If f(x) is an even function, which statement about the graph of f(x) must be true?
-It has rotational symmetry about the origin.
-It has line symmetry about the line y = x.
-It has line symmetry about the y-axis.
-It has line symmetry about the x-axis.

The magnitude of the size change of the figures formed by these matrices is:

                                         2

We are given a  first matrix as:

           [3   -2   1]

and second matrix is given by:

            [6   -4   2]

Since we could clearly observe that when we multiply first matrix by a constant 2 then we obtain a second matrix.

   i.e.   2[3 -2 1]=[2×3   2×(-2)   2×1]

                        = [6   -4   2]

   Hence, the change in the magnitude of the size of two matrices is:

                             2

The quadratic equation for the word problem, written in standard form is equal to: D. x² + 5x - 104 = 0.

Given the following data:

L = (W + 5) inches.

Area = 104 square inches.

Note: Let the width be x.

Mathematically, the area of a rectangle is calculated by using this formula:

LW = A

(x + 5)x = 104

x² + 5x = 104

x² + 5x - 104 = 0

In Mathematics, the standard form of a quadratic equation is given by ax² + bx + c = 0  ⇔  x² + 5x - 104 = 0.

Read more on quadratic equation here: brainly.com/question/1214333

Final answer:

The expression 16x^2+8x in factored form is 8x(2x + 1), obtained by factoring out the greatest common factor, which is 8x.

Explanation:

To factor the expression 16x^2+8x, we look for common factors in each term. Here, we can see that both terms contain a power of x and the number 8 is a common factor. We can factor out 8x from each term.

Step-by-step, this looks like:

We've now expressed the original expression in factored form.

Answer:

27

Step-by-step explanation:

Since coeficient in front of x is larger than coeficient in front of y that means that value of function P  depends more on x than on y. That means that we should look for highest posible x and see highest posible y for that x.

Highest x value is 9 and we can only pick y=0 for it

P = 27

Note that if u decrease x by 1 we can take y=1 but now our value is:

P = 8*3 + 2*1 = 26 which is just confirmation why P depends more on x than on y due to coefficient in front of x.

And or

Answer:

27

Step-by-step explanation:

To find the maximum, input the vertices (0,8), (5,4) and (9,0) into the objective function (P = 3x + 2y) to determine which vertex obtains the maximum value.

NOTE: I don't understand why (5,4) was given on your graph as a vertex.

(0,8): P = 3(0) + 2(8)  = 0 + 16   = 16

(5,4): P = 3(5) + 2(4)  = 15 + 8   = 23

(9,0): P = 3(9) + 2(0)  = 27 + 0   = 27      THIS IS THE LARGEST (MAX) P-VALUE

Answer:

4.5 gallons

Step-by-step explanation:

Answer: true.

Step-by-step explanation: Here we must see if the use of a compass can be replaced with the use of a tracing paper.

Now, suppose you have a sheet of paper in your table, you can apply pressure in it with your finger at some point, now you can drill a little hole with the point of a pencil at some distance of your finger. Now, with the pencil in place, you can start to rotate it and you will see that an almost perfect circle will appear.

So yes, you can do this, so it's true.

Answer:

3/4

Step-by-step explanation:

its 3/4 k

The number of food items Homeroom B needs to collect to have more food items per student than Homeroom A is 16

Food items collected by homeroom A:

Canned food = 30

Dry food = 42

Additional food items = 21

Number of students = 24

Food items per students = (30 + 42 + 21) / 24

= 93/24

Food items collected by homeroom B:

Canned food = 22

Dry food = 24

Additional food items = x

Number of students = 16

Food items per students = (22 + 24 + x) / 16

= (46 + x) / 16

Number of more food items Homeroom B need to collect to have more items per student than Homeroom A:

(46 + x) / 16 > 93/24

cross product

(46 + x) × 24 > 16 × 93

1,104 + 24x > 1,488

24x > 1,488 - 1,104

24x > 384

Divide both sides by 24

x > 384/24

x > 16

Hence, homeroom B should collect more than 16 food item to have a greater item per student

Read more on table:

https://brainly.com/question/30801679

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Homeroom B needs to collect at least 17 more items to exceed Homeroom A in items per student. The calculation is based on the total food items and the number of students in each homeroom.

To find out how many more items Homeroom B needs to collect to have more items per student than Homeroom A, we will first calculate the items per student for each homeroom, considering that Homeroom A collects 21 additional items.

First, calculate the total items of food collected by each homeroom:

Homeroom A:

- Canned food: 30 items

- Dry food: 42 items

- Additional items: 21 items

Total items for Homeroom A:

30 + 42 + 21 = 93 items

Number of students in Homeroom A: 24

Items per student in Homeroom A:

[tex]\[\frac{93}{24} \approx 3.875 \text{ items per student}\][/tex]

Homeroom B:

- Canned food: 22 items

- Dry food: 24 items

Total items for Homeroom B:

22 + 24 = 46 items

Number of students in Homeroom B: 16

Items per student in Homeroom B:

[tex]\[\frac{46}{16} = 2.875 \text{ items per student}\][/tex]

Determine additional items needed for Homeroom B:

Let ( x ) be the additional items needed for Homeroom B to exceed Homeroom A's items per student.

The new total items for Homeroom B would be:

46 + x

The new items per student for Homeroom B would be:

[tex]\[\frac{46 + x}{16}\][/tex]

We need this to be greater than Homeroom A's items per student:

[tex]\[\frac{46 + x}{16} > 3.875\][/tex]

Solving for ( x ):

46 + x > 3.875 × 16

46 + x > 62

x > 62 - 46

x > 16

Thus, Homeroom B needs to collect more than 16 additional items to have more items per student than Homeroom A.

In conclusion, Homeroom B needs to collect at least 17 more items to exceed Homeroom A in items per student.

9:27

she caught it just add 38 MINSA

the cone = 150.8

the cylinder= 301.6   the cones volume is 2x smaller than the cylinders volume. two cones equal one cylinder.

Final answer:

The question involves Physics concepts such as vector addition, moment of inertia, and gravitational force calculations. The incenter mentions seem irrelevant to the Physics calculations related to inertia and force.

Explanation:

The question asked is about calculating the moment of inertia for a specific geometric object (a cylinder) and involves understanding the mass distribution relative to an axis of rotation. This is a common concept in the field of Physics, particularly when dealing with rotational dynamics and inertia.

The mention of the incenter of a triangle appears to be unrelated to the main question, which is more focused on moments of inertia, vector addition, and gravitational force equations as indicated by the provided reference information.

For example, the moment of inertia of a cylinder about a given axis can be calculated using established mathematical formulas. Moreover, vector addition (such as Đ = Ả + 2B - F) includes principles such as scaling, displacement and direction, which are crucial in Physics for predicting the outcomes of combined vector forces.

Lastly, the reference to the mass m of an object cancelling in the equation for g is related to calculating the acceleration due to gravity on Earth, which does not depend on the mass of the falling object.

In the previous question, m represents the measure of an angle, and without specific information about which angle in Δ DEF is being referred to, a precise value cannot be determined.

The symbol m in geometry typically denotes the measure of an angle. In the context of the given diagram, G being the incenter of Δ DEF suggests that G is the point where the angle bisectors of the triangle intersect. However, to determine the specific measure (m) of an angle, additional details about which angle in Δ DEF is being considered are required.

In geometry, the measure of an angle can vary based on its location within a triangle. The incenter is where the angle bisectors meet, ensuring that the angle formed by connecting G to the vertices of Δ DEF is bisected equally. Without information about the specific angle being referenced, a numerical value for m cannot be provided.

Understanding angle measures and the role of an incenter in bisecting angles is crucial in geometry. Precision in describing angles requires clarity on the specific angle under consideration, allowing for accurate calculations and conclusions.

Answer:

SAS postulate

Step-by-step explanation:

Triangle ABD equal to triangle CBD.

The postulate that justifies the congruence is - Side angle side.

The Side Angle Side postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

Here, AD and CD sides are equal and the two triangles ABD and CBD share a common right angle , so these are congruent or equal as per SAS postulate.

AD and CD sides are equal and the two triangles ABD and CBD share a common right angle , so these are congruent or equal as per SAS postulate.

Triangle ABD equal to triangle CBD.

The postulate that justifies the congruence is - Side angle side

The Side Angle Side postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.

Here, AD and CD sides are equal and the two triangles ABD and CBD share a common right angle , so these are congruent or equal as per SAS postulate.