The perimeter of the rectangle below is 44 units. Find the length ab. If dc is 3z-3. And cb is 2z.

Answer:

27, it is divisible by 1, 3, 9, and 27

Step-by-step explanation:

By HL congruence,  triangle ABC congruent to triangle DEF. Therefore, option D is the correct answer.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

Consider the given triangles as ABC and DEF.

From the given triangles,

AC=DF=14 in.

BC=EF=20 in.

∠A=∠D=90°

The Hypotenuse-Leg (HL) Triangle Congruence Theorem is a special case that allows you to show that two right triangles are congruent. If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

By HL congruence, ΔABC ≅ ΔDEF

Therefore, option D is the correct answer.

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Answer:

\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2

Step-by-step explanation:

a recursive formula in a geometric sequence allows a term to be found by multiplying the preceding term by the common ratio r

here r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{-16}{-2}\) = 8 , then

\(a_{n}\) = 8\(a_{n-1}\) ; a₁ = - 2

If m = -5 or m = 3, the system of linear equations has no solution.

To determine the values of m for which the system of linear equations has no solution, we need to check the determinant of the coefficient matrix, which is:

| 3 m |

| m+2 5 |

The determinant is

=  (3 x 5) - (m x (m+2))

= 15 - m^2 - 2m

= -(m^2 + 2m - 15)

= -(m+5)(m-3)

So, for the system to have no solution, the determinant must be zero, so we have:

-(m+5)(m-3) = 0

This gives us two values of m: m = -5 and m = 3.

Thus, if m = -5 or m = 3, the system of linear equations has no solution.

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Answer:

Step-by-step explanation:

The answer to this should be 2(3x+5)

The simplified answer of this is 6x+10

I hope I helped you out.

Answer:

P: ()

E: 5^4 (example)

M:x

D: ÷

A:+

S:-

The height of the hill is approximately 25.73 ft. Where v0 is the initial velocity (108 ft/s), g is the acceleration due to gravity \((-32.2 ft/s^2)\),

To find the height of the hill, we can use the formula for the vertical position of an object under constant acceleration:

h = h0 + v0t + 1/2at^2

where h is the final height, h0 is the initial height, v0 is the initial velocity, t is the time, and a is the acceleration due to gravity (-32.2 ft/s^2).

In this case, we are given that the initial height h0 is 3 ft, the initial velocity v0 is 108 ft/s, and the time t is 9.5 s. We want to find the height of the hill, which we can denote as h_hill. The final height is the height of the plain, which we can denote as h_plain and assume is zero.

At the highest point of its trajectory, the arrow will have zero vertical velocity, since it will have stopped rising and just started to fall. So we can set the velocity to zero and solve for the time it takes for that to occur. Using the formula for velocity under constant acceleration:

v = v0 + at

we can solve for t when v = 0, h0 = 3 ft, v0 = 108 ft/s, and a = -32.2 ft/s^2:

0 = 108 - 32.2t

t = 108/32.2 ≈ 3.35 s

Thus, it takes the arrow approximately 3.35 s to reach the top of its trajectory.

Using the formula for the height of an object at a given time, we can find the height of the hill by subtracting the height of the arrow at the top of its trajectory from the initial height:

h_hill = h0 + v0t + 1/2at^2 - h_top

where h_top is the height of the arrow at the top of its trajectory. We can find h_top using the formula for the height of an object at the maximum height of its trajectory:

h_top = h0 + v0^2/2a

Plugging in the given values, we get:

h_top = 3 + (108^2)/(2*(-32.2)) ≈ 196.78 ft

Plugging this into the first equation, we get:

h_hill = 3 + 108(3.35) + 1/2(-32.2)(3.35)^2 - 196.78

h_hill ≈ 25.73 ft

If the arrow is launched at t0, the equation describing velocity as a function of time would be:

v(t) = v0 - gt

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Answer:

CD

Step-by-step explanation:

Look at the red lines corresponding the lengths of each triangle.

If the first quartile is 39 years old, it means that approximately one-fourth of the employees at CCNHS – Main Campus are 39 years old or younger.

The first quartile (Q1) of the ages of the 256 employees of CCNHS – Main Campus being 39 years old implies that 25% of the employees have an age equal to or less than 39 years old.

In statistical terms, the first quartile represents the point below which 25% of the data falls. It divides the data set into four equal parts, with each part containing 25% of the data. Therefore, if the first quartile is 39 years old, it means that approximately one-fourth of the employees at CCNHS – Main Campus are 39 years old or younger.

This information provides insight into the age distribution of the employees at the institution. It indicates that a significant portion of the employees are relatively young, with a quarter of them falling below the age of 39. Understanding the age demographics of the workforce can be useful for various purposes, such as planning professional development programs or implementing age-specific policies.

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Answer:

a

The 95% confidence interval is   \(0.5753<  p <0.62474\)  

b

 This 95% confidence interval tell us that there 95% confidence that the true proportion of adults in the US that now believe life imprisonment is a better approach for punishing murder lies within the interval

c

 The margin of error is   \(E =    0.02474 \)  

d

 The confidence interval becomes wider

Step-by-step explanation:

From the question we are told that

   The sample size is  n = 1506

    The sample proportion is  \(\^ p = 0.60\)

From the question we are told the confidence level is  95% , hence the level of significance is    

      \(\alpha = (100 - 95 ) \%\)

=>   \(\alpha = 0.05\)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  1.96\)

Generally the margin of error is mathematically represented as  

     \(E =  Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } \)

=>   \(E =    1.96 * \sqrt{\frac{0.60 (1- 0.60)}{1506} } \)    

=>   \(E =    0.02474 \)  

Generally 95% confidence interval is mathematically represented as  

      \(\^ p -E <  p <  \^ p +E\)

=>   \(0.60 - 0.02474 <  p <0.60 + 0.02474\)  

=>   \(0.5753<  p <0.62474\)  

This 95% confidence interval tell us that there 95% confidence that the true proportion of adults in the US that now believe life imprisonment is a better approach for punishing murder lies within the interval

Generally the level of confidence varies directly with the critical value of \(\frac{\alpha }{2}\) and this in turn varies directly with the margin of error which when sample proportion is constant it determines the width of the confidence interval so when the level of confidence increases the confidence interval becomes wider  

Commitment to goals can be promoted in through:

Goal commitment is the degree of determination a person uses to achieve an accepted goal, and it is determined by two major factors: importance and self-efficacy. The reasons a person has for achieving a goal, including expectations of certain outcomes, are significant. Commitment helps you stick to your goals in both good and bad times, when obstacles arise. Commitment is influenced by two factors: importance and

Goal commitment is generally defined as an individual's determination to devote time and effort to achieving a goal.

Goal commitment is the degree of determination a person uses to achieve an accepted goal, and it is determined by two major factors: importance and self-efficacy. The reasons a person has for achieving a goal, including expectations of certain.

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The Propositions are resulting

(a) ∀x∃y(x = y²) is False

(b) ∀x∃y(x² = y) is True.

(c) ∃x∀y(xy = 0) is True.

(d) ∀x∃y(x + y = 1) is True.

(a) ∀x∃y(x = y²)

This proposition states that for every x, there exists a y such that x is equal to y². To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any positive value for x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4 = 2². Similarly, if x = 9, then y = 3 satisfies the equation since 9 = 3².

Therefore, the proposition (a) is false.

(b) ∀x∃y(x² = y)

For any given positive or negative value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 4, then y = 2 satisfies the equation since 4² = 2. Similarly, if x = -4, then y = -2 satisfies the equation since (-4)² = -2.

Therefore, the proposition (b) is true.

(c) ∃x∀y(xy = 0)

The equation xy = 0 can only be satisfied if x = 0, regardless of the value of y. Therefore, there exists an x (x = 0) that makes the equation true for every y.

Therefore, the proposition (c) is true.

(d) ∀x∃y(x + y = 1)

To determine the truth value, we need to check if this statement holds true for every value of x.

If we take any value of x, we can find a corresponding value of y that satisfies the equation.

For example, if x = 2, then y = -1 satisfies the equation since 2 + (-1) = 1. Similarly, if x = 0, then y = 1 satisfies the equation since 0 + 1 = 1.

Therefore, the proposition (d) is true.

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Answer:

157 in

Step-by-step explanation:

2x3.14x25 = 157 in  

Answer:

2(w+11w)=1680

Step-by-step explanation:

If the width is w, then the length is 11w.

Using the formula for the perimeter of the rectangle, the equation is 2(w+11w)=1680

Answer:

666

Step-by-step explanation:

From this question,

a = 1-99%

a = 1-0.99

a = 0.01

5% = z(0.05) = 2.58 when we check the standard normal table

Therefore we calculate n as:

n = (z/E)²*p*1-p

Z = 2.58

E = 0.05

P = 0.5

1-p = 0.5

(2.58/0.05)²x0.5x0.5

= 51.6²x0.5x0.5

= 665.64

Therefore n is approximately 666.

Answer:

Are u guys solving for k?

Step-by-step explanation:

Answer:

Step-by-step explanation:

The numbers for the faculty members are

select: 83, 58, 64, 26, 47, 68, 29, 4, 78

23 comma 80 comma 37 comma 65 comma 54 comma 64 comma 70 comma 56 comma 9.

​(Use a comma to separate answers as​ needed.)

​(b) The president uses technology to produce the following random numbers.

Determine the numbers for faculty members who will be included in the sample.

Answer

Hi. I just sent you the answer.

Answer:

Step-by-step explanation:

Let's call the number of hotdogs sold "x". According to the problem, the number of sodas sold is three times the number of hotdogs sold, or 3x.

We know that the total number of sodas and hotdogs sold is 136. So we can set up an equation:

x + 3x = 136

Simplifying this equation, we get:

4x = 136

Dividing both sides by 4, we get:

x = 34

This means that 34 hotdogs were sold. To find the number of sodas sold, we can multiply the number of hotdogs sold by 3:

3x = 3(34) = 102

So, 102 sodas were sold.

We get an estimate of 36 movie cards in the deck.

Twο numerical sequences—οften experimental data—are prοpοrtiοnal οr directly prοpοrtiοnal if the ratiο between their cοrrespοnding elements is cοnstant.

Jοhnny chοse a tοtal οf 22 cards at randοm, which is 6 + 4 + 5 + 7.

The percentage οf each type οf card in the sample, if assumed tο be representative οf the percentage οf each type οf card in the entire deck, can be used tο calculate the apprοximate number οf mοvie cards in the deck.

The prοpοrtiοn οf mοvie cards in the sample is 4/22, which simplifies tο 2/11.

Sο we can estimate the number οf mοvie cards in the deck as:

(2/11) x 200 = 36.36

We estimate there are 36 mοvie cards in the deck by rοunding tο the nearest whοle number.

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Answer:

Yes, D = 5

Step-by-step explanation:

26 + 5 = 31, 31 + 5 - 36, and so on. It’s using addition, and is also having a constant difference, so it’s arithmetic.

The wheelchair access ramp must be 216.09 inches long.

To find the length of the wheelchair access ramp, we can use trigonometry.

The tangent function relates the angle of elevation to the ratio of the opposite side (height) to the adjacent side (length of the ramp).

Let's denote the length of the ramp as "x".

The height of the ramp is given as 18 inches.

Using the tangent function:

tan(angle of elevation) = height/length of the ramp

tan(4.8 degrees) = 18/x

To solve for x, we can rearrange the equation:

x = 18 / tan(4.8 degrees)

Using a calculator to evaluate the tangent of 4.8 degrees:

x = 18 / 0.08331

x= 216.09

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Answer:

4!

Step-by-step explanation:

Answer:

umm...

D...765 4th over 5th

Answer:

  AB ≈ 1.8 ft . . . . . ramp height

  BC ≈ 29.9 ft . . . distance along the ground

Step-by-step explanation:

The 30-ft length in the diagram is the hypotenuse of the right triangle. The vertical height of interest is the side of the triangle opposite the given angle. That means the relevant trig relation is ...

  Sin = Opposite/Hypotenuse

  sin(3.5°) = AB/(30 ft)

Multiplying by 30 ft gives ...

  AB = (30 ft)sin(3.5°) ≈ 1.831 ft

  AB ≈ 1.8 ft

__

The distance along the ground is the side adjacent to the angle, so the relevant trig relation is ...

  Cos = Adjacent/Hypotenuse

  BC = (30 ft)cos(3.5°) ≈ 29.944 ft

  BC ≈ 29.9 ft

Answer:

6

Step-by-step explanation:

Answer: 6
The factors of 12 are: 1, 2, 3, 4, 6, 12

The factors of 18 are: 1, 2, 3, 6, 9, 18

The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30

Then the greatest common factor is 6.

Answer:

Y= 2x^2+14x+12

Explaination:

When it gives you the roots you can automatically change the sign and put them with the x in factors such as

y = (x+6)(x+1)

Then you put the leading coefficient of 2

y = 2(x+6)(x+1)

Then to get it in standard form you distribute the parenthesis the the 2 to get:

Y= 2x^2+2x+12x+12

Combine like terms and you'll answer will be

Y= 2x^2+14x+12

We are given the following series

-6, -2, 2, 6

Common difference = last term - first term

For the first two terms

The common difference is calculated as

Last term - first term

Last term = -2

First term = -6

Common difference = -2 - (-6)

= -2 + 6

common difference = 4

Common difference = 2 - (-2)

common difference = 2 + 2

Common difference = 4

Last two terms

common difference = 6 - 2

Common difference = 4

The common difference for this sequence is 4

The sequence is arithmetic.

Answers:

=======================================================

Explanation:

This leads to the equation W = 33T + 500

------------------------

Plug in T = 14

W = 33T + 500

W = 33*14 + 500

W = 462 + 500

W = 962 liters of water are in the pond after 14 minutes