Which statements are true?



Choose all answers that are correct.



A.


All quadrilaterals can be classified as either parallelograms or trapezoids.


B.


All rhombuses are parallelograms.


C.


Some trapezoids are parallelograms.


D.


Some parallelograms are squares.

Answer:

The Edg answer is as follows -

The statement is not true for all real numbers. It is only true for decimal or fractional values of x .

If x is an integer, then the ceiling function returns x when the input is x . But, the flooring function returns x + 1 when the input is x + 1.

Since x does not equal x + 1 when x is an integer, the expressions are not equal when x is an integer.

Step-by-step explanation:

Real numbers are set of numbers that include rational and irrational numbers.

[x]=[x+1] is not true for all real numbers

Assume that: x is an integer

And x = 5

So, the equation becomes

[tex]5 = 5 + 1[/tex]

[tex]5 = 6[/tex]

The above equation is not true, because:

[tex]5 \ne 6[/tex]

Hence, [x]=[x+1] is not true for all real numbers

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The answer is:

5 hours, 246 miles.

Since we know the equations that represent the distances of both cars at certain times (function of time), we can calculate the time that they will be at the same distance by making their equation equal.

So, we are given the equations:

A-

[tex]y=44x+26[/tex]

B -

[tex]y=36x+66[/tex]

Now, by making both equation equal, we can calculate the time that they will have the same distance, so, we have:

[tex]44x+26=36x+66[/tex]

[tex]44x-36x=66-26[/tex]

[tex]8x=40[/tex]

[tex]x=\frac{40}{8}=5[/tex]

Hence, we have that they will have the same position after 5 hours.

Then, to calculate the distance, we need to substitute the obtained time in any of the given equations, so, substituting into A, we have:

[tex]y=44x+26[/tex]

[tex]y=44*5+26=220+26=246[/tex]

We have that the distance will be 246 miles.

Hence, we have that the answer is:

5 hours, 246 miles.

Have a nice day!

Answer:

163,380.48

Step-by-step explanation:

First find the average of the first 4 months' figures.

To do this, find the sum of the first 4 values and then divide by 4, the number of data points:

(14889.51+22936+9856.88+6777.77)/4 = 54460.16/4 = 13615.04

It costs on average £13615.04 per month to run the arena.

This means the estimated running costs for 12 months will be

13615.04(4) = £163,380.48

It says to check if [tex] \frac{3}{8} [/tex] satisfy each equation or not.

Checking first equation :-

96 x [tex] \frac{3}{8} [/tex]

⇒ [tex] \frac{96 * 3}{8} [/tex]

⇒ [tex] \frac{288}{8} [/tex] = 36

⇒ 36 = 36. First equation is "YES".

Checking second equation :-

38 x [tex] \frac{3}{8} [/tex]

⇒ [tex] \frac{38 * 3}{8} [/tex]

⇒ [tex] \frac{114}{8} [/tex] = [tex] \frac{57}{4} [/tex]

⇒ [tex] \frac{57}{4} [/tex] ≠ 14. Second equation is "NO".

Checking third equation :-

16 x [tex] \frac{3}{8} [/tex]

⇒ [tex] \frac{16 * 3}{8} [/tex]

⇒ [tex] \frac{48}{8} [/tex] = 6

⇒ 6 = 6. Third equation is "YES".

Checking fourth equation :-

56 x [tex] \frac{3}{8} [/tex]

⇒ [tex] \frac{56 * 3}{8} [/tex]

⇒ [tex] \frac{168}{8} [/tex] = 21

⇒ 21 = 21. Fourth equation is "YES".

Answer:

Solution: {Heads, Tails}.

Step-by-step explanation:

Solution: {Heads, Tails}.

Sample space is a list of all the possible outcomes for the event. For flipping a coin the outcomes are {Heads, Tails}.

Jensen stopped at A and planned to stop at B next. He has a map with a scale of 1 inch to 35 miles.

It is clear that 1 inch on map corresponds to 35 miles in actual.

From the map he has, we can see that both places A and B are 2.5 inches apart on map.

Let's assume those are "X" miles away in actual. Then we can use proportions to solve this problem.

1 inch to 35 miles would be same as 2.5 inches to X miles. Mathematically, we can write it as follows :-

[tex] \frac{1 \;inch}{35 \;miles} =\frac{2.5 \;inches}{X \;miles} \\\\
\frac{X \;miles}{35 \;miles} =\frac{2.5 \;inches}{1 \; inch} \\\\
\frac{X}{35} =\frac{2.5}{1} \\\\
Cross \;\;multiplying \\\\
X = 35*2.5=87.5 \;miles [/tex]

Hence, actual distance between A and B is 87.5 miles.

Answer:

12

Step-by-step explanation:

The perimeter of the isosceles trapezoid is 36cm.

An isosceles trapezoid is a quadrilateral with two parallel sides of unequal length. To find the perimeter of an isosceles trapezoid, we need to add the lengths of all its sides. In this case, the two bases have lengths of 10cm and 16 cm, and one of the side lengths is 5cm. Since the two bases are parallel, the other side length is also 5cm.

The perimeter is calculated by adding the lengths of the bases and the two side lengths: 10cm + 16cm + 5cm + 5cm = 36cm.

we know that

To find out the fraction of a pan of brownies that was left subtract [tex]1\frac{1}{5}[/tex] from [tex]2[/tex]

remember that

[tex]1\frac{1}{5}=(1*5+1)/5=\frac{6}{5}[/tex]

so

[tex]2-\frac{6}{5} =(2*5-6)/5=\frac{4}{5}[/tex]

therefore

the answer is

the fraction of a pan of brownies that was left is [tex]\frac{4}{5}[/tex]

The statements that can be inferred to be true regarding the regular dodecagon include:

A dodecagon simply means a twelve-sided star polygon that encloses space. It can be regular when all the interior angles and sides are equal.

It should be noted that the smallest angle of rotational symmetry for the dodecagon is 30° and it has a rotational symmetry of 180.

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The length in feet of the metal frame that surrounds the trampoline is 44 ft.

The circumference of a circle is the distance round the circle.

The circumference of a circle = πD

3.14 x 14 = 44 ft

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The circumference and the area of the circular bed are 14π feet = 43.9823 feet and 49π feet² = 153.9380 feet² respectively.

The circumference is the total length covered by the boundary of an object.

To calculate the circumference of a circle with radius r units, we use the formula: Circumference = 2πr units.

The area of an object is the space its planar face or two-dimensional face covers.

To calculate the area of a circle of radius r units, we use the formula: Area = πr² sq. units.

In the question, we are asked to find the circumference and the area of the circular flower bed that a gardener makes, having a diameter of fourteen feet.

We know that radius = diameter/2 = 14/2 = 7 feet.

To calculate the circumference of the circular bed, we will use the formula 2πr, where r is the radius.

Substituting the radius, r = 7 feet in the above formula, we get:

Circumference = 2(π)(7) feet = 14π feet = 43.9823 feet.

To calculate the area of the circular bed, we will use the formula πr², where r is the radius.

Substituting the radius, r = 7 feet in the above formula, we get:

Area = (π)(7)² feet² = 49π feet² = 153.9380 feet².

Thus, the circumference and the area of the circular bed are 14π feet = 43.9823 feet and 49π feet² = 153.9380 feet² respectively.

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Final answer:

The equation of the plane parallel to the given plane 9x - y - z = 7 and passing through the point (3, -8, -2) is 9x - y - z = 37.

Explanation:

The question involves finding an equation for a plane that is parallel to a given plane and passes through a specific point. Since the planes are parallel, they will have the same normal vector, and thus the same coefficients for x, y, and z. The given plane's equation is 9x - y - z = 7, so the normal vector is (9, -1, -1). Our plane must also have this normal vector, meaning our plane's equation will have the form 9x - y - z = D, where D is a constant we need to find such that the plane passes through the point (3, -8, -2).

Substituting this point into the equation gives us 9(3) - (-8) - (-2) = D, which simplifies to 27 + 8 + 2 = D. Therefore, D = 37 and the equation of our plane is 9x - y - z = 37.

Answer:

sample response:  None of the roots can have multiplicity because the polynomial is cubic and 3 roots are given. Write each root as a linear factor, then multiply the three factors to get the expression for the function.

Step-by-step explanation:

The coordinates of point Q are (-10, 10, 4).

To find the coordinates of point Q, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points P(x1, y1, z1) and Q(x2, y2, z2) are given by the average of the coordinates:

R = ((x1 + x2) / 2, (y1 + y2) / 2, (z1 + z2) / 2)

In this case, we are given that the midpoint R has coordinates (-3, 2, -1) and one of the points P has coordinates (4, -6, -6). Plugging in these values into the midpoint formula, we can solve for the coordinates of point Q:

Q = (2 * R - P)

Q = (2 * (-3, 2, -1) - (4, -6, -6))

Q = (-6, 4, -2) - (4, -6, -6)

Q = (-10, 10, 4)

Final answer:

The surface area of a right rectangular prism with dimensions of 6cm by 14cm by 5cm is calculated by summing up the areas of all faces, resulting in a total surface area of 368cm².

Explanation:

To calculate the surface area of a right rectangular prism, we need to find the area of all the faces and add them together. For a prism with dimensions of 6cm by 14cm by 5cm, it has three pairs of identical faces: two faces that are 6cm by 14cm, two faces that are 6cm by 5cm, and two faces that are 14cm by 5cm.

Using the area formula for rectangles (Area = length × width), we find the areas of these faces:

For the 6cm by 14cm faces: Area = 6cm × 14cm = 84cm². Since there are two such faces, their combined area is 2 × 84cm² = 168cm².

For the 6cm by 5cm faces: Area = 6cm × 5cm = 30cm². Since there are two such faces, their combined area is 2 × 30cm² = 60cm².

For the 14cm by 5cm faces: Area = 14cm × 5cm = 70cm². Since there are two such faces, their combined area is 2 × 70cm² = 140cm².

Adding up all these areas gives us the total surface area of the prism:

Total Surface Area = 168cm² + 60cm² + 140cm² = 368cm²

Therefore, the surface area of the right rectangular prism is 368cm².

The statement "If [tex]\( A \subset B \)[/tex], then [tex]\( A \cap B = A \cup B \)[/tex]" is not always true; it holds only if A = B.

The statement "If [tex]\( A \subset B \)[/tex], then [tex]\( A \cap B = A \cup B \)[/tex]" is not always true.

If [tex]\( A \subset B \)[/tex], it means that every element in set A is also in set B.

Now, consider the intersection of A and B [tex](\( A \cap B \))[/tex]. This intersection contains all elements that are common to both sets A and B.

On the other hand, the union of A and B [tex](\( A \cup B \))[/tex] contains all elements that are in either set A or set B, or both.

Since A is a subset of B, all elements in A are already in B, which means [tex]\( A \cap B = A \)[/tex]. However, [tex]\( A \cup B \)[/tex] would just be B, because all elements in A are also in B, so [tex]\( A \cup B \)[/tex] is simply B.

Therefore, the statement "If [tex]\( A \subset B \)[/tex], then [tex]\( A \cap B = A \cup B \)[/tex]" is not true in general; it is true only if A = B .