Solve |x| < 12
I’m so lost with this stuff.

Answer:

x=2 , y=3

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

Plug the 21 into the equation (21 + 19)

Answer: 400:18

and 200:9

Step-by-step explanation:

Answer:

y

Step-by-step explanation:

Answer I think you didn't care about the bad days

Step-by-step explanation:Have a nice day, thanks for the points

The form of point-slope of the linear equation is

Where:

m is the slope of the line

x1 , y1 are the coordinates of a point on the line

Perpendicular lines have additive multiplicative inverse slopes which means the product of their slopes is -1

If the slope of one is m, then the slope of the other is - 1/m

We change its sign and reverse its value

m * -1/m = -1

Since the slope of the line is -3/4

Then the slope of the line perpendicular to it is 4/3

We changed the sign and reciprocal the fraction

Therefor m = 4/3

The line passes through the point (3, 2)

Then x1 = 3 and y1 = 2

Let us substitute m, x1, y1 in the form of the equation above

This is the form of the equation

P(4, 60°) is not equal to P(4, π/2). The polar coordinate P(4, 60°) has a different angle (measured in radians) compared to P(4, π/2). It is important to convert angles to the same unit (radians or degrees) when comparing polar coordinates.

To determine if P(4, 60°) is equal to P(4, π/2), we need to convert both angles to the same unit and then compare the resulting polar coordinates.

First, let's convert 60° to radians. We know that π radians is equal to 180°, so we can use this conversion factor to find the equivalent radians: 60° * (π/180°) = π/3.

Now, we have P(4, π/3) as the polar coordinate in question.

In polar coordinates, the first value represents the distance from the origin (r) and the second value represents the angle measured counterclockwise from the positive x-axis (θ).

P(4, π/2) represents a point with a distance of 4 units from the origin and an angle of π/2 radians (90°).

Therefore, P(4, 60°) = P(4, π/3) is False, as the angles differ.

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Answer:

The possible number of students in Mrs. Hayko's class is limited to 15 or 30, as higher multiples of 15 would exceed the desired class size.

Step-by-step explanation:

a)

Let 'x' be the total number of students in Mrs. Hayko's class.

One-third of the students walk to school: (1/3)x.

The remaining students who do not walk to school: (2/3)x.

Four-fifths of the non-walking students take the bus: (4/5) * (2/3)x.

Simplify to find the fraction of students taking the bus: (8/15)x.

b)

Consider different values for 'x' to find a whole number of students taking the bus.

Start with a small number, such as x = 15.

Calculate the number of students taking the bus using (8/15)x.

If the result is a whole number, it's a possible class size.

Repeat with different values of 'x' until a whole number is obtained.

The possible number of students in Mrs. Hayko's class could be 15, 30, or any other multiple of 15.

we have, the diagonal bisect each other, therefore

answer: x = 12

Answer:

11.4

Step-by-step explanation:

15 divided by 5= 3 so ABC is 3 times bigger than EFD. you times 3.8 by 3 to get your answer. I hope this helps!!

The main concern in the scenario of a 9-year-old boy being hospitalized for 2 weeks is his emotional well-being. So correct answer is option a.

Hospitalization can be a stressful and challenging experience for anyone, especially for a young child. The main concern in this scenario is ensuring the emotional well-being of the boy during his hospital stay. Being away from home, undergoing medical treatments, and experiencing a disrupted routine can lead to feelings of fear, anxiety, and sadness. It is crucial to provide appropriate emotional support, create a comforting environment, and address the child's emotional needs to minimize distress and promote a positive experience during the hospitalization.

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This scene is an example of dramatic irony used to create suspense since the audience knows that this joyous occasion will ultimately lead to tragedy.

In the scene, Lord Capulet is preparing for his daughter Juliet's wedding to Paris, while the audience knows that Juliet is already secretly married to Romeo. Lord Capulet's excitement and eagerness to prepare for the wedding create suspense and tension for the audience, who knows that this joyous occasion will ultimately lead to tragedy.

Furthermore, the use of music within the scene also adds to the suspense. The audience hears the music, which signifies the arrival of the wedding party, but also knows that this will lead to the revelation of Juliet's secret marriage.

The urgency in Lord Capulet's instructions to the Nurse to wake up Juliet and make haste heightens the tension for the audience, who are aware of the impending disaster.

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Complete Question:

Read the excerpt from Act IV, scene iii of Romeo and Juliet.

Capulet Good faith! this day:

The county will be here with music straight,

For so he said he would. [Music within.] I hear him near.

35

This scene is an example of dramatic irony used to create suspense since the audience knows that

The relationship between x and y is a strong negative relationship.

For this question, we need to determine the correlation coefficient,

Thus,

The correlation coefficient

= (21 - 5*6)/ \(\sqrt{9 * 10}\)

= -0.948

The above answer is too close to -1. Therefore correlation coefficient is a strong negative.

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Answer:

Step-by-step explanation:

do I

We don't have enough information to determine how much liquid the second container can hold.

The height of the first container is not given, so we cannot use its height to determine the height of the second container.

Even if we knew the height of the first container, we would need additional information about the shape of the containers to calculate the volume of the second container. Without this information, we cannot determine how much liquid the second container can hold.

First, we need to identify the missing information in your question. The height of the first container and the amount of liquid it can hold are not provided. Let's assume the height of the first container is H1 meters, and it can hold V1 m^3 of liquid.
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If we sample the function x(t) = cos(75t) at the Nyquist frequency, the resulting discrete frequency would be half of the Nyquist frequency, which is equal to half of the highest frequency component in the continuous signal.

In this case, the highest frequency component in x(t) is 75 Hz, as determined by the coefficient of t in the cosine function. According to the Nyquist-Shannon sampling theorem, to accurately represent a signal, the sampling frequency must be at least twice the highest frequency component. Therefore, the Nyquist frequency in this scenario would be 2 * 75 Hz = 150 Hz.

Since we are sampling at the Nyquist frequency, the resulting discrete frequency would be half of the Nyquist frequency, which is 150 Hz / 2 = 75 Hz. Hence, when sampling x(t) at the Nyquist frequency, the resulting discrete frequency would be 75 Hz.

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The student completed 9 courses worth 4 credits. The solution has been obtained by using the linear equation.

What is a linear equation?

It follows that a linear equation has the highest degree of one. As a result, it is evident that there are no variables in a linear equation with an exponent bigger than one. A straight line is produced by this equation on the graph.

Let the courses worth 3 credits be 'x' and worth 4 credits be 'y'.

We are given that the student earned a total of 54 credits.

So,

3x + 4y = 54   ...(1)

Also, we are given that in total 15 courses were completed.

So,

x + y = 15   ...(2)

From (2), we get

x = 15 - y

Substituting this value in (1), we get

⇒3(15-y) + 4y = 54

⇒45 - 3y + 4y = 54

⇒45 + y = 54

⇒y = 9

Therefore, x = 15-9 = 6

Hence, the student completed 9 courses worth 4 credits.

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Answer:

262 square feet

Step-by-step explanation:

The required expression model for the cost of the ramp is y = 2.20x.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Let the area of the ramp be x and the cost to build the ramp be y,

According to the question,
The material Santiago will use to build the ramp costs $2.20 per square foot.

Total cost = 2.20 × area of the ramp

Substitute the variable in the above expression,

y = 2.20x

The above equation represents the equation model for the cost of ramp y for the x square foot area of the ramp.

Thus, the required expression model for the cost of the ramp is y = 2.20x.

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Using binomial probability, the probability of having exactly 4 dice on 4, 5 or 6 is 5/32.

Using binomial probability, we can calculate the probability that out of the 5 dice thrown, the probability of having exactly 4 dice on 4, 5 or 6 can be calculated as;

\(P(X=k) = C(n, k) * p^k * (1-p)^(^n^-^k^)\)

In the given data;

n = 5

k = 4

p = 3/6 = 1/2

Using the binomial probability formula, we can calculate:

P(X=4) = C(5, 4) * (1/2)⁴ * (1 - 1/2)⁵⁻⁴

P(X=4) = 5 * (1/2)⁴ * (1/2)¹

P(X=4) = 5 * (1/16) * (1/2)

P(X=4) = 5/32

Therefore, the probability that exactly 4 dice land on a 4, 5, or 6 when rolling five fair dice is 5/32.

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Answer:

18.

Step-by-step explanation:

3 x 6 = 18. He eats 3 slices every 5 minutes so 5 minutes x 6 is half an hour. so 18 is your answer.

If Takaya continues to eat three slices of pizza in five minutes, he could eat 18 slices in half of an hour.

The Linear equation in one variable is an algebraic equation of degree one.

it can be expressed in the form of Ax +B = 0 where x is a variable, and A and B are two integers.

Takaya can eat three slices of pizza in five minutes.

for half an hour it would be 6 times five minutes.

So, in half an hour Takaya can eat 3 × 6 = 18

Therefore, If Takaya continues to eat three slices of pizza in five minutes, he could eat 18 slices in half of an hour.

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We can say that Mai is correct and each person in the group should pay $41.23 to cover the bill, with very little measurement error.

To check if Mai is correct, we can start by multiplying $41.23 by the number of people in the group:

$41.23 x 5 = $206.15

This shows that if each person paid $41.23, the total amount collected would be $206.15, which is $0.02 less than the actual bill of $206.17.

To express this measurement error as a percentage of the actual cost, we can compute:

(0.02/206.17) x 100% ≈ 0.01%

So the measurement error is about 0.01% of the actual cost.

Based on these calculations, it appears that Mai's calculation is very close to being correct. The difference of $0.02 is likely due to rounding of the sales tax and tip, and so can be considered negligible.

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The exact value of cos^-1( √3/2) = 30°

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

There are special angles in trigonometry, this angles have exact value and can be obtained without using calculator. Examples of this calculator are; 30°, 60°, 45°

sin30 = 1/2

cos 30 = √3/2

tan 30 = 1/√3

cos 60 = 1/2

sin 60 = √3/2

tan 60 = √3

Therefore, if cos^-1( √3/2) = x

cos x = √3/2

cos 30 = √3/2

cos x = cos 30

therefore x = 30

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The value of x for the length A'E' of the similar shape A'B'C'D'E' is equal to 6⅔.

Similar shapes are two or more shapes that have the same shape, but different sizes. In other words, they have the same angles, but their sides are proportional to each other.

The side A'E' corresponds to the side A'E' and also E'D' corresponds to the side ED so;

(7). A'E'/AE = E'D'/ED

x/10 = 6/9

x = (10 × 6)/9 {cross multiplication}

x = 20/3

x = 6⅔

Therefore, the value of x for the length A'E' of the similar shape A'B'C'D'E' is equal to 6⅔

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The correct formula that defines an arithmetic sequence is option d) tn = 5n + 14.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms remains constant. In other words, each term can be obtained by adding a fixed value (the common difference) to the previous term.

In option a) tn = 5 + 14, the term does not depend on the value of n and does not exhibit a constant difference between terms. Therefore, it does not represent an arithmetic sequence.

Option b) tn = 5n² + 14 represents a quadratic sequence, where the difference between consecutive terms increases with each term. It does not represent an arithmetic sequence.

Option c) tn = 5n(n+14) represents a sequence with a varying difference, as it depends on the value of n. It does not represent an arithmetic sequence.

Option d) tn = 5n + 14 represents an arithmetic sequence, where each term is obtained by adding a constant value of 5 to the previous term. The common difference between consecutive terms is 5, making it the correct formula for an arithmetic sequence.

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The required answer is the current in the second parallel wire is approximately 0.446 A.

we can determine the current in the second wire using Ampere's law. Here's a step-by-step explanation:

1. A vertical straight wire carries an upward 29-A current.
2. The force per unit length between the two wires is given as 8.3×10^-4 N/m.
3. The distance between the two parallel wires is 5.5 cm, which is equal to 0.055 m.
The attractive force per unit length of 8.3×10−4 n/m is exerted by the first vertical wire, which carries an upward 29-aa current, on the second parallel wire located 5.5 cm away.
We'll use Ampere's law to find the current in the second wire. The formula for the force per unit length between two parallel wires is:
F/L = (μ₀ × I₁ × I₂) / (2π × d)

where F is the force, L is the length of the wires, μ₀ is the permeability of free space (4π × 10^-7 T·m/A), I₁ and I₂ are the currents in the wires, and d is the distance between the wires.
Rearranging the formula to find I₂, we get:
I₂ = (2π × d × F/L) / (μ₀ × I₁)
Now, plug in the given values:
I₂ = (2π × 0.055 × 8.3 × 10^-4) / (4π × 10^-7 × 29)
I₂ ≈ 0.446 A

So, the current in the second parallel wire is approximately 0.446 A.

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Answer:

48.69

Step-by-step explanation:

Step-by-step explanation:

30% off $53.50

= 70% of $53.50

= $53.50 * (70/100) = $37.45.

The problem involves the circle equation x^2 + (y-7)^2 = 49 and the equation x^2 + y^2 = 49, representing a circle with radius 7 centered at (0, 7) and a circle with radius 7 centered at the origin, respectively, in the first quadrant.

The task is to determine the region inside the first circle and outside the second circle. The equation x^2 + (y-7)^2 = 49 represents a circle with radius 7 centered at (0, 7). The equation x^2 + y^2 = 49 represents a circle with radius 7 centered at the origin. In the first quadrant, we consider the region where the first circle is present and the second circle is not. To determine this region, we observe that the first circle lies entirely within the second circle. Thus, the region inside the first circle and outside the second circle corresponds to the area between the two circles in the first quadrant, excluding the area covered by the second circle.

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The dividing by 0.5 is not the same as dividing by 2 , because 0.5 and 2 are different numbers  .

Let us understand the Division with the help of example ;

let the number be 10 ;

first we divide the number 10 by 0.5 ;

this can be written mathematically as ⇒ \(\frac{10}{0.5}\)  ;

⇒ \(\frac{10}{\frac{1}{2} }\) = \(10\times2\) = 20 ;

So , on dividing 10 by 0.5 , we get the answer as 20 .

Second , the number 10 is divided by 2 ;

this can be written mathematically as ⇒ \(\frac{10}{2}\) ;

⇒ \(\frac{10}{2 }\)  = 5  ;

So , on dividing 10 by 2 , we get the answer as 5  .

Therefore , dividing by 0.5 is not same as dividing by 2 .

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