Answer:
Both lines are equal (they are the same)
Step-by-step explanation:
Given
[tex]3y - 8 = -5x[/tex]
[tex]6y = -10x + 16[/tex]
Required
What is true about graph of both lines
Questions like this are better solved when there's option(s) to select from. However, some of the properties of line equation that I'll consider are to check if both lines are either parallel or perpendicular
To do this,
The first thing to do is to calculate the slope of both lines
[tex]3y - 8 = -5x[/tex]
Add 8 to both sides
[tex]3y - 8 + 8 = -5x + 8[/tex]
[tex]3y = -5x + 8[/tex]
Divide both sided by 3
[tex]\frac{3y}{3} = -\frac{5x}{3} + \frac{8}{3}[/tex]
[tex]y = -\frac{5x}{3} + \frac{8}{3}[/tex]
The slope of the line is the coefficient of x;
[tex]Slope = -\frac{5}{3}[/tex]
Solve for the y intercept; Let x = 0
[tex]y = -\frac{5 * 0}{3} + \frac{8}{3}[/tex]
[tex]y = 0 + \frac{8}{3}[/tex]
[tex]y = \frac{8}{3}[/tex]
Solve for the x intercept; Let y = 0
[tex]0 = -\frac{5x}{3} + \frac{8}{3}[/tex]
Subtract [tex]\frac{8}{3}[/tex] from both sides
[tex]0 - \frac{8}{3} = -\frac{5x}{3} + \frac{8}{3} - \frac{8}{3}[/tex]
[tex]- \frac{8}{3} = -\frac{5x}{3}[/tex]
Subtract both sides by [tex]-\frac{3}{5}[/tex]
[tex]-\frac{3}{5}*- \frac{8}{3} = -\frac{5x}{3} * -\frac{3}{5}[/tex]
[tex]-\frac{3}{5}*- \frac{8}{3} = x[/tex]
[tex]\frac{3}{5} * \frac{8}{3} = x[/tex]
[tex]\frac{8}{5} = x[/tex]
[tex]x = \frac{8}{5}[/tex]
------------------------------------------------------------------------------------------------------
[tex]6y = -10x + 16[/tex]
Divide both sides by 6
[tex]\frac{6y}{6} = -\frac{10x}{6} + \frac{16}{6}[/tex]
[tex]y = -\frac{10x}{6} + \frac{16}{6}[/tex]
Simplify fractions to lowest term
[tex]y = -\frac{5x}{3} + \frac{8}{3}[/tex]
The slope of the line is the coefficient of x;
[tex]Slope = -\frac{5}{3}[/tex]
Solve for the y intercept; Let x = 0
[tex]y = -\frac{5 * 0}{3} + \frac{8}{3}[/tex]
[tex]y = 0 + \frac{8}{3}[/tex]
[tex]y = \frac{8}{3}[/tex]
Solve for the x intercept; Let y = 0
[tex]0 = -\frac{5x}{3} + \frac{8}{3}[/tex]
Subtract [tex]\frac{8}{3}[/tex] from both sides
[tex]0 - \frac{8}{3} = -\frac{5x}{3} + \frac{8}{3} - \frac{8}{3}[/tex]
[tex]- \frac{8}{3} = -\frac{5x}{3}[/tex]
Subtract both sides by [tex]-\frac{3}{5}[/tex]
[tex]-\frac{3}{5}*- \frac{8}{3} = -\frac{5x}{3} * -\frac{3}{5}[/tex]
[tex]-\frac{3}{5}*- \frac{8}{3} = x[/tex]
[tex]\frac{3}{5} * \frac{8}{3} = x[/tex]
[tex]\frac{8}{5} = x[/tex]
[tex]x = \frac{8}{5}[/tex]
-------------------------------------------------------------------------------------------------------
By comparing the slope, x intercept and y intercept of both lines;
It'll be observed that they have the same slope, x intercept and y intercept
This implies that both lines are equal; in other words, they are the same.
The coordinate plane below represents a city. Points A through F are schools in the city. graph of coordinate plane. Point A is at negative 3, negative 4. Point B is at negative 4, 3. Point C is at 2, 2. Point D is at 1, negative 2. Point E is at 5, negative 4. Point F is at 3, 4. Part A: Using the graph above, create a system of inequalities that only contains points C and F in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points) Part B: Explain how to verify that the points C and F are solutions to the system of inequalities created in Part A. (3 points) Part C: Natalie can only attend a school in her designated zone. Natalie's zone is defined by y < −2x + 2. Explain how you can identify the schools that Natalie is allowed to attend. (2 points)
Answer:
Part A;
There are many system of inequalities that can be created such that only contain points D and E in the overlapping shaded regions.
Any system of inequalities which is satisfied by (-4, 2) and (-1, 5) but is not satisfied by (1, 3), (3, 1), (3, -3) and (-3, -3) can serve.
An example of such system of equation is
x < 0
y > 0
The system of equation above represent all the points in the second quadrant of the coordinate system.
The area above the x-axis and to the left of the y-axis is shaded.Part B:
Part B
It can be verified that points D and E are solutions to the system of inequalities above by substituting the coordinates of points D and E into the system of equations and see whether they are true.
Substituting D(-4, 2) into the system we have:
-4 < 0
2 > 0
As can be seen the two inequalities above are true, hence point D is a solution to the set of inequalities.
Also, substituting E(-1, 5) into the system we have:
-1 < 0
5 > 0
As can be seen the two inequalities above are true, hence point E is a solution to the set of inequalities.
Part C
:This part is different from yours because my equation is y> 4x + 3 and it's been a long time since I did that task and I don't remember anything. I hope you can do yours from my example.
Given that chicken can only be raised in the area defined by y > 3x - 4.
To identify the farms in which chicken can be raised, we substitute the coordinates of the points A to F into the inequality defining chicken's area.
For point A(1, 3): 3 > 3(1) - 4 ⇒ 3 > 3 - 4 ⇒ 3 > -1 which is true
For point B(3, 1): 1 > 3(3) - 4 ⇒ 1 > 9 - 4 ⇒ 1 > 5 which is false
For point C(3, -3): -3 > 3(3) - 4 ⇒ -3 > 9 - 4 ⇒ -3 > 5 which is false
For point D(-4, 2): 2 > 3(-4) - 4; 2 > -12 - 4 ⇒ 2 > -16 which is true
For point E(-1, 5): 5 > 3(-1) - 4 ⇒ 5 > -3 - 4 ⇒ 5 > -7 which is true
For point F(-3, -3): -3 > 3(-3) - 4 ⇒ -3 > -9 - 4 ⇒ -3 > -13 which is true
Therefore, the farms in which chicken can be raised are the farms at point A, D, E and F.
.Take that exam and got 100% .The exam was 05.13 Segment One Exam Part 3.I really hope this helps you.And please give me the brainliest
Answer:
give person above brainliest
Step-by-step explanation:
its right
What is the least common factor of 9 and 15? (Don’t say 45 please because that’s not the answer I’m looking for ;)
Answer:
The (GCF) greatest common factor is 3
hope this helps ;)
Step-by-step explanation:
Answer:
LCF = 3
Step-by-step explanation:
The factors of 9 are: 1, 3, 9
The factors of 15 are: 1, 3, 5, 15
The least common factor is 3. It is the lowest number that is a factor of both 9 and 15. Technically, 3 is the GCF and the LCF because it is the only common factor of 9 and 15.
I hope this helps!!
Every integer is a whole number
Please select the best answer from the choices provided
T
F
Answer:
This is true.
Find x. Round your answer to the nearest tenth of a degree.
Answer:
x ≈ 31.3°
Step-by-step explanation:
We can use sin∅ to solve this:
sinx = 13/25
x = [tex]sin^{-1}(13/25)[/tex]
x = 32.3323
Sara leaves home at 7 A.M. traveling at a rate of 45 mph. Her son discovers that she has forgotten her briefcase and starts out to overtake her. Her son leaves at 7:30A.M. traveling at a rate of 55 mph. At what time will he overtake his mother?
Answer:
B I think
Step-by-step explanation:
Answer:
Dude, there is no option?
Step-by-step explanation:
Solve 5(x - 4) = 2(x + 5)for x
5x-20 = 2x+10
3x-20= 10
3x= 30
x=10
Answer:
x = 10
Step-by-step explanation:
Step 1: Distribute parenthesis
5x - 20 = 2x + 10
Step 2: Add 20 to both sides
5x = 2x + 30
Step 3: Subtract 2x from both sides
3x = 30
Step 4: Divide by 3
x = 10
Express 5/7 as a decimal. (Round to the nearest thousandths place)
Answer:
rounding to the thousandths place, the answer is 0.714
Step-by-step explanation:
This can easily be looked up on google
A bridge connecting two cities separated by a lake has a length of 5.651 mi.
Use the table of facts to find the length of the bridge in yards.
Round your answer to the nearest tenth.
Answer:
The equivalent of 5.651 mi is 9945.76 yards
Step-by-step explanation:
Given:
Length of lake = 5.651 mi
Required:
Length of bridge in yards
From table of facts;
1 mile = 1760 yards
This implies that
5.651 miles will be:5.651 * 1760 yards
5.651 * 1760 yards = 9945.76 yards
5.651 * 1760 yards = 9945.8 yards (Aproximated)
Hence, the equivalent of 5.651 mi is 9945.76 yards
Which statement is true about the effects of the transformations on the graph of function f to obtain the graph of function g. g(x) = f(x − 3) + 4
Answer:
The correct option is D
D) The graph of function f(x) is shifted right 3 units and up 4 units
Step-by-step explanation:
Lets the function be y = f(x)
To shift the graph 3 units to the right, we add -3 to the x term of the function:
Function becomes y' = f(x-3)
Then to shift the graph up by 4 units, we add -4 to the y term of the function:
Function becomes:
y - 4 = f(x-3)
y = f(x-3) +4
g(x) = f(x-3) +4
Hence the correct option is D, as the graph is shifted to the right by 3 units and also shifted up by 4 units
Answer: The correct answer is D. The graph of function f is shifted RIGHT 3 units and up 4
Step-by-step explanation:
PLEASE HELP! 5 MINS! You are given an n×n board, where n is an even integer and 2≤n≤30. For how many such boards is it possible to cover the board with T-shaped tiles like the one shown? Each cell of the shape is congruent to one cell on the board.
Answer:
15
Step-by-step explanation:
30/2 = 15
Answer:
7
Step-by-step explanation:
Hey, sorry if this is a little late, but think of the tiles in an arrangement where 4 fit into a rectangle type thing. Now, since you want to find the maximum number of boards, find the closest number that you can multiply by 4 to get something close to 30. Here, you can see that 7x4=28, which is both an even number and the closest number to 30 as you can get. So, the answer is 7.
Someone please help
Answer:
A
Step-by-step explanation:
The 3D shape of the 5 cubes put to a 2D-plane will be representing the diagram A.
Answer: A
Step-by-step explanation:
This is because Option A has 5 cubes, as well as the model above which also has 5 cubes. When you change the angle of the way you are looking at Option A it will be similar to the plan above
If LMN XYZ, which congruence are true by cpctc? Check all that apply
Answer:
D, E, F
Step-by-step explanation:
After you prove that the two triangles are congruent, you just need to look for the similair placed angles and lines.
Answer:
D, E, F
Step-by-step explanation:
These three are the only ones that complete CPCTC requirements.
what is the area of the triangle below?
Which of the following is a result of shifting a circle with equation (x-2)2 +(y-3)2=25 to the left 2 units ?
A.) Both the x- and y-coordinates of the center of the circle increased by 2
B.) Both the x- and y-coordinate of the center of the circle decreased by 2
C.) The y-coordinate of the center of the circle decreased by 2
D.) The x-coordinate of the center of the circle decreased by 2
Answer:
D.) The x-coordinate of the center of the circle decreased by 2
Step-by-step explanation:
(consult the diagram attached below)
Consider a circle
(x - 2)² + (y - 3)² =25
Where (h, k ) = (2, 3) which is the center of the circle.
When we want to move the circle to the left by 2 units, it also means the the center of the circle will move 2 units to the left.
If center of the circle moves 2 units to the left, it means that the x coordinate of the center of the circle will be decreases by 2 units, while y coordinate will remain the same.
Hence the new coordinate for the center of the circle is (2-2, 3) = (0, 3)
The new equation of circle will be:
(x - 0)² + (y - 3)² =25
(x )² + (y - 3)² =25
Solve for x. ANSWERS: A) 12 B) 13 C) 11 D) 10
Answer:
A) 12
Step-by-step explanation:
Since triangles YRZ and QRS are similar by AA, the ratio of their sides should be constant. Since RY=QY, let's call that side length y.
[tex]\dfrac{x+2}{y}=\dfrac{3x-8}{2y}[/tex]
Multiply both sides by 2y:
[tex]2(x+2)=3x-8 \\\\2x+4=3x-8 \\\\4=x-8 \\\\x=12[/tex]
Hope this helps!
There are 96 people consisting of 48 married couples in a room. Assuming that no husband or wife shakes thr others hand but everyone else shakes hands exactly once, how many handshakes are there?
Answer:
4512 handshakes
Step-by-step explanation:
We are told in the question, that there are
96 people in the room = 48 couples
Assuming that no husband or wife shakes each others hand but everyone else shakes hands exactly once
This means
48 couples will shake 94 people because they are excluded
This is calculated as
48 × 94 = 4512 handshakes
Points O, A, B lie on a line. OA = 12 cm and OB = 9 cm. Find the distance between the midpoints of segments
OA
and
OB
in each case.
a
Point O lies on segment
AB
.
Answer:
10.5
Step-by-step explanation:
Let E be the midpoint of OA and F be the midpoint of OB.
If point O is placed between A and B, then points E and F are placed on different sides from O. The segment OE has length 12÷2=6 cm and segment OF has length 9÷2=4.5 cm. Than EF=6+4.5=10.5 cm.
If point O is placed outside the segment AB, then point B is closer to point O than point A, because OA>OB. Since OE=6 cm and OF=4.5 cm, EF=6-4.5=1.5 cm.
If the order of points is A, O, B, then the midpoints of AO and OB will be separated by half the length of AB: (12 cm + 9 cm)/2 = 10.5 cm.
please mark me brainliest :)
Answer:
10.5 cm
Step-by-step explanation:
The ratio of the number of Andys seashells to the number of Bens seashell is 4:9. Andy has 100 seashells. How many seashells does Ben have?
Answer:
225 seashells
Step-by-step explanation:
4:9
100:x
Cross multiply the ratios.
4x=900
x=900/4
x=225
I need help please!!!
Which of the following is the equation of a line in slope- intercept form fo a line with slope =2/3 and y-intercept at (0,-2)? A. y= -3/2x -2 B. y=-2/3x +2/3 C. y= -2x - 2/3 D. y= 2/3x -2
Answer:D
Step-by-step explanation:
The arithmetic mean (average) of four numbers is 85. If the largest of these numbers is 97, find the mean of the remaining three numbers.
Answer: A) = 81
Step-by-step explanation:
Say that the four numbers are a,b,c & 97.
Then a+b+c+97/4 = 85
a+b+c+97=340
a+b+c=243
a+b+c/3 = 81
The average of the remaining three numbers is 81.
What is the average of n numbers a₁, a₂, ..., aₙ?The average of the numbers a₁, a₂, ..., aₙ is calculated as
Average = (a₁ + a₂ + ··· + aₙ) / n.
Given
Average of the four numbers = 85,
The largest of the four numbers is 97.
Find the sum of all the four numbers
Let the four numbers be a, b, c, and d. Then, using their given average,
(a + b + c + d) / 4 = 85
⇒ a + b + c + d = 85 × 4 = 340.
Find the sum of the numbers excluding the largest one
Let the largest number be d. So, d = 97. Then, the sum of the remaining three is
a + b + c = 340 - d = 340 - 97 = 243.
Find the average of the three numbers
Using the above definition average of the remaining three numbers is calculated as
Av(a,b,c) = (a + b + c)/3 = 243 / 3 = 81.
The required average of the remaining three numbers is 81.
Learn more about the average here
https://brainly.com/question/1136789
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If ΔP′QR′ is a dilated image of ΔPQR, find the scale factor (k) and then find the value of x. answers: A) 7 B) 10.7 C) 6 D) 73.5
Answer:
see explanation
Step-by-step explanation:
To find k, calculate the ratio of corresponding sides, image to original, that is
k = [tex]\frac{P'R'}{PR}[/tex] = [tex]\frac{8}{28}[/tex] = [tex]\frac{2}{7}[/tex]
Thus
QR' = [tex]\frac{2}{7}[/tex] × QR = [tex]\frac{2}{7}[/tex] × 21 = 2 × 3 = 6 , that is
x = 6 → C
If y varies directly and y is 12 when x is 1.2 what is the constant of variation for this relation
Answer:
10
Step-by-step explanation:
The constant of variation would be 12 / 1.2 = 10.
Answer:
[tex]10[/tex]
Step-by-step explanation:
[tex]y \propto x[/tex]
[tex]y=kx[/tex]
[tex]12=k \times 1.2[/tex]
[tex]k=\frac{12}{1.2}[/tex]
[tex]k=10[/tex]
The constant of variation is [tex]k[/tex].
Tickets to a concert cost either $12 or $15. A total of 300 tickets were sold, and the total receipts were $4140. How many of each kind of ticket were sold?
Answer:
1,242,000
Step-by-step explanation:
Which statement is true?
The transformation is rigid because corresponding side
lengths and angles are congruent.
The transformation is rigid because corresponding side
lengths are congruent and corresponding angles are not
congruent.
The transformation is nonrigid because the two
triangles have different names.
The transformation is nonrigid because the three sides
and the three angles in each triangle have different
measures.
Answer:
Option A
Step-by-step explanation:
The triangle most likely got translated. A translation is a rigid transformation. Rigid transformed shapes have the same angle measure and side lengths.
Option A should be the correct answer.
Side Note: You can also tell that the markings on the triangle are the same. This means that the shapes are congruent. They are just in different positions.
The true statement is (a) the transformation is rigid because corresponding side lengths and angles are congruent.
How to determine the true statement?From the figure, we have the following highlights
Corresponding angles are congruentCorresponding sides are congruentThe above means that the transformation from one triangle to the other is a rigid transformation
Hence, the true statement is (a)
Read more about rigid transformation at:
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What is 10% of 66,743.22
Answer:
The answer is 6,674.322
Step-by-step explanation:
An easy way to solve this is to move the decimal point up by one space.
You could also multiply 66,743.22 by 0.1 and you would get the answer.
Hope this helps :)
Answer:
6674.322
Step-by-step explanation:
To find 10% we move the decimal one place to the left
66,743.22 moves one place to the left
6674.322
Can someone help please simply answer only
Answer:
2nd option
Step-by-step explanation:
there is no need to make a like of best fit because the x axis is already acting as one.
Which of the following equations describe the line shown below? Check all that apply!
Answer:
C and E
Step-by-step explanation:
Use the slope formula to first find the slope of the line.
The slope formula is y₂₋y₁ / x₂₋x₁ where (x₁ , y₁) is a point on the graph and (x₂ , y₂) is the other point on the graph. Substituting the values into the slope formula will give you 2 as the slope.
Now use the point-slope formula to find the correct answers.
Point-slope form is y₋y₁ = m(x₋x₁) where y₁ and x₁ are a point on the graph and m is the slope. Substitute both points into the formula (separately) to get C and E as your answers.
OMG HELPPP PLEASEEE plssss
Answer:
Brainliest goes to me
Step-by-step explanation:
if you solved it... it would be 8.75
but you can't like 0.75 of a color so it isn't possible
0.75 is to be rounded up so I would do 9
Answer:All you have to do is multiply
Step-by-step explanation:
Which equation has a graph that is parallel to the graph of 2x - y = -1?
A. 2x + y = 8
о В.
y=-x+3
O C. y-1 = 2(x - 3)
O D. y = -2x - 1
Answer:
C.
Step-by-step explanation:
Parallel lines have the same slope but different y-int. So if our original equation is y = 2x + 1, then the other equation would have to be y = 2x + b, where b ≠ 1. Only answer C. works.
Answer:
The answer is C) y-1=2(x-3)
Step-by-step explanation:
Two equations are parallel if they have the same slope and different y-intercepts. In the answer (c) 2 represents the slope which is also the slope of the original equation. y=2x-5is the equation that you get when you distibute and isolate y.
how does the fact that a parallelogram has rotational symmetry demonstrates that opposite side of a parallelogram are congruent ?
Answer:
See below.
Step-by-step explanation:
It is known that a parallelogram has rotational symmetry, rotated 180 degrees about it's center point. Now by definition a parallelogram is a quadrilateral with two pairs of parallel sides, hence it's name. If you were to take a look at the attachment below, you might see the connection.
Rotational Symmetry will make it so that side AB corresponds to CD, respectively AD and CB. The sides will coincide with one another after a 180 degree rotation, so that AB = CD, and AD = CB. Hence, in the same parallelogram, opposite sides are congruent.
Proved!