0.82 \: > \: 0.75 \: > \: 0.3333...[/tex]
This implies that,
[tex]84\% \: > \: 0.82 \: > \: \frac{3}{4} \: > \: \frac{1}{3} [/tex]
Hence from highest to least, we have
84%,0.82,¾,⅓
im confused on this one
Answer:
The first choice is correct;
(-∞,∞)
Step-by-step explanation:
We have been given the following functions;
[tex]f(x)=x^{2}-1\\\\g(x)=2x-3[/tex]
We are to determine the domain of (fog)(x).
The composite function, (fog)(x) is obtained by substituting g(x) in place of x in the function f(x);
(fog)(x) = f[g(x)] = [tex](2x-3)^{2}-1[/tex]
Clearly the function will be defined everywhere on the number line since it has no undefined points or domain constraints. The domain is thus;
(-∞,∞)
For this case we have the following functions:
[tex]f (x) = x ^ 2-1\\g (x) = 2x-3[/tex]
We must find [tex](f_ {0} g) (x):[/tex]
By definition of composite functions we have to:
[tex](f_ {0} g) (x) = f (g (x))[/tex]
So:
[tex](f_ {0} g) (x) = (2x-3) ^ 2-1\\(f_ {0} g) (x) = 4x ^ 2-12x + 9-1\\(f_ {0} g) (x) = 4x ^ 2-12x + 8[/tex]
The domain of the function is given by all the values for which the function is defined.
The function is defined for all real numbers.
Answer:
Domain: (-∞,∞)
On average, a herd of elephants travels 10 miles in 12 hours.
You can use that information to answer different questions.
Type each expression to show which question it answers.
Expressions:
10÷12
10×112
110×12
12÷10
How many miles does the herd travel in 1 hour?
How many hours does it take the herd to go 1 mile?
10/12 for 1. 12/10 for 2
Answer:
Look at explanation
Step-by-step explanation:
1. How many miles does the herd travel in an hour? : 10 divided by 12 and 10 divided by 1/12
2. How many hours does it take the herd to go 1 mile? : 12 divided by 10 and
1/10 x 12
This answer works on Imagine Math
Your parents ask you to choose between two offers for an allowance. The first offer is to receive one penny on the first day, 2 penny’s on the second day, 4 pennies on the third day, 8 pennies on the fourth day and so on. (365 days). Second offer is to receive 10 the first week, 20 the second week, 30 the third week, and so on, for the entire year (52 weeks). Which offer should you choose to make more money?
Answer:
pennies/first offer
Step-by-step explanation:
you would be rich
1x2=2 2^364= a lot of pennies
the pennies gives u the most money
https://lh5.googleusercontent.com/nNcMGuld4KbRoBooDf5Liva-NAJyj-IEknnSniAdiBKPNhKWtKqEw2SwN2uQUidgVX1Vh4rDHA=w739
Answer:
The answer is F: 108
Step-by-step explanation:
144 - 108 = 36
108 ÷ 3 = 36
Answer:
giytg8h0ygrubigrfbk
Step-by-step explanation:
PLS HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A pizza shop has 27 adult customers every hour. It has 12 younger customers every hour. It is open from 12 p.m. to 10 p.m. each day.
Write an expression for the total number of customers it would have in 3 days.
A. 27×10×3+12×10
B. (27+12)×10×3
C. (27+10)×12×3
D. 27+10×12×3
How many customers would it have in 3 days?
A. 387 customers
B. 930 customers
C. 1,170 customers
D.1,332 customers
387 customers or 930 customers
(27+12)x10x3 and 1,170
Which represents the imverse of the function f(x) = 4x?
For this case we must find the inverse of the following function:[tex]f (x) = 4x[/tex]
We follow the steps below:
We change f(x) to y:
[tex]y = 4x[/tex]
We exchange the variables:
[tex]x = 4y[/tex]
We solve for and:
[tex]4y = x[/tex]
We divide between 4 on both sides of the equation:
[tex]y = \frac {x} {4}[/tex]
then y by [tex]f ^ {-1} (x):[/tex]
[tex]f ^ {- 1} (x) = \frac {x} {4}[/tex]
ANswer:
[tex]f ^ {- 1} (x) = \frac {x} {4}[/tex]
A radio transmission tower is 190 feet tall. How long should a guy wire be if it is to be attached 13 feet from the top and is to make an angle of 31 with the ground? Give your answer to the nearest tenth of a foot.
Answer:
343.7 ft
Step-by-step explanation:
The wire is anchored 190 -13 = 177 ft from the ground. That distance is opposite the given angle (31°). The measure you want is the hypotenuse of the triangle with that side and angle measures.
The mnemonic SOH CAH TOA reminds you that the relation between the opposite side, hypotenuse, and angle is ...
Sin(angle) = Opposite/Hypotenuse
Filling in the given information, you have ...
sin(31°) = (177 ft)/hypotenuse
Solving for hypotenuse gives
hypotenuse = (177 ft)/sin(31°) ≈ 343.7 ft
The length of the guy wire should be 343.7 ft.
To find the length of the guy wire attached 13 feet from the top of a 190-foot tall tower at an angle of 31° with the ground, we can use the sine function and trigonometry. The length of the guy wire is approximately 380.8 feet.
Explanation:To find the length of the guy wire, we can use trigonometry. The guy wire, the height of the tower, and the distance from the top of the tower to the attachment point form a right triangle. We can use the sine function to find the length of the guy wire: sin(31) = height of the tower / length of the guy wire. Rearranging the equation gives us length of the guy wire = height of the tower / sin(31). Plugging in the values, we get length of the guy wire ≈ 190 / sin(31) ≈ 380.8 feet. Therefore, the guy wire should be approximately 380.8 feet long.
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what is 5/9 of 243??
Answer:
135
Step-by-step explanation:
[tex]\frac{5}{9}\times243=\frac{5\times243}{9}=
\frac{1250}{9}=\boxed{135}
[/tex]
round 9,631.4725 to the nearest thousandth
The answer would be 9,631.473. Since there is a 5 after the two, you round up one value. Hope this helps!
Answer:
9,631.473
Step-by-step explanation:
The five would make 2 into a 3.
You have $20dollar to spend on taxi fare. The ride costs $5dollar plus$2.50 dollar per kilometer. Write an inequality to determine the distance in kilometers, d, you can ride for $20.
Answer: ($2.50k) + $5
The distance you can ride is 6 kilometers.
($2.50 x 6) + $5 = $20
Answer:
[tex]2.50d+5\leq 20[/tex]
Step-by-step explanation:
Let d represent distance in kilometers.
We have been given that a taxi ride costs $2.50 per kilometer, so the cost of d kilometers would be [tex]2.50d[/tex] dollars.
We are also told that ride costs a fixed charge of $5, so total cost of d kilometers would be [tex]2.50d+5[/tex] dollars.
You have $20 to spend on taxi fare, so the total cost of riding d kilometers should be less than or equal to 20.
We can represent this information in an inequality as:
[tex]2.50d+5\leq 20[/tex]
Therefore, our required inequality would be [tex]2.50d+5\leq 20[/tex].
The Patel family looks at a map to plan their family vacation. They plan to travel from Smithville to Jonesville, which are 334inches apart on the map. Then they plan to travel from Jonesville to Clarksville, which are 514inches apart on the map. The scale on the map is 12 inch equals 4 miles. What is the actual distance the Patel family will travel by the time they reach Clarksville?
Answer:
Step-by-step explanation:
1/2 over 4 = 15/4 over x
4/1=/15/4= 60/4*2/1=120/4=30
repeat the step but instead of 15/4 to 21/4
anyways it's 72
Final answer:
The actual distance the Patel family will travel from Smithville to Clarksville is approximately 282.66 miles.
Explanation:
The scale on the map is 12 inches equals 4 miles. To find the actual distance the Patel family will travel from Smithville to Jonesville, we can set up a proportion:
12 inches / 4 miles = 334 inches / x miles
Cross multiplying, we get:
12x = 1336
Dividing both sides by 12, we find that x = 111.33 miles. So, the Patel family will travel approximately 111.33 miles from Smithville to Jonesville.
Similarly, to find the actual distance they will travel from Jonesville to Clarksville, we can set up another proportion:
12 inches / 4 miles = 514 inches / y miles
Cross multiplying, we get:
12y = 2056
Dividing both sides by 12, we find that y = 171.33 miles. So, the Patel family will travel approximately 171.33 miles from Jonesville to Clarksville.
Therefore, the total actual distance the Patel family will travel by the time they reach Clarksville is approximately 111.33 miles + 171.33 miles = 282.66 miles.
what is 3/9 of 612??
Answer:
204
Step-by-step explanation:
First you divide 612 by 9 (612÷9) which gives 68.
Then multiply 68 by 3 (68×3) giving the answer 204.
Answer:
3/9 of 612 = 204
Step-by-step explanation:
Step 1: convert 3/9 into a decimal so that its easier to work with, that will be 0.3333333333
Step 2: since we know that "of" means "X" in math, we times it by 612 to get the answer of 204
The formula for the volume sphere is V=4/3pie r^3 what is the formula solved for r?
Answer:
[tex]r = \sqrt[3]{\frac{3V}{4 \pi}}[/tex]
Step-by-step explanation:
From the formula of volume of a sphere we have to isolate "r" on one side of the equation i.e. we have to make "r" the subject of the equation.
[tex]V=\frac{4}{3} \pi r^{3}\\\\ \text{Multiplying both sides by 3/4 we get}\\\\\frac{3V}{4} = \pi r^{3}\\\\ \text{Dividing both sides by } \pi \\\\ \frac{3V}{4 \pi} = r^{3}\\\\\text{Takeing cube root of both sides}\\\\\sqrt[3]{\frac{3V}{4 \pi}} = r[/tex]
Therefore:
[tex]r = \sqrt[3]{\frac{3V}{4 \pi}}[/tex]
Answer:
The formula for radius of sphere is r = ∛(3V/4π)
or
r = (3V/4π)¹/³
Step-by-step explanation:
It is given formula for volume of sphere.
Volume of sphere = 4/3 πr³
Where r is the radius of sphere
To find the radius r of sphere
Volume V = 4/3 πr³
r³ = 3V/4π
r = ∛(3V/4π)
Therefore formula for radius of sphere is r = ∛(3V/4π)
or
r = (3V/4π)¹/³
If p is a zero of 2x^2 - 5x + 3 then find the value of p.
The answer is zero 2x -3=0 x-1=0
Which line segment is a diameter of circle L?
1. HL
2. GJ
3. GK
4. IL
the diameter is 2. GJ as it goes across the whole circle
Answer:
GJ
Hope this helps :)
Have a great day !
5INGH
Step-by-step explanation:
Diameter = Any straight line segment that passes through the centre of the circle.
Martin orders a pasta dish that is priced at $11.99. He also orders a drink. The total cost for the pasta and drink is $14.48. Which of the following equations can be used to find the cost of the drink?
14.48 + d = 11.99
11.99 + d = 14.48
11.99 + 14.48 = d
11.99 - d = 14.48
Nora has a coupon for $3 off of a calzone. She orders a beef and olive calzone, and her bill, with the discounted price, is $9.49. Which of the following equations can be used to find the regular price of the calzone?
c - 3 = 9.49
9.49 - c = 3
c + 3 = 9.49
c + 9.49 = 3
Martin's drink equation = option b, 11.99 + d = 14.48
Nora's calzone equation = option a, c - 3 = 9.49
Hope this helps
Consider the diagram shown where a tree that is 100 feet tall cast a shadow 120 feet long find the angle of elevation of the sun
It’s -125 and you welcome
Joe wants to paint the outside of a wooden box. He needs to find the surface area of the box
in order to buy paint. A net of the box is shown. What is the surface area of the box?
4*2=8
4*1.5=6
2*1.5=3
8*2=16
2*6=12
2*3=6
16+12+6=34 ft
Total surface area is sum of area of all parts of surface. The surface area of the box is 34 squared feet.
How to find the area of surface of a figure if its split in parts?The area of surface of a figure is sum of area of all sub-parts of it. It is because we want to get the total area of its surface.
For the given case, the box given has:
Area of top = Area of bottomArea of back = Area of frontArea of left side = Area of right side.(its all because of assuming box is cuboid or say rectangular prism)
Thus,
Surface area of box = twice of (area of top + area + left side + area of back)
Calculating these sub areas:
Area of top:Area of top = [tex]2 \times 4 = 8 \: \rm ft^2[/tex]
Area of back:Area of back = [tex]1\dfrac{1}{2} \times 4 = \dfrac{2+1}{2} \times 4 = 6 \: \rm ft^2[/tex]
Area of left:Area of left side: [tex]1\dfrac{1}{2} \times 2 = \dfrac{2+1}{2} \times 2 = 3 \: \rm ft^2[/tex]
Thus,
Surface area of box = [tex]2(8 + 6 + 3) = 2 \times 17 = 34 \: \rm ft^2[/tex]
Thus,
The surface area of the box is 34 squared feet.
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What is the maximum value that the graph of y=cos x assumes?
Answer: 1
Step-by-step explanation: the cosine function oscillates between the values -1 to 1
The amplitude of this particular function is understood to be 1
The maximum value that a graph of y = cos(x) assumes is y = 1.
What is the cosine function?In a triangle, the cos function (or cosine function) is the ratio of the base side to the hypotenuse.
What are some important values of cosine function?cos(0°) = 1
cos(30°) = √3/2
cos(45°) = 1/√2
cos(60°) = 1/2
cos(90°) = 0
Cosine function is a periodic function and the value repeat themselves at an interval of 2π. The maximum value the cosine function achieves is y=1. The graph of the function is shown below:
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how do you find the surface area of a rectangular prism ?
The official formula is 2B+ Ph
where B is the area of a base of the prism, P is the perimeter of a base, and h is the height of the prism (distance between the two bases)
However, length x width x height can also be used
Only number 14 pleaseee....
Answer:
c
Step-by-step explanation:
There are 6 red and 2 black balls.
The total number of balls = 2 + 6 = 8
The probability of drawing a black ball first is 2/8 = 1/4
The probability of drawing a red ball second is 6/7
P(black, red)=1/4 * 6/7 = 6/28 = 3/14
C