18 + x > 40
a. x > 58
b. x > 22
c. x > -58
d. x > -22

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.

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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The graph that best represents the solution to the given system is:

                    Graph A.

We are given a system of inequalities as:

           [tex]5x-2y\leq 10[/tex]

and  [tex]x+y<5[/tex]

           Hence, the graph is:

                     Graph A.

The error interval will be [3.65,3.75).

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).

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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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:

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]

Answer:

Its B and D.

Step-by-step explanation:

Answer:

E

Step-by-step explanation:

As we can see that only 7.2 x 10 has least value. Thus, option A is the correct answer.

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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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 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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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.

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.

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.

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:

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.

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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Answer:

it shifts the graph up four units

Step-by-step explanation:

it shifts the graph up four units because its outside of the phranthasies, in y=a(x+h)k k is the shift vertically

In the function y=-2(x-1)²+4, the number 4 represents a vertical translation, shifting the graph up by 4 units when compared to the function y=x². Option C) is the correct answer.

In the function y=-2(x-1)²+4, the number 4 acts as a vertical translation of the graph. Comparing this function to the standard parabola y=x², the addition of 4 to the equation represents shifting the entire graph of the parabola upwards by 4 units. Therefore, the correct answer to the effect of the number 4 on the graph, as compared to the graph of the function y=x² is: C. It shifts the graph up 4 units.

Understanding graph transformations is key in analyzing how different parts of the function equation affect the function's graphical representation.

A positive constant added to a function results in a vertical shift of the graph in the upward direction. This means that every point on the graph y=x² is moved 4 units higher on the y-axis to create the graph of y=-2(x-1)²+4.

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.

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.

Answer:

Step-by-step explanation:

=0

According to Edge. the answer is 0 :)

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.