Determine if parallel, perpendicular, or neither showing how to find the slope
4x-7y=10
7x+4y=1
Answer:
They're perpendicular
Step-by-step explanation:
Cause they interfere the point (47/65, 66/65) in a 90 degree angle
The radius of a circle is 10 meters. What is the angle measure of an arc bounding a sector
with area 150 square meters?
A Norman window is a rectangle with a semicircle on top. Suppose that the perimeter of a particular Norman window is to be 25 feet. What should the rectangle's dimensions be in order to maximize the area of the window and, therefore, allow in as much light as possible? (Round your answers to two decimal places.)width ________ ftheight _______ ft
Answer:
[tex]Length =\frac{25}{4 + \pi}[/tex] and [tex]Width = \frac{50}{4+\pi}[/tex]
Step-by-step explanation:
This question is better understood with an attachment.
See attachment for illustration.
Given
Represent Perimeter with P
[tex]P = 25ft[/tex]
Required
Determine the dimension of the rectangle that maximizes the area
First, we calculate the perimeter of the rectangular part of the window.
From the attachment, the rectangle is not closed at the top.
So, The perimeter would be the sum of the three closed sides
Where
[tex]Width = 2x[/tex]
[tex]Length = y[/tex]
So:
[tex]P_{Rectangle} = y + y + 2x[/tex]
[tex]P_{Rectangle} = 2y + 2x[/tex]
Next, we determine the circumference of the semi circle.
Circumference of a semicircle is calculated as:
[tex]C = \frac{1}{2}\pi r[/tex]
From the attachment,
[tex]Radius (r) = x[/tex]
So, we have:
[tex]C = \frac{1}{2}2\pi * x[/tex]
[tex]C = \pi x[/tex]
So, the perimeter of the window is:
[tex]P = P_{Rectangle} + C[/tex]
[tex]P =2y + 2x + \pi x[/tex]
Recall that: [tex]P = 25[/tex]
So, we have:
[tex]25 =2y + 2x +\pi x[/tex]
Make 2y the subject
[tex]2y = 25 - 2x - \pi x[/tex]
Make y the subject:
[tex]y = \frac{25}{2} - \frac{2x}{2} - \frac{\pi x}{2}[/tex]
[tex]y = \frac{25}{2} - x - \frac{\pi x}{2}[/tex]
Next, we determine the area (A) of the window
A = Area of Rectangle + Area of Semicircle
[tex]A = 2x * y + \frac{1}{2}\pi r^2[/tex]
[tex]A = 2xy + \frac{1}{2}\pi r^2[/tex]
Recall that
[tex]Radius (r) = x[/tex]
[tex]A = 2xy + \frac{1}{2}\pi x^2[/tex]
Substitute [tex]\frac{25}{2} - x - \frac{\pi x}{2}[/tex] for y in [tex]A = 2xy + \frac{1}{2}\pi x^2[/tex]
[tex]A = 2x(\frac{25}{2} - x - \frac{\pi x}{2}) + \frac{1}{2}\pi x^2[/tex]
Open Bracket
[tex]A = 2x * \frac{25}{2} - 2x * x - 2x * \frac{\pi x}{2} + \frac{1}{2}\pi x^2[/tex]
[tex]A = 25x - 2x^2 - \pi x^2 + \frac{1}{2}\pi x^2[/tex]
[tex]A = 25x - 2x^2 - \frac{1}{2}\pi x^2[/tex]
To maximize area, we have to determine differentiate both sides and set A' = 0
Differentiate
[tex]A' = 25 - 4x - \pi x[/tex]
[tex]A' = 0[/tex]
So, we have:
[tex]0 = 25 - 4x - \pi x[/tex]
Factorize:
[tex]0 = 25 -x(4 + \pi)[/tex]
[tex]-25 =-x(4 + \pi)[/tex]
Solve for x
[tex]x = \frac{-25}{-(4+\pi)}[/tex]
[tex]x = \frac{25}{4+\pi}[/tex]
Recall that
[tex]Width = 2x[/tex]
[tex]Width = 2(\frac{25}{4+\pi})[/tex]
[tex]Width = \frac{50}{4+\pi}[/tex]
Recall that:
[tex]y = \frac{25}{2} - x - \frac{\pi x}{2}[/tex]
Substitute [tex]\frac{25}{4+\pi}[/tex] for x
[tex]y = \frac{25}{2} - (\frac{25}{4+\pi}) - \frac{\pi (\frac{25}{4+\pi})}{2}[/tex]
[tex]y = \frac{25}{2} - (\frac{25}{4+\pi}) - \frac{\frac{25\pi}{4+\pi}}{2}[/tex]
[tex]y = \frac{25}{2} - (\frac{25}{4+\pi}) - \frac{25\pi}{4+\pi} * \frac{1}{2}[/tex]
[tex]y = \frac{25}{2} - \frac{25}{4+\pi} - \frac{25\pi}{2(4+\pi)}[/tex]
[tex]y = \frac{25(4+\pi) - 25 * 2 - 25\pi}{2(4 + \pi)}[/tex]
[tex]y = \frac{100+25\pi - 50 - 25\pi}{2(4 + \pi)}[/tex]
[tex]y = \frac{100- 50+25\pi - 25\pi}{2(4 + \pi)}[/tex]
[tex]y = \frac{50}{2(4 + \pi)}[/tex]
[tex]y = \frac{25}{4 + \pi}[/tex]
Recall that:
[tex]Length = y[/tex]
So:
[tex]Length =\frac{25}{4 + \pi}[/tex]
Hence, the dimension of the rectangle is:
[tex]Length =\frac{25}{4 + \pi}[/tex] and [tex]Width = \frac{50}{4+\pi}[/tex]
Plz help me with this
hi!
so you're trying to find the value of n, I assume.
(n +2) / 5 = -3
n + 2 = -3 * 5
n + 2 = -15
n = -17
hope this helped!
a drawer contains 8 blue socks and 8 black socks. it is dark and you cannot tell the difference between colors
Answer:
yes
Step-by-step explanation:
i will trun on the light and see what color the socks are
please write complete question
Classify the shape as precisely as possible based on its markings.
Question 11 options:
A)
Rhombus
B)
Quadrilateral
C)
Parallelogram
D)
Rectangle
Answer:
c is wrong
Step-by-step explanation:
The given shape is a rhombus.
Hence the correct option is A.
Given is a shape we need to identify its type,
Since all the sides are congruent shown, so we can conclude that the shape is a Rhombus.
A rhombus is a quadrilateral (a polygon with four sides) in which all four sides have equal length. Additionally, the opposite sides of a rhombus are parallel to each other.
The rhombus is also a special type of parallelogram, as it has all the properties of a parallelogram, including opposite sides being equal in length, all the sides being equal and opposite angles being equal in measure.
Hence the correct option is A.
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Use the ten blocks to draw a quick picture to solve the following division problem: 165/11.
Step-by-step explanation:
[tex]\begin{array}{c|c c|c} 11 & 165 & & 15 \\ \cline {2-3} & 11 & & \\ & & 55 & \\ \cline {2-3}& & 55 & \\ & & 0& \end {array}[/tex]
5) Find the distance between -9 and 12 on a number line.
Answer: Hope this helps!!!
Step-by-step explanation:Absolute Value: You need to find how far away both numbers are from zero, then add these values together to see how far apart these numbers. The absolute value of nine, |-9| is 9, and |12| is 12. This means that the nine is nine spots away from zero, and twelve is twelve spots from zero. This means that the numbers are 20 units from each other.
Distance -9 is from 12 You need to find how much of an increase from nine you need to reach the twelve. So -9 + ? = 12. What number can you add to equal twelve? You can add 20 to make the equation true. (? = 20) The distance from -9 to 12 is a positive 20.
Distance from 12 to -9 This is similar to the previous example. What number can you insert to make the 12 equal the negative nine? 12 - ? = -9. The number would be -20, which means that 12 is 20 spots away from the negative nine, as it took at negative twenty to get us to the negative nine.
Emilio wants to find 2/3 of 50. explain how emilio could estimate the answer
Answer:
Emilio could estimate the answer by thinkinng of 50 as 100. Then 2/3 of 100 is 66.66666666. Divide this by 2 to get 33.33333333
Step-by-step explanation:
Hopefully this helps! I kind of just thought of what ran through my head so I would say it's an estimate.
Elvira used 4 cups of grape juice, 15 cups of cranberry juice, and 2 1 / 2 cup of pineapple juice to make punch. One liter is
approximately equal to 4.23 cups.
Which measurement is closest to the number of liters of punch Elvira made?
The sum of the perimeters of an equilateral triangle and a square is 22. Find the dimensions of the triangle and the square that produce a minimum total area. dimension of triangle dimension of squar
Answer:
The dimension of the triangle is 4.144 m and the dimension of the square is 2.392 m
Step-by-step explanation:
let a side of the equilateral triangle = x
let a side of square = y
3x + 4y = 22
4y = 22 - 3x
[tex]y = \frac{11}{2} -\frac{3x}{4}[/tex]
subjective function, the total area is given by;
[tex]f(x,y) = \frac{x^2\sqrt{3} }{4} +y^2[/tex]
[tex]f(x) = \frac{x^2\sqrt{3} }{4} + (\frac{11}{2} -\frac{3x}{4})^2\\\\f(x) = \frac{x^2\sqrt{3} }{4} +\frac{121}{4} -\frac{33x}{4} +\frac{9x^2}{16} \\\\f(x)' = \frac{x\sqrt{3} }{2} -\frac{33}{4} +\frac{9x}{8} \\\\\frac{x\sqrt{3} }{2} -\frac{33}{4} +\frac{9x}{8}=0\\\\\frac{x\sqrt{3} }{2} + \frac{9x}{8} =\frac{33}{4}\\\\\frac{4x\sqrt{3} +9x}{8} = \frac{33}{4}\\\\4x\sqrt{3} +9x = 66\\\\x(4\sqrt{3} +9) = 66\\\\x(15.928) = 66\\\\x = \frac{66}{15.928}\\\\x = 4.144 \ m[/tex]
solve for y
[tex]y = \frac{11}{2} -\frac{3x}{4}\\\\y = \frac{11}{2} -\frac{3*4.144}{4}\\\\y = 5.5-3.108\\\\y = 2.392 \ m[/tex]
Therefore, the dimension of the triangle is 4.144 m and the dimension of the square is 2.392 m
Solve for n: 0.22n = 6.6.
Answer:
30
Step-by-step explanation:
Solve for n: 0.22n = 6.6.
6.6/0.22 (because for example 3/3 and n/n= 1 so 0.22/0.22 = 1 so we have to divide 6.6 since it is part of the equation and we have to do it on both sides.)=30
What is the quotient of -3/8 and -1/3?
A. -1 1/8
B. -1/8
C. 1/8
D. 1 1/8
Answer:
d. 1 1/8
Step-by-step explanation:
-3 -1
---- ÷ -----
8. 3
Keep, Change, Flip.
-3/8 stays the same.
Division becomes multiplication.
-1/3 becomes -3/1
-3. -3. = 9
----- × ----- ------
8. 1. = 8
9/8 = 1 1/8
Answer:
D. 1 1/8
Step-by-step explanation:
Please help me thanks.
y=(-2x)+5
Step-by-step explanation:
82 63 44 25 sequence
Answer:
the next number is 6
Step-by-step explanation:
i'm assuming you want to find what comes next after 25 so pretty much each number decreases by 19
The 10th term of the arithmetic sequence will be –89.
What is the arithmetic sequence?Let a₁ be the first term and d is the common difference between the terms. Then the nth term will be given as
[tex]\rm a_n = a_1 + (n - 1)d[/tex]
The sequence is given below.
82, 63, 44, 25, ......
The first term is 82 and the common difference will be
d = 63 – 82
d = –19
Then the equation will be
[tex]\rm a_n =82- (n - 1) \times 19[/tex]
Then the 10th term of the sequence will be
a₁₀ = 82 – (10 – 1) x 19
a₁₀ = 82 – 171
a₁₀ = –89
The complete question is 82 63 44 25 sequence. What is the 10 term of the sequence?
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During one month, a homeowner used 600 units of electricity and 100 units of gas for a total cost of 390. The next month, 400 units of electricity and 250 units of gas were used for a total cost of $326. Find the cost per unit of gas.
Answer:
$0.36
Step-by-step explanation:
Let the cost per unit of electricity = e
Let the cost per unit of gas = g
a homeowner used 600 units of electricity and 100 units of gas for a total cost of 390;
600e + 100g = 390 ----- i
400 units of electricity and 250 units of gas were used for a total cost of $326.
400e + 250g = 326 ----- ii
Now we have two equations, and we solve for g;
600e + 100g = 390 ----- i
400e + 250g = 326 ----- ii
Multiply equation i by 4 and equation ii by 6;
2400e + 400g = 1560 ---- iii
2400e + 1500g = 1956 ---- iv
Subtract equation iii from iv;
1100g = 396
g = [tex]\frac{396}{1100}[/tex] = 0.36
Cost per unit of gas $0.36
The average age of all the JSOM students is 24 years with a standard deviation of 9 years. Of 8,000 students, a random sample of 36 students is selected. What is the probability that the sample mean will be between 25.5 and 27 years?
Answer:
The probability that the sample mean will be between 25.5 and 27 years is 0.1359.
Step-by-step explanation:
Let X denote of age of JSOM students.
The information provided is:
[tex]\mu=24\\\sigma=9\\n=36[/tex]
According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\mu\\[/tex]
And the standard deviation of the sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
As the sample size is large, i.e. n = 36 > 30, the sampling distribution of the average age of all the JSOM students can be approximated by the normal distribution.
Compute the probability that the sample mean will be between 25.5 and 27 years as follows:
[tex]P(25.5<\bar X<27)=P(\frac{25.5-24}{9/\sqrt{36}}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{27-24}{9/\sqrt{36}})\\\\=P(1<Z<2)\\\\=P(Z<2)-P(Z<1)\\\\=0.97725-0.84134\\\\=0.13591\\\\\approx 0.1359[/tex]
Thus, the probability that the sample mean will be between 25.5 and 27 years is 0.1359.
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Evaluate the expression
Answer:
-15
Step-by-step explanation:
Which shows two expressions that are equivalent to (-8)(-12)(2)?
The solution is option C.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
(-8)(-12)(2)
=96*2
=192
so. we get,
It would be c because when you multiply 8 and 12 you get 96 and when you multiply 96x2 you get 192 .
so, therefore your answer is c.
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Error Analysis A contractor purchases 4 dozen pairs of padded work gloves for $54.24. She
incorrectly calculates the unit price as $13.56 per pair for the expense report. What is the correct
unit price? What is the error?
The correct unit price is $
per pair.
Answer:
the unit rate for each pair is $1.13
Step-by-step explanation:
Okay this is how you would do this problem correctly:
we know that 4 dozen pairs of gloves cost $54.24 however we want to know what the cost is for one pair so we have to make a equation by dividing total cost by the number of glove pairs.
$54.24/4 dozen
the reason we are putting 4 dozen instead of just dividing $54.24 by 4 is because we want to know the unit price for each pair of gloves so it would actually look like this:
$54.24/4(12)
Dozen = 12
so we multiply 12 by 4 to get 48 pairs of gloves, we then divide $54.24 by 48 to find our unit rate of pricing for each pair:
$54.24/48 = 1.13
so now we place a dollar sign in front of 1.13 to get your answer:
for every pair bought it costs $1.13
So how did the Analysis A contractor get the wrong answer? well when she had bought the 4 dozen gloves she divided $54.24 by 4, which in this case would make it seem as though the gloves came in a 12 pack of gloves. However she was buying the gloves individually so she would have to multiply 4 by 12 before dividing the total number of gloves from $54.24.
For Carly's birthday celebration her family took her out to eat at her favorite restaurant. The total bill was $135.
Her dad wants to leave an 18% tip.
How much money is the tip?
$
The OLS method A. minimizes the sum of the residuals. B. maximizes the sum of the residuals. C. maximizes the sum of the squared residuals. D. minimizes the sum of the squared residuals.
Answer: D. minimizes the sum of the squared residuals
Step-by-step explanation: The ordinary least square method is often used in locating the trendine which best fits a graphical linear model. The best is one in which the sum of the squared residual is smallest. The residual refers to the difference between the actual and the predicted points. The sum of the squared differences is obtained and the trend line is positioned where the residual is minimum. Choosing a OLS, and minimizing the sum.of the squared residual, the error difference between the predicted and actual score is minimized or reduced, hence, improving the prediction accuracy of our model.
At a certain school,5/9 of the students are boys. Today, 2/3 of the boys brought their lunch. What fraction of the students are boys who brought their lunch
The fraction of the students are boys who brought their lunch is 5/6.
It is required to find the fraction of the students are boys who brought their lunch.
What is fraction?A fraction having whole numbers for the numerator and denominator. A fraction is a number of the form: ab where a and b are integers and b≠0. It represents the division of two numbers.
Given:
At a certain school, students are boys =5/9
students are boys brought their lunch=2/3
According to given question we have,
Divide 5/9 by 2/3
[tex]\frac{5/9}{2/3} \\\\\frac{5}{6}[/tex]
Therefore, the fraction of the students are boys who brought their lunch is 5/6.
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The sum of two numbers is 14 and their difference is 4. What are the two numbers (02 6 8 Larger number Smaller number
Answer:
The two numbers are 9 and 5
Step-by-step explanation:
If u try adding 9 and 5 u will get 14
And if u subtract them u will get 4
I hope the answer is helpful
HELPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
its the first third and fith
Step-by-step explanation:
The length of a rectangular deck is 5 times its width. If the deck’s perimeter is 24 feet, what is the deck’s area?
Answer:
20ft²
Step-by-step explanation:
Let the length = L
Let the width = W
Perimeter of a rectangle = 2L + 2W
Translating the word problem into an algebraic equation, we have;
L = 5W .......equation 1
2L + 2W = 24 ........equation 2
To find the width
Substituting equation 1 into equation 2, we have;
2(5W) + 2W = 24
10W + 2W = 24
12W = 24
W = 24/12
Width, W = 2 ft
To find the length;
Substituting the value of "W" into equation 1, we have;
L = 5W
L = 5*2
L = 10 ft
To find the area of the rectangle;
Area = LW
Area = 10*2
Area = 20 ft²
Therefore, the deck's area is 20 feet square.
Harry needs 21 square meters of fabric for every 6 wizard cloaks he makes. Complete the table using equivalent ratios. help me pleaseeee
Answer:
21/6 = 7/2 = 14/4
Step-by-step explanation:
Answer:
21:6 7:2 14:4
Step-by-step explanation:
What is an equation of the line that passes through the points (0, -2) and (-5, 4)?
Put your answer in fully reduced form.
Answer:
I have no idea
Step-by-step explanation:
Answer: y= -6/5x-2
Step-by-step explanation:
That’s wut it said
Please answer it I will wait to see for brainliest
Answer:
D
Step-by-step explanation:
Answer:
ok so the odd one out is A) the measure of <ahd is 30°
Step-by-step explanation:
external angle is equal to the sum of the two interior angles on the opposite side
3x= x +15 +x +15
3x=x+x+15+15
3x= 2x +30
3x-2x= 30
x = 30