Solve -23.7 + d = -48.57.

-4.62
-46.2
-24.87
-72.27

Answer:

The vertex is (2, 4), the domain is all real numbers, and the range is y ≥ 4.

Step-by-step explanation:

The equation of the parabola is [tex]f(x)=(x-2)^2+4[/tex]

The vertex form of the parabola is given by

[tex]f(x)=a(x-h)^2+k[/tex], here (h,k) is the vertex.

Comparing given equation with the vertex form of the parabola, we get

h = 2, k = 4

Hence, the vertex of the parabola is (h,k) = (2,4)

Now, domain is the set of x values for which the function is defined. The given function is defined for all real values of x.

Hence, domain is all real numbers.

Range is the set of y values for which the function is defined.

Since, here a = 1>0 hence it is a upward parabola and the vertex is the minimum point of this parabola.

Since, vertex is (2,4) hence, y values never less than 4.

Hence, range is y ≥ 4.

D is the correct options.

Final answer:

Using the provided exponential growth function for frog population, 42000 (1.3^t/2), with t=3 for next year, the fraternity should order approximately 59621 tags.

Explanation:

To calculate the number of tags the Epsilon Delta fraternity should order for next year, we need to use the exponential population growth function provided: 42000 (1.3^{t/2}), where t is the number of years since the initial tagging. Since two years ago was t = 0, this year is t = 2. Next year will be t = 3.

Plugging t = 3 into the function, we get:

Tags needed = 42000 (1.3^{3/2})

This is an arithmetic problem involving an exponential function representing the population growth of frogs.

To solve the equation, first calculate 1.3^{3/2}, which is approximately 1.41907. Then multiply this by 42000 to get the number of tags needed for next year.

Tags needed ≈ 42000 * 1.41907

Tags needed ≈ 59621

So the fraternity should order approximately 59621 tags for next year.

After deducting the monthly membership fee of $4.95 from Shanti's budget, $37.05 remains for DVD rentals. At $1.95 per DVD rental, Shanti can rent 19 DVDs while staying within her budget.

To calculate how many DVDs Shanti can rent without going over her monthly budget of $42, we first need to deduct her monthly membership fee from her total budget. This leaves us with the amount she can spend on renting DVDs.

The monthly membership fee is $4.95. After subtracting this fee from her total budget, we have:

$42 - $4.95 = $37.05 available for DVD rentals.

Each DVD rental costs $1.95. To find out how many DVDs Shanti can rent, we divide the amount available for rentals by the cost per DVD rental:

$37.05 / $1.95 = 19 DVDs (rounded down since you cannot rent a fraction of a DVD)

Therefore, Shanti can rent 19 DVDs in her first month and stay within her budget of $42.

Let q = quarter

Let d = dime

Here is your system:

q + d = 23

0.25q + 0.10d = 3.80

Take it from here.

Answer:

On (-2/3, 1) the given function is decreasing

Step-by-step explanation:

Do you know calculus?  If so:

Differentiate y = 2x^3 – x^2 – 4x + 5 and set the derivative = to 0:

dy/dx = 6x^2 - 2x - 4 = 0, or 3x^2 - x - 2 = 0.

This factors as follows:  (x - 1)(3x + 2) = 0.

The roots of this equation are {1, -2/3}.  

Plot these two roots on a number line and then set up intervals as follows:

(-infinity, -2/3), (-2/3, 1), (1, infinity)

Choose a test number from each interval:  { -1, 0, 2 }

By evaluating the derivative 6x^2 - 2x - 4 at each of these three test numbers, we get:

dy/dx = 6x^2 - 2x - 4 is positive on (-infinity, -2/3), and so we conclude that the given function is increasing on that interval.

dy/dx = 6x^2 - 2x - 4 is negative on (-2/3, 1), and so we conclude that the given function is decreasing on that interval.   To the nearest tenth:

(-0.7, 1)

To find where the function y = 2x^3 - x^2 - 4x + 5 is decreasing, calculate the derivative, set it less than zero, solve for x, and use a sign chart to determine the intervals where the function is decreasing. The correct interval is (1, ∞).

To determine where the function y = 2x3 − x2 − 4x + 5 is decreasing, we need to analyze its derivative. The first derivative of the function represents the slope of the tangent line to the curve at any given point, and when this slope is negative, the function is decreasing. Let's find the first derivative, f'(x) which is 6x2 − 2x − 4. To find where f'(x) is negative, we look for the x-values that make the derivative less than zero. This inequality can be solved by looking for the critical points where the derivative equals zero or is undefined, and then testing intervals around these points to see when the derivative is negative.

By factoring or using the quadratic formula, we find the critical points of f'(x) and then use a sign chart or test values to determine where the derivative is negative. For example, if we find that the derivative switches from positive to negative at x = 1, we can conclude that the function is decreasing for x values greater than 1. Therefore, the correct answer would be that the function is decreasing over the interval (1, ∞).

yep, your answer is A.

Final answer:

The cross product a~ × b~, where a~ points south and b~ points west, is directed downwards. This direction is determined using the right-hand rule and is perpendicular to the original plane formed by a~ and b~.

Explanation:

If vector a~ points south and vector b~ points west, their cross product a~ × b~ can be determined using the right-hand rule. By pointing the fingers of your right hand towards the direction of a~ (south) and then rotating your wrist to point your fingers towards b~ (west), your thumb will point downwards. Therefore, the direction of a~ × b~ is downwards, which is into the ground if you are standing in the Northern Hemisphere.

The cross product of two vectors is always perpendicular to the plane that contains the original vectors. So in this case, since a~ and b~ are orthogonal and lie in the horizontal plane, their cross product a~ × b~ will be orthogonal to this horizontal plane. As the vectors move from a~ to b~ in an anticlockwise direction, the resultant vector points downward, opposite to the upward direction that would be indicated by b~ × a~.

Answer:$1000

Step-by-step explanation:my frend found this

The number of bottles which could be filled are:

   Approx 4 bottles ( since we got 4.260 )

One can case of cola holds- 355 mL

This means that:

 24 can case of cola will hold= 24×355 mL

                                                =  8520 mL

Also, 1 L=1000 mL

This means that:

1 mL= 0.001 L

Hence,

8520 mL= 8.520 L

Total amount of cola is: 8.520 L

Now, the number of bottles of 2 L which could be filled from this liquid is:

8.520/2=4.260 bottles.

Answer: 1) ASA

2) none

3) ASA

Step-by-step explanation:

In the first picture we have two angles and one included side of one triangle is congruent to corresponding two angles and one included side of another triangle, therefore by ASA postulate of congruence both triangles are congruent.

In the second picture , the two have two equal angles, the third angle of both triangles by using angle sum property =[tex]180^{\circ}-70^{\circ}-30^{\circ}=80^{\circ}[/tex],

Now, two corresponding angles and one included side (10 units) of both triangles are congruent  therefore by ASA postulate of congruence both triangles are congruent.

In the third picture, we have two triangle with one same vertex, then their vertical angles must be congruent.

Thus, in third picture, two angles and one included side of one triangle is congruent to corresponding two angles and one included side of another triangle, therefore by ASA postulate of congruence both triangles are congruent.

An equation that shows two ratios are equivalent is a proportion. Proportions can be applied in various fields like economics to show equivalent satisfaction based on price paid for goods, or in unit conversion to represent equivalent quantities in different units.

An equation showing that two ratios are equivalent is a proportion. A proportion is a mathematical statement that two ratios are equal. For example, 2/4 = 1/2 is a proportion because the two ratios are equivalent. Other forms of this equation could be obtained by rearranging terms, showing the direct and indirect proportions.

In a more practical context, ratios are used to compare the relationship between different quantities. For example, we could state the ratio of the prices of two goods should be equal to the ratio of the marginal utilities. When we divide the price of good 1 by the price of good 2, this should equal the marginal utility of good 1 divided by the marginal utility of good 2. This indicates that the utility or satisfaction obtained is equivalent based on the price paid.

Also, proportions can be used as a unit conversion factor where the ratio of two equivalent quantities expressed with different measurement units can lead to a conversion factor. For example, the lengths of 2.54 cm and 1 in. are equivalent, thus providing a ratio that could be used for conversion.

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