Stella is renting a car for a business trip. The agency charges a flat rate of $60 plus $0.50 per mile every mile she drives over 40 miles. Stella's company will pay up to $270, excluding the cost of gasoline , for the use of the rental car. What is the number of miles Stella can drive the rental car without spending more then$270

Answer: 10 square units.

Step-by-step explanation:

The area of triangle with vertices [tex](x_1,y_1),(x_2,y_2)\text{ and }(x_3,y_3)[/tex] is given by :-

[tex]A=\dfrac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)][/tex]

Given : The vertices of triangle : (2,0), (6,0), (8,5)

Then , the area of the triangle will be :_

[tex]A=\dfrac{1}{2}[(2)((0)-(5))+(6)((5)-(0))+(8)((0)-(0))\\\\\Rightarrow A=\dfrac{1}{2}[20]\\\\\Rightarrow A=10\text{ square units}[/tex]

Hence, the number of square units in the area of the triangle whose vertices are points (2,0), (6,0), (8,5) = 10

Answer:

b

Step-by-step explanation:

The outlier affects the median of the data sets collected by Ivan by reducing the median.

An outlier is a number that is way smaller or way larger than that of other numbers in a data set. The outlier in the data set is 62. Median is the number at the center of a data set.

To learn more about outliers, please check: https://brainly.com/question/27197311

#SPJ2

The zero with a multiplicity of 1 is x = 1, and the zero x = -2 has a multiplicity of 2.

For a general polynomial like:

[tex]p(x) = (x - x_1)^n*(x - x_2)^m*...[/tex]

The zero x₁ has a multiplicity of n (same as the exponent in the term where the zero appears), while the zero x₂ has a multiplicity m.

Now let's go to our polynomial:

[tex]f(x) = (x - 3)^2(x + 2)^2(x - 1)[/tex]

Here we can see that the only zero with a multiplicity of 1, is x = 1, while the zero x = -2 has a multiplicity of 2.

If you want to learn more about polynomials, you can read:

https://brainly.com/question/4142886

Answer:

first one is 1 and second is 2

Step-by-step explanation:

just got it right

The words typically associated with geometry are:

Points, Lines, Plane,  and angle.

We have,

In geometry,

There are some words that can be challenging to precisely define or may have different interpretations.

Here are a few examples:

- Point: While a point is commonly understood as a location with no size or dimension, providing an exact definition can be difficult without relying on terms like "location" or "position."

- Line: A line is often described as a straight path extending infinitely in both directions. However, defining it without using similar geometric concepts like "straight" or "infinitely" can be challenging.

- Plane: A plane is typically defined as a flat, two-dimensional surface that extends infinitely in all directions. However, explaining it without referencing terms like "flat" or "two-dimensional" can be complex.

- Angle: An angle is formed by two intersecting lines or line segments. Describing it precisely without using terms like "intersects" or "measures" can be difficult.

Thus,

These words require a level of understanding of basic geometric concepts and often rely on other geometric terms for precise definitions.

Learn more about geometry here:

https://brainly.com/question/31408211

#SPJ6

The value of Car 1 decreases linearly and can be described by a linear function. Without an exact exponential function for Car 2, we'll assume it may have a slower depreciation rate compared to Car 1. Autumn should consider Car 2 to likely have greater value after 6 years.

Part A: Identifying the Type of Function

To determine which type of function best describes the value of each car after a fixed number of years, we must look at the rate at which the car's value decreases. For Car 1, the value decreases by a constant amount each year ($6,000), which suggests a linear function. Conversely, Car 2 does not decrease by the same amount each year, but rather by amounts that seem to be getting progressively larger, hinting at an exponential function.

Part B: Writing the Functions

The linear function for Car 1 can be represented as f(x) = -6,000x + 44,000, since we start at $44,000 and decrease by $6,000 each year. For Car 2, an exponential decay function may fit the data; however, with only three points provided, determining the exact exponential function would require more complex regression analysis which we do not perform here. Assuming the rate of depreciation remains similar, we might estimate the function for Car 2 using a linear approximation for simplicity.

Part C: Future Car Value Comparison

Extending the linear depreciation model for Car 1, its value after 6 years would be f(x) = -6,000(6) + 44,000 = $8,000. A precise prediction for Car 2 after 6 years cannot be determined without an accurate exponential function, but it's apparent that Car 2 depreciates less rapidly than Car 1. Therefore, Autumn would likely find that Car 2 retains more value over 6 years.

a=adult

c=child

a+c=214

c=214-a

9c+14a=2081

9(214-a)+14a=2081

1926-9a+14a=2081

5a=155

a=155/5=31

31 adults

183 children

check

31*14 = 434

183*9=1647

1647+434=2081

The total number of cases I should have is 42.

Multiplication is the mathematical operation that is used to determine the product of two or more numbers.

Total number of cases = number of layers x cases per layer

14 x 3 = 42

To learn more about multiplication, please check: https://brainly.com/question/3385014

#SPJ6

circumference = 2 x pi x r

using 3.14 for pi

2 x3.14x114=715.92

 round to 716 yards

Answer:

The circumference of a circle is 715.92 yd.

Step-by-step explanation:

Formula

[tex]Circumference\ of\ a\ circle = 2\pi r[/tex]

Where r is the radius of a circle.

As given

The radius of a circular park is 114 yd.

[tex]\pi = 3.14[/tex]

Put in the formula

[tex]Circumference\ of\ a\ circle = 2\times 3.14\times 114[/tex]

Circumference of a circle = 715.92 yd

Therefore the circumference of a circle is 715.92 yd.

Answer:

Answer is C

Step-by-step explanation:

Area of an equilateral triangle can be found by the following formula,

A=[tex]\frac{\sqrt{3}} {4} a^{2}[/tex]

Where "a" is the length of one side of the triangle.

Now we can substitute the value given to the equation above and find the area of the given equilateral triangle.

A=[tex]\frac{\sqrt{3}} {4}(14\sqrt{3})^ {2}[/tex]

=[tex]\frac{\sqrt{3}} {4} 196*3[/tex]

=[tex]\frac{\sqrt{3}*196*3} {4}[/tex]

=[tex]254.611[/tex]

A=[tex]255[/tex] square feet.

Answer is C

693-57 = 636

636/2 = 318

cheeseburgers sold = 318

 hamburgers sold = 318 + 57 = 375

To determine the number of hamburgers sold on a specific day, an equation is set up and solved to find the value of hamburgers. In this scenario, 375 hamburgers were sold on Wednesday.

The question is asking how many hamburgers were sold on a specific Wednesday given the total combined sales of hamburgers and cheeseburgers and that fewer cheeseburgers were sold than hamburgers. To find the number of hamburgers sold, we can set up a system of equations. Let's define H as the number of hamburgers and C as the number of cheeseburgers. From the information provided, we have the following equations:

Substituting the second equation into the first gives us:

H + (H - 57) = 693

2H - 57 = 693

Adding 57 to both sides, we get:

2H = 693 + 57

2H = 750

Now divide both sides by 2:

H = 375

Therefore, 375 hamburgers were sold on Wednesday.

side 1 = x

side 2 = x+5

side 3 = x+14

perimeter = side 1 + side 2 + side 3

133 = x + (x+5) + (x +14)

133=3x + 19

114=3x

x=114/3 = 38

side 1 = 38

side 2 = x+5 = 38+5 = 43

side 3 = x+14 = 38+14 = 52

38+43+52 = 133

side lengths are 38, 43 & 52

Answer:

The volume is equal to [tex]18\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of each figure is equal to

[tex]V=LWH[/tex]

where

L is the length

W is the width

H is the height

Step 1

Find the volume of figure N 1

[tex]V1=1.5*2*3=9\ cm^{3}[/tex]

Step 2

Find the volume of figure N 2

[tex]V2=1.5*2*2=6\ cm^{3}[/tex]

Step 3

Find the volume of figure N 3

[tex]V3=1.5*2*1=3\ cm^{3}[/tex]

Step 4

Find the total volume

[tex]V=V1+V2+V3=9+6+3=18\ cm^{3}[/tex]

Answer:

[tex]\text{Volume of podium}=18\text{ ft}^3[/tex]

Step-by-step explanation:

We have been given a graph of podium for a track meet and we are asked to find the volume of our given podium.

To find the volume of podium we will find volume of each podium using volume of cuboid formula.

[tex]\text{Volume of cuboid}=l*b*h[/tex], where,

[tex]l=\text{ Length of cuboid}[/tex],

[tex]b=\text{ Breadth of cuboid}[/tex],

[tex]h=\text{ Height of cuboid}[/tex].

Upon substituting our given values in cuboid formula we will get,

[tex]\text{Volume of cuboid 1}=\text{3 ft*2 ft*1.5 ft}[/tex]    

[tex]\text{Volume of cuboid 1}=9\text{ ft}^3[/tex]    

[tex]\text{Volume of cuboid 2}=\text{2 ft*2 ft *1.5 ft}[/tex]

[tex]\text{Volume of cuboid 2}=6\text{ ft}^3[/tex]

[tex]\text{Volume of cuboid 3}=\text{1 ft*2 ft *1.5 ft}[/tex]

[tex]\text{Volume of cuboid 3}=6\text{ ft}^3[/tex]

Let us add volume of each cuboid to find the volume of our given podium.

[tex]\text{Volume of podium}=9\text{ ft}^3+6\text{ ft}^3+3\text{ ft}^3[/tex]

[tex]\text{Volume of podium}=18\text{ ft}^3[/tex]

Therefore, volume of our given podium is 18 cubic feet.