\(\frac{2}{5} x+\frac{1}{2} =\frac{3}{4}\)

Answer:

Step-by-step explanation:

A

The area of the region bounded by 2x = y² + 1 and the y-axis using the horizontal strip method is zero.

To find the area using the horizontal strip method, we divide the region into infinitesimally thin horizontal strips and sum up their areas.

The given equation, 2x = y² + 1, can be rearranged to solve for x in terms of y: x = (y² + 1)/2.

To determine the limits of integration for y, we set the equation equal to zero: (y² + 1)/2 = 0. Solving for y, we get y = ±√(-1), which is not a real value. Therefore, the curve does not intersect the y-axis.

Since the curve does not intersect the y-axis, the area bounded by the curve and the y-axis is zero.

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If Lionel has just received his monthly credit card statement. He placed 9 charges on his card in the last month with a mean of $29.02 per charge. The amount of the 9th charge is$10.97.

To determine the amount of the 9th charge, we can use the formula for the mean (average) of a set of numbers:

Mean = (Sum of all numbers) / (Number of numbers)

We know that the mean of the 9 charges is $29.02, and we know the sum of 8 of the charges, so we can use these values to find the 9th charge.

First, we need to find the sum of the 8 charges:

Sum of 8 charges = $29.88 + $35.21 + $32.93 + $28.18 + $34.08 + $26.89 + $26.76 + $36.28

= $250.21

Next, we can use the formula for the mean to find the sum of all 9 charges:

Mean = (Sum of all 9 charges) / 9

$29.02 = (Sum of all 9 charges) / 9

Multiplying both sides by 9, we get:

Sum of all 9 charges = (9× $29.02)

Sum of all 9 charges = $261.18

Finally, we can find the amount of the 9th charge by subtracting the sum of the 8 charges from the sum of all 9 charges:

Amount of 9th charge = Sum of all 9 charges - Sum of 8 charges

= $261.18 - $250.21

= $10.97

Therefore, the amount of the 9th charge is $10.97.

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The population of the bacteria colony in 52 minutes is 16,000.

The bacteria colony grows at an exponential rate. An exponential equation can be described as an equation with exponents. The exponent is usually a variable.

The general form of exponential equation is f(x) = \(e^{x}\)

Where:

The equation that can be used to determine the population in 52 minutes is:

FV = P(2^(t/13)

Where:

FV = 1,000(2^52/13)

= 1,000 x (2^4)

= 16,000

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Answer:

y < 5/2x + 5

Step-by-step explanation:

slope goes up 5, then over 2 ( 5 on top, 2 on bottom --> 5/2)

y intercept is +5

Answer:

Plug your slope and a point into the formula y = mx + B, in which "m" is the slope, (x, y) is a point on the line and "b" is the y-intercept, to find the equation governing the inequality line. Plugging in (0, 0), you obtain 0 = 0 + b, so b = 0. Rewriting the equation, you obtain y = x/2

The answer is (-3, -6)

Step-by-step explanation:

turn the x into a y, and the y into a opposite x.

Answer:

One of it culd be -3 or 3

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

-6+12y-7

Step-by-step explanation:

Who doesn't like short answers, instead of writing a hole paragraph.

Answer:

\(-6x + 12y - 7\)

Step-by-step explanation:

\((5x + 9y) - (11x - 3y + 7)\)

Lets open the brackets.

\(=> 5x + 9y - 11x + 3y - 7\)

Now lets add/substract the like terms only.

\(=> 5x - 11x + 9y + 3y - 7\)

\(=> -6x + 12y - 7\)

Answer:

C)

10(a + 10) = 12 2

Applying the secant-tangent segment theorem, the equation that will result using the figure given is: C. 10(a + 10) = 12².

The secant-tangent segment theorem states that if a tangent and a secant intersect at a point outside a circle, then the square of the measure of the products of the secant segment and its external secant segment equals the square of the measure of the tangent segment.

Thus, using the figure given, the equation that results from applying the secant-tangent segment theorem would be: C. 10(a + 10) = 12²

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The Scale used on blueprint is 1 inches represents 4/3 feet

Scaling is the increase or decrease in size of a figure or object so as to create an image of that object.

Since on the blueprint, the walls measure 10 feet by 12 feet but on the blue print it measures 7.5 inches by 9 inches. Hence:

Scale used on blueprint is 7.5 inches = 10 feet or 9 inches = 12 feet

1 inches = 4/3 feet

The Scale used on blueprint is 1 inches represents 4/3 feet

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Answer:

87.5%

Step-by-step explanation:

There are 376 students in 8th grade at Samuel's school. There are 47 8th graders trying out for football last Thursday.

The number is students not trying out for football last Thursday is calculated as:

376 students - 47 students

= 329 students

The percent of 8th graders that did not try out for football is calculated as:

329 students/376 students × 100

= 329/376 × 100

= 87.5 %

Step-by-step explanation:

Find 100% of the price:

100 - 15 = 85% (Sale price)

85% = 136

1% = 136 divide 85 = 1.6

100% = 1.6 x 100 = 160

Ans: £160

I tried helping but I cant figure it out let me see..

Answer: 0,3

Step-by-step explanation:

Answer:

It’s b

Step-by-step explanation

Answer: B

Step-by-step explanation:

Answer:

(D) 6yr

Step-by-step explanation:

The equation of the parabola is y = x² + 6x + 8.

The primary distinction between the two forms is that the vertex form informs us of the parabola's vertex while the standard form informs us of the quadratic equation's coefficients.

We can finish the square to change a parabola from standard form to vertex form. If the equation is in vertex form, it is simple to determine what the parabola's vertex is (h, k).

The standard form equation of a parabola:

y = a(x - h)² + k

where (h, k) is the vertex of the parabola.

Now, the x-intercepts at -2 and -4 thus:

y = a(x + 2)(x + 4)

Now, y-intercept at (0, 8) thus:

8 = a(0 + 2)(0 + 4)

8 = 8a

a = 1

Substitute the value of a we have:

y = (x + 2)(x + 4)

Hence, the equation of the parabola is y = x² + 6x + 8.

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The large gear needs to make 3 full turns, and the small gear needs to make 4 full turns for the arrows to line up again.

To find the number of times the gears need to turn, we need to determine the least common multiple (LCM) of the number of teeth on each gear. The LCM of 12 and 8 is 24. This means that it takes 24 teeth engagements for the gears to align again.

For the large gear with 12 teeth, it will complete one full turn when 12 teeth have engaged. Since the LCM is 24, the large gear needs to make 2 full turns to reach 24 teeth engagements. Therefore, it needs to make a total of 2 turns for the arrows to line up again.

Similarly, for the small gear with 8 teeth, it will complete one full turn when 8 teeth have engaged. Since the LCM is 24, the small gear needs to make 3 full turns to reach 24 teeth engagements. Therefore, it needs to make a total of 3 turns for the arrows to line up again.

The large gear needs to make 2 full turns, and the small gear needs to make 3 full turns for the arrows to line up again. When the arrows align, 24 teeth will have touched each other.

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Answer:

m/1 = 87

m/2 = 93

Step-by-step explanation:

m1 and m2 need to have an angle of 180

so 180-87 = 93

a) The two triangles that are congruent are △RUQ and △SPR.  b) The length of UQ is 7√2 cm. The length of PQ is 2√30 cm.

(a) The two triangles that are congruent are △RUQ and △SPR. This is because they have the same side lengths: RU=RP=7 cm, SU=SP=9 cm, and ∠RPQ=∠SPR=90°.

(b) To calculate the length of UQ, we can use the Pythagorean Theorem on △RUQ. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is UQ, and the other two sides are RU and RP.

\(UQ^2\) = \(RU^2\) + \(RP^2\)

\(UQ^2\) = \(7^2\) + \(7^2\) = 98

UQ = √98 = 7√2

Therefore, the length of UQ is 7√2 cm.

To calculate the length of PQ, we can use the Pythagorean Theorem on △PQR. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is PQ, and the other two sides are RP and QR.

\(PQ^2\) = \(RP^2\) + \(QR^2\)

\(PQ^2\) = \(7^2\) + \(9^2\) = 120

PQ = √120 = 2√30

Therefore, the length of PQ is 2 30 cm.

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SOLUTION

SUM OF ANGLES IN A TRIANGLE = 180 degrees

To lock in the highest amount of profit, you would perform the following trades: In Market #1: Buy the 20 Call option for $5.50. Sell the 20 Put option for $3.50.The underlying asset is priced at $22. In Market #2: Sell the 110 Put option for $9.50. Buy the 115 Put option for $2.50. The underlying asset is priced at $110.

By executing these trades, you would create a risk-free strategy known as an arbitrage opportunity. Here's how it works:

In Market #1, you buy the 20 Call option and sell the 20 Put option. Since the options have the same strike price (20), you effectively create a synthetic long position in the underlying asset. This means that if the price of the underlying asset increases, the value of the Call option will also rise, resulting in a profit. Conversely, if the price decreases, the Put option will offset the losses.

In Market #2, you sell the 110 Put option and buy the 115 Put option. This strategy allows you to create a synthetic short position in the underlying asset. If the price of the underlying asset drops, the value of the 110 Put option will increase, generating a profit. On the other hand, if the price increases, the losses will be limited by the 115 Put option.

The profit from this strategy is determined by the difference in premiums paid and received for the options. Since the option prices provided in the question do not specify the unit size, it is not possible to calculate the exact profit without that information.

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The number of perennials flower from 60 flowers seen by the students with of which 70% were perennials flowers is 42.

Perennials Flowers are plants that live more than two years.

To calculate the amount of perennial flowers seen by the students, we use the techniques of percentage.

Using the formula,

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the number of perennials flower is 42.

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To prove that G/nG is a cyclic group of order d, where d = (m, n), we need to show two things: (1) G/nG is a group, and (2) G/nG is cyclic with order d.

1. G/nG is a group:

First, note that G/nG is the set of left cosets of the subgroup nG in G. The operation in G/nG is defined as the coset multiplication:

(g₁nG)(g₂nG) = (g₁g₂)nG

We can verify the group properties for G/nG:

- Closure: For any two cosets g₁nG and g₂nG, their product (g₁g₂)nG is also a coset in G/nG since the product of two elements in G is still in G.

- Associativity: The operation is inherited from the group operation in G, which is associative.

- Identity: Thet  identity element in G/nG is the coset eG = nG, where e is the identity element in G.

- Inverses: For each coset gG in G/nG, its inverse is the coset (g⁻¹)G, where g⁻¹ is the inverse of g in G.

Therefore, G/nG is a group.

2. G/nG is cyclic with order d:

To show that G/nG is cyclic, we need to prove that there exists an element gG in G/nG such that the powers of gG generate all the elements in G/nG.

Consider the element aG ∈ G/nG, where a is a generator of G. Since G is cyclic of order m, we have a^m = e, where e is the identity element in G. This implies that (a^m)G = eG = nG, which means aG has order dividing m.

Let d = (m, n). It follows that d divides m, so we can write m = kd for some positive integer k. Since aG has order dividing m, we have (a^d)G = (a^kd)G = (a^m)G = nG, which means aG has order d in G/nG.

To show that aG generates all elements in G/nG, let gG be an arbitrary element in G/nG. Since G is cyclic, we can express g as g = a^r for some integer r. Then, gG = (a^r)G = (aG)^r, which shows that gG is a power of aG. Therefore, aG generates all elements in G/nG.

Thus, G/nG is a cyclic group of order d = (m, n).

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Answer:

y <= x+2

Step-by-step explanation:

Finding the curve equation,

the slope is 1 and the y-intercept is 2. Hence,

y = x + 2

Since the thing is under the graph,

y < x + 2

Since it is a solid line,

y <= x + 2

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Answer:

y = -3x + 13

Step-by-step explanation:

Assuming the line is linear, you can use the point-slope equation of a line.

(y - y) = m (x - x)

The y and x variables come from the points on the line. Points are written in the form (x, y). In the point (2,7), 2 is x and 7 is y.

1. Plug your points in.

(7 - - 2) = m (2 - 5)

2. Solve for m (the slope)

(7 + 2) = m (2 - 5)

(9) = m (-3)

9 = -3m

m = -3

3. Write an equation of the line with the slope you found.

You can write this equation in different forms, but I'll use the slope-intercept form.

y = mx + b

You'll have to find b, the y-intercept. You can plug one of your points in for x and y as well as your slope, m, and solve for b.

7 = -3(2) + b

7 = -6 + b

b = 13

Therefore, the equation is y = -3x + 13

A cargo ship left port A and is headed across the ocean to shipping port B. After one month, the ship stopped at a refueling station along a path described by a vector with components 〈14, 23〉. The characteristics of the vector representing the path of the ship are "components: 〈7, 11.5〉, magnitude: 13.46".

After another month, on the same path, the ship reached port B, twice the distance from port A as the fueling station. The distance between A and the fueling station is x units.

Then, the distance between B and the fueling station is 2x units.AB = 2x units. The fueling station is located at 〈14, 23〉. And A is located at (0, 0)Now we can calculate the distance between A and the fueling station using the distance formula.= √[(14 - 0)² + (23 - 0)²]= √(196 + 529)= √725= 26.92 approx.

After another month, on the same path, the ship reached port B, twice the distance from port A as the fueling station. The distance between A and the fueling station is 26.92 units. Then, the distance between B and the fueling station is 2 × 26.92 = 53.85 units.

Now we can calculate the vector AB using the below formula: AB = OB - OAwhere, OA = (0, 0)OB = (7, 11.5)

So, AB = OB - OA= (7, 11.5) - (0, 0)= (7, 11.5)

Magnitude of vector AB = √(7² + 11.5²)= √(49 + 132.25)= √181.25= 13.46 approx.

So, the correct answer is "components: 〈7, 11.5〉, magnitude: 13.46".

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