ii) (1, 3), (6,3), (6, 6) and (1, 6) are the vertices of a rectangle.
Answers
Given, (1, 3), (6,3), (6, 6) and (1, 6) are the vertices of a rectangle, the width is 1 unit shorter.
What is a rectangle?A rectangle is a quadrilateral with the four right angles in the Euclidean plane. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal (360°/4 = 90°). A square is a rectangle with the four equally long sides. Oblong is occasionally used to describe a rectangle that isn't square. Rectanglen is the symbol for a rectangle having the vertices ABCD. ABCD in PNG.
Rectangulus, a combination of rectus (as an adjective, right, proper), and angulus, is the source of the English word rectangle (angle).
A crossed rectangle is a quadrilateral that is formed by the intersection of two diagonals and the two opposite sides of a rectangle (therefore only two sides are parallel). Although opposite angles are equal, it is a specific example of an antiparallelogram in which the angles are not all right angles and equal. There exist so-called rectangles in other geometries, including spherical, elliptic, and hyperbolic ones, with opposite sides of equal length and equal angles that are not right angles.
Many tiling issues use rectangles, like tiling the plane with rectangles or tiling a rectangle with polygons.
By plotting given points in the coordinate plane,
We get rectangle ABCD having vertices,
A(-1,6), B (3,6), C (3,1), D (-1,1)
By distance formula,
Shorter side or width of rectangle,
AB= [tex]\sqrt{ [3-(-1)]^{2}+ (6-6)^{2}} = \sqrt{4^{2}+0 } = 4 units[/tex]
Longer side or length of rectangle,
BC= [tex]\sqrt{(3-3)^{2}+(1-6)^{2}}=\sqrt{5^{2} } = 5 units[/tex]
The difference between length and width,
BC-AB= 5-4= 1units
Hence, width of rectangle is 1 unit less than the length.
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Related Questions
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!!!!!!!!!!!!!!!!!
Answers
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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Two gongs strike at intervals of 22 and 77 minutes respectively. At what time will
they strike together again if they start simultaneously at 12 noon ?
Click here to enter answer
Answers
The time that both gongs will strike together again after striking simultaneously at 12 noon is 2 : 34 pm.
What time would the gongs strike together?The time the gongs will strike together again can be determined by calculating the least common multiple of 22 and 77. The multiple of a number is the product of a number and another number. For example, a multiple of 2 is 10. The least common multiple is the smallest multiple that is common to two or more numbers.
The least common multiple would be determined using the prime factorisation method.
Prime factors of 22 = 2 x 11
Prime factors of 77 = 7 x 11
The least common multiple = 2 x 7 x 11 = 154
The next time both gongs would strike at the same time is 154 minutes or 2 hours 34 minutes
12 noon + 2 hours + 34 minutes = 2 : 34 pm
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WILL GIVE BRAINLEIST
Which steps show how to use distributive property to evaluate 5 x 38
Answers
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!
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.
Answers
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.:
Laws of Exponents
please follow the laws of the exponents to find this answer
Answers
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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PLEASE HELP FAST!!!!
Answers
Answer: 0.01 more
Step-by-step explanation:
60% sure!
jimmy read 2/15 of a book on Monday, 1/3 on Tuesday, 2/9 on Wednesday and 3/4 of the remainder on Thursday. If he still had 14 pages left to read on Friday, how many pages were there in the book?
Answers
The total number of pages in the book is 180.
Total number of pages:
It refers the number of pages in the prescribed book.
And if we want to find the total number of pages, then we have to add the read pages and the remaining pages.
Given,
Jimmy read 2/15 of a book on Monday, 1/3 on Tuesday, 2/9 on Wednesday and 3/4 of the remainder on Thursday. If he still had 14 pages left to read on Friday.
Here we need to find the total number of pages in the book.
Let us consider x be the number of pages in the book.
The portion of book read by Jimmy on Monday is 2/15
The portion of book read by Jimmy on Tuesday is 1/3
The portion of book read by Jimmy on Wednesday is 2/9
The portion of book read by Jimmy on Thursday is 3/4
And the remaining pages to read on Friday is 14
So, the total of all is:
=> x (2/15 + 1/3 + 2/9)
=> x (6 + 15 + 10)/45
=> 31x/45
So, for Thursdays, he reads 3/4 of the remainder of the book.
He has (1 - 31/45)x left that is 14x/45.
So, he reads 3/4 of this; which is
=> 3/4(14x/45) = 42/180x.
Therefore, until Thursday he has read
=> 31/45x + 42/180x.
We know that here 180 would be a common denominator;
Now we have to convert these fractions,
Then we have,
124/180x + 42/180x = 166/180x
Up to this point, he has 14 pages left;
Therefore, this means he has read 14 pages less than x, the total number of pages.
Then the given equation is written as,
166/180x = x-14
0 = 14/180x - 14
Adding 14 to each side gives us, then we get,
14 = 14/180x
14(180)/14 = x
180 = x
Therefore, there are 180 pages in the book.
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the sum of four times a number and six divided by the number squared
Answers
Answer: 4x+6/x^2
Step-by-step explanation:
How many flowers spaced every 6 inches are needed to surround a circle garden with a 125 feet radius. Use three. 3.14 pi.
Answers
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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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
Answers
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
don’t know what to do
Answers
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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i need help with this i don't know what to do
Answers
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
Answers
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?
Louis and Michael met up for lunch. When they were done,
Louis traveled 4 blocks east and Michael traveled 1 blocks west. How many blocks away from Louis was Michael?
Answers
Answer:
five blocks away
Step-by-step explanation:
because 4 +1 =5
please if it is wrong let me know so I can correct
Explanation:
considering East and West are opposite from each other, all that is left to do, is add 4 and 1, which is 5
therefore, your answer is 5 blocks away
Kate used a 30% off coupon to purchase a sweater. If she paid $33.60, what was the original price of the sweater
Answers
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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please help will give brainliest
Answers
The correct answer to the question would be:
D. The manufacturer tests every 500th smartphone off the production line.
A. Use inductive reasoning to predict the next line in this sequence of computations. Then use a calculator or perform the arithmetic by hand to determine whether your conjecture is correct.B.Make a conjecture by predicting the correct numbers in the line below.
Answers
Answer: Following the pattern, the prediction for the next numbers is as follows:
[tex]\begin{gathered} 9\times9+7=88 \\ 98\times9+6=888 \\ 987\times9+5=888,8 \\ 9876\times9+4=888,88 \\ 98765\times9+3=888,888 \end{gathered}[/tex]Confirmation by calculator use:
[tex]\begin{gathered} 98,765\times9+3=888,888 \\ 888,885+3=888,888 \end{gathered}[/tex]Therefore the predicted numbers are the correct one.
Standard to slope intercept form
Answers
Answer: y = -3x - 2
Step-by-step explanation:
slope intercept form: y=mx+b
y = −3x - 1
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.
Answers
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
explain how to solve
2(4x-3)=2
Answers
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!
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?
Answers
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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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?
Answers
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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6,
12 24
5'25'
Find the 7th term.
Answers
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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write the midpoint formula
Answers
(X^1+X^2 / 2 , Y^1+Y^2 / 2)
Answer:
[tex]M (\frac{x1+x2}{2},\frac{y1+y2}{2} )[/tex]
Step-by-step explanation:
Aisha is working two summer jobs, making $7 per hour babysitting and $8 per hour landscaping. last week aisha worked 2 more hours babysitting than hours landscaping and earned a total of $134. write a system of equations that could be used to determine the number of hours aisha worked babysitting last week and the number of hours she worked landscaping last week. define the variables that you use to write the system.
Answers
Answer:
Let b represent the number of hours babysitting, and let l be the number of hours landscaping. We have this system of equations:
[tex]7b + 8l = 134[/tex]
[tex]b = l + 2[/tex]
5. Which of the following is parallel to the line y = 3/5x+1?
Answers
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!
Find the value of k if the line 2y+k=2+x is tangent to the parabola y=2x^2 +6x +3.
Answers
The value of k is -1 of tangent over the parabola.
Equation of a line: y = (2 + x - k) ÷ 2, in line form of y = mx + c.
Equation of the parabola: x² = (y - 6x - 3) ÷ 2
Given,
y = (x ÷ 2) + (1) - (k ÷ 2)
where, m = 1 ÷ 2 and c = (1 - k) ÷ 2
For parabola equation in parabola form,
y = 2x² + 6x - 3
y = 2(x² + 3x - n) - 3
n = (b ÷ 2)²
n = (6 ÷ 2)²
n = 9
y = 2(x² + 3x - 9 + 9) - 3
y = 2(x² + 3x + 9) - 9 - 3
y = 2(x² + 3x + 9) - 12
y = 2(x + 3)² - 12, Hence the parabola equation is in vertex form.
Now, comparing the above vertex form with the parabola equation,
x² = 4ay
(x + 3)² = (y ÷ 2) + 6
where a = 1 ÷ 2
Now using the condition of tangency c = a ÷ m
c = (1 - k) ÷ 2
m = 1 ÷ 2
a = 1 ÷ 2
(1 - k) ÷ 2 = (1 ÷ 2) ÷ (1 ÷ 2)
1 - k = 2
k = -1
Therefore, the value of k is -1.
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I NEED HELP ON THIS QUESTION. I CAN'T SEEM TO GET THE LAST MARK
Answers
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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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.
Answers
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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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.
Answers
Answer:
Step-by-step explanation:
u will have 1 niche of water in 2 hours