Quadrilateral ABCD with vertices A(0,7) B(1,3), C(-1,-4), and D(-5,1): <7,-3>

The domain and the range of the piecewise function in this problem are given as follows:

The function in this problem is defined for all values of x between -6 and 2, except x = 0, and assumes all values of y between 0 and 6, except y = 1, hence the domain and range are given as follows:

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Answer:

8a + 3a^2 + 8

To prove that line segment a is parallel to line segment d, based on the given information, we can utilize the properties of perpendicular and parallel lines.

Given that a is perpendicular to b and b is perpendicular to c, we know that angles formed between a and b, as well as between b and c, are right angles. Let's denote these angles as ∠1 and ∠2, respectively.

Now, since c is parallel to d, we can conclude that the corresponding angles ∠2 and ∠3, formed between c and d, are congruent.Considering the fact that ∠2 is a right angle, it can be inferred that ∠3 is also a right angle.

By transitivity, if ∠1 is a right angle and ∠3 is a right angle, then ∠1 and ∠3 are congruent.Since corresponding angles are congruent, and ∠1 and ∠3 are congruent, we can deduce that line segment a is parallel to line segment d.

Thus, we have successfully proven that a is parallel to d based on the given information and the properties of perpendicular and parallel lines.

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Answer:

d >= 235 miles

Step-by-step explanation

Since you that he needs to drive at LEAST 235, you know that he can drive exactly 235 miles or more than 235 miles. That means you would need to use the greater than or equal to sign.

Answer:

Step-by-step explanation:

Given,

        A={1,2,3,4}

        B={1,2,3}

Now,A∩B= {1,2,3,4} ∩ {1,2,3}

                ={1,2,3}

                                      Answer: {1,2,3}

Answer:

x = 15

Step-by-step explanation:

Since, BX is the bisector of \( \angle BAC\)

\(\therefore m\angle ABX = \frac {1}{2} m\angle ABC\\\\

\therefore 24= \frac {1}{2}\times (4x - 12)\\\\

\therefore 24= \frac {1}{2}\times 2(2x - 6)\\\\

\therefore 24= (2x - 6)\\\\

\therefore 24 = 2x - 6 \\ \\

\therefore 24 +6 = 2x\\\\

\therefore 30 = 2x \\\\

\therefore x = \frac{30}{2} \\\\

\therefore x = 15

\)

Answer:

The answer is "\(\bold{y=0.5 \cos 3 \theta}\)"

Step-by-step explanation:

The choices were missing the question so the answer to this question can be defined as follows:

The answer is \(y= 0.5 \cos 3\theta\) because:

\(\Rightarrow -1 \leq \cos 3 \theta \leq 1\\\\\Rightarrow -0.5 \leq \cos 3 \theta \leq 0.5\\\)

So, the maximum value is = 0.5 and the minimum value is = -0.5 of \(\frac{2\pi}{3}\).

Answer:

D. y= 0.5 cos 3 theta

Step-by-step explanation:

Answer:

B) 4:1

Step-by-step explanation:

It is because if you divide out 8:2 by 2, you will get 4:1 which is the answer!!!

Hope it helps and mark as Brainliest if possible!!! Good Luck!!!

Answer:

B , D , E

Step-by-step explanation:

Answer:

65

Step-by-step explanation:

The lines are parallell so m1 = m5, and m3=m8. 180-115 is 65

The inequality c ≥ 20 represents the minimum number of candles that need to be sold to pay for a visit to Knotts costing $100 when each candle is sold for $5.

To write the inequality that represents c, we need to consider the cost of the visit to Knotts and the price of each candle that is being sold. Let's assume that the cost of the visit to Knotts is $100 and each candle is being sold for $5.

We know that the total amount of money she earns from selling c candles is given by 5c, and this amount must be greater than or equal to the cost of the visit, which is $100. Therefore, we can write:

5c ≥ 100

Dividing both sides of the inequality by 5, we get:

c ≥ 20

Therefore, the inequality that represents c is c ≥ 20. This means that she needs to sell at least 20 candles to be able to pay for the visit to Knotts. If she sells fewer than 20 candles, she won't have enough money to cover the cost of the visit.

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Answer:

x = - 9

Step-by-step explanation:

2x + 7 = - 11 ( subtract 7 from both sides )

2x = - 18 ( divide both sides by 2 )

x = - 9

The answer is:

x = -9

Work/explanation:

The point of equations is to find the variable's value by isolating it step-by-step.

For this equation, the variable is x.

To isolate it, I will perform a few operations.

First, I will subtract 7 from each side:

\(\sf{2x+7=-11}\)

\(\sf{2x=-11-7}\)

\(\sf{2x=-18}\)

Divide each side by 2

\(\sf{x=-9}\)

Hence, x = -9.

\(\rule{350}{4}\)

bTo determine the percent of the original price you end up paying after the discounts, we can calculate the final price as a percentage of the original price.

Let's assume the original price of an item is $100.

The first discount reduces the price by 50%, so the price after the first discount is 50% of the original price, which is $100 * 0.5 = $50.

The second discount of 45% is applied to the price after the first discount. The price after the second discount is 45% of $50, which is $50 * 0.45 = $22.50.

Therefore, the final price you end up paying after both discounts is $22.50.\

To find the percent of the original price you end up paying, we divide the final price by the original price and multiply by 100:

Percent of original price = (final price / original price) * 100

In this case, the final price is $22.50 and the original price is $100:

Percent of original price = ($22.50 / $100) * 100

                       = 0.225 * 100

                       = 22.5%

Therefore, you end up paying 22.5% of the original price after the discounts.

It's important to note that the percent of the original price you end up paying will depend on the original price of the item. The calculations above were based on the assumption that the original price was $100. If the original price is different, the resulting percentage will vary accordingly.

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Answer:

Step-by-step explanation:

The angle of depression is the downward angle the air traffic controller

looks down from in the tower.  It also equals the angle of elevation which is the angle formed by the runway and the line of sight.

With this information you can find the remaining angle:

180 - (90 + 18)

180 - 108 = 72

Let Angle B = 72°

Angle A = 18°

Angle C =90°

We have one side - 140 feet - this is side a - it is across from angle A.

There is a right triangle formed by the runway (side b) the tower, side a, and the line of sight (side c)

Using the law of sines:

sin A/a = sinB/b

sin 18°/a = sin72°/b

.3090/140 = .9510/x

cross multiply and then divide

140 × .9510/.3090

133.14/.3090

430.873 ft

round to a tenth = 430.9 ft

a. exponential function is\(y = 397,000*(1+0.03)^t\) b. Rounding to the nearest thousand, the population after 15 years will be 605,000

A mathematical function with the following formula is an exponential function:

\(f(x) = a^x\)

where x: input variable and an is a positive constant known as the base. As x increases or decreases, the value of the function either rises or falls exponentially. In other words, the function always increases or decreases at a rate that is proportionate to its current value.

a. The formula: can be used to create an exponential function that depicts the population after t years.

\(y = y 0 * (1 + r)^t\)

where t: number of years, r: yearly growth rate expressed as a decimal, and y 0 is the initial population.

The initial population in this instance is 397,000, and the yearly growth rate is 3%, or 0.03 in decimal form. The exponential function that depicts the population after t years is as follows:

\(y = 397,000 * (1 + 0.03)^t\)

b. We may change the exponential function we discovered in part a to include t = 15 to determine the population after 15 years:

\(y = 397,000 * (1 + 0.03)^(15)y = 605,464\)

After 15 years, the population will be roughly 605,000, to the nearest thousand.

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Answer:

We have 5 cards, and if we assume that the probability of selecting a given card at random is the same for all the cards, then the probability of randomly drawing the card C out of the 5 cards is equal to:

P = 1/5 = 0.20

Now, for the experimental probability, we can see that out of 300 draws, 111 times he drew the card C.

The experimental probability is:

Pe = 111/300 = 0.37

You can see that the experimental probability is bigger than the theoretical one, this may happen for two things.

Not enough draws: as the number of draws, we should expect to see that the experimental probability gets closer and closer to the theoretical one.

The cards have some difference: There is a chance that card C has a difference with the other cards, and this difference makes that when Ryan draws a card has a bigger probability of drawing this one.

Answer:

Step-by-step explanation:

                                                   error

Answer:

x ≈ 75.2

Step-by-step explanation:

using the tangent ratio in the right triangle

tan62° = \(\frac{opposite}{adjacent}\) = \(\frac{x}{40}\) ( multiply both sides by 40 )

40 × tan62° = x , then

x ≈ 75.2 ( to the nearest tenth )

Answer:

a number is increased by 5%

Answer:

$20

Step-by-step explanation:

Gym city fees are:

Sign up = 30

6 monthly sub = 6 x 25 = 150

Total fees = 30 + 150

FitnessExpress fees are:

Sign up = 20

6 monthly sub = 6 x 30 = 180

Total fees = 20 + 180 = 200

Therefore, the difference between the two is $20

The required probability is given by  P(E') =4/35  .

Probability is the study of chance. It can also be defined as the ratio of the favorable outcomes to an event to the total number of outcomes of the event.

Given the total number of people in the USA = 273000000

Let E be the number of people who speak English at home.

Therefore the number of people who don't speak English at home is E'.

∴ E' = 31200000

S speak Spanish in their homes.

∴ S = 50% of 31200000 = 15600000

Now let us find the required probabilities.

We know that probability = favorable outcome ÷ total outcome

total outcome = 273000000

a) favorable outcome(E') = 31200000

P(E')=31200000/273000000

P(E') =4/35

b)favorable outcome(E) = 273000000 - 31200000 = 241800000

P(E) = 241800000/273000000

P(E)={31}/{35}

c)favorable outcome = 15600000

P(S)={15600000}/{273000000}

P(S)={2}/{35}

Therefore the required probability is given by P(E') =4/35 , \(P(E)=\frac{31}{35}\) P(E)=31/35 and P(E)=2/35and .

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The correlation coefficient is 0.053, Bettina has not yet found a perfect positive relationship.

The correlation coefficient is a numerical measure of the strength of the linear relationship between two variables. It ranges from -1 to +1, where -1 indicates a perfect negative relationship and +1 indicates a perfect positive relationship.

To calculate the correlation coefficient, we use the formula \(r = (Σxy) / √(Σx2 * Σy2)\). Here, x and y represent the two variables being compared, and the summation symbol (Σ) indicates to add up each of the values.

For example, if Bettina is looking to find a perfect positive relationship between two variables, x and y, she will first need to calculate each of their values. Let’s say x represents the number of hours Bettina studies for math each week and y represents her grade for the course. Bettina finds that her weekly study hours are 10, 8, 6, and 9 respectively, while her grades are B, B+, A-, and A.

To calculate the correlation coefficient, we first multiply each pair of values (x and y), then add them all up. In this example, that would be \((10*B) + (8*B+) + (6*A-) + (9*A) = 94\). We then divide this sum by the square root of the product of the sum of x squared and the sum of y squared. In this example, that would be\((10^2 + 8^2 + 6^2 + 9^2) * (B^2 + B+^2 + A-^2 + A^2) = 1764\). When we divide 94 by 1764, we get 0.053.

Since the correlation coefficient is 0.053, Bettina has not yet found a perfect positive relationship.

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Answer:

\(\displaystyle \frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Step-by-step explanation:

This can be solved with either the washer (easier) or the shell method (harder). For the disk/washer method, the slice is perpendicular to the axis of revolution, whereas, for the shell method, the slice is parallel to the axis of revolution.  I'll show how to do it with both:

Shell Method (Horizontal Axis)

\(\displaystyle V=2\pi\int^d_cr(y)h(y)\,dy\)

Radius: \(r(y)=2-y\) (distance from y=2 to x-axis)

Height: \(h(y)=2-(-\ln y)=2+\ln y\) (\(y=e^{-x}\) is the same as \(x=-\ln y\))

Bounds: \([c,d]=[e^{-2},1]\) (plugging x-bounds in gets you this)

Plugging in our integral, we get:

\(\displaystyle V=2\pi\int^1_{e^{-2}}(2-y)(2+\ln y)\,dy=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Washer Method (Parallel to x-axis)

\(\displaystyle V=\pi\int^b_a\biggr(R(x)^2-r(x)^2\biggr)\,dx\)

Outer Radius: \(R(x)=2-e^{-x}\) (distance between \(y=2\) and \(y=e^{-x}\))

Inner Radius: \(r(x)=2-1=1\) (distance between \(y=2\) and \(y=1\))

Bounds: \([a,b]=[0,2]\)

Plugging in our integral, we get:

\(\displaystyle V=\pi\int^2_0\biggr((2-e^{-x})^2-1^2\biggr)\,dx\\\\V=\pi\int^2_0\biggr((4-4e^{-x}+e^{-2x})-1\biggr)\,dx\\\\V=\pi\int^2_0(3-4e^{-x}+e^{-2x})\,dx\\\\V=\pi\biggr(3x+4e^{-x}-\frac{1}{2}e^{-2x}\biggr)\biggr|^2_0\\\\V=\pi\biggr[\biggr(3(2)+4e^{-2}-\frac{1}{2}e^{-2(2)}\biggr)-\biggr(3(0)+4e^{-0}-\frac{1}{2}e^{-2(0)}\biggr)\biggr]\\\\V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\biggr(4-\frac{1}{2}\biggr)\biggr]\)

\(\displaystyle V=\pi\biggr[\biggr(6+4e^{-2}-\frac{1}{2}e^{-4}\biggr)-\frac{7}{2}\biggr]\\\\V=\pi\biggr(\frac{5}{2}+4e^{-2}-\frac{1}{2}e^{-4}\biggr)\\\\V=\pi\biggr(\frac{5}{2}+\frac{4}{e^2}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4}{2e^4}+\frac{8e^2}{2e^4}-\frac{1}{2e^4}\biggr)\\\\V=\pi\biggr(\frac{5e^4+8e^2-1}{2e^4}\biggr)\\\\V=\frac{\pi(5e^4+8e^2-1)}{2e^4}\approx9.526\)

Use your best judgment when deciding on what method you use when visualizing the solid, but I hope this helped!

Answer:

{-5, -1, 2}

Step-by-step explanation:

domain is the inputs or x numbers

Answer:

First image attached

The error was done in Step E, because student did not multiply \(2\cdot x -8\) by the negative sign in numerator. Step E must be \(\frac{2\cdot x -5}{(x+4)\cdot (x-4)}\).

Second image attached

The error was done in Step C, because the student omitted the \(2\cdot a \cdot b\) of the algebraic identity \((a+b)^{2} = a^{2}+2\cdot a\cdot b +b^{2}\). Step C must be \(5\cdot x = x^{2}+4\cdot x + 4\)

Step-by-step explanation:

First image attached

The error was done in Step E, because student did not multiply \(2\cdot x -8\) by the negative sign in numerator. The real numerator in Step E should be:

\(3-(2\cdot x -8)= 3-2\cdot x+8 = 11-2\cdot x\)

Hence, Step E must be \(\frac{2\cdot x -5}{(x+4)\cdot (x-4)}\).

Second image attached

The error was done in Step C, because the student omitted the \(2\cdot a \cdot b\) of the algebraic identity \((a+b)^{2} = a^{2}+2\cdot a\cdot b +b^{2}\). Step C must be \(5\cdot x = x^{2}+4\cdot x + 4\)

And further steps are described below:

Step D

\(x^{2}-x+4 = 0\)

Which according to the Quadratic Formula, represents a polynomial with complex roots. That is: (\(a = 1\), \(b = -1\), \(c = 4\))

\(D = b^{2}-4\cdot a\cdot c\)

\(D = (-1)-4\cdot (1)\cdot (4)\)

\(D = -17\) (Conjugated complex roots)

Step E

\((x-0.5-i\,1.936)\cdot (x-0.5+i\,1.936) = 0\)

Step F

\(x = 0.5+i\,1.936\,\lor\,x = 0.5-i\,1.936\)

im not sure ask a professional

Answer:

1073.45 in²

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The equation to solve for the area of a circle is:

But wait, we don't have a radius to fix in the equation! Well to solve for the radius when given diameter, we can use the expression:

Now that we know this, we can insert 37 in for the diameter:

So, the radius of the circle is 18.5 inches.

Inserting 18.5 into the expression for the radius:

Using 3.14 for pi:

Therefore, the area of a circle with a diameter of 37 inches is 1073.45 in².

Answer:

D. y=-1/2x+5

Step-by-step explanation:

Slope-Intercept Form: y=mx+b

Line passes through y-axis at (0,5) so the "b" part of the equation is positive 5 on the y-axis. Slope is -1/2 so "m" is -1/2.

Answer:

Step-by-step explanation:

Letter B is the correct answer

Initial population is 200, tripled every hour

200 x 3 = 600

First hour 200

Second hour = 600 + 200 = 800

Third hour 800x3 = 2400 + 800 = 3200

and so on.