in the quadrilateral abcd, assume ∠a = 90º = ∠c. draw the diagonals ac and bd and show that ∠dac = ∠dbc.

If one angle in an isosceles triangle is 90 degrees then the measure of each angle of an isosceles triangle will be 45 degrees

What is an isosceles triangle ?

A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that have the same length.

If the sides AB and AC of a triangle ABC are equal, then the triangle ABC is an isosceles triangle with B = C. "If the two sides of a triangle are congruent, then the angle opposite to them is likewise congruent," states the theorem that characterizes the isosceles triangle.

Since this triangle's two sides are equal, the base of the triangle is the side that is not equal.

As we know that in an isosceles triangle set of two angles are equal

And

we also know that sum of all the angles of a triangle is 180 degrees

So, According to the question

90 degrees + other angles =180 degrees

other angles = 90 degrees

one angle = 90/2

one angle = 45 degree  

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The area of the triangle is 31.54 square units

From the question, we have the following parameters that can be used in our computation:

We have the following values

a = 7 units

c = 11 units

B = 55 degrees

The area of the triangle is calculated using the following area formula

Area = 1/2absin(C)

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 7 * 11 * sin(55 degrees)

Evaluate

Area = 31.54

Hence, the area is 31.54 square units

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The equivalent resistance of the circuit is given by:

D. 2 Ω

In this problem, there are two resistors in parallel, with resistances of 4 Ω, hence:

Req = 4 x 4/(4 + 4) = 16/8 = 2 ohms.

Hence option D is correct.

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Answer: x = 30

Step-by-step explanation:

Since AB and CD are straight lines, vertical angles formed by them are congruent. Angle DOB is equal to angle AOC which is equal to 2x. Since you know that a straight angle is equal to 180 degrees, you can say :

2x + 90 + x = 180

3x + 90 = 180

3x = 90

x=30

Hope this helped :)

The value of c²(δt′)² - (δx′)² can be expressed in terms of γ, δx, δt, and c. It represents a mathematical expression involving the speed of light, time dilation (δt'), and length contraction (δx') in the context of special relativity.

In the context of special relativity, the equation c²(δt′)² - (δx′)² represents the spacetime interval between two events, where c is the speed of light. The variables δt' and δx' represent the differences in time and space measurements as observed from different reference frames. The term c²(δt′)² represents the time component of the interval, accounting for time dilation due to relative motion. The term (δx′)² represents the space component of the interval, accounting for length contraction due to relative motion.

To express the expression in terms of γ, δx, δt, and c, we can use the Lorentz factor γ, which is defined as γ = 1 / √(1 - (v²/c²)), where v is the relative velocity between the frames. By rearranging the equation, we can substitute γ, δt, and δx into the expression to obtain the desired form. The Lorentz factor γ relates to the dilation and contraction effects observed in special relativity and allows us to express the spacetime interval in terms of the given variables.

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The correct statement regarding the quantities in this problem is given as follows:

C. The two quantities are equal.

The first quantity in this problem is given as follows:

\(\frac{2^{30} - 2^{29}}{2}\)

We can apply the common factor in the numerator, hence:

\(\frac{2^{29}(2 - 1)}{2} = \frac{2^{29}}{2}\)

When two terms have the same base and different exponents and are divided, we keep the base and subtract the exponents, hence:

\(\frac{2^{29}}{2} = 2^{29 - 1} = 2^{28}\)

Meaning that the two quantities are equal, hence option c is the correct option for this problem.

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According to the textbook, polygraph testing (lie detection) screening is prohibited as a condition of employment outside of government jobs, which means option (a) is correct.

The use of polygraph testing, also known as lie detection, as a screening tool for employment purposes is generally restricted. The rationale behind this restriction is based on concerns regarding the reliability and validity of polygraph tests in accurately detecting deception. Polygraph testing has been found to have limitations, as false positives and false negatives can occur, leading to inaccuracies in the results.

Due to these concerns, many jurisdictions have implemented legal restrictions on the use of polygraph testing in employment settings. It is important to note that there may be certain exceptions to this general prohibition. In some cases, such as certain high-security government positions or jobs that involve protecting the public from potential harm, polygraph testing may be permitted based on a countervailing need.

However, in the broader context of employment screening, polygraph testing is generally prohibited outside of government jobs.

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The limits of the expression \(\lim _{h\to 0}\left(\frac{7\left(x+h\right)^2-7x^2}{h}\right)\) is 14x

From the question, we have the following parameters that can be used in our computation:

\(\lim _{h\to 0}\left(\frac{7\left(x+h\right)^2-7x^2}{h}\right)\)

Expand the expression

So, we have

\(\lim _{h\to 0}\left(\frac{7\left(x+h\right)^2-7x^2}{h}\right) = \lim _{h\to 0}\left(\frac{7\left(x^2+2xh + h^2)-7x^2}{h}\right)\)

Open the brackets

So, we have

\(\lim _{h\to 0}\left(\frac{7\left(x+h\right)^2-7x^2}{h}\right) = \lim _{h\to 0}\left(\frac{7x^2+14xh + 7h^2-7x^2}{h}\right)\)

Evaluate the like terms

\(\lim _{h\to 0}\left(\frac{7\left(x+h\right)^2-7x^2}{h}\right) = \lim _{h\to 0}\left(\frac{14xh + 7h^2}{h}\right)\)

Evaluate the quotient

\(\lim _{h\to 0}\left(\frac{7\left(x+h\right)^2-7x^2}{h}\right) = \lim _{h\to 0}\left(14x + 7h)\)

So, we have

\(\lim _{h\to 0}\left(\frac{7\left(x+h\right)^2-7x^2}{h}\right) = 14x + 7(0)\)

This gives

\(\lim _{h\to 0}\left(\frac{7\left(x+h\right)^2-7x^2}{h}\right) = 14x + 0\)

Evaluate

\(\lim _{h\to 0}\left(\frac{7\left(x+h\right)^2-7x^2}{h}\right) = 14x\)

Hence, the value of the limits is 14x

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Question

Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is infinite, enter ∝ or -∝, as appropriate)

\(\lim _{h\to 0}\left(\frac{7\left(x+h\right)^2-7x^2}{h}\right)\)

1. The probability that the sample proportion will be greater than 0.34 is approximately 0.0192.

2. The probability that the sample proportion will be between 0.196 and 0.354 is approximately 0.8801.

1. Probability that the sample proportion will be greater than 0.34:

The sample proportion can be modeled as a normal distribution.

mean = 0.25

standard deviation = √(p(1-p)/n),

where p is the population proportion and n is the sample size.

Calculating the standard deviation:

σ = √(0.25 * 0.75 / 75)

σ  ≈ 0.0433

The z-score will be:

z = (0.34 - 0.25) / 0.0433

z ≈ 2.08

Using a calculator, the probability of obtaining a z-score greater than 2.08 is approximately 0.0192, or 1.92%.

2. Probability that the sample proportion will be between 0.196 and 0.354:

The z-scores for the two values are:

z1 = (0.196 - 0.25) / 0.0433 ≈ -1.25

z2 = (0.354 - 0.25) / 0.0433 ≈ 2.17

Using a calculator, the probability of obtaining a z-score less than -1.25 is approximately 0.1056, and the probability of obtaining a z-score less than 2.17 is approximately 0.9857.

Therefore, the between these two z-scores will be:

Probability = 0.9857 - 0.1056 ≈ 0.8801

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Complete question:

Nobel Dylan has determined that 25% of all its MP3-songs sales are credit sales. A random sample of 75 sales is selected.

1. What is the probability that the sample proportion will be greater than 0.34?

2. What is the probability that the sample proportion will be between 0.196 and 0.354?

The maximum volume of his box is approximately 15.

The maximum value of a graph that represents a function is the y-value of the vertex of the parabola, that is, the point where the graph begins to shift from increasing to decreasing.

Thus, in the graph given, the volume is plotted on the y-axis. The graph also shows a parabola that has a vertex at y = 15. This represents the maximum value.

The vertex, which is at y = 15, represents the maximum volume of the box.

Therefore, this means that the maximum volume of his box is approximately 15.

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Edna should leave at 2:07 PM in order to arrive at Jake's party by 2:30 PM

To determine the time Edna should leave, we need to subtract the travel time from the desired arrival time.

If Edna needs to be at Jake's party at 2:30 PM and it takes her 23 minutes to drive there, she should leave 23 minutes before 2:30 PM.

To calculate the departure time, we subtract 23 minutes from 2:30 PM:

2:30 PM - 23 minutes = 2:07 PM

Therefore, Edna should leave at 2:07 PM in order to arrive at Jake's party by 2:30 PM

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Answer:

The answer is D

Answer:

B.   3,158

Step-by-step explanation:

h(x) = -49x − 125

Let x = -67

h(-67) = -49(-67) − 125

          =3283-125

          = 3158

Answer:

Answer B

Step-by-step explanation:

To find the value of h(-67) for the function h(x) = -49x - 125,

we substitute -67 for x in the function and evaluate it.

h ( - 67 ) = - 49 ( - 67 ) - 125

Now we can simplify the expression:

h ( -67 ) = 3283 - 125

h ( -67 ) = 3158

Answer: 1

Step-by-step explanation:

Answer:

The correct option is;

A vertical line can be represented using a table but not a function because the slope is undefined

Step-by-step explanation:

A function, f(x), representing a linear relationship can be presented as follows;

f(x) = m·x + c

Where;

m = The slope = Δy/Δx = (y₂ - y₁)/(x₂ - x₁)

c = The y-intercept

Whereby the line is a vertical line, x₂ = x₁ and x₂ - x₁ =

Therefore;

The slope of a vertical function, m =  (y₂ - y₁)/(x₂ - x₁) = (y₂ - y₁)/0 = ∞ from which we have;

f(x) = ∞·x + c = ∞ which is undefined and the vertical line can only be represented using a table but not a function because the slope is undefined

Where are you confused?

The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x. The cab charges $0.88 for a ride of 2 miles. And the cab charges $1.72 for a trip of 8 miles.

a. The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x

b. To find the number of miles for a cab ride that costs $0.88, we can set up the equation:

$0.88 = $0.60 + $0.14 * x

Subtracting $0.60 from both sides, we get:

$0.88 - $0.60 = $0.14 * x

$0.28 = $0.14 * x

Dividing both sides by $0.14, we find:

x = $0.28 / $0.14

x = 2 miles

Therefore, the cab charges $0.88 for a ride of 2 miles.

c. To calculate the cost of a trip of 8 miles, we can substitute x = 8 into the equation:

Cost = $0.60 + $0.14 * 8

Cost = $0.60 + $1.12

Cost = $1.72

Therefore, the cab charges $1.72 for a trip of 8 miles.

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Answer:

Step-by-step explanation: answer 1.25 per pound

Answer:

5568

Step-by-step explanation:

Answer:

EF = -120 inches

Step-by-step explanation:

AB + BC + CD + EF = 4G

AB + 2BC + 4CD + EF = 140

AB + 2(2AB) + 4(2(2AB)) + EF = 140

AB + 4AB + 8AB + EF = 140

13AB + EF = 140

EF = 140 - 13AB

EF = 140 - (13)(20)

EF = 140 - 260

EF = -120 inches

The length of EF is 40 inches long.

The triangle proportionality theorem states that if a line is drawn inside the triangle which is parallel to any side of the given triangle, then the line intersects other two sides at two different points. Then the division of the other two sides of the triangle will be in the same ratio.

Here we can use the proportionality theorem to find the length of EF.

Using the proportionality theorem,

AD / AG = BC / EF  [Equation 1]

Given that,

BC = 2 AB ⇒ AB = BC / 2

CD = 2 BC

Now, AD = AB + BC + CD

               = (BC / 2) + BC + 2 BC

               = 7/2  BC

AG is given as 140 inches.

Substituting the values in the Equation 1,

(7/2 BC) / 140 = BC / EF

BC get cancelled on both sides.

7 / (2 × 140) = 1 / EF

Cross multiplying,

7 EF = (2 × 140)

EF = 40 inches

Hence the length of EF is 40 inches long.

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The complete question is given below.

Answer:

y = 2/3x - 3

Step-by-step explanation:

Given equation :-

Transformations :-

Solving :-

The correct reasons why the given series converges are (c) Integral test, (e) Converges by limit comparison test and (f) Converges by alternating series test.

a) The series ∑n=2[infinity]n2+n‾√n4−4 is a divergent series because its terms do not approach zero as n approaches infinity. Therefore, option a is not correct.

b) The series ∑n=2[infinity]n2+n‾√n4−4 is not a p-series because its terms do not have the form 1/n^p. Therefore, option b is not correct.

c) We can use the integral test to determine the convergence of the series ∑n=2[infinity]n2+n‾√n4−4 by comparing it with the integral ∫2[infinity]x2+x‾√x4−4 dx. Since the integrand is continuous, positive, and decreasing for x >= 2, we can evaluate the integral using the substitution u = x^2 - 4, which gives us an antiderivative of (1/2)ln|x^2 - 4| + (1/4)arctan(x/2) + C. Evaluating the integral from 2 to infinity, we obtain a finite value, which implies that the series ∑n=2[infinity]n2+n‾√n4−4 converges. Therefore, option c is correct.

d) We cannot use the comparison test with a convergent p-series to determine the convergence of the series ∑n=2[infinity]n2+n‾√n4−4 because it is not a p-series. Therefore, option d is not correct.

e) We can use the limit comparison test with the series ∑n=1[infinity]1/n^2 to determine the convergence of the series ∑n=2[infinity]n2+n‾√n4−4. By comparing the two series and taking the limit as n approaches infinity of the ratio of their terms, we obtain a finite nonzero limit, which implies that the two series have the same convergence behavior. Since the series ∑n=1[infinity]1/n^2 converges, the series ∑n=2[infinity]n2+n‾√n4−4 also converges. Therefore, option e is correct.

f) We can use the alternating series test to determine the convergence of the series ∑n=1infinitynn‾√n+4. Since the absolute value of each term is decreasing and approaches zero as n approaches infinity, and since the series is alternating, the series converges. Therefore, option f is correct.

We cannot use any standard convergence tests to determine the convergence of the series ∑n=1[infinity]n2+ln(n)n2−9n because it does not satisfy the conditions of any of the tests. Therefore, option f 2 is not correct.

We cannot use any standard convergence tests to determine the convergence of the series ∑n=1infinityln(6n) because it does not satisfy the conditions of any of the tests. Therefore, option f 3 is not correct.

We cannot use any standard convergence tests to determine the convergence of the series ∑n=2[infinity]4n(ln(n))2 because it does not satisfy the conditions of any of the tests. Therefore, option f 4 is not correct.

Therefore, the correct options are c, e, and f.

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The rectangular coordinates for (4.5, -30 degrees) are (3.9, -2.3), which is option B.

What is rectangle ?

A rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal; or a parallelogram containing a right angle.

To find the rectangular coordinates for a point in a plane given its polar coordinates, use the following formula:

x = r * cos(θ)

y = r * sin(θ)

Where (r, θ) are the polar coordinates and (x, y) are the rectangular coordinates.

For the point (4.5, -30 degrees), have:

r = 4.5

θ = -30 degrees = -30 * (π / 180) radians

x = r * cos(θ) = 4.5 * cos(-30 * (π / 180)) = 3.9

y = r * sin(θ) = 4.5 * sin(-30 * (π / 180)) = -2.3

So, the rectangular coordinates for (4.5, -30 degrees) are (3.9, -2.3), which is option B.

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The rectangular coordinates for (4. 5, -30 degrees) are (3.9, -2.3).

The rectangular coordinates for (4.5, -30 degrees) can be found using the following formula:

x = r * cos(θ)

y = r * sin(θ)

where r is the magnitude (or distance from the origin) and θ is the angle in radians.

In this case, r = 4.5 and θ = -30 degrees = -30 * (π/180) radians.

So:

x = 4.5 * cos(-30 * (π/180)) = 4.5 * cos(-π/6) = 4.5 * sqrt(3)/2

y = 4.5 * sin(-30 * (π/180)) = 4.5 * sin(-π/6) = -4.5 / 2

Therefore, the rectangular coordinates are (x, y) = (4.5 * sqrt(3)/2, -4.5 / 2), which is approximately (3.9, -2.3).

Option B (3.9, -2.3) is the right response as a result.

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Answer:

3(3+4n)

Step-by-step explanation:

3x3=9

3x4=12

so, gcf is 3

Answer:

c. function g has A y intercept of (0,4)

Answer:

165.065% increase

Step-by-step explanation:

The number of square inches of glass are needed to repair the window is 432 square inches

The given parameters are:

Length = 24 inches

Width = 18 inches

The number of square inches of glass are needed to repair the window is calculated as:

Area = Length * Width

So, we have

Area = 24 inches * 18 inches

Evaluate the product

Area = 432 square inches

Hence, the number of square inches of glass are needed to repair the window is 432 square inches

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The equation that can be used to model the total cost is y = 18x

The given parameters are:

Cost = $72

Time = 4 hours

The hourly rate is calculated as:

k = Cost/Time

So, we have

k = 72/4

Evaluate

k = 18

The form of the equation is given as
y = kx

Substitute k = 18 in y = kx

y = 18x

Hence, the equation that can be used to model the total cost is y = 18x

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Answer:

22.78ft

Explanation (｡･∀･)ﾉﾞ

           ↡

  > ¡‣Formula

     C=2πr

      d=2r

   > ¡‣Solving for C

C= πd = π · 7.25 ≈ 22.77655ft