The nth term of a sequence is
2n² + 4n 3
Work out the 10th term of the
sequence.

Answer:

1.7

to the nearest tenth

Step-by-step explanation:

Since the triangle is equilateral, all three sides are the same which is x

The vertical line of length [tex]\sqrt{7}[/tex] bisects the base so each of the two right triangles that is formed has lengths x, x/2 and [tex]\sqrt{7}[/tex]

Using the Pythagorean theorem,

c² = a² + b²

where c is the hypotenuse which has a length x and a and b are the two shorter sides which are x/2 and √7 in this case

Substituting for c, a and b we get

x²= (√7)² + (x/2)²

==> x² = 7 + x²/4

==> x² - x²/4 = 7

==> 3x²/4 = 7

==> x² = 7 x 4/3 = 28/3

x = √(28/3) = 1.732 or 1.7 to the nearest tenth

The length of Adrian's shadow measured by his friend and the distance directly from Adrian's head to the tip of his shadow can be used to find Adrian's height using Pythagorean Theorem. Using an example of the measurement values, Adrian's height is about 5.5 feet

Pythagorean Theorem states that the sum of the square of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse side.

The diagram in the question appears left out. Please find attached a drawing made using the measurement lengths in the following example, created with MS Word.

The measurements Adrian had his friend to do are;

The length of Adrian's shadow on the sidewalk and the length from Adrian's head to the tip of the shadow.

Let x represent the length of Adrian's shadow, let r represent the distance from Adrian's head to the tip of the shadow, and let y represent Adrian's height

According to Pythagorean Theorem, we get;

r² = x² + y²

Therefore, the Adrian's height, h = √(r² - x²)

When r ≈ 8.14, and x = 6, we get;

h = √(8.14² - 6²) ≈ 5.5

Adrian's height is about 5.5 feet in the example situation

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After doing the equation the area of ΔABC is 15√7.

The Heron area formula is what?

Heron of Alexandria (c. 62 ce) is credited with developing the Heron's formula, which determines the area of a triangle in terms of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: Area is equal to the square root of (a + b + c)/2, where s is half the perimeter.

Given that:

Let AB = 6x , BC = 5x , AC = 4x

then 6x+5x+4x = 30

15x = 30

x = 2

so AB = 12

BC = 10

AC = 8

Area = √s(s - a)(s - b)(s - c)

s = a+b+c/2

s = 12+10+8/2

s = 30/2

s = 15

Area = √15(15- 12)(15 - 10)(15 - 8)

Area = √15(3)(5)(7)

Area = √1575 = 15√7

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The solution of the system of equations:

x = 2y+  3

4x - 5y = 9

Is x = 1, y = -1.

Here we have the following system of equations:

x = 2y+  3

4x - 5y = 9

To solve it, we can notice that the variable x is already isolated on the first equation, then we can take it and replace it on the other equation, then we will get:

4*(2y + 3) - 5y = 9

Now we can solve that equation for y:

4*(2y + 3) - 5y = 9

8y + 12 - 5y = 9

8y - 5y = 9 - 12

3y = -3

y = -3/3

y = -1

And the value of x is:

x = 2y + 3

x = 2*(-1) + 3

x = -2 + 3 = 1

So the solution is x = 1 and y = -1.

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Answer:

B

Step-by-step explanation:

(m^-2 n^-3)^-4

-2 x -4 = 8

-3 x -4 = 12

m^8n^12

The given expression (m − 2n − 3) − 4 is equivalent to →

(m - 2n - 7).

Given is the expression -

(m − 2n − 3) − 4

The given expression is -

(m − 2n − 3) − 4

m - 2n - 3 - 4

m - 2n - 7

Therefore, the given expression (m − 2n − 3) − 4 is equivalent to →

(m - 2n - 7).

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The second cyclist will cover  (9 + 3b/4) miles in 45 minutes of cycling at (12 + b) miles per hour

The problem is solved using the formula for speed which is

= distance / time

The speed of the first cyclist is 12 miles per hour

the speed of the second cyclists is 12 + b miles per hour

In 45 minutes the distance covered by the second cyclist is

distance = speed * time

60 minutes = 1 hour

45 minutes= ?

? = 45/60 = 3/4

distance = (12 + b) * 3/4

= (9 + 3b/4) miles

the distance covered by the second cyclist is (9 + 3b/4) miles

complete question

Two cyclists are 7 miles apart when they begin biking away from each other in opposite directions. The speed of the first cyclist is 12 miles per hour. The speed of the second cyclist is b miles per hour greater than the speed of the first cyclist.

How many miles does the second cyclist bike in 45 minutes?

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Answer:

Step-by-step explanation:

If three numbers a, b and c verify the relation a^2+b^2=c^2 they are said to form a Pythagorean triple, therefore the triangle is right-angled.

verify

13^2 + 82^2 = 90^2

169 + 6724 = 8100

6893 = 8100

it's not a right triangle (it's an obtuse triangle)

Answer:

(3,0)

Step-by-step explanation:

move it :)

Hello,

I hope you and your family are doing well!

To find the serving size of vitamin C for a toddler, we need to know how much vitamin C is in each serving of orange juice. If we assume that each serving of orange juice contains a certain amount of vitamin C, then we can use the following equation to find the serving size:

serving size = (total amount of vitamin C in container) / (number of servings)

Since there are 2 1/4 cups of orange juice in the container, and the container holds 3 servings, the serving size is:

serving size = (2 1/4 cups) / (3 servings) = 3/4 cup per serving

So the serving size of vitamin C for a toddler is 3/4 cup.

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Happy Holidays!

The cubic polynomial with zeros (3,0), (-6,0) and (1,0) is given as follows:

D. x³ + 2x² - 21x + 18.

We are given the zeros of the polynomial, which then can be obtained using the Factor Theorem.

The zeros of the polynomial are given as follows:

x = 3, x = -6, x = 1.

Then, applying the Factor Theorem, considering a leading coefficient of 1, the polynomial is given as the product of it's linear factors as follows:

(x - 3)(x + 6)(x - 1)

(x² + 3x - 18)(x - 1)

x³ + 2x² - 21x + 18.

Meaning that option D is correct.

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A triangle with coordinates (1,1) (4,2) (3,5) is translated three units down and five units to the left. New coordinates will be (-4,-2), (-1,-1),(-2, 2).

A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction. A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.

Given

A triangle with coordinates (1,1) (4,2) (3,5)

The value of a coordinate is impacted by translations left or right but not by translations up or down or left or right.

We multiply all of the numbers by 3 since we are translating the entire triangle down three units.

Additionally, we are converting the entire triangle to left-to-right units of five, thus we will multiply all values by 5.

A = (1 - 5, 1 - 3)

B = (4 - 5, 2 -3)

C = (3 - 5, 5 - 3)

New coordinates will be:

A = (-4,-2)

B = (-1,-1)

C = (-2, 2)

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Answer: m = -1 , b = -8

Step-by-step explanation:

y=mx+c

m = gradient of the line / slope of the line

c = y intercept

-x=-1x so the gradient is -1

-8 = y intercept

The probability that a randomly selected product will be assembled in less than 91.630 minutes or more than 130.35 minutes is 0.0474 or 0.033.

Given,

In a normal random variable

Mean , [tex]\mu[/tex] = 110 minutes

Standard deviation , [tex]\sigma[/tex] = 11 minutes

then

The probability that a randomly selected product will be assembled in less than 91.630 minutes or more than 130.35 minutes will be

a)

To find the Probability that a randomly selected product will be assembled in less than 91.630 minutes, first calculate the z-score at 91.360 minutes

[tex]z-score = \frac{x-\mu}{\sigma}\\\\z-score=\frac{91.63-110}{11}\\\\z-score=\frac{-18.37}{11}=-1.67\\[/tex]

from z-score table , [tex]p(x < -1.67)=0.04746[/tex]

b)

To find the Probability that a randomly selected product will be assembled in more than 130.35 minutes, first calculate the z-score at 130.35 minutes.

[tex]z-score = \frac{130.35-110}{11}\\\\z-score=\frac{20.35}{11}=1.85[/tex]

From z-score table,

[tex]p(x > 1.85)\\\\=1-p(x < 1.85)\\\\=1-0.967\\\\=0.033[/tex]

Thus, the probability for product assembled in more than 130.35 minutes is 0.033

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The sum of x and y is 5.

An equation is a statement of two expressions connected by equal sign.

Given that, the system of equations, y=-3x-1 and y = -2/3x + 6

Simplifying the equations,

-3x-1 = -2x/3+6

Multiplying the both sides by -3

9x +3 = 2x-18

7x = -21

x = -3

Put x = -3 in any one of the equations,

y = -3(-3)-1

y = 9-1

y = 8

Hence, the sum is 5

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Answer:

[tex]\displaystyle \frac{9}{4}[/tex]

Step-by-step explanation:

[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} )[/tex]

The second term of this sum is an Infinite Geometric Progression
To find the sum of an Infinite Geometric Progression,

- Find the first term ( 1/5 ) of the progression and call it a
- Find the common ratio, (divide any term by it's predecessor. i.e [tex]\displaystyle \frac{\frac{1}{5^2} }{\frac{1}{5} } = \frac{5}{5^2} = \frac{1}{5}[/tex]) and call it r

Finding the sum of given Geometric Progression:
Sum of Infinite GP: [tex]\displaystyle \frac{a}{1-r}[/tex]

Plugging our values in this equation, we get:
Sum of Geometric Progression = [tex]\displaystyle \frac{\frac{1}{5} }{1 - \frac{1}{5} } = \frac{\frac{1}{5} }{\frac{5 - 1}{5} } = \frac{1}{4}[/tex]

Adding to find the actual answer:
[tex]\displaystyle (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = \frac{1}{4}[/tex]
[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = 2 + \frac{1}{4}[/tex]
[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = \frac{9}{4}[/tex]

The probability that Yasmin will not be offered a coupon on at least one of the days she visits the website will be;

⇒ 0.9375

The term probability refers to the likelihood of an event occurring

Given that;

The probability that a visitor is offered a coupon (p) = 50%

Now,

Since, The probability that a visitor is offered a coupon (p) = 50%

Hence, The probability that he gets coupon all 4 days is,

⇒ p (4) = p⁴

⇒ p (4) = (50%)⁴

⇒ p (4) = 0.0625

Hence, By using the complement rule, the probability that he is not offered a coupon at least one day is,

⇒ p' = 1 - 0.0625

⇒ p' = 0.9375

Thus, The probability that Yasmin will not be offered a coupon on at least one of the days she visits the website = 0.9375

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The initial mass of the sample after two days = 8483.45 kg

Given that,

It is known as exponential decay when a population or group of something is deteriorating and the quantity of decline is proportional to the size of the population. In an exponential decay, the overall value falls but the percentage that departs stays the same throughout time.

The exponential decay formula aids in determining the exponential drop, which is a rapid reduction over time. To calculate population decay, half-life, radioactivity decay, and other phenomena, one uses the exponential decay formula.

The standard  formula for this type of behavior which is written below:

A = [tex]Pe^{-rt}[/tex]  

Where

A refers the amount left after time t

P refers the initial amount at t = 0

r refers the rate

Here we have given that the mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of per day.

A sample of this radioactive substance was taken after two days.

And we need to find if the sample has a mass of today, then the initial mass of the sample.

Now, we have to substituting the values,

Let us assume,

P = 9575 kg

r = 0.12

t = 1

Then we get the equation as,

A = (9575 kg) [tex]e^{-0.12*1}[/tex]

When we simplify this one, then we get,

A = (9575 kg) [tex]e^{-0.12}[/tex]

A = (9575 kg) 0.886

A = 8483.45 kg

Therefore,

The initial mass of the sample after two days = 8483.45 kg

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Answer: 1350 kilometers

Step-by-step explanation: 300 kilometers per hour x 4.5 hours = 1350

H1: The treatment affected the patients' memories.The alternative hypothesis, H1, states that the treatment affected the patients' memories.

To test this hypothesis, the researcher needs to compare the test scores to the population mean of 50. The researcher will use a one-tailed t-test with a .01 level of significance. If the calculated t-value is greater than the critical value, then the null hypothesis will be rejected and the alternative hypothesis will be accepted.

To conduct the t-test, the researcher will need to calculate the mean of the patient's test scores, the standard deviation, and the t-value. The mean is calculated by taking the sum of the test scores and dividing by the number of test scores. The standard deviation is calculated by taking the square root of the sum of the squared deviations from the mean divided by the number of test scores minus one. The t-value is calculated by taking the difference between the mean of the patient's test scores and the population mean, divided by the standard deviation of the patient's test scores, multiplied by the square root of the number of test scores. If the calculated t-value is greater than the critical value, then the null hypothesis can be rejected and the alternative hypothesis can be accepted, indicating that the treatment did affect the patient's memories.

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Answer:

It will take approximately 20.454545454545455 weeks for the amount of water in the two tanks to be the same.

Step-by-step explanation:

To find the number of weeks it will take for the amount of water in the two tanks to be the same, we can set up the following equation:

675 - 4w = 900 - 7w

Then, we can solve for w by adding 4w to both sides and then adding 7w to both sides:

11w = 225

w = 225 / 11

thus, It will take approximately 20.454545454545455 weeks for the amount of water in the two tanks to be the same.

The percentage increase of Seraphina's speed will be A. 19.4%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

Given that Seraphina is driving two hours to visit her family. For the first hour, she traveled at a speed of 62 miles per hour. Then, in the second hour, she traveled at a speed of 74 miles per hour.

The percentage increase of Seraphina's speed will be:

= Increase in speed / Initial speed × 100

= (74 - 62) / 62 × 100

= 12 / 62 × 100

= 19.4%

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Answer:

  parallel

Step-by-step explanation:

You want to know the parallel/perpendicular status of the lines described by the equations ...

Parallel lines have the same slope. The slope is the coefficient of x when the equation is written in the form ...

  y = mx +b

as is the second equation.

The first equation can be put in that form by solving for y.

  2x -5y = 25 . . . . . . given equation

  2x -25 = 5y . . . . . . add 5y -25

  2/5x -5 = y . . . . . . divide by 5

The coefficient of x (slope) is 2/5, same as the second equation.

The lines are parallel.

__

Additional comment

Your graphing calculator can help you figure this out, too. The graphed lines are parallel.

Answer:

To determine how many miles Naomi's car can go on one gallon of gas, we first need to determine how many gallons of gas the car used to travel 15\tfrac{1}{2}15 2 1 ​ miles. We are told that the car used \frac{2}{5} 5 2 ​ of a gallon to travel this distance, so we can multiply this value by 15\tfrac{1}{2}15 2 1 ​ to get the total number of gallons used:

\frac{2}{5} \cdot 15\tfrac{1}{2} = 9

Therefore, the car used 9 gallons of gas to travel 15\tfrac{1}{2}15 2 1 ​ miles. To determine how many miles the car can go on one gallon of gas, we need to divide the total number of miles traveled by the number of gallons used:

15\tfrac{1}{2} \div 9 = \frac{31}{18}

This means that the car can go 31/18 miles on one gallon of gas. Since this fraction is not in simplest form, we can further simplify it by dividing the numerator and denominator by the greatest common factor, which is 3:

\frac{31}{18} \div \frac{3}{3} = \frac{31}{18} \cdot \frac{3}{3} = \frac{31 \cdot 3}{18 \cdot 3} = \frac{93}{54}

Therefore, the car can go 93/54 miles on one gallon of gas. This fraction can be further simplified by dividing the numerator and denominator by the greatest common factor, which is 1:

\frac{93}{54} \div \frac{1}{1} = \frac{93}{54} \cdot \frac{1}{1} = \frac{93 \cdot 1}{54 \cdot 1} = \frac{93}{54}

Therefore, the final answer is that the car can go 93/54 miles on one gallon of gas.

Answer:

look at the explanation below

Step-by-step explanation:

The cube root of a number can be determined by using the prime factorization method. In order to find the cube root of a number:

Step 1: Start with the prime factorization of the given number.

Step 2: Then, divide the factors obtained into groups containing the same factors.

Step 3: After that, remove the cube root symbol and multiply the factors to get the answer. If there is any factor left that cannot be divided equally into groups of three, that means the given number not a perfect cube and we cannot find the cube root of that number

i hope this helps

Answer:

Concave Up: (-∞, [tex]-\sqrt{\frac{5}{3}}[/tex]), ([tex]\sqrt{\frac{5}{3}}[/tex], ∞)

Concave Down: ([tex]-\sqrt{\frac{5}{3}[/tex],[tex]\sqrt{\frac{5}{3}[/tex])

Points of Inflection: (-1.2910, 2.1111), (1.2910, 2.1111)

Step-by-step explanation:

To find the concavity of a function, we need to take the second derivative.

y' = 4x^3 - 20x

y'' = 12x^2 - 20

Finding the points of inflection involves setting the second derivative equal to 0. Add 20 over, divide by 12, and take the square root. The positive and negative square roots of 5/3 are the potential points of inflection.

Setting up a number line can help to determine concavity. Let's plug in -2 into the second derivative. From this, we have found that from negative infinity to the negative square root of 5/3, the graph is concave up, as f''(-2) > 0. f''(0) < 0, so from the negative square root of 5/3 to the positive square root of 5/3, the graph is concave down. f''(2) is also > 0, and therefore from the positive square root of 5/3 to infinity, the graph is concave up.

Since the graph shifted direction at both potential points of inflection, they are both actually points of inflection. To find the y-values for each point of inflection, plug the x-value back into the original polynomial equation.

Answer:

Step-by-step explanation:

6.5

The number of cast members are in the play given the equation is 16 cast members

7(210 – c) = 1,358

where,

7(210 – c) = 1,358

open parenthesis

1,470 - 7c = 1,358

Subtract 1,470 from both sides

- 7c = 1,358 - 1,470

- 7c = -112

divide both sides of by -7

c = -112 / -7

c = 16

Therefore, there are 16 cast members in the play.

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Answer:

The tallest player on the team was 78 inches tall

Step-by-step explanation: