quadratic equation y=(x+4)²+3

Answer:

21

Step-by-step explanation:

Since the girls have the same age, let their age be x.
Then, their average is

\(\frac{x+x}{2} = \frac{2x}{2} = x\)

Let \(S_{i}\) denote the age of 'i' girls.
Then, \(S_{8} = S_{6} + x + x - eq(1)\)

Also, we have,

\(\frac{S_{8}}{8} =15 - eq(2)\)

\(\frac{S_{6}}{6} =13 - eq(3)\)

Then eq(2):

(from eq(1) and eq(3))

\(\frac{S_{6} + 2x}{8} =15\\\\\frac{13*6 + 2x}{8} = 15\\\\78+2x = 120\\\\2x = 120-78\\\\x = 21\)

The average of the other two girls with equal age​ is 21

Answer:

If you round it to nearest tenth it will be 50

Step-by-step explanation:

14x3.14=49

Answer:

Step-by-step explanation:

There are 15,504 ways to randomly select a team of 5 people from a group of 20 people

If there are 20 people trying out for a team, the number of ways to select a team of n people can be calculated using the formula for combinations, which is:

C(20, n) = 20! / (n! * (20 - n)!)

where C(20, n) represents the number of ways to select n people from a group of 20 people.

For example, if we want to select a team of 5 people, we can plug in n = 5 and calculate:

C(20, 5) = 20! / (5! * (20 - 5)!) = 15,504

Therefore, there are 15,504 ways to randomly select a team of 5 people from a group of 20 people. Similarly, we can calculate the number of ways to select teams of different sizes by plugging different values of n into the formula for combinations.

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Answer:

D. 2/3 1/6 1/5

Step-by-step explanation:

Answer:

Explanation:

Answer:

A

Step-by-step explanation:

4 divided by 12 is 0.3333 so anything you do has to be more than 0.3333 and 2 divided by 4 is .5 which is more then 0.333. Hope this helps

Answer:

The second one

Step-by-step explanation:

Answer:

Simplify  

58 /35

(Decimal: 1.657143)

Step-by-step explanation:

Answer:

y = 5x + 19

Step-by-step explanation:

y = 5x + b

4 = 5(-3) + b

4 = -15 + b

19 = b

The arc length of the polar curve r = e^5θ from 0 to 2π is √26 [(e^10π - 1) / 5].

To find the arc length of a polar curve, we use the formula:

L = ∫[a,b] √(r(θ)² + [dr(θ)/dθ]²) dθ

where r(θ) is the polar equation of the curve, and dr(θ)/dθ is its derivative with respect to θ.

In this case, we have r(θ) = e^5θ, so:

dr(θ)/dθ = 5e^5θ

Plugging these into the arc length formula, we get:

L = ∫[0,2π] √(e^10θ + (5e^5θ)²) dθ

Simplifying the integrand, we have:

L = ∫[0,2π] √(e^10θ + 25e^10θ) dθ

L = ∫[0,2π] √(26e^10θ) dθ

L = √26 ∫[0,2π] e^5θ dθ

Using the formula for the integral of e^x, we get:

L = √26 [e^5θ / 5] |_0^(2π)

L = √26 [(e^10π - 1) / 5]

So the arc length of the polar curve r = e^5θ from 0 to 2π is √26 [(e^10π - 1) / 5].

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Step-by-step explanation:

Number 1

\( log_{10}( {x}^{2} - 3x + 12 ) = 1 \\ log_{10}( {x}^{2} - 3x + 12 ) = log_{10}(10) \\ cancelling \: both \: logs \: we \: have \\ {x}^{2} - 3x + 12 = 10 \\ {x}^{2} - 3x + 12 - 10 = 0 \\ {x}^{2} - 3x + 2 = 0 \\ \)

\(solve \: \: by \: factorisation \: method \\ {x}^{2} - 2x - x + 2 \\ {x}(x - 2) \: - 1(x - 2) \\ (x - 2)(x - 1) \\ therefore \: x = 2 \: or \: x = 1\)

Number 2

There are 22 cards in the Caleb trading card deck.

A deck of playing cards contains 52 total cards. Each of the four suits contains 13 playing cards. These are the diamonds, clubs, hearts, and spades. Although hearts and diamonds are red, spades and clubs are black.

In total, Missy has 156 cards. We split 156 by 4 since she has four times as many as they have.

156/4= 39

Ashe possesses 17 cards, while Caleb's number is still a mystery. They each have 39 cards, thus to determine how many cards Caleb has, we must take Ashe's cards away.

39-17=22

presently going over our work

Caleb has 22 cards in his hand.

Ashe is holding 17 cards.

They each have 39.

Which is 4 times less than how many cards Missy has

Missy has 156 cards.

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The correct option for image coordinate is  M′ is the right response.

(0, 3).

It is possible to find any point in a 2D plane or 3D space using coordinates, which are ordered pairs of points. You may have observed the use of grids in mathematics. Which grids are these? We can plot any point using these grids and its coordinates. So, in mathematics, what are coordinates? Let's look at the mathematical definition of coordinates.

Cartesian coordinates, also known as the coordinates of a point in a 2D plane, are two integers, or occasionally a letter and a number, that identify a specific point's precise location on a grid. This grid is referred to as a coordinate plane.

We must add 4 to the y-coordinate of point M in order to obtain the image coordinates of M′ after a translation of 4 units up.

M (0, 1) becomes M′ when translated four units up. (0, 3).

Therefore, M′ is the right response.(0, 3).

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Answer:

D) M′(0, 3)

Step-by-step explanation:

I took the quiz and got a 100 meaning that i got this question right :)

The center of the circle, and consequently the central point of the resort's swimming pool, is located at the intersection of the two legs of the right triangle, approximately 60 feet from one vertex and 120 feet from the other.

The upscale resort has ingeniously designed its circular swimming pool to encompass a central area containing a restaurant. This central area takes the form of a right triangle with legs measuring 60 feet and 120 feet, while the hypotenuse, the longest side of the triangle, spans approximately 103.92 feet. The vertices of the triangle neatly coincide with points on the circumference of the circular pool.

Due to the properties of a right triangle, the hypotenuse is also the diameter of the circle. This means that the circular pool is precisely constructed around the right triangle, with its center located at the midpoint of the hypotenuse.

To determine the exact coordinates of the center of the circle, we can consider the properties of right triangles. Since the legs of the right triangle are perpendicular to each other, the midpoint of the hypotenuse coincides with the point where the two legs intersect.

In this case, the center of the circle is the point of intersection between the 60-foot leg and the 120-foot leg of the right triangle.

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Answer:

1.5 Pounds

Step-by-step explanation:

Assuming that they only get 1 quarter-pound burger it would be 6/4 which is one and one-half. He and Five friends makes a total of 6 people.

Answer:

$1350.

Step-by-step explanation:

If Justin files a claim for $2100, he will pay the first $750 toward the claim, and his insurance company will pay the remaining costs.

So, Justin will pay $750.

And, the insurance company will pay $2100 - $750 = $1350.

Answer:

-8°C Degrees in Toronto

Step-by-step explanation:

Just calculate it.

If you minus 3 from -5, then you will get -8, so hence, your answer is -8.

Answer:

-8 (degrees)C

Step-by-step explanation:

-5-3=-8

The area of the triangle is 30.8 cm²

The triangle’s area may be determined using the given formula:

Area = 0.5 x base x height (in this instance, the base is 10 cm).Now we have to find the height. We may do it with the use of the formula: h = sinθ × b / 2

where h = height of the triangle

θ = the angle (in radians) opposite the height

b = base length

Using these equations, we may determine the height and then calculate the triangle's area. Here is the complete answer to the given question:

Given that, base = 10 cm, angle (opposite to height) = 105°, and a = 13 cm

We can calculate the height (h) using the formula: h = sin(105°) × 13 / 2

h = 6.15 cm

Now, using the formula to calculate the triangle's area:

Area = 0.5 × 10 × 6.15 = 30.75 cm²

Therefore, the area of the triangle is 30.8 cm² (rounded to one decimal place).

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Answer:

3x + 9)(x - 2) = 3x(x - 2) + 9(x - 2) = (3x 2 - 6x) + (9x - 18) = 3x 2 + 3x - 18

The orange will fall 64 feet in 8 seconds.

Distance:

Distance is defined as how much ground an object has covered despite its starting or ending point.

Given,

The distance a falling object travels towards the earth is directly proportional to the square of the time that it falls.

And an orange falls 16 feet in 4 seconds.

Here we need to find the how far it will fall in 8 seconds.

Based on the given details,

We know the that distance is,

D = kt²  

where

k is the constant of proportionality.  

To find the value of k we have to apply the given values on the equation.

=> 16 = k x (4)²

=> 16 = k x 16

=> k = 16/16

=> k = 1.

So, in 8 seconds it will fall at

=> D = 1 x (8)²

=> D = 1 x 64

=> D = 64 feet.

Therefore, the orange will fall at 64 feet in 8 seconds.

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Market classes and grades are used to describe the quality and characteristics of agricultural products, including meat, poultry, fruits, and vegetables.  True

They provide a common language for buyers and sellers to communicate about the characteristics, such as the age, sex, fat content, and muscling, of the product. Market classes and grades help ensure that buyers receive products that meet their quality standards and help sellers receive a fair price for their products. For example, beef is graded based on marbling, maturity, and lean color, with the highest grade being USDA Prime, followed by USDA Choice and USDA Select.

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Full Question: market classes and grades encompass descriptive terminology of carcasses and products for the understanding of different groups or buyers. T/F

This standardized system of classification allows for easier communication and understanding between buyers and sellers, and ensures consistency and fairness in the marketplace.

Market classes and grades refer to the categorization and labeling of carcasses and products based on their quality and characteristics. These classifications use descriptive terminology that is understood by different groups of buyers, such as meat packers, wholesalers, retailers, and consumers. Market classes typically group animals based on their intended use, such as beef cattle for slaughter, while grades are assigned based on factors such as maturity, marbling, and fat content. This standardized system of classification allows for easier communication and understanding between buyers and sellers, and ensures consistency and fairness in the marketplace.

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Answer:

The quotient of 902 divided by 27 equals 33 and the remainder is 11.

Answer:

l >= 60

Step-by-step explanation:

l greater than or equal to 60

Answer:

l ≥ 60

Step-by-step explanation:

This means the l is greater than or equal to 60. In conclusion, the lightbulb is greater than or equal to 60 watts.

Therefore , the magical ratio for muffins is therefore 2:2:1:1, which is the answer to the ratio problem that was provided.

An ordered combination of numbers “ a ” and “ b that is stated as just a / b, where b not greater than zero, is referred to as a ratio. A ratio is the result of equating two ratios. If there were one boy and three girls, the ratio could be shown as 1:3.   1/4 are boys, and 3/4 are girls. A part is a number, a proportion of size, or a difference among two or more things.

Here,

Since: Marco To avoid your batter and bakery items acquiring a purple-blue tinge, wash freeze blueberries multiple times in water it until water becomes lighter in color.

The magic muffin ratio is 2:2:1:1, which equals 1-two cups and 2,8 cups.

With a paper towel, dry them off, and then delicately fold it into the batter. Maintaining the lightness of rapid breads is the aim of this process.

The magical ratio for muffins is therefore 2:2:1:1, which is the answer to the ratio problem that was provided.

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Answer:

x=18

Step-by-step explanation:

see answer

Answer:

1,296 cubic cm

Step-by-step explanation:

V = lwh

V = 4(3) x 2(3) x 6(3)

V = 12 x 6 x 18

Answer:

1,296 cm

Step-by-step explanation:

lenght=4

Width=2

Height=6

Volume of rectangular prism= lenght*Width*height

4*2*6

4(3)*2(3)*6(3)=

1,296 cm

Question 1a

To calculate the book value at the end of the first year using straight-line depreciation, we need to determine the annual depreciation expense first. The straight-line method assumes that the asset depreciates by an equal amount each year over its useful life. Therefore, we can use the following formula to calculate the annual depreciation:

Annual Depreciation = (Cost - Salvage Value) / Useful Life

Substituting the given values, we get:

Annual Depreciation = ($200,000 - $20,000) / 10 years = $18,000 per year

This means that the tractor will depreciate by $18,000 each year for the next 10 years.

To determine the book value at the end of the first year, we need to subtract the depreciation expense for the year from the original cost of the tractor. Since one year has passed, the depreciation expense for the first year will be:

Depreciation Expense for Year 1 = $18,000

Therefore, the book value of the tractor at the end of the first year will be:

Book Value = Cost - Depreciation Expense for Year 1

= $200,000 - $18,000

= $182,000

So the book value of the tractor at the end of the first year, December 31, 2022, using straight-line depreciation is $182,000. so the answer is D

Question 1(b)

To determine the farmer's noncurrent liabilities, we need to use the information provided to calculate the total liabilities and then subtract the current liabilities from it. Here's the step-by-step solution:

Calculate the total current liabilities using the current ratio:

Current Ratio = Current Assets / Current Liabilities

2 = $80,000 / Current Liabilities

Current Liabilities = $80,000 / 2

Current Liabilities = $40,000

Calculate the total liabilities using the debt/equity ratio:

Debt/Equity Ratio = Total Liabilities / Owner Equity

1.0 = Total Liabilities / $100,000

Total Liabilities = $100,000 * 1.0

Total Liabilities = $100,000

Subtract the current liabilities from the total liabilities to get the noncurrent liabilities:

Noncurrent Liabilities = Total Liabilities - Current Liabilities

Noncurrent Liabilities = $100,000 - $40,000

Noncurrent Liabilities = $60,000

Therefore, the farmer's noncurrent liabilities are $60,000. so the answer is B.

Answer:

y = 2x + 3

Step-by-step explanation:

( 0, 3) and (-1, 1)

m= (y2 -y1)/ (x2 - x1)

m= (1 - 3)/( -1 - 0)

m = (-2)/(-1)

m = 2

y - y1 = m (x - x1)

y - 3 = 2(x -0)

y - 3 = 2x + 0

y = 2x + 3

The midterm exam offers more risk than the final exam because there is a greater degree of variability in the scores.

To determine which exam offers more risk, we need to compare the standard deviations of the midterm scores and the final exam.

The standard deviation is a measure of the spread of the data around the mean. A larger standard deviation indicates a wider spread of the data points and hence, a greater degree of variability in the scores.

In this case, the standard deviation of the midterm scores is 8, while the standard deviation of the final exam is 6. This means that the spread of scores for the final exam is smaller than that of the midterm scores.

This means that there is a higher chance that a student's grade on the midterm exam may be significantly lower or higher than their average grade, while the final exam scores are likely to be more consistent.

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