The given system of equation can be solved if x = 2/3 and y = -4/3.
So we need to find another system which can be solved by these values.
From the given 4 options lets find out which can be solved by x = 3/2 and y = -4/3
1.
y = -2y^2 -2 , x = y - 2
lets put the value of y here
y = -2(16/9)-2 = -32/9-2= -50/ 9
So not an equivalent equation.
2.
y = -2y^2 + 2 , x = y + 2
y = -2(16/9)+2=-32/9+2=-14/9
So not an equivalent system.
3.
y = -2y^2 - 8y - 8 , x = y + 2
y = -2(16/9)-8(-4/3)-8 = -32/9+32/3-8=64/9-8=-8/9
So not an equivalent system.
4.
y = -2y^2 + 8y - 8 , x = y -2
y = -2(16/9)+8(-4/3)-8=-32/9-32/3-8=-128/9-8=-22.22
So this is not an equivalent equation too
Answer:
C. [tex]\left \{ {{y=-2y^{2}-8y-8 } \atop {x=y+2}} \right.[/tex]
Step-by-step explanation:
Edge 2020
A club has 5 members. From these members, the position of president and Vice Presidents have to be filled. In how many different ways can these 2 positions be filled?
1,2
1,3
1,4
1,5
2,1
2,3
2,4
2,5
3,1
3,2
3,4
3,5
4,1
4,2
4,3
4,5
5,1
5,2
5,3
5,4
20 looks like the number.
Please Vote my answer brainliest. thanks!
If statement q is angles ABC and QRT are vertical angles then ~q is angles ABC and QRT are congruent
True or false?
Answer:
true
Step-by-step explanation:
vertical angles are congruent
Melissa’s family is driving out of state to her grandmother’s house. They know that it takes 20 gallons of gas to get there, and the cost of three gallons of gasoline is $10.50. How much should the family budget to make the one-way trip?
Answer:
$70
Step-by-step explanation:
10.50/ 3 = 3.5
3.5 times 20 =70
Simplify the expression given below.
1|2x^2-4x-2/x
Answer:
[tex]\large\boxed{D.\ \dfrac{-4x+9}{2x(x-2)}}[/tex]
Step-by-step explanation:
[tex]\dfrac{1}{2x^2-4x}-\dfrac{2}{x}=\dfrac{1}{2x(x-2)}-\dfrac{2}{x}=\dfrac{1}{2x(x-2)}-\dfrac{(2)(2)(x-2)}{2x(x-2)}\\\\=\dfrac{1-4(x-2)}{2x(x-2)}\qquad\text{use the distributive property}\\\\=\dfrac{1-4x+8}{2x(x-2)}=\dfrac{-4x+9}{2x(x-2)}[/tex]
Answer:
The correct option is D.
Step-by-step explanation:
Consider the provided expression.
[tex]\frac{1}{2x^2-4x}-\frac{2}{x}[/tex]
Now take the LCM of the denominator and solve the above expression as shown:
[tex]\frac{x-2(2x^2-4x)}{x(2x^2-4x)}[/tex]
[tex]\frac{x-4x^2+8x}{x(2x^2-4x)}[/tex]
[tex]\frac{9x-4x^2}{x(2x^2-4x)}[/tex]
Cancel out the x as it is common in numerator and denominator.
[tex]\frac{9-4x}{2x^2-4x}[/tex]
[tex]\frac{-4x+9}{2x(x-2)}[/tex]
Hence, the correct option is D.
The vertex form of the equation of a parabola is y=6(x-2)2-8. What is the standard form of the equation?
The answer is D!!!
y=6x^2-24x+16
Answer:
Option 4 - [tex]y=6x^2-24x+16[/tex]
Step-by-step explanation:
Given : The vertex form of the equation of a parabola is [tex]y=6(x-2)^2-8[/tex]
To find : What is the standard form of the equation?
Solution :
The vertex form of the equation of a parabola is [tex]y=6(x-2)^2-8[/tex]
We solve the equation to get standard form,
[tex]y=6(x^2-2^2-2(x)(2))-8[/tex]
[tex]y=6(x^2+4-4x)-8[/tex]
[tex]y=6x^2+24-24x-8[/tex]
[tex]y=6x^2-24x+16[/tex]
The standard form of the equation is [tex]y=6x^2-24x+16[/tex]
Therefore, Option 4 is correct.
20 PTS!! PLEASE HELP
Denise has conducted an observational study to learn about different influences that affect which colleges students choose to attend. Denise surveyed 400 students at her new college and found that 80% of the students chose their college based on a friend who also attends that college.
What conclusion can Denise make from her study?
A. There may be a link between knowing current students and choosing a college, and she can draw a cause-and-effect conclusion from an observational study.
B. There may be a link between knowing current students and choosing a college, but she cannot draw a cause-and-effect conclusion from an observational study.
C. Knowing a current student enrolled at a college causes incoming students to choose that college, but she cannot draw a cause-and-effect conclusion from an observational study.
D. Knowing a current student enrolled at a college causes incoming students to choose that college, and she can draw a cause-and-effect conclusion from an observational study.
Denise has conducted an observational study to learn about different influences that affect which colleges students choose to attend. Denise surveyed 400 students at her new college and found that 80% of the students chose their college based on a friend who also attends that college.
What conclusion can Denise make from her study?
A. There may be a link between knowing current students and choosing a college, and she can draw a cause-and-effect conclusion from an observational study.
B. There may be a link between knowing current students and choosing a college, but she cannot draw a cause-and-effect conclusion from an observational study.
C. Knowing a current student enrolled at a college causes incoming students to choose that college, but she cannot draw a cause-and-effect conclusion from an observational study.
D. Knowing a current student enrolled at a college causes incoming students to choose that college, and she can draw a cause-and-effect conclusion from an observational study.
The conclusion that Denise can make from her observational study is B. There may be a link between knowing current students and choosing a college.
What is an observational study?An observational study is a study that observes individuals and measures variables of interest but doesn't influence the responses.
In this case, Denise has conducted an observational study to learn about different influences that affect which colleges students choose to attend.
Here, the conclusion that Denise can make from her study is that there may be a link between knowing current students and choosing a college even though she cannot draw a cause-and-effect conclusion from the study.
Learn more about an observational study on:
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The first number of three consecutive even integers equals the sum of the second and third. Find the three numbers.
If x represents the smallest integer, then which of the following equations could be used to solve the problem?
Ox= 2x + 6
Ox= 2x + 3
2x + 2 = x + 4
Answer:
x=2x+6 is the equation that to solve for the smallest.
The three numbers are -6, -4 , and -2.
Step-by-step explanation:
Let x be the smallest of three consecutive even integers.
The next even integer would then have to be x+2 (because x+1 is odd if x is even).
The third one in this sequence would have to be x+4 (because x+3 is odd if x is even).
We are given the first of these numbers equals the sum of the second and third.
So we have x=(x+2)+(x+4).
Combine like terms on right hand side:
x=x+x+2+4
Simplify the combining:
x=2x+6
Subtract 2x on both sides:
x-2x=6
Simplify left hand side:
-x=6
Multiply both sides by -1:
x=-6
If x=-6, then the three mentioned numbers are:
x=-6
x+2=-6+2=-4
x+4=-6+4=-2
The three numbers are -6, -4 , and -2.
What is the solution to the equation 6x + 2 = 9x - 1
Answer:
X=1
Step-by-step explanation:
1. You subtract 6x with 9x so it should equal 2=3x-1
2.You add 1 to the 2 so it should be 3=3x
3.You divide 3 on both sides so it should be 3/3=3x/3
4.After you divide you finally get the answer 1=x or x=1
6x + 2 = 9x - 1
6x - 9x = - 1 - 2
-3x = -3
x = -3/-3
x = 1
Prove:
Let x = 1
6x + 2 = 9x - 1
6(1) + 2 = 9(1) - 1
6 + 2 = 9 - 1
8 = 8
It checks to be true.
The answer is x = 1.
What is the absolute value of I -32 I?
The absolute value of I-32I = 32
What is an absolute value of a number?"It is the distance of a number from zero, without considering direction.""It is always positive."For given question,
We need to find the absolute value of -32
We know that, for any number 'a',
the absolute value of a is |a| = a (positive value)
|-32| = 32
Therefore, the absolute value of I-32I = 32
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The two sides of the triangle are 6 cm and 12 cm and the included angle is 60°. What's the measure of the third side.
A. 6.7
B. 8.5
C. 10.4
D. 12 5
Answer:
C. 10,4
Step-by-step explanation:
Using the Law of Cosines [Solving for Angle Measures → cos<A = -a² + b² + c²\2bc, cos<B = a² - b² + c²\2ac, cos<C = a² + b² - c²\2ab; Solving for Sides → a² = b² + c² - 2bc cos<A, b² = c² + a² - 2ac cos<B, c² = b² + a² - 2ab cos<C], set up your triangle with your angles and sides OPPOSITE from each other.
Suggestion: make Side b 12 and Side a 6, leaving you with Side c to find. According to the problem and how you set up your triangle, <C can be 60°. This is how you should set it up:
c² = 36 + 144 - 144 cos 60°; 108 = c²
The reason being is because 6² is 36, 12² is 144, 2ab → 2[12][6] is 144, and cos 60° is ½. Putting this altogether will give you 108 = c². Obviously, the final step is to take the square root of 108, which rounded to the nearest tenth, is 10,4.
If you are ever in need of assistance, do not hesitate to let me know by subscribing to my channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.
**Whenever you are solving for an angle using the Law of Cosines, towards your final answer, use the cos⁻¹ function to cancel the cos to isolate your angle measure.
Final answer:
Using the law of cosines with the given sides 6 cm and 12 cm and included angle of 60 degrees, the length of the third side is approximately 10.4 cm, corresponding with answer choice C.
Explanation:
To calculate the length of the third side of a triangle when two sides and the included angle are known, we can use the law of cosines. The law of cosines states that c² = a² + b² - 2abcos(C), where a and b are the lengths of the sides, C is the included angle, and c is the length of the third side opposite to angle C.
In this question, we have been given two sides of lengths 6 cm and 12 cm with an included angle of 60 degrees. Plugging these values into the law of cosines formula, we get c² = 6² + 12² - [tex]2\(\cdot\)6\(\cdot\)12\(\cos(60^\circ)\)[/tex].
Since [tex]\(\cos(60^\circ)\)[/tex] equals 0.5, the calculation simplifies to c² = 36 + 144 - 72 = 108. Taking the square root of both sides, we find that c ≈ 10.4 cm, which aligns with answer choice C.
f(x) = 2x - 1
g(x) = 7x -12
what is h(x)=f(x)+g(x)?
A) h(x)=9x-13
B) h(x)=9x-12
C) h(x)=-5x+11
D) h(x)=5x-13
Answer:
A) h(x)=9x-13
Step-by-step explanation:
f(x) = 2x - 1
g(x) = 7x -12
Add them together
f(x) = 2x - 1
g(x) = 7x -12
-------------------------
f(x)+g(x) = 9x-13
h(x) = 9x-13
Answer:
A
Step-by-step explanation:
I took the test
35.6 = the square root of 15.3^2 + the square root of x^2. Find x.
Answer:
x = 50.9
Step-by-step explanation:
35.6 = √(15.3²) + √(x²)
35.6 = 15.3 + x
x = 35.6 + 15.3
x = 50.9
Which of the following expressions results in 0 when evaluated at x = 4?
O A. (x - 10)(x - 4)
OB. (x + 4)(x - 10)
O C.
(x + 6)(x - 2)
OD. 4x(x-6)
Answer:
A. (x - 10)(x - 4)
Step-by-step explanation:
The product is 0 if one of the factors is 0.
(4 - 10)(4 - 4)
= (4 - 10)*0
= 0
Answer:
A. (x - 10)(x - 4)
Step-by-step explanation:
Let x=4
O A. (4 - 10)(4 - 4) = -6 * 0 = 0
OB. (4 + 4)(4 - 10) = 8* -6 = -48
O C. (4 + 6)(4 - 2) = 10 * 2 = 20
OD. 4*4(4-6)=16*-2 = -32
A hot tub is 75 percent full with 600 gallons
of water. How many gallons of water are in
the hot tub when it's half full?
Answer:
When the hot tub is half full, there are 400 gallons of water in it.
Step-by-step explanation:
If 75% or 3/4 of the hot tub is 600 gallons and you need to find 50% or 1/2. Divide 600 by 3 to get 200 then simply multiply by 2 to get 400.
When the hot tub is half full, it would contain 400 gallons of water.
To find out how many gallons are in the hot tub when it's half full, calculate the total capacity of the hot tub using the information that 75% equals 600 gallons. Then, take 50% of that total capacity to find that when the hot tub is half full, it contains 400 gallons.
If a hot tub is 75 percent full with 600 gallons of water, that means the hot tub's total capacity when it's 100% full is larger than 600 gallons. To find out how many gallons are in the hot tub when it's half full, we must first determine the hot tub's total capacity. We can set up a proportion to find the total capacity (T) since 75% of T is 600 gallons.
75% of T = 600 gallons
0.75 imes T = 600 gallons
Now, to find the total capacity (T), divide both sides by 0.75:
T = 600 gallons / 0.75
T = 800 gallons
So, the hot tub's total capacity is 800 gallons. To find the amount of water when the hot tub is half full, simply take 50% of the total capacity:
50% of 800 gallons = 0.5 imes 800 gallons
50% of 800 gallons = 400 gallons
Therefore, when the hot tub is half full, it would contain 400 gallons of water.
The graph of the function f(x) is shown below.
What is x when f(x)=0?
-1.8
-1.2
0
5
Answer:
a -1.8
Step-by-step explanation:
f(x)=y=0
when y = 0, x=-1.8
Answer:
A. [tex]-1.8[/tex]
Step-by-step explanation:
We have been graph of a function. We are asked to find the value of x, when [tex]f(x)=0[/tex].
We know that [tex]f(x)=0[/tex] stands for x-intercept. [tex]f(x)[/tex] stands for value of y. We know that y is zero on x-axis.
Upon looking at our given graph, we can see that our function has only one x-intercept that is at point [tex](-1.8,0)[/tex].
This means that [tex]f(-1.8)=0[/tex], therefore, the value of x is [tex]-1.8[/tex] and option A is the correct choice.
What are the coordinates of the vertices of the image of rectangle WXYZ after the transformation Ro, 90•(x,y)? W’(-4,-1)
Answer:
W (-1, 4) ---> W' (-4, -1)
X (-1, 2) ---> X' (-2, -1)
Y (2, 2) ---> Y' (-2, 2)
Z (2, 4) ---> Z' (-4, 2)
Step-by-step explanation:
We have with a rectangular figure WXYZ and we are to find the coordinates of its vertices W'X'Y'Z' after the transformation of 90° rotation.
We know that, the rule for 90° rotation of a point (x, y) gives (-y, x).
So,
W (-1, 4) ---> W' (-4, -1)
X (-1, 2) ---> X' (-2, -1)
Y (2, 2) ---> Y' (-2, 2)
Z (2, 4) ---> Z' (-4, 2)
What value of x will make this proportion true 14/x=1/2?
Answer:
x = 28
Step-by-step explanation:
Given
[tex]\frac{14}{x}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
x = 14 × 2 = 28
Answer:
x = 7
Step-by-step explanation:
14 / x = 1 / 2
14 / x = 0.5
14 = x(0.5)
14 / 0.5 = x
7 = x
Hope this helps!
What is the area of Figure ABCD?
Answer:
66 in^2.
Step-by-step explanation:
We can use the formula for the area of a trapezoid:
Area = (h/2) (a + b) where h = the height and a and b are the lengths of the opposite parallel lines.
so the Area of ABCD = (6/2)*(10 + 12)
= 3 * 22
= 66 in^2.
For this case we have that the area of the figure is given by the sum of the area of a rectangle plus the area of a triangle.
By definition, the area of a reactangle is given by:
[tex]A = a * b[/tex]
Where:
a, b:they are the sides of the rectangle.
According to the figure we have:
[tex]a = 10\\b = 6[/tex]
Substituting we have:
[tex]A = 10 * 6\\A = 60[/tex]
Thus, the area of the rectangle is [tex]60in ^ 2[/tex]
On the other hand, the area of a triangle is given by:
[tex]A = \frac {b * h} {2}[/tex]
Where:
b is the base and h is the height of the triangle.
According to the figure we have to:
[tex]b = 12-10 = 2\\h = 6[/tex]
Substituting in the formula:
[tex]A = \frac {2 * 6} {2} = \frac {12} {2} = 6[/tex]
Thus, the area of the rectangle is[tex]6in ^ 2[/tex]
Then, the total area of the figure is:
[tex]A_ {T} = 60in ^ 2 +6in ^ 2 = 66 \ in ^ 2[/tex]
Answer:
[tex]66 \ in ^ 2[/tex]
For his phone service, Justin pays a monthly fee of $24, and he pays an additional $0.06 per minute of use. The least he has been charged in a month is $113.28.
What are the possible numbers of minutes he has used his phone in a month?
Use m for the number of minutes, and solve your inequality for m.
M= 1488
This is how many number of minutes Justin has used his phone in a month.
I solved this by first subtracting 24 from 113.28, which is 89.28.
Next I knew multiplication would have to be involved.
I had to figure out 0.06 times what equals 89.28.
Well that would be 1488.
Please Vote my answer brainliest. thanks!
Based on the given monthly fee and per-minute charge for Justin's phone, if the minimum monthly charge is $113.28, this indicates that he has used his phone for at least 1488 minutes in that month.
Explanation:To solve this question, we can start by setting up an inequality because we want to find the possible numbers of minutes Justin can use his phone. Given that Justin pays a monthly fee of $24 and $0.06 per minute of use, the total charge (T) in a month is given by the equation:
T = 24 + 0.06m
It is stated that the least he has been charged in a month is $113.28. To find the possible number of minutes, we need to solve this inequality for m:
113.28 <= 24 + 0.06m
If we subtract $24 from each side, it becomes:
89.28 <= 0.06m
Then by dividing each side by 0.06, we get:
m >= 1488
So, Justin has used his phone for at least 1488 minutes in a month.
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describe the graph of the equation y=0. is the equation a function
Answer:
The function is defined along the x-axis. Yes the equations y = 0 is a function
Step-by-step explanation:
It means that y is 0 in all values of x
The graph y = 0 would be a horizontal line that overlaps the x-axis. This would be a function because the y-value (zero) never has the same x-value. This means that it would pass the vertical line test since the graph would only pass through it once.
Hope this helped!
~Just a girl in love with Shawn Mendes
i dont understand this can someone please help me.
Answer:
Difference = 2.25°
Step-by-step explanation:
Here we are given that at depth the Temperature T is inversely proportional to the depth x.
[tex]T[/tex] ∝ [tex]\frac{1}{x}[/tex]
[tex]T= 4500 \times \frac{1}{x}[/tex]
Where 4500 is constant
Now we have to find the difference in the temperature at 1200 mts and 3750 mts
1. x=1200
[tex]T= 4500 \times \frac{1}{x}[/tex]
[tex]T= 4500 \times \frac{1}{1200}[/tex]
[tex]T= 3.75[/tex]
2. x=3750
[tex]T= 4500 \times \frac{1}{x}[/tex]
[tex]T= 4500 \times \frac{1}{3750}[/tex]
[tex]T=1.2[/tex]
Hence Difference is
T = 3.75 -1.20
= 2.25
Therefore The difference of the temperature at 1200 mts and 3750 mts is T=2.25°
A square has a perimeter of 296 millimeters. What is the length of each side?
Answer:
74mm
Step-by-step explanation:
296 divided by 4 sides is 74 mm each side
Gray looks up the definition of point. A point is a location in a region. What is true about the statement describing the word point?
Answer:
Definition of Point by Gray:
A point is a location in a region.
→A point is smallest and simplest representation of any location or any thing or an object in two, three, or n-dimensional plane.
This can be explained in following way.
For a large enclosed room , Lighting a small bulb will represent a point.Similarly , stars in the sky appear as a point with respect to earth.Sun in the Universe can be called as a point.
Answer:
A
Step-by-step explanation:
The statement uses the terms location and region that are defined based on an understanding of a point.
Brainliest Please
Have a nice day *smiley face emoji
Multiply (6 + 2i)(6 – 2i)
O 32
O 40
O 36 + 12i
O 36 - 12i
Answer:
40
Step-by-step explanation:
6*6/6*-2i/2i*6/2i*-2i
Answer:
40
Step-by-step explanation:
Select the two values of x that are roots of this equation.
2x-5=-3x^2
A. x= 3
B. X=1
C. x=-5/3
D. x=-1/2
Answer:
[tex]\large\boxed{B.\ x=1,\ C.\ x=-\dfrac{5}{3}}[/tex]
Step-by-step explanation:
[tex]2x-5=-3x^2\qquad\text{add}\ 3x^2\ \text{to both sides}\\\\3x^2+2x-5=0\\\\3x^2+5x-3x-5=0\\\\x(3x+5)-1(3x+5)=0\\\\(3x+5)(x-1)=0\iff3x+5=0\ \vee\ x-1=0\\\\3x+5=0\qquad\text{subtract 5 from both sides}\\3x=-5\qquad\text{divide both sides by 3}\\x=-\dfrac{5}{3}\\\\x-1=0\qquad\text{add 1 to both sides}\\x=1[/tex]
which of the following is the correct graph of the linear equation below?
y+2=1/5(x-1) giving brainlest answer
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y+2=\frac{1}{5}(x-1)[/tex]
This is the equation of the line into point slope form
The point is (1,-2) and the slope is m=1/5
we know that
To correctly identify the graph find out the x and y intercepts of the graph
Find the y-intercept
The y-intercept is the value of y when the value of x is equal to zero
For x=0
[tex]y+2=\frac{1}{5}(0-1)[/tex]
[tex]y=-\frac{1}{5}-2[/tex]
[tex]y=-\frac{11}{5}=-2.2[/tex]
The y-intercept is the point (0,-2.2)
Find the x-intercept
The x-intercept is the value of x when the value of y is equal to zero
For y=0
[tex]0+2=\frac{1}{5}(x-1)[/tex]
[tex]10=x-1[/tex]
[tex]x=11[/tex]
The x-intercept is the point (11,0)
To graph the line plot the intercepts and join the points
see the attached figure
Which of these is a point-slope equation of the line that is perpendicular to
y-3 = 4(x-10) and passes through (-3, 7)?
A. y-7 = -4(x + 3)
B. y+7= -1/4(x-3)
C. y+ 7 = 4(x - 3)
D.y-7=-1/4(x+3)
Answer:
D
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
y - 3 = 4(x - 10) ← is in point- slope form
with slope m = 4
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{4}[/tex]
The perpendicular line passes through (- 3, 7), hence
y - 7 = - [tex]\frac{1}{4}[/tex](x - (- 3)), that is
y - 7 = - [tex]\frac{1}{4}[/tex](x + 3) → D
Fill in the other coordinate line y=7/2x+6:(8,)
Answer:
The other coordinate for the given equation is 34.
Step-by-step explanation:
We are given the following equation and we are to fin the value of the y coordinate given that the value of the x coordinate is [tex] 8 [/tex]:
[tex] y = \frac { 7 } { 2 x + 6 } [/tex]
Substituting the given value of x in the above equation to find y:
[tex]y = \frac { 7 } { 2 } ( 8 ) + 6 [/tex]
y = 34
(8, 34)
About 50% of 5500 commuters carpool to work. Find the number of commuters who carpool
How many commuters carpool?
Answer:
2750
Step-by-step explanation:
5500 ÷ 2 (multiplying by 50% is the same as dividing by 2)= 2750
50% of 5500 commuters is calculated as 2750. Hence, 2750 commuters carpool to work.
Explanation:To find the number of commuters who carpool, we'll use a very basic principle in mathematics: percentage calculation. The problem states that 50% of the 5500 commuters carpool to work. To find the number of commuters carpooling, we multiply the total number of commuters by the percentage of those who carpool. In mathematical terms, it looks like this:(50/100) * 5500 = 2750. Therefore, 2750 commuters carpool to work.
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What is the slope of a line that is parallel to the line whose equation is y= 4/5x−3 ?
Answer:
A line parallel to this line will have slope 4/5.
Step-by-step explanation:
2 parallel lines will have the same slope.
y = mx + c is the general form of the slope-intercept formula of a line, the slope is given by m.
y = 4/5 x - 3
-we see by comparing the 2 equations that the slope of this line (m) is 4/5.
Final answer:
The slope of a line parallel to the one given by the equation y = 4/5x - 3 is 4/5. This maintains the definition that parallel lines have identical slopes.
Explanation:
The slope of a line that is parallel to the line represented by the equation y = 4/5x - 3 is 4/5. This is because parallel lines have the same slope. In the context of algebra and straight lines, the slope of a line is a measure of its steepness, commonly identified as 'm' in the slope-intercept form y = mx + b, where 'b' is the y-intercept. Each of the provided figures and examples illustrate that the slope of a straight line remains constant regardless of other changes.
Looking specifically at the equation y = 4/5x - 3, this is in slope-intercept form where the coefficient of 'x' is the slope, which is 4/5. Therefore, any parallel line would have the same slope of 4/5.