Answer: Let's call the length of the box "x". Then, the height of the box is 4x and the width is x + 7. The volume of the box is given by the equation:
x * 4x * (x + 7) = 102
Expanding and simplifying the equation, we get:
4x^3 + 28x^2 - 102 = 0
To find the length of the box, we need to solve for x in this equation. One way to do this is to use the cubic formula. However, this formula can be quite complex, so a simpler method would be to use numerical methods such as the bisection method or Newton's method.
Step-by-step explanation:
What is the equation of a line with slope 1/4 which passes through the point (0,7)?
Answer:
y - 7 = 1/4 ( x - 0 )
y -7 = 1/4 x
y = 1/4 x + 7
Dilations produce similar shapes. The size of the figure changes, but the shape does not change. Notation for a
dilation with a scale factor of n is Dn(x, y) (nx, ny).
After dilation, the size of the new image is not the same as the original. Therefore, dilation cannot produce a congruent figure.
Does a dilation produce a congruent figure?When two figures are congruent, it means they have the same shape and size, whereby, all pairs of corresponding angles and sides of both figures are congruent or equal in measure.
The image attached below shows a dilated figure.
Dilation is a transformation that enlarges a figure or reduces the figure.
After dilation, the new figure maintains the same shape of the original figure.
However, after dilation, the size of the new image is not the same as the original. Therefore, dilation cannot produce a congruent figure.
Study more about dilation on https://brainly.com/question/13176891
#SPJ1
Riley, Nathan, and Jeremy had a challenge to see who could
bike the farthest in one day. Riley biked 15 miles, Nathan biked
3 times as many miles as Jeremy and Jeremy biked 3 times as
many miles as Riley. How many miles did Nathan bike?
Nathan biked a total of 135 miles.
What is miles?Miles unit of distance between 2.1 map of the link of a johnny the tomb my list divided for the letting word thousand and the world to 1.609 kilometers my life report unit measurement is a united states uk kannada some other countries.
To solve this problem, we need to use the given information to find the amount of miles that Jeremy biked. Since Jeremy biked 3 times as many miles as Riley, we know that Jeremy biked 15 x 3 = 45 miles.
Since Nathan biked 3 times as many miles as Jeremy, we know that Nathan biked 45 x 3 = 135 miles. Therefore, Nathan biked a total of 135 miles.
To know more about miles click-
https://brainly.com/question/25631156
#SPJ1
Find the sum of 7 1/3 and 4 7/10
Answer:
12 1/30
Step-by-step explanation:
What does sum mean?Sum is the term used for the total amount of something when two or more numbers are added.
In order to add the two fractions, they must have the same denominator.
To do this, we need to find a common denominator.
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
Multiples of 10: 10, 20, 30
Both 3 and 10 have 30 in common, so this is the common denominator.
In order to get to 30, 3 must be multiplied by 10. Whatever you do to the bottom must be done to the top and vice versa.
7 1/3 becomes 7 10/30.
4 7/10 becomes 4 21/30
Now, we add the whole numbers.
7 + 4 = 11
Now, add the fractions.
10/30 + 21/30 = 31/30
Put it all together.
11 31/30
This is an improper fraction, so we must make it a proper fraction. To do this, we divide 30 into 31. It can only go in evenly one time and has a remainder of one. The remainder is added to the whole numbers and the numerator of the fraction takes the evenly divided one.
11 + 1 1/30 This is adding the remainder to the whole number.
12 1/30 This is the result of adding the remainder and fixing the fraction.
12 1/30 is the answer.
why is infinity divided by infinity undefined?
Answer:
Infinity divided by infinity is undefined because infinity is not a number and cannot be treated as one in mathematical operations. In mathematics, division is a process that involves finding the ratio between two numbers. However, infinity is not a number and has no finite value, so it cannot be used as the denominator or numerator in a division operation.
When dividing infinity by infinity, you are asking for the ratio of two quantities that are both infinite, and the result is not well-defined. The concept of infinity can be useful in certain mathematical contexts, such as limits and calculus, but it cannot be used as a number in the usual sense.
In mathematical terms, the expression infinity divided by infinity is considered indeterminate and has no defined value. This is why it is undefined in mathematical analysis.
Step-by-step explanation:
( 5 m ^ 2 + 3 mn - 3 n ^2 ) - ( m ^ 2 - n ^2 )=
Options:
A- 4m ^ 2 + 2 n ^ 2
B- 4 m ^ 2 - 4 n ^ 2
C- 4 m ^ 2 + 3 mn - 2 n ^2
D-4 m ^ 2 + 3 mn - 4 n ^2
answer quick
The simplification of the algebraic expression gives:
(5m² + 3mn - 3n²) - (m² - n²) = 4m² + 3mn - 2n²
How to simply an algebraic expression?
An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.
(5m² + 3mn - 3n²) - (m² - n²) = 5m² + 3mn - 3n² - m² + n²
= 5m²- m² + 3mn - 3n²+ n²
= 4m² + 3mn - 2n²
Therefore, (5m² + 3mn - 3n²) - (m² - n²) simplifies to 4m² + 3mn - 2n²
Learn more about algebraic expressions on:
brainly.com/question/4344214
#SPJ1
List each zero of f according to its multiplicity in the categories below.
The zeros of f(x) are:
zeros x = 9 and x = 7 → multiplicity 1. zero x = -13 → multiplicity 2. zero x = -5 → multiplicity 3.Which are the zeros and multiplicities?Here we have the polynomial:
f(x) = 6*(x - 9)*(x - 7)*(x + 13)^2*(x + 5)^3
In each factor of the form:
(x - k)^n
the zero is x = k
and the multiplicity is n.
Then:
The zeros x = 9 and x = 7 have multiplicity 1.
The zero x = .13 has multiplicity 2.
The zero x = -5 has multiplicity 3.
These are the zeros of the polynomial.
Learn more about polynomials at:
https://brainly.com/question/4142886
#SPJ1
name each type of special quadrilateral that can meet the given condition. four right angles. make sketches to support your anwers
The name special quadrilateral that have four right angles. are Square , Rhombus , Rectangle have 4 right angle.
A two-dimensional shape with four sides, four vertices, and four angles is referred to as a quadrilateral. Convex and concave are the two main forms. Convex quadrilaterals can also be divided into a number of subgroups, including trapezoids, parallelograms, rectangles, rhombus, and squares.
Square - The properties of square is it have 4 side and all side are equal and make 90 degree angle on all 4 side. that's why it has 4 right angle.
Rhombus - The properties of rhombus is it have 4 side and all side are equal and there diagonal cut each other at 90 degree that's why it has 4 right angle
Rectangle- The properties of square is it have 4 side and parallel sides are equal and make 90 degree angle on all 4 side.that's why it has 4 right angle.
Know more about quadrilateral with right angle click here ;https://brainly.com/question/29018314
#SPJ4
write each rate as a unit rate.
3 inches of rain in 6 hours
Answer: 0.5 inches of rain per hour or 0.5/1
Step-by-step explanation:
divide 3/6 gets you 0.5
WHAT IS THE MEANING TO THE ANSWERR OF LIFE THAT IS SQUARED BY TWO
Answer: I'm sorry, but the statement "the answer to the meaning of life that is squared by two" is not a coherent or meaningful concept. The meaning of life is a philosophical question that has been debated by scholars, theologians, and thinkers throughout history and has no single, universally agreed-upon answer. Additionally, squaring by two does not have any inherent relationship to the meaning of life.
Step-by-step explanation:
Evelyn works in a greenhouse and planted 22 flowers in pots. 8 of the flowers were daisies.
If she wants the ratio of daisies to flowers to stay the same how many daisies would she need to plant if she fills 66 pots?
Answer: 24 Daisies
Step-by-step explanation:
14 flowers are normal and the other 8 are daisies, there are currently 22 flowers.
To fill 66 plots, she'd need to plant 3 times as many flowers as there are now, so there'd be 14*3 non daisies and 8*3 daisies. 8*3 = 24.
Answer:
24
Step-by-step explanation:
[tex]\frac{daisies}{total flowers}[/tex] = [tex]\frac{daisies}{total flowers\\}[/tex]
[tex]\frac{8}{22}[/tex] = [tex]\frac{d}{66}[/tex]
22 x 3 = 66
8 x 3 = 24
Replace * with a digit so that the value of x is a whole number. Find all possibilities.
3x-694-10*
Water flows at 2 feet per second through a pipe with a diameter of 8 inches. A cylindrical tank with a diameter of 15 feet and a height of 6 feet collects the water.
a. What is the exact volume, in cubic inches, of water flowing out of the pipe every second? Leave your answer in terms of π.
To find the volume of water flowing out of the pipe every second, we first need to find the cross-sectional area of the pipe. The formula for the area of a circle is π * r^2, where r is the radius. So, the radius of the pipe is 8/2 = 4 inches.
The cross-sectional area of the pipe is π * 4^2 = 16π square inches.
Now, since the water is flowing at a rate of 2 feet per second, and 1 foot is equal to 12 inches, the flow rate in inches per second is 2 * 12 = 24 cubic inches per second.
So, the exact volume of water flowing out of the pipe every second is the cross-sectional area of the pipe times the flow rate:
16π * 24 = 384π cubic inches per second.
To know more about Volume
https://brainly.com/question/1972490
Which investment results in the greatest total amount?
Investment A: $4,000 invested for 5 years compounded semiannually at 6%.
Investment B: $5,000 invested for 3 years compounded quarterly at 2.7%.
Find the total amount of investment A.
$ (Round to the nearest cent as needed.)
Answer:
Step-by-step explanation:
The formula to calculate the future value of an investment with compound interest is:
FV = PV * (1 + (r/n))^(n*t)
Where:
PV is the present value (the initial investment)
r is the annual interest rate
n is the number of compounding periods per year
t is the number of years
For Investment A:
PV = $4,000
r = 6% = 0.06
n = 2 (semiannual compounding)
t = 5 years
FV = $4,000 * (1 + (0.06/2))^(2*5) = $4,000 * (1.03)^10
FV = $4,000 * 1.664131669 = $6,656.53
So, the total amount of Investment A is $6,656.53 (rounded to the nearest cent).
The following composite figure is made up of a right triangular prism and right triangular pyramid if the height of the prism is 12 feet what is the volume of the figure
The volume of the composite figure is equal to 3425.333 cubic feet.
How to determine the volume of a composite figure
In this problem we need to determine the volume of a composite figure, that is, the sum of the volumes of a right prism and a pyramid, whose formulae are described below:
Right prism
V = 0.5 · w · l · h
Pyramid
V = (1 / 3) · (0.5 · w · l) · h
Where:
w - Width of the base, in feet.l - Length of the base, in feet. h - Height, in feet.V - Volume, in cubic feet.Now we proceed to determine the volume of the composite figure:
V = 0.5 · (8 ft) · (7 ft) · (12 ft) + (1 / 3) · 0.5 · (8 ft) · (7 ft) · (7 ft)
V = 3425.333 ft³
To learn more on volume of composite figures: https://brainly.com/question/1284145
#SPJ1
Answer D is cut off but if you come to a different conclusion you can always use process of elimination
The total monthly payments is $2169.49
What is mortgage payment?You should understand that a mortgage is a home loan that is secured by the property the borrower finances with the loan funds.
The mortgage payment is
A = (210,000·0.95)(0.045/12)/(1 -(1 +0.045/12)^(-12·15)) ≈ 1526.16
The monthly set-aside for taxes is
3.5%*200,000/12 = 583.33
The monthly set-aside for insurance is
720/12 = 60
So the total of P&I + taxes + insurance will be
In conclusion, the monthly payment is given by :
$1526.16 +583.33 +60.00 = $2169.49
Learn more about mortgage on https://brainly.com/question/15074748
#SPJ1
Using the diagram below, write a. in terms of Au b. in terms of AB and B A 2. Add the following vectors using the Triangle Law. a. 9 N on a heading of (S2"W) and 11 N on a heading of (N31*W). b. 7 m/s on a bearing of 30 and 2 m/s from a bearing of 343". (HINT: a vector "on" a bearing extends "out" from the origin and a vector "from" a bearing is directed in "toward" the origin) 3. Add the following vectors using the Component law a. 9 m/s (N30°E) and 2 m/s [N 80'E). b. 3 N in a direction 15" south of west and 4 N in a direction 12 east of south. 4. A plane is heading on a bearing of 200 with an airspeed of 400 km/h when it is blown off course by a wind of 100 km/h from the northeast Determine the resultant ground velocity of the plane. в M 0 18 Feb 血
Answer:
a. Au = 9cos(30) + 11cos(31)
b. AB = 9sin(30) + 11sin(31) and B = -9sin(30) + 11sin(31)
3. a. 9cos(30) + 2cos(80)
b. 3cos(15) + 4cos(12)
4. The ground velocity of the plane would be 349.4 km/h on a bearing of 225°.
6
Blood pressure. A company held a blood pressure screen-
ing clinic for its employees. The results are summarized in
the table below by age group and blood pressure level:
Blood
Pressure
Low
Normal
High
Under 30
27
48
23
Age
30-49 Over 50
37
91
51
31
93
73
a) Find the marginal distribution of blood pressure level.
b) Find the conditional distribution of blood pressure
level within each age group.
c) Compare these distributions with a segmented bar
graph.
d) Write a brief description of the association between
age and blood pressure among these employees.
e) Does this prove that people's blood pressure increases
as they age? Explain.
As people get older, the proportion of employees with low blood pressure falls and the proportion with high blood pressure rises.
what is proportionality ?Interactions are regarded to as appropriate when they usually have the same ratio. For instance, the number of plants in an orchard and the number of apples in a production of apples depend upon this average number of apples produced by each tree. A linear relationship among two numbers or objects is considered to as being proportional in mathematics. When the first quantity doubles, the other amount also does so. As soon as one variables is reduced to 1/100th of its previous value, other decreases as well. If two variables are proportional, it means that if one rises, the other climbs as well, and their relationship stays constant at all values. The diameter and circumference of a circle are used as an example.
given
a) 20%, 49.4%, 30.6% (equal 100)
b) 29.7%, 45.5%, 24.8%
20%, 52.6%, 27.4%
14.9%, 48.5%, 36.6%
c) As people get older, the proportion of employees with low blood pressure falls and the proportion with high blood pressure rises.
d) No, because the association between age and blood pressure can only be determined through a carefully designed trial.
To know more about proportionality visit:
https://brainly.com/question/29126727
#SPJ1
Maria played a game with her little sister for 2/5 hour and read her little sister a book for 5/8 hour.
What is the best estimate for the total time Maria spent with her little sister?
Fill in the blanks with the options bellow please!
0 hours, 1/2 hours, 1 hour, 1 1/2 hours, 2 hours.
I have put question marks where the blanks are.
2/5 hour is closest to Response area. 5/8 hour is closest to Response area. Therefore, the best estimate for the total time Maria was with her sister is close to Response area.
Answer: The best estimate for 2/5 hour is 1/2 hour and the best estimate for 5/8 hour is 1/2 hour. So, the total time spent would be 1/2 hour + 1/2 hour = 1 hour.
Therefore, the best estimate for the total time Maria spent with her little sister is 1 hour.
Step-by-step explanation:
find the measure of the angles. please show process!
Answer:
1st question:
10°, 80°, 90°
2nd question:
76°, 52°, 52°
Step-by-step explanation:
For both of these questions we will use the idea that the three angles of a triangle add up to 180°.
In the triangle on the left, two angles are marked and the third is a right angle. The tiny square marking on the third angle means it is a right angle, so it is 90°.
We can write an equation.
x + 8x + 90° = 180°
combine like terms
9x + 90 = 180
subtract 90
9x = 90
divide by 9
x = 10
So the angles are x, 8x and 90°
Since x = 10
the 3 angles are 10°, 80° and 90°
For the second question, two sides are marked to show they are congruent (same, equal) that means the two angles on the base (base angles) are congruent (the same)
One angle is 3x+1 and both the other two angles are 2x+2. Write an equation.
3x+1 + 2x+2 + 2x+2 = 180°
combine like terms
7x + 5 = 180
subtract 5
7x = 175
divide by 7
x = 25
Calculate the angle measures using x = 25
3x+1 = 3(25)+1 = 76°
2x+2 = 2(25)+2 = 52°
The 3 angles of the triangle are 76°, 52° and 52°
he figure shows triangle DEF and line segment BC, which is parallel to EF:
Triangle DEF has a point B on side DE and point C on side DF. The line BC is parallel to the line EF.
Part A: Is triangle DEF similar to triangle DBC? Explain using what you know about triangle similarity. (5 points)
Part B: Which line segment on triangle DBC corresponds to line segment EF? Explain your answer. (3 points)
Part C: Which angle on triangle DBC corresponds to angle F? Explain your answer.
Therefore , the solution of the given problem of triangle comes out to be it shares an angle with triangle DEF that is equal in measure to angle F.
What does a triangle actually mean?If a triangle has four quadrants or more, it is referred to as a polygon. It has a straightforward rectangular shape. The letters ABC when combined form a right-angled triangular. A new parallelogram with rectangular shape corners is created by Euclidean geometry when the limits are incompatible. Due to their three edges but also three points, triangles are categorised as polygons. The location of a triangle's corners is determined by where its three edges meet. The sum of the angles on the inside of a trapezoid is 180.
Here,
Part A: To determine if triangle DEF is similar to triangle DBC, we need to check if their corresponding angles are equal in measure and if their corresponding sides are proportional. If both conditions are satisfied, the triangles are similar. Since BC is parallel to EF, we know that angle DBC and angle DEF are corresponding angles and are therefore equal in measure.
Part B: The line segment on triangle DBC that corresponds to line segment EF is the side opposite to angle DBC, which is segment DC. This is because segment DC is parallel to segment EF and shares an angle with triangle DEF that is equal in measure to angle DBC.
Part C: The corresponding angle to angle F in triangle DBC is angle BCD. This is because angle BCD is opposite to side BC, which is parallel to EF and shares an angle with triangle DEF that is equal in measure to angle F.
Therefore , the solution of the given problem of triangle comes out to be it shares an angle with triangle DEF that is equal in measure to angle F.
To know more about triangle visit:
https://brainly.com/question/2773823
#SPJ1
Carbon-141414 is an element which loses \dfrac{1}{10}
10
1
start fraction, 1, divided by, 10, end fraction of its mass every 871871871 years. The mass of a sample of carbon-141414 can be modeled by a function, MMM, which depends on its age, ttt (in years).
We measure that the initial mass of a sample of carbon-141414 is 960960960 grams.
Write a function that models the mass of the carbon-141414 sample remaining ttt years since the initial measurement.
The function that models the mass of the carbon-14 sample remaining {t} years since the initial measurement is → M{t} = 960 - 0.012t.
What are algebraic expressions?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 that Carbon-14 is an element which loses (1/10) of its mass every 871 years. The initial mass of a sample of Carbon-14 is 960 grams. The mass of a sample of carbon-14 can be modeled by a function {M} which depends on its age {t} (in years).
(1/10) x 96 = 96/10 = 9.6 grams.
Carbon - 14 looses 9.6 grams in 871 years.
In 1 year, Carbon - 14 will loose (9.6/871) = 0.012 gram.
We can write the function {M} as -
M{t} = 960 - 0.012t
Therefore, the function that models the mass of the carbon-14 sample remaining {t} years since the initial measurement is → M{t} = 960 - 0.012t.
To solve more questions on functions, visit the link below-
brainly.com/question/17613163
#SPJ1
The distance between earth and one of the brightest stars in the night sky is 33.7 light-years. one light-year is 6,000,000,000,000 [6 trillion] miles , find the distance between the earth and the star in miles. write answer in scientific notation.
Answer: To find the distance between Earth and the star in miles, we need to multiply the number of light-years by the number of miles in a light-year.
33.7 light-years * 6,000,000,000,000 miles/light-year = 2.022 x 10^17 miles
So, the distance between Earth and the star is approximately 2.022 x 10^17 miles, written in scientific notation.
Step-by-step explanation:
complete the following program to implement the user interface of the preceding exercise. for simplicity, only the units cm, m, and in are supported.
This program implements a user interface that can convert between the units centimeters (cm), meters (m), and inches (in) using the conversion formulas outlined.
#include <iostream>
using namespace std;
int main()
{
// Declare variables
double value;
char fromUnit;
char toUnit;
// Get input
cout << "Enter a value and the units you wish to convert from and to (cm, m, in): ";
cin >> value >> fromUnit >> toUnit;
// Convert the value
if (fromUnit == 'm' && toUnit == 'cm') {
value *= 100;
} else if (fromUnit == 'cm' && toUnit == 'm') {
value /= 100;
} else if (fromUnit == 'in' && toUnit == 'm') {
value /= 100 * 2.54;
} else if (fromUnit == 'm' && toUnit == 'in') {
value *= 100 * 2.54;
}
// Output the result
cout << "Result: " << value << toUnit << endl;
return 0;
}
The formula used in this program is the conversion between the units centimeters (cm), meters (m), and inches (in). The conversion formula used is as follows:
1 meter (m) = 100 centimeters (cm)
1 inch (in) = 2.54 centimeters (cm)
Therefore, if we are converting from centimeters (cm) to meters (m), the conversion formula is to divide the value by 100. If we are converting from meters (m) to centimeters (cm), the conversion formula is to multiply the value by 100. For the conversion from inches (in) to meters (m), the conversion formula is to divide the value by 100 and multiply it by 2.54. For the conversion from meters (m) to inches (in), the conversion formula is to multiply the value by 100 and divide it by 2.54.
For example, if we want to convert 5 meters (m) to centimeters (cm), we use the formula 5 * 100 = 500 centimeters (cm).
This program implements a user interface that can convert between the units centimeters (cm), meters (m), and inches (in) using the conversion formulas outlined above.
Learn more about conversion formula here:
https://brainly.com/question/29634168
#SPJ4
Out of 10,551 passing attempts, Drew Brees
completed 7,142
What is the completion percentage for
Drew Brees? Show or explain how you got
your answer.
Answer: 67.69%
Step-by-step explanation:
To calculate the completion percentage,
Divide the completed passes by the total passing attempts.
> 7142/10551
Then, multiply that answer by 100 to get the percentage.
> 67.69%
The researcher who conducted the study discovered that the number of hours spent studying reported by the student represented by P was recorded incorreetly. The corrected data point for this student is represented by the letter Q in the scatterplot below. Explain how the least squares regression line for the corrected data (in this part) would differ from the least squares regression line for the original data
The least squares regression line for the corrected data would be shifted upwards compared to the original data, indicating that increasing the amount of time spent studying would likely have a greater impact on a student's grades.
The least squares regression line for the corrected data would be shifted upwards compared to the least squares regression line for the original data, since the corrected data point has a higher value than the original data point. This shift in the regression line would indicate that, in general, increasing the amount of time spent studying would have a greater impact on the student's grades than the original data indicated.
The least squares regression line for the corrected data would be shifted upwards compared to the original data, indicating that increasing the amount of time spent studying would likely have a greater impact on a student's grades.
Learn more about data here
https://brainly.com/question/14893265
#SPJ4
Find the exact value of cos N in simplest radical form.
the simplest radical form of the exact value of cos A will be 7/8.
What is the right-angle triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
Given a right-angle triangle that has a base of 14 height of √60 and a hypotenuse of 16.
From the general formula of cosine in a right-angle triangle:
Cos α = base/ hypotaneuse
In our case,
base = 14 and
hypotenuse = 16
Thus,
Cos A = 14/16
A = 0.5053 radians
Therefore, the simplest radical form of the exact value of cos A will be 7/8.
Learn more about right-angle triangles here:
https://brainly.com/question/3770177
#SPJ1
Complete question:
Simplify. (5 × 10^6) ÷ (1 × 10^3) Give the answer in scientific notation.
Answer:
5 x 10^9
Step-by-step explanation:
= ( 5x1) X (10^(6+3) ) = 5 x 10^9
ABCD rectangle HELPP!
The equation of line M is given by y = 3x + 6 , where the slope is m = 3
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
x + 3y = 18 be equation (1)
when x = 0 , y = 6
So , one point is P ( 0 , 6 )
Now , the line L has the points A , E and B
where ABCD is a rectangle , so AD is perpendicular to the line L
So , the product of slopes of the perpendicular line will be = -1
On simplifying the equation (1) , we get
Subtracting x on both sides of the equation , we get
3y = -x + 18
Divide by 3 on both sides of the equation , we get
y = -( 1/3 )x + 6
Substituting the values in the equation , we get
Slope of line L x Slope if line M = -1
The slope of line L = -1/3
So , the slope of line M = 3
Now , the equation of line L is given by
y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 6 = 3 ( x - 0 )
y - 6 = 3x
Adding 6 on both sides of the equation , we get
y = 3x + 6
Hence , the equation of line is y = 3x + 6
To learn more about equation of line click :
https://brainly.com/question/14200719
#SPJ1
Both circles have the same center. The circumference of the inner circle is 31.4 miles. What is the area of the shaded region?
The radius of the inner and outer circles is 5 miles and 10 miles. Then the area of the shaded region will be 235.5 square miles.
What is the area of the circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let r be the radius of the circle. Then the area of the circle will be
A = πr² square units
Both circles have the same center. The circumference of the inner circle is 31.4 miles. Then the radius of the inner circle is given as,
2πr = C
2 x 3.14 x r = 31.4
r = 5 miles
Then the ratio of the outer circle to the inner circle is 2. Then the radius of the outer circle is given as,
R/r = 2
R / 5 = 2
R = 10 miles
The area of the shaded region is given as,
A = πR² - πr²
A = 3.14 x 10² - 3.14 x 5²
A = 3.14 x (100 - 25)
A = 3.14 x 75
A = 235.50 square miles
The area is 235.50 square miles.
More about the area of a circle link is given below.
https://brainly.com/question/11952845
#SPJ1