3. A catering service paid $520 for 10 center pieces and 60 glasses. The guest list grew, requiring an
additional 2 centerpieces and 36 glasses at a cost of $152. Follow the steps outlined below in order
to use a system of equations to find the cost of each centerpiece and each glass.

a. Name your variables.
Let x = the cost of a single centerpiece.
Let y = the cost of a single glass
b. Fill in the table.

First Bill- cost of centerpieces-cost of glasses-total cost
Second Bill-cost of centerpieces-cost of glasses-total cost

c. Write a system of equations to represent both orders.
10x+60y=520.
2x+30y=152

d. Solve the system using any preferred method.

e. Interpret your answer to part d using a complete sentence.​

Answer:

Yes, the number of mosquito bites can be represented as a function of the amount of repellent used.

Step-by-step explanation:

Let x represents the number of cans of repellent and y represents the number of mosquitos,

If f be the relation from x to y,

Then by the given table,

f(x) = { (0, 11), (1, 8), (5, 2), (4,5), (2, 9), (3, 6)}

∵ If for each input in a relation has exactly one output, the relation is called a function.

Here, for each value of x there is exactly one value of y,

Hence, f(x) is a relation from x to y,

That is, the number of mosquito bites can be represented as a function of the amount of repellent used.

Check the picture below.

well, the purple trapezoid, has a height of 5, and its bases are of 5 units and 8 units, recall the bases are the parallel sides in a trapezoid.

now, the yellow rectangle, is a 6x5, and it has those two green triangles in it, well, if we simply get the area of the rectangle, 30 anyway, and subtract the areas of those green triangles, what's leftover, is the rest of the shape on points DEFA.

keeping in mind that the green triangles have a base of 4 and a height of 3 for the one atop and base of 5 and height of 2 for the bottom one.

[tex]\bf \stackrel{\textit{purple trapezoid}}{\cfrac{\stackrel{h}{5}(\stackrel{a}{5}+\stackrel{b}{8})}{2}}~~+~~\left[ \stackrel{\textit{yellow square}}{(6\cdot 5)}-\stackrel{\textit{two green triangles}}{\cfrac{1}{2}(4)(3)-\cfrac{1}{2}(5)(2)} \right] \\\\\\ \cfrac{5(13)}{2}+[30-6-5]\implies \cfrac{65}{2}+[19]\implies \cfrac{103}{2}\implies 51\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]-\sqrt5-3\sqrt5=-1\sqrt5-3\sqrt5=(-1-3)\sqrt5=-4\sqrt5[/tex]

Final answer:

The two-digit number in question is 96, as it has one digit as 9 and is divisible by 6.

Explanation:

The student is asking to find a two-digit number where one of the digits is 9, and the number is divisible by 6 without any remainder. To solve this, we need to remember that for a number to be divisible by 6, it must be divisible by both 2 and 3. A two-digit number is divisible by 2 if its last digit is even.

Since one of the digits is 9 (an odd number), the other digit must be even, so our options for the two-digit numbers with a 9 are 90, 92, 94, 96, and 98. To be divisible by 3, the sum of the digits must be divisible by 3. Out of our options, only 96 has a sum of digits (9 + 6) that is divisible by 3. Therefore, the number we are looking for is 96.

Answer:

30

Step-by-step explanation:

Problem = 3x + 21 for x=3

3(3) +21 --- subsitute the three for the x

9 + 21 ---- multiply the 3s together

30 ----- add

Answer:

C. (-2,2π/3)

Step-by-step explanation:

Given:

In the given plane, each line represents angles and the circles shows the radii. Now as full circle is of 360 degrees or 2π and there are 12 straight lines that means

every angle is π/6 apart (30 degrees).

As the given red point is on circle 2, this means the radii, r=2

and Ф=300 degrees or 5π/3

r=(2,5π/3)

but above is not given in the options.

Polar coordinates can have positive or negative theta and also have positive or negative radii. In case of negative radii the polar coordinate moves in opposite direction of the pole.

if we consider r=-2 then we have to move in opposite direction of pole of  Ф=300 degrees or 5π/3 is 120 degrees or 2π/3.

hence r=-2 andФ=2π/3

Correct option is C:(-2,2π/3)!

Answer:

D. of any age

Step-by-step explanation:

A driver  can be charged with Driving While Intoxicated of any age.

It doesn't matter how old you are because a crime is a crime. If you are younger there will most likely be less of a punishment as adults.

Answer: 25200

Step-by-step explanation:

I hope that this is helpful, I'm bad at explaining answers so i wont. XD

Answer:

(x + 2)^2 + (y - 1)^2 = 2^2

Step-by-step explanation:

The equation of this circle is

(x + 2)^2 + (y - 1)^2 = r^2, and we are to determine the values of r^2 and r by substituting -4 for x and 1 for y:

(-4 + 2)^2 + (1 - 1)^2 = r^2, or:

(-2)^2                        =  r^2, or

4 = r^2

Then r = 2.

The desired equation is:

(x + 2)^2 + (y - 1)^2 = 2^2

Answer:

5xy^2(y + 3x^2 - 6x).

Step-by-step explanation:

5xy^3 + 15x^3y^2 − 30x^2y^2

The GCF is 5xy^2 so dividing through by this we get the factors:

= 5xy^2(y + 3x^2 - 6x).

Answer:

[tex]5xy^2(y+ 3x^2- 6x)[/tex]

Step-by-step explanation:

[tex]5xy^3 + 15x^3y^2 - 30x^2y^2[/tex]

To factor out an expression, factor out GCF

[tex]5xy^3= 5 \cdot x \cdot y \cdot y \cdot y[/tex]

[tex]15x^3y^2= 5 \cdot 3 \cdot x \cdot x \cdot x \cdot y \cdot y[/tex]

[tex]30x^2y^2= 5 \cdot 2 \cdot 3 \cdot x \cdot x \cdot y \cdot y[/tex]

GCF  is 5 times x times y time y

GCF is 5xy^2. Factor out GCF

[tex]5xy^3 + 15x^3y^2 - 30x^2y^2[/tex]

[tex]5xy^2(y+ 3x^2- 6x)[/tex]

Answer:

(3x^2+5)(x+3)

Step-by-step explanation:

The given expression is:

3x3 + 9x2 + 5x + 15

First of all group the first two terms and last two terms:

(3x3 + 9x2) + (5x + 15)

Now factor out the greatest common factor from each group:

3x^2(x+3)+5(x+3)

(3x^2+5)(x+3)

Thus the factors of 3x3 + 9x2 + 5x + 15 are:

(3x^2+5)(x+3) ....

Answer:(3x^2 + 5)(x + 3)

Step-by-step explanation:

B.

Answer:

[tex]\large\boxed{y-3=-(x-3)}[/tex]

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

We have the slope m = -1 and the point (3, 3).

Substitute:

[tex]y-3=-1(x-3)[/tex]

Answer:

x = 44

Step-by-step explanation:

sqrt(x+5) -3 =4

Add 3 to each side

sqrt(x+5) -3+3 =4+3

sqrt(x+5)  =7

Square each side

(sqrt(x+5))^2  =7^2

x+5 = 49

Subtract 5 from each side

x+5-5 = 49-5

x=44

Answer:

x is 44

Step-by-step explanation:

Answer:

4) (1,-1)

Step-by-step explanation:

Let the points be

[tex](x_1,y_1) = K(-5,-4)\\(x_2,y_2) = L(5,1)\\[/tex]

The formula for finding the coordinates of point that divides the line in a:b is:

[tex]x = \frac{bx_1+ax_2}{a+b} \\y = \frac{by_1+ay_2}{a+b}[/tex]

Here x and y are the coordinates of the point that will partition the line into given ratios

Our ratio is 3 to 2,

So,

a=3

b=2

Putting the values in the formula

[tex]x = \frac{(2)(-5)+(3)(5)}{3+2}\\x = \frac{-10+15}{5}\\x =\frac{5}{5}\\ x =1\\y = \frac{(2)(-4)+(3)(1)}{3+2}\\y = \frac{-8+3}{5}\\y = \frac{-5}{5}\\ y = -1[/tex]

Hence, the correct answer is:

4) (1,-1) ..

The coordinate of the point on the directed line segment is (1, -1). Then the correct option is D.

Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of line, etc.

The coordinates of the point on the directed line segment from K (-5,-4) to L (5,1) portions the segment into a ratio of 3: 2.

Let the coordinate of the point be (x,y).

We know that the section formula

[tex]\rm (x,y) = (\dfrac{m_1x_2+m_2x_1}{m_1+m_2} ,\dfrac{m_1y_2+m_2y_1}{m_1+m_2})[/tex]

We have

m₁: m₂ = 3: 2

(x₁, y₁) = (-5, -4)

(x₂, y₂) = (5, 1)

Then we have

[tex]\rm (x, y) = (\dfrac{3*5 + 2*(-5)}{3+2} , \dfrac{3*1 + 2*(-4)}{3+2})\\\\\\(x, y) = (\dfrac{5}{5}, \dfrac{-5}{5})\\\\\\(x, y) = (1,-1)[/tex]

More about the coordinate geometry link is given below.

https://brainly.com/question/1601567

Answer:

The function is odd because it is symmetric about the origin.

Step-by-step explanation:

we know that

A function f(x) is even when

f(x)=f(-x) ----> the function is symmetry about the y-axis

A function is odd when

-f(x)=f(-x) ---> the function is symmetry about the origin

In this problem we have

f(x)=-5x

Verify if the function is even

For x=1 ----> f(1)=-5(1)=-5

For x=-1 ---> f(-1)=-5(-1)=5

so

f(x) is not equal to f(-x)

therefore The function is not even

Verify if the function is odd

we have

f(1)=-5

f(-1)=5

so

-f(1) is equal to f(-1)

-f(x)=f(-x)

therefore

The function is odd because it is symmetric about the origin.

Answer:

The function is odd because it is symmetric about the origin.

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

f(x) = 2x

Let x = 6

f(6) = 2*6 = 12

If you meant f(x) = 2^x

Let x = 6

f(6) = 2^6 = 64

Answer:

If parabolas open down, then their vertices are at a maximum point, whereas if parabolas open up, their vertices are at a minimum point.

I hope this was the answer you were looking for, and as always, I am joyous to assist anyone at any time.

To find the max/min of a function, find where the function's first derivative is zero. Check those points with the second derivative: a positive value indicates a minimum and a negative value indicates a maximum.

To find the maximum or minimum of a function, you should first understand that these points occur where the derivative of the function is zero, which corresponds to the points with a flat tangent line (no slope). To derive this, differentiate the function and mark all the points where the derivative equals zero. These are potential maximum or minimum points, also known as extrema.

However, it's also important to note that a zero derivative does not always mean a maximum or minimum is present. To confirm this, you need to perform the second-derivative test. If after differentiating the first derivative you get a positive value, the original function has a minimum at that point. If it's negative, the function has a maximum.

For example, let's take the function f(x) = x². The derivative f'(x) = 2x, and setting this to zero gives us x = 0 as the only point whose derivative equals zero. Further, the second derivative, f''(x), equals 2, which is positive, indicating a minimum occurs at x = 0.

https://brainly.com/question/17800323

#SPJ12

Answer:

{3,23,39}

Step-by-step explanation:

I think that thing inside the box says 4x-5.

The numbers we are putting in are 2,7, and 11.

So when we put 2 in we get 4(2)-5 which is 8-5=3.

When we put 7 in we get 4(7)-5 which is 28-5=23.

When we put 11 in we get 4(11)-5 which is 44-5=39

So the answer is {3,23,39}.

Answer:

Second one

Step-by-step explanation:

Second choice.

Second one is growing by a factor of 2 because the exponent on 2 tells me that 2 is is being repeated as a factor.

If x=0 then 15*2^0=15(1)=15 which is what we have initially.

Final answer:

The correct option is f(x)=15⋅2^x. The function that best models the cell growth after x hours is f(x) = 15⋅ 2^x, illustrating the exponential nature of cell division starting with 15 cells.

Explanation:

The amount of cells in the laboratory after x hours, when the number of cells doubles every hour, is best represented by the function f(x) = 15⋅ 2^x. This is because the cell population increases exponentially, starting with 15 cells and doubling each hour. The formula represents exponential growth where the original amount of cells (15) is multiplied by two raised to the power of the number of hours elapsed (x).

Answer:

Graph C is your answer

Step-by-step explanation:

Draw the following graph using the easy coordinates, those are were y axis is zero, and the other were x axis is 0:

[tex]y=-2x+2[/tex]

First point is (1,0) and the other (0,2)

The entire region that belongs to your graph is greater than drawn line.

Draw another graph using the same easy coordinates.

[tex]y=2x-1[/tex]

First point is (0.5,0) and the other (0,-1)

The entire region that belongs to your graph is lesser than the drawn line.

When you merge those graphs into one, you can clearly see that they correspond to the C answer.

Answer:

Graph A.

Step-by-step explanation:

The given inequalities are

[tex]y>-2x+2[/tex]

[tex]y<2x-1[/tex]

The related equation of given inequalities are

[tex]y=-2x+2[/tex]

[tex]y=2x-1[/tex]

The slope of line (1) is -2 and the y-intercept is 2.

The slope of line (2) is 2 and the y-intercept is -1.

Both related lines are dotted line because the points on the line are not included n the solution set.

Check each inequality by (0,0).

[tex]0>-2(0)+2\Rightarrow 0>2[/tex] False statement

[tex]0<2(0)-1\Rightarrow 0<-1[/tex] False statement

So, (0,0) is not included in the shaded area of any of these two inequities.

Therefore, graph A shows the solution to the system of linear inequalities.

Answer:

6

Step-by-step explanation:

=81−43+(9)(2)−50

=38+(9)(2)−50

=38+18−50

=56−50

=6

Answer:

6.

Step-by-step explanation:

81-86÷2+(9×2)-50

work out the parentheses first;

= 81 - 86 / 2 + 18 - 50

Now the division:

= 81 - 43 + 18 - 50

= 38 + 18 - 50

= 56 - 50

= 6.

Answer:

True

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

1st mean: 65

2nd mean: 106.5

Answer:

For every real number x, C expresses the solution to the inequality

Final answer:

To find the solution to the inequality x + 3 < 1, subtract 3 from both sides to get x < -2. The number line would have an open circle at -2 and be shaded to the left, indicating all numbers less than -2.

Explanation:

To solve the inequality x + 3 < 1, we need to find the value of x that makes the inequality true. We start by subtracting 3 from both sides of the inequality:

The number line for this inequality would have an open circle at -2 (since -2 is not included in the solution) and shade to the left of -2 to show that all numbers less than -2 are included. The reason we shade to the left is because those are the numbers that are less than -2, thus satisfying the inequality.

Answer:

The correct option is C.

Step-by-step explanation:

Given information: BCDE is a rectangular casing, DE = 3 cm and BE = 3 cm.

We need to find the smallest diameter of pipe that will fit the fiber optic line. It means we have to find the measure of DB.

The measure of all interior angles of a rectangle or square is 90°.

[tex]\angle DEB=90^{\circ}[/tex]

It means the DEB is right angled triangle.

According to the Pythagoras theorem:

[tex]hypotenuse^2=leg_1^2+leg_2^2[/tex]

In triangle DEB,

[tex](DB)^2=(DE)^2+(BE)^2[/tex]

[tex](DB)^2=(3)^2+(3)^2[/tex]

[tex](DB)^2=9+9[/tex]

[tex](DB)^2=18[/tex]

Taking square root both sides.

[tex]DB=\sqrt{18}[/tex]

[tex]DB=4.24264068712[/tex]

[tex]DB\approx 4.24[/tex]

Therefore the correct option is C.

Based on the information given, the smallest diameter will be C. 4.24 cm.

DB² = 3² + 3²

DB² = 9 + 9

DB² = 18

DB = ✓18

DB = 4.24

Therefore, the correct option is 4.24.

Learn more about diameter on:

https://brainly.com/question/1649593

Answer:

Let's evaluate each rental shop:

For one hour, the cost is $5 + $1.5 = $6.5. For ten hours the total cost is: $5 + 10×$1.5 = $20

For one hour, the cost is $6 + $1.25 = $7.25. For ten hours the total cost is: $6 + 10×$1.25 = $18.5

If Clara and her brother are thinking about renting a bike for an hour, Bargain Bikes is the best option. On the other hand, if they want to rent it fr several hours Frugal Wheels is the best option.

Answer:

5

Step-by-step explanation:

The matrix is in the form

a  b

c   d

The determinant is

ad -bc

2 *4 - 1 *3

8 - 3

5

Answer:

930

Step-by-step explanation:

To use the division method

Write the given numbers in a horizontal row separated by commas.

Divide them by a suitable prime number

Place the quotient under the numbers in the next row. If a number is not divided exactly then bring it down to the next row.

Repeat the process until only co prime numbers are left in the last row.

Multiply all the prime numbers used as divisors.

The product is the LCM

Given 30 and 62, then

2 | 30, 62

3 | 15, 31

5 | 5, 31

31 | 1, 31

    | 1, 1 ← co primes left

Hence LCM = 2 × 3 × 5 × 31 = 930

Answer:

[tex]\Huge \boxed{20}[/tex]

Step-by-step explanation:

This question is about order of operations. It stands for parenthesis, exponent, multiply, divide, add, and subtract from left to right.

First thing you do is parenthesis.

[tex]\displaystyle [2-6]=-4[/tex]

[tex]\displaystyle -4-[-24][/tex]

Then, add and subtract numbers from left to right to find the answer.

[tex]\displaystyle -4-[-24][/tex]

[tex]\displaystyle -4-[-24]=-4+24=20[/tex]

20, which is our answer.

Hope this helps!