Given:
The system of equations is:
Line A: [tex]y=x-4[/tex]
Line B: [tex]y=3x+4[/tex]
To find:
The solution of given system of equations.
Solution:
We have,
[tex]y=x-4[/tex] ...(i)
[tex]y=3x+4[/tex] ...(ii)
Equating (i) and (ii), we get
[tex]x-4=3x+4[/tex]
[tex]-4-4=3x-x[/tex]
[tex]-8=2x[/tex]
Divide both sides by 2.
[tex]-4=x[/tex]
Substituting [tex]x=-4[/tex] in (i), we get
[tex]y=-4-4[/tex]
[tex]y=-8[/tex]
The solution of system of equations is (-4,-8).
Now verify the solution by substituting [tex]x=-4, y=-8[/tex] in the given equations.
[tex]-8=-4-4[/tex]
[tex]-8=-8[/tex]
This statement is true.
Similarly,
[tex]-8=3(-4)+4[/tex]
[tex]-8=-12+4[/tex]
[tex]-8=-8[/tex]
This statement is also true.
Therefore, (-4,-8) is a solution of the given system of equations, because the point satisfies both equations. Hence, the correct option is C.
I have to solve the equation:
[tex] |4 \sqrt{2} - 6 | + |2 \sqrt{10} - 6| [/tex]
The first thing I tried is simply removing the modules, it seemed like the most logical solution and this is the answer I got, but it wasn't any of the options:
[tex]4 \sqrt{2} + 2 \sqrt{10} + 12[/tex]
The second thing I tried is putting both equations in one module and sum the first one with the second one in parentheses like this:
[tex] |4 \sqrt{2} - 6 + (2 \sqrt{10} - 6 | = \\ = |4 \sqrt{2} - 6 + 2 \sqrt{10} + 6 | = \\ = 4 \sqrt{2} + 2 \sqrt{10}[/tex]
But this wasn't in the answers either.
After I checked, the correct answer was:
[tex]2 \sqrt{10} - 4 \sqrt{2} [/tex]
So I was wondering where does the minus come from?
It is in a module and between the modules, there's a plus and even if that plus somehow turns into a minus when it goes inside the modules, which I'm not aware of, it would still turn into a plus because it is in a module ;-; Or I'm just st*pid, I don't know.
Think back to the definition of absolute value:
• If x ≥ 0, then |x| = x.
• If x < 0, then |x| = -x.
In other words, the absolute value always returns a positive number. So if x is positive, leave it alone; but if it's negative, then you have to negate it to get a positive number back.
This means that you cannot simply reduce |x - y | to x - y because you need to consider the possibility that x - y may be negative, in which case |x - y | would reduce to -(x - y) = y - x.
In this case,
|4√2 - 6| = -(4√2 - 6) = 6 - 4√2
because 4√2 < 6, which you can determine by comparing both of these numbers as square roots:
4√2 = √16 √2 = √32
6 = √36
and √32 < √36 because 32 < 36.
Similarly,
|2√10 - 6| = 2√10 - 6
because
2√10 = √4 √10 = √40
6 = √36
So ultimately,
|4√2 - 6| + |2√10 - 6| = (6 - 4√2) + (2√10 - 6) = 2√10 - 4√2
In January, a bookstore sells 450 books, but in February, it sells only 300 books. What is the percent of change from January to February?
66.7%
-50%
-33.3%
50%
Answer:
-33.33%
Step-by-step explanation:
((450-300)÷450)×100
(150÷450)×100
-33.33%
I need help please! ASAP!
Answer:
Step-by-step explanation:
The measure of 1 in the diagram below is 113º.
What is the measure of <4?
Answer: 67°
Step-by-step explanation:
From the diagram given, we can see that 1 and 4 are angles on a straight line. It should be noted that sum of angles on a straight line equals to 180°.
Therefore,
Angle 1 + Angle 4 = 180°
113° + Angle 4 = 180°
Angle 4 = 180° - 113°
Angle 4 = 67°
Therefore, the measure of <4 is 67°
Find the value of k if the slope of the line 2x-ky+3=0 is 5/3
Answer:
6/5
Step-by-step explanation:
2x+3=ky
ky=2x+3
y=(2x+3)/k
y=2x/k + 3/k - > equation 1
y=mx + c - >equation 2
Comparing equation 1 and 2,
2/k=m
2/k=5/3
6/5=k
k=6/5
Ms.Jane runs a boutique in Jumeirah. She bought 50 m cloth to stitch shirts for her boutique.If one shirt requires 2m 15cm of the cloth then
Answer: 23 shirts
Step-by-step explanation:
Given
Ms. Jane bought 50 m cloth to stitch shirts
If one shirt requires 2m and 15 cm cloth i.e. [tex]2+0.15=2.15\ m[/tex]
No of shirts that can be made using 50 m cloth
[tex]\Rightarrow \dfrac{50}{2.15}=23.25\approx 23\ \text{Shirts}[/tex]
Therefore, Ms. Jane can made 23 shirts from 50 m cloth.
please please please help
Answer:
a S(-3) = 2(-3)(-3)+5(-3)-12
=18-15-12
=-9
b 2x2+5x-12=0
2x2+8x-3x-12=0
2x(x-4)-3(x+4)=0
(2x-3)(x+4)=0
2x-3=0
x=3/2
x=-4
sorry I couldn't answer the other question
Use the image to complete the equation below
Each month, Kelsey donates 1/5 of her allowance to her school for supplies. 1/2 of that amount goes to the chorus class. How much of her allowance goes to supplies for the chorus class?
Please show your work.
Thank you :)
What happens if simultaneous Equations have two of the same variable like below? How would I solve it?
6A + 4B + 5C = 390
6A + 4B + 5.75C = 405
Answer:
C = 20
Step-by-step explanation:
What happens if simultaneous Equations have two of the same variable like below? How would I solve it?
6A + 4B + 5C = 390
6A + 4B + 5.75C = 405
Step 1
We solve for C first
6A + 4B + 5C = 390....Equation 1
6A + 4B + 5.75C = 405... Equation 2
We substract Equation 1 from Equation 2
0.75C = 15
C = 15/0.75
C = 20
Question 2 of 10
What is the equation of the following line? Be sure to scroll down first to see
all answer options.
10+
(7.2)
-10
(0,0)
10
- 10+
A. y=-7x
O B. y = 2x
Answer:
D)
[tex]y = \frac{2}{7} x[/tex]
Step-by-step explanation:
[tex]slope = \frac{rise}{run} = \frac{2}{7} [/tex]
Y-intercept=0
The equation of line is y = ( 2/7 )x where the slope of line is m = 2/7
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 0 , 0 )
Let the second point be Q ( 7 , 2 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 2 - 0 ) / ( 7 - 0 )
Slope m = 2/7
Now , the equation of line is y - y₁ = m ( x - x₁ )
On simplifying , we get
y - 0 = ( 2/7 ) ( x - 0 )
y = ( 2/7 )x
Therefore , the value of A is y = ( 2/7 )x
Hence , the equation of line is y = ( 2/7 )x
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1 Solve the compound inequality 4x>-16 or 6x <-48
Answer:
Step-by-step explanation:
4x > -16 reduces to x > -4: All numbers greater than x = -4 (shaded area to the right of -4).
6x < -48 reduces to x < -8: All numbers to the left of -8 (shaded area to the left of -8).
Solution: (-infinity, -4) ∪ (-8, infinity)
The number line between -8 and -4 is not part of the solution set (is not shaded or darkened)
Draw an open circle at -8 and extend an arrow to the left of this circle. Then draw an open circle at -4 and extend an arrow to the right of this circle.
Sin 0 = 7/25 and cos 0 = -24/25. Find tan 0
Answer:
[tex]tan \theta = - \frac{7}{24}[/tex]
Step-by-step explanation:
[tex]sin \theta = \frac{7}{25} \ , \ cos\theta = \frac{-24}{25}\\\\tan \theta = \frac{sin\theta}{cos\theta}[/tex]
[tex]=\frac{\frac{7}{25}}{\frac{-24}{25}} \\\\=\frac{7}{25} \times \frac{25}{-24}\\\\= - \frac{7}{24}[/tex]
is x = 3 a function or not a function ?!
Answer:
x = 3 is not a function because, for one thing, its graph does not pass the vertical line test.
Help with this ASAP please
Answer:
86
Step-by-step explanation:
43×2=86
bisector means halves an angle into two equal angles
1. the surface area of the rectangular prism
5 cm
20 cm
4cm
Answer:
430 cm^2
thankuhh
have a nice day
Is how far from work do all the employees live a statistical question
Answer:
need more info sry
Step-by-step explanation:
A group of friends wants to go to the amusement park. They have no more than $230 to spend on parking and admission. Parking is $8, and tickets cost $27.75 per person, including tax. Write and solve an inequality that can be used to determine xx, the number of people who can go to the amusement park.
Answer:
6 people
Step-by-step explanation:
$230 - $8 = $222
x · 35.75 = 222
x · 35.75 ÷ 35.75 = 222 ÷ 35.75
[tex]x=6\frac{30}{143}[/tex]
Rewrite the following quadratic function in vertex form. Then, determine if it has a maximum or minimum and say what that value is.
y = -x 2 + 6x + 5
HELP PLEASE!!!!!!
Answer:
-(x-3)²+14
maximum
(3,14)
Step-by-step explanation:
y= -x²+6x+5
y-5= -x²+6x
y-5= -(x²-6x)
complete the square
y-14= -(x²-6x+9)
x²-6x-9= -(x-3)²
y-14= -(x-3)²
y= -(x-3)²+14
maximum because a is negative
vertex is (3,14)
In the United States, the average public school teacher currently earns an annual salary near $55,202. Reported national average salaries for the last six decades are listed below.
Year National Average
Teachers’ Salary
1960 $4,995
1970 $8,626
1980 $15,970
1990 $31,367
2000 $41,807
2010 $55,202
Determine the average salary increase per year between the years 1980 and 1990.
$1,539.70
$8,367.80
$2,566.20
$1,004.10
A is right
Step-by-step explanation:
Obviously A is the correct answer you have already gave us hint. Btw thanks for the pts
Write 5/8 as a sum of fractions two different ways.
Answer:
2/8 + 3/8
1/8 + 4/8
Step-by-step explanation:
I hope this is what you mean!
If this helps you, please mark brainliest!
The requried, 5/8 can be expressed in two different ways of the sum as 1 / 8 + 4 / 8 and 2/8 + 3/8.
What is the fraction?Fraction is defined as the number of compositions that constitutes the Whole.
Here,
As mentioned in the quesiton, to determine 5/8 as a sum of fractions in two different ways.
5 / 8 = a / 8 + b / 8
5 = a + b
So the above-modeled equation, gives the required fraction, by assuming a value that satisfies the equation,
For a = 1, 2, 3, 4 , b = 4, 3, 2, 1
So different combination is given as, 1 / 8 + 4 / 8 and 2/8 + 3/8.
Thus, the requried, 5/8 can be expressed in two different ways of the sum as 1 / 8 + 4 / 8 and 2/8 + 3/8.
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Please help me it's urgent!
Match the graph with the correct set of equations for each linear system.
4. Find the solution for the following problem. Explain your reasoning."
What is the solution to the equation below?
2(x - 3) = 2x + 5
Answer:
no solution
Step-by-step explanation:
Given
2(x - 3) = 2x + 5 ← distribute parenthesis on left side
2x - 6 = 2x + 5 ( add 6 to both sides )
2x = 2x + 11 ( subtract 2x from both sides )
0 = 11 ← not possible
This indicates the equation has no solution
How do I do this ( answer please )
Answer:
I think see what circuit is connected to the light
Step-by-step explanation:
Distribute 5x\left(1+3x\right).5x(1+3x)
Answer:
5x + 15x²
Step-by-step explanation:
Given the expression 5x(1+3x)
Generally, according to the distribution rule,
A(B+C) = AB + AC
A is distributed over B and C
Similarly,
5x(1+3x)
= 5x(1) + 5x(3x)
= 5x + 15x²
Hence the expression required is 5x + 15x²
Explain how to use the standard normal table to
find the probability associated with the shaded
area under the curve.
A
^
-3
-2.
0
1
2
3
0.4
1.9
The probability associated with the shaded area under the curve is 0.6267
How to determine the probabilities?From the curve, we have the following parameters:
z1 = 0.4
z2 = 1.9
Using the standard normal table, determine the p values at the respective z-scores
P(z >0.4) = 0.3446
P(z<1.9) = 0.9713
The probability is then calculated using:
P = P(z<1.9) - P(z >0.4)
Substitute the known values
P = 0.6267
Hence, the probability associated with the shaded area under the curve is 0.6267
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Answer:
The standard normal table gives areas under the curve to the left of z-scores.
Find the probability in the standard normal table that a value is to the left of 1.9.
Find the probability in the standard normal table that a value is to the left of 0.4.
Subtract the probability of a value being to the left of 0.4 from the probability of a value being to the left of 1.9.
Paula reside em uma cidade em que a densidade demográfica é igual a 5 500 hab/km2. Nessa cidade, a população está distribuída em um território de 80 km2. Qual é a população da cidade em que Paula reside? 11 078. 440 000. 880 000. 1 760 000.
Answer:
RESPOSTA:B) 440.000
Step-by-step explanation:
UMA BASICA EXPLICAÇÃO: BASTA PEGAR OS 5 500HAB/KM
E MULTIPLICAR ELE PELO TERRITORIO QUE É:80KM
5 500HAB × 80KM = 440.000
Jacob drove 450 miles at an average rate of 65 miles per hour. Rounded to the nearest tenth of an hour, how long did the trip take
Time = distance / speed
Time = 450 miles / 65 miles per hour
Time = 6.9 hours
A building casts a 21 foot shadow along the ground. A person 5 feet 3 inches casts a shadow 7 feet long.
How tall is the building?
Answer:
~28
Step-by-step explanation:
5 feet 3 inches is 5.25 feet.
We divide 7/5.25 which equals 1.3333333333333 (repeating)
That means we multiply 21 by 1.333333333333 which would round up to 28 feet. (the exact answer is 27.99999999999999999)
the expression -7y is called what
Answer:
called "pi".
Step-by-step explanation: