Read the following description of a relationship:
The maple tree in Maggie's backyard is 5 years younger than the willow tree.
Let w represent the willow tree's age and m represent the maple tree's age.
Use the function m = w- 5 to find the value of m when w = 6.
m =

The present value (PV) of the investment today is approximately $2,965.05.

To find the present value (PV) of the investment today, we need to calculate the present value of each individual contribution and then sum them up. We can use the formula for the present value of an annuity to do this calculation.

The formula for the present value of an annuity is given by:

PV = C * [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present Value

C = Cash flow per period

r = Interest rate per period

n = Number of periods

In this case, the cash flow per period (C) is $500, the interest rate per period (r) is 10.5% (or 0.105), and the number of periods (n) is 20 years.

Let's plug in these values into the formula and calculate the present value (PV):

PV = $500 * [(1 - (1 + 0.105)^(-20)) / 0.105]

Using a calculator, we can evaluate the expression inside the brackets:

PV = $500 * [(1 - 0.376889) / 0.105]

Simplifying further:

PV = $500 * [0.623111 / 0.105]

PV = $500 * 5.930105

PV = $2,965.05

Therefore, the present value (PV) of the investment today is approximately $2,965.05.

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Answer:

6/x^2

1/(fg)

1/y^3

1/125.

1/9

-1/8

Step-by-step explanation:

6x^-2 can be simplified to 6/x^2, since a negative exponent means "inverse".

f^-1g^-1 can be simplified to 1/(fg), since a negative exponent means "inverse".

y^-3 can be simplified to 1/y^3, since a negative exponent means "inverse".

5^-3 can be simplified to 1/5^3, which is equal to 1/125.

3^-2 can be simplified to 1/3^2, which is equal to 1/9.

(-2)^-3 can be simplified to -1/2^3, which is equal to -1/8. When a negative exponent is applied to a negative base, it is important to remember that the negative sign remains.

The value of angle x based on the information will be 131°.

Alternate interior angles are the angles formed when a transversal intersects two coplanar lines.

The two marked angles are on opposite sides of the transversal, so they are called "alternate" angles. They are both between the parallel lines, so they are called "interior" angles.

In this geometry, alternate interior angles are congruent. They have the same measure. x° = 131°.

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Answer:

3.36 cm

Step-by-step explanation:

24 - 5 1/2 = 18.5

To find the distance on the map, we can set up a proportion:

1 cm / 5.5 miles = x cm / 18.5 miles

5.5 times 37/11 equals to 18.5; 1 times 37/11 is approximately equals to 3.36 cm (rounded to the nearest hundredths).

This is the same as writing y = sqrt(4(x+5)) - 1

===============================================

Explanation:

The given graph appears to be a square root function.

The marked points on the curve are:

Reflect those points over the line y = x. This will have us swap the x and y coordinates.

Recall the process of reflecting over y = x means we're looking at the inverse. The inverse of a square root function is a quadratic.

----------

Let's find the quadratic curve that passes through (1,-4), (3,-1) and (5,4).

Plug the coordinates of each point into the template y = ax^2+bx+c.

For instance, plug in x = 1 and y = -4 to get...

y = ax^2+bx+c

-4 = a*1^2+b*1+c

-4 = a+b+c

Do the same for (3,-1) and you should get the equation -1 = 9a+3b+c

Repeat for (5,4) and you should get 4 = 25a+5b+c

We have this system of equations

Use substitution, elimination, or a matrix to solve that system. I'll skip steps, but you should get (a,b,c) = (1/4, 1/2, -19/4) as the solution to that system.

In other words

a = 1/4, b = 1/2, c = -19/4

We go from y = ax^2+bx+c to y = (1/4)x^2+(1/2)x-19/4

----------

Next we complete the square

y = (1/4)x^2+(1/2)x-19/4

y = (1/4)( x^2+2x )-19/4

y = (1/4)( x^2+2x+0 )-19/4

y = (1/4)( x^2+2x+1-1 )-19/4

y = (1/4)( (x^2+2x+1)-1 )-19/4

y = (1/4)( (x+1)^2-1 )-19/4

y = (1/4)(x+1)^2- 1/4 - 19/4

y = (1/4)(x+1)^2 + (-1-19)/4

y = (1/4)(x+1)^2 - 20/4

y = (1/4)(x+1)^2 - 5

The equation is in vertex form with (-1,-5) as the vertex. It's the lowest point on this parabola. Placing it into vertex form allows us to find the inverse fairly quickly.

----------

The last batch of steps is to find the inverse.

Swap x and y. Then solve for y.

y = (1/4)(x+1)^2 - 5

x = (1/4)(y+1)^2 - 5

x+5 = (1/4)(y+1)^2

(1/4)(y+1)^2 = x+5

(y+1)^2 = 4(x+5)

y+1 = sqrt(4(x+5))

y = sqrt(4(x+5)) - 1

I'll let the student check each point to confirm they are on the curve y = sqrt(4(x+5)) - 1.

You can also use a tool like GeoGebra to verify the answer.

The total surface area of the prism is determined as  216 cm².

The surface area of the prism is calculated by applying the following formula.

The area of the two triangular faces is calculated as follows;

Area of the two triangles = 2 (¹/₂ x base x height )

Area of the two triangles = 2 (¹/₂ x 6 cm x 4 cm )

Area of the two triangles = 24 cm²

The area of rectangular faces is calculated as follows;

A = ( 5 cm x 12 cm ) + (5 cm x 12 cm ) + ( 6 cm x 12 cm )

A = 192 cm²

The total surface area of the prism is calculated as follows;

Area = 24 cm² + 192 cm²

Area = 216 cm²

The sketch of the triangular prism is in the image attached.

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The axis of symmetry of the function f(x) = x² - 6x-1 is equal to 3.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry, Xmin = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

By substituting the parameters, we have the following:

Axis of symmetry, Xmin = -b/2a

Axis of symmetry, Xmin = -(-6)/2(1)

Axis of symmetry, Xmin = 6/2

Axis of symmetry, Xmin = 3.

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Answer:

Step-by-step explanation:

3

x

−

4

y

+

15

=

0

.

y

=

3

4

x

−

1

2

Correct answers 5.4

Distance from point (2,3) to the line 3x+4y+9=0

=>r=

3

2

+4

2

∣3(2)+4(3)+9∣

=>r=

9+16

∣16+12+9∣

=>r=

5

27

=>r=5.4

Answer:

9 × √3 cm or approximately 15.59 cm

Step-by-step explanation:

(look at the picture)

Answer:

3/10

Step-by-step explanation:

Numbers Given are:

1 1/2, 2 1/2, 1 2/3, and 2 5/6

The result at the end of all the math is 2 5/6.

1 2/3 + 2 5/6 = 4 1/2

Divide 4 1/2 by 1 2/3 to get 2 7/10.

Subtract 2 2/3 from 2 7/10 to get 1/5.

Multiply 1/5 by 1 1/2 to get 3/10.

So the number they thought of was 3/10.

Answer:

(2x+7)(x−2)

Step-by-step explanation:

The exponential growth is 1.95% and after 35.72 years the population will double.

It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent \(\rm y = a^x\)

where a is a constant and a>1

Let's suppose the exponential growth function is:

\(\rm y = Ae^{rt}\)

A = 163,000

y = 1,686,000

t = 2020 – 1900 = 120 years

Plug all the values in the function:

\(\rm 1686000 = 163000e^{120r}\)

\(\rm e^{120r} = 10.343\)

Taking ln both side and solving:

r = 0.0194

r = 1.946 ≈ 1.95%

\(\rm 2A = Ae^{0.0194t}\)  (the population to double)

After solving:

t = 35.72 years

Thus, the exponential growth is 1.95% and after 35.72 years the population will double.

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Answer:

Step-by-step explanation:

Given expression:

It is the product of two factors, in other words it has two factors:

Correct choice is A

Step-by-step explanation:

Given expression = 5(m - 1)

5(m - 1) = 0

So, the factors are

5 and (m - 1)

Store sell 97 cases of pop for the week.

" Selling is defined as the transactions  done by a vendor in exchange of certain amount of money fixed on it."

According to the question,

Number of cases of pop at the beginning of the week = 40

Number of cases bought from the vendor = 120

Number of cases on hand at the end of the week = 63

Total number of cases in the store = 40 + 120

                                                          = 160

Number of cases store sell for the week = 160 - 63

                                                           = 97 cases

Hence, store sell 97 cases of pop for the week.

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Answer:

I have completed the answers and attached them to the explanation.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question asks for a subtraction expression:

length is always a positive number so bigger number first here.

OB = 4-(-1)              >only moves in x direction so subtract x's

AB = 4-(-2)             >only moves in y direction so subtract y's

Answer:

g=93 h=87 k=122 m=58

Step-by-step explanation:

If you flip two coins 68 times, the best prediction for the number of times both coins will land on heads is 17.

If you flip two coins 68 times, the best prediction for the number of times both coins will land on tails is 17.

The possible outcomes when two coins are flipped are;

head - head = HH

tail - tail = TT

Head and tail = HT

Tail and head = TH

The probability of getting two heads = 1/4

If you flip two coins 68 times, the best prediction for the number of times both coins will land on heads is calculated as;

Expected value = (68 flips) x (1/4 probability of getting HH) = 17

The probability of getting two tails = 1/4

Expected value = 68 x 1/4 = 17

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Answer:

Yea it does

Step-by-step explanation:

Julia needs to buy 42 packets of patties to make 500 hamburgers for the school function

An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.

Hamburger patties are sold in packets of 12. Let x represent the number of packet of patties to be bought to make 500 hamburgers. Hence:

12x = 500

x = 500/12

x = 41.67

x≅ 42

Julia needs to buy 42 packets

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Answer:

1) x² + 4x +1 = 1 (You have to put in +1)

2) True

Step-by-step explanation:

1)

2) A range is a representation of values between two points. When you're calculating the range of a parabola, you only know one of those points to start with. Your parabola will go on forever either up or down, so the end value of your range is always going to be ∞ (or −∞ if your parabola faces down.)

Answer: the answer is true

Step-by-step explanation: There are an infinite amount of numbers the parabola can hit, and there is no limit

hence the statement is true

Answer:B

Step-by-step explanation:

Answer:

Step-by-step explanation:

From the given information:

              Passed          Failed        Total

Male            17                   6            23

Female        34                 12            46

Total             51                 18             69

\(P(male | fail) = \dfrac{P(male \cap fail)}{ P(fail)}\)

\(P(male | fail) = \dfrac{\dfrac{6}{69} }{\dfrac{18}{69}}\)

\(P(male| fail) = \dfrac{1}{3}\)

\(P(male | fail) = 0.333\)

\(P(male) = \dfrac{23}{69}\)

\(P(male) = \dfrac {1}{3}\)

\(P(male) = 0.333\)

The two results are equal:

So the events are dependent.

Dado que el repartidor cobra $5 por cada entrega e hizo 27 entregas en el día, la panadería debería multiplicar 27 por 5. Además, el repartidor cobra una tarifa diaria de $25, así que se tendría que multiplicar 27 por 5 y luego añadir 25 para calcular su salario del día.

Por lo tanto, la respuesta correcta es la segunda opción:

Debería haber multiplicado 27 por 5 y luego añadir 25.

The area of the green region of the circle is 96.4 ft².

Area is the region bounded by a plane shape.

To calculate the area of the green region of the circle, we use the formula below

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

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The area of the green region in the circle given is expressed as approximately: a. 96.5 square feet.

The sector of a circle is calculated as:

A = ∅/360 * πr², where r is the radius and ∅ is the reference or central angle of the sector.

Given the following:

Central or reference angle (∅) = 180 - 27 = 153 degrees

Radius (r) = 17/2 = 8.5 feet

Plug in the values:

Area of the green region = 153/360 * π * 8.5²

Area of the green region ≈ 96.5 square feet.

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A. The angles 7 and 9 are are alternate interior angles.

B. The angle 2 and 8 are are alternate exterior angles.

Given the Rational Function:

(1.1) You can rewrite it in this form:

• By definition, the x-value is zero when the function intersects the y-axis. Therefore, you need to substitute this value into the equation and then evaluate, in order to find the y-intercept:

Then, you get:

As an ordered pair, this is:

• In order to find the x-intercept, you need to substitute this value into the function and solve for "x", because the y-value is zero when the function intersects the x-axis:

Then, you get:

As an ordered pair, this is:

• In order to find the Vertical asymptote, you need to make the denominator equal to zero and solve for "x":

Notice that you get two Vertical Asymptotes:

(1.2) By definition, the Domain of a function is the set of all the possible input values for which the function is defined.

Rational Functions are not defined for those numbers that make the denominator equal to zero. If you make the equation equal to zero and solve for "x", you get:

Therefore:

By definition, the Range is the set of all the possible output values of the function. For Rational Functions, the Range of the Rational Function is the Domain of its inverse.

In this case, you can find the inverse of the given function as follows.

- Solve for "x":

Applying the Quadratic Formula:

Where:

You get:

- Interchange the variables:

Notice that:

Hence, the Range of the original function is:

(1.3) By definition, if the degree of the numerator is less than the degree of the denominator, the Horizontal Asymptote is:

In this case, you can identify that the degree of the numerator is 1 and the degree of the denominator is 2:

Therefore, the Horizontal Asymptote is:

By definition, the Horizontal Asymptote indicates the end behavior of the Rational Function. In this case, it indicates that:

(1.4) Knowing all the data of the function, you can graph it:

Hence, the answers are:

(1.1) x-intercept:

y-intercept:

Vertical Asymptotes:

(1.2) Domain:

Range:

(1.3)

Other Asymptote:

End Behavior:

(1.4)

the answer to the equation is x=15