Tn=n^2+bn+c. Find the values of b and c if the sequences starts with - 1,2,7,14,..​

Answer:

x = 68°

Step-by-step explanation:

cos x = 10/27

cos x = 0.3704

x = 68.26°

Answer:

68

Step-by-step explanation:

Cosine=Adjacent/Hyp.

Cos(x)=10/27, or 0.37

Cos^-1(0.37)=68.3 degrees

\(w^2 - 6w + 4\) is a polynomial that represents how much more profit is earned by selling w apple trees than w pear trees.

The profit earned by selling w pear trees is 2w + 10

To find the difference in profit, we need to subtract the profit earned by selling w pear trees from the profit earned by selling w apple trees:

\((w^2 - 4w + 14) - (2w + 10)\)

Simplifying the expression:

\(w^2 - 6w + 4\)

Therefore, the polynomial that represents how much more profit is earned by selling w apple trees than w pear trees is \(w^2 - 6w + 4\).

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Answer: The equation of a circle with center (a,b) and radius r is given by:

(x - a)^2 + (y - b)^2 = r^2

In this case, the center is (9,10) and the point on the circle is (7,4). To find the radius, we can use the distance formula between the center and the point on the circle:

r = sqrt((7 - 9)^2 + (4 - 10)^2) = sqrt((-2)^2 + (-6)^2) = sqrt(40)

So, the equation of the circle is:

(x - 9)^2 + (y - 10)^2 = 40

Alternatively, we can also expand the equation to get:

x^2 - 18x + 81 + y^2 - 20y + 100 = 40

Simplifying and rearranging, we get:

x^2 + y^2 - 18x - 20y + 41 = 0

Therefore, the equation of the circle is either (x - 9)^2 + (y - 10)^2 = 40 or x^2 + y^2 - 18x - 20y + 41 = 0.

Step-by-step explanation:

Answer:

The slope is -4 and the y-intercept is 8.

Step-by-step explanation:

y+4x=8

y=8-4x

y=-4x+8

y=mx+b where m=slope and b=y-intercept.

Hello!

The equation of this line is written in slope-intercept form (y=mx+b)

Where

m is the slope

b is the y-intercept

m is 4

b is 8

Hope it helps!

If you have any questions, feel free to ask! :)

~An excited gal

\(MagicalNature\) here to help

The profit earned if 53 mowers are sold is $1104.50.

To find the profit polynomial, we need to subtract the cost polynomial from the revenue polynomial:

Profit = Revenue - Cost

P(x) = R(x) - C(x)

P(x) = (-0.5x^2 + 91x) - (38x + 300)

P(x) = -0.5x^2 + 53x - 300

So the profit polynomial is P(x) = -0.5x^2 + 53x - 300.

To find the profit earned if 53 mowers are sold, we substitute x = 53 into the profit polynomial:

P(53) = -0.5(53)^2 + 53(53) - 300

P(53) = -0.5(2809) + 2809 - 300

P(53) = -1404.5 + 2509

P(53) = 1104.5

Therefore, the profit earned if 53 mowers are sold is $1104.50.

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Answer:

Step-by-step explanation:

base area=41.57 in²

height=9 in

volume=41.57×9=374.13 in³

Answer: 1.6

Step-by-step explanation:

each golf is 1.6 ounces and you 20 golf balls in order to reach 32 ounces

Answer:

shown below

Step-by-step explanation:

golf balls per ounce = 5/8 or 0.625

ounces per gold ball = 8/5 or 1.6

Answer:

Part 1. 7 inches (longer piece)

Part 2: 5 inches (shorter piece)

Step-by-step explanation:

There is 12 inches in total, given that one piece is 5 inches longer, the other part of the 5 inches would be 7 inches which is the longer side.

5 inches would be the shorter side.

Answer:

correct me if i'm wrong but it's 57.32 degrees?

The final answer is (f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

To find the composite functions (f o g)(x) and (g o f)(x), we need to substitute one function into the other.

(f o g)(x):

To find (f o g)(x), we substitute g(x) into f(x):

(f o g)(x) = f(g(x))

Let's substitute g(x) = x^2 - 8 into f(x) = x^2 + 8:

(f o g)(x) = f(g(x)) = f(x^2 - 8)

Now we replace x in f(x^2 - 8) with x^2 - 8:

(f o g)(x) = (x^2 - 8)^2 + 8

Simplifying further:

(f o g)(x) = x^4 - 16x^2 + 64 + 8

(f o g)(x) = x^4 - 16x^2 + 72

Therefore, (f o g)(x) = x^4 - 16x^2 + 72.

(g o f)(x):

To find (g o f)(x), we substitute f(x) into g(x):

(g o f)(x) = g(f(x))

Let's substitute f(x) = x^2 + 8 into g(x) = x^2 - 8:

(g o f)(x) = g(f(x)) = g(x^2 + 8)

Now we replace x in g(x^2 + 8) with x^2 + 8:

(g o f)(x) = (x^2 + 8)^2 - 8

Simplifying further:

(g o f)(x) = x^4 + 16x^2 + 64 - 8

(g o f)(x) = x^4 + 16x^2 + 56

Therefore, (g o f)(x) = x^4 + 16x^2 + 56.

(f o g)(2):

To find (f o g)(2), we substitute x = 2 into the expression (f o g)(x) = x^4 - 16x^2 + 72:

(f o g)(2) = 2^4 - 16(2)^2 + 72

(f o g)(2) = 16 - 64 + 72

(f o g)(2) = 24

Therefore, (f o g)(2) = 24.

In summary:

(f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

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Answer:

Step-by-step explanation:

sp = 504

gain = 12%

in this case

sp =100%+12%=504

112%=504

1%=504/112 =4.5

100%=450

so cost =$450

Hope im correct, if i am im glad to be of service.

Answer:

I Believe your answer is B, put all the numbers in order then find the middle number

Step-by-step explanation:

it may be thought of as the "middle" value of a data set. For example, in the data set {1, 3, 3, 6, 7, 8, 9}, the median is 6,

\(\bold{Heya!}\)

Because you will always have to put the numbers from the smallest, and to the Iargest/biggest Then you need to find the middle number and that's how you will get your answer from that point of view.

Hopefully This Helps ! ~

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\(\underline{Answer :}\)

Jaceysan ~

Answer:

The length of the hypotenuse of each right triangle is approximately 12.7 inches, rounded to the nearest tenth.

Step-by-step explanation:

Let's start by finding the length of one side of the square posterboard.

Since the perimeter is 36 inches, and a square has four equal sides, we can divide the perimeter by 4 to get the length of one side:

36 ÷ 4 = 9

So each side of the square posterboard is 9 inches long.

When Miranda cuts the posterboard along a diagonal, she forms two right triangles. Let's call the length of the hypotenuse of each right triangle "c".

We can use the Pythagorean theorem to find the length of "c":

a² + b² = c²

Since the posterboard is a square, each of the legs of the right triangle has a length of 9 inches.

9² + 9² = c²

81 + 81 = c²

162 = c²

c ≈ 12.7

So, the length of the hypotenuse of each right triangle is approximately 12.7 inches, rounded to the nearest tenth.

The value of the circumference (C) of a circle, having a radius (r) = 0.8695 mm, using the formula C = 2πr, is calculated to be 5.4632296245926504416865368435231‬ mm.

A circle is a shape formed by all points in a plane that are at a particular distance from the center.

The linear distance around a circle is defined as its circumference. In other words, if a circle is opened to produce a straight line, the length of that line equals the circumference of the circle.

The formula for the circumference of a circle is given:

C = 2πr,

where C is the circumference of the circle, r is its radius, and π is a constant.

We are asked to find the circumference of the circle (C), given its radius (r) = 0.8695 mm.

Using the formula of the circumference C = 2πr, we can find the circumference as:

C = 2*π*(0.8695) mm,

or, C = 5.4632296245926504416865368435231‬ mm.

Thus, the value of the circumference (C) of a circle, having a radius (r) = 0.8695 mm, using the formula C = 2πr, is calculated to be 5.4632296245926504416865368435231‬ mm.

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Answer: 1

Step-by-step explanation:

Let's look at two points on this line (0, 1), and (1, 2)

Using the slope formula (\(\frac{(y_2-y_1)}{(x_2-x_1)}\))

\(\frac{(2-1)}{(1-0)} =\frac{1}{1}=1\)

Hope it helps :)

Answer:

bro be more specific plssssaass

Answer:

y = \(\frac{3}{4}\) x + 14

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 3, - 2) and (x₂, y₂ ) = (5, 4) ← 2 points on the line

m = \(\frac{4-(-2)}{5-(-3)}\) = \(\frac{4+2}{5+3}\) = \(\frac{6}{8}\) = \(\frac{3}{4}\) , then

y = \(\frac{3}{4}\) x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (5, 4 )

4 = \(\frac{3}{4}\) (5) + c = \(\frac{15}{4}\) + c ( subtract \(\frac{15}{4}\) from both sides )

4 - \(\frac{15}{4}\) = c , then

c = \(\frac{16}{4}\) - \(\frac{15}{4}\) = \(\frac{1}{4}\)

y = \(\frac{3}{4}\) x + \(\frac{1}{4}\) ← equation of line

Answer: B(t) = 16*(1.2)t

Step-by-step explanation:

the solutions to the equation \(2x^2 - x - 3 = 0\) are x = 1.5 or x = -0.5.

The square root of 25 can be expressed simply as 5:

x = (1 ± 5) / 4

This provides us with two potential answers:

x = (1 + 5) / 4 = 1.5

or

x = (1 - 5) / 4 = -0.5

The square root of a negative number is not a real number, so this equation does not have a real solution using geometric mean.

By dividing the sum of the given numbers by the entire number of numbers, the mean—the average of the given numbers—is determined.

Based on the provided data set, the fundamental formula to determine the mean is calculated. When calculating the mean, every term in the data set is taken into account. The ratio between the total number of terms and the sum of all the terms provides the general formula for the mean. Hence, we may state;

Mean is equal to the product of the given data and the total amount of data.

from the question:

The following formula can be used to find x using geometric mean:

\(x = \sqrt{(ab)}\)

where a and b are the two numbers whose geometric means we're interested in finding.

The two roots of the quadratic equation \(ax^2 + bx + c = 0\) in standard form can be used here as a and b. Applying the previous solutions, we obtain:

\(x = \sqrt{(1.5 (-0.5)}\)

\(x = \sqrt{(-0.75)}\)

As the square root of a negative number is not a real number, the geometric mean method cannot find a real solution to this problem.

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Here, lots of questions are asking.

The study of shapes, sizes, locations, and qualities of objects in space is referred to as geometry. It covers the examination of points, lines, angles, planes, and solid figures as well as their interrelationships. In areas including architecture, engineering, physics, and computer graphics, among others, geometry is used in real-world settings. It is frequently taught to kids starting at a young age and is a crucial component of mathematics education.

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Answer:

Add 3 to both sides.

Step-by-step explanation:

Add 3 to both sides.

This is how you figure it out. Imagine you have a value you want to use for x on the left side, such as 5.

In other words, evaluate 3/4 x - 3 for x = 5

The left side turns into 3/4 × 5 - 3.

What order of operations would you use now on the left side.

1) Multiply 3/4 by 5

2) Subtract -3

To solve an equation, you do the opposite operations in the opposite order.

Since to evaluate the left side with a number for x, you end by subtracting 3, to solve the equation you start by adding 3. Then you divide by 3/4.

Answer: add 3 to both sides

Suppose that g is a function from A to B and F is a function from B to C.

a)  If fog is onto, then f must also be onto.

Assume that f∘g  is onto. Let c ∈ C . Since f∘g is onto, then is a ∈A such that c = (f∘g) (a) by the definition of onto function. By the definition of function composition, c = f(g(a)). Let b = g(a). This b belongs to B  and is such that c = f(b) . Therefore, for every c ∈ C , there is b ∈ B such that c = f(b). By the definition of onto function, f is onto.

(b) If fog is one-to-one, then g must also be one-to-one.

Let \(a_1,a_2\) ∈ A such that \(g(a_1)=g(a_2)\). Then

(f∘g)\((a_1)\)  = \(f(g(a_1))=f(g(a_2))\) = (f∘g)\((a_2)\)

Since f∘g is one - to - one, \(a_1=a_2\). Therefore, for all \(a_1,a_2\) ∈ A such that

\(g(a_1)=g(a_2)\), \(a_1=a_2\). By the definition  of one-to-one function, g  is one-to-one. \(b_1=g(a_1)=g(a_2)\)

(c)  If fog is a bijection, then g is onto if and only if f is one-to-one.

Assume that f∘g  is a bijection.

Assume that g is onto. Let \(b_1,b_2\) ∈ B such that \(f(b_1)=f(b_2)\). Since g is onto,  by the definition of onto function, there are \(a_1,a_2\) ∈A such that

\(b_1=g(a_1) and b_2=g(a_2)\) We have

(fog)\((a_1)\) = \(f(g(a_1) )=f(b_1)\)

= \(f(b_2) =f(g(a_2))= (fog)(a_2)\)

Since fog is a bijection, it is one-to-one, hence \(a_1=a_2\), and

\(b_1=g(a_1)=g(a_2)=b_2\)

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The graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

The functions for this problem are defined as follows:

When a function is multiplied by 2, we have that it is vertically stretched by a factor of 2.

Hence the graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

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Answer:

x=5

Step-by-step explanation:

4×3x=12x

4×-2=-8

(12×x)-8=52

So you balance it to make it:

12x=60

60÷12=5

I hope this helps and please give brainliest and thank me

Step-by-step explanation:

Open bracket

use 4 to multiply what is in the bracket

12x - 8 = 52

collect like terms (CLT)

12x = 52 + 8

12x = 60

divide both sides by 12

x = 5

The ball is in the air for approximately 2.8 + √7 seconds, which rounds to 5.2 seconds when rounded to one decimal place.To write the equation in vertex form, we need to complete the square.

The given equation is h = -4.9t² + 27.44t + 0.584. We can rewrite it as:

h = -4.9(t² - 5.6t) + 0.584

Now, we want to complete the square inside the parentheses. To do this, we need to add and subtract the square of half the coefficient of t. In this case, the coefficient is -5.6, so we have:

h = -4.9(t² - 5.6t + (5.6/2)² - (5.6/2)²) + 0.584

Simplifying, we get:

h = -4.9((t - 2.8)² - 2.8²) + 0.584

Expanding further:

h = -4.9(t - 2.8)² + 4.9(2.8)² + 0.584

Thus, the equation in vertex form is: h = -4.9(t - 2.8)² + 34.328

b) The ball's height when it was hit can be found by evaluating the equation at t = 0:

h = -4.9(0 - 2.8)² + 34.328

h = -4.9(-2.8)² + 4.328

h = -4.9(7.84) + 34.328

h ≈ 0.784 meters

To find the time at which the ball reaches its maximum height, we can use the fact that the maximum height occurs at the vertex of the parabolic equation. The vertex of a parabola in the form h = a(t - h₀)² + k is given by (h₀, k). Comparing this to our equation, we can see that the vertex occurs at t = 2.8 and h = 34.328. Therefore, the ball reaches its maximum height at 2.8 seconds, and the maximum height is 34.328 meters.

The total time the ball is in the air can be determined by finding the time it takes for the ball to reach the ground. When the ball hits the ground, its height is 0. To find this time, we can set the equation equal to 0 and solve for t:

0 = -4.9(t - 2.8)² + 34.328

4.9(t - 2.8)² = 34.328

(t - 2.8)² ≈ 7

t - 2.8 ≈ ±√7

t ≈ 2.8 ± √7

Since time cannot be negative in this context, we can ignore the negative value.

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The city that you should live in if you want a greater variability in temperature is city Y.

In order to determine the city that has the greater variability in temperature, the interquartile range has to be determined. The interquartile range is used to measure the variation in a dataset.

The interquartile range is the difference between the third quartile and the first quartile.

interquartile range = third quartile - first quartile

Interquartile range for City X = 50 - 30 = 20

Interquartile range for City Y = 50 - 25 = 25

The interquartile range for city Y is greater than that of city X. This means that city Y has a greater variation in temperature.

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