The system of equations is consistent and dependent and it can be determined by using the properties of the equation.
Given that,
System of the equation,[tex]\rm y=4x-4\\y=-4x+4[/tex]
We have to determine,
The system of equations is consistent and independent, consistent and dependent, or inconsistent.
According to the question,
When a system has at least one solution, it's called consistent. When it has only one solution, it's called independent.
System of the equation,[tex]\rm y=4x-4\\y=-4x+4[/tex]
On adding both the equation,
[tex]\rm y+ y=4x-4+(-4x+4)\\\\2y = 4x-4-4x+4\\\\2y = 0\\\\ y = 0[/tex]
Substitute y = 0 to evaluate the value of x.
[tex]\rm y = 4x-4\\\\(0)= 4x-4\\\\ 4x=4\\\\ x = \dfrac{4}{4}\\\\x = -1[/tex]
The solution of the equation is (1, 0).
Hence, The system of equations is consistent and dependent.
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Classify the following triangle as acute, obtuse, or right.
O A. Acute
O B. Obtuse
O C. Right
O D. None of these
Answer:
It is an obtuse angle so correct
The given triangle is an obtuse angle triangle.
The correct option is (B).
What is a Triangle?A triangle in geometry is a three-sided polygon with three edges and three vertices.
As per the given data in the diagram:
We are given a triangle and all the angles of the triangle are also given.
We have to find out the type of the triangle.
If all angles of a triangle are less than 90°, then it's an acute angle triangle.
If any angle of the triangle is greater than 90°, then it's an obtuse angle triangle.
If any angle of the triangle is equal to 90°, then it's a right angle triangle.
For the given triangle:
30° < 90°
24° < 90°
126° > 90°
The given triangle is an obtuse angle triangle.
Hence, the given triangle is an obtuse angle triangle.
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Please help! (Only answer if correct)
Erica used 50 pounds of type B coffee
Let the number of pounds of type A coffee be A
Let the number of pounds of type B coffee be B
Total number of pounds = 123
A + B = 123.........................................(1)
Cost of 1 pound of type A coffee = $5.95
Cost of 1 pound of type B coffee = $4.40
Total cost = $654.35
5.95A + 4.40B = 654.35..........................(2)
Make A the subject of the formula in equation (1)
A = 123 - B........................(3)
Substitute equation (3) into equation (2)
5.95(123 - B) + 4.40B = 654.35
731.85 - 5.95B + 4.40B = 654.35
5.95B - 4.40B = 731.85 - 654.35
1.55B = 77.5
B = 77.5/1.55
B = 50
Erica used 50 pounds of type B coffee
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if sarah works 40 hours a week and earns 660 dollars per payroll. how much does she make an hour
Answer:16.50
Step-by-step explanation: hope it helps
Answer:
16.50
Step-by-step explanation:
Ricardo changed $600 into pounds when the exchange rate was $1 = 0.60 pounds
He later changed all the pounds back into dollars when the exchange rate was $1 = 0.72 pounds
How many dollars did he receive ??
600 x 0.60 = 360 pounds
360 /0.72 = 500
He got $500
will mark brainiest
Hans is riding his bicycle. He takes 6 hours to ride 38.4 kilometers. What is his speed?
___ kilometers per hour
Help pleaseeeeieneeiejne
Answer:
Pretty sure the domain for this is all positive numbers and range is all positive numbers over 1.
Step-by-step explanation:
domain refers to x values.
range refers to y values.
PLEASE ANSWER THIS QUESTION!!!! ASSIGNMENT DUE BY 3:15!!!!!!
create an event that would give me a PROBABILITY of 1/2
Answer:
This is a really simple example, but imagine you had two marbles in a bowl. One is blue and one is green. Without looking, you reach into the bowl and pick one marble. What is the probability that the marble is blue?
There are two total marbles and you pick one, with one being blue and one being green. The probability that you pick the blue marble instead of the green marble is 1/2. The 2 represents the total number of marbles and the 1 represents the favorable outcome of drawing a blue marble.
Hope this helps!
solve the equations 3/4x = 21
Therefore, the answer is 28.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
How many match sticks will be in the 8th picture?
What is the solution set for the given inequality if the replacement set for r is {5, 6, 7, 8, 9, 10}? 16-r> 8
Answer:
{5, 6, 7}
Step-by-step explanation:
The solution to the inequality is ...
16 -r > 8 . . . . . given
16 -8 > r . . . . . add r-8
8 > r . . . . . . . simplify
The values in the replacement set that are less than 8 are {5, 6, 7}.
HELP. GIVING BRAINLIST. BRAINLIST. DONT MESS AROUND PLEASE IM DESPERATE.
Answer:
make me brain list
thank u
Step-by-step explanation:
Someone please help me
Some nuts cost $22/kg. How much would 150 g cost?
Answer:
$3.30
Step-by-step explanation:
1 kg = 1000 g
therefore, 150 g = 0.15 kg
multiply the cost by the amount
22 x 0.15 = 3.3, or $3.30
HELP PLEASE!!!!!!!!!!!!
I need help anyone please help.
Answer:
1/4 or 1/2 good luck my guy
Step-by-step explanation:
A 3-gallon jug of water costs $16.80. What is the price per cup?
Answer:
$0.35
Step-by-step explanation:
A gallon is equal to 16 cups, so the 3-gallon jug is equal to 48 cups. You when then divide $16.80 by 48, to get $0.35 or the price per cup! Hope this helps :)
Answer:
0.35
Step-by-step explanation:
Calculate the volume of cuboids with the following dimensions
length= 1.2 m, breadth= 1 m, height= 150 cm
Answer:
1.8 m^3
Step-by-step explanation:
We just have to multiply the lenghts, but careful: the height is in cm. 100 cm = 1 m. Therefore 150cm = 1,5m.
V = 1.2 m * 1m * 1.5m = 1.8 m^3
if m angle 2 =70, find m angle 6
m angle 6= 210
I'm not sure about this question
pls help i really dont understand this
Answer:
Slope: -1
y intercept: -3
equation: y=-1x-3
Step-by-step explanation:
The y intercept is when x is zero.
The blueprint for Moreno's living room has a scale of 2 inches equals 3 feet. The family wants to use a scale of 1 inch equals 2 feet. What is the width of the living room on the new blueprint? (The width is 8)
6) An ice cream factory makes 200 quarts of ice cream in 5 hours. How many
quarts could be made in 12 hours? What was that rate per day?
Answer:
480 quarts could be made in 12 hours
Rate: 40 quarts per hour
Step-by-step explanation:
Rate: 200/5 = 40 quarts per hour
(40)(12) = 480 quarts
What is the measure of a third angle of this triangle
Please explain how to solve in a easy way
I need help with this
Answer:
a and b
Step-by-step explanation:
can someone help me with these? it's a study guide and I lost the notes I took for these
Step-by-step explanation:
[tex]thanks \: you \: the \: point \\ pls \: follow \: me[/tex]
if x(square) plus y(square) is 8.and the froduvt is . what are x and y?
Given :-
x² + y² = 8Product of x and y is 4 .( say )To Find :-
The value of x and y .Answer :-
Here we are given that,
[tex]\red{\longrightarrow}[/tex] x² + y² = 8 .
And ,
[tex]\red{\longrightarrow}[/tex] xy = 4
[tex]\red{\longrightarrow}[/tex] y = 4/x
So that ,
[tex]\red{\longrightarrow}[/tex] x² + (4/x)² = 8
[tex]\red{\longrightarrow}[/tex] x² +16/x² = 8
[tex]\red{\longrightarrow}[/tex] x⁴ + 16 = 8x²
[tex]\red{\longrightarrow}[/tex] x⁴ - 8x² + 16 = 0
Assume k² = x⁴ and k = x²
[tex]\red{\longrightarrow}[/tex] k² - 8k + 16 = 0
[tex]\red{\longrightarrow}[/tex] k² -4k -4k +16 = 0
[tex]\red{\longrightarrow}[/tex] k(k-4) -4(k-4) = 0
[tex]\red{\longrightarrow}[/tex] (k-4)² = 0
[tex]\red{\longrightarrow}[/tex] k = 4
So ,
[tex]\red{\longrightarrow}[/tex] k = x²
[tex]\red{\longrightarrow}[/tex] 4 = x²
[tex]\red{\longrightarrow}[/tex] x = √4
[tex]\red{\longrightarrow}[/tex] x = ±2
Hence the required answer is ±2.
The values of x and y of the given function are; x = y = ±2
Roots of a Polynomial
We are given;
x² + y² = 8 -----(1)
Product of x and y = 4;
Thus; xy = 4
Now, making y the subject we have;
y = 4/x
Putting 4/x for y in eq 1 gives us;
x² + (4/x)² = 8
x² + (16/x²) = 8
Multiply through by by x² to get;
x⁴ + 16 = 8x²
⇒ x⁴ - 8x² + 16 = 0
using online polynomial root calculator, we have x = ±2
Thus, y will also be ±2
Complete question is;
If x² + y² = 8 and the product of x and y is 4, what are x and y?
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What is the slope of the graph of
y= 5/2x+3?
-
Answer:
The slope would be 5/2.
Step-by-step explanation:
Use the formula Y=mx+b. m always represents the slope and the b is the intercept. Therefore the slope of this would be 5/2.
Can someone please give me the (Answers) to this? ... please ...
Answer:
To be congruent at b. no. UV= VK,V=V,UW=KM.
To be congruent at C no. M=S,LM=ST,LK=TU.
The e of the function f(x) = e* has a value of:
a
3.14
2.718
1.98
None of these choices are correct.
Answer: 2.718
Step-by-step explanation:
You don’t need the star there but it is Euchre’s number when you look it up it is 2.718
a train which is 100 meters long is traveling at a speed of 90km per hour. How many seconds will it take for this train to pass completely through a 300 meter tunnel
The train will take 16 seconds to pass completely through a 300 meter tunnel.
Let suppose that the train moves itself at constant velocity, the vehicles needs to cover the tunnel length ([tex]L[/tex]) and its length ([tex]l[/tex]), both in meters, to pass through the tunnel, the time taken by the train ([tex]t[/tex]) is described by the following kinematic formula:
[tex]t = \frac{L+l}{v}[/tex] (1)
Where [tex]v[/tex] is the train velocity, in meters per second.
If we know that [tex]L = 300\,m[/tex], [tex]l = 100\,m[/tex] and [tex]v = 90\,\frac{km}{h}\,\left(25\,\frac{m}{s} \right)[/tex], then the time taken by the train is:
[tex]t = \frac{300\,m + 100\,m}{25\,\frac{m}{s} }[/tex]
[tex]t = 16\,s[/tex]
The train will take 16 seconds to pass completely through a 300 meter tunnel.
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someone pleeeeease help me
Answer:
22.4cm
Step-by-step explanation:
The formula for the diagonal is:
[tex]d = \sqrt{l^{2} + b^{2} +h {}^{2} } [/tex]
Where:
l is the length (AB, CD)
b is the width (BC, AD)
h is the height (AE, BF, CG, DH)
We know d, l, b and we can calculate h
[tex]25 = \sqrt{10^{2} + 8^{2} + h^{2} } [/tex]
We evaluate both sides to ² to remove the square root:
[tex]25^{2} = 100 + 64 + h {}^{2} [/tex]
[tex]625 = 164 + h {}^{2} [/tex]
To find the value of h we have to do the square root, as it is to the ²:
[tex] \sqrt{625 - 124} = h[/tex]
[tex] \sqrt{501} = h = 22.4cm[/tex]