how do you know if two lines are parallel?

The area between [tex]\( y = x^2 \)[/tex] and [tex]\( y = -x \) from \( x = 0 \) to \( x = 2 \) is \( \frac{14}{3} \)[/tex] square units, found by integrating [tex]\( x^2 + x \)[/tex] from 0 to 2.

Intersection Points: To find the area between [tex]\( y = x^2 \)[/tex] and [tex]\( y = -x \)[/tex] from [tex]\( x = 0 \) to \( x = 2 \)[/tex], first find their intersection points by setting [tex]\( x^2 = -x \)[/tex]. This gives [tex]\( x^2 + x = 0 \)[/tex], which factors to [tex]\( x(x + 1) = 0 \)[/tex], yielding [tex]\( x = 0 \)[/tex] and [tex]\( x = -1 \)[/tex] as the intersection points.

Limits of Integration: We are interested in the area between these curves from [tex]\( x = 0 \) to \( x = 2 \)[/tex]. Since[tex]\( x = -1 \)[/tex] lies outside this interval, we only consider [tex]\( x = 0 \)[/tex].

Integration: The area can be calculated by integrating the difference between the upper curve [tex]\( y = x^2 \)[/tex] and the lower curve [tex]\( y = -x \) from \( x = 0 \) to \( x = 2 \):[/tex]

[tex]\[ \text{Area} = \int_{0}^{2} (x^2 - (-x)) \, dx \][/tex]

Sure, here is the rewritten line:

[tex]\[ \text{The area can be found by integrating} \, x^2 + x \, \text{from} \, x = 0 \, \text{to} \, x = 2: \, \int_{0}^{2} (x^2 + x) \, dx \][/tex]

Integrating term by term:

[tex]\[ = \left[ \frac{x^3}{3} + \frac{x^2}{2} \right]_{0}^{2} \][/tex]

[tex]\[ = \left( \frac{2^3}{3} + \frac{2^2}{2} \right) - \left( \frac{0^3}{3} + \frac{0^2}{2} \right) \][/tex]

[tex]\[ = \left( \frac{8}{3} + 2 \right) - 0 \][/tex]

[tex]\[ = \frac{8}{3} + 2 \][/tex]

[tex]\[ = \frac{14}{3} \][/tex]

Complete question:

What is the area of the region between the graphs of y=x² and y=-x from x=0 to x=2?

Answer:158

Step-by-step explanation:∠6 = 68 + 90 = 158°

The answer is 3.

Bonus: Here is a fun challenge, try to decipher what Im saying here. (Use an online binary website.)

01001001 01100110 00100000 01111001 01101111 01110101 00100000 01100110 01101001 01101110 01100100 00100000 01101111 01110101 01110100 00100000 01110111 01101000 01100001 01110100 00100000 01110100 01101000 01101001 01110011 00100000 01110011 01100001 01111001 01110011 00101100 00100000 01001001 00100000 01110111 01101001 01101100 01101100 00100000 01100110 01101111 01101100 01101100 01101111 01110111 00100000 01111001 01101111 01110101 01110010 00100000 01100010 01110010 01100001 01101001 01101110 01101100 01111001 00100000 01100001 01100011 01100011 01101111 01110101 01101110 01110100 00100000 00111010 00101001

Answer:

The area of rectangle =21 sq units .

Step-by-step explanation:

Given the four vertices of rectangle are 1+4i,-2+4i, -2-3i and 1-3i.

Consider ABCD is  a rectangle and its vertices are 1+4i,-2+4i,-2-3i and 1-3i.

First we find sides of rectangle

AB=vertices of B- vertices of A

AB= -2+4i-(1+4i)=-3

BC= Vertices of C - vertices of B

BC=-2-3i-(-2+4i)=-7i

Length of BC=[tex]\sqrt{(-7)^2}[/tex]=7 ( Magnitude always positive)

CD= vertices of D- vertices of C

CD= 1-3i-(-2-3i)=3

Length of CD= [tex]\sqrt{3^2}[/tex]=3 ( Magnitude  always positive)

DA= vertices of A - vertices of D

DA= 1+4i-(1-3i) =7i

Length of DA= [tex]\sqrt{7^2}[/tex]=7 ( Magnitude always positive)

AB=CD and DA= BC

Length BC=7 units

Breadth AB=3 units

Area of the rectangle = [tex]length\times breadth[/tex]

Area of rectangle =[tex]AB\times BC[/tex]

Final answer:

To solve for 'r' in the given equation, add 9s to both sides and then divide by 4, resulting in r = (9s + K) / 4.

Explanation:

To solve for r in the equation 4r - 9s = K, we need to isolate r on one side of the equation. Here's how we can do this:

Answer:

$20.00 is the correct answer

Step-by-step explanation:

I promise this is correct

The graph of the circle with the equation (x - 3)² + (y + 3)² = 36, is a circle with center (3, -3) and radius of 6 units

Please find attached the graph of the circle (x - 3)² + (y + 3)² = 36, created with MS Excel

The details of the steps used to graph of the circle are as follows;

The standard form of the equation of a circle is; (x - h)² + (y - k)² = r², where the center of the circle is (h, k)

The equation of the circle in standard form is; (x - 3)² + (y + 3)² = 36

The comparison of the above equation with the form of the general equation of a circle in standard form indicates that the center of the circle is (3, -3)

The comparison of the radius of the circle with equation (x - 3)² + (y + 3)² = 36, with the general form of the equation of a circle in standard form indicates that the radius of the circle is; √(36) = 6

Answer:

38

Step-by-step explanation:

Answer:

D. (8^2 × 3) × 3

Step-by-step explanation:

its d on plato

Answer:

Step-by-step explanation:

Given that a triangle has sides 4,7 and 9

A student Gabe tried to use law of cosines to find unknown angle measure

The angle is opposite side 9 because angle across the longest side is given

He used cosine formula for triangles

[tex]a^2=b^2+c^2-2bccosA\\9^2 = 4^2+7^2-2(4)(8) cosA\\81-65 =-56 cosA\\[/tex]

But instead he adjusted -56 with 16 +49 which is wrong

Because -56 has product as cosA it is not like term as other constants

So correct step should be

81 = 65-56 Cos A

Gabe should not have subtracted 56 from  

16 + 49.

This is the correct answer

The measure of the subtended angle by the arc is approximately 1.20 radians or 68.75 degrees. This is determined using the formula θ = s/r to find the subtended angle.

To find the subtended angle, we need to use the formula θ = s/r, where s is the arc length and r is the circle's radius. The area of the circle with radius r, is πr², and given that it is 78.5 cm², we first need to find the radius. By solving the area equation, we get r = √(78.5/π), or approximately 5.00 cm. Using the radius in the angle formula (θ = 6/5.00), we get θ to be approximately 1.20 radians. However, if the question is asking for the result in degrees, we need to convert the result from radians to degrees by using the conversion factor 180/π. Thus, θ = 1.20 * (180/π) which gives approximately 68.75 degrees.

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Calculate the circle's radius first from the given area. Then, find the circumference of the circle and compare the arc length to the circumference to obtain the subtended angle. Therefore, the subtended angle is approximately 68.79 degrees.

The subject of this question falls under the domain of geometry in Mathematics, where we identify the measure of angle subtended by a certain arc. In order to achieve this, we must understand that a complete circle with a 360-degree angle covers an arc length equivalent to its circumference. If we know the radius of the circle, calculated from the area, we can compare the known arc length to the circumference of the circle to find the angle subtended.

First, we find the radius using the given circle area using the formula [tex]A=\pi r^2[/tex], which gives r= √(A/π). So r= √(78.5 cm² / 3.14) =approx. 5cm. Now, the full circumference of a circle (C) is 2πr, which gives [tex]C = 2*3.14*5 cm = 31.4 cm.[/tex] The full angle covered by the circumference is 360 degrees. To find the angle subtended by an arc of length 6cm, we calculate as follows: (6 cm / 31.4 cm) * 360 degrees = approx. 68.79 degrees.

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Answer:

The answer is D. 52

Step-by-step explanation:

edg 2020

The correct answer is option B). The size of a crowd standing along 1 mile section of parade route that is 10 feet deep on both sides of the street is 42,240.

To estimate the size of the crowd, we need to calculate the total area occupied by the crowd and then divide by the area occupied by each person.

First, let's calculate the total area available for the crowd on both sides of the street:

The length of the parade route is 1 mile. Since there are 5280 feet in a mile, the length in feet is 5280.

The depth of the crowd on both sides of the street is 10 feet.

Therefore, the total area available for the crowd on both sides is:

Total area = 2 [tex]\times[/tex] (Depth of crowd) [tex]\times[/tex] (Length of parade route)

Total area = 2 [tex]\times[/tex] 10 feet [tex]\times[/tex] 5280 feet

Total area = 105,600 square feet

Next, we need to calculate how many people can fit in this area:

Each person occupies 2.5 square feet.

The number of people that can fit in the total area is:

Number of people = Total area / Area per person

Number of people = 105,600 square feet / 2.5 square feet per person

Number of people = 42,240.

Answer:

D.

Step-by-step explanation:

Answer:

Option b - The actual price is $3.89 higher than the expected price.

Step-by-step explanation:

Given : In 1983, a year-long newspaper subscription cost $12.75. Today, a year-long newspaper subscription costs $28.50. If the CPI is 193

To find : What is the relation of the actual price of a year-long newspaper subscription to the expected price, to the nearest cent?

Solution :

CPI is the consumer price index.

The formula of CPI is

[tex]\text{CPI}=\frac{\text{Cost of newspaper subscription in Given Year}}{\text{Cost of newspaper subscription in Base Year}}\times 100[/tex]

We have given CPI = 193

Cost of newspaper subscription in Base Year = $12.75

We have to find cost of newspaper subscription in Given Year

[tex]193=\frac{\text{Cost of newspaper subscription in Given Year}}{12.75}\times 100[/tex]

[tex]\text{Cost of newspaper subscription in Given Year}=\frac{193\times12.75}{100}[/tex]

[tex]\text{Cost of newspaper subscription in Given Year}=\frac{2460.75}{100}[/tex]

[tex]\text{Cost of newspaper subscription in Given Year}=24.61[/tex]

The actual price of newspaper subscription  = $28.50

The expected price of newspaper subscription = $24.61

Now, to find how much higher they expected is

$28.50 -$24.61 = $3.89

Therefore, Option b is correct.

The actual price is $3.89 higher than the expected price.

Final answer:

Options A, B, and D are geometric sequences because they have a constant ratio between successive terms. Option A has a ratio of 3, option B has a ratio of 0.5, and option D has a ratio of 2. Option C is an arithmetic sequence and not geometric.

Explanation:

The question asks which of the listed sequences are geometric sequences. A geometric sequence is characterized by a constant ratio between successive terms. Let's analyze each option:

A. 1,3,9,27,81 - Each term is multiplied by 3 to get the next term, hence it is a geometric sequence with a common ratio of 3.

B. 10,5,2.5,1.25,0.625, 0.3125 - Each term is multiplied by 0.5 (or divided by 2) to get the next term, hence it is a geometric sequence with a common ratio of 0.5.

C. 3,6,9,12,15,18 - The difference between successive terms is constant (+3), making it an arithmetic sequence, not geometric.

D. 5,10,20,40,80,160 - Each term is multiplied by 2 to get the next term, hence it is a geometric sequence with a common ratio of 2.

Therefore, options A, B, and D are geometric sequences, while option C is not.

Answer: The expression for the given statement is [tex]t-7[/tex]

Step-by-step explanation:

We are given a statement:

7 less than a number t

Let the number be considered as 't'

'Less' in the above statement means subtraction operation.

The numerical value written before the 'less' operation is written after in the expression.

Thus, the expression for the given statement is [tex]t-7[/tex]

The algebraic expression for '7 less than a number t' is t - 7. This represents taking the number t and subtracting 7 from it.

The question requires an algebraic expression. '7 less than a number t' translates to t - 7 in algebraic terms. The phrase 'less than' is a clear indication to subtract in math context. So, take the number t and subtract 7 from it, hence, t - 7 is our answer. This is a common way to express relative quantities and operations in algebra.

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