The exact interval notation of given equation is x > - 8.
What is interval notation for compound inequalities?
The numbers that bound a continuous set of real numbers can be used to express the continuous set in interval notation. Intervals have many characteristics in common with ordered pairs when written.
We have,
3x+1 > 2x-3 > x-11
Apply the rule that if m > v > n, then m > v and v > n to the given compound inequality to find the solution.
∴ m = 3x + 1,
v = 2x - 3,
n = x - 11.
Hence, by applying the rule of compound inequality we get,
3x + 1 > 2x - 3 and 2x - 3 > x - 11
3x + 1 > 2x - 3
3x + 1 - 1 > 2x - 3 -1
3x > 2x - 4
3x - 2x > 2x - 4 - 2x
x > - 4
2x - 3 > x - 11
2x - 3 + 3 > x - 11 + 3
2x > x - 8
2x - x > x - 8 - x
x > - 8
The two computations above indicate that the acquired intervals, x > - 4 and x > - 8, will be combined to yield the answer to the given inequality.
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PLEASE HELP! f(2)=3x^2+2x+4 find f(-2)
The value of f(-2) in the function f(x) = 3x² + 2x + 4 is 12.
How to solve function?A function is defined as a relation between a set of inputs having one output each. In a simpler term a function relates input and output.
In other words, a function relates each element of a set with exactly one element of another set (possibly the same set).
Therefore, let's solve the function below:
f(x) = 3x² + 2x + 4
Let's find f(-2) as follows;
To solve f(-2), we have to substitute the value of x in the function f(x) = 3x² + 2x + 4 with -2.
Therefore,
f(x) = 3x² + 2x + 4
f(-2) = 3(-2)² + 2(-2) + 4
f(-2) = 3(4) - 4 + 4
f(-2) = 12 - 4 + 4
f(-2) = 12
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What is the equation of this graph the line?
The equation of line in slope intercept form is y=−9/8x+7.
In the given question we have to write the equation of the graph line in slope intercept form.
The give points are(0,7) and (8,−2)
Let x(1)=0, y(1)=7, x(2)=8 and y(2)=−2.
The slope intercept form of equation is
y−y(1)=m(x−x(1))+c.........(1)
Before finding the equation we find the slope of equation.
Slope(m)={y(2)−y(1)}/{x(2)−x(1)}
Now putting the value
m=(−2−7)/(8−0)
m= −9/8
Now putting the value in equation 1
y−7=−9/8(x−0)
Now the equation is
y−7=−9/8x
Add 7 on both side
y−7+7=−9/8x+7
y=−9/8x+7
Hence, the equation of line in slope intercept form is y=−9/8x+7.
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Find the y-coordinate of the y-intercept of the polynomial function defined below.
f(x) = 2(5x² − 2)(x − 5) (4x² − 2)
Answer:
-40
Step-by-step explanation:
The y-intercept occurs when x is equal to 0. In order to find the y-coordinate, you would just plug in x with 0:
2(5x² − 2)(x − 5) (4x² − 2)
2(5[0]^2 - 2)(0 - 5)(4[0]^2 - 2)
2(-2)(-5)(-2)
-40
The perimeter of a field is 840 m. If
the length is 25 metres longer than the
width, calculate the length.
Identify the length of the missing section of each line. Assume that the lines are divided into equal parts.
The identification of the length of the missing section of each line, assuming that the lines are equally divided, is as follows:
a) The missing section is 24 units.
b) The missing section is 18 units.
c) The missing section is 10 units.
How are the missing sections computed?The missing sections can be computed using the mathematical operations of division and multiplication.
The product (quotient) of a division operation involves applying the divisor on the dividend using a division operand (÷).
The product of a multiplication operation applies the multiplier on the multiplicand using the multiplication operand (×).
a) The total units = 36
Division parts = 3
The units of each division = 12 (36/3)
The missing section = 24 (12 x 2)
b) The total units = 36
Division parts = 4
The units of each division = 9 (36/4)
The missing section = 18 (9 x 2)
c) The total units = 16
Division parts = 8
The units of each division = 2 (16/8)
The missing section = 10 (2 x 5)
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a rocket is 1 mile above the earth One minute and 5 miles above earth in three minutes. what is the rocket rate of change in miles per minute
Answer:
1.6repeat miles per minute
Step-by-step explanation:
I'm not totally sure, but i just divided 5/3 and that's how I got the answer
Graph the line by plotting any two ordered pairs that satisfy the equation.
y=43x−6
Evaluate the function at the given values.
K(x) =−x+2
K(1) =
K(-2) =
K(0) =
Hargray Telephone earned 155.27 interest on a $20,000 deposit in an account paying 6%.
Find the number of days that the funds were on deposit.
46 Days the number of days that the funds were on deposit on Interest rate.
What exactly does "interest rate" mean?
An interest rate informs you of how much borrowing will cost you and how much saving will pay off. Therefore, the interest rate is the amount you pay for borrowing money and is expressed as a percentage of the total loan amount if you are a borrower.Interest earned = Principal*Interest rate*Time period
155.27 = 20,000 * 0.06 * Time period
Time period = 155.27/(20,000*0.06)
= 0.129339 years
=(0.129339 * 360)
= 46.56204 days
= 46 days(Approx)
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URGENT PLS HELPPPP!!!!!
Write the point-slope form of the equation of the line with a slope of -2 and an x-intercept of -1.
a. Using variables, write out the formula for the point-slope form of the equation.
b. Identify the values for m, x1, and y1.
c. Fill these values into the point-slope form of the equation from part (a), and simplify as needed.
Use the box provided to submit all of your calculations and final answers. Simplify the answer as needed.
The equation of the line that has a slope of -2 and x-intercept of -1 in point slope form is y = -2(x + 1).
How to write equation in point slope form?Linear equations can be represented in different form such as point slope form, slope intercept form, general form and standard form.
Therefore, let's represent the equation of the line in point slope form.
Using point slope form,
y - y₁ = m(x - x₁)
where
m = slopex₁ and y₁ are the variables.Therefore, the equation of the line has a slope of -2 and an x-intercept of -1.
The slope of a line is the change in the dependent variable with respect to the change in the independent variable.
The x-intercept is where a line crosses the x-axis. The x-intercept is the value of x when y = 0.
hence,
m = -2 and (-1, 0)
x₁ = -1
y₁ = 0
Therefore,
y - 0 = -2(x + 1)
y = -2(x + 1)
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An oil refinery is located 1 km north of the north bank of a straight river that is 3 km wide. A pipeline is to be constructed from the refinery to storage tanks located on the south bank of the river 5 km east of the refinery. The cost of laying pipe is $300,000/km over land to a point P on the north bank and $600,000/km under the river to the tanks. To minimize the cost of the pipeline, how far downriver from the refinery (in km) should the point P be located? (Round your answer to two decimal places.)
Answer:
3.36 km
Step-by-step explanation:
You want the distance P east of a refinery so that the cost of laying pipe from the refinery 1 km north of a river and under a 3 km wide river to storage on the south bank is minimized. The cost of under-river pipe is double the cost of overland pipe.
SetupLet p represent the distance east of the refinery where the river crossing starts. Then the distance in km from the refinery to the river crossing is ...
d1 = √(1² +p²)
The storage facility is 5 km east of the refinery, so is (5-p) km east of the north-bank point where the river crossing starts. The length of the pipe under the 3 km-wide river is ...
d2 = √(3² +(5-p)²) = √(p² -10p +34)
The cost is the sum of costs of laying pipe for each segment. The cost for each unit of distance is double for the under-river pipe, so the total cost can be described by ...
c ∝ d1 + 2×d2
c ∝ √(1² +p²) +2√(p² -10p +34)
SolutionThe cost is minimize for the value of p that makes dc/dp = 0. The implicit derivative is ...
c' = p/√(p² +1) +(2p -10)/√(p² -10p +34) = 0
Subtracting the second term and squaring gives ...
p²/(p² +1) = (4p² -40p +100)/(p² -10p +34)
Cross-multiplying gives the 4th-degee equation ...
p⁴ -10p³ +34p² = 4p⁴ -40p³ +104p² -40p +100
In standard form, this is ...
3p⁴ -30p³ +70p² -40p +100 = 0
The only positive real solution in the domain (0, 5) is p ≈ 3.362.
P should be located about 3.36 km downriver from the refinery.
__
Additional comment
This problem does not ask for the cost, so we only need to know the relative cost of two routes.
The solution of the quartic equation is found using a graphing calculator in the first attachment.
The same graphing calculator can find the minimum of 'c' without bothering with differentiation and reducing the equation to a polynomial. This is shown in the second attachment. Note that graph also shows the cost in units of $300,000. That is, the cost of the pipeline will be about $3.1 million.
Consider the following y-intercept and slope:
(0,−3), m=12
Step 2 of 2 : Determine the graph of the line with the given y-intercept and slope.
The equation of the line will be y = 12x -3 and the graph of the line with the given y-intercept and slope is shown below.
First, let us understand the slope intercept form of a line:
The equation of the line is written in the slope-intercept form, which is: y = mx + b, where m represents the slope and b represents the y-intercept.
We are given:
(0, −3), m = 12.
We need to determine the graph of the line with the given y-intercept and slope.
To find the value of b;
substitute the given values in the equation of the line, we will get;
y = mx + b
-3 = 12 *0 + b
b = -3
So, the equation of the line will be:
y = 12x -3
Thus, the equation of the line will be y = 12x -3 and the graph of the line with the given y-intercept and slope is shown below.
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A list of numbers is given below. If x is a number
in this list, which inequality could represent x?
{-5,
-12,-2,-9}
A. x < -13
B. X<-1
C. x>-12
D. X<-2
Answer:
B
Step-by-step explanation:
Since -1 is greater the values given then x is less than -1
3. Your original purchase price was $825.00 plus 7% sales tax. You enter into an agreement
where the interest (12.5% APR) is waived for the first 12 months provided you make the
required monthly payments; otherwise the interest is accrued from the date of purchase. You
miss the first payment due date. The late fee is $35.00. How much is the interest?
O$103.13
O $110.34
O $8.59
O $9.20
The original price of purchasing is $825 plus 7% sales tax, then the interest will be $9.20. Hence, option D is correct.
What is the Percentage?The Latin term "per centum," which signifies "by the hundred," is where the word "percentage" originally came from. With 100 as the denominator, percentages are fractions. To put it another way, it's the relationship here between a component and a whole, in which the value of the whole is always assumed to be 100.
As per the given data in the question,
The original purchase price = $825
The sales tax = 7% of $825 = 825 × 7/100 = $57.75
Total credit = $825 + $57.75 = $882.75
The monthly interest rate = 12.5%/12 = 1.0417%
Interest = $882.75 × 1.0417/100
Interest = $9.20
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Becky and lewis´s hamster cages have the same perimeter. Lewis´s cage has a length of 0.75 times becky´s cage. what is the width, w, of Lewis´s cage? Write your answer as a mixed number in simplest form
The width of Lewis´s rectangular cage as a mixed number in simplest form is equal to 14.86 inches.
How to calculate the perimeter of a rectangle?Mathematically, the perimeter of a rectangle can be calculated by using this formula;
P = 2(L + W)
Where:
P represents the perimeter of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.For the perimeter of Becky's rectangular cage, we have:
Perimeter, P = 2(L + W)
Perimeter, P = 2(15 + 11)
Perimeter, P = 2(26)
Perimeter, P = 52 inches.
For the perimeter of Lewis's rectangular cage, we have:
Length, L = 0.75W
Perimeter, P = 2(L + W)
52 = 2(0.75W + W)
26 = (0.75W + W)
1.75W = 26
Width, W = 26/1.75
Width, W = 14.86 inches.
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5. The corresponding sides of the similar shapes have same
- In the figure given below, what is the value of x? (RED)
2 cm
3 cm
3 cm
2 cm
4 cm
x cm
(GR
4 cm
Using easy mathematical operations, we know that the value of x in the given rectangle is 6 cm.
What exactly are mathematical operations?An operation, in mathematics, is a mathematical function that transforms zero or more input values into a precisely defined output value.
The arity of the operation is influenced by the number of operands.
PEMDAS, parenthesis, exponents, multiplication, and division.
So, the value of x will be:
The given two rectangles have similar sides.
2cm is similar to 4cm.
3cm is similar to xcm.
Now, we can calculate x as follows:
2/4 = 3/x
2x = 4×3
2x = 12
x = 12/x
x = 6
Therefore, using easy mathematical operations, we know that the value of x in the given rectangle is 6 cm.
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If the area of a rectangular sign is approximately 4218 sq ft, and the width is approximately 57 ft, what is the height of this sign?
The vertex of the function f(x) = 2x² + 12x + 19 is at the coordinate (x, y), where:
x =
y =
Answer:
x = -3
y = 1
Step-by-step explanation:
Desmos is free and it will graph for you. See picture.
At a sale this week, a desk is being sold for $108.80 This is a 66% discount from the original price.
What is the original price?
Answer:
[tex]\$320.29[/tex]
Step-by-step explanation:
Determine the formula:
[tex]x - (x \times 0.66) = 108.90[/tex]
Solve for x to get the original price:
[tex]x - (x \times 0.66) = 108.90\\x - 0.66x = 108.90\\x(1-0.66) = 108.90\\x = \frac{108.90}{1-0.66}\\x = \frac{108.90}{0.34}\\x \approx 320.29[/tex]
Indigo went shopping for a new pair of sneakers. Sales tax where she lives is 3.75%. The price of the pair of sneakers is $20. Find the total price including tax. Round to the nearest cent.
Step-by-step explanation:
price=$20tax rate=$3.75multiply the price with rate and you will get tax the add it to the real pricetotal price incl. tax= 20+(20*3.75/100)=20.75there is your answer...The total price of sneakers including tax will be equal to $20.75.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the given information in the question,
Price of sneakers = $20
Tax on sneakers = 3.75%
Then, the amount of tax will be,
(20 × 3.75)/100
= 75/100
= $0.75
Then, the total price of the sneakers will be,
$20 + $0.75
= $20.75
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ANSWER NOW TAKING A TEST PLS
What is the equation in point slope form of the line that passes through the point (2, 6) and has a slope of 5?
Responses
y−2=5(x−6)
y minus 2 equals 5 open parenthesis x minus 6 close parenthesis
y+2=5(x+6)
y plus 2 equals 5 open parenthesis x plus 6 close parenthesis
y+6=5(x+2)
y plus 6 equals 5 open parenthesis x plus 2 close parenthesis
y−6=5(x−2)
The equation of the line in point slope form that passes through the point (2, 6) and has a slope of 5 is y - 6 = 5(x - 2) .
How to find the equation of a line?The equation of a line can be represented in different form such as standard form, general form, point slope form and slope intercept form.
Therefore,
y - y₁ = m(x - x₁)
where
m = slopeThe line passes through (2, 6) and has a slope of 5.
Hence,
m = 5
The equation of the line in point slope form is as follows;
y - 6 = 5(x - 2)
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Circular area rugs are priced at $5 per foot based on the circumference of the carpet used. What is the cost of the largest circular area rug that will fit in Susie’s dining room? Round your answer to the nearest whole number. Do not include the dollar sign in your answer.
A rectangle has length 12 feet and width 7 feet.
Answer:
The area of the room is 34*21 = 714 ft^2
the cost of the carpet is $5 per square foot, so the cost to carpet the whole room will be
5*714 = $3570
Step-by-step explanation:
3570 is the cost of the largest circular area rug that will fit in Susie’s dining room.
What is Area of Rectangle?The area of Rectangle is length times of width.
Given that, Circular area rugs are priced at $5 per foot based on the circumference of the carpet used.
We need to find the cost of the largest circular area rug that will fit in Susie’s dining room.
The area of the room is 34×21 = 714 ft²
The cost of the largest circular area rug that will fit in Susie’s dining room
$5 per foot based on the circumference of the carpet
Multiply 5 with 714
5×714
3570
Hence, 3570 is the cost of the largest circular area rug that will fit in Susie’s dining room.
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What is the value of N?
The value of n in the line segment is - 9 / 4.
How to find the length of a line segment?The length of a line segment can be found as follows:
Two point of the line segment are 2n + 9 / 2 and 9 / 2. The distance of the line segment is 9 / 2.
Therefore, let's find n as follows:
9 / 2 - (2n + 9 / 2) = 9 / 2
9 / 2 - 2n - 9 / 2 = 9 / 2
9 / 2 - 9 / 2 - 2n = 9 / 2
- 2n = 9 / 2
cross multiply
-2n × 2 = 9
- 4n = 9
divide both sides by -4
n = 9 / -4
n = - 9 / 4
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write 804 billion in ordinary decimal notation and in scientific notation
Answer:804,000,000,000 & 8.0e+11
Step-by-step explanation:
logic
PLEASE HELP SOLVE!!!
Answer:37 number
Step-by-step explanation:
what are the factors of -120
Answer:
-1 x 120
-2 x 60
-3 x 40
-4 x 30
-5 x 24
-6 x 20
-8 x 15
-10 x 12
1 x -120
2 x -60
3 x -40
4 x -30
5 x -24
6 x -20
8 x -15
10 x -12
Answer:
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60 and 120.
Step-by-step explanation:
I NEED HELP PLEASE HELP
Answer:
Step-by-step explanation:
h(1) = -17
h(n) = h(n
1) - 0.2
Find an explicit formula for h(n).
h(n)
h(n) = -17·0.2^(n-1)
Step-by-step explanation:
The explicit formula for a geometric sequence with first term a1 and common ratio r is ...
an = a1·r^(n-1)
Your sequence h has first term a1 = -17 and common ratio r = 0.2. Then the explicit formula is ...
h(n) = -17·0.2^(n-1)
Identify the greatest common factor.
8y, -12x, 4xy
The greatest common factor, GCF, of 8y, -12x, and 4xy is 4
Determining the Greatest common factor (GCF) of expressionsFrom the question, we are to determine the greatest common factor of the given expressions.
The given expressions are 8y, -12x, and 4xy
To determine the greatest common factor, we will express each of the expressions as a product of their factors.
8y = 2 × 2 × 2 × y
-12x = 2 × 2 × 3 × -x
4xy = 2 × 2 × x × y
From above, we can observe that the greatest common factor is
2 × 2
= 4
Hence, the greatest common factor is 4
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54 3. Joey opened a new store that sells jars of jelly. Joey sold 3 jars of jelly in his first week of business and 10 jars in his second week. He sold 31 jars in week 3 and 94 jars in week 4. If the number of jars he sells continues to increase in this pattern, how many jars of jelly will Joey sell in the fifth and sixth weeks?
Answer:
7
Step-by-step explanation:
THe answer is 7 because 10-3=7 SOrry if wrong