Answer: To obtain the standard form of a linear equation, we want to rearrange the equation in the form Ax + By = C. Here are the standard forms of the given equations:
5x - 6y = 12
3y - 2x - 6 = 0
7x + y - 63 = 0
14x - y + 16 = 0
To obtain the slope-intercept form of a linear equation, we want to rearrange the equation in the form y = mx + b, where m is the slope and b is the y-intercept. Here are the slope-intercept forms of the given equations:
There is no y-intercept, so this equation does not have a slope-intercept form.
y = (2/3)x + 2
y = (1/7)x + 9
y = (-7/2)x + 8
Step-by-step explanation:
The Garcia family bought 400 yards of fencing to enclose a circular wildflower garden. They will use all of the fencing whats the area
The area of the windflower garden that is enclosed by a circular fence of 400 yards length is equal to 12732.39 square yards.
What is circumference of a circle?The measurement of the circle's perimeter, also known as its circumference, is called the circle's border. It is the length around the border of the circular object or the circle itself.
What is the formula for calculating the perimeter of a circle?The formula for calculating the perimeter of a circle is ,
Perimeter/ Circumference of a circle = 2 * pi * r, where pi = 3.14 and r is the radius of the circle.
Taking the given information in the question, i.e circumference of the circular fencing wire , i.e C = 400 yards
or , 2 * pi * r = 400
or , r = 400/(2* 3.14)
r = 63.66 yards
Now the area of the circular fence is given by,
Area = pi * r^2
Area = 3.14 * 63.66^2
Area = 12732.39 square yards
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T h e r e a r e 235 seven t h - g r a d e st u d e n t s g o i n g o n a fi e l d t r i p . T h e sc h o o l h a s 5 b u se s t o t a k e t h e st u d e n t s. E a c h b u s h a s 22 se a t s, a n d 2 st u d e n t s c a n si t i n e a c h se a t . B a se d o n t h i s i n f o r m a t i o n , h o w m a n y st u d e n t s w i l l n o t b e a b l e t o r i d e o n a b u s f o r t h e fi e l d t r i p ?
The number of students who will not be able to ride on the bus for the school trip is given by the equation A = 15 students
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The total number of students for the trip = 235 students
The number of buses = 5 buses
The number of students in a bus be = B
Now , each seat on the bus can occupy = 2 students
So , 22 seats can occupy = 22 x 2 students
22 seats in the bus can occupy = 44 students
So , the number of students in a bus B = 44 students
And , the total number of students in 5 buses = 5 x number of students in a bus B
Substituting the values in the equation , we get
The total number of students in 5 buses = 5 x 44
The total number of students in 5 buses = 220 students
So , the remaining number of students A = total number of students for the trip - total number of students in 5 buses
Substituting the values in the equation , we get
The remaining number of students A = 235 - 220
The remaining number of students A = 15 students
Therefore , the value of A is 15 students
Hence , the number of students is 15 students
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Does 4 5 6 make a right triangle?
The side lengths measuring 4 units , 5 units and 6 units does not make a Right Triangle as they do not satisfy the condition of the Pythagoras Theorem that the square of the longest side is equal to the sum of square of other two side .
The Pythagoras Theorem states that the square of the lonest side (hypotnuse) is equal to the sum of the square of the other two sides ,.
The side lengths of the triangle are given as 4 units , 5 units and 6 units ,
According to the condition , [tex]6^{2} = 4^{2} + 5^{2}[/tex]
On simplifying ;
we get ;
[tex]36 = 16 + 25[/tex] ;
[tex]36 \neq 41[/tex]
that means the given side do not form a right triangle .
Therefore , the side 4 units , 5 units and 6 units do not make a right triangle .
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please help: solve for x
Answer:
x=3
Step-by-step explanation:
Since the altitude of this triangle is at the midpoint of the base,
It is a isosceles triangle making MJ=MK
9x-18=3x
6x-18=0
6x=18
x=3
Finn jumped 200 times in 10 hours. At what rate, how many times would he jumped in 12 minutes?
Answer: 4 times
Step-by-step explanation: I got 4 times. Here's how to solve it:
Set up a proportional relationship, but first, we need to convert 10 hrs into mins:
1 hour = 60 mins
To find how many minutes are in 10 hours, we multiply 60 by 10, which equals 600.
So, therefore there are 600 mins in 10 hours. Now, we can set up our proportional relationship:
[tex]\frac{200}{60} = \frac{?}{12}[/tex]
So, if we know 12 is a factor of 60, we should divide 60 by 12, and we should get 5. So, now we do the same with the 200. We do 200 / 50, and we get 4. I hope this helps!
What is the distance of 2/3 from the horizontal axis in Cartesian plane?
Distance of 2/3 from the horizontal axis is 2 for a cartesian plane.
What is cartesian coordinate system?
The coordinate system in where the location of a point is identified by a pair of numerical terms and that has two reference axis is termed as cartesian coordinate system.
In cartesian plane the reference axis are named as X - axis and Y -axis.
In this system, location of a point p is identified by p (x, y) that means x is the x coordinate of point p and y is the y coordinate of point p. Generally, X-axis is horizontal, and Y-axis is vertical. Both axes are intersected at the origin.
What is the distance of 2/3 from the horizontal axis in cartesian plane?The point coordinate 2/3 denotes the location of a point with respect to a reference direction in the polar coordinate system. In the polar coordinate system, the angle between horizontal axis and a reference point is called polar angle. we know tan angle = vertical coordinate / horizontal coordinate.
hence, tan angle = 2/3
for this reason, if we imagine a cartesian coordinate system 2 is the y coordinate and 3 is the x coordinate.
Finally, the distance of 2/3 from the horizontal axis is 2.
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Solve the inequality 3 x+2 y≥−6 graphically.
Answer:
Step-by-step explanation:
Answer: y ≥ −3/2x − 3
Step-by-step explanation:
Graph the inequality by finding the boundary line, then shading the appropriate area.
Hope this helps!
Ben Nevis has a height of approximately 1300 metres above sea level.
Assuming that temperature decreases by 1°C for every 100 metres above
sea level, work out the temperature at the summit of Ben Nevis when the
sea level temperature is 5°C.
The temperature at the summit of Ben Nevis, when the sea level temperature is 5°C is -15°C.
To work out the temperature at the summit of Ben Nevis, we can use the formula:
Temperature at summit = Sea level temperature - (Altitude above sea level / 100) ×Temperature change per 100 metres
We are given that the sea level temperature is 5°C and the height of Ben Nevis is 1300 metres above sea level, and the temperature decreases by 1°C for every 100 metres above sea level.
So, after putting the values into the formula:
Temperature at summit = 5 - (1300/100) × 1 = -15°C
Therefore, the temperature at the summit of Ben Nevis, when the sea level temperature is 5°C is -15°C
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find the total surface area of this cuboid.
The total surface area of the cuboid is 2 (lh + lw+ hw) square units.
What is surface?A surface is the part of solid matter that can be touched by hand or seen with eyes. In other words, it is the place where the solid matter encounters the outside world through contact, light, etc. Solid matter not only effects humans with its surface, but also air, water, and other solid matter. Therefore, things around us work cooperatively with the outside world and with other things through surfaces, without a surface, solid matter would not be able to interact with anything.By changing the characteristics of solid matter, interactions such as the impact on the solid matter from other things (such as environmental conditions and people) as well as the effect that solid matter has on other things can be changed. In other words, certain features of the solid matter can be controlled as needed.To learn more about surface refer to:
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Twelve eggs cost $2.04. How much will 18 eggs cost
Answer: $3.06
Step-by-step explanation: In order to get $3.06, you will have to find half $2.04 and then add that number to the price of 12 eggs.
Find $(-1)^{-10} (-1)^{-9} (-1)^{-8} \cdots (-1)^9 (-1)^{10}$. (The dots $\cdots$ mean that there are 21 numbers being added, one for each integer from $-10$ to 10.)
The sum of the sequence [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex] is 1
Consider given sequence [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex]
here, the dots . . . means that there are 21 numbers being added, one for each integer from −10 to 10.
We need to find the sum.
We can observe that the above sequence is a geometric sequence with the common ratio r = -1 and the first term a1 = [tex](-1)^{-10}[/tex] i.e., a1 = 1
We know that the formula of the sum of n-terms of a geometric sequence is:
[tex]S_n= a_1 \times (\frac{1-r^n}{1 -r} )[/tex]
For n = 21, r = -1 and a1 = 1
[tex]S_{21}=1 \times (\frac{1-(-1)^{21}}{1-(-1)} )\\\\S_{21 }= 1\times (\frac{1-(-1)}{1 +1} )\\\\S_{21 }=\frac{1+1}{2} \\\\S_{21 }= \frac{2}{2} \\\\S_{21 }= 1[/tex]
Therefore, [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex] = 1
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(#7) A cube has an edge length given by the variable “s” as shown. It’s surface area and volume can be given in terms of the edge length by: surface area= 6s^2 volume= s^3 Find the ratio of the surface area to the volume in simplest terms of “s”.
The ratio of surface area to volume is 6:s
What is a cube?A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.
Given that, A cube has an edge length given by the variable “s”. It’s surface area and volume can be given in terms of the edge length by: surface area= 6s² volume= s³
The ratio = 6s² / s³
= 6 / s
Hence, the required ratio is 6:s
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A simple random sample of 10 people were asked how many first cousins they have. The results are listed below.
10, 19, 20, 13, 13, 2, 10, 8, 25, 10
What is the mean number of first cousins for this sample?
10
11.5
13
13.5.
answer is 13
Answer:
13
Step-by-step explanation:
mean= (10+19+20+13+13+2+10+8+25+10)/10=130/10=13
The mean number of first cousins for the given sample is 13. Thus, Option C is correct.
Mean is the arithmetic average of the given set of observations.
Mean for ungrouped or raw data is obtained by adding all the observations and dividing it by the number of observations.
Mean = Sum of all the observations/ Total number of observations.
Mean = ∑( x1 + x2 + x3 .... xn /n)
Where X bar represents mean, n is no. of observations and ∑ denotes sigma i.e. sum of all the values.
No. of observations (n) =10
Mean = ∑ (10 + 19 + 20 + 13 + 13 + 2 + 10 + 8 + 25 + 10) / 10
Mean = 130 / 10
= 13
Therefore, Option C is the correct answer.
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given the expression 1/4-3/5 select the addition problem that is equivalent to it
The expression (1/4 - 3/5) is equivalent to the following expressions -
(3/20 - 10/20) (13/20 - 1)(23/20 - 3/2)What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression as -
(1/4 - 3/5)
The given expression is -
(1/4 - 3/5)
1/4 - 3/5
(5 - 12)/20
-7/20
We can write the fraction : -7/20 in many ways as given below -
-7/20 = (3/20 - 10/20) = (1/4 - 3/5)
-7/20 = (13/20 - 1) = (1/4 - 3/5)
-7/20 = (23/20 - 3/2) = 1/4 - 3/5)
Therefore, the expression (1/4 - 3/5) is equivalent to the following expressions -
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What is the interval of zero?
If the confidence interval for a difference between groups includes zero, that means that if you run your experiment again you have a good chance of finding no difference between groups.
If the confidence interval for a difference between groups includes zero, that means that if you run your experiment again you have a good chance of finding no difference between groups.
If the confidence interval for a correlation or regression includes zero, that means that if you run the experiment again there is a good chance of finding no correlation in the data.
In both of these cases, you will also find a high p-value when you run the statistical test, meaning that the results could have occurred under the null hypothesis of no relationship between variables or no difference between groups.
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What literary devices are used in The Importance of Being Earnest?
Oscar Wilde mocks upper-class Victorian society in "The Importance of Being Earnest" by using the literary devices of irony and hyperbole to a humorous effect.
What is The Importance of Being Earnest?
Oscar Wilde wrote a play titled The Importance of Being Earnest, A Trivial Comedy for Serious People.
It is a farcical farce that was first presented on February 14, 1895, at the St James's Theatre in London.
The characters maintain false personae to avoid onerous social duties.
The play's main themes, which are based on late Victorian London social customs, are the triviality with which it treats institutions as important as marriage and the satire that results.
In "The Importance of Being Earnest," Oscar Wilde employs the literary devices of irony and hyperbole to hilarious effect as he criticizes upper-class Victorian society.
Therefore, Oscar Wilde mocks upper-class Victorian society in "The Importance of Being Earnest" by using the literary devices of irony and hyperbole to humorous effect.
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PLEASE HELP Water flowed out of a tank at a steady rate. A total of 18 and one-half gallons flowed out of the tank in 4 and one-fourth hours. Which expression determines the quantity of water leaving the tank per hour?
The expression determines the quantity of water leaving the tank per hour is (18 1/2 gallons)/(4 1/4 hours)
How to find which expression determines the quantity of water leaving the tank per hour?
Rate is the ratio of a certain number of units of one quantity to units of another quantity. Mathematically, rate is one quantity divided by the other quantity.
If a total of 18 and one-half gallons flowed out of the tank in 4 and one-fourth hours. We can write that the rate as follows:
rate = (18 1/2 gallons)/(4 1/4 hours)
rate = 4 6/17 gallons per hour
Thus, the expression determines the quantity of water leaving the tank is (18 1/2 gallons)/(4 1/4 hours)
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What is the simplified value of the expression below?
1/3 divided by 2/3
0
1/3
1/2
1
Answer: 1/2
Step-by-step explanation:
( see image ) ( Keep Change Flip )
Find the value of k so that the point (1,2) lies on the locus y²-2x-ky+5=0.
Write 108:96 in the form 1:n.
Answer:
it will be [tex]1:\frac{8}{9}[/tex]How do you find the third side of a triangle that is not right?
The third side of a triangle can be found using the Pythagorean Theorem.
The Pythagorean Theorem states that for a triangle with sides of length a, b, and c (with c being the length of the unknown side) a^2 + b^2 = c^2.
To find the third side of a triangle that is not right, first calculate the lengths of the two known sides. Let's say the lengths of the two known sides are a = 5 and b = 12.
Next, plug the values into the Pythagorean Theorem and solve for c.
[tex]a^2 + b^2 = c^2[/tex]
[tex](5)^2 + (12)^2 = c^2 \\25 + 144 = c^2[/tex]
[tex]169 = c^2[/tex]
Finally, take the square root of both sides to solve for c.
sqrt(169) = c
13 = c
Therefore, the length of the third side is 13.
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Rich is going to a 4-year college. He was given a 10-year, unsubsidized student loan for $7,900 at 4.29%. He has to option of beginning to repay the loan in 4.5 years. He also knows that during the time he is not making payments, interest will be charged at 4.29%. If Rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period. What will his monthly payments be? Round to the nearest cent.
If Rich is going to a 4-year college. He was given a 10-year, unsubsidized student loan for $7,900 at 4.29%. His monthly payment is $87.31.
What is monthly payment?Monthly payment can be defined as the amount a person received on a monthly basis.
Now let find the monthly payment
Monthly payment = 7900 (0.0429/12) ( 1+ 0.0429/12)^12×10 ÷ ( 1+ 0.0429/12)^12×10 -1
Monthly payment = 7900 (0.003575) ( 1+ 0.003575)^120÷ ( 1+ 0.003575)^120 -1
Monthly payment =7900 (0.003575) ( 1.003575)^120 ÷ ( 1.003575)^120 -1
Monthly payment = $87.31
Therefore the monthly payment is $87.31.
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The complete question is:
Rich is going to a 4-year college. He was given a 10-year, unsubsidized student loan for $7,900 at 4.29%. He has to option of beginning to repay the loan in 4.5 years. He also knows that during the time he is not making payments, interest will be charged at 4.29%. If Rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period. Suppose that Rich had decided to apply for a private loan rather than a federal loan. He is considering a 10-year lo"an with an interest rate of 5.9% .What will his monthly payments be?
What is the difference 19√5 - 3√5 A.16 B.22 C.16√5 D.25
Answer:
C - 16√5
Step-by-step explanation:
Simply subtract 19 and 3 while keeping √5 the same.
19√5 - 3√5 = 16√5
If it takes 10 hours to travel from North Carolina to Florida driving an
average speed of 60 mph, how long will it take to travel from North
Carolina to Florida driving an average speed of 70 mph?
Is it direct variation or indirect variation?
Answer:
8.5 hrs? direct variation
Step-by-step explanation:
60 per hour is 600 for 10 hours so 70 per hour to go 600 miles is 8.57142857143 in the calculator
600/60 =10
600/70 = 8.5
and its direct variation because on a graph 8.5 8.5 squares up for ever 1 square going over every time and the graph does curve but I haven't learned this stuff in years so I'm not 100% sure
Melissa wants to check the accuracy of the finance charge on her loan. She has a $6,000, 4-year loan at an APR of 3.11%. What is her monthly payment? Round to the nearest cent.
Answer: $133.10.
Step-by-step explanation:
Answer:
To calculate the monthly payment for a loan, you can use the following formula:
Monthly payment = (APR/12) * loan amount / (1 - (1 + APR/12)^(-number of payments))
In this case, the loan amount is $6,000, the APR is 3.11%, and the loan is for 4 years, or 48 months. Plugging these values into the formula, we have:
Monthly payment = (0.0311/12) * $6,000 / (1 - (1 + 0.0311/12)^(-48))
Calculating, we find that the monthly payment is approximately $147.26. Rounded to the nearest cent, the monthly payment is $147.26.
Step-by-step explanation:
This is algebra 2, please help.
The vertex and axis of symmetry of the graph is shown in image.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The function is,
⇒ f (x) = 1/4 (x + 6)² - 5
Now,
Since, The function is,
⇒ f (x) = 1/4 (x + 6)² - 5
Hence, The points corresponds to x = - 2 and - 4 are;
For x = - 2;
⇒ f (x) = 1/4 (x + 6)² - 5
⇒ f (x) = 1/4 (-2 + 6)² - 5
⇒ f (x) = 1/4 (4)² - 5
⇒ f (x) = 4 - 5
⇒ f (x) = - 1
For x = - 4;
⇒ f (x) = 1/4 (x + 6)² - 5
⇒ f (x) = 1/4 (-4 + 6)² - 5
⇒ f (x) = 1/4 (2)² - 5
⇒ f (x) = 1 - 5
⇒ f (x) = - 4
Thus, The points are;
⇒ (- 2, - 1) , (- 4, - 4)
And, The vertex of the function is,
⇒ ( - 6, - 5 )
And, The axis of symmetry of the graph is,
⇒ x = - 6
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How many solutions does 3x 2y 6 have?
The linear equation 3x – 2y = 6 has one real solution. To find it, you can solve the equation for one of the variables (either x or y) and then substitute the result into the equation to find the other variable.
For example, you can solve for y to get y = (6 + 3x)/2, and then substitute this into the equation to get 3x – 2((6 + 3x)/2) = 6, which you can then solve for x. Doing this will give you x = 3, which means that the solution is (3, 3).
The linear equation 3x – 2y = 6 has infinitely many solutions. To find them, you can solve the equation for one of the variables (either x or y) and then substitute the result into the equation to find the other variable
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will mark u brainliest
Answer:
( - 7, - 1, 1, 4 )
Step-by-step explanation:
( x, y )
where,
x is Domain
y is Range
Hence,
Domain is ( - 7, - 1, 1, 4 )
A lawn sprinkler located at the corner of a yard rotates through 80 degrees
and sprays water of 20 ft. What is the length of the arc of the sector watered?
(Express your answer to the nearest tenths.)
The length of the arc of the sectored watered is 27.9 feets
What is length of an arc?length of arc is the distance between two points along a section of a curve.In other words, it's the distance from one point on the edge of a circle to another, or just a portion of the circumference
The length of an arc is given by :
L = theta/360 × 2πr
where tetha is the angle substends
r is the radius
Here the radius is the length at which water is sprayed = 20 ft
tetha = 80°
therefore l = 80/360 × 2×3.14 × 20
L = 29feets
Therefore the length of the arc formed by the water is 27.9 feets
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If the sum of n term of an ap is sn = 3n^2+5n writ its common difference
In the given arithmetic progression Common difference is 14.
what is an arithmetic progression?An arithmetic progression is a set of integers with a fixed difference between any two succeeding numbers (A.P.).
Given, the n term of ap is Sₙ = 3n² + 5n
Where n is the number of terms
S₁ = 3* 1 + 5*1
S₁ = 8
S₂ = 3 * 4 + 5*2
S₂ = 22
common difference = 22-8
Common difference = 14
therefore, the Common difference in the given AP is 14.
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