Using technology, we determined that Mary’s investment account can be modeled by the function, M(x) = 3.03(2.18)^x in thousands of dollars. What was Mary’s initial investment?$3.03
$4.96
$3,030
$4,960

Answers

Answer 1

Answer: Initial investment can be calculated by setting the value of x to zero since it is an initial value where time is zero. Using the given model, we calculate as follows:

M(x) = 3.03(2.18)^x
M(0) = 3.03 (2.18)^0
M(0) = 3.03 <---------FIRST OPTION

Answer 2

Answer:

The standard form of writing exponential function is given as:

y = ab^x. Mary’s initial investment is $3.03

Exponential equations

The standard form of writing exponential function is given as:

y = ab^x

where

a is the base

x is the exponent

Given the Mary’s investment account can be modeled by the function M(x) = 3.03(2.18)^x

Her initial investment is the point where x = 0

Substitute

M(x) = 3.03(2.18)^x

M(0) = 3.03(2.18)^0
M(0) = 3.03

Hence Mary’s initial investment is $3.03

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Which is the standard form of the equation of the parabola that has a vertex of (3, 1) and a directrix of x = –2?a) (x-3)^2 = 20(y-1)
b) (y-1)^2 = 20(x-3)
c) (y-1)^2 = -20(x-3)
d) (x-3)^2 = 20(y-1)

Answers

Answer with Step-by-step explanation:

We have to find:

the standard form of the equation of the parabola that has a vertex of (3, 1) and a directrix of x = –2

General form of Parabola that opens left or right:

(y−k)²=4p(x−h)

Vertex =(h,k)

Directrix: x=h−p

Here, h=3,k=1 and h-p=-2 i.e. p=h+2=5

Hence, equation of parabola in this case equals

(y-1)²=4×5(x-3)

i.e. (y-1)²=20(x-3)

Hence, correct option is:

b) (y-1)²=20(x-3)

Hello,

Remenber:
if S=(0,0) y²=2px then F=(p/2,0 and d:x=-p/2

Let's pose
x'=x-3
y'=y-1 axes passing by the point (3,0) in base (x,y) and (0,0) in base (x',y')

y'²=2p'x'
d': x'=-5=-p'/2 ==> p'=10 and y²=20x'
Returning in base (x,y) : (y-1)²=20(x-3)

Answer B

the relationship between x and y is proportional. when x is 3 and y is 15. what is x when y is 60? what is the value of x.

Answers

12. 15 divided by 5 is 3, and 60 divided by 5 is 12. Hope this helps and hangs a great day!

Given the two triangles are similar, what are the values of q and t? Round to the nearest hundredth.

Answers

Answer:

t = 7.5 cm , q= 7.5 cm.

Step-by-step explanation:

Given : Two similar triangle .

To find : what are the values of q and t ,Round to the nearest hundredth.

Solution : We have given Two similar triangle GHI and DEF.

Property of two similar triangle : The ratios of the lengths of their corresponding sides are equal.

Corresponding sides HI ≅ EF and GI≅DF. GH≅DE

HI = t , EF = 4.5 , GI = 12.5 , DF = q , Gh = 10 , DE = 6

$(t)/(4.5) = (10)/(6)$ .

On cross multiplication

t * 6 = 4.5 * 10.

t * 6 = 45 .

On dividing both sides by 6

t = 7.5 cm.

Now, for q

$(q)/(12.5) = (6)/(10)$ .

On cross multiplication

q * 10 = 12.5 * 6.

q * 10 = 75.0

On dividing both sides by 10

q= 7.5 cm.

Therefore, t = 7.5 cm , q= 7.5 cm.

Set up proportions. 6/10 = 4.5/t. Cross multiply 6t = 45. Divide both sides of the equation by 6 and get t = 7.5.
Next proportion is q/12.5 = 6/10. Cross multiply 10q = 750. Divide both sides of the equation by 10 and get q = 7,5.

Approximate Square root of 498 to the nearest tenth.A.22.4

B.22.2

C.22.3

D.22.5

Answers

22.3 is the value of Square root of 498 to the nearest tenth. Option C is correct

What is Number system?

A number system is defined as a system of writing to express numbers.

An approximation is anything that is similar, but not exactly equal, to something else.

A number can be approximated by rounding.

We need to find the Square root of 498 to the nearest tenth.

square root of Four hundred ninety eight

22.315

On tenth place right side the value is one which is less than five, so the tenth position remains same.

22.3 is the value Square root of 498.

Hence 22.3 is the value Square root of 498.

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The square root of 498 to the nearest 10 is 22.3

Use the functions f(x) = 3x – 4 and g(x) = x2 – 2 to answer the following questions. Complete the tables.

x f(x)–3–1 0 2 5

x g(x)–3–1 0 2 5

For what value of the what value of the domain {–3, –1, 0, 2, 5} does f(x) = g(x) {–3, –1, 0, 2, 5} does f(x) = g(x)? Answer:

consider the relation {(–4, 3), (–1, 0), (0, –2), (2, 1), (4, 3)}.Graph the relation.
State the domain of the relation. State the range of the relation. Is the relation a function? How do you know? Answer:

2. graph the function f(x) = |x + 2|.

Answer:

consider the following expression. Rewrite the expression so that the first denominator is in factored form. Determine the LCD. (Write it in factored form.) Rewrite the expression so that both fractions are written with the LCD. Subtract and simplify.

Answer:

Answers

$1)\nf(x)=3x-4\n|\ \ \ x\ \ \ |\ \ -3\ \ \ |\ \ -1\ \ \ |\ \ \ 0\ \ \ |\ \ \ 2\ \ \ |\ \ \ 5\ \ \ |\n=========================\n|\ f(x)\ |\ \ -13\ \ |\ \ -7\ \ |\ -4\ \ |\ \ \ 2\ \ \ |\ \ \ 11\ \ |\n\nf(-3)=3\cdot(-3)-4=-9-4=-13\nf(-1)=3\cdot(-1)-4=-3-4=-7\nf(0)=3\cdot0-4=0-4=-4\nf(2)=3\cdot2-4=6-4=2\nf(5)=3\cdot5-4=15-4=11$

$g(x)=x^2-2\n|\ \ \ x\ \ \ |\ \ -3\ \ \ |\ \ -1\ \ \ |\ \ \ 0\ \ \ |\ \ \ 2\ \ \ |\ \ \ 5\ \ \ |\n=========================\n|\ g(x)\ |\ \ \ \ \ 7\ \ \ \ |\ \ -1\ \ \ |\ -2\ \ |\ \ \ 2\ \ |\ \ \ 23\ \ |\n\ng(-3)=(-3)^2-2=9-2=7\ng(-1)=(-1)^2-2=1-2=-1\ng(0)=0^2-2=0-2=-2\ng(2)=2^2-2=4-2=2\ng(5)=5^2-2=25-2=23\n\nf(x)=g(x)\ \ \ \Leftrightarrow\ \ \ x=2,\ \ \ \ because\ \ \ \ f(2)=2\ \ \ and\ \ \ g(2)=2$

$2)\nthe\ relation:\ \{(-4, 3), (-1, 0), (0, -2), (2,1), (4, 3)\}.\n\nthe\ domain:\ D=\{-4,-1,0,2,4\}\nthe\ range:\ R=\{3,0,-2,1\}\n\nThis\ relation\ is\ the\ function,\ because\ \ each\ number\n of\ the\ domain\ D\ has\ exactly\ one\ value\ in\ the\ range\ R.$

$3)\nf(x)=|x+2|\n\n|x+2|= \left \{ {\big{x+2\ \ \ \ \ if\ \ \ x \geq -2} \atop \big{-x-2\ \ \ if\ \ \ x<-2}} \right.$

Answer:

-11 and 0 for EDGE2020

f(4)= -11

If g(x)=2, x= 0

Step-by-step explanation:

Let a=x^2+4. Use a to find the solutions for the following equation: (x^2+4)^2+32=12x^2+48. Which one of the following are solutions for x? Select any/all that apply. -8, -2, 4, 0, 2, -4, 8

Answers

$(x^2+4)^2+32=12x^2+48 \n(x^2+4)^2+32=12(x^2+4) \ \ \ |-12(x^2+4) \n(x^2+4)^2-12(x^2+4)+32=0 \n\hbox{substitute a for } x^2+4: \na^2-12a+32=0 \na^2-4a-8a+32=0 \na(a-4)-8(a-4)=0 \n(a-8)(a-4)=0 \na-8=0 \ \lor \ a-4=0 \na=8 \ \lor \ a=4 \n \n\hbox{substitute 8 and 4 for a and solve for x:} \na=8 \n\Downarrow \n8=x^2+4 \ \ \ |-4 \n4=x^2 \nx=-2 \ \lor \ x=2 \n \na=4 \n\Downarrow \n4=x^2+4 \ \ \ |-4 \n0=x^2 \nx=0 \n \n\boxed{x=-2 \hbox{ or } x=0 \hbox{ or } x=2}$

The solutions for x are -2, 0, 2.

Answer:

-2,0,2

Step-by-step explanation:

The given equation is:

$(x^2+4)^(2)+32=12x^2+48$