An investment fund starts at $0 and grows at a rate of $100 per month. Another fund starts at $4000 and reduces by $720 per year. After how long will the funds have the same amount of money?

Answer:

C. [tex]N(t)=150\cdot 3^t[/tex]

Step-by-step explanation:

You are given the exponential function [tex]n(t)=ab^t.[/tex]

From the table, [tex]N(t)=150[/tex] at [tex]t=0,[/tex] thus

[tex]N(0)=a\cdot b^0\\ \\150=a\cdot 1\ [\text{ because }b^0=1][/tex]

Also [tex]N(t)=450[/tex] at [tex]t=1,[/tex] thus

[tex]N(1)=a\cdot b^1=a\cdot b.[/tex]

Since  [tex]a=150,[/tex] substitute it into the second equation

[tex]450=150\cdot b\\ \\b=\dfrac{450}{150}\\ \\b=3[/tex]

and the expression for the exponential function is

[tex]N(t)=150\cdot 3^t[/tex]

[tex]\bf ~\hspace{10em}\textit{function transformations} \\\\\\ \begin{array}{llll} f(x)= A( Bx+ C)^2+ D \\\\ f(x)= A\sqrt{ Bx+ C}+ D \\\\ f(x)= A(\mathbb{R})^{ Bx+ C}+ D \end{array}\qquad \qquad \begin{array}{llll} f(x)=\cfrac{1}{A(Bx+C)}+D \\\\\\ f(x)= A sin\left( B x+ C \right)+ D \end{array} \\\\[-0.35em] ~\dotfill\\\\ \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\ \bullet \textit{ flips it upside-down if } A\textit{ is negative}[/tex]

[tex]\bf ~~~~~~\textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if } B\textit{ is negative}\\ ~~~~~~\textit{reflection over the y-axis} \\\\ \bullet \textit{ horizontal shift by }\frac{ C}{ B}\\ ~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}[/tex]

[tex]\bf ~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by } D\\ ~~~~~~if\ D\textit{ is negative, downwards}\\\\ ~~~~~~if\ D\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{ B}[/tex]

now with that template in mind

[tex]\bf h(x)=\stackrel{A}{2}|\stackrel{B}{1}x+\stackrel{C}{3}|\stackrel{D}{-1}\qquad \qquad \stackrel{\textit{C=C-2 a translation to the right}}{h(x)=2|x\boxed{+3-2}|-1} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill h(x)=2|x+1|-1~\hfill[/tex]

Using shifting concepts, it is found that the equation after a translation of 2 units to the right is:

d. f(x)=2|x+1|−1

The parent function is:

[tex]h(x) = 2|x + 3| - 1[/tex]

Shifting a function 2 units to the right, the equivalent function is:

[tex]f(x) = h(x - 2)[/tex]

Then:

[tex]h(x - 2) = 2|x - 2 + 3| - 1[/tex]

[tex]f(x) = 2|x + 1| - 1[/tex]

Thus, the function is:

d. f(x)=2|x+1|−1

A similar problem is given at https://brainly.com/question/24465194

Answer:

AB = (2+2√3)r

Step-by-step explanation:

All three sides of an equilateral triangle equals 60° each.

Given that the circles are equal and are inscribed in a triangle, the angle bisectors pass right through the center of the circle present in front of that angle.

For example a figure has been attached with the answer, where angle bisectors make a triangle with center of the circle and a perpendicular projection of the center on side AB.

Finding AB:

Let us divide the side AB into three parts. One is the line joining the center of the two circles which is = 2

Then we have two equal parts, each joining one vertices with the center of the circle.

Let us assume that there is a point P on the side AB which forms a line segment PO₁ ⊥ AB.

We have the right angled triangle APO₁. Angle A = 30°    PO₁ = r

let the base AP = x

We know that tan 30° = perp/base

1/√3 = r/x

=> x = √3  r

Hence Side AB = √3  r + 2r + √3  r

AB = (2+2√3)r

ANSWER

True

EXPLANATION

The given trigonometric equation is:

[tex] { \tan}^{2} x + 1 = { \sec}^{2} x[/tex]

We take the LHS and simplify to arrive at the RHS.

[tex]{ \tan}^{2} x + 1 = \frac{{ \sin}^{2} x}{{ \cos}^{2} x} + 1[/tex]

Collect LCM on the right hand side to get;

[tex]{ \tan}^{2} x + 1 = \frac{{ \sin}^{2} x + {\cos}^{2} x}{{ \cos}^{2} x} [/tex]

This implies that

[tex]{ \tan}^{2} x + 1 = \frac{1}{{ \cos}^{2} x} .[/tex]

[tex]{ \tan}^{2} x + 1 = {( \frac{1}{ \cos(x) }) }^{2} [/tex]

[tex]{ \tan}^{2} x + 1 = { \sec}^{2} x[/tex]

This identity has been verified .Therefore the correct answer is true.

Final answer:

The equation tan²(x) + 1 = sec²(x) is true and is derived from the fundamental Pythagorean trigonometric identity.

Explanation:

The statement tan²(x) + 1 = sec²(x) is true. This is based on a well-known trigonometric identity from mathematics.

In trigonometry, the Pythagorean identity for tangent and secant states that:

tan²(x) + 1 = sec²(x)

Which comes from the primary Pythagorean identity:

sin²(x) + cos²(x) = 1

by dividing each term by cos²(x) and recognizing that:

tan(x) = sin(x)/cos(x) and sec(x) = 1/cos(x).

ANSWER

[tex]g(2) = 3[/tex]

[tex]g( - 2) = - 4[/tex]

[tex]g(5) = 5[/tex]

EXPLANATION

The given step function have constant y-values on certain interval.

To find g(2), we plug x=2 into

g(x) =3, because 2 belongs to the interval

2≤x<4

This implies that

[tex]g(2) = 3[/tex]

To find g(-2), we substitute x=-2 into g(x)=-4, because x=-4 belongs to

-3≤x<-1

This implies that,

[tex]g( - 2) = - 4[/tex]

Similarly,

[tex]g(5) = 5[/tex]

because x=5 belongs to the interval,x≥4

Answer:

g(2)=3,

g(-2)=-4,

g(5)=5

Step-by-step explanation:

g(2) means find the value of function g(x) when x=2

from given restriction we see that x=2 lies withing [tex]2 \leq x <4[/tex]

corresponding function value is 3

Hence g(2)=3

-------

g(-2) means find the value of function g(x) when x=-2

from given restriction we see that x=-2 lies withing [tex]-3 \leq x <-1[/tex]

corresponding function value is -4

Hence g(-2)=-4

-------

g(5) means find the value of function g(x) when x=5

from given restriction we see that x=5 lies withing [tex]x \geq 4[/tex]

corresponding function value is 5

Hence g(5)=5

Answer:

12y+12x

Step-by-step explanation:

6(2(y+x))

=6(2y+2x)

=12y+12x

Answer:

12x+12y

The peeps below explained it enough! just here to give them a chance for B:)

The slope is 3/1 or 30/10.

Explanation:

You subtract 96 and 66 which equals 30. Then you subtract 30 and 20 which then equals 10. Then you simplify it which then equals 3/1

answer is B) 3/9= 4/12 = 1/3

Answer:

the Ratio between the small and big triangles is that of b. [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

We can solve this ratio problem by using the Rate of Change formula as shown below,

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

In this situation y would be the smaller triangle and x would be the larger triangle. Since all the values are given to use we can just plug those values in and solve for the rate of change / ratio.

[tex]\frac{4-3}{12-9} = \frac{1}{3}[/tex]

So the rate of change or ratio between the small and big triangles is that of [tex]\frac{1}{3}[/tex]

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer:

16.67

Step-by-step explanation:

3x² - 10 = 40

3x² = 40 + 10

x² = 50

x = 50 / 3

x = 16.67

Answer:

±5√6 / 3

Step-by-step explanation:

3x² - 10 = 40

3x² = 50

x² = 50/3

x = ±√(50/3)

x = ±5 √(2/3)

Writing in proper form:

x = ±5 (√2 / √3) × (√3 / √3)

x = ±5√6 / 3

The answer is negative one

Answer:

x = -3

-3+2 = -1

-1 = f(x)

The answer would be 14-12i. Hope this helps! Please mark brainliest! Thanks v much! :)

Answer:

Correct option is:

B. 5

Step-by-step explanation:

The triangle is a right angled triangle.

Let a be a angle adjacent to 90°

then, tana=Side opposite to angle a/Side adjacent to angle a which is not the hypotenuse

Here, Let a=60°

[tex]tan60\°=\dfrac{5\sqrt{3}}{Length\ of\ short\ leg}[/tex]

[tex]\sqrt{3}=\dfrac{5\sqrt{3}}{Length\ of\ short\ leg}[/tex]

⇒ Length of short leg=5

Hence, Correct option is:

B. 5

Find the value of the missing angle for the following oblique triangle.

C = 58.1°

The value of missing angle C for the Oblique triangle is [tex]58.1^{0}[/tex]

In given oblique triangle, angle A is [tex]67.7^0[/tex] and angle B is [tex]54.2^0[/tex].

What is Oblique triangle?

An oblique triangle is any triangle that is not a right triangle. It could be an acute triangle (all three angles of the triangle are less than right angles) or it could be an obtuse triangle (one of the three angles is greater than a right angle).

As we know that, Sum of all angles of a triangle is [tex]180^0[/tex].

A + B + C =[tex]180^0[/tex]

[tex]67.7^0 + 54.2^0 + C = 180^0[/tex]

[tex]C = 180^0 - 121.9^0[/tex]

[tex]C = 58.1^0[/tex]

Thus, the missing angle C of oblique triangle is [tex]58.1^0[/tex].

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ANSWER

[tex]g(x) = (4 {x)}^{2} [/tex]

EXPLANATION

We were given that,

[tex]f(x) = {x}^{2} [/tex]

Let

[tex]g(x) = a \times f(x)[/tex]

Or

[tex]g(x) = a {x}^{2} [/tex]

The point (1,16) is on the graph of g(x), hence it must satisfy its equation:

This implies that,

[tex]a {(1)}^{2} = 16[/tex]

[tex]a = 16[/tex]

We substitute the value of 'a' to get,

[tex]g(x) = 16 {x}^{2} [/tex]

Or

[tex]g(x) = (4 {x)}^{2} [/tex]

The correct choice is B.

Answer:

There are 1/7 cookies in the cookie jar. I give 4 to my friends. How many are left?

Step-by-step explanation:

Answer:

The lateral area is [tex]LA=125\ in^{2}[/tex]

Step-by-step explanation:

we know that

The lateral area of a right prism is equal to

[tex]LA=PH[/tex]

where

P is the perimeter of the base of the prism

H is the height of the prism

in this problem we have

[tex]P=25\ in[/tex]

[tex]H=5\ in[/tex]

substitute

[tex]LA=(25)(5)=125\ in^{2}[/tex]

Answer:

90% increase.

Step-by-step explanation:

Percent change in altitude = (difference in altitude * 100) / original altitude

= (95-50) * 100 / 50

= 90%.

Answer:

Percent of change in altitude = 90 %

Since the altitude increases from 50 ft to 95 ft the change is positive.

Step-by-step explanation:

Initial altitude, = 50 ft

Final altitude, = 95 ft

Increase in altitude = 95 - 50 = 45 ft

Percentage increase

              [tex]=\frac{45}{50}\times 100=90\%[/tex]

Percent of change in altitude = 90 %

Since the altitude increases from 50 ft to 95 ft the change is positive.

Freya begins started with 200 yards.

Freya then increased her distance by adding five yards a day for two days.

x = 200 + (n - 1)5.

[x = The distance Freya sprints on day 21]

x = 200 + (21 - 1)5

x = 200 +  (20) 5 = 300 yards

Answer:

[tex] a _ n = 200 + ( n - 1 ) 5 [/tex]

Step-by-step explanation:

We are given that initially, Freya started with sprinting 200 yards and then gradually increased the distance by adding 5 yards a day for 21 days.

So our initial value for distance is [tex]a_1=200[/tex]

and since she keeps on adding 5 yards everyday to her distance so this will be our common difference.

Therefore, the explicit formula will be:

[tex]a_n=200+(n-1)5[/tex]

Answer:

The answer would be d

Step-by-step explanation:

The value of given factorial 4! in the given problem is A. 24.

In mathematics, the factorial of a non-negative integer, denoted by the symbol "!", is the product of all positive integers less than or equal to that number. It is a fundamental mathematical operation used in combinatorics, probability theory, and other areas of mathematics.

Factorials have various applications, such as counting the number of permutations and combinations, calculating probabilities, solving equations, and representing coefficients in mathematical series. They are also used in formulae for binomial coefficients, as well as in calculus and other areas of mathematics.

4! = 4 [tex]\times[/tex] 3 [tex]\times[/tex] 2 [tex]\times[/tex] 1

   = 24

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ANSWER

B,C,E

EXPLANATION

The given exponentiial expression is

[tex] {7}^{8} \times 7 = {7}^{8 + 1} = {7}^{9} [/tex]

The expression that simplify to

[tex] {7}^{9} [/tex]

are all equivalent to the above expression.

A

[tex] {7}^{3} \times {7}^{3} = {7}^{3 + 3} = {7}^{6} [/tex]

B

[tex] \frac{ {7}^{18} }{ {7}^{9} } = {7}^{18 - 9} = {7}^{9} [/tex]

C

[tex]( {7}^{3} )^{3} = {7}^{3 \times 3} = {7}^{9} [/tex]

D

[tex] {7}^{4} + {7}^{5} = {7}^{4} (1 + 7) = 8( {7}^{4} )[/tex]

E.

[tex] {7}^{4} \times {7}^{5} = {7}^{4 + 5} = {7}^{9} [/tex]

Therefore options B, C and E are all equivalent to the given expression.

Answer:

Use Desmos, it is an online graphing calculator. You just input the function and you can play around with the graph.

This screenshot is from that :

A function assigns the values. The graph of the function can be made as shown in the image below.

A function assigns the value of each element of one set to the other specific element of another set.

For the given function, the graph can be made as shown below. The graph of the function is a parabola with the vertex at (0.215, 3.287).

Also, the parabola opens upwards, this is because the leading coefficient of the function is positive.

Further, the graph never touches the x-axis of the graph because the roots of the parabola are imaginary, which can be known by calculating the discriminant.

Hence, the graph of the function can be made as shown in the image below.

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I think the answer is December

Answer:

D

Step-by-step explanation:

First Rhonda makes a 20% down payment.  20% of $85 is:

0.20 × $85 = $17

So what's left is:

$85 - $17 = $68

So the number of monthly payments at $8 per month is:

$68 / 8 = 8.5

Rounding up, it will take 9 months to make all the payments.  If her father's birthday is on the third Sunday of June, she needs to make her ninth and final payment on June 1.  So her first monthly payment needs to be 8 months before that, or October 1.

Answer is D.

Answer:

Step-by-step explanation:

[tex]\text{4250 cm} \dfrac{1 m}{100 cm}=42.50m[/tex]

the answer is 42.5 meters

[tex]

x^3-1=x^3-1^3 \\

(x-1)(x^2+2x+1)=\boxed{(x-1)(x+1)(x+1)}

[/tex]

Hope this helps.

r3t40

For this case, we have by definition that, the median of a set of numbers is the average number in the set, after the numbers have been ordered from lowest to highest. If there is an even number in the set, the median is the average of the two middle numbers.

So, the given set is:

{4,5,5,6,10,11,12,13}

Since there are 8 numbers, the set is even. Then we find the average of the two numbers in the middle:

[tex]\frac {6 + 10} {2} = \frac {16} {2} = 8[/tex]

The median is 8

ANswer:

8

So, you would reflect it over the y-axis first. (x,y)->(-x,y) and get A’ (1,2) B’ (2,6) C’ (4,4). Then, you rotate 90 degrees clockwise (x,y)->(y,-x). So, A”(2,-1) B” (6,-2) C” (4,-4). Hope this helps.

Answer:

Step-by-step explanation:

A(-1, 2), B(-2, 6), C(-4, 4)

You got the reflection part correct.

A'(-1, -2), B'(-2, -6), C'(-4, -4)

To rotate 90° clockwise, apply the following transformation:

A(x, y) = A(y, -x)

A"(-2, 1), B"(-6, 2), C"(-4, 4)

Answer:

1/6

Step-by-step explanation:

Since anything to a negative power is 1/(a^b) where the original was a^-b, we get 6^-1 is 1/6.

6^(-1) = 1 / 6

The process of how to work out of the fractions as multiplications to each other is the simple 1:

Since anything to the negative power is 1/(a^b)

where the original were a^-b,

we get 6^-1 is 1/6.

In this we have to learn to add, or subtract, or multiply, and divide fractions or use these operations to solve the problems. Students need the clear-cut model of the fraction in order to come the grips with all the arithmetic operations. The shift of the emphasis by the multiple.

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Step-by-step explanation:

It's easy. Just line up the denominators, and then say what's 16 divided by 2, 8, and then do the same thing for the numerators. Which is 2 divided by 2 and that equals 1. 1 is your answer.

Check the picture below.

so is horizontal parabola, meaning the squared variable is the "y".  It has a "p" distance of 2 units, let's notice that it opens to the right, meanign "p" is positive.

[tex]\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} \stackrel{\textit{we'll use this one}}{4p(x- h)=(y- k)^2} \\\\ 4p(y- k)=(x- h)^2 \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=0\\ k=0\\ p=2 \end{cases}\implies 4(2)(x-0)=(y-0)^2\implies 8x=y^2\implies x=\cfrac{1}{8}y^2[/tex]

Answer:

10.8 cm

Step-by-step explanation:

we know that

The perimeter of the triangular face is equal to the sum of its sides

P=a+b+c

we have

a=28 mm=28/10=2.8 cm

b=4 cm

c=4 cm

substitute the values

P=2.8+4+4=10.8 cm

Answer:

10.8 cm

Step-by-step explanation: