To use substitution to identify if two lines intersect,
1. Rearrange one of the two given equations so that only one variable is on one side of the equation with all other values on the other side of the equation. (if needed)
2. Plug this new equation into the other (in place of a variable)
3. Solve the equation to get the answer of one of the variables
4. Plug this variable into one of the two original equations and solve for the second variable (if needed)
5. Plug both variables back into one of the original equations. If both sides of the equation are equal, the two lines do coincide.
Example:Equation 1: 2x+3y=9
Equation 2: x+8=3
1. Rearrange equation 2
x+8=3
x=3-8
x=-5
2. Plug -5 into the first equation as x
2x+3y=9
2(-5)+3y=9
3. Solve this equation
-10+3y=9
3y=9+10
3y=19
y=[tex]\frac{19}{3}[/tex]
4. Plug x and y back into the first equation
2x+3y=9
2(-5)+3([tex]\frac{19}{3}[/tex])=9
-10+19=9
9=9
Therefore, these two lines do coincide. The point of intersection is (-5,[tex]\frac{19}{3}[/tex]).
Using Elimination:To use elimination to identify if two lines intersect:
1. Multiply one or both of the equations by a factor so both equations have either an x or y coefficient that are equal or opposite of each other (if needed)
2. Add or subtract the two equations to get rid of one variable
3. Solve this new equation for a variable
4. Substitute this variable into one of the two equations to solve for the other
5. Plug both variables back into one of the equations. If both sides are equal, the two lines do coincide.
Example:Equation 1: 2x+3y=4
Equation 2: 4x+2y=3
1. For this specific system of equations, we would multiply the first equation by 2.
2x+3y=4
4x+6y=8
Notice how now, both equations have 4x in them, so we can subtract them:
2. Subtract the new equation from the second original equation
4x+6y=8
- 4x+2y=3
4y=5
3. Solve
4y=5
y=[tex]\frac{5}{4}[/tex]
3. Substitute y back into the first equations (any of the two equations will work) to solve for x
2x+3y=4
2x+3([tex]\frac{5}{4}[/tex])=4
2x+[tex]\frac{15}{4}[/tex]=4
2x=4-[tex]\frac{15}{4}[/tex]
2x=[tex]\frac{16}{4}[/tex]-[tex]\frac{15}{4}[/tex]
2x=[tex]\frac{1}{4}[/tex]
x=[tex]\frac{\frac{1}{4} }{2}[/tex]
x=[tex]\frac{1}{4}*\frac{1}{2}[/tex]
x=[tex]\frac{1}{8}[/tex]
4. Plug both variables back into the first equation (either equation works)
2x+3y=4
2([tex]\frac{1}{8}[/tex])+3([tex]\frac{5}{4}[/tex])=4
[tex]\frac{1}{4}[/tex]+[tex]\frac{15}{4}[/tex]=4
[tex]\frac{16}{4}[/tex]=4
4=4
Since the left side equals the right side, the two lines are coinciding.
Using Graphing Methods:To use graphing methods to identify if two lines coincide, we would just have to graph the line and identify if the two lines meet at a point of intersection/overlap each other.
I hope this helps!
A local park is in the shape of a square. A map of the local park is made with the scale 1 inch to 200 feet.
If each side of the park on the map is 12 inches long, how long is each side of the actual square park?
1 inch to 100 feet
12 inches = 1200 feet.
Just multiply both sides by 12.
The answer is 1200 feet.
Triangles ABC and DEF are shown above. Write ratio equal to BC/AB.
Which trigonometric ratio does this represent?
Answer:
Step-by-step explanation:
From the picture attached,
From ΔABC,
m∠B = 180° - (m∠C + m∠A)
= 180° - (90° + 32°)
= 180° - 122°
= 38°
Now we have to find the trigonometric ratio of BC and AB from ΔABC,
Since, sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
sin(32°) = [tex]\frac{BC}{AB}[/tex]
[tex]\frac{BC}{AB}=0.53[/tex]
Therefore, ratio of BC and AB represents the "sine of angle A".
Give an example of an event that has a probability of 1 (100%).
Answer:
meteor hitting earth
Step-by-step explanation:
not sure of actual probability but i believe one that would cause mass extinction is quite improbable
The movies has 4 bathrooms in 16 theaters what is the bathroom to theaters ratio?
Answer:
1 bathroom to 4 theaters
Step-by-step explanation:
Ms. Canciano was putting ribbon around a bulletim broard. She used 28 inches of ribbon to go all the way around and knew that the length of her board was 6 inches what is the area of her board
Answer:
48 sq inches
Step-by-step explanation:
Given that,
Ribbon used around a bulletin broard is 28 inches
The length of her board is 6 inches
Let B is breadth of her board. 28 inches is perimeter. The perimeter of rectangle is given by :
P = 2(L+B)
28=2(6+B)
14=6+B
B=8 inches
The area of a rectangle is given by :
A = L×B
A = 8×6
A=48 sq inches
So, the area of her board is 48 sq inches
What is the least common denominator for 2/7 & 9/10
7 is prime so the least common denominator is 7 times 2 times 5 which is 70.
3^-3 find the value of power
Answer:
0.037
hope thats the answer
Answer:
Answer= 0.037
Step-by-step explanation:
([tex]3^{-3}[/tex]) is the same as [tex]\frac{1}{3^{3} }[/tex]
(the negative power rule states that [tex]x^{-y}[/tex] is the same as [tex]\frac{1}{x^{y} }[/tex])
which is equal to [tex]\frac{1}{27}[/tex]
or converted to decimals it will be equal to 0.037
In ΔUVW, u = 8 inches, v = 2.7 inches and w=5.9 inches. Find the measure of ∠W to the nearest 10th of a degree.
Answer:32.4
Step-by-step explanation:
The measure of ∠W to the nearest 10th of a degree is, 32.9°.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know, The cosine rule of triangles, In a triangle, ABC with sides opposite to A is a and similar for b and c.
We have. cosA = (b² + c² - a²)/2bc.
Therefore, m∠W = (u² + v² - w²)/2uv.
m∠W = 0.84.
So, cosФ = 0.84.
Ф = cos⁻¹(0.84).
Ф = 32.9°.
learn more about the cosine rule of triangles here :
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Anyone know the answer
Answer:
129
Step-by-step explanation:
angle DCE= 180-(12X+15)
12X+15=20X-9
X=3
It’s timed please help
3.2b-4.7b=3b-3.3
What dose b equal
Answer:
zero
Step-by-step explanation:
Find each key feature of the function shown in the graph. Enter all intervals using interval notation. Enter the x-intercepts as values of x only.
range=
domain=
x-intercepts=
average rate of change over the interval [0,2]=
the right-most interval where the graph is positive=
Answer:
Step-by-step explanation:
Range of the function is the set of y-values (output values) of the function on the graph.
Domain of the function is the set of x-values (input values) of the function.
Domain of the function : [-5, 4)
(including x = -5 and excluding x = 4)
Range : [-4, 2)
(Including y = -4 and excluding y = 2)
x - intercepts : x = -5, -2, 2
Average rate of change over the interval [0, 2]
= [tex]\frac{f(2)-f(0)}{2-0}[/tex]
= [tex]\frac{0-(-4)}{2-0}[/tex] [Since, f(2) = 0, f(0) = -4]
= 2
Right most interval where the graph is positive → [2, 4]
The key feature of a function include the intercepts and intervals of the function
The range is [-4,2)The domain is [-5,4)The x-intercepts are -2 and 2The average rate of change over the interval [0,2] is 2The right-most interval where the graph is positive is [2,4](a) The range
The least y value on the graph is at y = -4, and the maximum is at y = 2, with an open circle.
So, the range is:
[tex]\mathbf{Range = [-4,2)}[/tex]
(b) The domain
The least x value on the graph is at x = -5, and the maximum is at x = 4, with an open circle.
So, the domain is:
[tex]\mathbf{Domain = [-5,4)}[/tex]
(c) The x-intercepts
This is the point where the graph crosses the x-axis.
So, we have:
[tex]\mathbf{x-intercept =-2 \ and\ 2}[/tex]
(d) Average rate of change over [0,2]
From the graph, we have:
f(0) = -4
f(2) = 0
So, the average rate of change (m) is:
[tex]\mathbf{m = \frac{f(2) - f(0)}{2 - 0}}[/tex]
[tex]\mathbf{m = \frac{0 - -4}{2 - 0}}[/tex]
[tex]\mathbf{m = \frac{4}{2}}[/tex]
[tex]\mathbf{m =2}[/tex]
(d) The right-most interval where the graph is positive
The graph is positive from x = 2 to x = 4.
Hence, the right-most interval where the graph is positive is [2,4]
Read more about features of a function at:
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HELP PLS I can’t get this one done
Answer:
B
Step-by-step explanation:
Take it one term at a time
Answer: its B
Step-by-step explanation:
[tex]\sqrt[3]{256x^1^0y^7}[/tex]
256 = 2³(2³)(2²)
x^10 = x³(x³)(x³)x
y^7 = y³(y³)y
Good night!
Given the functions:
f(x) = x2 – 9, and g(x) = x3 + 4x² + 8x - 7, find h(x) = f(x) + g(2).
h(x) =
x3 + 5x2 + 80 -16
h(x) = x3 + 3x² + 80 + 2
h(x) = x3 + 5x2 + 8x - 16
h(x)
- 23 - 3x? 8.2 - 2
h(x)
x3 + 3x2 + 8x + 2
Answer:
h(x) = x² + 24
Step-by-step explanation:
First solve for g(2) in g(x) = x³ + 4x² + 8x - 7 by simply substituting 2 in x variable. The result is 33.
Then get the sum of f(x) and 33 to find h(x).
Together, Iris and Ivan weigh 120 pounds. Iris weighs 10 pounds less than Ivan. How much does each child weigh?
Answer:
Iris weighs 55 pounds, Ivan weighs 65 pounds.
Step-by-step explanation:
Divide 120 by 2: 60
Then make the 10 pound difference by adding and subtracting 5 to 60 for each answer: 55 and 65.
Iris = 55 pounds
Ivan = 65 pounds
Let x be Iris and y be Ivan.
x+ y = 120
y-10+ y = 120
2y - 10 = 120
2y = 120 + 10
2y = 130
y = 130/2
y = 65 pounds
x = y-10
= 65-10
x = 55 pounds
nicholas started a canned food drive at school. the equation representing this is y=235=15, where x is the number of days, and y is the number of cans collected. explain how to determine how many days it would take to collect 2600 cans.
Answer:
195 cans will be left after 10 days
Sample Answer: I am given a number of cans, which is y, and I need to find the number of days, which is x. To do this, I would substitute 2600 for y, to get 2600 = 235x + 15. Solving for x, I would get x = 11. Thus, it would take 11 days to collect 2600 cans.
Step-by-step explanation:
i did the edge thing
Answer:
I am given a number of cans, which is y, and I need to find the number of days, which is x. To do this, I would substitute 2600 for y, to get 2600 = 235x + 15. Solving for x, I would get x = 11. Thus, it would take 11 days to collect 2600 cans.
Step-by-step explanation:
hope this helps
did it on edge
have a good day
Escribe tres números distintos qué sean divisibles por 2,3,5,9,10
Answer: 90, 180, 270
Step-by-step explanation: 90 es divisible por todos esos números. Para obtener dos números más que sean divisibles por esos, simplemente multiplique 90 por 2 y 3.
2 1\2 diveded by3 2\5
Answer:
2
Step-by-step explanation:
Are the ratios 1:2 and 14:18 equivalent?
Answer:
no
Step-by-step explanation: 1:2 is like half of the whole so basically what i mean is the first number has to be half of the second number for example 2:4 or 4:8
Answer:
No
Step-by-step explanation:
If these ratios were equivalent the second would read 14:24. So if the first ratio was 1:3 the second would read 14:42.
SIMPLIFY:
√75r2
a. 5√3r
b. 5r√3r
c. NO SOLUTION
d. 5r√3
Answer:
d.5r√3
Step-by-step explanation:
5 and r is common when square root, so,
√5×5×3×r×r
=5r√3
Convert the following: 20 meters/30 Seconds to miles per hour
Can anyone help with this please
Answer:the correct answer is b
Step-by-step explanation:
Took the test also download the app called photo math all I have to do is take the photo of the problem it’s free of charge
Simplify the expression 10+ (a + 9)
Answer:
19+a
Step-by-step explanation:
Can someone help me I am confused
passes through (0, 1) and (2, 5)
Answer:
y = 2x + 1
Step-by-step explanation:
1. Find the slope: change in y/change in x
[tex]\frac{5-1}{2-0}[/tex] = 2
Slope: 2
2. Find y-intercept by substituting in a point (0, 1)
y = 2x + b
1 = b
3. Put the equation together
y = 2x + 1
The equation of the line passing through the points (0, 1) and (2, 5) is y = 2x + 1.
What is y intercept?y intercept is the y coordinate of the point on the line where it touches the Y axis. The x coordinate will be 0 there.
The equation of a line in slope intercept form is,
y = mx + c
Here m is the value of the slope and c is y intercept.
Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
Given two points (0, 1) and (2, 5).
Slope, m = (5 - 1) / (2 - 0)
= 4 / 2
= 2
c is the y coordinate when x = 0.
We have that point given (0, 1).
So c = 1
Substituting m = 2 and c = 1 in the general form, we get,
y = 2x + 1
Hence the equation of the line is y = 2x + 1.
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Ngo has a collection of dimes and quarters with a total value of $5.20. The number of dimes is 4 less than the number of quarters. How many of each coin does he have?
9514 1404 393
Answer:
16 quarters12 dimesStep-by-step explanation:
Let Q represent the number of quarters. Then (Q-4) is the number of dimes, and the total amount of money is ...
25Q +10(Q -4) = 520
35Q = 560 . . . . . add 40
Q = 560/35 = 16
Ngo has 16 quarters and 12 dimes.
Here is 1 and 2 but I need 3 and 4 done ASAP thankssss!
Problem 1
Answers:
A = 2x2B = 2x2C = 3x2D = 2x3E = 3x3----------------------------------------
Explanation:
The size of a matrix is simply the number of rows and the number of columns. Something like 2x3 means we have 2 rows and 3 columns.
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Problem 2
Answers:
[tex]A_{11} = -1\\\\B_{12} = 6\\\\C_{13} = \text{DNE}\\\\D_{13} = 0\\\\E_{34} = \text{DNE}\\\\A_{22} = 0\\\\B_{21} = 5\\\\C_{31} = -5\\\\D_{23} = 4\\\\E_{22} = -7\\\\[/tex]
----------------------------------------
Explanation:
When saying something like [tex]E_{23}[/tex] we are looking at the item in the second row and third column of matrix E.
The acronym DNE stands for "Does Not Exist". It's another way of saying "Undefined". For instance, note how matrix E has only 3 columns. When we write [tex]E_{34}[/tex] we're asking about something in the fourth column, but no such column exists.
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Problems 3 and 4 seem to be cut off because I don't see them on the screenshot.
Can someone help me please
Answer:
The answer is y = 1/3 |x|
Step-by-step explanation:
Slope for (-1,4) (-5,-8)
Answer: M=3
Step-by-step explanation:
write three numbers that round to 60,000 when rounded to the nearest ten thousand
On a number line, the coordinate of X is 52, the coordinate of Y
is 121, the coordinate of Zis-21 and the coordinate of Wis 25.
Is XY = ZW? Explain your reasoning.
Answer:
No
Step-by-step explanation:
since the magnitude of xy ≠ zw,
|x-y| = xy = |52-121|= 69, |z-w| = zw = |-21-25| = 46
69 ≠ 46