what three consecutive integers equal 81

To find 'z', utilise the properties of a parallelogram where opposite sides are equal. Setting these sides equal to each other and solving for 'z' provides the answer, 'z' = 3.5.

In this problem, you're given a quadrilateral ABCD for which you are supposed to find the value of 'z' when the quadrilateral is a parallelogram. In a parallelogram, the opposite sides are equal. Therefore, we can set AB = CD and BC = AD, and then solve for 'z'. From AB = CD (13w + 5 = 13w + 5), no information is required as their lengths are already equal. From BC = AD (5z - 2 = 3z + 5), solving for 'z' would give us 'z' = 7/2 or 3.5.

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To solve for the surface area of the pyramid, we make use of the formula:

A= l w + l [sqrt ((w / 2)^2 + h^2)] + w [sqrt ((l / 2)^2 + h^2))

where,

l and w are the base of the pyramid = 100 mm

h is the height of the pyramid = 75 mm

Substituting the given values into the equation:

A= 100 * 100 + 100 [sqrt ((100 / 2)^2 + 75^2)] + 100 [sqrt ((100 / 2)^2 + 75^2))

A = 10,000 + 100 (sqrt 2575) + 100 (sqrt 2575)

A = 20,148.90 mm^2

Therefore the surface area of the pyramid is about 20,149 mm^2.

The triangle ABC is mapped to A'B'C' through a 180-degree rotation about the origin, as all the points' x and y coordinates have changed signs, consistent with this transformation.

To determine which transformations can map the original triangle ABC to the new triangle A'B'C', we must closely examine the coordinates given and analyze the possible transformations.

Looking at the coordinates:

A(2, 2) to A'(-2, -2) suggests a reflection over the origin, which can be considered as a 180-degree rotation around the origin.

B(4, 1) to B'(-1, -4) also suggests a similar transformation, as the x and y values are negated and swapped in position.

C(4, 5) to C'(-5, -4) follows the same pattern.

All these transformations indicate that the original triangle has been rotated 180 degrees about the origin. This can also be observed by noting that the x and y coordinates have simply changed their signs, an effect of 180-degree rotation about the origin. This satisfies the claim of the classical geometry theorem which states that such transformations can be expressed as either a translation or a rotation. In this case, it's purely a rotation as there's no translation component.

Hence, the inequality that will represent the marks he needs  is:

4x+8y≥50

On a final exam, each multiple-choice question is worth 4 points and each word problem is worth 8 points.

Lorenzo needs at least 50 points on the final to earn a "B" in the class.

Let x be the number of correct multiple-choice questions, and y, the number of correct word problems.

Hence, the inequality that will represent the marks he needs  is:

4x+8y≥50

The least common multiple of 2/3 5/6 and 9/4 is 12.

A fraction represents a part of a number or any number of equal parts.

A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.

We are given that;

The numbers 2/3 5/6 and 9/4

Now,

To find the least common multiple of fractions, we need to find the least common multiple of their denominators and divide it by the greatest common factor of their numerators. The steps are:

Multiples of 3: 3, 6, 9, 12, 15, 18,

Multiples of 6: 6, 12, 18,

Multiples of 4: 4, 8, 12,

Find the greatest common factor of 2, 5 and 9. This is the largest number that can divide all three numbers without leaving a remainder. One way to do this is to list the factors of each number and find the largest one that they have in common. For example:

Factors of 2: 1 and 2

Factors of 5: 1 and 5

Factors of 9: 1,3 and9

The only common factor is 1, so this is the greatest common factor of the numerators.

Divide the least common multiple of the denominators by the greatest common factor of the numerators. This gives us:

12 /1 =12

Therefore, the LCM of given fraction will be 12.

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The expanded form of 310, 763, 136 is:

300,000,000 + 10,000,000 + 700,000 + 60,000 + 3,000 + 100 + 30 + 6

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

310, 763, 136

This can be written in expanded form as,

300,000,000 + 10,000,000 + 700,000 + 60,000 + 3,000 + 100 + 30 + 6

Thus,

The expanded form is:

300,000,000 + 10,000,000 + 700,000 + 60,000 + 3,000 + 100 + 30 + 6

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Answer:

It takes to the plane [tex]162.792[/tex] seconds to fly once around a circle whose radius is 2850 m at a speed of [tex](110)\frac{m}{s}[/tex]

Step-by-step explanation:

The first step in this exercise is to find the total distance that the plane will fly.

This distance is equal to the perimeter of a circle whose radius is 2850 m.

Given a circle of radius R, the perimeter ''P'' can be calculated as :

[tex]P=\pi .d=\pi  .2.R[/tex]

Where ''d'' is the diameter of the circle that is equal to 2.R

The distance that the plane will fly in the exercise is :

[tex]P=\pi .2.R=\pi .2.(2850m)=17907.078m[/tex]

Now, the speed is equal to distance divided by time.

[tex]speed=\frac{distance}{time}[/tex]

We have the speed of the plane and the distance (that is the perimeter ''P'' of the circle). We only need to replace this values in the equation and find the time variable.

[tex](110)\frac{m}{s}=\frac{(17907.078)m}{t}[/tex]

[tex]t=\frac{(17907.078)m}{(110)\frac{m}{s}}=(162.792)s[/tex]

[tex]t=(162.792)s[/tex]

We find that the time is [tex]162.792[/tex] seconds.

To find the angle formed by a diagonal of a rectangular box with its base, calculate the base diagonal using the Pythagorean Theorem and then use the inverse tangent function with the height and base diagonal as arguments.

The angle formed by a diagonal of the rectangular box with the base of the box can be found using the Pythagorean Theorem. In this case, the box has a length of 6, a width of 4, and a height of 5. The diagonal of the base can be calculated as the hypotenuse of a right triangle formed by the length and the width. According to the Pythagorean theorem, this diagonal (D) is √(6² + 4²) which is √(36 + 16) or √52. To find the angle between the box's base diagonal and the body diagonal (which includes the height), we need to use trigonometry, specifically the inverse tangent function (tan-1). So we have the length of the box's base diagonal (D) and the height (H), forming a right triangle with the body diagonal as the hypotenuse. The angle θ can be calculated using tan-1(H/D), where H is the height of the box and D is the length of the diagonal on the base. This equates to tan-1(5/√52). Evaluating this expression with a calculator gives us the angle θ formed by the body diagonal with the base of the box.

Answer: Second option is correct.

Step-by-step explanation:

Since we have given that

All real numbers have a reciprocal.

But we know that 0 has no inverse, means there is no reciprocal exists for 0.

Because,

[tex]\dfrac{1}{0}=\infty[/tex]

So, 0 is a counter example to the statement.

Hence, Second option is correct.

Answer: the answer will be 165.2

Step-by-step explanation:

Answer:

[tex]A. \frac{5}{143}[/tex]

Step-by-step explanation:

Given,

Number of women = 5,

Number of men = 8,

Total persons = 5 + 8 = 13,

∵ Ways of selecting any 3 persons = [tex]^{13}C_3[/tex]

Also, the ways of selecting 3 women = [tex]^5C_3[/tex]

Hence, the probability of selecting 3 women

[tex]=\frac{\text{Ways of selecting any 3 women}}{\text{ Ways of selecting any 3 persons}}[/tex]

[tex]=\frac{^5C_3}{^{13}C_3}[/tex]

[tex]=\frac{\frac{5!}{2!3!}}{\frac{13!}{3!10!}}[/tex]

[tex]=\frac{10}{\frac{13\times 12\times 11}{6}}[/tex]

[tex]=\frac{60}{13\times 12\times 11}[/tex]

[tex]=\frac{5}{143}[/tex]

Hence, OPTION A is correct.

Answer:

The graph of y > mx, where m > 0, consists of a dashed line and a shaded half plane. The line has a positive slope and passes through the origin. The shaded half plane is above the line.    

Step-by-step explanation:

Hope this helps any of you! :)

Answer:

Figure 3.

Step-by-step explanation:

We perform the rotation first.  A 180° rotation about the origin maps every point

(x, y)→(-x, -y).  This means it negates both the x- and y-coordinates.

The pre-image points are:

K(3, -4); L(3, -1); M(5, -1); N(5, -4).  Performing the rotation and negating the coordinates will give us:

K'(-3, 4); L'(-3, 1); M'(-5, 1); N'(-5, 4).

Now we perform the translation.  The translation rule is <1, -4>; this means we add 1 to each x-coordinate and subtract 4 from each y-coordinate.  This maps to our new points:

K''(-2, 0); L''(-2, -3); M''(-4, -3); N''(-4, 0)

These are the points of figure 3.

Answer:

The answer by Equinimity is incorrect. On my test, those weren't even options. The answer is:

C = 10n; A = 25n

(the symbol that looks like 'n' anyway)

1. It's what the answer is on pretty much every other version of this question on brainly.

2. I did the math.