WILL GIVE BRAINLIEST Patrick decided to start his own business. his business made 35,000 the first year his profits have increased annually by an average of 2.5%

a. write and iterative (explicit) rule to model the sequence formed by patricks profits each year. Show your work

b. use the rule you wrote to determine what the profits will be after twelve years from the start of his business. round your answer to the nearest dollar. do not round until the end! show all fo your work

Answer:

23

Step-by-step explanation:

The notation (f∘g)(1) means f(g(1)). We can first find g(1), then use that value as the argument to the f function.

g(1) = 2·1-6 = -4

f(-4) = -4(-4)+7 = 16+7 = 23

DC = [tex]\frac{5}{2}[/tex] = 2.5

since the triangles are similar then the ratios of corresponding sides are equal

[tex]\frac{AC}{AD}[/tex] = [tex]\frac{BC}{DE}[/tex]

[tex]\frac{7.5+DC}{7.5}[/tex] = [tex]\frac{8}{6}[/tex] (cross-multiply )

45 + 6DC = 60

6DC = 60 - 45 = 15 ( divide both sides by 6 )

DC = [tex]\frac{5}{2}[/tex]

View the image to see how I solved this problem.

There is an obvious factor of x², so we can reduce this to the problem of finding zeros of a quadratic by factoring that out. Then, we can determine the zeros of the quadratic factor to complete the finding of zeros for the function.

A factor of x² can be factored out, leaving ...

... f(x) = x²(x² +x +4)

The latter factor has only complex zeros. It can be rewritten by completing the square.

... x² +x +4 = (x² +x +1/4) +(3 3/4) = (x +1/2)² +(3 3/4)

So, the real zeros are where x² = 0, at x = 0. The complex zeros are where the above expression is zero, ...

... (x +0.5)² +3.75 = 0

... (x +0.5)² = -3.75

... x + 0.5 = √-3.75 = ±0.5i√15

... x = -0.5(1 ±i√15)

The function zeros are 0 (multiplicity 2) and -0.5±0.5i√15.

Answer: First option. y-15=5(x-3)

Solution:

We can take any pair of points of the table. For example:

P1=(3, 15)=(x1, y1)→x1=3, y1=15

P2=(5, 25)=(x2,y2)→x2=5, y2=25

And we can find the slope m using the following formula:

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

m=(25-15)/(5-3)

m=(10)/(2)

m=5

Now we can apply the point-slope formula to find the equation of the right line:

y-y1=m(x-x1)

Replacing y1=15, m=5, and x1=3

y-15=5(x-3)

The equation in point-slope form that represents the plant's growth over time would be 'y - 9 = 3x', given that the y-intercept is 9 and the slope is 3.

Based on the information given, it is clear that the y-intercept where the line intersects the y-axis is 9 and the slope of the line is 3. We know that y stands for the height of the plant and x for time in months. Using these values, the equation in point-slope form, which is normally written as y - y1 = m(x - x1) where m is the slope and (x1, y1) is a given point on the line, can be simplified assuming that x1=0 and y1 is our y-intercept which is 9.

Therefore, the equation of the line that represents the growth of the plant over time in point-slope form would be y - 9 = 3x.

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the new price is reduced by 10% of $3000.

10% of $3000 is one tenth of 3000, so 3000/10 = $300

so the original price was reduced by $300 to be $2700

Answer: Please, see the attached file.

Thanks.

Solution:

We can graph using the intercepts:

(1) y-intercept, when x=0

y=4x-3→y=4(0)-3→y=0-3→y=-3

Point=(x,y)=(0,-3)

(2) x-intercept, when y=0

y=4x-3→0=4x-3

Solving for x: Adding 3 both sides of the equation:

0+3=4x-3+3

3=4x

Dividing both sides of the equation by 4:

3/4=4x/4

3/4=x

x=3/4=0.75

Point=(x,y)=(3/4,0)=(0.75,0)

With these pair of points (0, -3) and (0.75,0) we can draw the right line

EXPLANATION

The nth term of the sequence is given by

[tex]U_n=a+(n-1)d [/tex]

Where

[tex]a[/tex]

is the first term and

[tex]d[/tex]

is the constant difference.

We were given that,

[tex]a=6[/tex]

S we just need the common difference to write the nth term.

We can get that from another information given to us.

We were also given that the 4th term is 6. This gives the equation.

[tex]a+3d=-6[/tex]

We substitute

[tex]a=6[/tex]

to obtain

[tex]6+3d=-6[/tex]

Or

[tex]2+d=-2[/tex]

This implies,

[tex]d=-2-2[/tex]

[tex]d=-4[/tex]

We substitute these values into the general formula to obtain,

[tex]U_n=6+(n-1)\times-4[/tex]

This gives us,

[tex]U_n=6+-4n+4[/tex]

[tex]U_n=10-4n[/tex]

Hence the nth term of the sequence is,

[tex]10-4n[/tex]

[tex]a_{n}[/tex] = 10 - 4n

this is an arithmetic sequence with n th term

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1 )d

where [tex]a_{1}[/tex] is the first term and d the common difference

given [tex]a_{4}[/tex] = - 6, then

6 + 3d = - 6 ( subtract 6 from both sides )

3d = - 12 ( divide both sides by 3 )

d = - 4 ← common difference hence

[tex]a_{n}[/tex] = 6 - 4 (n - 1 ) = 6 - 4n + 4 = 10 - 4n

Your answer is C.The relation passed the vertical line test.

Answer:

22.9 m

Step-by-step explanation:

Circumference = π × diameter

Using a calculator to evaluate 7.3π, we get 22.933626...

Rounding this to the nearest tenth gives 22.9. Units are meters.

The circumference of a circle with a diameter of 7.3m is approximately 22.9 meters.

The circumference of a circle is calculated by using the formula C = πd, where 'C' is the circumference and 'd' is the diameter. Given that the diameter of the circle is 7.3 m, you can plug this value into the formula to find the circumference.

So, C = π × 7.3

To find the circumference of a circle with diameter 7.3m, we can use the formula C = π x d, where C is the circumference and d is the diameter. Plugging in the given value, we get C = 3.14 x 7.3 = 22.922. Rounding to the nearest tenth, the circumference is approximately 22.9 meters.

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Answer: [tex]x^4[/tex]

Step-by-step explanation:

Here, the given expressions are,

[tex]x^4[/tex]

[tex]x^5[/tex]

The factors of [tex]x^4[/tex] = x × x × x × x

While, the factors of [tex]x^5[/tex] = x × x × x × x × x

Hence, the common factors = x × x × x × x = [tex]x^4[/tex]  

So, the greatest common factor of the given expression is [tex]x^4[/tex]          

Answer:

A. x4

Step-by-step explanation:

A plot of the points shows you the triangle is an acute triangle.

_____

All angles are less than 90°.

A graph shows that the best choice is ...

... b. 2.3

_____

Finding real roots of higher-degree polynomials is often done most easily with the help of a graphing calculator.

Substitute the value of the variable into the expression and simplify.

1. 24

2. 17

Initial amount: $210,000

Setting aside: $50,000

Remaining: $160,000

3/4 of remaining amount: 160,000 times 0.75 = $120,000

1/4 of remaining amount: 160,000 times 0.25 = $40,000

Distributive property: ⇒ a(b+c)=ab+ac

First you had to rewrite down as the nine and its should be three times three is equal to nine. Then you rewrite down as the twenty-seven and its should be nine times three is equal to twenty-seven. Next, you rewrite down as fifteen and its should be five times three is equal to fifteen.

And it gave us ⇒ [tex]=5*3y+9*3-3*3x[/tex].

Then you had to factor out by the common term of three.

And it gave us ⇒ [tex]3(5y+9-3x)[/tex]

Final answer ⇒ [tex]\boxed{=3(5y+9-3x)}[/tex]

Hope this helps!

And thank you for posting your question at here on brainly, and have a great day.

-Charlie

All 3 terms have a common factor 3 which we can take out

=3 ( 9 - 3x + 5y )

21.6 units

Calculate the length of the 2 inclined sides using the distance formula

d = √(x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 3, 3 ) and (x₂, y₂ ) = (3, 4 )

d = √(3 + 3 )² + (4 - 3)² = √(36 + 1 ) = √37

repeat for (x₁, y₁ ) = (- 3, 3 ) and (x₂, y₂ ) = (3, - 3 )

d = √(3 + 3 )² + (- 3 - 3 )² = √(36 + 36 ) = √72

the vertical side has a length of 7 units

perimeter = √37 + √72 + 7 = 21.6 ( nearest tenth of a unit )

The perimeter of the triangle shown on the coordinate plane is 15.5 units

The perimeter of the triangle is the sum of the lengths of its three sides. To find the lengths of the sides, we can use the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

The coordinates of the three points are:

A = (0, 0)

B = (10, 0)

C = (5, 10)

The length of side AB is:

distance from A to B = sqrt((10 - 0)^2 + (0 - 0)^2) = sqrt(10^2) = 10

The length of side BC is:

distance from B to C = sqrt((5 - 10)^2 + (10 - 0)^2) = sqrt((-5)^2 + 10^2) = sqrt(125) = 5 \sqrt{5}

The length of side AC is:

distance from A to C = sqrt((5 - 0)^2 + (10 - 0)^2) = sqrt(5^2 + 10^2) = sqrt(125) = 5 \sqrt{5}

Therefore, the perimeter of the triangle is:

perimeter = AB + BC + AC = 10 + 5 \sqrt{5} + 5 \sqrt{5} = 10 + 10 \sqrt{5}

To the nearest tenth of a unit, the perimeter of the triangle is 15.5 units.

Therefore, the answer is 15.5 units.

For such more question on perimeter

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Answer:

7x+6 = 5(x+6)

Step-by-step explanation:

x represents Harry's age now, so 7x represents Nick's age now. (Nick is 7 times as old as Harry.)

In 6 years, Harry's age will be x+6.

In 6 years, Nick's age will be 7x+6, which is 5 times Harry's age at that time, 5(x+6). Hence an appropriate equation is ...

... 7x+6 = 5(x+6)

_____

Please note that finding the value of x does not give the answer to the question. We are asked for Harry's age in 6 years, so the answer is x+6 (=18).

Answer:

Its D) aka the last option

Step-by-step explanation:

Try this solution (see the attachment, there is not the only way).

The short explanation: the target - to prove, PN≠OM; PN⊥OM; point S is midpoint of OM&PN, - the properties of rhombus.

A) The price elasticity of demand is given by

... Ed = (dx/dp)·(p/x)

... = -250·(15/(9500-250·15)) ≈ -0.652

B) This value has a magnitude less than 1, so price can be increased to increase revenue.

_____

The price at which Ed has a magnitude of 1 is ...

... 250p/(9500 -250p) = 1

... 250p = 9500 -250p

... 500p = 9500

... p = 9500/500 = 19

Revenue will increase as price increases up to $19 per pair.

Answer:

2

Step-by-step explanation:

Answer:

Evaluate from left to right

Evaluate using order of operations

Step-by-step explanation:

To evaluate any complex expression that contains addition, subtraction , multiply or divide, exponents , parenthesis etc we use order of operation.

Order of operation is PEMDAS

To evaluate , first we simplify the parenthesis part and then exponents

Then do the multiplication and division from left to right.

Finally we do addition and subtraction from left to right

So the rules for evaluating a complex expression is

Evaluate from left to right

Evaluate using order of operations

(A) Subtracting the right side from both sides, we get ...

... (20 -4x) -(12 -x +8 -3x) = 0

... (20 -12 -8) +x(-4 +1 +3) = 0

... 0 = 0 . . . . . true for all values of x (infinite solutions)

(B) Subtracting the right side from both sides, we get ...

... (5x +4x -3) -(24 +8x) = 0

... x(5 +4 -8) +(-3 -24) = 0

... x -27 = 0

... x = 27 . . . . . . (one solution)

(C) Subtracting the right side from both sides, we get ...

... (5x +6) -(2x +6 +3x -15) = 0

... x(5 -2 -3) +(6 -6 +15) = 0

... 15 = 0 . . . . . . . not true for any value of x (no solutions)

(d)

This equation does not factor, but we can solve using the quadratic formula

x = ( - b ± √(b² - 4ac) )/ 2a

given the equation in standard form : ax² + bx + c = 0

divide through by - 1, to obtain

x² + 7x + 2 = 0

with a = 1, b = 7 and c = 2, then

x = ( - 7 ± √(49 - 8) ) / 2

  = ( - 7 ± √41 ) / 2

x = - [tex]\frac{7}{2}[/tex] ± √41 / 2 → (d)

Yes.  Notice that the Pythagorean Theorem applies here.  3^2 + 4^2 = 5^2, so this triangle is a right triangle.

C.) Dilation changes the size