which of the following are necessary when proving the opposite sides of a parallelogram are congruent? Check all that apply. A) Opposite sides are perpendicular B) Corresponding parts of similar triangles are similar C) Opposite sides are congruent D) Corresponding parts of congruent triangles are congruent

To graph the solution set of the inequality 15x + 10y ≥ 1100, find the intercepts of the graph and draw a line passing through them. Then, test a point not on the line to determine which side represents the solution set. The solution set of the inequality is the region below the line on the graph.

To graph the solution set of the inequality 15x + 10y ≥ 1100, we can start by identifying the intercepts of the graph. An intercept is a point where the graph intersects either the x-axis or the y-axis. To find the x-intercept, we set y = 0 in the inequality: 15x + 10(0) ≥ 1100. Simplifying this equation, we have 15x ≥ 1100. Dividing both sides by 15, we get x ≥ 73.33. Therefore, the x-intercept is (73.33, 0).

To find the y-intercept, we set x = 0 in the inequality: 15(0) + 10y ≥ 1100. Simplifying this equation, we have 10y ≥ 1100. Dividing both sides by 10, we get y ≥ 110. Therefore, the y-intercept is (0, 110).

After finding the intercepts, we can draw a line passing through these two points. Since the inequality is ≥, the line will be solid (including the points on the line). Finally, we determine which side of the line represents the solution set. We can choose a test point not on the line, such as (0, 0), and substitute its coordinates into the inequality. If the inequality is true, the shaded region representing the solution set should be below the line.

If the inequality is false, the shaded region should be above the line. In this case, substituting (0, 0) into the inequality gives 15(0) + 10(0) = 0, which is less than 1100. Therefore, the shaded region should be below the line. The solution set of the inequality 15x + 10y ≥ 1100 is the region below the line on the graph.

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LCM 14 & 24 = 168

then use the highest exponents for the variables

 answer = 168x^6y^6z^8

     Original equation 
     4 = √-6-2x+√31-3x

     Isolate
     -√-6-2x = -4+√31-3x

      Tidy up 
     √-6-2x = 4-√31-3x

     Raise both sides to the second power
     (√-6-2x)2 = (4-√31-3x)2

     After squaring 
     -6-2x = 31-3x+16-8√31-3x

     Current equation 
     -6-2x = 31-3x+16-8√31-3x

     Isolate radical on the left hand side
     8√31-3x = 6+2x+31-3x+16

      Tidy up 
     8√31-3x = 53-x

     Raise both sides to the second power
     (8√31-3x)2 = (53-x)2

     After squaring 
     1984-192x = x2-106x+2809

     Rearranged equation
     x2  + 86x  + 825 = 0

     This equation has two rational roots:
       {x1, x2}={-11, -75}
 

     Original equation, root isolated, after tidy up
     √-6-2x = 4-√31-3x

     Plug in  -11 for  x 
      √-6-2•(-11) = 4-√31-3•(-11)

      Simplify
      √16 = -4
      Solution does not check 
      4 ≠ -4 

     Original equation, root isolated, after tidy up
     √-6-2x = 4-√31-3x

     Plug in  -75 for  x 
      √-6-2•(-75) = 4-√31-3•(-75)

      Simplify
      √144 = -12
      Solution does not check 
      12 ≠ -12 

Hopefully this helped You

count the lines horizontally and vertically to see where the lines connect

 x = left to right

y = up and down.

 the black lines are the origins ( 0,0)

 so 3 to the right of a black line and 3 up from the black line equals (3,3)

 Answer is B

Answer:

Option D is correct.

The measure of [tex]\angleWYX = 150^{\circ}[/tex]

Step-by-step explanation:

[tex]\triangle WXY[/tex] is isosceles  and [tex]\angle YWX[/tex] and [tex]\angle YXW[/tex] are base angles.

Isosceles Triangle:

A triangle with two equal sides, and two congruent base angles that means the angles are equal

By the definition, the base angles are equal i.e, [tex]m\angle YWX=m\angle YXW[/tex]

Since, YZ bisects [tex]m\angle WYX[/tex]

Angle Bisector theorem: An angle bisector is a line or ray that divides an angle into two equal angles

then, [tex]\angle WYX =2\angle XYZ[/tex] or

Substitute the value of [tex]\angle XYZ=(15x)^{\circ}[/tex] ;

[tex]\angle WYX =2(15x)^{\circ} = (30x)^{\circ}[/tex]

The sum of measures of these three angles of  triangle WXY is equal to the 180 degree.

In triangle WXY we have;

[tex]\angle YXW+\angle WYX+\angle YWX=180^{\circ}[/tex]

Substitute the value of [tex]m\angle YWX=m\angle YXW=(2x+5)^{\circ}[/tex] and [tex]\angle WYX=(30x)^{\circ}[/tex] in above formula:

[tex]2\angle YXW+30x=180^{\circ}[/tex] or

[tex]2\cdot(2x+5)+30x=180^{\circ}[/tex]

Simplify:

[tex]4x+10+30x=180^{\circ}[/tex]

Combine like terms ;

[tex]34x+10^{\circ}=180^{\circ}[/tex] or

[tex]34x=170^{\circ}[/tex]

Simplify;

[tex]x= \frac{170}{34} =5^{\circ}[/tex]

Substitute the value of x in  [tex]\angle WYX [/tex];

[tex]\angleWYX = (30x)^{\circ} = 30 \cdot 5 = 150^{\circ}[/tex]

Therefore, the measure of [tex]\angleWYX = 150^{\circ}[/tex]

Answer:

150 D

Step-by-step explanation:

the answer would be B :) hope this helps

The expression to show how much money he has left is  $(33.5 - 10.45).

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given that, Tim earned $16 babysitting and $17.50 mowing a lawn.

What Tim has earned we'll add which is $(16 + 17.50) = $33.5.

He paid $8.50 for a movie and bought a small popcorn for $1.95.

His spendings we'll also add which is $(8.5 + 1.95) = $10.45.

Now, to write an expression for how much money he has left we'll subtract

his total spending from his total earnings which is,

= $(33.5 - 10.45).

= $23.05.

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Final answer:

The rate of change for the equation y=9x+4 is 9, representing a constant slope where for every unit increase in x, y increases by 9 units.

Explanation:

The rate of change in the linear equation y=9x + 4 is the coefficient of the x term, which represents the slope of the line. In this case, the rate of change is 9. This means that for every one unit increase in x, the value of y increases by 9 units. Since this is a linear equation, the rate of change is constant, meaning it does not change regardless of the value of x.

Answer:

226.08

Step-by-step explanation:

To find the average number of car rentals processed per day, we first calculate that 70% of the 200-car fleet equates to 140 cars. Each car is rented for 4 days, so, therefore, the total number of cars rented in four days is 560. Hence, the average daily rentals are 140 cars.

To calculate the average number of car rentals processed per day, we need to consider that the company rents 70% of their 200-car fleet daily. That is, 70/100 * 200 = 140 cars.

Since each car is rented for an average of 4 days, each day's rentals represent 1/4 of the number of cars that will be rented over the next four days. Therefore, the total number of cars rented in four days would be divided by 4 to get the daily average. In this case, it's 140 * 4 = 560, and 560 / 4 = 140 car rentals per day.

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the average value of f(x) = 1/x over the interval [e, 2e] is, ln(2)/e.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

f(x) = 1/x over the interval [e, 2e].

i.e. we get,

[tex]\frac{1}{2e-e}[/tex] × [tex]\int\limits^{2e}_e {1/x} \, dx[/tex] =1/e. ln (x)[2e, e]

                        =ln(2e)/e - ln(e)/e

                        =[ln2+lne/e] - 1/e

                        =ln2/e +1/e -1/e

                        =ln(2)/e

hence,  the average value of f(x) = 1/x over the interval [e, 2e] is, ln(2)/e.

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The limit as x approaches zero of sin3x all over x is indeed 3.  

Below is a step by step display of how to derive this answer.

To solve this problem, we simply have to use ratio and proportion.

We know that 15 gallons is consumed in 10 minutes therefore the conversion factor is:

15 gallons / 10 minutes

Therefore in 77 minutes:

water consumed = (15 gallons / 10 minutes) * 77 minutes

water consumed = 115.5 gallons

The ages of James, Paul and Dan is required.

James is 30 years old, Paul is 80 years old and Dan is 10 years old.

Let the ages of James be [tex]j[/tex], Paul be [tex]p[/tex] and Dan be [tex]j[/tex].

James is three times the age of Dan

[tex]j=3d[/tex]

Paul is two times the sum of the ages of James and Dan

[tex]p=2(j+d)\\\Rightarrow p=2(3d+d)\\\Rightarrow p=2(4d)=8d[/tex]

The combined ages of the people is 120

[tex]j+p+d=3d+8d+d\\\Rightarrow 120=12d\\\Rightarrow d=\dfrac{120}{12}\\\Rightarrow d=10[/tex]

[tex]j=3d=3\times 10\\\Rightarrow j=30[/tex]

[tex]p=8d=8\times 10\\\Rightarrow p=80[/tex]

So, James is 30 years old, Paul is 80 years old and Dan is 10 years old.

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Answer:

The answer is C, 40