The inequality that represents the values of x that ensure the triangle ABC exists is 0.5 < x < 7.5
Inequality is a term used in mathematics to represent a relation that makes an unequal comparison between two functions.
As the lengths of the sides of the triangle are 6.5 units, 3.5 units, and 2.5 + x units, we can use the property which states that the sum of two sides of the triangle is always greater than the third side, therefore;
6.5 + 3.5 > 2.5 + x
10 > 2.5 + x
10 - 2.5 > x
x < 7.5
Now we use the property which states that the difference between two sides of the triangle is always less than the third side of that triangle as follows;
6.5 - 3.5 < 2.5 + x
3 < 2.5 + x
3 - 2.5 < x
0.5 < x
Now we combine both values as follows;
0.5 < x < 7.5
Therefore the inequality that represents the values of x is 0.5 < x < 7.5
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Autumn has a points card for a movie theater.
She receives 40 rewards points just for signing up.
She earns 12.5 points for each visit to the movie theater.
She needs at least 225 points for a free movie ticket.
Write and solve an inequality which can be used to determine v, the number of visits Autumn can make to earn her first free movie ticket.
HURRY PLEASE!!!!!!!!!!!!!!!!!
On Solving inequality 40 + 12.5 v ≥ 225, we get solution v ≥ 14.8. It means Autumn can earn movie ticket from 15 visits.
What is an inequality and how to solve it?An inequality is a statement that compares two expressions using ≤, ≥, <, > .
We can solve an inequality by adding same number to both sides or by subtracting same number from both side. While adding or subtracting the sign of the inequality will not change.
When we multiply both sides of the inequality with a positive number then the sign of the inequality does not change, but when we multiply both sides by an negative number then the sign of inequality reverses.
Given that Autumn receives 40 points for signing up and 12.5 points for each visit to the theatre.
Let the number of visits to the theatre be v
Then points earned by v visits = v × 12.5 = 12.5 v
Total points earned = signing up points + points of v visits
⇒ Total points earned = 40 + 12.5 v
For earning a free movie tickets the total points must be at least 225 or greater than or equal to 225
Then the inequality becomes:
40 + 12.5 v ≥ 225
Subtracting 40 from both sides
⇒ 12.5v ≥ 225-40
⇒12.5v ≥185
Multiplying both sides by 1/12.5
⇒ v ≥ 185/12.5
⇒ v ≥ 14.8
∴ The number of visits must be greater than or equal to 14.8 or nearest integer 15
∴After 15 visits, Autumn will earn a free movie ticket
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explain how to solve
2(4x-3)=2
Answer:
x=1
Step-by-step explanation:
1. distribute through the parentheses
8x-6=2
2. Combine like terms
8x=8
3. Divide by 8
x=1
Hello!
Let's solve:
[tex]\text{Copy down the equation}\\2(4x-3)=2\\\\\text{Multiply 2 into the equation in the parentheses}\\8x - 6 = 2\\\\\text{Add 6 to both sides of the equation}\\8x-6+6=2+6\\8x=8\\\\\text{Divide by 8 on both sides}\\\dfrac{8x}{8} =\dfrac{8}{8} \\\\x=1[/tex]
Answer: x = 1
Hope that helps!
a marine aquarium has a small tank and a large tank, each containing only red and blue fish. in each tank, the ratio of red fish to blue fish is 333 to 444. the ratio of fish in the large tank to fish in the small tank is 464646 to 555. what is the ratio of blue fish in the small tank to red fish in the large tank?
The ratio of the blue fish in the small tank to red fish in the large tank is 10 to 69.
Ratio is the relationship between two quantities.
Let x : y = ratio of the blue fish in the small tank to red fish in the large tank
Hence, there are x blue fish in the small tank for every y red fish in the large tank.
If in each tank, the ratio of red fish to blue fish is 3 to 4, then in each tank, in terms of x and y, the ratio is:
small tank :
red : blue = 3 : 4 = (3/4)x : x
large tank :
red : blue = 3 : 4 = y : (4/3)y
If the ratio of fish in the large tank to fish in the small tank is 46 to 5, then
(y + (4/3)y) : ((3/4)x + x) = 46 : 5
Simplifying the proportion,
(y + (4/3)y) : ((3/4)x + x) = 46 : 5
(7/3)y : (7/4)x = 46 : 5
(161/2)x = (35/3)y
x/y = (35/3) / (161/2)
x/y = x : y = 10 : 69
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a random sample of 130 mortgages in the state of mississippi was randomly selected. from this sample, 20 were found to be delinquent on their current payment. what is the mean of the sampling distribution of the proportion of delinquent payments?
For a random sample of 130 mortgages with 20 delinquents on their current payment, the mean of the sampling distribution of the proportion of delinquent payments is not possible to say because population proportion is not known.
A random sample refers to a randomly selected subset of the population. In random sampling, each member of the population has an equal chance of selection, reducing the risk of selection bias. Random sampling ensures that the conclusion drawn from the sample should approximate the results obtained if entire population had been measured. The mean of the sampling distribution is the mean of the population from which results were sampled. As the population proportion (fraction of the population with certain characteristic) is unknown, the mean cannot be determined.
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A circular wimming pool has a radius of 15 ft. There is a path all the way around that pool that is three feet wideWhat is the circumference of the outer edge of the path around the pool? Use 3.14 for pi
Given:
Radius of circular swimming pool = 15ft
Radius of the path around the pool = 3ft
radius of outer edge of the pool = 15 + 3 = 18ft
To find the circumference of the outer edge of the path around the pool, use the formula below:
[tex]C\text{ = 2}\pi\text{ r}[/tex]where,
r = 18 ft
pi = 3.14
Thus, we have:
[tex]C\text{ = 2 }\ast\text{ 3.14 }\ast18\text{ = }113.04\text{ ft}[/tex]Therefore, the circumference of the outer edge of the path around the pool is 113.04 ft
ANSWER:
113.04 ft
Which answer choice correctly identifies the extraneous information in the problem?
Samuel is 10 years old. He mowed the neighbors lawn on Saturday and earned $40. It took him 4 hours to mow the lawn and 2 hours to clean his room. How much money did Samuel earn an hour?
A. The extraneous information is Samuel earned $40 and it took him 4 hours to mow the lawn.
B. The extraneous information is Samuel took 4 hours to mow the lawn and 2 hours to clean his room.
C. The extraneous information is Samuel is 10 years old and earned $40.
D. The extraneous information is Samuel is 10 years old.
Option D is correct.
Extraneous information means irrelevant or unrelated to the problem or issue.
In this question, Samuel's Age is not a matter of concern and totally unrelated to the money he earns by mowing the lawn and cleaning the room
don’t know what to do
The domain and range of the function f(x) = 3x⁵ is all real numbers, the x-intercept = 0 and y-intercept = 0.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The equation for the function is:
f(x) = 3x⁵
The domain of the function: D = all real number
The range of the function: R = all real number
x-intercept = 0
y-intercept = 0
Increasing interval: x ∈ [0, ∞)
Decreaing interval: x ∈ (-∞, 0]
Symmetry = The function is not symmetric
End behavior:
x → ∞, y →∞
x → -∞, y → -∞
Thus, the domain and range of the function f(x) = 3x⁵ is all real numbers, the x-intercept = 0 and y-intercept = 0.
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How many solutions exist for the following system if m1 ≠ m2?
y = m1x + b
y = m2x + b
answers:
1.an infinite number
2.none
3. one
4. the number of solutions cannot be determined.
Answer:
3
Step-by-step explanation:
Since the graphs aren't parallel due to not having the same slope we can assume they will intercept once
100 pts for who solves
I have no : idea
Step-by-step explanation: WHat grade is this for I might be able to help you.
I NEED HELP ON THIS QUESTION. I CAN'T SEEM TO GET THE LAST MARK
The dimensions of this cuboid are 2 cm, 11 cm, and 17 cm respectively.
How to calculate the volume of a geometric figure?Mathematically, the volume of a cuboid can be calculated by using this following formula:
Volume = L × W × H
Where:
L is the length of a cuboid.W is the width of a cuboid.H is the height of a cuboid.Substituting the given parameters into the formula, we have;
Volume = 2 × (x + 3) × (x + 9)
374 = 2 × (x² + 9x + 3x + 27)
374 = 2 × (x² + 12x + 27)
Dividing both sides by 2, we have:
187 = x² + 12x + 27
Rearranging the equation, we have:
x² + 12x + 27 - 187 = 0
x² + 12x - 160 = 0
Next, we would solve the quadratic equation by using the factorization method as follows:
x² + 12x - 160 = 0
x² + 20x - 8x - 160 = 0
x(x + 20) - 8(x + 20) = 0
(x - 8)(x + 20) = 0
x = 8 or x = -20
Since the dimensions cannot be negative, the value of x is equal to 8.
Check:
x² + 12x - 160 = 0
8² + 12(8) - 160 = 0
64 + 96 - 160 = 0
160 - 160 = 0 (True).
For the dimensions, we have:
Width = x + 3 = 8 + 3 = 11 cm.
Height = x + 9 = 8 + 9 = 17 cm.
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If f(x) = –3(1 – x – 2x squared by 2) give f-2.
The value of the function f(x) = 3(1 - x - 2x²)/2 at x = -2 is f(-2) = -15/2 after plugging x = -2.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The function is:
f(x) = 3(1 - x - 2x²)/2
It is required to find the value of f(-2)
Plug x = -2
f(-2) = 3(1 - (-2) - 2(-2)²)/2
f(-2) = 3(1 + 2 - 8)/2
f(-2) = 3(-5)/2
f(-2) = -15/2
Thus, the value of the function f(x) = 3(1 - x - 2x²)/2 at x = -2 is f(-2) = -15/2 after plugging x = -2.
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Kate used a 30% off coupon to purchase a sweater. If she paid $33.60, what was the original price of the sweater
The original price of the sweater is $48.
Given that, Kate used a 30% off coupon to purchase a sweater.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The cost of sweater is $33.60
Let the original price of the sweater be x
Now, x-30% of x=33.60
⇒ x-30x/100 = 33.60
⇒ x -3x/10 =33.60
⇒ 7x/10 =33.60
⇒ 7x=336.0
⇒ x=48
Therefore, the original price of the sweater is $48.
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From your home, the route to the store tat passes the beach is 2 miles shorter than the route to the store that passes the park. What is the length of each route.
Answer:
Step-by-step explanationFrom your home, the route to the store tat passes the beach is 2 miles shorter than the route to the store that passes the park. What is the length of each route.:
How many flowers spaced every 6 inches are needed to surround a circle garden with a 125 feet radius. Use three. 3.14 pi.
You would require 1,570 flowers in space of every 6inch to surround the garden with 125feet radius.
First, we need to calculate the circumference of the circle. The formula for the circumference of the circle is:
C = 2πr
If we substitute 125ft for r and use 3.14 to approximate π
we get a circumference of:
C = 2 * 3.14 * 125
C = 6.28 *125
C = 785ft
We can now convert the circumference in feet to inches as follow;
As we know that 1ft = 12inches
∴ 785ft = 12(785) inches = 9,420 inches.
To find how many flowers we need we can divide the circumference in inches by the 6 inches between flowers giving:
=[tex] 9,420in\ X \ \frac{1\ flower}{6 in} [/tex]
=[tex] \frac{9,420}{6 } \ flower [/tex]
=1,570 flowers
Hence You would require 1,570 flowers in space of every 6inch to surround the garden with 125feet radius.
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6,
12 24
5'25'
Find the 7th term.
The general form of terms of a Geometric Progression Formulas is a, ar, [tex]$$\mathrm{a} r^2[/tex], [tex]$$\mathrm{a} r^3$[/tex], and so on then the 7th term of the series 6, 12, 24, ........... is 384
How to find the 7th term of the series?Let the first term (a) be 6.
The given series is in geometric progression,
we know that, 7th term = a × [tex]$$r^{7-1}[/tex] = a[tex]$ r^6[/tex]= [tex]6 \times(2)^{6}[/tex] = 384
The general form of terms of a Geometric Progression Formulas is a, ar, [tex]$$\mathrm{a} r^2[/tex], [tex]$$\mathrm{a} r^3$[/tex], and so on.
Here, a is the first term and r is the common ratio.
The nth term of a Geometric Progression Formulas is [tex]$T_n=a r^{n-1}$[/tex]
Common ratio [tex]$=\mathrm{r}=T_n / T_{n-1}$[/tex]
Therefore, the correct answer is 384.
The complete question is:
Find the 7th term of the series 6,12,24,....?
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the sum of four times a number and six divided by the number squared
Answer: 4x+6/x^2
Step-by-step explanation:
find the rate of change of the volume of a cylinder when its radius is 6 feet if its height is always (3/2) times its radius and its radius is increasing at the rate of 2 feet per minute.
When the radius of a cylinder is 6 ft. and it is increasing at the rate of 2 feet per minute, its volume will change at rate of 509.14 ft³/minute.
Given a cylinder with:
r = radius
h = height = 3/2 . r
The volume of the cylinder is:
V = πr².h
Substitute h = 3/2 . r,
V = πr².(3/2 r)
V = 3/2 . πr³
Take the derivative with respect to t:
dV/dt = 9/2 . πr² . dr/dt
Substitute dr/dt = 2 ft./minute and r = 6 ft.,
dV/dt = 9/2 . π.6²
dV/dt = 9/2 . π.6² = 509.14 ft³/minute.
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The value of a machine. V at the end of years is given by V = C(1-r)^t, where C is the original cost of the machine and r is the rate of depreciation. A machine thatoriginally cost $13,500 is now valued at $10,419. How old is the machine if r= 0.12? Round your answer to two decimal places.AnswerHow to enter your answer (Opens in new window)KeypadKeyboard Shortcuts
The value of a machine at the end of t years with a rate of depreciation, r is given by the function:
[tex]V=C(1-r)^t[/tex]It is required to find the age of a machine that originally costs $13,500, but is now valued at $10,419 and has a rate of depreciation of 0.12.
To do this, substitute C=13500, V=10419, and r=0.12 into the function:
[tex]\begin{gathered} 10419=13500(1-0.12)^t \\ \Rightarrow10419=13500(0.88)^t \end{gathered}[/tex]Solve the resulting equation for t:
[tex]\begin{gathered} \text{swap the equation:} \\ \Rightarrow13500(0.88)^t=10419 \\ Divide\text{ both sides by 13500:} \\ \Rightarrow\frac{13500(0.88)^t}{13500}=\frac{10419}{13500} \\ \Rightarrow0.88^t=\frac{3473}{4500} \end{gathered}[/tex]Take the Logarithm of both sides:
[tex]\begin{gathered} \ln(0.88^t)=\ln(\frac{3473}{4500}) \\ \Rightarrow t\cdot\ln(0.88)=\ln(\frac{3473}{4500}) \\ \Rightarrow t=\frac{\ln(\frac{3473}{4500})}{\ln(0.88)}\approx2.03 \end{gathered}[/tex]Hence, the machine is about 2.03 years.
The machine is about 2.03 years.
Laws of Exponents
please follow the laws of the exponents to find this answer
The answer to the given expression 2⁴· [(2²·2⁴)⁻³/2¹⁴] would be 2⁻²⁸ which is determined by the laws of the exponents.
What are the laws of the exponents?The product rule is an exponent rule that states that when you multiply similar bases, the add exponents.
For example, (a²)·(a³) = a²⁺³ = a⁵
In the power rule, elevating one exponent to a second multiplies the exponents.
For example, (a²)³ = a²ˣ³ = a⁶
The given expression would be as
⇒ 2⁴· [(2²·2⁴)⁻³/2¹⁴]
As per the laws of the exponents, the solution would be as :
⇒ 2⁴· [(2²⁺⁴)⁻³/2¹⁴]
⇒ 2⁴· [(2⁶)⁻³/2¹⁴]
⇒ 2⁴· (2⁻¹⁸/2¹⁴)
⇒ 2⁴· (2⁻¹⁸⁻¹⁴)
⇒ 2⁴· (2⁻³²)
⇒ 2⁴⁻³²
⇒ 2⁻²⁸
Therefore, the answer would be 2⁻²⁸.
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write the midpoint formula
Answer:
[tex]M (\frac{x1+x2}{2},\frac{y1+y2}{2} )[/tex]
Step-by-step explanation:
PLEASE HELP FAST!!!!
Answer: 0.01 more
Step-by-step explanation:
60% sure!
Let’s say you want to borrow $500 for two weeks from a pay lender that charges a $100 fee for the loan. It’s takes you a year before your are able to pay them back
The interest rate for the loan is 20%.
What is the interest rate?The interest rate represents the percentage or the proportion of the interest over the total loan.
The interest is the finance charge for the credit extended by the pay lender.
The interest rate, R = Interest x 100/Principal x Time, where the simple interest equals principal x rate x time.
The total amount borrowed = $500
The total finance charge = $100
The period of the loan = 1 year
The interest rate
= $100 x 100/$500 x 1
= 20%
Thus, the pay lender is charging an interest rate of 20% per annum.
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Question Completion:What is the interest rate?
please help will give brainliest
The correct answer to the question would be:
D. The manufacturer tests every 500th smartphone off the production line.
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Which steps show how to use distributive property to evaluate 5 x 38
Answer:
A
Step-by-step explanation:
When distributing, you multiply the outside number to each number in the inside as well as looking at the operation inside the parenthesis. Hope this helps!
Water is filling a swimming pool at a constant rate. After 4 hours, 2 inches of water have filled the pool.
C) Write an equation that gives the amount of water, w, after t hours.
Answer:
Step-by-step explanation:
u will have 1 niche of water in 2 hours
i need help with this i don't know what to do
9. the school district is served by four buses, each of which delivers students to three different schools. you know the cost of transporting each of the students to each of the schools, and you want to determine the least expensive way to get all of the students to their schools. if you use excel solver for this analysis, how many different variable cells should you use?
If you use excel solver for this analysis, the number of different variable cells should you use are 12
Option- C
The right answer is 12.
Given that,
There are four buses that transport children to the district's three main schools. You are aware of the price of transporting each student to each school.
Since there are four buses and three schools according to the supplied description, each bus has three school alternatives, thus 4*3=12, bearing in mind that there must be the least expensive route to transport all of the students to their schools.
There must therefore be 12 separate variable cells employed.
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5. Which of the following is parallel to the line y = 3/5x+1?
Answer:
y=3/5x-7
Step-by-step explanation:
when lines are parallel they have the same slope and the slope of the first line was 3/5
Hello!
Let's consider the equation given:
⇒the coefficient before the x is the slope
When lines are parallel:
⇒the slopes are equal
Since the line given has a slope of 3/5
⇒ the line parallel is [tex]y = \dfrac{3}{5} x - 7[/tex] <==Answer
Hope that helps!
Paloma made a list to track the number of minutes she spent practicing piano.
24, 18, 23, 25, 30, 32, 35, 28, 25, 32, 28, 24
What was her median practice time? please help me
Paloma's median practice time would be = 26.5
What is median?Median is defined as the middle of a set of data which will be selected after the data has been grouped in an ascending or descending order.
The list to track the number of minutes Paloma spent practicing piano in ascending order include the following:
18, 23, 24, 24, 25, |25, 28,| 28, 30, 32, 32, 35
The middle figures are 25 and 28 which should be added and divided into two.
That is;
25 + 28 = 53/2
= 26.5
Therefore, the median practice time for Paloma = 26.5
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Find the value of x.
Answer: 90 degree
Step-by-step explanation: the diameter of a circle compounds to an inscribed angle of 90 degree