Final answer:
Set-builder notation is a method to define intervals through a property shared by all members. The notation for the given intervals includes conditions that represent the endpoints or infinity, expressing the range of the variable in each set.
Explanation:
Writing intervals in set-builder notation involves describing a set through a property that its members share. Here is the set-builder notation for each interval provided:
10. (-infinity, 6) in set-builder notation is: [tex]\{x | x < 6\}[/tex]11. (4, infinity) in set-builder notation is:[tex]\{x | x > 4\}[/tex]12. [-3,5) in set-builder notation is: [tex]\{x | -3 \leq x < 5\}[/tex]13. [-4,1]U[9, infinity) in set-builder notation is: [tex]\{x | -4 \leq x \leq 1\} \cup \{x | x \geq 9\}[/tex]14. (-infinity, infinity) in set-builder notation is simply the set of all real numbers, which can be written as: [tex]\{x | x \text{ is a real number}\}[/tex]To express these sets, we use 'x' as our variable and conditions such as x < 6 that define the range of values 'x' can take. The 'U' symbol represents the union of two sets, indicating that the set includes all elements from both intervals.
Twenty times a square of a positive integer, plus 50 equals negative 40 times the square of the positive integer, plus one-hundred and ten times the positive integer. Which equation could be used to solve for the unknown positive integer.
A) 60x2 + 110x + 50 = 0
B) 60x2 + 110x − 50 = 0
C) 60x2 − 110x + 50 = 0
D) 60x2 − 110x − 50 = 0
Answer:
c
Step-by-step explanation:
Twenty times a square of a positive integer, plus 50 equals negative 40 times the square of the positive integer, plus one-hundred and ten times the positive integer. Which equation could be used to solve for the unknown positive integer.
A) 60x2 + 110x + 50 = 0
B) 60x2 + 110x − 50 = 0
C) 60x2 − 110x + 50 = 0
D) 60x2 − 110x − 50 = 0
The correct equation to solve for the unknown positive integer is 60x^2 - 110x + 50 = 0.
Explanation:To solve for the unknown positive integer, you'll need to form an equation. Start by writing down the mathematical expressions as given in the equation.
20x^2 + 50 = -40x^2+ 110x based on the statement given. Then, to simplify the equation, combine like terms. To do this, you'll need to move -40x^2 to the left side of the equation and move 50 to the right side of the equation. This gives us: 20x^2 + 40x^2 = 110x - 50. The result is 60x^2 - 110x + 50 = 0. The correct answer is choice C: 60x^2 - 110x + 50 = 0.
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Brenda considers geometric figures and concepts that are related to lines. Which terms are considered undefined?
Check all that apply.
line
line segment
distance along a line
O parallel lines
perpendicular lines
point
Answer:
A, C, F
Step-by-step explanation:
Answer:
1,3&6
Step-by-step explanation:
line
distance along a line
point
HELP PLEASE HARDEST QUESTION IN THE WORLD :(
MICKEY AND MINNIE ARE EXPECTING.
THEY ARE A VERY HAPPY COUPLE.
THE DOCTOR SAID THEY ARE HAVING 5 BOYS AND 5 GIRLS.
MICKEY AND MINNIE ARE RATS.
EVERY THREE WEEKS AN ADULT RAT COUPLE CAN HAVE BABIES.
IT TAKES 6 WEEKS FOR A BABY RAT TO BECOME AN ADULT
AND BE OLD ENOUGH TO HAVE A BABY.
ASSUMING MICKEY AND MINNIE WANT TO HAVE AS MANY CHILDREN AS POSSIBLE AND THEIR OFFSPRING WANT TO HAVE AS MANY CHILDREN AS POSSIBLE,
WHAT WILL BE THEIR ENTIRE POPULATION IN ONE YEAR? (52 WEEKS)
(INCLUDING MICKEY AND MINNIE)
(ASSUME EVERY PREGNACY WILL CONSIST OF 5 BOYS AND 5 GIRLS)
Answer: 6, 570
Step by step explanation: If Minnie and Mickey have 5 girls and 5 boys every 3 weeks for 52 weeks this means they will have 17 pregnancies. At the end of one year Minnie and Mickey alone will have produced 170 children. It takes these children 6 weeks to grow up and be ready to reproduce. Every 6 weeks 10 new rats will be able to have children at a rate of 10 per 3 weeks. This means that a single set of 10 offspring will have 100 children every 3 weeks. There will be 8 sets of offspring that can reproduce before the year is over. This means if the sets have 100 children every 3 weeks starting with one set and adding one more set every 6 weeks, at the end of the year the offspring's offspring will total 6,400. 6,400 + 170 will equal 6,570. The total population is 6,570.
17 more than twice Gail’s age
Answer:
34
Step-by-step explanation:
i just know t hat this is th answer
Nancy Gardener is making dresses for her granddaughters. For each dress she will
need between three and four yards of fabric. The fabric she is using costs $4.34
per yard after sales tax is added. If she has four granddaughters, about how much
should she expect to spend at the fabric store?
A- $72 to $96
B- more than $96
C- $48 to $72
D- $24 to $48
Answer:
the answer is c
Step-by-step explanation:
A waterfall has a height of 1400 feet. A pebble is thrown upward from the top of the falls with an initial velocity of 16 feet per second. The height, h, of the pebble aftert
seconds is given by the equation hs - 167" + 16 + 1400. How long after the pebble is thrown will it hit the ground?
The pebble hits the ground approximately 8.88 seconds after it is thrown, based on the given equation for its height.
To find out when the pebble hits the ground, we need to find the time when the height h(t) equals 0.
Given that the height h(t) of the pebble after t seconds is given by the equation:
[tex]\[ h(t) = -16t^2 + 16t + 1400 \][/tex]
We set h(t) to 0 and solve for t:
[tex]\[ -16t^2 + 16t + 1400 = 0 \][/tex]
Now, we can use the quadratic formula to solve for t :
[tex]\[ t = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]
where a = -16, b = 16, and c = 1400.
Plugging these values into the quadratic formula:
[tex]\[ t = \frac{{-16 \pm \sqrt{{16^2 - 4(-16)(1400)}}}}{{2(-16)}} \]\[ t = \frac{{-16 \pm \sqrt{{256 + 89600}}}}{{-32}} \]\[ t = \frac{{-16 \pm \sqrt{{89856}}}}{{-32}} \]\[ t = \frac{{-16 \pm 300.1}}{{-32}} \][/tex]
We'll ignore the negative solution because time can't be negative in this context. So, we use the positive solution:
[tex]\[ t = \frac{{-16 + 300.1}}{{-32}} \]\[ t = \frac{{284.1}}{{-32}} \]\[ t \approx -8.88 \][/tex]
Since time can't be negative, we discard this solution. The only meaningful solution is when the pebble hits the ground. Thus, the pebble hits the ground approximately 8.88 seconds after it is thrown.
Simplify the expression.
Answer:
I'm pretty sure the answer is 5.2h-2.9d-16
what is negative seven divided by four
Answer: -1.75
Step-by-step explanation:
Answer:
-1.75 is the answer ....
Mr. william bought an old table for RS 850 and spent 1/10 of the cost price on its repairs. He sold the table for Rs 1050. Find his gain or loss percent.
fast please!
Answer:
115
Step-by-step explanation:
1/10 of 850= 85
he spent and additional RS 85 on its repairs
cost price + repairs price =935
he sold it for 1050
to find his gain =1050-935
=115
Find the perimeter of the square:
6x + 1
Answer:
Do you have a photo
Step-by-step explanation:
I'll be happy to help
8x raise 2 -36 is a linear expression true or false
Answer:
False. [tex]8x^2-36[/tex] is not a Linear expression.
Step-by-step explanation:
Given: [tex]8x^2-36[/tex]
we need to find whether it is a linear expression or not.
By Definition of Linear expression we say,
Linear expression is an algebraic expression where the power of variable(s) is equals to 1
Or we can say that:
Polynomial having power of variable(s) as 1, is known as Linear Expression
In the above expression the power of variable is 2 hence it is not a linear expression.
Hence the statement is False, the [tex]8x^2-36[/tex] is not a Linear expression.
Please help me idk howwwwww
Answer:
OPTION B: y = [tex]$ \frac{1}{2} $[/tex]x - 2
Step-by-step explanation:
To find the equation of the line substitute the value of x and compare the corresponding value of y.
OPTION A:
y = 2x + 4
Substitute x = 0. We get, 2(0) + 4 = 4
When x = 0, y = -2 [tex]$ \ne $[/tex] 4.
OPTION B:
y = [tex]$ \frac{1}{2} $[/tex]x - 2
Substitute x = 0, we get [tex]$ \frac{1}{2} (0) - 2$[/tex]
= -2
When x = 2, [tex]$ \frac{1}{2}(2) - 2 $[/tex] = 1 - 2
=-1
Similarly, When x = 4, [tex]$ \frac{1}{2}(4) - 2 = 2 - 2 $[/tex]
= 0.
Since, all the values are satisfied, OPTION B is the answer.
Substitute OPTION C and OPTION D. They do not satisfy the values either.
How do you evaluate the expression 7x + 4 for x = 6
Answer:
46
Step-by-step explanation:
7x+4
7(6)+4
42+4
46
Step-by-step explanation:
7x+4=6
substitute 6 in x
7(6)+4
42+4=46
Given the function f(x) = 4(2)x, Section A is from x = 1 to x = 2 and Section B is from x = 3 to x = 4.
Part A: Find the average rate of change of each section. (4 points)
Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other. (6 points)
(10 points)
Answer:
Part A: Section A- 8, Section B- 32.
Part B: 4 times.
Step-by-step explanation:
The function is given by [tex]f(x) = 4(2)^{x}[/tex].
Section A is from x = 1 to x = 2.
Now, f(1) = 4 × 2 = 8 and f(2) = 4 × 2 × 2 = 16
Again, section B is from x = 3 to x = 4.
Now, f(3) = 4 × 2 × 2 × 2 = 32 and f(4) = 4 × 2 × 2 × 2 × 2 = 64
Part A:
In section A, the average rate of change is = [tex]\frac{f(2) - f(1)}{2 - 1} = 16 - 8 = 8[/tex] (Answer)
And in section B, the average rate of change is = [tex]\frac{f(4) - f(3)}{4 - 3} = 64 - 32 = 32[/tex] (Answer)
Part B:
Therefore, the number of times the average rate of change of section B is greater than section A is [tex]\frac{32}{8} = 4[/tex] (Answer)
Answer:
Part A: Section A- 8, Section B- 32.
Part B: 4 times.
Step-by-step explanation:
The function is given by .
Section A is from x = 1 to x = 2.
Now, f(1) = 4 × 2 = 8 and f(2) = 4 × 2 × 2 = 16
Again, section B is from x = 3 to x = 4.
Now, f(3) = 4 × 2 × 2 × 2 = 32 and f(4) = 4 × 2 × 2 × 2 × 2 = 64
Part A:
In section A, the average rate of change is = 8
And in section B, the average rate of change is = 32
Part B:
Therefore, the average rate of change of section B is greater than section A is (32 / 8 = 4)
Ben starts commision as a real estate agent last month his total sales for all the houses he sold $950,000.If ben earns a 3% rate of commision what was his gross income kast month
Ben's gross income was $28,500.
Step-by-step explanation:
Sales for the month = $950000
Commission rate = 3%
Amount of commission = 3% of sales for the month
Amount of commission = [tex]\frac{3}{100}*950000[/tex]
Amount of commission = [tex]\frac{2850000}{100}[/tex]
Amount of commission = $28500
Ben's gross income was $28,500.
Keywords: percentage, division
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what is the median,lower quartile,maximum,upper quartile,and the minimum of 34, 37, 39, 32, 48, 45, 53, 62, 58, 61, 60, 41
Answer:
Median = 46.5
Minimum = 32
Maximum = 62
Lower quartile = 38
Upper quartile = 59
Step-by-step explanation:
Before we can proceed to solving any of these, it is best you arrange your data first from least to greatest
32 34 37 39 41 45 48 53 58 60 61 62
First we have the median. The Median is the middle value. In this case we an even number of data, which is 12 data points. The middle value of the data would be found in between the 6th and 7th data point:
45 and 48
To get the middle value, you need to solve for the value that is in the middle of 45 and 48 by getting the sum of both numbers and dividing it by two.
45 + 48 = 93
93 ÷ 2 = 46.5
The minimum and maximum value is merely the least and greatest number.
Here we have:
Minimum = 32
Maximum = 62
To get the lower and upper quartiles, just remember that quartiles divide the data into 4 equal parts. All you need to do is find the value that is in between each quarters of the data:
Q1 (Lower) Q2(Median) Q3(Upper)
32 34 37 | 39 41 45 | 48 53 58 | 60 61 62
Like the median, we will find the value that comes in between each quarter.
Q1
37 + 39 = 76
76 ÷ 2 = 38
Lower quartile = 38
Q3:
58 + 60 = 118
118 ÷ 2 = 59
Upper quartile = 59
Answer:
the person on top has it right ^^^^^^^^^^ did the work and it right thx :))
Which of these sets could represent the side lengths of a right triangle?
Group of answer choices
{4, 8, 12}
{6, 8, 10}
{6, 8, 15}
{5, 7, 13}
Answer:
{6, 8, 10} is a set which represents the side length of a right triangle.
Step-by-step explanation:
In a right triangle:
[tex](Base)^{2} + (Perpendicular)^{2} = (Hypotenuse)^{2}[/tex]
Now, in the given triplets:
(a) {4, 8, 12}
Here, [tex](4)^{2} + (8)^{2} = 16 + 64 = 80\\\implies H = \sqrt{80} = 8.94[/tex]
So, third side of the triangle 8.94 ≠ 12
Hence, {4, 8, 12} is NOT a triplet.
(b) {6, 8, 10}
Here, [tex](6)^{2} + (8)^{2} = 36 + 64 = 100\\\implies H = \sqrt{100} = 10[/tex]
So, third side of the triangle 10
Hence, {6, 8, 10} is a triplet.
(c) {6, 8, 15}
Here, [tex](6)^{2} + (8)^{2} = 36 + 64 = 100\\\implies H = \sqrt{100} = 10[/tex]
So, third side of the triangle 10 ≠ 15
Hence, {6, 8, 15} is NOT a triplet.
(d) {5, 7, 13}
Here, [tex](5)^{2} + (7)^{2} = 25 + 49 = 74\\\implies H = \sqrt{74} = 8.60[/tex]
So, third side of the triangle 8.60 ≠ 13
Hence, {5, 7, 13} is NOT a triplet.
100 POINTS AND MARKED AS BRAINLIEST IF YOU ANSWER THIS
Create an expression that you would use to solve the problem below.
YOU DO NOT NEED TO SOLVE. Just set up the expression to represent the situation below.
A tool rental cost $0.65 per minute. If the total bill for the rental was $18.20, then for how many minutes was the tool used?
The expression that represents the situation is 0.65 x = 18.2
The tool used for 28 minutes
Step-by-step explanation:
The given is:
A tool rental cost $0.65 per minuteIf the total bill for the rental was $18.20Assume that the tool rent for x minutes
∵ The tool rental cost is $0.65 per minute
∵ The number of minutes is x
∵ The total bill for the rental = $18.20
∴ 0.65 x = 18.20
The expression that represents the situation is 0.65 x = 18.2
Solve the equation to find x
∵ 0.65 x = 18.20
- Divide both sides by 0.65
∴ x = 28
The tool used for 28 minutes
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2 + 1.25f = 10 - 2.75f
Answer:
f=2
Step-by-step explanation:
1.25f+2.75f= 10-2
You must take positive two to the other side to get negative 2. Also, you should take the negative 2.75f to the other side to get positive 2.75f.
4f= 8
f= 2
Answer:
f=2
Step-by-step explanation:
frome 12 to 16 in a month what is the percent of increase for that month round if needed
Answer:
33.33%
Step-by-step explanation:
The value of a variable change from 12 units to 16 units in a month.
We have to calculate the percentage increase for that month.
Therefore, the increase of value from 12 to 16 means by (16 - 12) = 4 units
So, the percentage increase for the month is [tex]\frac{4}{12} \times 100 = 33.33[/tex]%. (Rounded to the two decimal). (Answer)
Brian buys 6 books and the total cost is $24.18. What is the constant of proportionality that relates the cost in dollars, y, to the number of books, x?
Answer:
4.03
Step-by-step explanation:
Y = kx
y = 24.18
x = 6
k = constant of proportionality
Y =kx
Step 1. Substitute number based on the formula
24.18 = k6
Step 2. Transpose Y to the left to find the ratio of constant proportionality
K = 24.18/6
Step 3. Divide Y over X
K = 4.03 (answer)
I have 9 hundreds, 9 ones, 19
tens, and 3 tenths. What number
am I?
Answer:
1099.3
Step-by-step explanation:
9 hundreds = 900
9 ones = 9
19 tens = 190
3 tenths = 0.3
Answer:
1099.3
Step-by-step explanation:
9 hundreds => 900
19 tens => 190
9 ones => 9
3 tenths => 0.3
This number is: 1099.3
The length of the rectangle garden is three more than twice its width. If the perimeter of the garden is 114 feet, what is its width of the garden?
Dimensions of rectangular garden is: length = 39 feet and width = 18 feet
Solution:Given that length of the rectangle garden is three more than twice its width.
The perimeter of the garden is 114 feet
Need to determine width of the garden
Let assume width of the garden be represented by variable "x"
=>Twice of the width = [tex]2 \times x = 2x[/tex]
=> 3 more than Twice of the width= 3 + 2x = 2x + 3
As length of the rectangle garden is three more than twice its width ,
=> Length of the rectangle garden = 2x + 3
Perimeter of the rectangle = 2( length + width)
=> Perimeter of the rectangular garden = 2 (Length of the rectangle garden + width of the garden)
= 2 (2x + 3 + x) = 2 (3x + 3 ) = 6x + 6
=> Perimeter of the rectangular garden = 6x + 6
As it is also given that Perimeter of the rectangular garden = 114 feet
=> 6x + 6 = 114 feet
=> 6x = 114 – 6
x = 18
Width of the garden = x = 18 feet
Length of the garden = = 2x + 3 = 2(18) + 3 = 39 feet
Hence dimensions of rectangular garden is length = 39 feet and width = 18 feet
A college student receives an interest-free loan of $9,400 from a relative. The student will repay $200 per month until the loan is paid off.
(a) Express the amount P (in dollars) remaining to be paid in terms of time t (in months). (Give your answer in slope-intercept form.)
(b) After how many months will the student owe $5000?
Answer:
(a) P = - 200 T + 9,400
(b) After 22 months the student will owe $5000.
Step-by-step explanation:
Here, the amount loaned out to the student = $9,400
The installment amount of each month = $200
(a) P : Amount remaining to be paid
T: time in months
Now, the remaining amount = Actual amount - Amount paid in T months
or, P = 9,400 - $200 (T)
⇒ P = - 200 T + 9,400 ( y = mx + C form)
(b) The remaining amount left = $5000
As we know, P = 9,400 - $200 (T)
⇒ 5,000 = 9,400 - 200 T
⇒200 T = 9,400 - 5,000 = 4,400
⇒ T = 4400/200 = 22
or T = 22 Months
Hence, After 22 months the student will owe $5000.
What is the length of line segment BC?
2 cm
3 cm
6 cm
8 cm
Answer:
3
Step-by-step explanation:
100 POINTS AND MARKED AS BRAINLIEST IF YOU ANSWER THIS
Create an expression that you would use to solve the problem below.
YOU DO NOT NEED TO SOLVE. Just set up the expression to represent the situation below.
A tool rental cost $0.65 per minute. If the total bill for rental was $18.20, then for how many minutes was the tool used.
Answer:
$18.20/0.65=28 minutes
Step-by-step explanation:
$18.20 was the cost of the rental divide it by the cost per minute and that will give you the total number of minutes used which is 28.
Answer:
since one mins = 0.65
for 18.20= 18.20/0.65= 28mins
In a two-digit number the units digit is three less than the tens digit. If the digits are reversed, the sum of the reversed number and the original number is 121. Find the original number.
answer: 74
explanation:
7-3=4
74
+47
---
121
Answer:
The digits are 7 and 4. The number would be 74.Step-by-step explanation:
In a two-digit number we have the unit's digit and the ten's digit. The unit's digit is represented by [tex]u[/tex]. Then ten's digit must be represents with a number 10 as a coefficient, and the variable would be [tex]d[/tex]. So, the numerical vale of the number would be:
[tex]10d+u[/tex]
Also, we know that [tex]d=u+3[/tex], because the unit digit is three less than tens digit, or tens digit is three more units than the unit digit.
Then, the sum of the reversed number and the original number is 121, this would be expressed:
[tex]10d+u+10u+d=121\\11d+11u=121[/tex]
But, we know that [tex]d=u+3[/tex], so, we replace it:
[tex]11(u+3)+11u=121\\11u+33+11u=121\\22u+33=121\\22u=121-33\\u=4[/tex]
Then, if tens digits is 3 more, [tex]d=7[/tex]
Therefore, the digits are 7 and 4. The number would be 74.
Solve the system of linear equations.
x + y = 4
2x − 3y = 18
A) (6, 2)
B) (−6, 2)
C) (6, −2)
D) (−6, −2)
Answer:
The answer is C) (6, -2).
Step-by-step explanation:
First, subtract both sides by y in the first equation, to figure out what x is.
x+y-y=4-y
x=4-y
x is equal to 4-y. Use substitution to plug that in to the second equation for x.
2x-3y=18
2(4-y)-3y=18
Now, solve for y. Expand.
2(4-y)-3y=18
8-2y-3y=18
Combine like terms.
8-2y-3y=18
8-5y=18
To get y by itself, subtract 8 from both sides.
8-8-5y=18-8
-5y=10
Lastly, divide both sides by -5.
-5/-5y=10/-5
y=-2
Since we know that y is equal to -2, we can solve for x in the equation x=4-y.
x=4-y
x=4-(-2)
*Negative & Negative makes a Positive*
x=6
Therefore, your answer is x being equal to 6, and y being equal to -2.
Hope this helped!
Final answer:
To solve the system of linear equations, we first solve one equation for a variable and then substitute it into the other. Through simplification and combination of like terms, we find that the solution is (6, -2), which is option C.
Explanation:
The subject question involves solving a system of linear equations. We are given the first equation, x + y = 4, and the second equation, 2x - 3y = 18. To find the solution, we will use the method of elimination or substitution to solve for the values of x and y.
Step-by-Step Solution
Solve the first equation for y: y = 4 - x.
Substitute y in the second equation: 2x - 3(4 - x) = 18.
Simplify: 2x - 12 + 3x = 18.
Combine like terms: 5x = 30.
Divide by 5: x = 6.
Substitute x in the first equation: 6 + y = 4.
Solve for y: y = -2.
The solution to the system of equations is (6, -2), which corresponds to option C.
Solve this please and list your steps
Answer:
√125 + 5 or 16.180
Step-by-step explanation:
√5 · 5 · 5 + √5 · 5
√25 · 5 + √25
√125 + 5 or 16.18
A girl paid the property tax of RS. 2068 at the rate of 0.8%. Find the worth of property?
Answer:
Let the worth of the property be x
0.8x/100 = 2068
8x = 2068000
x = 258500 Rs.
Hope this helps!