How many solutions does the following system have?

y=2x-12
y=3x+12

f(x) * g(x) = 4 (x² + 5x + 6)

Step-by-step explanation:

f(x) * g(x) = (4x + 8) (x + 3)

              = 4x² + 12x + 8x + 24

              = 4x² + 20x + 24

              = 4 (x² + 5x + 6)

Answer:

16 feet.

Step-by-step explanation:

Given:

Ben’s living room is a rectangle measuring 10 yards x 168.

Question asked:

How many feet does the legs of the room exceed the width ?

Solution:

By applying unitary method:

Length of rectangle = 10 yards = 30 feet (1 yard = 3 feet)

                                                                    (10 yard = [tex]3\times10 = 30)[/tex]

Breadth of  rectangle = 168 inch = 14 feet   (12 inch = 1 feet)

                                                                       (1 inch = [tex]\frac{1}{12}[/tex])

                                                                       ( 168 inch = [tex]\frac{1}{12}[/tex][tex]\times168 = 14 feet)[/tex]

By subtracting the breadth from the length of rectangle,

30 feet - 14 feet = 16 feet

Therefore,  by 16 feet, length of the room exceed the width.

Answer:

I think its 226800.

Step-by-step explanation:

8% of 210,000 is 16800. I added that to 210,000 and got my answer.

First off, rename your equation as -6x=5x+22

You solve the equation by subtracting 5x on both sides to get:

-11x=22

Now divide both sides by -11 to get x=-2

So the answer is C: -2

Hope this helped! This is my first time answering!

Answer:

It is -2 (B)

Because you add  -5x to both sides and you get -11x=22 and 22 divided by -11 is -2

To combine like terms, group terms with the same variable and combine their coefficients. The simplified expression is -3y + 7x^2 + 9.

To combine like terms, we group terms with the same variable and combine their coefficients. In this case, we have:

2y - y + 7 - 1 + 3 + 7x2 - 4y

Combining the like terms:

2y - 4y - y + 7 - 1 + 3 + 7x2

Combining the coefficients:

(2 - 4 - 1)y + (7 - 1 + 3) + 7x2

-3y + 9 + 7x2

So, the simplified expression is -3y + 7x2 + 9.

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Answer:

x = 25

Step-by-step explanation:

You would need to start by creating an equation.  X would represent the numbers of weeks.

500 + 30x = 750 + 20x

Now get the numbers on one side.  To do this subtract 500 form each side.

30x = 250 + 20x

Next, get the variables to one side.  This can be done by subtracting 20x from each side.

10x = 250

Finally divide by 10 to get the variable by its self.

x = 25

Hope this helps.

After 25 weeks, Collin and Kamryn have the same amount of

money in their accounts.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let's suppose the after x weeks, Collin and Kamryn have the same amount of money in their accounts:

Then we can frame a linear equation as per the problem:

Collin's amount of money  = 500 + 30x

Kamryn amount of money = 750 + 20x

500 + 30x = 750 + 20x

10x = 250

x = 25

Thus, after 25 weeks Collin and Kamryn have the same amount of

money in their accounts.

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Answer:

Option D) (k − 12)/m                          

Step-by-step explanation:

We have to write an expression:

the quotient of the quantity k minus 12 and m.

k minus 12 can be written as:

[tex]k - 12[/tex]

The quotient of (k-12) and m means (k-12) is divided by m.

This can be written as:

[tex]\dfrac{k-12}{m}[/tex]

Thus, the correct answer is

Option D) (k − 12)/m                                                                      

Final answer:

The expression for the quotient of 'k minus 12' and 'm' is correctly written as (k - 12) ÷ m, making option D the accurate choice.

Explanation:

The expression for the quotient of the quantity k minus 12 and m should be written as a fraction where the numerator is k minus 12 and the denominator is m. This is mathematically represented by the fraction (k - 12) ÷ m, which indicates the division of the expression k minus 12 by m. Therefore, the correct expression from the given options is D) k - 12 ÷ m.

Final answer:

To determine the maximum number of adults and children that can attend the play without exceeding the bus capacity of 40 people and the $400 budget, set up and solve a system of equations representing the capacity and budget constraints. The solution is 8 adults and 32 children.

Explanation:

We are given a situation where a company charges $18 for each adult (a) and $8 for each child (c) for a bus trip to an upcoming play, with the constraints that the bus holds a maximum of 40 people and the available budget is $400. To find the maximum number of adults and children that can attend under these constraints, we need to set up a system of equations:

For the capacity constraint: a + c = 40

For the budget constraint: 18a + 8c = 400

We can solve this system using substitution or elimination. Let's use elimination. Multiply the first equation by -8 and add it to the second equation to eliminate c:

-8a - 8c = -320

18a + 8c = 400

Adding these two equations together gives us:

10a = 80

Thus, a = 8. Plugging a = 8 back into the first equation, we get c = 32.

The maximum number of adults and children that can attend the play is 8 adults and 32 children.

Answer:

She is not correct

x = -9

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180° therefore if you add all three angles in this triangle it must add up to 180°

50 - 5x + 5 - 4x + 17 - 3x = 180 add/subtract the like terms

72 - 12x = 180

- 12x = 108 divide both sides by 12

-x = 9

x = -9

Answer:

-2x + 4

Step-by-step explanation:

Probably too late, but still need to know how to do this.

Formula for the area of a circle: A = πr²     [pi times radius(r) squared]

The radius is half of the diameter. [diameter would be a line that would go through the whole circle, the radius would be a line that would stop/end halfway through the circle - see attached image]

They gave you the diameter, which is 3, so divide it by 2 or multiply by 1/2 to get the radius, which will be 1.5.

A = πr²    Plug in 1.5 for r

A = π(1.5)²         Find 1.5²  [or 1.5 x 1.5 = 2.25]

A = 2.25π meters²

Answer:

47.314

Step-by-step explanation:

We want find the results of the multiplication,

[tex]4.7314 \times 10[/tex]

When we multiply by 10, we move the decimal point forward once.

When we divide by 10, we move the decimal point backwards once.

In this case, we are multiplying, so

[tex]4.7314 \times 10 = 47.314[/tex]

Option C:

Surface area of the three dimensional figure is 166 unit².

Solution:

Let us find the area of the net of the figure.

Length = 7, Width = 5, Height = 4

Area of the bottom = length × width

                                = 7 × 5

                                = 35 unit²

Area of the Top =  length × width

                          = 7 × 5

                          = 35 unit²

Area of the left = width × height

                         = 5 × 4

                         = 20 unit²

Area of the right = width × height

                         = 5 × 4

                         = 20 unit²

Area of the front = length × height

                            = 7 × 4

                            = 28 unit²

Area of the back = length × height

                            = 7 × 4

                            = 28 unit²

Surface area = 35 + 35 + 20 + 20 + 28 + 28

                     = 166 unit²

Surface area of the three dimensional figure is 166 unit².

Answer: for the third one you use x= 55

so angle = 110

for the fourth one x= 102

angle = 100

Step-by-step explanation:

Answer:

[tex]\displaystyle \frac{1-x}{(5-x)(-x)} =-\frac{x-1 }{ x(x-5)}[/tex]

[tex]\displaystyle \frac{5}{s}\times \frac{2}{5} =\frac{2}{s}[/tex]

Step-by-step explanation:

Errors in Algebraic Operations

It's usual that students make mistakes when misunderstanding the application of algebra's basic rules. Here we have two of them

The first expression is

[tex]1-x / (5-x)(-x)=x-1 / x(x-5)[/tex]

Let's arrange into format:

[tex]\displaystyle \frac{1-x}{(5-x)(-x)} =\frac{x-1 }{ x(x-5)}[/tex]

We can clearly see in all of the factors in the expression the signs were changed correctly, but the result should have been preceeded with a negative sign, because it makes 3 (odd number) negatives, resulting in a negative expression. The correct form is

[tex]\displaystyle \frac{1-x}{(5-x)(-x)} =-\frac{x-1 }{ x(x-5)}[/tex]

Now for the second expression

[tex]5/s+2/5=2/s[/tex]

Let's arrange into format

[tex]\displaystyle \frac{5}{s}+\frac{2}{5} =\frac{2}{s}[/tex]

It's a clear mistake because it was asssumed a product of fractions instead of a SUM of fractions. If the result was correct, then the expression should have been

[tex]\displaystyle \frac{5}{s}\times \frac{2}{5} =\frac{2}{s}[/tex]

Answer:

110°

Step-by-step explanation:

the supplement of an angle is 30 degrees less than twice the measure of the angle itself. find the angle and its supplement.

Let the angle be A, then its supplement = (180 - A)

Now, since the supplement is 30 degrees less than twice the measure of the angle itself, then we'll have:

180 - A = 2A - 30

-3A = - 210

A, or the angle = [tex]\frac{-210}{-3}[/tex]= 70 °

Its supplement, (180 - A) = 180 - 70 = 110°

First off, use carats so its more clear that there's exponents (I'm using parentheses for simplicity):

(4*a^3*b^5)-(16*a^5*b^2)+(12*a^2*b^3)

It's best to divide the whole expression by 4a^2b^2 because it's the least common factor.

So we get (a*b^3)-(4*a^3)+(3b)

I hope this helped. It's been a while since I've done problems like these!

Answer:

Therefore,

[tex]x=\dfrac{1}{2}[/tex]

Step-by-step explanation:

Given:

[tex]4x-2=0[/tex]

To Find:

x = ?

Solution:

[tex]4x-2=0[/tex]

Step 1 : Add 2 on both the side we get

[tex]4x-2+2=0+2\\4x=2[/tex]

Step 2 : Dividing  by 4 on both the side we get

[tex]\dfrac{4x}{4}=\dfrac{2}{4}\\\\x=\dfrac{1}{2}[/tex]

Step 3 :The final  solution is

[tex]x=\dfrac{1}{2}[/tex]

Therefore,

[tex]x=\dfrac{1}{2}[/tex]

The constant of proportionality for the given ratios is 1.5.

The constant of proportionality for the given ratios can be found by dividing the second value of each ratio by the first value. Let's take the first ratio (2,3) as an example:

Constant of proportionality = 3 / 2 = 1.5

Following the same steps for the other ratios, we can find the constant of proportionality for each of them. For the second ratio (4,6), the constant of proportionality is 6 / 4 = 1.5. For the third ratio (6,9), the constant of proportionality is 9 / 6 = 1.5. And for the fourth ratio (8,12), the constant of proportionality is 12 / 8 = 1.5.

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Final answer:

The constant of proportionality for the given ratios is 1.5, as each second number in the ratio is 1.5 times the corresponding first number.

Explanation:

To find the constant of proportionality for the given set of ratios, we first look at each pair to determine if there is a common constant that each first number is multiplied by to result in the second number. Inspecting the given ratios (2, 3), (4, 6), (6, 9), and (8, 12), we can see that in each case, the second number is 1.5 times the first number.

For example, for the ratio (2, 3), if you multiply 2 by 1.5, you get 3. Similarly, for the ratio (4, 6), multiplying 4 by 1.5 gives you 6, and so on. This consistency across the ratios confirms that the constant of proportionality is 1.5.

Answer:

93

Step-by-step explanation:

9      8 3 7

− 0    

 8 3  

− 8 1  

   2 7

 − 2 7

     0

Answer:

In order to be a quadrilateral, a polygon must have 4 sides, and parallelograms always have 4 sides. In order to be a parallelogram, a polygon must have 4 sides with opposite sides parallel. Quadrilaterals always have 4 sides, but do not always have opposite sides parallel.

Step-by-step explanation:

In order to be a quadrilateral, a polygon must have 4 sides, and parallelograms always have 4 sides. In order to be a parallelogram, a polygon must have 4 sides with opposite sides parallel. Quadrilaterals always have 4 sides, but do not always have opposite sides parallel.

t = 1.33 sec

Solution:

Given data:

Velocity [tex](v_0)[/tex] = 17.5 ft/s

Height [tex](h_0)[/tex] = 5 ft

The height can be modeled by a quadratic equation

[tex]h(t)=-16t^2+v_0t+h_0[/tex]

where h is the height and t is the time

[tex]h(t)=-16t^2+17.5t+5[/tex]

[tex]-16t^2+17.5t+5=0[/tex]

a = –16, b = 17.5, c = 5

It looks like a quadratic equation. we can solve it by quadratic formula,

[tex]$\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]

[tex]$\Rightarrow t=\frac{-17.5 \pm \sqrt{(-17.5)^{2}-4\times (-16)(5)}}{2 (-16)}[/tex]

[tex]$\Rightarrow t= \frac{-17.5 \pm \sqrt{306.25+ 320}}{-32}[/tex]

[tex]$\Rightarrow t= \frac{-17.5 \pm 25.025}{-32}[/tex]

[tex]$\Rightarrow t= \frac{-17.5 - 25.025}{-32}, \ t= \frac{-17.5 + 25.025}{-32}[/tex]

[tex]$\Rightarrow t= 1.33, \ t= -0.24[/tex]

Time cannot be in negative. So neglect t = –0.235.

t = 1.33 sec

Hence Amy have to react  1.33 sec before the volleyball hits the ground.

Answer: 3.12:16

Step-by-step explanation:

Answer:

2, 3 and 4

Step-by-step explanation:

6:8

3:4

1. 36/40 = 9/10

2. 9:12 = 3:4

3. 12 to 16 = 3/4 = 3:4

4. 15/20 = 3/4 = 3:4

5. 24:36 = 2/3

6. 16 to 24 = 2/3

The sentence 'The product of b and 6 is less than -16' translates to the inequality '6b < -16' in Mathematics.

In mathematics, translating a sentence into an inequality involves identifying the mathematical symbols and operations represented by the words in the sentence. In this case, 'the product of b and 6' translates to '6 * b' and 'is less than' translates to '<'. So, the sentence 'The product of b and 6 is less than -16' translates to the inequality '6 * b < -16' or '6b < -16' in simplified form.

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Answer:

0.004 or 1/250

Step-by-step explanation:

the word "of" means multiply. so just multiply 1/0 by 0.04. :)

Answer:

0.004

Step-by-step explanation:

you move the decimal a place to the left

Answer:

105 is the least common denominator

Step-by-step explanation:

Since 7, 5 and 3 are all prime.

LCM would be 7×3×5 = 105

Answer:

if Jara has [tex]\$4[/tex] and she wants to buy pen the Prince of each pen is [tex]\$\frac{1}{2}[/tex].

How many pens she can buy.

Step-by-step explanation:

If Jara has [tex]\$4[/tex] and she wants to buy pen the wants to buy pen the Prince of each pen is [tex]\$\frac{1}{2}[/tex] .

How many pen she can buy.

[tex]Let\ Jara\ can\ buy=x\ pens\\\\each\ pen\ cost=\$\frac{1}{2}\\\\Then\ Jara\ can\ buy\ pens=\$\frac{1}{2}x\\\\\frac{1}{2}x=4\\x=8\\Jara\ can\ buy\ =8\ pens[/tex]

Make two equations:

Carlos: y=10x+85

Michael: y=5x+120

Set them equal to each other and solve:

10x+85=5x+120

5x+85=120

5x=35

x=7

So therefore, B is the correct answer

Hope this helped!

Final answer:

To determine when Carlos and Michael will have the same number of baseball cards, set up an equation based on their weekly acquisitions. After solving the equation, it is revealed that they will have the same amount in 7 weeks.

Explanation:

The subjects of interest are Carlos and Michael's baseball card collections.

Carlos starts with 85 cards and adds 10 each week, while Michael starts with 120 and receives 5 more weekly.

To find when they will have the same amount, set up an equation:

Carlos's cards: 85 + 10x (x representing the number of weeks)Michael's cards: 120 + 5xSolve the equation: 85 + 10x = 120 + 5xTherefore, x = 7 weeks, so the answer is B: in 7 weeks.

Answer:

Marcos had 6 nickel coins and 9 quarter coins.

Step-by-step explanation:

We are given the following in the question:

Let x be the number of nickel coins and y be the number of quarter coins.

Marcos had 15 coins in nickels and quarters.

Thus, we can write the equation:

[tex]x + y =15[/tex]

He had 3 more quarters than nickels. We can write he equation,

[tex]y = x + 3[/tex]

Solving the two equations, we get,

[tex]2y = 18\\y = 9\\x + 9 = 15\\x = 6[/tex]

Thus, Marcos had 6 nickel coins and 9 quarter coins.

The solution to the system of equations representing Marcos's coins is x = 6 and y = 9. Hence, Marcos had 6 nickels and 9 quarters.

This question pertains to creating and solving a system of equations in mathematics. Given Marcos had 15 coins in nickels and quarters and considering the information that he had 3 more quarters than nickels, two equations can be formed from this. The first equation sets up the total number of coins: x + y = 15. The second equation sets ups the difference in quantity of each coin: y = x + 3.

To find the solution, substitute the second equation in for y in the first equation. This gives: x + (x + 3) = 15. Solve the equation and find x = 6. Furthermore, using x in our second equation, we get y = 6 + 3 = 9. Therefore, Marcos had 6 nickels and 9 quarters.

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Answer:

1/6

Step-by-step explanation:

1/3 divided by 2 people= 1/6 each

Answer:

Step-by-step explanation:

1/3