x–2(x+1)+3(x+2)=x–4
(show work too please)

Sum of two opposite angles in a Cyclic Quadiratral is 180°

\(\\ \sf\longmapsto 110+<CDE=180\)

\(\\ \sf\longmapsto <CDE=180-110\)

\(\\ \sf\longmapsto <CDE=70°\)

Answer:

let <CDE be x:

\({ \tt{110 \degree + x = 180\degree}} \\ \\ { \tt{x = 180 \degree - 110 \degree}} \\ \\ { \tt{x = 70 \degree}}\)

Answer:

X-axis

Y-axis

Step-by-step explanation:

(x, y)

The x-axis moves horizontally, the y axis moves vertically.

Answer:

22.5 degrees

Step-by-step explanation:

First angle = n

Second angle = x

Third angle = m

n = 30 + x

m = 2(30 + x) = 60 + 2x

60 + 2x + 30 + x + x = 4x + 90 = 180

4x = 90

x = 22.5

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Answer:

Step-by-step explanation:

Step-by-step explanation:

12n + 34n = 12

46n = 12

n = 12/46

= 0.2609

Answer:

6/23

Step-by-step explanation:

Answer:

2/6 chance the dice be rolled to the total of 12

{a,b,c,d,e,f} each have 63 distinct subsets, including distinct proper subsets.

Currently, an empty set always makes up this number of subsets.

There are:

in all, appropriate subsets.

= 2ⁿ - 1

Given set: {a,b,c,d,e,f}

Total number of digits in the set :

n(S) = 6

Thus,

The total number of subsets in this given set:

= 2ⁿ

= 2⁶

= 64

There are always an empty set in this amount of subsets.

Thus, there are 63 appropriate subsets in all of the given set.

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The equation that represents the different transformations on the function f(x) = x³ should be written as follows;

1a. g(x) is f(x) reflected across the x-axis, and translated 4 units left is g(x) = -(x + 4)³.

1b. k(x) is f(x) vertically stretched by a factor of 3 is k(x) = 3x³.

1c. h(x) is f(x) translated 2 units right and 5 units up is h(x) = (x - 2)³ + 5.

2a. k(x) = 7(-x)³ is reflected across the y-axis, and vertically stretched by a factor of 7.

2b. h(x) = (x + 5)³ - 1 is translated 5 units left and 1 unit down.

In Mathematics and Geometry, the translation of a graph to the right adds a digit to the numerical value on the x-coordinate of the pre-image:

g(x) = f(x - N)

Conversely, the translation of a graph upward adds a digit to the numerical value on the y-coordinate of the pre-image;

g(x) = f(x) + N

Part 1a:

When the parent function f(x) is reflected across the x-axis, and then translated 4 units left, the transformed function g(x) is given by;

g(x) = -(x + 4)³.

Part 1b.

When the parent function f(x) is vertically stretched by a factor of 3, the transformed function k(x) is given by;

k(x) = 3x³.

Part 1c.

When the parent function f(x) is translated 2 units right and 5 units up, the transformed function k(x) is given by;  

h(x) = (x - 2)³ + 5.

Part 2a.

The equation k(x) = 7(-x)³ simply means the parent function is reflected across the y-axis, and vertically stretched by a factor of 7.

Part 2b.

The equation h(x) = (x + 5)³ - 1 simply means the parent function is translated 5 units left and 1 unit down.

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Answer:

So a rotation means that it will be rotated, a translation means that it will be drawn the same thing without rotation but in a different place. So we can easily see here that the red figure is the exact same thing as the black figure so its a translation

Answer:

9

Step-by-step explanation:

it's an isosceles right ∆.

so (9√2)^2 = 81*2= 162 = 2s^2

let x=y=s

s^2 = 81

s = 9

Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.

Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12

We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.

Take the provided linear equation system into consideration.

3x - 2y = 4 ................(1)

9x - 6y = 12 ..................(2)

Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12

The slopes of the provided equations are also same.

Difference with regard to x for equation (1) yields,

additional to equation (2),

With regard to x, we can differentiate to get,

The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.

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The cost of raising a lawn on the field at the rate of rupees 5.50 per square meter is 21,142.

We know that the area of a square field is written as Area = side²,

In this case, the side of the square field is 62 meters,

So, the area of square field is :

⇒ Area = 62² = 3844 square meters.

Now, to find cost of raising a lawn on field at rate of rupees 5.50 per square meter, we multiply area of field by cost per square meter,

we get,

⇒ Cost = (Area)×(Cost per square meter),

⇒ Cost = 3844 × 5.50

⇒ Cost = Rs. 21142

Therefore, the cost of raising a lawn on the square field is Rs. 21,142.

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The constant of proportionality from the proportional relationship is 3/2

A proportional relationship is a mathematical relationship between two variables in which their ratio is always equal. In other words, if x and y are in a proportional relationship, then y/x is always equal to a constant value, called the constant of proportionality. This can be expressed mathematically as y = kx, where k is the constant of proportionality and x and y are the variables in the relationship.

To determine the constant of proportionality, we need to use the proportional relationship given.

y = kx

k = constant of proportionality

3/8 = k(1/4)

Solve for k

k = [(3/8) / (1/4)]

k = 3/2

k = 1.5

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To find an equation of a plane through a given point and perpendicular to a given line, you can follow these steps:

1. Find the direction vector of the given line. This can be done by subtracting the coordinates of any two points on the line. Let's denote this vector as "d".

2. Find the normal vector of the plane. Since the plane is perpendicular to the line, its normal vector will be the same as the direction vector of the line. So, the normal vector of the plane is "d".

3. Use the coordinates of the given point on the plane to find the equation of the plane. Let's denote the coordinates of the point as (x₀, y₀, z₀).

The equation of the plane can be written as:

Ax + By + Cz = D,

where A, B, C are the components of the normal vector "d", and x, y, z are the variables representing any point on the plane.

To find the values of A, B, C, and D, substitute the coordinates of the given point into the equation:

A(x₀) + B(y₀) + C(z₀) = D.

Therefore, the equation of the plane through the given point and perpendicular to the line is:

d₁(x - x₀) + d₂(y - y₀) + d₃(z - z₀) = 0,

where (d₁, d₂, d₃) are the components of the direction vector "d" of the line, and (x₀, y₀, z₀) are the coordinates of the given point.

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Find the equation of the plane passing through the point (−1,3,2) and perpendicular to each of the planes x+2y+3z=5 and 3x+3y+z=0.

Answer:

288

Step-by-step explanation:

3/4=216/x

then solve

864=3x

x=288

Answer:

c

Step-by-step explanation:

The expression would be 2(3x+5)(x-1) and (x+1) is not in that expression

Answer:

If a fair coin is tossed a great many times, you

expect the results to be 50-50 or close to it.

First coin:  24 and 26.   48%  and  52%.

Second coin:  25%  and  75% .

Third coin:  9/16  and  7/16.  56.25%  and  43.75% .

Fourth coin:  12,505  and  12,495 .  50.02%  and  49.98% .

Step-by-step explanation:

**answer not mine**

Answer:

2.625 cups or 21 ounces

Step-by-step explanation:

Ava needs 3/4 cup of blue paint for every 1 cup of white paint. So, the ratio is 0.75 : 1.

She has 28 ounces of white paint. But, you have to convert ounces to cups.

1 cup = 8 ounces

28 ounces ÷ 8 ounces/cup = 3.5 cups

Now set up a ratio.

\(\frac{0.75}{1} = \frac{x}{3.5}\)

X (how much blue paint is needed) is over 3.5 cups (the amount of white paint she has)

Cross multiply and divide.

\(\frac{0.75}{1} = \frac{x}{3.5}\)

x = 0.75 × 3.5

x = 2.625 cups

To convert to ounces, multiply by 8.

2.625 cups × 8 ounces = 21 ounces

Therefore, Ava needs 2.625 cups or 21 ounces of blue paint.

Hope that helps.

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

Explanation:

Point C is located at (-2, -3).

When we apply an x axis reflection, the x coordinate stays the same and the y coordinate flips from negative to positive.

The x axis reflection rule is \((x,y) \to (x,-y)\)

So that's how we go from (-2,-3) to (-2,3)

Answer:

-2,3

Step-by-step explanation:

Reflection in the x -axis:

A reflection of a point over the x -axis is shown. The rule for a reflection over the x -axis is. (x,y)→(x,−y) .

A) The null hypothesis (H0) is that there has been no change in the prevalence of HIV since the last census. The alternative hypothesis (Ha) is that there has been a change in the prevalence of HIV since the last census

B) At a 95% confidence level, the critical value for a two-tailed test is ±1.96.

A) The null hypothesis (H0) is that there has been no change in the prevalence of HIV since the last census, i.e., the current prevalence of HIV is still 7.5%. The alternative hypothesis (Ha) is that there has been a change in the prevalence of HIV since the last census, i.e., the current prevalence of HIV is different from 7.5%.

B) To test the hypothesis, we can use a z-test for proportions. The test statistic can be calculated as:

z = (p - p0) / \(\sqrt{(p0(1-p0)/n)}\)

where p is the sample proportion of HIV positive cases, p0 is the hypothesized proportion under the null hypothesis, and n is the sample size.

In this case, p = 468 / 4706 = 0.099, p0 = 0.075, and n = 4706. Plugging these values into the formula, we get:

z = (0.099 - 0.075) / \(\sqrt{0.075(1-0.075)/4706}\) = 8.80

At a 95% confidence level, the critical value for a two-tailed test is ±1.96. Since the calculated z-value (8.80) is much larger than the critical value, we can reject the null hypothesis and conclude that there is strong evidence to suggest that the prevalence of HIV has changed since the last census. In other words, the prevalence of HIV is different from 7.5%.

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The equation that describes the simple harmonic motion of the particle is:

x = 7 * sin(2t + φ)

The equation that describes the simple harmonic motion of a particle moving uniformly around a circle can be represented as:

x = A * sin(ωt + φ)

In this equation:

x represents the displacement of the particle at time t.

A represents the amplitude of the motion.

ω represents the angular frequency or angular speed of the motion.

t represents time.

φ represents the phase constant.

In the given scenario, the particle is moving uniformly around a circle of radius 7 units, with an angular speed of 2 radians per second. In circular motion, the displacement can be represented by the arc length along the circumference of the circle.

Since the angular speed is 2 radians per second, the angular frequency (ω) is also 2 radians per second.

Since the particle is moving uniformly, the amplitude of the motion (A) is equal to the radius of the circle, which is 7 units.

The phase constant (φ) determines the initial position of the particle at t = 0.

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Answer:

y = 0.3x (pizza delivery driver)

Step-by-step explanation:

For pizza delivery driver:

\( \frac{15}{50} = \frac{.3}{1} \)

15 pizza deliveries in 50 minutes would be equal to 3 pizza deliveries in 10 minutes, or 0.3 pizza deliveries per minute. So the equation here would be y = 0.3x

For hamburger delivery driver:

1.6 hamburger deliveries in 8 minutes would be equal to 0.2 hamburger deliveries per minute. So the equation here would be y = 0.2x

So the pizza delivery driver's rate is faster.

Answer:

C(x) = 97 + 1,25x

Step-by-step explanation:

A função (C) que representa o custo total em função do número de hambúrgueres produzidos (x) contém duas partes: uma constante referente ao custo fixo de R$ 97,00, e uma variável referente ao custo de R$ 1,25 por hambúrguer para "x" hambúrgueres. A função C(x) é:

\(C(x) = 97 + 1,25x\)

Answer:

D

Step-by-step explanation:

3 (4x + 18y) means that 3 will multiply 4x and 18y factor which results to 12x + 54y

hence dissimilar to the original expression

The slope-intercept form of the equation of each line is  y=-x+4.

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a. Total depreciation = $9700

b. Depreciation per kilometer = $0. 388 per kilometer

c. Vₙ = $35400 +  ₙt

d. Distance = 4723. 16 kilometers

e. Total distance =  29723. 16 kilometers.

i. The formula for total depreciation is given as;

Total depreciation = Cost of asset - Residual value

Cost of car = $ 35400

Residual value = $25700

Total depreciation = $35400 - $25700

Total depreciation = $9700

b. Depreciation per kilometer = Total depreciation/ distance travelled in kilometers

Depreciation per kilometer = $ \(\frac{9700}{25000}\)

Depreciation per kilometer = $0. 388 per kilometer

c. Vₙ = V₀ + ₙt

t = time of depreciation

V₀ = $35400

Vₙ = $35400 +  ₙt

d. When the car costs $35400, it travelled 25000 kilometers

It costs $6688, it would travel 'x' kilometers

Cross multiply

$35400 × x = $ 6688 × 25000 kilometers

Make 'x' subject

x = \(\frac{6688 * 25000}{35400}\)

x = \(\frac{167200000}{35400}\)

x = \(4723. 16\) kilometers

The car would travel 4723. 16 kilometers

e. To find the total distance

Total distance = 25000 + 4723. 16

Total distance =  29723. 16 kilometers.

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Step-by-step explanation:

the circumference of a whole circle is

2×pi×r

with r being the radius. which is in our case a.

so,

2×pi×a

the part arc of just a sector of the circle is just the angle/360 part (as the whole circle is 360°).

we therefore know

27×pi = 2×pi×a × 60/360 = 2×pi×a × 1/6 = pi×a × 1/3

3×27×pi = pi×a

81×pi = pi×a

a = 81

The event is randomly selecting one card from a standard deck of 52 playing cards. We need to determine the number of outcomes in this event and whether it is a simple event or not.

In a standard deck of 52 playing cards, there are 4 suits (hearts, diamonds, clubs, spades) and each suit has 13 cards (Ace, 2-10, Jack, Queen, King). Therefore, there are 52 possible outcomes or cards to choose from in this event.
Now, let's determine if this event is a simple event or not. A simple event is an event that consists of a single outcome. In this case, since we are randomly selecting one card from the deck, the event of selecting a specific card (e.g., Ace of Hearts) would be a simple event because it has a single outcome. However, if the event is defined as selecting a card of a specific suit or a card of a specific rank (e.g., selecting a heart or selecting a King), then it would not be a simple event as there are multiple outcomes associated with that event.
When randomly selecting one card from a standard deck of 52 playing cards, there are 52 possible outcomes in the event. The event of selecting a specific card, like the Ace of Hearts, would be a simple event with a single outcome. However, events defined by selecting cards of a specific suit or rank would not be simple events as they have multiple outcomes.

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The Central Limit Theorem is a fundamental concept in statistics that states that the sampling distribution of the mean of a random sample approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

To validate the Central Limit Theorem, you can follow these steps in any computation language of your choice:

1. Define the population distribution: Choose a probability distribution, such as a uniform, exponential, or binomial distribution, to represent the population from which samples will be drawn.

2. Generate random samples: Use the chosen distribution to generate random samples of different sizes. For example, you can generate 100 samples of size 10, 100 samples of size 30, and so on. Make sure to record the means of these samples.

3. Calculate the sample means: For each sample, calculate the mean by summing up all the values in the sample and dividing by the sample size.

4. Plot the sampling distribution: Create a histogram or a density plot of the sample means. This plot will show the distribution of the sample means.

5. Compare with the theoretical distribution: Overlay the theoretical normal distribution on the plot of the sample means. The mean of the sample means should be close to the mean of the population, and the shape of the distribution should resemble a normal distribution.

6. Repeat the process: Repeat steps 2-5 with different sample sizes to observe how the shape of the sampling distribution changes as the sample size increases. The Central Limit Theorem predicts that the distribution of the sample means will approach a normal distribution as the sample size increases.

By following these steps and comparing the distribution of the sample means with the theoretical normal distribution, you can validate the Central Limit Theorem in your chosen computation language.

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