Find the zeros of the function.
Enter the solutions from least to greatest.
h(x) = (-2x + 3)(-+ + 3)

Answer:

1) 5

2) 7

3) 11

4) 4

Step-by-step explanation:

The simplified expression is 12 * sqrt(5) / 5.

Simplifying a square root just means factoring out any perfect squares from the radicand, moving them to the left of the radical symbol, and leaving the other factor inside the radical symbol. If the number is a perfect square, then the radical sign will disappear once you write down its root.

To simplify the expression, let's rationalize the denominator by multiplying both the numerator and denominator by the square root of 5.

6 * sqrt(20) / sqrt(5) * sqrt(5)

Now, simplify each square root:

6 * sqrt(4 * 5) / sqrt(5) * sqrt(5)

Since the square root of 4 is 2, we can further simplify:

6 * 2 * sqrt(5) / sqrt(5) * sqrt(5)

The square root of 5 in the numerator and denominator will cancel out:

6 * 2 * sqrt(5) / sqrt(5) * sqrt(5) = 12 * sqrt(5) / 5

Therefore, the simplified expression is 12 * sqrt(5) / 5.

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Answer:

2.5

Step-by-step explanation:

The object distance is 0, which implies that the object is at the focus of the concave mirror.

For a concave mirror, the magnification is given by the formula:

m = -di/do

where m is the magnification, di is the image distance, and do is the object distance. Since we are given that the magnification is -2.0, we can write:

-2.0 = -di/do

Simplifying this expression, we get:

di = 2do

We can also use the mirror formula for a concave mirror:

1/f = 1/do + 1/di

where f is the focal length of the mirror. Substituting di = 2do and f = -16 cm (since the mirror is concave), we get:

1/-16 = 1/do + 1/(2do)

Multiplying both sides by -16do, we get:

do - 2f = -32

Substituting f = -16 cm, we get:

do - (-32) = -32 + 32

do = 0

This means that the object distance is 0, which implies that the object is at the focus of the concave mirror. This is a valid result, since a concave mirror can form a real, inverted image for an object placed at a distance equal to its focal length. In this case, the magnification would be -1, not -2. So, it is not possible to have a magnification of -2 for an object distance in front of a concave mirror with a focal length of 16 cm.

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Answer:

\((5p - 3) + (2 {p}^{2} - 3p) \\ = 2 {p}^{2} + (5 - 3)p - 3 \\ = 2 {p}^{2} + 2p - 3\)

Answer: the answer is 2p^2+2p−3

Step-by-step explanation:

1. Combine Like Terms: these are 5p and 3p

2. which gives us 2p

3. Always put the squared first and the constant (without any variable last)

which makes 2p^2+2p-3

The equation of the parabola represented by the graph is y = 9x²

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

Point = (2, 36)

See attachment for the graph

This means that

(x, y) = (2, 36)

The vertex of the parabola is represented as

(h, k) = (0, 0)

The equation of the parabola is represented as

y = a(x - h)² + k

When the vertices are substituted, we have

y = a(x - 0)² + 0

So, we have

y = ax²

Using the point, we have

a * 2² = 36

So, we have

a = 9

Hence, the equation of the parabola is y = 9x²

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To find the volume of each pris you multiply the measures

So

first prism

then first blanck is 12

Second prism

if we multiply 5 and 14

then second blanck is 70

Total volume

then last blanck is 1180cu cm

Answer:

x=2g+1

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

Given g(x) = 3x - 3 and g(x) = 6, then equating gives

3x - 3 = 6 ( add 3 to both sides )

3x = 9 ( divide both sides by 3 )

x = 3

To find the selling price that will yield the maximum profit, we need to find the vertex of the quadratic function given by the profit equation y = -5x² + 286x - 2275.The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -5 and b = 286.

x = -b/2a

x = -286/(2(-5))

x = 28.6

So, the selling price that will yield the maximum profit is $28.60 (rounded to the nearest cent).

Therefore, the widgets should be sold for $28.60 to maximize the company's profit.

Hope I helped ya...

Answer:

29 cents

Step-by-step explanation:

The amount of profit, y, made by the company selling widgets, is related to the selling price of each widget, x, by the given equation:

\(y=-5x^2+286x-2275\)

The maximum profit is the y-value of the vertex of the given quadratic equation. Therefore, to find the price of the widgets that maximises profit, we need to find the x-value of the vertex.

The formula to find the x-value of the vertex of a quadratic equation in the form y = ax² + bx + c is:

\(\boxed{x_{\sf vertex}=\dfrac{-b}{2a}}\)

For the given equation, a = -5 and b = 286.

Substitute these into the formula:

\(\implies x_{\sf vertex}=\dfrac{-286}{2(-5)}\)

\(\implies x_{\sf vertex}=\dfrac{-286}{-10}\)

\(\implies x_{\sf vertex}=\dfrac{286}{10}\)

\(\implies x_{\sf vertex}=28.6\)

Assuming the value of x is in cents, the widget should be sold for 29 cents (to the nearest cent) to maximise profit.

Note: The question does not stipulate if the value of x is in cents or dollars. If the value of x is in dollars, the price of the widget should be $28.60 to the nearest cent.

See your Question is not clear .I am writing steps to do .

The difference between an implicitly defined function and an explicitly defined function lies in how the relationship between the variables is expressed.

In an explicitly defined function, the dependent variable (usually y) is expressed directly in terms of the independent variable (usually x), such as y = f(x). In an implicitly defined function, the relationship between the variables is expressed indirectly through an equation involving both variables, such as F(x, y) = 0, making it not straightforward to solve for y in terms of x.

Explicitly defined functions provide a clear and explicit expression for the dependent variable in terms of the independent variable, allowing for direct evaluation and computation. They are commonly used when the relationship between variables can be easily represented by a formula or equation.

On the other hand, implicitly defined functions are often used when the relationship between variables is more complex or cannot be easily expressed in a single equation. They require additional manipulation or solving techniques to determine the relationship between the variables.

Implicit functions are commonly encountered in calculus and differential equations, where the relationships may involve derivatives or multiple variables.

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The for statement Triangle RST is congruent to QUT is by SAS criterion.

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.

Given:

As, Triangle QRT is an Equilateral Triangle then

QR = RT = QT

So, the reason for QT = RT is that QRT is an Equilateral Triangle.

So, by SAS criterion Triangle RST is congruent to QUT.

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Answer:

logx a + logx b

Step-by-step explanation:

7.36 for each cap

$36.80 is the cost for 5 caps. if we divide the cost of the pack to the individual number of idems (caps), the equation (36.80÷5) will come out to $7.36, meaning $7.36 is the cost for each individual cap.

Answer:

19

Step-by-step explanation:

tigers=38 goals

clubs=19 fewer than tigers

equation: 38-19=19

Answer:

A.

Step-by-step explanation:

The sum of interior angles in a triangle is 180°

2y + 54 = 180

2y = 126

y = 63

Answer:

A.)63°

Step-by-step explanation:

54°+63°+63°=180°

For this, you would use the Angle Sum Theorem which means the sum of the measures of a triangle's angles should always end up equaling 180°

A P E X Hope this helps Happy Holidays

The planar cross-section's perimeter is most accurately estimated to be 50.24 inches.

A circle with a diameter equal to the diameter of the cone's base is formed by the planar cross-section of the cone that goes through its apex and is perpendicular to its base.

The base's diameter is equal to the radius times two, or 2 * 8 inches, or 16 inches.

The perimeter of a circle is given by the formula P = π * d,

Where

Therefore, the perimeter of the planar cross-section is approximately:

P = π * 16 inches

Using an approximate value of π = 3.14, we can calculate:

P ≈ 3.14 * 16 inches

P ≈ 50.24 inches

So, the planar cross-section's perimeter is most accurately estimated to be 50.24 inches.

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A generic graph would be

Where:

A = amplitude

p = period

φ = phase

D = middle line

First let's evaluate the period of the function, see that x = -1/4 we have y = 5, it will have again at x = 3/4.

The period is

Let's put it in our function already

To find out the amplitude, we take the max value, the minimum value (all in modulus) and take the average, the max value here is 5 and the minimum -3 (in modulus it's 3), the average is

Therefore

And the D value will be the average too, of the maximum two, but here we don't use the modulus on negative values, therefore

Hence.

We know that when x = 0 we have y = 1, then

When cos(φ) = 0? when φ = π/2 for example. Of course, there are other solutions but we just need one. Now we have all the parameters of our cosine

The final answer is:

Answer:

1482

Step-by-step explanation:

2n+5

1) when n= 1

2(1)+5

= 7

2) when n=12

2(12)+5

=29

3) when n=29

2(29)+5

=63

4) when n=36

2(36)+5

=77

5) when n=216

2(216)+5

=437

6) when n=433

2(432)+5

=869

therefore, 7+29+63+77+437+869 = 1482

The complete statement is folk tales and fairy tales

Both folk tales and fairy tales are types of fiction because they are imaginative stories that are not based on factual events or characters.

Folk tales

Folk tales are stories with no known creator. They were originally passed down from one generation to another by word of mouth. Folk tales are a type of traditional literature that is deeply rooted in the culture of a particular region or community.

They often feature supernatural elements, and their origins can be traced back many centuries.

Because they were passed down orally, different versions of the same tale may have developed in different regions, with variations in characters, plot, and theme.

Fairy tales

Fairy tales were often created to teach children behavior in an entertaining way. Fairy tales are a type of story that typically features magical creatures or events and often have a moral or lesson to teach. They were originally intended for both adults and children and were used as a way to teach moral values, societal norms, and important life lessons in an entertaining way.

The fairy tale genre has evolved over time, and modern fairy tales may have different themes and messages than traditional ones.

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The number of trees more than 10m tall but not more than 20m tall is 18 trees.

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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Answer:

Area of shaded proton =42cm²

Microeconomics is a branch of economics that focuses on the behavior of individuals and firms in making decisions regarding the allocation of limited resources

Microeconomics is a branch of economics that studies the behavior of individuals and firms in making decisions about the allocation of limited resources, specifically focusing on the interaction of supply and demand in specific markets and how different factors influence the behavior of individuals and firms. It is concerned with the study of how people and firms make decisions about production, consumption, and distribution of goods and services.

Microeconomics analyzes how supply and demand in specific markets interact to determine the prices of goods and services. It also examines how different factors, such as taxes, government regulations, and technological changes, affect the behavior of individuals and firms.

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Option B: Min 4x + 3y + (2/3)z is the valid objective function for a linear programming problem as it is a linear expression involving the decision variables x, y, and z.

Among the options provided, the valid objective function for a linear programming problem is option B: Min 4x + 3y + (2/3)z.

In linear programming, the objective function represents the quantity that needs to be either maximise or minimize. It is a linear expression involving the decision variables of the problem.

Option A: Max 5xy is a valid objective function as it is a linear expression involving the variables x and y. However, it is important to note that an objective function in linear programming must be linear and not involve multiplication between decision variables.

Option C: Max 5x^2 + 6y^2 is not a valid objective function because it includes the square terms (x^2 and y^2). In linear programming, the objective function needs to be linear, meaning it must consist of the variables and their coefficients without any nonlinear terms.

Option D: Min (x1 + x2)/x3 is not a valid objective function because it includes the division between decision variables (x1 + x2) and x3. Similar to multiplication, division between decision variables is not allowed in a linear programming objective function.Therefore, option B: Min 4x + 3y + (2/3)z is the valid objective function for a linear programming problem as it is a linear expression involving the decision variables x, y, and z.

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The equation that represents the linear equation is t = 4d + 5.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

The table is given in the attached image.

To find the equation:

First, find the common difference.

So,

13 - 9 = 4

17 - 13 = 4

21 - 17 = 4

25 - 21 = 4

Here, the first difference 4 is common.

That means, the equation is a linear equation.

And the general form of the linear equation is,

t = md + c

Here, m = 4

So,

t = 4d + c

To find C:

Substitute the value of t = 9 and d = 1,

So, c = 5

So, the linear equation is t = 4d + 5.

Therefore, t = 4d + 5 is the linear equation.

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The price of one pen or 2 copies is Rs. 40. The price of 5 pens and 20 copies is Rs. 600.

Given, that the price of 1 pen or 2 copies is Rs.40. Therefore, we have the price of one pen to be 40 or 2 copies to be 40.

Thus, the price of one pen is Rs.40.

The price of one copy is 40/2 = Rs.20.

Therefore,

Price of 5 pens is = 40*5 = Rs.200

Price of 20 copies is = 20*20 = Rs.400

The total price of 5 pens and 20 copies is = 200+400 = Rs.600.

Therefore, the total price is Rs.600.

What are Comparing quantities?

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Answer:

55.9548

Step-by-step explanation:

35.64 ÷ 2 = 17.82

17.82 × 3.14 = 55.9548

Answer: 111.97

Step-by-step explanation:

Circumference of a circle= 2πr

r= d/2

diameter= 35.64

Therefore circumference= 2*(3.14)*(35.64/2)

= 111.97

Answer:

The first four terms are:  -3, -1, 1, and 3

Step-by-step explanation:

First 4 terms are:

f(1) = 2 (1) - 5  = -3

f(2) = 2 (2) - 5  = -1

f(3) = 2 (3) - 5  = 1

f(4) = 2 (4) - 5  = 3

Answer:

7

Step-by-step explanation: