Which graph best represents the solution to the following system?
5x - 2y < (less than or equal to) 10
x + y < 5
The graph that best represents the solution to the given system is:
Graph A.
Step-by-step explanation:We are given a system of inequalities as:
[tex]5x-2y\leq 10[/tex]
and [tex]x+y<5[/tex]
i.e. the graph of first inequality is a solid straight line( since the inequality is not strict) that passes through (2,0) and (0,-5) and the shaded region is towards the origin( since it passes the zero point test)whereas the graph of second inequality is a dotted straight line(since the inequality is strict) that passes through (0,5) and (5,0) and the shaded region is towards the origin( since it passes the zero-point test)Hence, the graph is:
Graph A.
Why is the absolute value of a number always positive?
It's not. The absolute value of any number is the positive version of that number except for the absolute value of 0. This is the only situation where the absolute value of a number is not positive. The absolute value of 0 is just 0.
On a certain map 3/4 inch represents one mile, what distance, in miles is represented by 1 3/4 inches
How is each function related to y=x? Graph the function by translating the parent function
1) y=x+2 2) y=x-1.2
I need help with this. I don't know what to do. I was sick and stayed home but I had homework and I wasn't taught how to do it could. Someone help me with this by explaining it step by step? Thank you.
Which expression is equivalent to 3x(-4x^2+5x-8)-6(x^2-5x+7)?
A. 12x^3-9x^2+6x-42
B.-12x^3-54x^2+6x-42
C.-12x^3+9x^2+6x-42
D.-27x^3-6x^2+6x-42
What is the principle for f)? The math is Simple Interest
Answer:
E
Step-by-step explanation:
a number , x,rounded to 1 decimal place is 3.7 what is the error interval for x
The error interval will be [3.65,3.75).
What is an error interval?The error interval is the limit or range of accuracy where the number is truncated or rounded. This interval simply shows the range which it could be before rounding.
Given here the decimal number is 3.7 which is after rounded to 1 decimal place.
As the number is rounded to the nearest 0.1 unit, therefore, the error will be half of 0.1 which is 0.1/2= 0.05
Then the lower limit of the error interval will be 3.7-0.05= 3.65
the higher limit of the error interval will be 3.7+0.05= 3.75
the error interval will be 3.65≤x<3.75
As we are rounding 1st decimal unit, if the second decimal unit is greater than 5 then the first decimal unit will be 6. Similarly, if the second decimal unit is less than 5 then the first decimal unit will be 7.
There are the numbers below which on rounding give 3.7
3.65 ,3.66,3.67 ,3.68,3.69,3.70,3.71,3.72,3.73,3.74
Therefore the error interval will be [3.65,3.75).
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The error interval for a number x, which when rounded to one decimal place is 3.7, is [3.65, 3.75).
Explanation:When a number, x, rounded to one decimal place is 3.7, the error interval for x represents the range of actual values x could be to give that rounded figure. So, if x is rounded to 3.7, it means that the value must be at least 3.65 and less than 3.75 when considering rounding to one decimal place. Essentially, the number must be in the half-open interval [3.65, 3.75).
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help with 8th grade math! will upvote!! <33
Which of these is a simplified form of the equation 8p + 4 = − p + 7 + 2p + 3p?
A. 14p = 11
B. 8 = 4
C. 4p = 3
D. 12 = 13
Find the difference. (-ab+8a-5)-(-8ab-4)
"A 23kg kg child goes down a straight slide inclined 38∘ above horizontal. The child is acted on by his weight, the normal force from the slide, kinetic friction, and a horizontal rope exerting a 30N force as shown in the figure.(Figure 1)
How large is the normal force of the slide on the child?"
Force is simply the pull or push that acts on an object.
The normal force acting on the child is 159.12 N
The forces acting on the child are
The 30 N force at 38 degreesThe weight of the childThe weight of the child along the vertical component is:
[tex]\mathbf{Weight = mg \times cos(theta)}[/tex]
So, we have:
[tex]\mathbf{Weight = 23 \times 9.8 \times cos(38)}[/tex]
[tex]\mathbf{Weight = 177.62}[/tex]
The horizontal component of the 30 N force is:
[tex]\mathbf{F_2 = 30 \times sin (38)}[/tex]
So, we have:
[tex]\mathbf{F_2 = 18.50}[/tex]
The normal force (F) on the child is:
[tex]\mathbf{F = Weight - F_2}[/tex]
[tex]\mathbf{F = 177.62N - 18.50N}[/tex]
[tex]\mathbf{F = 159.12N}[/tex]
Hence, the normal force is 159.12 N
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a system of equations consisting of a linear equation and a quadratic equation has infinitely many solutions. is this statement true?
Always
Sometimes
Never
I think the answer is Sometimes . X=Y and X^2-Y^2=0 Has infinitely Solutions
Answer:
The statement that says that a system constructed by a linear and a quadratic equation, has infinitely solutions is never true.
Step-by-step explanation:
This situations can be explained more easy by the graphic solution of the system of equations. As we know, a cuadratic equation represents a parabola and the linear equation a line, so the solution of the system can be understood as the interseption od the parabola and the line.
In the attached figure above we expouse the three different cases could hapend. In the first case, we have two interceptions, so 2 solutions. For the second case, we have 1 interseption, which represents one solution. In the third case the line doesnt touch the parabola in any point thus we get no solution.
Therefore in none of the cases explained we found infinite solutions, this situacion can never happens.
In the example the second equation doesnot represents a quadratic equation. A quadratic equation has the form of:
Y = aX^2 + BX + C
Thus the given system cannot be understood as a the example of the kind.
The pair of points (3,8) and (x, 6) are on the graph of am inverse variation. What is the missing value?
Your neighbor leaves his yard, which is 120 ft from the bus stop. He begins to walk toward you at the bus stop and then passes you. He walks at a speed of 4 ft/s. His distance d from you after t seconds is given by d = |120 − 4t|. After how many seconds is your neighbor 30 ft from you?
To find the amount of time it takes for your neighbor to be 30 ft from you, you set up and solve an equation using the given information.
Explanation:To find the amount of time it takes for your neighbor to be 30 ft from you, we need to set up an equation and solve for t. The distance d is given by d = |120 - 4t|. The absolute value represents the distance in one direction, so it does not matter if your neighbor is walking towards you or past you. We want to find when the distance is 30 ft, so we set up the equation 30 = |120 - 4t|.
Solving this equation gives us two possibilities: 30 = 120 - 4t and 30 = -(120 - 4t). We can solve each equation separately.
For the first equation, 30 = 120 - 4t, we subtract 120 from both sides to get -90 = -4t. Dividing both sides by -4 gives us t = 22.5.
For the second equation, 30 = -(120 - 4t), we multiply both sides by -1 to get -30 = 120 - 4t. Subtracting 120 from both sides gives us -150 = -4t. Dividing both sides by -4 gives us t = 37.5.
So your neighbor is 30 ft from you after 22.5 seconds and 37.5 seconds.
Lydia bought a shirt at 20% off its retail price of $40. She paid 5% tax on the price after the discount. How much did Lydia pay for the shirt?
$42
$36.60
$34
$33.60
Answer:
$33.60 is the correct answer.
Step-by-step explanation:
Price of the shirt = $40.00
discount rate = 20% or 20/100
so price of the shirt = 40 × 0.20 = 8
Shirt's price after 20% discount = 40 - 8 = $32.00
Now she paid 5% tax on the price after discount.
5% tax of 32.00
0.05 × 32 = $1.60
This amount will be added to his discounted price of a shirt.
= 32.00 + 1.60 = $33.60
Lydia pay $33.60 for the shirt.
Solve this problem
-2=c+2
The momentum of a system before a collision is 2.4 × 103 kilogram meters/second in the x-direction and 3.5 × 103 kilogram meters/second in the y-direction. What is the magnitude of the resultant momentum after the collision if the collision is inelastic?
A. 1.7 × 103 kilogram meters/second
B. 2.1 × 103 kilogram meters/second
C. 3.4 × 103 kilogram meters/second
D. 4.2 × 103 kilogram meters/second
E. 5.7 × 103 kilogram meters/second ...?
Answer:
Option D - [tex]4.2\times 10^3[/tex] kilogram meters/second.
Step-by-step explanation:
Given : The momentum of a system before a collision is [tex]2.4 \times 10^3[/tex] kilogram meters/second in the x-direction and [tex]3.5 \times 10^3[/tex] kilogram meters/second in the y-direction.
To find : What is the magnitude of the resultant momentum after the collision if the collision is inelastic?
Solution :
In inelastic,
The magnitude of the resultant momentum after the collision (and before) can be determined by using the Pythagorean theorem.
[tex]c^2 = a^2 + b^2[/tex]
Where, a is the momentum before collision [tex]a=2.4 \times 10^3[/tex]
b is the momentum after collision [tex]b=3.5 \times 10^3[/tex]
c is the total amount of momentum before and after collision.
Substitute the value,
[tex]c^2 = (2.4\times10^3)^2 + (3.5\times10^3)^2[/tex]
[tex]c^2 =5760000+ 12250000[/tex]
[tex]c=\sqrt{18010000}[/tex]
[tex]c=4243.819[/tex]
[tex]c=4.2\times 10^3[/tex] kg m/s
Therefore, Option D is correct.
The magnitude of the resultant momentum after the collision if the collision is inelastic is [tex]4.2\times 10^3[/tex] kilogram meters/second.
Which of these numbers has the least value?
a. 7.2 x 10
b. 8.1 x 10
c. 9,100,000
d. 9.5 x 10
As we can see that only 7.2 x 10 has least value. Thus, option A is the correct answer.
What is rounding a number to some specific place?Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.
Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.
The digit 5 acts as a limit.
After solving we get.
a. 7.2 x 10 will gives 72.
b. 8.1 x 10 will gives 81.
c. 9,100,000
d. 9.5 x 10 will gives 95.
As we can see that only 7.2 x 10 has least value. Thus, option A is the correct answer.
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A number a is a root of P(x) if and only if the remainder, when dividing the polynomial by x - a, equals zero.
A. True
B. False
Answer:
statement is true .
Step-by-step explanation:
Given : Statement A number a is a root of P(x) if and only if the remainder, when dividing the polynomial by x - a, equals zero.
To find : Statement is true or false.
Solution : By polynomial theorem if x-a divide the polynomial P(x) and we get reminder zero then a would be the factor.
Therefore, statement is true .
Answer:
true
Step-by-step explanation:
Which equation does the graph of the systems of equations solve? It's a quadratic graph opening down and quadratic graph opening up. They intersect at (0,3) and (2,-5).
(a)x2 - 2x + 3 = 2x2 - 8x - 3
(b)x2 - 2x + 3 = 2x2 - 8x + 3
(c)-x2 - 2x + 3 = 2x2 - 8x - 3
(d)-x2 - 2x + 3 = 2x2 - 8x + 3
Answer:
D. [tex]-x^{2} -2x+3=2x^{2} -8x+3[/tex]
Step-by-step explanation:
We are given that,
The graph of the system of equations is a 'quadratic graph opening down and a quadratic graph opening up'.
This means that one quadratic equation will have leading co-efficient positive and other will have leading co-efficient negative.
So, we get that options A and B are discarded.
Further it is provided that the graph intersect at ( 0,3 ) and ( 2,-5 ).
This means that the pair of points must satisfy the given system of equations.
So, according to the options:
C. [tex]-x^{2} -2x+3=2x^{2} -8x-3[/tex]
Putting x = 0, gives 3 = -3, which is not possible.
So, option C is dicarded.
D. [tex]-x^{2} -2x+3=2x^{2} -8x+3[/tex]
Putting x = 0 gives 3 = 3 and x = 2 gives -5 = -5.
Hence, the graph of the given system solves the equation [tex]-x^{2} -2x+3=2x^{2} -8x+3[/tex].
Answer:
(d)-x2 - 2x + 3 = 2x2 - 8x + 3
Step-by-step explanation:
Explain why a point in the polar plane cannot be named by a unique ordered
pair (r, theta).
A point in the polar plane can have multiple representations due to the periodic nature of angles and the possibility of using negative radii to represent a point in the opposite direction from the pole.
Explanation:The question asks to explain why a point in the polar plane cannot be named by a unique ordered pair (r, θ). In the polar coordinate system, each point is determined by a radius (r) and an angle (θ).
However, a point can have multiple representations due to the periodic nature of angles. If you add or subtract multiples of 2π radians (or 360 degrees) from θ, you will land on the same point in the polar plane.
Additionally, if the radius (r) is negative, the direction is reversed, which also leads to the same point being represented by (-r, θ + π), where θ is the initial angle.
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A car is traveling at a speed of 90 kilometers per hour. What's the car's speed in meters per second? How many meters will the car travel in 10 seconds? Do not round your answers.
Solve for x: 3 − (2x − 5) < −4(x + 2)
x < −8
x > −8
x < −3
x > −3
I just need help because i don't know how i would do it with x on both sides
Answer: [tex]x<-8[/tex]
Step-by-step explanation:
The given inequality : [tex]3-(2x-5)<-4(x+2)[/tex]
To solve the inequality for x , first we open the parenthesis , we get
[tex]3-2x+5<-4x+(-4)2[/tex]
[tex]\Rightarrow\ 3-2x+5<-4x-8[/tex] [Note : (-)(+)=(-)]
[tex]\Rightarrow\ 3+5-2x<-4x-8[/tex]
[tex]\Rightarrow\ 8-2x<-4x-8[/tex]
Add 4x on both sides , we get
[tex]8-2x+4x<-4x-8+4x[/tex]
[tex]8+2x<-8[/tex]
Subtract 8 from both sides , we get
[tex]2x<-16[/tex]
Divide both sides by 2 , we get
[tex]x<-8[/tex]
Hence, the correct answer is : [tex]x<-8[/tex]
Three fractions that are equivalent to:
12/36
4/5 and
3/12 ...?
Evaluate the expression –0.4(3x – 2) + for x = 4
Answer:
Step-by-step explanation:
=0
According to Edge. the answer is 0 :)
the slope of the line below is 0.8 write the equation of the line in point slope form using the coordinates of the coordinates of the labeled point do not use parenthesis on the y side
Final answer:
The equation of the line in point-slope form is y - y1 = 0.8(x - x1), where the point on the line and the slope are given.
Explanation:
To write the equation of a line in point-slope form, we need the slope of the line and the coordinates of a point on the line. In this case, the slope is given as 0.8. Let's assume the labeled point has coordinates (x, y). The equation in point-slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) are the coordinates of the labeled point. Substituting the given slope and the coordinates of the point, the equation becomes:
y - y1 = 0.8(x - x1)
Remember to not use any parentheses on the y side of the equation.
Given the vector "v" and its inital point, find the terminal point:
"v"=<-1,3>;Initial Point:(4,2) ...?
Which of the statements about the following quadratic equation is true?
6x2 - 8 = 4x2 + 7x
The discriminant is greater than zero, so there are two real roots.
The discriminant is greater than zero, so there are two complex roots.
The discriminant is less than zero, so there are two real roots.
The discriminant is less than zero, so there are two complex roots.
If the discriminant of a quadratic equation is positive then, there are two real roots. Here, the discriminant obtained is 113 which is greater than zero. Hence, option a is correct.
What is quadratic equation ?A quadratic equation are polynomial equation with one variable having the degree of 2. This general form a quadratic equation is written as follows:
ax² - b x + c = 0
The discriminant for a quadratic equation is the term b² - 4ac.
Given the quadratic equation is 6x² - 8 = 4x² + 7 x
it can be rearranged as: 2x² - 7x - 8 =0
If the discriminant of the equation is greater than zero, then there will be two real roots.
solving the discriminant here:
b² - 4ac = (-7)² - 4× 2×(-8) = 113
Here, the discriminant is greater than zero. Therefore, there are two real roots.
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Which of the following are solutions to the equation sinx cosx = 1/4? Check all that apply.
A. π/3+nπ/2
B. π/12+nπ
C. π/6+nπ/2
D. 5π/12+nπ ...?
Answer:
Its B and D.
Step-by-step explanation:
Why do new cars costing $20,000 rent for $40 a day, while tuxedos costing only $500 rent for around $90?
name the property of real numbers illustrated by the equation step by step
-10+4=4+(-10)