Simplify the expression to a + bi form:
(1 – 6i) + (12 + i)

Answer: 0.2

happy learning

Answer:

$600

Equation:

(Base) x (percent as a decimal) x (years) = interest

(B x .16 x 7.5 = 720)

Steps:

(Base) x (percent as a decimal) = (interest) / (years)

(B x .16 = 96)

Base = (interest / years) / (percent as a decimal)

(B = 600)

Answer:

$8,704

Step-by-step explanation:

Answer:

A. 17 feet

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

To write the equation of line when slope and one point is given

[tex]y2 - y1 = m(x2 - x1)[/tex]

here m = 3/4

(x1,y1) = 3,-2

Substitute all the values in Formula

[tex]y + 2 = \frac{3}{4} (x - 3) \\ y + 2 = \frac{3}{4} x - \frac{9}{4} \\ y = \frac{3}{4} x - \frac{9}{4} - 2 \\ = \frac{3}{4} x - \frac{17}{4} \\ 4y = 3x - 17 \\ - 3x + 4y = - 17[/tex]

multiply by 4 on both sides

[tex]4y = 3x - 17 \\ - 3x + 4y = - 17[/tex]

Answer:

221

Step-by-step explanation:

109×2+3=221, pattern is x2+3

--

4×2+3=11

11×2+3=25

25×2+3=53

53×2+3=109

Answer:

5+5+9+9 = 28 cm

Step-by-step explanation:

to determine perimeter add the length of each side (2 sides = 5cm and two sides = 9cm.)

Answer:

y =  4x - 3

Step-by-step explanation:

When writing an equation of a line, keep in mind that you always need the following information in order to determine the linear equation in slope-intercept form, y = mx + b:

1. 2 sets of ordered pairs (x, y)

2. Slope (m)

3. Y-intercept (b)

First, we need to choose 2 points from the graph to solve for the slope:

Let (x1, y1) = (0, -3)

(x2, y2) = (1, 1)

Use the following slope formula:

[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]

Substitute the values of the coordinates into the formula:

[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{1 - (-3)}{1 - 0} = \frac{1 + 3}{1} = \frac{4}{1} = 4[/tex]

Therefore, the slope (m) of the line = 4.

Next, we need the y-intercept, (b). The y-intercept is the y-coordinate of the point where the graph of the linear equation crosses the y-axis. The y-intercept is also the value of y when x = 0. The y-coordinate of the point (0, -3) is the y-intercept.  Hence, the y-intercept (b) = -3.

Given our slope, m = 4, and the y-intercept (b) = -3, the linear equation is:

y = 4x - 3

Please mark my answers as the Brainliest if you find my explanations/solution helpful :)

Answer:

-4/4 = -1

Step-by-step explanation:

yeah-ya...... right?

Answer:

B. The slope is –400

Answer: -400

Step-by-step explanation:

Answer:

12 Super Giant Pizzas

Step-by-step explanation:

36 ÷ 3 = 12

Answer:

Step-by-step explanation:

You will need to get 12 pizzas

Explanation:36÷3=12

Answer:

you are 15

Step-by-step explanation:

9-4=5

5x3=15

Answer:

The  tenths place

4 is in the tenths place of 7.486

Step-by-step explanation:

Answer:

38 meters below sea level.

Step-by-step explanation:

if the sub dives 155 BELOW sea level, this equals -155.

then it RISES 117 meters, which equals +117.

we can make this into an  equation

-155+117=-38!

the location of the sub is 38 meters below sea level.

Functions can be used to model real life scenarios

The function is given as:

[tex]\mathbf{V(t) = -t^3 + t^2 + 12t}[/tex]

(a) Sketch V(t)

See attachment for the graph of [tex]\mathbf{V(t) = -t^3 + t^2 + 12t}[/tex]

(b) The reasonable domain

t represents the number of weeks.

This means that: t cannot be negative.

So, the reasonable domain is: [tex]\mathbf{[0,\infty)}[/tex]

(c) Average rate of change from t = 0 to 2

This is calculated as:

[tex]\mathbf{m = \frac{V(a) - V(b)}{a - b}}[/tex]

So, we have:

[tex]\mathbf{m = \frac{V(2) - V(0)}{2 - 0}}[/tex]

[tex]\mathbf{m = \frac{V(2) - V(0)}{2}}[/tex]

Calculate V(2) and V(0)

[tex]\mathbf{V(2) = (-2)^3 + (2)^2 + 12 \times 2 = 20}[/tex]

[tex]\mathbf{V(0) = (0)^3 + (0)^2 + 12 \times 0 = 0}[/tex]

So, we have:

[tex]\mathbf{m = \frac{20 - 0}{2}}[/tex]

[tex]\mathbf{m = \frac{20}{2}}[/tex]

[tex]\mathbf{m = 10}[/tex]

Hence, the average rate of change from t = 0 to 2 is 20

(d) The instantaneous rate of change using limits

[tex]\mathbf{V(t) = -t^3 + t^2 + 12t}[/tex]

The instantaneous rate of change is calculated as:

[tex]\mathbf{V'(t) = \lim_{h \to \infty} \frac{V(t + h) - V(t)}{h}}[/tex]

So, we have:

[tex]\mathbf{V(t + h) = (-(t + h))^3 + (t + h)^2 + 12(t + h)}[/tex]

[tex]\mathbf{V(t + h) = (-t - h)^3 + (t + h)^2 + 12(t + h)}[/tex]

Expand

[tex]\mathbf{V(t + h) = (-t)^3 +3(-t)^2(-h) +3(-t)(-h)^2 + (-h)^3 + t^2 + 2th+ h^2 + 12t + 12h}[/tex][tex]\mathbf{V(t + h) = -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h}[/tex]

Subtract V(t) from both sides

[tex]\mathbf{V(t + h) - V(t)= -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h - V(t)}[/tex]

Substitute [tex]\mathbf{V(t) = -t^3 + t^2 + 12t}[/tex]

[tex]\mathbf{V(t + h) - V(t)= -t^3 -3t^2h -3th^2 - h^3 + t^2 + 2th+ h^2 + 12t + 12h +t^3 - t^2 - 12t}[/tex]

Cancel out common terms

[tex]\mathbf{V(t + h) - V(t)= -3t^2h -3th^2 - h^3 + 2th+ h^2 + 12h}[/tex]

[tex]\mathbf{V'(t) = \lim_{h \to \infty} \frac{V(t + h) - V(t)}{h}}[/tex] becomes

[tex]\mathbf{V'(t) = \lim_{h \to \infty} \frac{ -3t^2h -3th^2 - h^3 + 2th+ h^2 + 12h}{h}}[/tex]

[tex]\mathbf{V'(t) = \lim_{h \to \infty} -3t^2 -3th - h^2 + 2t+ h + 12}[/tex]

Limit h to 0

[tex]\mathbf{V'(t) = -3t^2 -3t\times 0 - 0^2 + 2t+ 0 + 12}[/tex]

[tex]\mathbf{V'(t) = -3t^2 + 2t + 12}[/tex]

(e) V(2) and V'(2)

Substitute 2 for t in V(t) and V'(t)

So, we have:

[tex]\mathbf{V(2) = (-2)^3 + (2)^2 + 12 \times 2 = 20}[/tex]

[tex]\mathbf{V'(2) = -3 \times 2^2 + 2 \times 2 + 12 = 4}[/tex]

Interpretation

V(2) means that, 20 people were infected after 2 weeks of the virus spread

V'(2) means that, the rate of infection of the virus after 2 weeks is 4 people per week

(f) Sketch the tangent line at (2,V(2))

See attachment for the tangent line

The slope of this line is:

[tex]\mathbf{m = \frac{V(2)}{2}}[/tex]

[tex]\mathbf{m = \frac{20}{2}}[/tex]

[tex]\mathbf{m = 10}[/tex]

The slope of the tangent line is 10

(g) Estimate V(2.1)

The value of 2.1 is

[tex]\mathbf{V(2.1) = (-2.1)^3 + (2.1)^2 + 12 \times 2.1}[/tex]

[tex]\mathbf{V(2.1) = 20.35}[/tex]

(h) The maximum number of people infected at the same time

Using the graph, the maximum point on the graph is:

[tex]\mathbf{(t,V(t) = (2.361,20.745)}[/tex]

This means that:

The maximum number of people infected at the same time is approximately 21.

The rate of infection at this point is:

[tex]\mathbf{m = \frac{V(t)}{t}}[/tex]

[tex]\mathbf{m = \frac{20.745}{2.361}}[/tex]

[tex]\mathbf{m = 8.79}[/tex]

The rate of infection is 8.79 people per week

Read more about graphs and functions at:

https://brainly.com/question/18806107

Answer:

[tex]\sf\longmapsto \: x = 4[/tex]

Step-by-step explanation:

[tex]\sf\longmapsto \: 4x = 16[/tex]

[tex]\sf\longmapsto \: x = \frac{16}{4} [/tex]

[tex]\sf\longmapsto \: x = 4[/tex]

Answer:

.7314

Step-by-step explanation:

I plugged this number into the calculator and got .7313537016, and then rounded it to the fourth decimal place, which gave me my answer

Answer:

A child experiencing emotional.........

Answer:

1) = 9³

2) = 4*4*4*4*4

   = 4 to the fifth power

Step-by-step explanation:

Answer:

5 would be the dependent variable.

Step-by-step explanation:

5 would be the dependent variable because that is the number that is that depends on the others in the equation for it to be the final answer.

Answer:

180

Step-by-step explanation:

k = 72/2=36

y =kx

y =36(5)

y = 180

Answer:

You forgot to put the picture please redo and ill edit my answer

Step-by-step explanation:

Answer:

40i²-5i+45

Step-by-step explanation:

Answer:

64.2857

Step-by-step explanation:

take the distance traveled divided by the distance which will give you the speed traveling multiplying the distance and the speed will give you the time ot takes

Simplify the expression:

7 + -10c² + 100

collect like terms:

7+100-10c²

107-10c²

If you meant, 7+ -10c² + 10c, then it can't be simplified further as there are no like terms.

Answer:

We want to find the value of 'x' and we are asked to set up an equation to find the value of x. In equation we must remember to get all the numerical values to one side and all the non-numerical values to the other while remembering to keep the equation balanced for example if we add 4 on one side we must do it to the other side to keep the equation balanced so, → x + 5.2 + 11.1 + 6.4 = 34.6 ⇒ Simplify equation → x + 22.7 = 34.6 ⇒ Minus 22.7 from both sides to isolate x → x = 11.9 feet

Step-by-step explanation:

mark brainliest

Answer:

1.08 feet

Step-by-step explanation:

5.2+6.4+11.1+x = 34.6

11.1x = 34.6 - 22.7

11x = 11.9

x = 11.9/11

1.08 feet

9514 1404 393

Answer:

  D.  J(x) = 1/4(-x)^3

Step-by-step explanation:

Reflection across the y-axis replaces x with -x. Then if Fr(x) represents the reflected function, we have ...

  Fr(x) = (-x)^3.

Compression by a factor of c < 1 multiplies the function value by c. Then ...

  J(x) = 1/4·Fr(x)

  J(x) = (1/4)(-x)^3