In the last election, candidate C received 15,000 fewer votes than candidate B. If a total of 109,000 votes were cast, how many votes did candidate B receive?

Step-by-step explanation: Given radical expression 4√12 + √75.

Let us simplify each of the radical separately first.

√12 = √(2×2×3) = 2√3

Therefore, 4√12 = 4 × 2√3 = 8√3.

√75 = √(3×5×5) = 5√3

Therefore 4√12 + √75  => 8√3 + 5√3.

Adding like radicals, we get

8√3 + 5√3 = 13√3.

A quadrilateral cannot have 4 obtuse angles

From the question, we have the following parameters that can be used in our computation:

A quadrilateral

By definition, the sum of angles in a quadrilateral is 360

And an obtuse angle is greater than 90

So, we have

Sum = 4 * greater than 90

Evaluate

Sum = greater than 360

This means that a quadrilateral cannot have 4 obtuse angles

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[tex]\dfrac{x}{3} > -1\ \ \ \ |\cdot3\\\\x > -3\to x\in(-3;\ \infty)[/tex]

Final answer:

A negative y-intercept in a real-world context indicates that the system or condition being measured starts below the baseline or has a deficit to begin with. It can represent an initial loss in economics, such as starting with debt or needing initial investment. The slope of the line is critical to understanding how changes in one variable affect another.

Explanation:

A negative y-intercept in a real-world application can have various implications depending on the context. In many scientific experiments, the y-intercept represents the baseline level of the system without any experimental conditions applied. If the y-intercept is negative, this might indicate that in the absence of a certain factor (represented by the x-variable), the system has a deficit or a reduction in the measured quantity. For instance, if we are plotting a graph of growth over time, a negative y-intercept could imply that there was an initial debt or loss before measurements began.

When it comes to economics and data models, a negative y-intercept on a graph could represent a starting deficit. For example, a company might have initial losses (negative y-intercept) that it seeks to overcome as production (x-variable) increases. Supply and demand models, cost projections, and similar economic graphs can also have negative y-intercepts indicating starting positions below zero on the graph—such as starting with a debt or having to invest before seeing any return.

The y-intercept and the slope (m-term) together specify a particular line on a graph that can offer a reasonable approximation of real-world data. Economists find the slope particularly useful as it shows the relationship between two variables, like how a change in price affects the quantity supplied.

The sum of the three internal angles in a triangle is equal to 180 degrees.

a = 55°

b = 55°

c = 70°

The triangle abc is an acute isosceles triangle.

It is a two-dimensional figure which has three sides and the sum of the three internal angles is equal to 180 degrees.

We have,

Three angles of the triangle:

a = 3x + 1

b = 4x - 17

c = 5x - 20

The sum of the three angles of a triangle is 180 degrees.

a + b + c = 180

3x + 1 + 4x - 17 + 5x - 20 = 180

12x - -36 = 180

12x = 180 + 36

12x = 216

x = 216/12

x = 18

Now,

The angles are :

a = 3 x 18 + 1 = 54 + 1 = 55

b = 4 x 18 - 17 = 72 - 17 = 55

c = 5 x 18 - 20 = 90 - 20 = 70

We see that all their internal angles are acute angles.

This is an acute isosceles triangle.

Thus,

The triangle abc is an acute isosceles triangle.

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Answer: [tex]6\times10^3[/tex] square meters.

Step-by-step explanation:

Given : The soccer field at Mario's school has an area of 6,000 square meters.

Here, 6,000 can be written as [tex]6\times1,000[/tex]

And [tex]1000=10\times10\times10=10^3[/tex]   [using exponents]

Then, 6,000 can be written in the form of a whole number multiplied by a power of 10 as [tex]6,000=6\times10^3[/tex]

Hence, Maria can show the area as [tex]6\times10^3[/tex] square meters. .

Answer:

3

Step-by-step explanation:

The equation that models the balance b after m months is b = 1800 - 150m

Initial cost = 1800

Difference in balance = 1350 - 1050 = 300

Number of months used = 5 months - 3 months = 2 months

Therefore, the equation that models the balance b after m months will be:

b = 1800 - (300/2)m

b = 1800 - 150m

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Answer:

Range = 85

Step-by-step explanation:

The formula for range of a data set is

Range = Maximum value - Minimum value

The given data set is

34, 56, 13, 98, 75

In this data set we have,

Maximum value = 98

Minimum value = 13

The range of given data set is

Range = 98 - 13

Range = 85

Therefore, the range of the data is 85.

The water desalination plant can produce 1.58 x 10^8 gallons of water in 79 days, expressed in scientific notation.

To calculate how many gallons of water a desalination plant can produce in 79 days, we will multiply the daily production capacity by the number of days. The plant's daily production capacity is given as 2 x 106 gallons. So, for 79 days, the calculation would be:

(2 x 106 gallons/day) x 79 days = 1.58 x 108 gallons

Expressed in scientific notation, the plant can produce 1.58 x 108 gallons of water in 79 days.

The solution is Option C.

The equation A = -2x⁴ - x³ + 8x² = 12 is a quartic equation as the degree of the equation is 4

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

-2x⁴ - x³ + 8x² = 12   be equation (1)

On simplifying the equation , we get

Adding 2x⁴ + x³ on both sides of the equation , we get

2x⁴ + x³ + 12 = 8x²

Subtracting 8x² on both sides of the equation , we get

2x⁴ + x³ - 8x² + 12 = 0   be equation (2)

Now , the highest degree of the variable x in the equation is x⁴ which is 4

Therefore , the equation is quartic

Hence , the equation is 2x⁴ + x³ - 8x² + 12 = 0

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Final answer:

To calculate Jeff's tip, multiply 13% as a decimal (0.13) by the bill amount of $29.62, which equals a tip of $3.85.

Explanation:

To calculate how much Jeff left as a tip at the restaurant, we need to find 13% of his bill total, which was $29.62. To do this, convert the percentage to a decimal by dividing by 100 (which makes 13% become 0.13) and multiply that by the bill amount.

So, the calculation will be:

0.13 * $29.62

When you perform this calculation:

$3.85 (rounded to the nearest cent)

Jeff left a $3.85 tip at the restaurant.

1. The minimum number of hours is 5 hours, so the minimum money earned is:

minimum money = 15.30 * 5 = $76.50

The maximum number of hours is 10 hours, so the maximum money earned is:

maximum money = 15.30 * 10 = $153

2. Since the words “at least” and “not more than” are used, hence this is inclusive.

3. The practical range is:

$76.50 ≤ f(t) ≤ $153

Answer:

$76.50 ≤ f(t) ≤ $153

Step-by-step explanation:

volume = 216

 side = cubic root(216)

 the length of a side = 6 centimeters

Danielle's estimate of earning about $20,000 per year is accurate, as the calculation based on her hourly wage and weekly hours worked gives an actual annual income of $20,020.

Danielle's estimate of earning about $20,000 per year is accurate based on her hourly wage and weekly hours worked. To assess the accuracy of her estimate, we need to calculate her actual annual income.

Danielle earns $11 per hour and works 35 hours a week. Therefore, her weekly earnings are:

35 hours/week × $11/hour = $385/week.

As there are typically 52 weeks in a year, her estimated annual income would be:

52 weeks/year × $385/week = $20,020/year.

This calculation shows that Danielle's estimate of making about $20,000 per year is indeed accurate.