Answer:
Question 1) Option C: 2(2x+1) = y, y = 2x + 8.
Question 4) Option C: y = x + 4, 2y = 2x + 8
Step-by-step explanation:
Definitions:Perpendicular LinesThe graph of perpendicular lines will show an intersection of two lines at a single point, forming 90° adjacent angles. Since perpendicular lines intersect at exactly one point, then it means that they will have one solution. Additionally, perpendicular lines have negative reciprocal slopes for which multiplying the slopes of both lines result in a product of -1.
Coinciding LinesLines that have the same slope and y-intercept. Therefore, they are equivalent equations that will result in an infinitely many solutions. The graph of these lines will coincide on top of each other, as if they are the same line. The systems of linear equations that result in an infinitely many solutions are dependent and consistent. They are dependent if they have an infinite number of solutions, and consistent because they have at least one solution.
Parallel linesParallel lines have the same slope. A systems of linear equations whose graph involve parallel lines have no solution, as there is no point of intersection between those two lines. Therefore, parallel lines have no solution, making it an inconsistent system.
Question 1:We must transform these equations in its slope-intercept form, y = mx + b, which will allow us to easily determine the type of lines a given system has based on their slopes.
Option A:Equation 1: 2x + y = 10
Equation 2: y = −2x + 8
Transform Equation 1 to slope-intercept form:
2x + y = 10
Subtract 2x from both sides:
2x - 2x + y = - 2x + 10
y = -2x + 10 ⇒ This is the slope-intercept form of Equation 1.
Since Equations 1 and 2 have the same slope, but different y-intercepts, then it means that they are parallel lines that have no point of intersection.
Option B:
Transform both equations to slope-intercept form:
Equation 1: 2x + 4y = 10
[tex]\large\bf\sf{y\:=\:-\frac{1}{2}x\:+\:\frac{5}{2}}[/tex] ⇒ This is the slope-intercept form of Equation 1.
Equation 2: 2(x+2y) = 10
Distribute 2 into the parenthesis:
2(x+2y) = 10
2x + 4y = 10 ⇒ It is clear at this point that this equation matches Equation 1. Thus, the slope-intercept form of Equation 2 will be the same:
[tex]\large\bf\sf{y\:=\:-\frac{1}{2}x\:+\:\frac{5}{2}}[/tex] ⇒ Slope-intercept form of Equation 2.
It turns out that Equations 1 and 2 are equivalent, as they have exactly the same slope and y-intercept. Therefore, they have coinciding lines and have infinitely many solutions.
Option C:Transform both equations to slope-intercept form:
Equation 1: 2(2x+1) = y
y = 4x + 2 ⇒ Slope-intercept form of Equation 1.
Equation 2: y = 2x + 8
Option D:Equation 1: y = 10 − 2x
y = − 2x + 10 ⇒ This is the slope-intercept form of Equation 1.
Equation 2: y = −2x + 7
Since Equations 1 and 2 have the same slope, but different y-intercept, then it means that they are parallel from each other.
Answer for Question 1:Out of all the given four options, Option C seems to be the correct answer, since the given system has varying slopes and y-intercept. Therefore, the correct answer for Question 1 is Option C: 2(2x+1) = y, y = 2x + 8.
Question 4:For Question 4, I will not elaborate as thoroughly as in Question 1 since I'll be using the same techniques.
Option A)Equation 1: 2x+ 7x + y = 6
Combine like terms:
2x+ 7x + y = 6
9x + y = 6
Subtract 9x from both sides:
9x - 9x + y = - 9x + 6
y = - 9x + 6 ⇒ Slope-intercept form of Equation 1.
Equation 2: y = 9x + 6
Option A Explanation:
Equations 1 and 2 have different slopes and the same y-intercept. This implies that they will have a point of intersection = one solution. However, they don't have perpendicular lines because their slopes are not negative reciprocal of each other. Hence, Option A is not a valid answer for question 4.
Option B)Equation 1: y = 5x + 7
Equation 2: y = 2x + 8
Option B explanation:
Similar to Option A, Equations 1 and 2 have different slopes and varying y-intercepts. Since they are not parallel from each other, and do not have coinciding lines, then Option B is not a valid answer for question 4.
Option C)Equation 1: y = x + 4
Equation 2: 2y = 2x + 8
Transform Equation 2 to Slope-intercept form:
Divide both sides by 2 to isolate y:
[tex]\displaytext\mathsf{\frac{2y}{2}\:=\:\frac{2x\:+\:8}{2}}[/tex]
y = x + 4 ⇒ This is the slope-intercept form of Equation 2.
Option C explanation:
Equations 1 and 2 are equivalent, as they have exactly the same slope and y-intercept. They also have coinciding lines, having infinitely many solutions.
Therefore, Option C is the correct answer for Question 4.Option D)
Equation 1: 7x − y = 10
y = 7x - 10 ⇒ This is the slope-intercept form of Equation 1.
Equation 2: y = 6x + 8
Option D explanation:
Similar to Option B, Equations 1 and 2 have different slopes and varying y-intercepts. Since they are not parallel from each other, and do not have coinciding lines, then Option D is not a valid answer for question 4.
1) If v2x - 4 = 13x – 8, what is the value of x?
A) 1.
B) 2
4
D) 8
Step-by-step explanation:
is it really v2x?? or smthg else
1. A scuba diver wants to dive more than 2 1/2, times his previous deepest dive. That means he has to dive at least 80 feet below the surface of the ocean. This dive is represented by the inequality 2 1/2p < -80, where p is the distance below the surface of his previous deepest dive.
The scuba driver's previous deepest dive was ____ feet below the surface of the ocean.
________________________________
Veronica live on a straight road that goes east and west. She starts from a point 5.1 miles west of her home and drives a certain distance to the store the store is more than 3 and 1/2 miles east of her home. let D represent the distance Veronica drove. which inequality represents this situation?
A. -5.1 + d > 3 1/2
B.-5.1 + d > -3 1/2
C.-5.1 + d > 3 1/2
D.- 5.1 + d > -3 1/2
________________________________
Alex needs to represent the statement as an inequality half of a number is more than 1 and 1/3
The questions can be represented on a number line so that they become more clear and meaningful. The answers to each question are:
1. The scuba diver's previous deepest dive was 32 feet below the surface of the ocean.
2. Option A. -5.1 + d > 3.5 OR C. -5.1 + d > 3.5
3. Alex would represent it as: [tex]\frac{1}{2} n[/tex] > [tex]1\frac{1}{3}[/tex]
A number line is a system that can be used to show the positions of all directed numbers.
Thus, the solutions to the given questions are stated below:
1. Let the scuba diver's previous deepest dive be represented by d . Such that,
2.5 d = - 80 .......... 1
So that;
d + p = -80 ............ 2
From equation 1,
2.5 d = -80
d = -32 feet
From equation 2,
-32 + P = - 80
p = -80 + 32
= -48 feet
p = -48 feet
⇒ -32 + (-48) = -80
Therefore, the scuba diver's previous deepest dive was 32 feet below the surface of the ocean.
2. This situation can easily be represented by a number line, so that Veronica's home is located at point zero of the number line.
Then, the total distance that Veronica drove, d = (5.1 + 3.5) miles
= 8.6 miles
Thus, since the distance to the store is more than 3.5 miles east of her home, thus the appropriate inequality that represents the situation is:
-5.1 + d > 3.5
The correct option is: A or C
3. Let the number be represented by n, so that:
[tex]\frac{1}{2}[/tex]n > [tex]1\frac{1}{3}[/tex]
Alex would represent the statement as: [tex]\frac{1}{2} n[/tex] > [tex]1\frac{1}{3}[/tex]
Visit: https://brainly.com/question/17800079
what is 5 x 1284
plz answer thanks
Answer:
6420
Step-by-step explanation:
hope this helps
A leaky pipe drips 2 fluid ounces of water per hour. How many cups of water does it leak in 2 days? Remember that 8 fluid ounces = 1 cup
Answer:
12 cups
Step-by-step explanation:
There are 48 hours in two days.
48 · 2 = 96 ( 2 being fluid ounces per hour )
96 ÷ 8 = 12 ( 8 being fl oz in each cup )
I hope that this helped!!!
pls help asap MIDSEGMENTS
Answer:
56 degrees
Step-by-step explanation:
The midsegment is parallel to a side and the other side is a transversal. Using the Corresponding Angles Theorem, you get that m<1=56 degrees
or
Find the slope of the line
y
=
9
5
x
−
9
5
.
Cual es el resultado de 12/6?
Answer:
Resultado es dos (2)
Answer:
2
Step-by-step explanation:
The mean, median, and mode of a distribution are __________. A. Measures of central tendency B. Measures of variability C. Types of transformed scores D. Types of deviations Please select the best answer from the choices provided A B C D.
The mean, median, and mode of a distribution are measures of central tendency.
A measure of central tendency of a data set determines its central value. Measures of central tendency are mean median and mode.
Mean is the average of a set of numbers.
Mode refers to a value that appears most frequently in a data set.
Median is the number in the centre of a data set.
To learn more about mode, please check: https://brainly.com/question/300591
Answer:
A
Step-by-step explanation:
Select all of the expressions which are equivalent to-4/3p-2/5
Answer:
-2/5 -4/3 p and -4/3p+ (-2/5)
True or false
1: 4h and 4g are like terms: True or false?
2: 4x and 4xy are like terms. True or false?
3: the coefficient is the number by its self. True or false?
4: in the expression x-4+(-5x), the constant is 4. True or false?
5: in the expression x-4+(-5x), the constant is -4. True or false?
6: in the expression x-4+(-5x), the coefficient -5 is . True or false?
You dont need to explain the steps, if you like you may
Answer:
1 is true
2 is true
3 is true
4 is false
5 is true
6 is true
3/8 rounded to the nearest thousand
Answer:
0.38
Step-by-step explanation:
First, we convert the fraction to a decimal number by dividing the numerator by the denominator:
3 / 8 = 0.375
There are two parts to the decimal number above:
Integer Part: 0
Fractional Part: 375
Now, we will make the Fractional Part just two digits (nearest hundredth) by using our rounding rules.*
In this case, Rule II applies, so 3/8 (or 0.375) rounded to the nearest hundredth in decimal format is:
0.38
Answer:
.375
Step-by-step explanation:
3/8=.375
Mother is M years old, and she is 4 times as old as her daughter, her age is x+8/x. how much older is the mother than her daughter, Mary?
[tex]4(x + \frac{8}{x}) - (x + \frac{8}{x}) = 3(x + \frac{8}{x}) = 3x + \frac{24}{x}[/tex]
ok done. Thank to me :>
What time is it where you guys are at??
5 in the morning unfortunately cuz I have massive insomnia
Answer:
dose meen nambars
Step-by-step explanation:
dont ansor kweschins nambars kweschins
PLEASE HELP I REALLY NEED HELP!
Answer:
It should be C. AAS
Step-by-step explanation:
There are symbols on the triangle indicating a shared right triangle, congruent angles, and a shared congruent side.
Hope this helps :)
Answer:
Yes, AAS
Step-by-step explanation:
a 20 pound platter of cookies costs $77. the platter is a mix of peanut butter that costs $4 per pound, sugar that costs $3 per pound, and chocolate chip that’s costs $4.50 per pound. there are two more pounds of sugar cookies than peanut butter. how many pounds of sugar cookies are on the platter?
Answer: 7 pounds of sugar cookies
X+Y+Z = 20
4x + 3y +4.50z = 77
-x + y + 0z = 2
X+Y+Z = 20 4x + 3y + 4.50z = 77
-x + y +Oz = 2 (-x + y + 0z = 2) x 4 (-4x +4y+0z=8)
Add the problems vertically
0x + 2y + z = 22 0x +7y + 4.50 z = 85
Rewrite the problem
2y + z = 22 (Times 7)
7y + 4.50 = 85 (Times -2)
14y +7z = 154
-14y - 9z = -170
Add Vertically
-2z = -16
divide by -2
z = 8
there are 8 Chocy Chips
if we plug 8 for z in 2y + z = 22 we get y = 7
making 5 be X (Cause X+Y+z = 20)
8 Chocy
7 Sugar
5 Peanut butter
-- Gage Millar, Alg 1/2 tutor
heeeeeyyyyy someone can aswer plz? Thx
Answer:
b)
x=65+32 [ being ext. angle of triangle is equal to the sum of two opposite interior angle]
therefore x=97°
Singer A and Singer B had the two top-grossing concert tours for a certain year, together generating $334 million in ticket sales. If Singer B took in $26 million less than Singer A, how much did each tour generate?
What’s the range of = 1 2 ⋅ 2 + 6 + 6
Answer: the range of 12 * 2 + 6 + 6 is 36
Step-by-step explanation:
need help with both questions please
Answer:
vertical angle are congruent
because BD and CE intersect and intersecting lines make vertical angle
Step-by-step explanation:
PLS HELP WILL MARK BRAINLIEST! ANSWER W/ SOLUTION
[tex] = \: \: \: c = 0 \\ \\ hope \: it \: \: helps \\ \\ see \: \: the \: \: attachement[/tex]
pls help asap MIDSEGMENTS
Answer:
RT and KS
Step-by-step explanation:
isosceles triangle
At Keller's Bike Rentals, it costs $36 to rent a bike for 7 hours.
How many hours of bike use does a customer get per dollar
Answer:
I'm sure it's 43 rent a bike cause I'm fat
What are the slope and the y-intercept of the line shown in the graph?
A. y-intercept = 2 and slope = -3
B. y-intercept = 2 and slope = 3
C. y-intercept = 3 and slope = 2
D. y-intercept = 3 and slope = 2
Auntie Anne raked leaves for
more than 10 minutes but less
than 40 minutes. The number
of minutes is a multiple of 5.
The digits add up to 7. For
how long did Anne rake?
The time taken by auntie Annie to rake is 25 minutes.
What is inequality?
A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions is called inequality.
Let the time taken by auntie Anne to rake be ab minutes.
Now, according to the given question.
Auntie Anne situation is represented by an inequality
10 < ab <40
Since, it is given that sum of the digits of time taken by Anne to rake is 7.
⇒ a + b = 7
Also, ab is a multiple of 5.
Now,
When, a = 4 and b = 3 (or vice-versa)
4 + 3 = 7 but 43 is not a multiple of five.
When, a = 6 and b = 1 ( or vice versa)
6 + 1 = 7, but 61 is not a multiple of five.
When, a = 2 and b = 5 (or vice versa)
2 + 5 = 7 and 25 is multiple of 5.But 52 is not a multiple of 5.
Also, 25 is less than 40 and greater than 10.
Therefore, the time taken by auntie Annie to rake is 25 minutes.
Find out more information about inequality here:
https://brainly.com/question/20383699
#SPJ2
On a coordinate plane, parallelogram P Q R S is shown. Point P is at (negative 2, 5), point Q is at (2, 1), point R is at (1, negative 2), and point S is at (negative 3, 2). In the diagram, SR = 4 StartRoot 2 EndRoot and QR = StartRoot 10 EndRoot. What is the perimeter of parallelogram PQRS?
Answer:
B
Step-by-step explanation:
jus belive me
The perimeter of parallelogram PQRS will be 8√2 + 2√10 units.
What is a parallelogram?It is a polygon with four sides. The total interior angle is 360 degrees. A parallelogram's opposite sides are parallel and equal.
On a coordinate plane, parallelogram PQRS is shown.
Point P is at (-2, 5), point Q is at (2, 1), point R is at (1, -2), and point S is at (-3, 2).
In the diagram, SR = 4√2 and QR = √10.
We know SR = PQ and RQ = SP
Then the perimeter of the parallelogram is the sum of all sides.
P = PQ + QR + RS + SP
P = 4√2 + √10 + 4√2 + √10
P = 8√2 + 2√10
Then the perimeter of parallelogram PQRS will be 8√2 + 2√10 units.
More about the parallelogram link is given below.
https://brainly.com/question/1563728
#SPJ6
HELP 10 POINTS + BRAINLIEST Determine the equation of the line shown in the graph:
y=0
x=0
y=5
X=5
Answer:
y=0
Step-by-step explanation:
the x coordinate is 5 and the y coordinate is 0 because the line does not move up the y axis
Answer:
your question is a little messed up.
the equation for the blue line is x = 5
y=x if you're looking for an equation that satisfies (0,0) and (5,5)
Helppppppppplplppppai
Answer:
D.
Step-by-step explanation:
Well, here we look at the frequency to determine probability. As a dice has 3 even and odd numbers, the probability shall be gotten by dividing the total number of frequencies for even numbers (2,4,6) by the total number of trials.
i.e (10+10+9)/50
so the probability is 29/50 or 0.58 or 58%
Since the probability of getting even numbers is 0.58 and since the total probability is always 1, we can clearly see that the probability of one rolling an even number as per the sample is higher than that of rolling an odd number.
Which of the following is not equivalent to 23 + (-27) - 16-(-32)?
23 – 27 – 16 + 32
o 23 – 27 – 16 – (-32)
O
23 + (-27) + 16 + 32
o
23 + (-27) + (- 16) - (- 32)
Answer: 23 + (-27) + 16 + 32 is not correct
Step-by-step explanation:
23 + (-27) + 16 + 32 is not correct
23 + (-27) + 16 + 32 The +16 should be -16
CAN SOMEONE HELP ME PLEASE ASAP!
Answer:
P and R
Step-by-step explanation:
P and R are similar because R is the same thing as P but 2 times bigger.
PARALLEL PERPENDICULAR OR NEITHER OR SAME LINE
Answer:
Parallel
Step-by-step explanation:
So if they have the same slope but different y-intercepts, it would be parallel because the slope stays the same so the line doesnt change, just the starting point
For example use the following equations
y = x + 2
y = x + 3
In the graph, these equations are parallel