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Explanation:
When two lines have different slopes like this, it means the two lines are not parallel. Recall parallel lines are when the slopes are equal (the rise and run are the same, so you can think of it like the same stair-step pattern).
Non-parallel lines intersect at exactly one location. This point of intersection is the solution to the system of equations.
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A more in-depth look (optional section)
Let's consider the system of equations shown below
[tex]\begin{cases}y = mx+b\\y = mx+c\end{cases}[/tex]
For each equation shown here, the m values are the same slope. However, b and c are different values (in other words, [tex]b \ne c[/tex]). This system describes any two parallel lines that aren't vertical.
Since we're dealing with the same y value, we can apply substitution to try to solve for x. But we run into a problem
y = mx+b
mx+c = mx+b ... replace y with mx+c
c = b .... subtract mx from both sides
But we stated that c and b were different, and not equal. This is a contradiction. So if we had a system of this form, then we have 2 parallel lines that lead to no solution. We call this an inconsistent system.
Next, we'll consider this system of equations
[tex]\begin{cases}y = mx+b\\y = nx+c\end{cases}[/tex]
The only thing different here is the second equation has n instead of m as its slope. We'll assume that m and n are not equal to each other. If m = n, then we just end up with the previous scenario. Let's try to solve x now
y = mx+b
nx+c = mx+b
nx-mx = b-c
(n-m)x = b-c
x = (b-c)/(n-m)
Assuming [tex]m \ne n[/tex], we can generate one solution for x as shown above. This single solution for x generates a corresponding single solution for y. So overall, this proves that we have one ordered pair (x,y) solution to this system.
In short, I've shown that if m and n are different slopes, then the system of equations has exactly one solution.
3y - 5x = 15 slope intercept form
Answer:
Y=3/5x-3
Step-by-step explanation:
Answer:
y=5/3x+5
Step-by-step explanation:
1)3y-5x=15
2)3y=15+5x
3)y=5+5/3x
4)y=5/3x+5
1) Write the equation out
2) Add 5x to both sides of the equation
3) Divide both sides of the equation by 3
4) Reorder the terms
Suppose you have a bag that contains 2 black and 8 striped marbles. You select one marble, replace it, and then select another. Find the probability that you will select two black marbles in a row.
P(black & black) =
Answer:
2/10 (1/5)
Step-by-step explanation:
to do this, you know that the marble is put back, so you have an equal chance each time. then, find how many black marbles there are, and go from there.
Can somebody tell me what's 43 divided by 1032 in long division? (Step by step) Or send a picture please
Answer:
24
Step-by-step explanat
Divide both the numerator and denominator by the GCD
1032 ÷ 43
43 ÷ 43
Reduced fraction:
24
1
Therefore, 1032/43 simplified to lowest terms is 24/1.
(points on a circle) PLEASE HELP THIS IS DUE TONIGHT
A circle is centered at C(0,0)C(0,0)C, left parenthesis, 0, comma, 0, right parenthesis. The point M(0,\sqrt{38})M(0,38 )M, left parenthesis, 0, comma, square root of, 38, end square root, right parenthesis is on the circle.
Where does the point N(-5,-3)N(−5,−3)N, left parenthesis, minus, 5, comma, minus, 3, right parenthesis lie?
Answer:
Inside the circle, a distance of [tex]\sqrt{34}[/tex] from the center of the circle.
Step-by-step explanation:
Center of circle is at (0,0)
One point of the circle is at (0,[tex]\sqrt{38}[/tex])
Since the only known point is in the y-axis, the radius of the circle must be [tex]\sqrt{38}[/tex].
[tex]\sqrt{38}[/tex] = 6.164
So the point (-5,-3) is still inside the circle as the distance from point (-5,-3) to the center of the circle is [tex]\sqrt{(5)^2+(-3)^2}[/tex] or [tex]\sqrt{34}[/tex] which is less than the radius of the circle.
Point N(-5, -3) lies inside the circle.
We have,
To determine the location of point N(-5, -3) in relation to the given circle centered at C(0, 0), we can calculate the distance between point C and point N.
- If the distance is equal to the radius of the circle, then N lies on the circle.
- If the distance is greater than the radius, N lies outside the circle.
- If it is smaller, N lies inside the circle.
Let's calculate the distance between C(0, 0) and N(-5, -3):
Distance = √[(x2 - x1)² + (y2 - y1)²]
= √[(-5 - 0)² + (-3 - 0)²]
= √[25 + 9]
= √34
Since the distance (√34) is less than the radius of the circle, which is √38 (distance between C and M), we can conclude that the point N(-5, -3) lies inside the circle centered at C(0, 0).
Thus,
Point N(-5, -3) lies inside the circle.
Learn more about Circle here:
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The complete question:
Given that a circle is centered at C(0, 0) and passes through the point M(0, √38), determine the location of the point N(-5, -3) in relation to the circle. Does point N lie inside, outside, or on the circle?
a rectangle has an area of 25 in squared. itis dilated by a scale factor of 4. what is the area of the new image ?
Helpp (please tell me if you can’t see the numbers so I can tell you them)
Answer:
-6 is the y coordinate
Step-by-step explanation:
pleassee if you help i will mark you BRAINLIST
A store pays $85 for a table. The markup is 90%. What is the selling price?
What is the total bill for a $54 dinner with a 5% sales tax and a 20% tip?
Answer:
1. $161.50
2. $68.04
Step-by-step explanation:
please help!!!!!!!!!
Answer:
64
Step-by-step explanation:
to be honest i just looked it up it thats what i do with my work and i always get it right so...
Don's favorite cheese snack come in a box of 6 pieces. Each piece is in the shape of a triangular prism that is 4 cm tall. The triangular base has an area of 20 cm. Find the volume of all of the cheese in the box in cubic centimeters.
Don's favorite cheese snack come in a box of 6 pieces. Each piece is in the shape of a triangular prism that is 4 cm tall. The triangular base has an area of 20 cm. Find the volume of all of the cheese in the box in cubic centimeters.
Answer:
the answer is 80 cubic cm.
Step-by-step explanation:
it is simply height X width so 20 X 4= 80 meaning the answer is 80 cm
Which of the following statements about XY and XZ is true?
2
6
8
X(1, -1)
Y(8, -2)
4
Z(-5.-5)
00
do
10
12
14
Answer:
[tex]\boxed{\textsf{ The correct option is \textbf{Option (D)} .}}[/tex]
Step-by-step explanation:
For complete solution kindly refer to the attachment .
Related Information :-
• Midpoint formula :-
The midpoint formula for points (x1,y1) and (x2,y2) is ,
[tex]\boxed{\sf Midpoint =\bigg( \dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg) }[/tex]
• Section Formula :-
The coordinate of point dividing the line joining points (x1,y1) and (x2,y2) in ratio m:n is ,
[tex]\boxed{\sf Section\ Formula = \bigg(\dfrac{nx_1+mx_2}{m+n},\dfrac{ny_1+my_2}{m+n}\bigg)}[/tex]
Kayla bought 8 hot dogs and hamburgers for her and her friends. Hot dogs cost $1.50 and hamburgers cost $1.75. If she spent a total of $13.25, how many hot dogs did she buy?
Answer:
5 hamburgers and 3 hot dogs
Step-by-step explanation:
D = number of hot dogs
H = number of hamburgers
D + H = 8 then D = 8 - H
1.50D + 1.75H = 13.25
substitute for D
1.50(8-H) + 1.75H = 13.25
12-1.50H + 1.75H = 13.25
subtract 12 from each side
-1.50H + 1.75H = 1.25
0.25H = 1.25
divide both sides by 0.25
H = 5
D = 8-5
D = 3
Will give, Branliest.
Thanks,
:)
Answer:
250p-195
Step-by-step explanation:
did the quiz
Answer:
250p-195
~Sophia
find the product (3x - 5) (3x + 5)
Answer:
9x ^2 − 25
Explanation:
( a + b ) ( a − b ) = a ^2 − ^b 2
substitute a with 3 x and b with 5:
( 3 x + 5 ) ( 3 x − 5 ) = ( 3 x ) 2 −5^ 2 = 9 x ^2 − 25
( 3 x + 5 )( 3 x − 5 ) = 9 x ^2 − 25
Answer:
9x² - 25
Step-by-step explanation:
(a - b)(a + b)= a² - b²
a = 3x ; b = 5
(3x - 5 )(3x + 5)= (3x)² - 5²
= 3²x² - 25
= 9x² - 25
I need help pleases thank you.
Answer:
C. x < -2.
good luck, i hope this helps :)
Directions: Read the instructions for this self-checked activity. Type in your response to each question, and check your answers. At the end of the activity, write a brief evaluation of your work
Activity: You will use the GeoGebra geometry tool to explore how a line parallel to one side of a triangle divides the other two sides of the triangle. Go to
segments parallel to sides of a triangle e, and complete each step below. If you need help, follow these instructions for using GeoGebra.
Question 1: Check the box labeled Show Segment Parallel to BC. Notice that DE intersects two sides of AABC creating a smaller triangle. AADE. How is
AADE related to AABC? How do you know?
Angle D and angle B are congruent because they are corresponding angles. Angle E and C are also congruent because they are corresponding angles.
Find the next three terms in each geometric sequence.
3. 400,200,100,50, .......
4. 4,-12,36,-108, ........
Answer:
3) 25, 12.5, 6.25
4) 324, -972, 2916
Step-by-step explanation:
Need help with this assignment!
Answer:
x=3
Mark me if I helped you❤️
I need some help with these problems
Answer:
calculate by yourself
Step-by-step explanation:
use sin theorem
1.
[tex] \frac{s}{ \sin(60) } = \frac{12}{ \sin(30) } [/tex]
2.
[tex] \frac{s}{ \sin(90) } = \frac{4}{ \sin(30) } [/tex]
3.
[tex] \frac{s}{ \sin(60) } = \frac{10}{ \sin(90) } [/tex]
The ratio of the perimeter of a square A and square B is 4:3. The side of square B is 3 m less than the side
of square A. What is the length of the side of square A?
please answer
Answer:
x = 12
Step-by-step explanation:
x = length of side of square A
'x-3' represents length of side of square B
Perimeter of square A = 4x
Perimeter of square A = 4x - 12
we can set up the following proportion based on ratio of 4:3
4x / 4 = 4x - 12 / 3
cross-multiply:
4(3x) = 4(4x-12)
12x = 16x - 48
-4x = -48
x = 12
PLEASE HELP! WILL ADD BRAINLIEST!!! SHOW YOUR WORK!!!!
Polly’s room is a rectangle. It has a width represented by the expression 4x – 2 and a length represented by the expression
2x – 5. If the room has a perimeter of 73 feet, find the area of Polly’s room.
Answer: 80
Step-by-step explanation: A=LxW.
4x-2=-8
2x-5=-10
-10x-8=80
A 1.5 m tall woman stands next to the Eiffel Tower. At this time of day, her shadow is 0.5 m long. At the same time, the tower's shadow is 90 m
long. How tall is the Eiffel Tower? Show your work.
In a class of 20 students, the number of boys was the number of girls. How many girls were in the class?
Answer:
10
Step-by-step explanation:
Because if the number of girls is the same as the boys you just devide 20 by 2 and get 10
Simplify numbers with units 1.
Answer:
1. 1 min : 2 min
2. 1 min : 4 min
3. 1 : 5
4. 1 : 2
5. 1 hr : 4 hrs
6. 7 p : 10 p
7. 5 : 2 : 3
8. 1 : 3
9. 3 : 5
Step-by-step explanation:
break it down to the lowest, which means to keep dividing it till it can't anymore.
hope that helps
Help!!!!!!!!!!!!!!!!!!
Answer:
y > 0
Step-by-step explanation:
When we are given a linear function, how is one way we can graph it
10) What is the area of the figure below? Round your answer to the nearest tenth (1 place
value)
The area of the figure is
un?
solve 3x+ k= c for x.
The value of variable x in the equation is x = c - k / 3
How to make a variable subject of the formula?3x+ k = c
let's find x or make it the subject of the formula,
3x + k = c
subtract k from both sides of the equation
3x + k - k = c - k
3x = c - k
divide both sides by 3
3x / 3 = c - k / 3
Therefore,
x = c - k / 3
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suppose that the functions s and t are defined for all real numbers x as follows
s(x)=x+6
t(x)=2x^2
write the expressions for (s+t)(x) and (s*t)(x) and evaluate (s-t)(2)
Answer:
(s+t)(x) = s(x) + t(x)
(s*t)(x) = 2x³ + 4x²
Step-by-step explanation:
(s+t)(x) = s(x) + t(x)
= x + 2 + 2x²
= 2x² + x + 2
(s*t)(x) = s(x) * t(x)
= (x + 2) * 2x²
= 2x³ + 4x²
please give me brainliest if my answer is helpful
Solve:
log2 (x + 5) = 3
Answer:
simplified is -2
Step-by-step explanation:
......
Answer:
First one is 2^5 = 3x+5
Second is x = 2
Third one is x^3 = 64
last one is x = 4
Find the number that makes the ratio equivalent to 1:8.
7:__
Answer:
56
Step-by-step explanation:
1:8= 7:?
1*?=7
/1 /1
1*7=7
8*7=56
1:8 = 7:56
Answer:
7:56
Step-by-step explanation:
1:8
we need to turn the one into seven. Turn the ratio 1:8 into the fraction 1/8.
multiply by 7/7 to turn the one into seven and 8 into 56
7/56 can now be turned into ratio 7:56. You could omit the turning of the ratio into the fraction at the beginning, but I find it makes it simpler.