Mike deposited $850 into the bank in July. From July to December, the amount of money he deposited into the bank increases by 25% per month. What's the total amount of money in his account after December? Round your answer to the nearest penny.

Answer:

[tex]x^{2} -2x-3 or the factored form (x+1)(x-3)[/tex]

Step-by-step explanation:

p(x) -q(x)=

[tex]x^{2} -x-6-x+3\\=x^{2} -2x-3[/tex]

Answer:

y < 1

Step-by-step explanation:

8y - 5 < 3

To solve this inequality,  add 5 to both sides.

8y - 5+5< 3+5

8y < 8

Divide by 8 on both sides

8y/8 < 8/8

y <1

Answer:

D

Step-by-step explanation:

The pentagon has 5 interior angles that add up to 360. To find the angle of rotational symmetry, divide 360 by 5 (you get 72). So if you rotated the shape 72 degrees, it will map onto itself. 72 times 2 is 144, and that's rotating the shape 72 degrees twice, so it will stay the same.

A mathematical transformation that carries a pentagon onto itself is a rotation by 72 degrees or a multiple of 72 degrees, which are the internal angles of a regular pentagon.

The question is referring to certain mathematical transformations that can be applied to shapes, specifically a pentagon. A transformation that will carry a shape onto itself, maintaining its form, is a symmetry operation. For a pentagon, one of these transformations could be a rotation. For example, if you rotate the pentagon 72 degrees or a multiple of 72 degrees (such as 144, 216, 288 degrees, etc.), it will land on itself because 72 degrees represents each internal angle of a regular pentagon.

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Answer:14

Step-by-step explanation:

(4)(5)−6

=14

Answer:

(7)

error percentage is 0.6%

(8)

Graph-C

Step-by-step explanation:

(7)

we are given cube

Let's assume edge of cube =x

so, volume of cube will be

[tex]V(x)=x^3[/tex]

we are given

V=125000

so, we can find 'x'

[tex]125000=x^3[/tex]

[tex]x=50[/tex]

So,

[tex]a=50[/tex]

now, we can use linear approximation formula

[tex]L(x)=V(a)+(x-a)V'(a)[/tex]

[tex]L(x)=V(a)+(\Delta x)V'(a)[/tex]

we have

[tex]\Delta x=0.1[/tex]

we can plug a=50

[tex]L(x)=V(50)+(0.1)V'(50)[/tex]

[tex]V(x)=x^3[/tex]

we can find derivative

[tex]V'(x)=3x^2[/tex]

now, we can plug x=50

[tex]V'(50)=3(50)^2[/tex]

[tex]V'(50)=7500[/tex]

now, we can plug these values

and we get

[tex]L(x)=V(50)+(0.1)\times 7500[/tex]

[tex]L(x)=V(50)+750[/tex]

[tex]L(x)-V(50)=750[/tex]

so, error is

[tex]error=750[/tex]

now, we can find percentage error

Percentage is

[tex]=\frac{750}{125000}\times 100[/tex]

=0.6%

so, error percentage is 0.6%

(8)

we are given

[tex]s(t)=2e^{-1.5t}sin(2\pi t)[/tex]

We will find derivative

To get velocity , we will find derivative

[tex]s'(t)=\frac{d}{dt}\left(2e^{-1.5t}\sin \left(2\pi t\right)\right)[/tex]

we can use product rule

and we get

[tex]s'(t)=-3e^{-1.5t}sin(2\pi t)+4\pi e^{-1.5t} sin(2\pi t)[/tex]

so, we get velocity equation as

[tex]v(t)=-3e^{-1.5t}sin(2\pi t)+4\pi e^{-1.5t} sin(2\pi t)[/tex]

now, we can draw graph

we can see that firstly , we get maxima and then minima

so, our graph would be

graph-C........Answer

Final answer:

To estimate the percentage error in volume, use the tangent line approximation and find the derivative of the volume function. Then divide the change in volume by the actual volume and multiply by 100%.

Explanation:

To estimate the percentage error in volume, we need to find the derivative of the volume function with respect to the length of one edge of the cube. The volume of a cube is given by V = a^3, where a is the length of one edge of the cube. So, the volume function is V = a^3.

Using the tangent line approximation, we can approximate the change in volume as the derivative of the volume function multiplied by the change in length of one edge of the cube. The derivative of the volume function is dV/da = 3a^2. The change in length of one edge is ±0.1 cm. So, the change in volume is approximately dV = (3a^2) * (±0.1 cm).

To find the percentage error in volume, we divide the change in volume by the actual volume and multiply by 100%. The actual volume is 125,000 cm^3. So, the percentage error in volume is approximately [(3a^2) * (±0.1 cm)] / (125,000 cm^3) * 100%.

Answer:

Subtract the 4 additional poems from what was published first:

22 - 4 = 18

Now 18 is 2/3 of what she wrote.

To find the total poems written divide 18 by 2/3:

18 / 2/3 = 27

Sh wrote 27 poems total.

Answer:

10m-16

Step-by-step explanation:

3(4m-2)-2(m+5)

Distribute 3 into the equation

12m-6 than do the same with -2

-2m-10

combine like terms

10m-16

simplify

Equivalent expressions are expressions that have equal values

The equivalent expression is [tex]10m - 16[/tex]

The expression is given as:

Open the brackets

[tex]3(4m - 2) -2 (m + 5) = 12m - 6 - 2m - 10[/tex]

Collect like terms

[tex]3(4m - 2) -2 (m + 5) = 12m- 2m - 6 - 10[/tex]

Evaluate the like terms

[tex]3(4m - 2) -2 (m + 5) = 10m - 16[/tex]

Hence, the equivalent expression is [tex]10m - 16[/tex]

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Answer:

The simplified form of the equation is 9x^3/10y^2   Good Luck!

Step-by-step explanation:

Answer:

if you go to a site called math papa it gives you the answer and how to do it

Step-by-step explanation:

Answer:

z = 62

y = 117

Step-by-step explanation:

Z

118 and z are supplementary.

z + 118 = 180 Supplementary angles add to 180. Subtract 118 from both sides.

z = 180 - 118  Do the subtraction        

z = 62            Answer

Y

The interior angles of all quadrilaterals (convex) add up to 360 degrees.

y + z + 84 + 97 = 360           Given

62 + y + 84 + 97=360          Add

y + 243 = 360                       Subtract 243 from both sides

y = 360 - 243                        combine

y = 117                                    Answer  

Answer:

[tex]72^{\circ}[/tex] is the measure of the smallest angle in the hexagon.

Step-by-step explanation:

As, we know that the sum of all the angles is 720 degrees.

Given: The measures of the angles of the hexagon are in the extended ratio 4 : 5 : 5 : 8 : 9 : 9.

Let  x  be the number used to simplify the size of each angle.

Sum of all the measure angles is 720 degrees

⇒[tex]4x+5x+5x+8x+9x+9x = 720^{\circ}[/tex]

Combine like terms;

[tex]40x = 720^{\circ}[/tex]

Divide both sides by 40 we get;

[tex]x = \frac{720}{40} = 18[/tex]

The measure of angles are:

[tex]4x = 4 \times 18 = 72^{\circ}\\5x = 5 \times 18 = 90^{\circ}\\5x = 5 \times 18 = 90^{\circ}\\8x = 8 \times 18 = 144^{\circ}\\9x = 9 \times 18 = 162^{\circ}\\9x = 9 \times 18 = 162^{\circ}[/tex]

Therefore; the measure of the smallest angle in the hexagon is, [tex]72^{\circ}[/tex]

Answer:

The sign is positive.

Step-by-step explanation:

a > 0 and b < 0

So, a·b < 0

⇒ -4·a·b > 0

⇒ -4·a·b - 4·a·b > 0

Hence, the sign will be positive

Answer:

the answer is on top of me

Step-by-step explanation:

my mom is angry at me and im bored

Answer:

The average rate is 35 miles per hour

Step-by-step explanation:

To get from town A to town B takes 3 hours.  The distance is 100 miles

To get from town B to  town c takes 1 hours.  The distance is 40 miles

To find the average rate , we need to find the total distance and divide by the total time

Total distance = 100 + 40 = 140 miles

Total time = 3 hrs + 1 hr = 4 hours

distance = rate * time

140 miles = rate * 4 hours

140/4 = rate

35 = rate

The average rate is 35 miles per hour

QUESTION 1

The point  C(3.6, -0.4) divides AB in the ratio 3 : 2.

The coordinates of A are (-6, 5).

Let the coordinates of B be [tex](x_2,y_2)[/tex]

We use the formula:

[tex]x=\frac{mx_2+nx_1}{m+n}[/tex] to determine the x-coordinate of B.

We substitute the known values to obtain:

[tex]3.6=\frac{3x_2+2(-6)}{3+2}[/tex]

[tex]3.6=\frac{3x_2-12)}{5}[/tex]

[tex]3.6\times 5=3x_2-12[/tex]

[tex]18=3x_2-12[/tex]

[tex]18+12=3x_2[/tex]

[tex]30=3x_2[/tex]

This implies that:

[tex]x_2=10[/tex]

We also use the formula:

[tex]y=\frac{my_2+ny_1}{m+n}[/tex] to find the y-coordinate.

[tex]-0.4=\frac{3y_2+2(5)}{3+2}[/tex]

[tex]-0.4=\frac{3y_2+10}{5}[/tex]

[tex]-0.4\times 5=3y_2+10[/tex]

[tex]-2-10=3y_2[/tex]

[tex]-12=3y_2[/tex]

[tex]-4=y_2[/tex]

The coordinates of B are (10,-4)

QUESTION 2.

If point D divides CD in the ratio 4 : 5.

Then the coordinates of D are:

[tex](\frac{4(10)+5(3.6)}{4+5}, \frac{4(-4)+5(-0.4)}{4+5})[/tex]

[tex](\frac{58}{9}, \frac{-18}{9})[/tex]

The coordinates of D are [tex](\frac{58}{9}, -2)[/tex]

Answer:

5

Step-by-step explanation:

For direct variation y=kx, where k is the constant of proportionality

We need to get the equation in this form

3y = 15x

Divide each side by 3

3y/3 =15x/3

y = 5x

The constant is 5

Answer:

you put your divisor and add Dividend and see what that adds up to and get your answer

Step-by-step explanation:

Answer:

You add more 0

Step-by-step explanation:

Answer:

Range = 24

Step-by-step explanation:

Record of percentage

59, 61, 83, 67, 81, 80, 81

We need to find the range

To find the range , we order the numbers from smallest to largest.

Then Subtract the smallest number from largest number.

When we arrange the numbers it becomes

59, 61, 67, 80, 81, 81, 83

Smallest number is 59 and largest number is 83

Range = 83 - 59 =24

-3x + 6 = 2x - 24.

Add 3x to both sides.

6 = 5x - 24.

Add 24 to both sides.

30 = 5x.

Divide it all by 5.

x = 6.

Answer:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48

Step-by-step explanation:

4*1 = 4

4*2 = 8

4*3 = 12

and so on...

Answer:

4,8,12,16,20,24,28,32,36,40,44, and 48

Step-by-step explanation:

Answer:

15.8125 lb

Step-by-step explanation:

Answer:

15 lb. 13oz.

Step-by-step explanation:

no need

Answer:

g(x) = |x + 3|

Step-by-step explanation:

The x is replaced by x + 3

The equation of g(x) is | x + 3 | when g ( x ) is translated 3 units to the left

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs)

Horizontal shift (also called phase shift):

Given data ,

The function f(x) = | x | , this function is needed to be translated 3 units to the right. Therefore, the new function can be written as ,

g ( x ) = f ( x + 3 )

     = | x + 3 |

Hence, the equation of g(x) is | x + 3 |.

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Average rate of change formula:

[tex]\dfrac{\Delta y}{\Delta x}[/tex]

[tex]\Delta y=6-1=5\\\\\Delta x=4.95-0.40=4.55[/tex]

[tex]\dfrac{\Delta y}{\Delta x}=\dfrac{5}{4.55}=\dfrac{500}{455}=\dfrac{100}{91}\approx1.1[/tex]

Answer:

[tex]x^3-x^2(4+i\sqrt{3} )+x(5+i2\sqrt{3} )-(2+i\sqrt{3} )=0[/tex]

Step-by-step explanation:

We have given that this polynomial has the given zeroes of 1, 1, and [tex]2+i\sqrt{3}[/tex], we can express the polynomial in a factored form where each zero has the form x-a (where a is our zero):

polynomial= [tex](x-1) (x-1) (2+i\sqrt{3})[/tex]

                  =[tex](x^2+1-2x) (2+i\sqrt{3})[/tex]

                   =[tex]x^3-x^2(4+i\sqrt{3} )+x(5+i2\sqrt{3} )-(2+i\sqrt{3} )=0[/tex]

Answer:

Step-by-step explanation: The reason is is because when adding and subtracting integers, you flip the operation sign that will be used to solve the problem.So when you flip the sign of this equation, you subtract. So that's how your answer was 11/17. Also it is positive because the biggest number is positive so that is what the solution will be.

Please mark brainliest!!!!!!

Answer:

3

Step-by-step explanation:

Answer:no it is not reasonable

Step-by-step explanation: take the Max average number and multiply it by six, it only reaches 10.26

John's estimation of 28 units of electricity usage for the six houses on Philips Road is considered reasonable since it falls within the calculated possible range of 18.96 to 40.08 units.

To verify John's estimate, we need to consider the maximum and minimum electricity usage for the houses based on their given range of usage and time. On the high end, each house could use 1.71 units for 4 hours, which gives a total of 6.84 units per house.

Therefore, the total usage for all six houses would be 40.08 units (6 x 6.84 = 40.08). On the low end, each house could use 1.58 units for 2 hours, amounting to 3.16 units per house. The total for all houses would then be 18.96 units (6 x 3.16 = 18.96). Given this, John's estimate of 28 units falls within this range and can be considered reasonable.

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Answer:

60% of 30 is 18 and 40% of 30 is 12

18 x 12 = 216

12 x 10 = 120

216 + 120 = 336

Step-by-step explanation:

Answer: IN ORDER: 18,12,216,120,336

Step-by-step explanation: Got it right on TTM

Answer:

8/30 (Simplified answer: 4/15)

Step-by-step explanation:

Find common denominators. Note the what you do to the denominator, you do to the numerator.

Multiply 10 to both the denominator & numerator of 2/3, and multiply 3 to both the denominator & numerator of 4/10

(10/10)(2/3) - (3/3)(4/10)

Simplify.

(20/30) - (12/30)

Simplify. Combine the terms

(20/30) - (12/30) = (20 - 12)/30 = 8/30

Simplify the fraction

(8/30)/(2/2) = 4/15

~

Answer: Yes

Step-by-step explanation:

When two triangles are congruent they will have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position (if there is a turn or a flip), but they are there.

Answer:

{3, 5, 6, 7 }

Step-by-step explanation:

to find the range of f(x) substitute the given values of x from the domain into f(x)

f(- 3) = - (- 3) + 4 = 3 + 4 = 7

f(- 2) = - (- 2) + 4 = 2 + 4 = 6

f(- 1) = - (- 1) + 4 = 1 + 4 = 5

f(1) = - 1 + 4 = 3

range y ∈ {3, 5, 6 , 7 }