The measures of the legs of a right triangle both measure 7 yards. What is the length of the hypotenuse? Round your answer to the nearest tenth.

Answer:

\(3(x+y)(x+y)\)

Step-by-step explanation:

\(3x(x+y)+3y(x+y)\)

\(3x^{2} +6xy+3y^{2}\)

\(3(x+y)(x+y)\)

hope this helps.....

Answer:

6930 cm.

Step-by-step explanation:

To find the LCM, we can start by listing the prime factors of each number:

63 = 3 × 3 × 7

70 = 2 × 5 × 7

77 = 7 × 11

Next, we take the highest power of each prime factor that appears in the factorizations:

3² × 2 × 5 × 7 × 11 = 6930

Therefore, the minimum distance each boy should cover so that they can all cover the distance in complete steps is 6930 cm.

Answer:

don´t ge it sorry

Step-by-step explanation:

Answer:

54000000

Step-by-step explanation:

Answer:

is 54000000

Step-by-step explanation:

I got it right

Yes, One of them must be even and this is because Pigeonhole Principle.

What is Pigeonhole Principle?

According to the pigeonhole principle, at least one container must hold more than one item if n things are placed into m containers, where n > m.  As an illustration, if one has three gloves (none of which are ambidextrous or reversible), at least two of them must be right-handed or left-handed as there are three items but only two categories of handedness to classify them into. It is possible to establish potentially surprising consequences using this seemingly obvious assertion, a type of counting argument.

From series {1,2......2n},  we need to select 'n+1' integers.

Even integers series from above series is {2,4,6..........2(n-1), 2n}

Odd integers series from above series is {1,3,5......2(n-2), 2n-1}

We can choose only n odd integers from the series. Therefore, if we choose n+1 integers, at least one of them must have to be even integer.

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First, let's calculate the standard deviation of the bricks.

Standard deviation = 5.75 - 5 = 0.75

Now, we need to use the z-score formula to calculate the mean.

z-score = (observed value - mean) / standard deviation.

Let's plug our values into the formula above.

1 = (5 - mean) / 0.75

Multiply both sides by 0.75

0.75 = 5 - mean

Subtract 5 from both sides.

-4.25 = -mean

Divide both sides by -1

4.25 inches = mean

Answer: A. 4.00 inches

The assertion that which shows that P(k + 1) is true provided Pk in the Inductive step is true. Moreover, P(1) is also true. Hence, by induction principle, we can say that P(n) is true for all positive integer n.

What is Integer?

A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.

Given that P(n) be the assertion

∑j² = n (n+1)(2n+1)/6

(a) For n = 3, we get

∑j² = 1² + 2²+3² =14

= 3(3+1)(6+1)/6

=14

Hence, P(3) is true.

(b) Expression for P(k) may take the form

∑j² = k (k+1)(2k+1)/6

(c) Expression for P(k + 1) may take the form

∑j² = (k+1) (k+2)(2k+3)/6

(d)Base case:

In base case, we must prove that P(1) is true.

(e) To prove P(n) will be true for every positive integer n, we need to prove that P(k + 1) is true in the inductive step, where k is a positive integer.

(f) In the Inductive step, the Inductive hypothesis is that Pk is true for positive integer k.

(g)Base case:

a) For n=1, we get

RHS= 1(1+1)(2+1)/6

=1

Hence, P(1) is true.

Inductive hypothesis:

Assume P(k) is true:

∑j² = k (k+1)(2k+1)/6

Inductive step:

Now,

∑j² = k (k+1)(2k+1)/6 +(K+1)²

which shows that P(k + 1) is true provided P(k) in the Inductive step is true. Moreover, P(1) is also true. Hence, by induction principle, we can say that P(n) is true for all positive integer n.

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Answer:

m∠D = 49°
m∠E = 41°
m∠F = 90°

Step-by-step explanation:

        We know a triangle's angles add up to 180, so we can create an equation and solve for x. We also know the little box represents 90 degrees.

Given:

        90° + 5x° + 14° + 3x° + 20° = 180°

Combine like terms:

        8x° + 124° = 180°

Subtract 124 from both sides of the equation:

        8x° = 56°

Divide both sides of the equation by 8:

        x = 7

        Now, we will plug this value of x back into the angles to solve. Again, the little box represents that Angle F is equal to 90 degrees.

m∠D = 5x° + 14° = 5(7)° + 14° = 49°
m∠E = 3x° + 20° = 3(7)° + 20° = 41°
m∠F = 90°

The reason why f(1) = -20 - 5 is because of the given function formula f(0) = -20 and f(n) = f(n - 1) - 5 for n ≥ 1.

We are told that the sequence is defined as;

f(0) = -20

f(n) = f(n - 1) - 5 for n ≥ 1

Using that formula above we can say that;

f(1) = f(1 - 1) - 5

f(1) = f(0) - 5

Thus;

f(1) = -20 - 5

Similarly;

f(2) = f(2 - 1) - 5

f(2) = f(1) - 5

Thus;

f(2) = -20 - 5 - 5

Similarly;

f(3) = f(3 - 1) - 5

f(3) = f(2) - 5

Thus;

f(2) = -20 - 5 - 5 - 5

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Answer: 56 + 12 = 68

y + 12 = x

x = 68

Step-by-step explanation:

The rectangular coordinates (in simplest radical form) are (2, -2√3).

To convert polar coordinates (r, θ) into rectangular or Cartesian form (x, y), we can use the following formulas:

x = r * cos(θ)

y = r * sin(θ)

In this case, the polar coordinates are (4, 5π/3). Therefore, we have:

r = 4

θ = 5π/3

Using the formulas, we can calculate the rectangular coordinates as follows:

x = 4 * cos(5π/3)

y = 4 * sin(5π/3)

To evaluate cos(5π/3) and sin(5π/3), we can use the unit circle or trigonometric identities.

In the unit circle, we know that cos(5π/3) = cos(π/3) = 1/2, and sin(5π/3) = -sin(π/3) = -√3/2.

Substituting these values into the formulas:

x = 4 * (1/2) = 2

y = 4 * (-√3/2) = -2√3

Therefore, the rectangular coordinates (in simplest radical form) are (2, -2√3).

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Given question is incomplete, the complete question is below:

Convert the polar coordinates (4, 5π/3) into rectangular form. Express your answer in simplest radical form.

We have proved that the expression \(Var(x) = E(x^2) - [E(x)]^2.\)

To prove that \(Var(x) = E(x^2) - [E(x)]^2\), where \(Var(x)\) represents the variance of a random variable x and E(x) represents the expected value of x, we can start by using the definition of variance:

\(Var(x) = E[(x - E(x))^2]\)

Expanding the square:

\(Var(x) = E[x^2 - 2x*E(x) + [E(x)]^2]\)

Using linearity of expectations, we distribute the expectation operator:

\(Var(x) = E(x^2) - 2E(x*E(x)) + E([E(x)]^2)\)

Now, let's focus on the term E(x*E(x)). Since E(x) is a constant with respect to the inner expectation operator, we can take it out:

\(E(x*E(x)) = E(x) * E(E(x))\)

The inner expectation, E(E(x)), is just the expected value of a constant, which is equal to that constant:

\(E(E(x)) = E(x)\)

Substituting this back into the equation, we have:

\(Var(x) = E(x^2) - 2E(x*E(x)) + E([E(x)]^2)\)

           \(= E(x^2) - 2E(x*E(x)) + E(x^2)\)

Now, consider the term \(E(x*E(x))\). This can be written as:

\(E(x*E(x)) = E(E(x^2|x))\)

This is the conditional expectation of \(x^2\) given x. However, when we take the unconditional expectation E, the conditional expectation collapses to the unconditional expectation of \(x^2\):

\(E(x*E(x)) = E(x^2)\)

Substituting this back into the equation, we get:

\(Var(x) = E(x^2) - 2E(x*E(x)) + E(x^2)\)

     \(= E(x^2) - 2E(x^2) + E(x^2)\)

     \(= E(x^2) - E(x^2)\)

     \(= E(x^2) - [E(x)]^2\)

Hence, we have proved that \(Var(x) = E(x^2) - [E(x)]^2.\)

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The sentence "There is exactly one person who has been sent an email by everyone" can be written as a logical expression as follows:

∃x ∀y (S(y,x) → (∀z (S(y,z) → z = x)))

This expression uses the existential quantifier ∃x, which states that there exists at least one x such that the statement inside the quantifier is true. The universal quantifier ∀y states that the statement inside the quantifier is true for all y.

The statement S(y,x) says that y has sent an email to x, and the implication (→) says that if y has sent an email to x, then the statement inside the implication is true.

The statement ∀z (S(y,z) → z = x) states that for all z, if y has sent an email to z, then z must equal x. This expression states that there is exactly one person who has been sent an email by everyone, meaning that there is one person who is the recipient of all emails sent.

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Factor by grouping: 16x³ +28x² - 28x - 49 = 0 is  (4x² - 7) (4x - 7) = 0

Large polynomials can be divided into groups based on a common factor. As a result, we may factor each distinct group and then merge like words. We refer to this as factoring by grouping.

We have the equation,

16x³ +28x² - 28x - 49 = 0

In order to solve the equation by using factor by grouping:

We find common terms in between,

So, we arrange the terms,

16x³ +28x² - 28x - 49 = 0

4x² (4x - 7) -7 (4x - 7) = 0

Here, we have common term (4x-7).

Factor out the common binomial.

(4x² - 7) (4x - 7) = 0

Therefore, (4x² - 7) (4x - 7) = 0 is the factor.

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Answer:

3 also greece needs to chill on the sweets

Step-by-step explanation:

Answer:

3

steps

a quarter of 12 is 3

The missing variables after translation mapping are;

r = 100°

s = 8

t = 5

w = 54°

When we map one figure to the other and it provides a congruent object, then it means that the corresponding sides and angles of both figures are congruent to each other.

Thus, it means that;

3w° = 162°

r = 100°

2t = 10

s = 8

Solving the variables gives us;

3w° = 162°

w = 162/3

w = 54°

2t = 10

t = 10/2

t = 5

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The height of the cat is solved to be

4 m

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Examining the figure shows that pair of equivalent sides are

distance of the tree and the cat from the mirror

then height of the tree and height of the cat

The solution is worked out taking the proportions

distance of the tree from the mirror / distance of the cat from the mirror

=

height of the tree / height of the cat

plugging in the values

24/6 = 16 / height of the cat

height of the cat  = 16 * 6 / 24

height of the cat  = 4 m

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Answer:

10 *6= 60

60÷2=30

1÷2×b×h formula

answer- 30

Answer:

t needs 68 feet to enclose the garden.

Step-by-step explanation:

In this problem, we are to solve the sides of a parallelogram ABCD to know the measurement to enclose a garden.

Take note that a parallelogram has two equal lengths and two equal widths. Let us assume that the parallelogram AB = CD is the length and AD = BC is the width.

Solving the problem

First, let us solve for r using the condition AD = BC

AD = BC

3r + 8 = 2r + 12

Simplify the equation

3r - 2r = 12 - 8

r = 4

Next, let us substitute the value of r to AB, BC, CD, and AD.

For AB:

AB = 4r - 2

AB = 4(4) - 2

AB = 16 - 2 = 14

For BC:

BC = 2r + 12

BC = 2(4) + 12

BC = 8 + 12 = 20

For AD:

AD = 3r + 8

AD = 3(4) + 8

AD = 12 + 8 = 20

For CD:

But AB = CD Therefore, CD = 14

Finally, let us solve the perimeter of the parallelogram

Perimeter = AB + BC + CD + AD

Perimeter = 14 + 20 + 20 + 14

Perimeter = 68 feet

Therefore, the fencing needed to enclose the garden is 68 feet.

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Step-by-step explanation:

Answer:

its B

Step-by-step explanation:

The ultimate goal of these activities is to increase the visibility of a product or service to potential customers.

Promotional activity that may be the most effective tool to the manager of a Fixed Base Operator (FBO) is customer referrals.

In the aviation industry, the Fixed Base Operator (FBO) is the primary point of contact for general aviation aircraft. This entity provides several important services to pilots and passengers alike.

These services range from fueling, ground handling, and aircraft storage to custom office facilities. For any FBO, customer referrals should be the most effective tool for promotional activity. Customers trust the opinions of those they know and respect.

Furthermore, in a competitive environment, word-of-mouth referral advertising is inexpensive and requires minimal effort by the FBO to generate.

What is promotional activity? Promotional activities refer to any effort to create public awareness and gain exposure for a product or service.

The aim of promotional activity is to increase public awareness, create interest, and generate sales. Promotional activities can include a variety of tools, including advertising, personal selling, and public relations.

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Answer:

B. is the answer to the question-- 2x^2 -29

Step-by-step explanation:

Answer:

C

The line is from -3 to 3 and the circles are closed

Answer:

4. - 3

5. 5 / 11

6. - 2

Step-by-step explanation:

4.

9 / x = - 3

x = 9 / - 3

x = - 3

5.

11 = 5 / x

x = 5 / 11

6.

- 2 = 4 / x

x = 4 / - 2

x = - 2

The simplified expression for -3(2x - y)²y²(xy) is -12x²y³ + 6xy⁴.

When simplifying expressions, it is important to remember the order of operations, which is parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right). To simplify this expression, we first need to simplify the terms within the parentheses.

The expression within the parentheses is 2x - y, so we can square it to get (2x - y)², which is equal to 4x² - 4xy + y². We can then substitute this expression back into the original expression to get:

-3(4x² - 4xy + y²)y²(xy)

Simplifying the expression within the parentheses first we get,

-3(4x² - 4xy + y²)y²(xy) = -12x²y³ + 12xy⁴ - 3y⁵x

Next, we can simplify the term y²(xy) to get y³x, and then distribute the negative 3 throughout the expression to get:

-3(4x²y³ - 4xy⁴ + y³x)

This can be further simplified by distributing the negative 3 and combining like terms to get:

-12x²y³ + 6xy⁴

Therefore, the simplified expression for -3(2x - y)²y²(xy) is -12x²y³ + 6xy⁴.

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Answer: 80 feet

Step-by-step explanation:

We can write these as fractions and do cross multiplication with the numerator being the height of the object while the denominator being the length of the shadow:

5 * 128 = 8x

640 = 8x

80 = x

Thus, the height of the lighthouse is 80 feet tall.

Answer:

Step-by-step explanation:

let a be the first term and r be common ratio.

\(a_{3}=ar^2=-45\\a_{5}=ar^4=-405\\divide\\\frac{ar^4}{ar^2} =\frac{-405}{-45} =9\\r^2=9\\r=\pm3\\9a=-45\\a=-5\\a_{7}=ar^{7-1}=ar^6=ar^4 \times r^2=-405 \times 9=-3645\)

Answer:

Step-by-step explanation:

Cups: servings

8 : 22  :: x : 3

Product of means = product of extremes

22*x = 3*8

   \(x = \dfrac{3*8}{22}=\dfrac{3*4}{11}=\dfrac{12}{11}=1\dfrac{1}{11}\)