PLEASE HELP ME

The first two steps in the derivation of the quadratic formula by completing the square are shown below.
Which answer choice shows the correct next step?

The area οf the cοmpοsite shape is 541 square meters.

Cοmpοsite shapes refer tο 2D shapes that are made up οf twο οr mοre simple shapes. These simple shapes can be cοmbined tο fοrm a mοre cοmplex shape.

Tο find the area οf this cοmpοsite shape, we need tο divide it intο smaller shapes and add up their areas. Let's divide it intο twο rectangles and a triangle:

First rectangle:

Length = 18 m

Width = 11 m

Area = length x width = 18 m x 11 m = 198 m²

Secοnd rectangle

Length = 14 m

Width = 20 m

Area = length x width = 14 m x 20 m = 280 m²

Triangle:

Base = 14 m

Height = 9 m (we can find this by subtracting the height οf the tοp rectangle frοm the height οf the entire shape: 20 m - 11 m = 9 m)

Area = (base x height) / 2 = (14 m x 9 m) / 2 = 63 m²

Nοw we add up the areas οf the three shapes tο get the tοtal area οf the cοmpοsite shape:

Tοtal area = 198 m² + 280 m² + 63 m² = 541 m²

Hence, the area οf the cοmpοsite shape is 541 square meters.

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The following solutions with regard to resolving or simplifying the radii of the circular pond are given below.

Part A: 5√100 + √164 meters = 5 × 10 + 2√41 meters

Part B: 5 × 10 + 2√41 meters = 50 + 2√41 meters

Part C: The radius of Pond B is 10√2 meters.

Part D: the radius of Pond B is greater than the radius of Pond A.

Part A: The mistake is in Step 1. To simplify the square root of 164, we need to find its prime factors:

164 = 2 × 2 × 41

So, we can write:

√164 = √(2 × 2 × 41) = 2√41

Using this, we can rewrite Step 1 as:

5√100 + √164 meters = 5 × 10 + 2√41 meters

Part B: Using the corrected step from Part A, we can simplify the radius of Pond A as:

5 × 10 + 2√41 meters = 50 + 2√41 meters

So, the radius of Pond A is 50 + 2√41 meters.

Part C: The radius of Pond B is already simplified, so we don't need to do any additional steps. It is:

25√200/5 meters = 5√200 meters

We can simplify this further by finding the prime factorization of 200:

200 = 2 × 2 × 2 × 5 × 5

So, we can write:

√200 = √(2 × 2 × 2 × 5 × 5)

= 2 × 5√2

Using this, we can rewrite the expression for the radius of Pond B as:

5 × 2 × √2 meters

= 10√2 meters

Thus, the radius of Pond B is 10√2 meters.

Part D: We can compare the radii of the ponds using the original expressions by writing:

√164 < 25√200/5

Simplifying both sides:

2√41 < 10√2

Dividing both sides by 2:

√41 < 5√2

Squaring both sides (since both sides are positive):

41 < 25 × 2

41 < 50

So, the inequality is true. Therefore, the radius of Pond B is greater than the radius of Pond A.

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Full Question:

Two circular ponds at a botanical garden have the following radii:

Pond A: Sqrt(164) meters;

Pond B: 25Sqrt(200)/5 meters:

Todd simplified the radius of pond A this way:

5sqrt(164)

Step 1: 5sqrt(100) + Sqrt(164) meters

Step 2: 5(10 + 8)

Step 3: 5(18)

Step 4: 90

One of the steps above is incorrect.

Part A: Rewrite the steps so that it is correct

Part B: Using the corrected step from Part A, simplify the radius of Pond A.

Part C: Simplify the expression for the radius of pond B.

Part D: Write an inequality to compare the radii of the ponds, using the original expressions.

Given the slope of the line and the intercept it forms with the y-axis, one of the mathematical forms used to derive the equation of a straight line is called the slope intercept form. Y = mx + b, where m is the slope of the straight line and b is the y-intercept, is the slope intercept form.

The equation of the line, as determined by the slope-intercept formula, is: y = mx + b, where m is the line's slope and b is its y-intercept. As x and y represent each point on the line, they must be maintained as variables when using the formula above.

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The one real solution of the equation 6x^(2)+7x-h=0 can be expressed in terms of equality as h = -49/24 using discriminant formula.

To find all values of h for which the quadratic equation 6x^(2)+7x-h=0 has one real solution, we need to use the discriminant formula. The discriminant formula is given by:

D = b^(2) - 4ac

Where a, b, and c are the coefficients of the quadratic equation. In this case, a = 6, b = 7, and c = -h. Plugging these values into the formula, we get:

D = 7^(2) - 4(6)(-h)

D = 49 + 24h

For the quadratic equation to have one real solution, the discriminant must be equal to 0. Therefore, we can set D = 0 and solve for h:

49 + 24h = 0

24h = -49

h = -49/24

Therefore, the value of h for which the quadratic equation has one real solution is h = -49/24. We can write this as an equality:

h = -49/24

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We can use the fact that 32 is equal to 2 raised to the power of 5:

32 = 2^5

Substituting this into the equation gives:

16^x = 2^5

We can then rewrite 16 as 2^4, since 16 is equal to 2 raised to the power of 4:

(2^4)^x = 2^5

Simplifying the left side of the equation gives:

2^(4x) = 2^5

Now we can see that the bases of both sides of the equation are equal, so we can set the exponents equal to each other:

4x = 5

Dividing both sides by 4 gives:

x = 5/4

Therefore, the solution to the equation 16^x = 32 is x = 5/4.

Answer:

sin 45°= x/110 ft

sin45° * 110 = x

Step-by-step explanation:

try it i dont have calculator here

The solutions to the equation z^2 = -361 are:

z = ±19i and z = ±19i*(-1)^k, k = 0 or 1.

To find all n complex solutions of the equation x^n = k, where k is a complex number, we can use the polar form of complex numbers. If we write k in polar form as k = re^(iθ), where r = |k| is the modulus of k and θ = arg(k) is the argument of k, then we can write x in polar form as x = ρe^(iφ), where ρ = |x| is the modulus of x and φ = arg(x) is the argument of x.

Substituting these polar forms into the equation x^n = k, we get:

(ρe^(iφ))^n = re^(iθ)

Taking the modulus of both sides, we get:

|ρ^n| = |r|

Since r is a complex number, its modulus is a positive real number, so we can write r = Re^(i0) in polar form, where R = |r|.

Substituting this into the equation above, we get:

|ρ^n| = R

Taking the argument of both sides, we get:

nφ = 0 + 2πk

where k is an integer. Solving for φ, we get:

φ = (2π*k) / n

Substituting this expression for φ back into the polar form of x, we get:

x = ρe^(i(2π*k)/n)

where ρ is a positive real number. This gives us n complex solutions for x, which are:

x = ρe^(i(2π*k)/n), k = 0, 1, 2, ..., n-1.

Now let's apply this method to solve the equation z^2 = -361.

Writing -361 in polar form, we have:

-361 = 361e^(iπ)

Taking the square root of both sides, we get:

z = ±sqrt(361)e^(iπ/2 + iπk)

where k = 0 or 1. Simplifying, we get:

z = ±19e^(i(π/2 + π*k))

So the solutions to the equation z^2 = -361 are:

z = ±19i and z = ±19i*(-1)^k, k = 0 or 1.

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I hope you're doing well and this gives a clear understanding to you.

The value of x from the similar triangles is x = 4

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be ΔQRS

Let the second triangle be ΔLMN

Now , the measure of ∠QRS = measure of ∠NLM

And , the triangles are similar

Now , the corresponding sides of similar triangles are in the same ratio

On simplifying , we get

LM / RQ = LN / QS

( 2x + 4 ) / 8 = 9 / 6

Multiply by 8 on both sides , we get

2x + 4 = ( 3/2 ) 8

2x + 4 = 12

Subtracting 4 on both sides , we get

2x = 8

Divide by 2 on both sides , we get

x = 4

Therefore , the value of x is 4

Hence , the similar triangles are solved

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t = 8.46 days

To solve this problem, we can use the equation A = A0e-0.1t, where A0 is the original wound area (22 square centimeters in this case). We can rearrange the equation to solve for t:

t = -(ln(A/A0))/0.1

Plugging in the values for A (14 square centimeters) and A0 (22 square centimeters) gives us t = 8.46. Rounding to two decimal places, the answer is t = 8.46 days.

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Answer:

Karla Saved for 15 months.

Step-by-step explanation:

Tom saved 60 each month if he saved for 8 months then he made $480. Karla saved 32 each month, each of them saved the same amount, 480 because 480 + 480 = 960. divide 480 by 32 and you'll get 15. therefore Karla saved her money for 15 months.

Hope this helps :)

Answer:

Hey I would love to help you but can you just add the photo of the graph? That would help a lot!

Step-by-step explanation:

Using Pythagoras Theorem, The height of the screen is approximately 27.18 inches.

Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle.

We can use the Pythagorean theorem to solve this problem. Let's call the height of the screen "h". Then, according to the Pythagorean theorem, we have:

[tex]h^2 + 32^2 = 42^2[/tex]

Simplifying this equation, we get:

[tex]h^2 + 1024 = 1764[/tex]

Subtracting 1024 from both sides, we get:

[tex]h^2 = 740[/tex]

Taking the square root of both sides, we get:

[tex]h = \sqrt{(740)}[/tex]

Using a calculator to approximate the square root, we get:

h ≈ 27.18 inches

Hence, the height of the screen is approximately 27.18 inches.

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if we take a peek at the tickmarks on the sides, that means that the line that cuts the side is the median, so we have three medians meeting at the centroid of the triangle, bearing in mind that the centroid cuts all three medians in a 2 : 1 ratio, then we can say that line AC is being cut by it in a 2 : 1 ratio, the hell all that means?  well, it means

[tex]\cfrac{AB}{BC}=\cfrac{2}{1}\implies \cfrac{10}{BC}=\cfrac{2}{1}\implies 10=2BC\implies \cfrac{10}{2}=BC\implies \boxed{5=BC} \\\\\\ \stackrel{AB+BC}{10+5}\implies \stackrel{ AC }{\boxed{15}}[/tex]

Answer:

See below.

Step-by-step explanation:

We are asked to identify BC and AC.

Before we start, we should know that this triangle has a center called a Centroid.

A Centroid is a point that is formed by 3 concurrent medians.

A Median is a line segment that connects the vertex of a triangle to the midpoint of the opposite side.

The top part of a Median is 2/3 of the entire line segment. The bottom part of a Median is 1/3 of the entire line segment.

Using the information from above, we can identify that AB (10) is 2/3 of AC, and that BC is 1/3 of AC.

Divide 10 by [tex]\frac{2}{3}[/tex] to find AC.

[tex]10 \div ( \frac{2}{3} )=15 \ (AC)[/tex]

Since we know AC, we can now find BC by simply subtracting AC - AB.

[tex]15-10=5 \ (BC)[/tex]

Therefore, AC = 15; BC = 5.

The model is a good fit because the data are randomly distributed above and below the x-axis.

In Mathematics, a residual value can be defined as a difference between the measured (given or observed) value from a residual plot (scatter plot) and the predicted value from a residual plot (scatter plot).

Generally speaking, the independent variable (fitted values) are generally plotted on the x-axis of a residual plot (scatter plot) while the residual value is plotted on y-axis of a residual plot (scatter plot).

Additionally, a line of best fit simply refers to a trend line on a residual plot (scatter plot) and the given model represents a good fit because the data set are randomly distributed below and above the x-axis.

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Answer: The answer is C: [tex]17\sqrt{13}[/tex]

Step-by-step explanation: Since both Radicands have the same, add the indexes together to get 17

To find the total distance Henri hiked, we can multiply the distance he hiked each day (7/10 mile) by the number of days he hiked (9 days):

Total distance = (7/10) mile/day * 9 days

We can simplify this expression by multiplying the fractions and then multiplying by 9:

Total distance = (7/10) * 9 mile

Total distance = 63/10 mile

Therefore, the equation equivalent to the total amount hiked is:

Total distance = 63/10 mile

or, if we prefer to write the distance in decimal form:

Total distance = 6.3 miles

The value of x in the chord is 4.8 units

From the question, we have the following parameters that can be used in our computation:

The circle

Next, we calculate the radius using each chord using the Pythagoras theorem

Using the above as a guide, we have the following:

r² = x² + (37/2)²

r² = 13² + (28/2)²

By substitution, we have

x² + (37/2)² = 13² + (28/2)²

So, we have

x² = -(37/2)² + 13² + (28/2)²

Evaluate

x² = 22.75

Take the square root

x = 4.8

Hence, the value of x is 4.8 units

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The average rate of change of f the first function is 3,  the average rate of change of the second function is 10, and the average rate of change of the third function is 0.2.

The average rate of change of a function from x1 to x2 can be calculated using the formula:

Average rate of change = (f(x2) - f(x1))/(x2 - x1)

For the first function, f(x) = 3x, we can plug in the values of x1 = 0 and x2 = 5 to get:

Average rate of change = (f(5) - f(0))/(5 - 0) = (15 - 0)/5 = 3

For the second function, f(x) = x2 + 2x, we can plug in the values of x1 = 3 and x2 = 5 to get:

Average rate of change = (f(5) - f(3))/(5 - 3) = (25 + 10 - 9 - 6)/2 = 10

For the third function, f(x) = square root of x, we can plug in the values of x1 = 4 and x2 = 9 to get:

Average rate of change = (f(9) - f(4))/(9 - 4) = (3 - 2)/5 = 0.2

The slope of a function is interpreted as the average rate of change of the function. Therefore, the slope of the first function is 3, the slope of the second function is 10, and the slope of the third function is 0.2.

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Answer:

Step-by-step explanation:

you can set two ratios equal to each other to solve for the unknown (the amount of bananas).

11:3 as x:1

then cross multiply to get an equation. divide both sides by 3 to isolate X. plug that into a calculator and your answer is 3.6 repeating which rounds to 4 oz of bananas

For the given observations 48, 12, 11, 45, 48, 48, 43, 32, the values are -

Mean = 37.5 , Median = 44, and Mode = 48

The median is the best measure for the data.

What is mean?

In statistics, in addition to the mode and median, the mean is one of the metrics of central tendency. Simply put, the mean is the average of the values in the given collection. It indicates that values in a particular data collection are distributed equally. The three most frequently employed metrics of central tendency are the mean, median, and mode.

To find the measure that best represents the given data, we can calculate the mean, median, and mode and choose the measure that gives us the most representative value.

Mean -

To find the mean of the data, we add up all the values and divide by the total number of values -

Mean = (48 + 12 + 11 + 45 + 48 + 48 + 43 + 32) / 8 = 37.5

Median -

To find the median of the data, we arrange the values in order from smallest to largest and then find the middle value.

If there are an even number of values, we take the average of the two middle values.

11, 12, 32, 43, 45, 48, 48, 48

There are eight values in the data set, so the median is -

(43 + 45) / 2

88 / 2

44

Mode -

To find the mode of the data, we look for the value that occurs most frequently.

In this case, 48 occurs three times, which is more than any other value, so the mode is 48.

Conclusion:

In this data set, the mean is 37.5, the median is 44, and the mode is 48. Since the data set has some values that are higher than the others, such as 48 occurring three times, the mean may be influenced by these outliers.

In this case, the median is a better measure of central tendency because it is not influenced by outliers.

Therefore, the median is the measure that best represents the data.

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The best deal is the one with the lowest total cost. To find the total cost of each option, we can use the compound interest formula:

A = P(1 + r/n)^(nt)

Where A is the total cost, P is the principal amount ($24,790), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Option 1: A = 24,790(1 + 0.04/12)^(12*6) = $31,617.64

Option 2: A = 24,790(1 + 0.0427/4)^(4*6) = $31,814.57

Option 3: A = 24,790(1 + 0.04/365)^(365*5) = $30,248.29

Option 4: A = 24,790(1 + 0.0424/12)^(12*5) = $30,506.55

Option 5: A = 24,790(1 + 0.04/4)^(4*4) = $28,793.32

Option 6: A = 24,790(1 + 0.0422/365)^(365*4) = $28,992.84

Option 7: A = 24,790

The best deal is Option 7, paying cash, with a total cost of $24,790. However, if paying cash is not an option, the next best deal is Option 5, with a total cost of $28,793.32.

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After eight leaps, there is a 0.3828 percent chance that the bug will still be within three units of where it started.

a. To return to the origin after eight jumps, the bug must take an equal number of left and right jumps. Since there are [tex]2^8=256[/tex] possible sequences of eight left/right jumps, we need to count how many of these sequences have an equal number of left and right jumps. To do this, we can use the binomial coefficient:

[tex]C(8,4) = 8! / (4! * 4!) = 70[/tex]

This counts the number of ways to choose 4 out of 8 jumps to be leftward, with the other 4 jumps being rightward. Therefore, the probability of returning to the origin after eight jumps is:

[tex]P(return to origin) = 70 / 256 = 0.2734[/tex]

b. To be within three units of the origin after eight jumps, the bug must take at most three more rightward than leftward jumps or three more leftward than rightward jumps. We can compute the probabilities of each of these cases separately and add them up. Let's first consider the case where there are three more rightward jumps than leftward jumps. To count the number of such sequences, we can choose three out of the eight jumps to be leftward, with the other five jumps being rightward. Therefore, the probability of this case is:

P(3 more rightward) = C(8,3) / 256 = 0.1094

Similarly, the probability of having three more leftward jumps than rightward jumps is also 0.1094. To count the number of sequences where there are two more rightward jumps than leftward jumps, we can choose two out of the eight jumps to be leftward, with the other six jumps being rightward. There are also C(8,2) sequences with two more leftward jumps than rightward jumps. Therefore, the probability of being within three units of the origin after eight jumps is:

[tex]P(within 3 units) = 2 * 0.1094 + 2 * C(8,2) / 256 = 0.3828[/tex]

Therefore, the probability that the bug is within three units of the point of departure after eight jumps is 0.3828.

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Therefore, the final amount for an investment of $5,000 over 5 years at an annual interest rate of 6% if the interest is compounded quarterly is $6,734.27.

SI unit is defined as (P, R, and T) / 100.

SI stands for Straightforward Interest in this instance. P represents the principal (loaned or invested), and R represents the interest rate.

To solve this problem, we need to use the formula for compound interest:

A = P (1 + r/n)^(nt)

Where:

A = the final amount

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time (in years)

Here, we have:

P = $5,000

r = 6% = 0.06 (annual interest rate)

n = 4 (compounded quarterly)

t = 5 years

Plugging these values into the formula, we get:

A = 5000 (1 + 0.06/4)^(4*5)

A = 5000 (1.015)^20

A = 5000 (1.349858807)

A = $6,734.27 (rounded to the nearest cent)

Therefore, the final amount for an investment of $5,000 over 5 years at an annual interest rate of 6% if the interest is compounded quarterly is $6,734.27.

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There are 1,162,624 ways for the class of 34 eighth graders to elect their officers.

There are 34 eighth graders in the class and 4 officer positions to be elected, which are class president, vice president, secretary, and treasurer.

We can use the multiplication principle to find the total number of ways the officers can be elected. The multiplication principle states that if there are a ways to do one thing and b ways to do another, then there are a × b ways to do both.

First, let's consider the class president position. There are 34 students who can be elected as class president. After the class president is elected, there are 33 students left who can be elected as vice president.

Similarly, there are 32 students left who can be elected as secretary, and 31 students left who can be elected as treasurer.

Therefore, the total number of ways the officers can be elected is:

34 × 33 × 32 × 31 = 1,162,624

So, there are 1,162,624 ways for the class of 34 eighth graders to elect their officers.

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The first runner is covering a mile in 9.25 minutes and the second runner is covering a mile in 18.5 minutes the first runner is traveling at a greater speed.

Travel is the movement of people between distant geographical locations for any purpose. It can be done by foot, bicycle, car, boat, bus, train, or plane. Travel can also include relatively short stays between successive movements, such as in the case of tourism or business travel. Travel can be for leisure, recreational, or business purposes, and can be one way or round trip. It may involve travel to different places within the same country, or to another country altogether.

The first runner is traveling at a greater speed because their time to complete each mile is less than the second runner.
For example, the first runner takes 18.5 minutes to complete 2 miles, while the second runner takes 37 minutes to complete the same distance.
This means that the first runner is covering a mile in 9.25 minutes, while the second runner is covering a mile in 18.5 minutes.
Therefore, the first runner is traveling at a greater speed.

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Answer: Runner 1

Jonson family I think  sorry if im wrong

Step-by-step explanation:

The measure of arc AE is 77 degrees.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

We have to find the measure of the arc AE.

The measure of BC is 38 degrees.

The measure of DE is 103 degrees.

The value of p is 77 degrees which is measure of CD.

The arc CD is opposite to the AE

Which makes the measure of AE is vertical to P.

They are equal

Hence, the measure of arc AE is 77 degrees.

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Answer:

p = 78.8 m

mass of chain = 134 kg

Step-by-step explanation:

a)  sin28 = 37/p             sin = opposite/hypotenuse

p = 37/sin28 = 78.8 m

b)  78.8 m  x 1.7 kg/m = 134 kg

It is reported that a survey had a standard error of the mean of 20, and it is assumed that the population standard deviation is 500. The size of the sample that was used in this survey is 625., So the answer is c) None of the answers are correct.

The size of the sample used in the survey can be determined using the formula for standard error of the mean:

Standard error of the mean = (Population standard deviation) / (Square root of sample size)

Rearranging the formula to solve for sample size, we get:

Sample size = (Population standard deviation / Standard error of the mean)^2

Plugging in the given values:

Sample size = (500 / 20)^2

Sample size = 25^2

Sample size = 625

Therefore, the size of the sample used in the survey is 625.

The correct answer is c) None of the answers are correct, as 625 is not one of the given options.

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