Which statement is true about the x-intercepts?

A) The x-intercept is 3.
B) The x-intercepts are –3 and –1.
C) The x-intercept is at (–1, 2).
D) There are no x-intercepts.

Answer:

Hello There. ☆°~-----__▪●▪__-----~°☆

If points A, D and C lie on a straight line, then angles ∠ADB and ∠BDC are supplementary angles and

m\angle ADB+m\angle BDC=180^{\circ}.

1. If you move point B right from the initial position, then m∠ADB increases and m∠BDC decreases, but m\angle ADB+m\angle BDC=180^{\circ}.

2. If you move point B left from the initial position, then m∠ADB decreases and m∠BDC increases, but m\angle ADB+m\angle 
BDC=180^{\circ}.

3. When point B lie on the line ADC, then:

a. Point B lies on the right hand from point D: m\angle ADB=180^{\circ} \\m\angle BDC=0^{\circ} ;

b. Point B lies on the left hand from point D: m\angle ADB=0^{\circ} \\m\angle BDC=180^{\circ} .

4. When point B is reflected about the line ADC situation is the same as in parts 1 and 2.

Hope It Helps!~ ♡

ItsNobody~ ☆

Answer:

The sum of m∠ADB and m∠BDC remains the same: m∠ADB + m∠BDC = 180°.

Step-by-step explanation:

PLATO answer.

The given differential equation is y(8x + y + 8)dx + (8x + 2y)dy = 0.

To solve this equation, we can use the integrating factor method. First, we identify the coefficients of dx and dy, which are y(8x + y + 8) and (8x + 2y), respectively. Then, we compare the equation with the standard form of a first-order linear differential equation, which is M(x, y)dx + N(x, y)dy = 0.

In our equation, M(x, y) = y(8x + y + 8) and N(x, y) = (8x + 2y). We can see that the coefficient of dy is not a function of x only, so we need to find an integrating factor.

The integrating factor (IF) can be found by multiplying both sides of the equation by the appropriate function. In this case, the integrating factor is \(e^{(f(N - M)/N dx).\)

By substituting the given values of M(x, y) and N(x, y) into the formula for the integrating factor, we can calculate the integrating factor and proceed with solving the differential equation.

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The following can be answered by the concept of Maclaurin series

a. Maclaurin series: f(x) = ln(3)
The expansion is valid for all x in the domain of real numbers (-∞, ∞).
b. The Maclaurin series for f(x) = xe²ˣ is: f(x) = x + 2x² + …
The expansion is valid for all x in the domain of real numbers (-∞, ∞).

(a) f(x) = ln(1 + 2)
Since the function is a constant, its Maclaurin series is just the constant value itself.
Maclaurin series: f(x) = ln(3)
The expansion is valid for all x in the domain of real numbers (-∞, ∞).

(b) f(x) = xe²ˣ
To find the Maclaurin series for this function, we need to find its derivatives and evaluate them at x = 0.

f(x) = xe²ˣ
f'(x) = e²ˣ + 2xe²ˣ
f''(x) = 4xe²ˣ + 4e²ˣ

Now, evaluate the derivatives at x = 0:

f(0) = 0
f'(0) = 1
f''(0) = 4

Using the Maclaurin series formula, we get:

f(x) = f(0) + f'(0)x + (f''(0)x²)/2! + …
f(x) = 0 + 1x + (4x²)/2 + …

So, the Maclaurin series for f(x) = xe²ˣ is:

f(x) = x + 2x² + …

The expansion is valid for all x in the domain of real numbers (-∞, ∞).

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In a large population, 64 % of the people have been vaccinated. If 5 people are randomly selected, then the probability that AT LEAST ONE of them has been vaccinated is 99.78% or 0.9978.

The probability that at least one person is vaccinated among a sample of five people selected randomly from a population in which 64% have been vaccinated is the complement of the probability that none of the five selected have been vaccinated. The probability of at least one vaccinated person is:

Probability of at least one vaccinated person = 1 - Probability that none of the selected have been vaccinated.

To find this probability, you first need to find the probability that none of the five selected have been vaccinated.

Probability of selecting one person who is not vaccinated = 1 - 0.64 = 0.36

Probability of selecting five persons who are not vaccinated = 0.36 × 0.36 × 0.36 × 0.36 × 0.36= 0.0022

So, the probability of at least one vaccinated person in the sample of five is:

Probability of at least one vaccinated person = 1 - Probability that none of the selected have been vaccinated

                                                                           = 1 - 0.0022

                                                                           = 0.9978

Therefore, the probability that at least one person is vaccinated among a sample of five people selected randomly from a population in which 64% have been vaccinated is 0.9978.

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The value of x is -3 for the given equation.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression 4 *3 + 4*x = 0

Simplify the equation using PEMDAS

=> 4*3 + 4*x = 0

=> 12 + 4x = 0

=> 4x = -12

=> x = -3

Therefore, the simplified value of the Given equation is x = -3.

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Answer:

516

Step-by-step explanation:

to solve this equation, multiply both sides by 4

a/4 * 4 = 129 * 4

a = 516

Answer:

a= 516

Step-by-step explanation:

a= 129*4

4*129 = 516

Gradual, long-term movement in time-series values is called temporal variation. Therefore, the correct option is (a) temporal variation.

Temporal variation is one of the components of a time series, along with seasonal variation, cyclical movement, and irregular or random variation. Temporal variation refers to the long-term trend or pattern of movement in the time series, which can be increasing, decreasing, or remaining constant over time. It is often caused by underlying factors such as population growth, economic changes, or technological advancements.

Cyclical movement refers to the regular, repeating up and down patterns in the time series, which are usually longer than a year and can be caused by factors such as business cycles or political cycles. Exponential smoothing and linear regression are statistical methods used to forecast or model time series data, but they do not describe the components of the time series themselves.

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The 95% confidence interval for the true average increase in total cholesterol among individuals who took aripiprazole for short periods of time is approximately (-3.14, 10.24) mg/dl.

Antipsychotic drugs are commonly prescribed for conditions like schizophrenia and bipolar disease. A recent article investigated the effects of various antipsychotic drugs on body composition and metabolic changes. Specifically, the study examined the impact of aripiprazole on total cholesterol levels in a sample of 41 individuals who had taken the medication for short periods of time.

The mean change in total cholesterol was found to be 3.55 mg/dl, with an estimated standard error of 3.778 mg/dl. To determine the confidence interval for the true average increase in total cholesterol, we use a 95% confidence level.

Using these statistics, we can calculate the confidence interval as follows:

Calculate the margin of error.

The margin of error (ME) is given by:

ME = critical value * standard error

Determine the critical value.

For a 95% confidence level, the critical value corresponds to a z-score of approximately 1.96.

Calculate the confidence interval.

The confidence interval is given by:

Confidence interval = sample mean ± margin of error

Substituting the given values into the formulas, we find:

ME = 1.96 * 3.778 = 7.40

Confidence interval = 3.55 ± 7.40 = (-3.14, 10.24) mg/dl

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Answer:

-43

Step-by-step explanation:

-1-7(6)

-1-42

-43

Answer: C.51

Step-by-step explanation:

3 2/5*15=51

Among these expressions, (4+1)x(12-6) has a total value of 30.

To determine which expression has a total value of 30, let's evaluate each expression one by one:

4+1x12-6

Following the order of operations (PEMDAS/BODMAS), we first do the multiplication:

4 + (1x12) - 6 = 4 + 12 - 6

Now, we do the addition and subtraction from left to right:

16 - 6 = 10

(4+1x12-6)

This expression has the same operations as the first one, so its total value is also 10.

(4+1)x(12-6)

First, we evaluate the expressions within the parentheses:

(5)x(6)

Now, we do the multiplication:

5 x 6 = 30

(4+1)x12-6

First, we evaluate the expression within the parentheses:

(5)x12 - 6

Now, we do the multiplication:

60 - 6

Finally, we do the subtraction:

54
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Answer:

the answer is c

Step-by-step explanation:

Answer: 7 tens and 6 ones

Step-by-step explanation: 76 is two numbers, with a 7 in the tens place and a 6 in the ones place.

76 can be represented as 7 tens and 6 ones or as 6 tens and 16 ones. This involves understanding the place value of digits in a number and knowing that a ten can be broken down into ones.

The number 76 can be broken down into tens and ones in multiple ways. First, let's understand what tens and ones mean in the context of a number. In the number 76, '7' is the tens place, and '6' is the ones place, meaning there are 7 tens (70) and 6 ones (6) making up 76.

One way to show 76 with tens and ones is to say that there are 7 tens and 6 ones. This is a very direct method where we just count the number of tens and ones in the number.

Another way we could break down 76 is to say there are 6 tens and 16 ones. This method involves taking one of the tens and breaking it down into 10 ones, giving us a total of 6 tens and 16 ones.

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Answer: -3x+2y=16 equals y = 3/2x+8

2x+y=1 equals y= -2x+1

Step-by-step explanation:

Answer:

for the first equation the answer will be,

\(x = - \frac{2(8 - y)}{3} \)

if you want me to solve for y instead then the answer will be,

\(y = \frac{16 + 3x}{2} \)

for the second equation the answer will be.

\(x = \frac{1 - y}{2} \)

if you want me to solve for y instead then the answer will be

\(y = 1 - 2x\)

~hope this helps~

Let:

x = Speed of the jet

y = Speed of jetstream

so:

and

Solve the system using elimination method:

Replace x into (1)

Answer:

Rate of the jet in still air: 726 mph

Rate of the jetstream: 65mph

Answer:

Step-by-step explanation:

tan (60)=(sin 60)/cos 60=(√3/2)/(1/2)=√3≈1.732

The value of expression tan 60° is,

⇒ tan 60° = √3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

To find the value of expression tan 60°

Now, We can find the value of expression as;

⇒ tan 60°

⇒ sin 60° / cos 60°

⇒ (√3 / 2) / (1 / 2)

⇒ √ 3

Thus, The value of expression tan 60° is,

⇒ tan 60° = √3

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A - Growth (25%)

B- Growth (75%)

C - Growth

D - Growth (100%)

E - Growth (99%)

An rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay.

The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.

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Answer:

To find the answer, we need the measurement of the sides. However just by looking at the triangle I would say it is a Isosceles triangle.

Step-by-step explanation:

An Isosceles triangle has has 2 side that are the same length. Looking at the picture the bottom appears to be longer than the sides of the triangle.

Answer:

(1,-2) They are only asking for one inequality which is like (-3,0) which is the other point.

Step-by-step explanation:

The time study is 8 hours, the observed time is approximately 17.14 minutes, and the standard time is approximately 2.28 hours.

To solve the given problem, we can follow these steps:

1. Time study:

  First, we calculate the number of cycles using the formula: Number of cycles = Total time ÷ Cycle time.

  Given that the total time is 8 hours (8 × 60 = 480 minutes) and the cycle time is LI × RWL = 4.763 × 3.6 = 17.1468 minutes, we find:

  Number of cycles = 480 ÷ 17.1468 ≈ 28 cycles.

  Therefore, the time study is calculated as the number of cycles multiplied by the observed time per cycle: Time Study = 28 × 17.1468 ≈ 480 minutes = 8 hours.

2. Observed time:

  We can calculate the average observed time per cycle using the formula: Average observed time per cycle = Total observed time ÷ Number of cycles.

  The total observed time given is 480 minutes, and the number of cycles is 28. So, we have:

  Average observed time per cycle = 480 ÷ 28 ≈ 17.1429 minutes.

  The observed time is then found by multiplying the average observed time per cycle by the rating, which is 100% since no allowance is given:

  Observed time = 17.1429 × 100% = 17.1429 minutes ≈ 17.14 minutes.

3. Standard time:

  The standard time is calculated using the formula: Standard time = Observed time × Performance rating.

  To determine the performance rating, we need to find the standard time for the job and the total time allowed.

  Since no allowance is given, we assume the total time allowed is equal to the observed time, which is 17.1429 minutes.

  The standard time for the job can be calculated as the number of cycles multiplied by the standard time per cycle.

  The standard time per cycle is determined by multiplying LI × RWL × Elemental time.

  Since there's only one element given, the elemental time is equal to the observed time, which is 17.1429 minutes.

Therefore, the standard time per cycle is 4.763 × 3.6 × 17.1429 = 292.5 seconds.

With the number of cycles given as 28, the standard time for the job is 28 × 292.5 = 8190 seconds ≈ 136.5 minutes.

Finally, we calculate the performance rating using the formula: Performance rating = (Standard time for job ÷ Total time allowed) × 100.

Here, the total time allowed is the observed time, which is 17.1429 minutes.

So, the performance rating is (136.5 ÷ 17.1429) × 100 = 797.14%.

Thus, the standard time is found by multiplying the observed time by the performance rating:

Standard time = 17.1429 × 797.14% = 136.5 minutes ≈ 2.28 hours.

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In the last basketball game, the ratio of baskets made to the total shots taken was 4:7 and if the team shot a total of 56 baskets in the game then the total basket they made is 40.

The ratio is 4:7, this means that for every 7 shots taken, 4 of them were made. If the team shot a total of 56 shots in the last game, then they made

(4/7) ×56 = 40 baskets.

This calculation can be broken down into simpler terms. For every 7 shots, 4 shots were made. Therefore, for 56 shots, 40 shots were made. Therefore, the team made 40 baskets in the last game.

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Answer:

The area of the shaded region is \(49.5 cm^{2}\) to 3. significant figures

Step-by-step explanation:

Step one: find the two diagonals of the kite.

The Horizontal diagonal can be obtained using the cosine rule:

\(AC^{2}=OA^{2}-OC^{2}- 2\times (OA)\times (OC)cos (\theta)\)

\(AC^{2}=8^{2}+8^{2}- 2\times 8 \times 8 \times cos (120)= 212\\AC =\sqrt{212}=14.56cm\)

The vertical diagonal of the kite can be obtained by Pythagoras' Theorem:

Please note the law in circle geometry which states that a radius and a tangent always meet at right angles.

This implies that triangle OBC is a right-angled triangle, with angle OCB being 90 degrees, and COB being 60 degrees. This is because the diagonal divides the 120-degree angle into half.

\(cos 60 = \frac{8}{OB}\\OB=\frac{8}{cos 60}= 16cm\)

Step two: Use the dimensions of the two diagonals of the Kite to find the area:

The area of a Kite is obtained using this formula:

\(Area = \frac{pq}{2}\), where p and q are the two diagonals.

hence,

\(Area = \frac{14.56 \times 16}{2}= 116.48cm^{2}\)

Step three: Calculate the area of the sector of the circle.

Area of the sector is obtained using this formula

\(Area = \frac{\theta}{360}\times \pi\times r^{2}\\Area = \frac{120}{360} \times \pi \times 8^{2}=67.03cm^{2}\)

Step Four: Subtract the area of the sector from the area of the kite:

Area of the shaded region will be \(116.48cm^{2} -67.03cm^{2} = 49.45cm^{2}\)

This will be\(49.5 cm^{2}\) to 3. significant figures

Answer:

43.8 cm²

Step-by-step explanation:

1. Split the kite in two and find the length of OB

When split the kite in two, you will find that the 120° becomes 60°, as they are divided into two.

Then, use the sine rule we can find out the length of OB. It goes like this:

\(\frac{OB}{sin90} = \frac{8}{sin30}\\ \\{OB} = \frac{8sin90}{sin30}\\\\ {OB} = 16cm\)

2. Calculate the area of the kite

Since we have split the kite into two triangles and we know two side of the triangles, then we can calculate the area of one triangle using the formula of \(area of triangle=\frac{1}{2}absinc\).

\(\frac{1}{2}\)×8×16×sin60 = \(32\sqrt{3}\)

But as there are two triangles, we duplicate the answer.

2×\(32\sqrt{2}\) = \(64\sqrt{3}\)

2. Calculate the area of the sector

area of sector =\(\frac{angle of sector}{360} \\\)×πr²

\(\frac{120}{360}\)×8²π = \(\frac{64}{3}\)π

3. Subtract the area of the sector from the area of the kite

\(64\sqrt{3}\) - \(\frac{64}{3}\)π = 43.83060841 ≈ 43.8 cm² (to 3 s.f.)

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Answer:

what is P'Q'R'S

Step-by-step explanation:

Answer:

4x + 5

Step-by-step explanation:

Answer: 1st option

Step-by-step explanation:

Black to Red is the transformation

C to C'

I to I'

Q to Q'

G to G'

1st, graph is moved up by 1 unit(+1 in x direction)

Then, graph is moved to right by 5 units(+5 in y direction)

(1, 5) is the change ==> 1st option

It took both Sandy and Tom 54 seconds to cover the same distance.

We can set up an equation based on their relative speed

Take the supposition that Tom needs "t" seconds to travel the distance. Sandy started jogging 12 seconds before Tom, so it will take her "t + 12" seconds longer to complete the same distance.

To determine the distance traveled by Sandy, multiply her speed (7 meters per second) by her time (t + 12) seconds. Tom's distance traveled may be determined by dividing his speed (9 meters per second) by his time (t) seconds.

Equating the distances covered by Sandy and Tom:

7(t + 12) = 9t

Expanding the equation:

7t + 84 = 9t

Subtracting 7t from both sides:

84 = 2t

Dividing both sides by 2:

t = 42

Tom traveled the distance in 42 seconds as a result. We add the 12-second lead Sandy had to determine the time it took for both Sandy and Tom to travel the same distance:

t + 12 = 42 + 12 = 54

So, it took both Sandy and Tom 54 seconds to cover the same distance.

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After expansion the expression is,

⇒ 65x/4 + 39/16

We have to given that;

Expression is,

⇒ 13/4 (5x + 3/4)

Now, We can simplify the expression by expansion,

⇒ 13/4 (5x + 3/4)

⇒ 5x × 13/4 + 13/4 × 3/4

⇒ 65x/4 + 39/16

Thus, After expansion the expression is,

⇒ 65x/4 + 39/16

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Answer:

4 weeks

Step-by-step explanation:

14.50 (4) + 20= 78

12.50 (4) + 28= 78

The cartesian equation of the curve is y^2 = 1 + x^2.

To eliminate the parameter and find the cartesian equation, we need to express x and y in terms of a single variable. We can start by using the trigonometric identities:

x = tan^2(θ) = sin^2(θ)/cos^2(θ)

y = sec(θ) = 1/cos(θ)

Now, we can eliminate the parameter θ by substituting for x and y in terms of cos(θ):

x = (sin^2(θ))/(cos^2(θ)) = (1 - cos^2(θ))/(cos^2(θ))

y = 1/cos(θ)

We can rearrange the equation for x:

x * cos^2(θ) = 1 - cos^2(θ)

x * cos^2(θ) + cos^2(θ) = 1

x * cos^2(θ) + cos^2(θ) - 1 = 0

Now, we substitute 1/cos(θ) for y:

(x * cos^2(θ) + cos^2(θ) - 1)(cos(θ))^2 = (1/cos(θ))^2

(x * cos^2(θ) + cos^2(θ) - 1)(cos(θ))^2 = y^2

Simplifying this equation, we get:

x * (cos(θ))^2 + (cos(θ))^2 - 1 = y^2

Therefore, the Cartesian equation of the curve is y^2 = 1 + x^2.

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