What is the value of the discriminant in the equation shown below?
x^2+3x-6=0
...?

The function x^3 + 7x^2 + 10x / (x + 5) is discontinuous at x = -5, where it has a jump discontinuity. The function is otherwise continuous and does not approach infinity, indicating no infinite discontinuity.

The given function is x^3 + 7x^2 + 10x / (x + 5). To determine the continuity of the function, it's crucial to identify any values of x that would make the denominator zero since the function is undefined at these points.

In this case, if x is -5, the denominator will be zero, making the function undefined. Therefore, the function has a point of discontinuity or a jump discontinuity at x = -5.

The function does not have an infinite discontinuity because it never approaches infinity as x approaches any particular value. This function is continuous at every point except for x = -5. Therefore, "the function x^3 + 7x^2 + 10x / (x + 5) has one point of discontinuity at x = -5."

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Answer:

The correct option is D. The cost of natural gas is $0.83 per unit.

Step-by-step explanation:

Consider the provided equation.

[tex]116y = 96.28[/tex]

We need to solve the above equation for y.

Divide both the sides by 116.

[tex]\frac{116y}{116} = \frac{96.28}{116}[/tex]

[tex]y=0.83[/tex]

Now consider the provided options.

Hence, the correct option is D. The cost of natural gas is $0.83 per unit.

The inequality -4t ≥ -2/5, where t is the variable in question, simplifies to t ≤ 1/10, indicating that t must be less than or equal to 0.1. Negative time values are a conceptual tool used in physics to discuss intervals before a chosen start time.

The student's question is about solving an inequality involving a variable t and understanding the concept of negative time. The inequality is given as a number t multiplied by -4 is at least -2/5. Mathematically, this can be written as -4t ≥ -2/5. To solve for t, we can divide both sides by -4 (remembering that dividing by a negative switches the inequality sign), so t ≤ 1/10 or t is less than or equal to 0.1. This condition must hold true for any value of t for the statement to be correct.

The concept of negative time is often used in physics to describe events that occurred before a certain reference point in time. The references to negative time values represent periods before some initial event, similar to counting backward. A negative t value does not imply 'backward' time travel in the literal sense, but rather a point in time before the designated start (t = 0).

Answer:

Step-by-step explanation:

First you have to know that you if you divide 24 by 6 you would have to take 7 multiplied by 4 to get 28

Answer: The answer is 80

Step-by-step explanation: because first of all divide 24 by 30% which equals 80 and second I took the USATP Test and got it right

The graph is attached and 68 sunflowers will be taller than 71 inches in the field.

Given that:

- Mean (average height) = 64 inches

- Standard deviation = 3.5 inches

Standardizing the height 71 inches using the z-score formula, we have

[tex]\[ z = \frac{{x - \mu}}{{\sigma}} \][/tex]

Substitute the known values into the equation

[tex]\[ z = \frac{{71 - 64}}{{3.5}} \][/tex]

[tex]\[ z = \frac{{7}}{{3.5}} \][/tex]

[tex]\[ z = 2 \][/tex]

Using the standard distribution table, we have

P(z > 2) = 0.02275

To find the number of sunflowers taller than 71 inches:

[tex]\[ 3000 \times 0.02275[/tex]

Evaluate

68

Hence, 68 sunflowers will be taller than 71 inches in the field.

The measure of  ∠2 is 70° .

The corresponding angles definition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other and are equal in measure.

When the sum of two angles is 180°, then the angles are known as supplementary angles. In other words, if two angles add up, to form a straight angle, then those angles are referred to as supplementary angles.

According to the question

line a is parallel to line b and c and d are transversal for them

line c is parallel to line d and a and b are transversal for them

m∠13 = (12x - 22)°  

m∠14 = (9x - 29)°

Now

As, ∠13 and ∠14 forms supplementary angles .

i.e

m∠13 + m∠14 = 180°

12x - 22° + 9x - 29° = 180°

21x - 51° = 180°

21x = 180° + 51 °

21x = 231 °

x = 11°

So,

m∠13 = 12*11 - 22° = 110°

m∠14 = 9*11 - 29°  = 70°

Now,

according to  corresponding angles

m∠14 = m∠6 = m∠2  = 70°

Hence, the measure of  ∠2 is 70° .

To know more about corresponding angles and supplementary angles here:

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Answer:

A. 216

Step-by-step explanation:

This is because the volume of a cube is worked out by doing .  being the edge. Therefore, you just have to do  (6 × 6 × 6), which is 216.

The projection of the space curve C, resulting from the intersection of the two given paraboloids, onto the xy-plane is the line y=0.

The surfaces provided are of the paraboloids x^2 + y^2 + z = 4 and x^2 + 3y^2 = z. We can find the space curve, which is the curve of intersection of these two surfaces, by setting the two equations equal to each other. We would get x^2 + y^2 + z = x^2 + 3y^2 which simplifies to 2y^2 - z = 0. The projection of this space curve C onto the xy-plane would just be the shadow this curve casts on the xy-plane. Thus, we eliminate the z variable and the result would be 2y^2 = 0 -> y = 0 , so, the projection of the curve on the xy-plane is y=0.

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Answer

b and d

Step-by-step explanation:

The form of a linear equation that shows the slope and one point is known as the point-slope form, which is written as y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line.

The form of a linear equation that shows the slope and one point is known as the point-slope form. Unlike the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept, the point-slope form is typically written as y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line.

For example, if you are given a slope of 3 and a point (2, 5), the equation of the line in point-slope form would be y - 5 = 3(x - 2). To visualize this, consider a line graph with the x-axis as the horizontal axis and the y-axis as the vertical axis.

If this was plotted, the line would rise 3 units on the vertical axis for every 1 unit it rises on the horizontal axis, illustrating the concept of slope as the rise over run, which is consistent along the entire length of a straight line.

4x-y=19 is the correct answer for this problem

Final answer:

An equation that sets two fractions equal to each other is known as a proportion, where equivalent ratios or fractions indicate the same value. This maintains the equality governed by the rules of algebra, important when performing operations on both sides of an equation.

Explanation:

An equation that sets two fractions equal to each other is called a proportion. This type of equation indicates that two ratios or fractions are equivalent. For example, if we have ½ on one side of the equation and 2/4 on the other, we have a proportion because both fractions represent the same amount.

When we have fractions with the same value in the numerator and the denominator, such as ¹¹/₁₀⁰ for micrometers to meters, we can simplify this to 1 because the quantities cancel each other out. This is true by the rules of algebra, specifically the property that if we perform the same operation on both sides of an equality, the equation remains balanced. This concept is crucial when working with proportions and equations involving fractions.

It's also important to remember that when adding fractions, they must have a common denominator. Ratios and percentages are other forms of expressing relative sizes or amounts which can also be related back to fraction and proportion concepts.