what is the range of the function shown below?

Answer:

A generic exponential function can be written as:

f(x) = A*e^(b*x)

Where A and b are real numbers, that we need to find.

We know that the points (3, 6) and (7, 18) are solutions to the equation, then we have that:

A*e^(b*3) = 6

A*e^(b*7) = 18

This is a system of equations, to solve this we can take the quotient between the two equations, so we remove the variable A.

(A*e^(b*7))/(A*e^(b*3)) = 18/6

e^(b*7)/e^(b*3) = 3

e^(b*7 - b*3) = 3

e^(4*b) = 3

Now we can apply the Ln(x) to both sides, because:

Ln(e^y) = y

then:

Ln(e^(4*b)) = Ln(3)

4*b = Ln(3)

b = Ln(3)/4

Then we have:

f(x) = A*e^(Ln(3)/4*x)

And we can use one of the equations to find the value of A. for example:

6 = A*e^(Ln(3)/4*3)

6/e^(Ln(3)/4*3) = 2.632

Then the exponential function is:

f(x) = 2.632*e^(Ln(3)/4*x)

Then we have that:

f(20) = 2.632*e^(Ln(3)/4*20) = 639.576

Rounding to the next integer, we have:

f(20) = 640

An exponential function can represent growth or decay.

The value of f(20) is 673

An exponential function is represented as:

[tex]y = ab^x[/tex]

At point (3,6), we have:

[tex]6 = ab^3[/tex]

At point (7,18), we have:

[tex]18 = ab^7[/tex]

Divide both equations

[tex]\frac{18}{6}= \frac{ab^7}{ab^3}[/tex]

[tex]3= b^4[/tex]

Take 4th roots of both sides

[tex]\sqrt[4]{3}= b[/tex]

Rewrite as:

[tex]b = \sqrt[4]{3}[/tex]

[tex]b = 1.32[/tex]

Substitute 1.32 for b in [tex]6 = ab^3[/tex]

[tex]a(1.32)^3 = 6[/tex]

[tex]2.30a = 6[/tex]

Divide both sides by 2.3

[tex]a = 2.61[/tex]

So, the function is:

[tex]y =2.61(1.32)^x[/tex]

When x = 20, we have:

[tex]y =2.61(1.32)^{20[/tex]

[tex]y =673[/tex]

Rewrite as:

[tex]f(20)=673[/tex]

Hence, the value of f(20) is 673

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Answer:

x=(3/2)  OR  1.5

Step-by-step explanation:

2x+3=6

2x=6-3

2x=3

x=(3/2)  OR  1.5

Answer:

x=1.5

i hope this help :3 mark brainliest please!

thank you! <3

Answer:

x = 2

Step-by-step explanation:

The equation of a vertical line parallel to the y- axis is

x = c

where c is the value of the x- coordinates the line passes through.

The line passes through (2, 3), (2, 5), (2, 7) all with an x- coordinate 2, thus

x = 2 ← equation of vertical line

Answer:

x = 2

Step-by-step explanation:

Firstly, when a line is parallel to the y axis, the equation of the line is x = the x position common to the points, in this case, x = 2.

but if you want to calculate,

from the points,

x1 = 2, y1 = 3

x2 = 2, y2 = 5

x3 = 2, y3 = 7

using the formula,

y-y1/x-x1 = y2-y1/x2-x1

y-3/x-2 = 5-3/2-2

y-3/x-2 = 2/0

crossing we have,

2(x-2) = 0(y-3)

2x - 4 = 0

2x = 4

x = 2

Answer:

A. and C.

Step-by-step explanation:

We don't know the area of the roof or the number of people in the group so they would both be represented by variables in an equation.

Hey there!

The answer you're looking for is C.

Answer:

c

Step-by-step explanation:

Answer:

1 1/2

Step-by-step explanation:

Given the improper fraction 3÷2, this can also be written as 3/2.

Writing as a mixed fraction means writing as a combination of a whole number and fraction e.g a b/c

a is the whole number

b/c is the fraction

3/2 = 1.5

1.5 = 1 + 0.5

1+0.5 = 1 + 5/10

3/2 = 1 + 1/2

Hence 3÷2 expressed as mixed fraction is 1 1/2

The mixed number representation of 3 ÷ 2 is 1 1/2.

To write the quotient of 3 ÷ 2 as a mixed number, we use the whole number part of the quotient as the whole number part of the mixed number.

We write the remainder (1) in the numerator of the fraction, and the divisor (2) in the denominator of the fraction.

As, the whole number part of the quotient is the number of times the divisor (2) can be divided into the dividend (3) evenly.

In this case, 2 can go into 3 once, with a remainder of 1.

To express this as a mixed number, we write 1 as the whole number part, and the remainder (1) as the numerator of the fraction. The divisor (2) is written in the denominator of the fraction.

Therefore, the mixed number representation of 3 ÷ 2 is 1 1/2.

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Answer:

Definitely not math but English

Step-by-step explanation:

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[tex]y - 2 = 3(x - 7)[/tex]

[tex]y - 2 = 3x - 21[/tex]

Add sides 2

[tex]y - 2 + 2 = 3x - 21 + 2[/tex]

[tex]y = 3x - 19[/tex]

Subtract sides 3x

[tex] - 3x + y = - 3x + 3x - 19[/tex]

[tex] - 3x + y = - 19[/tex]

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Answer:

Step-by-step explanation:

From the given information:

The null and the alternative hypothesis can be well written as:

[tex]H_o:P=0.6[/tex]

[tex]H_1:P>0.6[/tex]

Given that:

n = 200

x = 135

Alpha ∝ = 0.05 level of significance

Then;

⇒ [tex]n \times p\times (1-P)[/tex]

= 200 × 0.6 × (1 -0.6)

= 200 × 0.6 × 0.4

= 48 ≥ 10

The sample proportion [tex]\hat P = \dfrac{x}{n}[/tex]

[tex]= \dfrac{135}{200}[/tex]

= 0.675

The test statistics [tex]Z = \dfrac{\hat P - P}{\sqrt{ \dfrac{P(1-P)}{n} }}[/tex]

[tex]Z = \dfrac{0.675 - 0.6}{\sqrt{ \dfrac{0.6 \times 0.4}{200} }}[/tex]

[tex]Z = \dfrac{0.075}{\sqrt{ \dfrac{0.24}{200} }}[/tex]

Z = 2.165

The P-value = P(Z > 2.165)

= 1 - P(Z < 2.165)

From the z tables

= 1 - 0.9848

= 0.0152

Reject the null hypothesis since P-Value is lesser than alpha. ( i.e. 0.0152 < 0.05).

Thus, there is enough evidence to conclude that the value of the population proportion is greater than 0.6

Answer:

ok

Step-by-step explanation:

Answer:

i think its b

Step-by-step explanation:

Answer:

Choice B.

Step-by-step explanation:

BC ≅ FE.

You need 2 sides and the included angle to be congruent.

Answer:

Step-by-step explanation:

Coefficient: If a term has a variable, the numerical factor before the variable

Like Terms: A term that only has numerical factors and variables

Constant: Terms that have the exact same amount of variable factors

Equation: Two algebraic expressions that are equal

Solution: A value that makes an algebraic equation true

The correct match is given below:-

Coefficient:- If a term has a variable, the numerical factor is before the variable.

Like Terms:- A term that only has numerical factors and variables.

Constant:- Terms that have the exact same amount of variable factors.

Equation:- Two algebraic expressions that are equal.

Solution:- A value that makes an algebraic equation true.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The appropriate pairing is shown below: -

Coefficient: The numerical factor comes before the variable if a term has one.

Similar Terms: A term with only numerical variables and factors.

Terms with the same number of variables are said to be constants.

Equation: The equality of two algebraic expressions.

A value that makes an algebraic equation true is the answer.

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x 2 + 9  has no (Real) factors (Unlike  x 2 − 9 )

Explanation:

The most you could do with this is use the quadratic formula on

XXXX x 2 + 0 ⋅ x + 9

to get

XXXX ± 3 i

So you could factor using Complex values:

XXXX x 2 + 9 = ( x + 3 i ) ( x − 3 i )

Answer:

hi! so we have 2 points right? you will need to use something called the slope formula  y2-y1/x2-x1 we're subtracting our y values of both points and x values of both points while dividing them this gives us a slope of a line

now I want you to label before you do this in your head! it can get confusing to think about it so label label (x1-1,y1 4) (x2 14,y2 -2) now you have them labeled this parts easy! use the formula -2-4/14--1 okay now use your calculator you get -2/5 and now you have your m or slope!

memorize y2-y1/x2-x1  now! it will save you!

Step-by-step explanation:

Answer:

-2/5 is the answer

Answer:

DBE=50 degrees

ABD=140 degrees

Step-by-step explanation:

CA is a line which means that it equals 180 degrees total. Subtract the other angle measurements to find that DBE is 50 degrees. Then add the angles DBE, EBF, and FBA. Hope this helps!

Answer:

b

Step-by-step explanation:

i took the test

Answer:

slope equals 3

Answer:

angle 1: 92

angle 2: 24

angle 3: 64

angle 4: 35

angle 5: 81

Answer:

1.

B swap the order of equation

2. yes, they are equivalent and yes, they give same solution

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

X is about 4.5 times the amount given, so B. 337 1/2

Answer:

337.5 or 337½

Step-by-step explanation:

y∞x

y=kx(where k is the constant)

75=½k

cross multiplication

75×2=k

150=k

therefore the formula connecting x,k and y is y=150x

y=150×2¼

y=150×9/4

y=1350÷4

y=337.5or 337½

Answer:

Two quantities A and B have an equal ratio of a constant value direct proportion.

Answer:

a proportion of two variable quantities when the ratio of the two quantities is constant.Step-by-step explanation:

Answer:

9x-12

Step-by-step explanation:

3*x = 3x

3*-4= -12

3x - 12 = 12x

12x-3x = 9x

9x-12

Answer:  x = -4/3

Step-by-step explanation:

3(x−4)=12x

Step 1: Simplify both sides of the equation.

3(x−4)=12x

(3)(x)+(3)(−4)=12x  (Distribute)

3x+−12=12x

3x−12=12x

Step 2: Subtract 12x from both sides.

3x−12−12x=12x−12x

−9x−12=0

Step 3: Add 12 to both sides.

−9x−12+12=0+12

−9x=12

Step 4: Divide both sides by -9.

-9x/-9 = 12/-9

x = -4/3

Answer:

this is how you solve this equation

Step-by-step explanation:

300= (5x+4)+(2x-14)+(x-10)

Step-by-step explanation:

the answer is going to be 10

Answer:

The answers are in the screenshot. There wasn't much information to go by, so if the domain and range (and graph) look a little weird, that's why

Answer:

The quotient is:

Please check the attached diagram.

Step-by-step explanation:

As this question involves proper formatting.

So, I am attaching the method in the attached diagram.

i am pretty aure its one

Answer:

24

Step-by-step explanation:

hope this help if it dont sorry i tried