Answer:
r and s are parellel
Step-by-step explanation:
The correct answer is that lines 4 and 5 are parallel if [tex]\( m_4 = m_5 \).[/tex]
To justify this answer, we must understand the concept of slope in the context of lines in a plane. The slope of a line, denoted by m is a measure of its steepness and is defined as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. Mathematically, if two points on a line have coordinates [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \),[/tex] then the slope m is given by: [tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex] For two lines to be parallel, they must have the same slope. This is because parallel lines have the same steepness and never intersect. Therefore, if the slope of line 4, [tex]\( m_4 \)[/tex], is equal to the slope of line 5, [tex]\( m_5 \)[/tex], then lines 4 and 5 are parallel. In mathematical notation, if [tex]\( m_4 = m_5 \),[/tex] then line 4 and line 5 are parallel, which can be written as: [tex]\[ m_4 = m_5 \Rightarrow \text{Line 4} \parallel \text{Line 5} \][/tex] This conclusion is based on the fundamental properties of slopes and parallel lines in Euclidean geometry. If the slopes of two lines are equal, it means that they rise and run at the same rate, and thus, they will maintain a constant distance from each other, never intersecting, which is the definition of parallel lines.
Compare 0.409 and 0.490 with >,<,=
An increase in total assets can be financed by an increase in which of the following capital components:
a. debt
b. preferred stock
c. common equity
d. All of the above ...?
"Find the value of the derivative (if it exists) at each indicated extremum. (If an answer does not exist, enter DNE.)
f (x) = cos(πx/2)
Answer: The derivate is f'(x) = -sin(πx/2)*(π/2)
Step-by-step explanation:
We want the value of the derivate at each point marked:
As you may know, the derivate of cos(x) is equal to -sin(x)
And in our case:
f(x) = cos(πx/2)
f'(x) = -sin(πx/2)*(π/2)
Where the rule used is that the derivate of f(g(x)) is equal to f'(g(x))*g'(x)
Now, as you may see, in both the marked points the curve changes of direction, so the tangent line in that point must be zero, letsinput the values of x in the derivate and see if this is true:
f'(0) = -sin(π*0/2)*(π/2) = -sin(0)*(π/2) = 0
f'(2) = -sin(π*2/2)*(π/2) = -sin(π)*(π/2) = 0
So this makes sense.
For a $1,000 loan at a rate of 16 3/4 % for 5 years, the simple interest is a. $83.75
b. $167.50
c. $500.00
d. $837.50
How to know if true or false?? HELP ASAP thank you!
picture added.
A jug of juice holds 8 cups. convert 8 cups to pints
8 cups convert to pints = 4 pints
Further explanation7 main quantities have been determined based on international standards, namely:
1. Length, meters (m)2. Time, second (s)3. Mass, kilograms (kg)4. Temperature, kelvin (K)5. Light intensity, candela (cd)6. Electric current, ampere (A)7. Amount of substance, mol (m)Volume is a derivative quantity derived from the length
The unit of volume can be expressed in liters or milliliters or cubic meters
The conversion is
1 cc = 1 cm³
1 dm = 1 Liter
1 mL = 1 cm³
1 L = 1 dm³
The other common units for US standart volume are :
Fluid OuncesCupsPintsQuartsGallonsThe conversion for all those units :
1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces
The conversion for pints and cups :
[tex]\large{\boxed{1\:pints=2\:cups}}}[/tex]
A jug of juice holds 8 cups
so 8 cups = 8 : 2 pints
8 cups = 4 pints
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Keywords: volume,pints, cups, a jug, juice
3^x : write in terms of base e and simplify! ...?
Three water pipes are used to fill a swimming pool. The 1st pipe alone takes 8 hours to fill the pool, the 2nd pipe alone takes 12 hours to fill the pool, and the 3rd pipe takes 24 hours to fill the pool. If all 3 pipes are opened at the same time, how long will it take all 3 together to fill the pool?
If 6 is 24% of a number, what is 40% of the same number?
(A) 8
(B) 10
(C) 15
(D) 20
To find 40% of the number where 6 is 24%, we first determine the whole number by dividing 6 by 0.24 to get 25. Then we calculate 40% of 25, which is 10.
If we know that 6 is 24% of a number, we can find the whole number by dividing 6 by 0.24. Once we have the full number, we can calculate 40% of it. Let's do the calculation step by step.
Calculate the whole number using the given percentage: Whole number = 6 / 0.24.
Perform the division to find the whole number: Whole number = 25.
Calculate 40% of the whole number: 40% of 25 = 0.40 * 25.
Perform the multiplication to find 40% of the number: 40% of 25 = 10.
Therefore, 40% of the same number is 10.
for the parallelogram, if m<2+5x-28 abd m<4=3x-10, find m< 3. ...?
Final answer:
After finding the value of x by equating m<2 and m<4, we calculate m<4 and then use the property of supplementary angles in a parallelogram to find that m<3 is 163 degrees.
Explanation:
To solve for m<3 in the parallelogram with m<2 = 5x - 28 and m<4 = 3x - 10, we first find the value of x. Given that opposite angles in a parallelogram are equal (m<2 = m<4), we set the two equations equal to each other and solve for x:
5x - 28 = 3x - 10
5x - 3x = 18
2x = 18
x = 9
Now that we have the value of x, we can substitute it into the equation for either angle to find the measure of that angle. Since m<4 = 3x - 10:
m<4 = 3(9) - 10 = 27 - 10 = 17
In a parallelogram, adjacent angles are supplementary, meaning they add up to 180 degrees. Therefore, to find m<3, we subtract m<4 from 180 degrees:
m<3 = 180 - m<4
m<3 = 180 - 17 = 163
Thus, m<3 in the parallelogram is 163 degrees.
The measure of angle 3 in the parallelogram is [tex]\( m\angle 3 = 2x - 18 \).[/tex]
Explanation:In a parallelogram, opposite angles are equal. Therefore, we can set up an equation based on the given angle measures:
[tex]\[ m\angle 2 + m\angle 3 = 180^\circ \][/tex]
Substitute the given expressions for[tex]\( m\angle 2 \) and \( m\angle 4 \):[/tex]
[tex]\[ (2 + 5x - 28) + (3x - 10) = 180 \][/tex]
Combine like terms:
[tex]\[ 5x + 3x - 28 - 10 + 2 = 180 \][/tex]
[tex]\[ 8x - 36 = 180 \][/tex]
Add 36 to both sides:
[tex]\[ 8x = 216 \][/tex]
Divide by 8:
[tex]\[ x = 27 \][/tex]
Now that we have the value for x, substitute it into the expression for \( [tex]m\angle 3 \):[/tex]
[tex]\[ m\angle 3 = 2(27) - 18 \][/tex]
[tex]\[ m\angle 3 = 54 - 18 \][/tex]
[tex]\[ m\angle 3 = 36 \][/tex]
Therefore, the measure of angle 3 in the parallelogram is [tex]\( m\angle 3 = 36^\circ \).[/tex]
Solve the inequality.
p – 9 < –9
4x^2+4y^2=64
what are the domain and range
An electrician charges a $50 house call fee and $65 per hour for the work. Which algebraic expression represents this situation to represent the total cost for h hours of work?
The algebraic expression is Total Cost = 65h + 50.
Explanation:To represent the total cost for h hours of work, we need to consider the house call fee of $50 and the hourly rate of $65. The total cost will depend on the number of hours worked.
We can calculate the total cost using the expression: Total Cost = (Hourly Rate * Number of Hours) + House Call Fee.
Therefore, the algebraic expression that represents this situation is: Total Cost = 65h + 50.
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Perform the operations, multiply, and simplify.-a^3b (3a^2 b^5 - ab^4 - 7a ^2
b.
The folding chair has different settings that change the angles formed by its parts. Suppose m2 is 34 and m3 is 76. Find m1The diagram is not to scale.
A. 130
B. 110
C. 100
D. 120
A box has a width 9 inches less than its height and a length 7 inches more than its height.
a. If h is the height of the box, write a polynomial that represents the volume of the box.
b. Use this polynomial to calculate the volume for h = 17 inches.
what is the answer to n * $3.25 = 325.00 ?
solve for x. round to nearest tenth if needed.
1. 7r-7=2r+18
a.r=-5
b.r=5
c.r=2.2
d.r=1.2
2. 2x+12=18-x
a.x=3
b.x=10
c.x=6
d.x=2
3. 8x-3=15x+18
a.x=-3
b.x=3
c.x=2.1
d.x=0.9
4. 6y-6=4y+16
a.y=2.2
b.y=-2.2
c.y=11
d.y=5
5. 3(x-4)=5(x+2)
a.x=11
b.x=-11
c.x=1
d.x=-1
On solving the linear equations given, we get the values as 5, 2, -3, 11 and -11 for the equations 7r - 7 = 2r + 18, 2x + 12 = 18 - x, 8x - 3 = 15x + 18, 6y - 6 = 4y + 16 and 3(x - 4) = 5(x + 2) respectively.
What is Linear Equation?Linear equations are equations which includes one or more variables and constants with the highest degree of the variable being 1.
1. 7r - 7 = 2r + 18
Taking the variables on one side and constants on the other side,
7r - 2r = 18 + 7
5r = 25
r = 5
2. 2x + 12 = 18 - x
2x + x = 18 - 12
3x = 6
x = 2
3. 8x - 3 = 15x + 18
8x - 15x = 18 + 3
-7x = 21
x = -3
4. 6y - 6 = 4y + 16
6y - 4y = 16 + 6
2y = 22
y = 11
5. 3(x - 4) = 5(x + 2)
Multiplying each term inside the bracket by the term outside,
3x - 12 = 5x + 10
3x - 5x = 10 + 12
-2x = 22
x = -11
Hence we got the values of the unknowns as 5, 2, -3, 11 and -11 for the equations 7r - 7 = 2r + 18, 2x + 12 = 18 - x, 8x - 3 = 15x + 18, 6y - 6 = 4y + 16 and 3(x - 4) = 5(x + 2) respectively.
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If you subtract the death rate from the birth rate of a population, you will calculate what?
A. the arithmetic growth rate.
B. the expansion rate.
C. the carrying capacity.
D. the intrinsic growth rate.
Subtracting the death rate from the birth rate of a population calculates its intrinsic growth rate, expressed as dN = (b - d)N, where 'r' is the intrinsic rate of increase.
When you subtract the death rate (D) from the birth rate (B) of a population, you calculate the intrinsic growth rate of the population. The birth rate is typically expressed on a per capita basis, shown as B = bN, where 'b' represents the per capita birth rate and 'N' is the number of individuals in the population. Similarly, the death rate is expressed as D = dN, where 'd' is the per capita death rate. To find the population growth rate at a specific point in time, differential calculus is used to obtain an instant-specific measurement:
dN = (b - d)N
This formula simplifies the relationship between the birth and death rates, where 'b - d' is substituted with 'r', representing the intrinsic rate of increase. Therefore, the correct answer to the student's question is D. the intrinsic growth rate.
What is the inverse of f(x)=-3x^3 6?
When you multiply or divide an inequality by a ______ number, you must flip the inequality symbol.
name all opisties of -12
Write a proportion that can be used to find the cost of 10 notebooks if 3 notebooks cost $1.98.
Which answer describes the type of sequence?
1, 6, 7, 13, ...
A. geometric
B. neither arithmetic nor geometric
C. arithmetic
b: neither arithmetic nor geometric
The given sequence describes the type of sequence that is neither arithmetic nor geometric. which is the correct answer would be an option (B).
What is an arithmetic sequence?An arithmetic sequence is defined as an arrangement of numbers that is a particular order.
The sequence is given in the question following as:
1, 6, 7, 13, ...
We have to identify the type of given sequence
As per the given question, we have
1, 6, 7, 13, ...
For checking as an arithmetic sequence :
Common difference between 1 and 6 is d = 6 - 1 = 5
Common difference between 6 and 7 is d = 7 - 6 = 1
Since the common difference between consecutive terms is not the same, this means it's not an arithmetic sequence.
For checking as a geometric sequence :
Common ratio between 1 and 6 is r = 6/1 = 6
Common ratio between 6 and 7 is r = 7/6
Since the common ratio between consecutive terms is not the same, this means it's not a geometric sequence
Thus, the given sequence describes the type of sequence that is neither arithmetic nor geometric.
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If M(-8, 12) is the midpoint of segment PQ, and P(8, 0), find the coordinates of Q.
Transform the formula for the given variable: I=Prt solve for t
Solve 16 1/2 ÷ 2 1/4
A:7 1/3
B:5 3/7
C:133/8
find the missing angle of the triangle.
your weekly wage is $400 what is your annual?
can u show work 39472/78 ...?