Scott takes gets a student loan to go to college after high school. If he pays $750 in interest at a rate of 3%, how much must the loan have been for originally?

Answer:

8% difference I think.

Step-by-step explanation:

72 - 64 = 8.

The temperature increase from 64 degrees to 72 degrees represents a 12.5% increase. You calculate this by dividing the difference in temperature by the original temperature and then multiplying by 100.

To calculate the percent increase in temperature from 64 degrees to 72 degrees, you subtract the original temperature from the new temperature and divide by the original temperature. Then, multiply the result by 100 to get the percentage.

Here is the calculation:

Percent Increase = ((New Temperature - Original Temperature) / Original Temperature) × 100

Percent Increase = ((72 - 64) / 64) × 100

Percent Increase = (8 / 64) × 100

Percent Increase = 0.125 × 100

Percent Increase = 12.5%

Therefore, the temperature has increased by 12.5%.

8 hours is 480 minutes

480 minutes is 2800 bottles

2800 bottles per day

28000 devided by 2800 is 100

100 days

Answer:

100 days

Step-by-step explanation:

1) first find brian’s score

a.) 171+17=188

2) Add brian and colin’s score.

a.) 171+188= 359

Colin scored 171. Brian scored 17 more than Colin, which is 188. Adding both scores together, their combined score is 359.

This is a straightforward arithmetic problem. Colin scored 171 points and Brian scored 17 more than Colin. So first, you need to determine Brian's score by adding 17 to 171, which equals 188. Then, to find their combined score you need add Colin's and Brian's scores together. Therefore, 171 (Colin's score) + 188 (Brian's score) = 359. So, their combined score is 359.

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Answer:

  x = -7

Step-by-step explanation:

The vertex form of this equation tells us it is a downward-opening parabola with its vertex at (-7, -3). The line of symmetry is the vertical line through the vertex: x = -7.

___

Vertex form is ...

  y = a(x -h) +k

where a is the vertical expansion factor, and (h, k) is the vertex. When a < 0, the parabola opens downward. When a > 0, it opens upward. (When a=0, the "parabola" is a horizontal line at y=k.)

The equation of the axis of symmetry for [tex]f(x) = -4\cdot (x+7)^{2}-3[/tex] is [tex]x = -7[/tex].

The function given in statement represents a parabola whose axis of symmetry is parallel to the y-axis. The standard form of the function is described below:

[tex]f(x) -k = C\cdot (x-h)^{2}[/tex] (1)

Where:

The equation for the axis of symmetry is of the form [tex]x = h[/tex]. By direct comparison, we determine that the equation of the axis of symmetry for [tex]f(x) = -4\cdot (x+7)^{2}-3[/tex] is [tex]x = -7[/tex].

We kindly invite to check this question on parabolae: https://brainly.com/question/8495869

Answer:

c(m)<=45+0.4m

Step-by-step explanation:

A linear inequality involves a linear function. It contains one of the symbols of inequality. It exactly looks like a linear equation,with the inequality sign replacing the equality sign.

According to the statement Nancy has negotiated a special rate and the maximum charge is $45.00 per day with the addition of $ 0.40 per mile.

So,

a linear inequality that models the total cost of the daily rental as a function of the total miles driven,m is:

c(m)<=45+0.4m

Answer: so bc. a length not can being minus so this mean that the width of the rectangle is equal 9 in

Final answer:

Ken will require 150 cm² of decorative paper to cover his triangular prism souvenir. This is calculated by determining the area of the two triangular bases and the three rectangular sides and adding them together.

Explanation:

To calculate the total area of decorative paper Ken requires to cover his triangular prism souvenir, we need to consider the area of all the sides of the prism. The prism has two triangular bases and three rectangular sides.

For the triangular bases, we use the formula for the area of a triangle: A = (base × height) / 2. Since we have two bases with base=5 cm (a) and height=6 cm (h), the total area for the two triangular bases would be

2 × (5 cm × 6 cm) / 2 = 30 cm²

For the three rectangular sides, the dimensions are height (h=6 cm) and width (w=10 cm), plus two sides with a side length equal to the height of the triangular base. The area of each rectangle is given by length × width. Therefore, the total area for the rectangular sides is:

2 × (5 cm × 6 cm) + (10 cm × 6 cm) = 60 cm² + 60 cm² = 120 cm²

Adding the areas of the bases and the sides, we obtain the total area of decorative paper needed:

Total area = Area of bases + Area of sides = 30 cm² + 120 cm² = 150 cm²

Therefore, Ken will require 150 cm² of decorative paper to cover his triangular prism souvenir.

It takes 90 days for a single drop of water to travel the Mississippi River's entire length.

Following the equation

[tex]V(t) = V_0(1-r)^t[/tex]

We start with an initial price of

[tex]V(0)=V_0[/tex]

and we're looking for a number of years t such that

[tex]V(t)=\dfrac{V_0}{2}[/tex]

If we substitute V(t) with its equation, recalling that

[tex]r = 0.075 \implies 1-r = 0.925[/tex]

we have

[tex]V_0\cdot (0.925)^t=\dfrac{V_0}{2} \iff 0.925^t = \dfrac{1}{2} \iff t = \log_{0.925}\left(\dfrac{1}{2}\right)\approx 8.89[/tex]

So, you have to wait about 9 years.

Final answer:

The expression to determine the number of years it takes for the car to reach a value that is 50% of its purchase price is t = ln(0.5) / ln(1 - 0.075), using the given formula V = Vo(1 - r)^t.

Explanation:

To determine the number of years t after purchase for the car to reach a value that is 50% of its purchase price, we can use the model V = Vo(1 - r)^t where V is the car's value after t years, Vo is the original purchase price, r is the constant annual rate of decrease, and t is the number of years.

V is set to be 50% of Vo, which can be written as V = 0.5Vo, and we know the constant annual rate of decrease r is 0.075. Plugging these values into the formula gives us:

0.5Vo = Vo(1 - 0.075)^t

Dividing both sides by Vo and taking the natural logarithm of both sides, we obtain:

ln(0.5) = ln((1 - 0.075)^t)

Using the properties of logarithms, we can rewrite this as:

ln(0.5) = t * ln(1 - 0.075)

Solving for t yields:

t = ln(0.5) / ln(1 - 0.075)

This expression can be used to find the number of years it takes for the car to be worth half of its purchase price.

The length of the hypotenuse of a right triangle with legs of 5 cm and 12 cm is 13 cm.

The length of the hypotenuse of a right triangle can be found by using the Pythagorean theorem. The theorem states that the square of the hypotenuse is equal to the sum of the squares of the two legs.

In this case, we have a right triangle with legs of 5 cm and 12 cm. To find the length of the hypotenuse, we can use the formula c = √(a² + b²).

Substituting the given values, we get c = √(5² + 12²) = √(25 + 144) = √169 = 13 cm.

Answer:

Step-by-step explanation:

Add 29 to both sides of this equation, obtaining:  x² - 10x + 25.  At this point it becomes obvious that this is a perfect square, the square of x - 5.

Thus, in the first two blanks, write x - 5.

In the second two blanks, write 5 (since 5 is the root corresponding to the factor x - 5).

Answer:

y = 3.4

Step-by-step explanation:

Given 2 secants and a tangent drawn to the circle from an external point then

The square of the measure of the tangent is equal to the product of the external part of the secant to the entire secant.

Using the secant with measure y + 11, then

y(y + 11) = 7²

y² + 11y = 49 ( subtract 49 from both sides )

y² + 11y - 49 = 0 ← in standard form

with a = 1, b = 11 and c = - 49

Using the quadratic formula to solve for y

y = ( - 11 ± [tex]\sqrt{11^2-4(1)(-49)}[/tex] ) / 2

  = ( - 11 ± [tex]\sqrt{121+196}[/tex] ) / 2

  = ( - 11 ± [tex]\sqrt{317}[/tex] ) / 2

y = [tex]\frac{-11-\sqrt{317} }{2}[/tex] or y = [tex]\frac{-11+\sqrt{317} }{2}[/tex]

y = - 14.4 or y = 3.4

However y > 0 ⇒ y = 3.4 ( nearest tenth )

Answer:

  32. -30°

  33. 45° or 135°

  34. 90°

Step-by-step explanation:

The table below shows a short list of trig function values.

32. -tan(x) = tan(-x)

33. -cos(x) = cos(180°-x)

34. sec(x) = 1/cos(x). 1/0 is "undefined".

The values shown above are the ones that are in the range of the inverse trig functions: arctan (-90°, 90°), arccos [0°, 180°], arcsec [0°, 90°)∪(90°, 180°].

[tex]32.\quad tan\theta=-\dfrac{\sqrt3}{3}\\\\.\qquad \dfrac{sin\theta}{cos\theta}=-\dfrac{\sqrt3}{3}\\\\\text{Since there is no "3" on the Unit Circle, un-rationalize the denominator:}\\.\qquad \dfrac{sin\theta}{cos\theta}=-\dfrac{\sqrt3}{3}\bigg(\dfrac{\sqrt3}{\sqrt3}\bigg)\implies \dfrac{sin\theta}{cos\theta}=-\dfrac{3}{3\sqrt3}=-\dfrac{1}{\sqrt3}\\\\\implies sin\theta =\pm\dfrac{1}{2}\quad and \quad cos\theta = \pm\dfrac{\sqrt3}{2}\quad and \text{ coordinate is in Quadrant 2 or 4}[/tex]

[tex]\text{Look on the Unit Circle (below) for coordinates }\bigg(\dfrac{-\sqrt3}{2},\dfrac{1}{2}\bigg)\ and\ \bigg(\dfrac{\sqrt3}{2},\dfrac{-1}{2}\bigg)\\\\\bold{Answer:}\large\boxed{150^o\ and\ 330^o\implies \dfrac{5\pi}{6}\ and\ \dfrac{11\pi}{6}}[/tex]

[tex]33.\quad cos^2\theta=\dfrac{1}{2}\\\\\\.\qquad \sqrt{cos^2\theta}=\sqrt{\dfrac{1}{2}}\\\\\\.\qquad cos\theta=\pm\dfrac{1}{\sqrt2}\\\\\\\text{Rationalize the denominator:}\\.\qquad cos\theta=\pm\dfrac{1}{\sqrt2}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)\implies cos\theta=\pm\dfrac{\sqrt2}{2}\\\\\\\text{Look on the Unit Circle to find when }cos\theta=\dfrac{\sqrt2}{2}\ and\ \dfrac{-\sqrt2}{2}[/tex]

[tex]\bold{Answer:}\large\boxed{45^o, 135^o, 225^o, 315^o\implies \dfrac{\pi}{4}, \dfrac{3\pi}{4}, \dfrac{5\pi}{4}, \dfrac{7\pi}{4}}[/tex]

[tex]34.\quad sec\theta=\text{unde fined}\implies sec\theta=\dfrac{1}{0}\\\\\\.\qquad \dfrac{1}{cos\theta}=\dfrac{1}{0}\implies cos\theta=0\\\\\\\text{Look on the Unit Circle to find when }cos\theta=0\\\\\bold{Answer:}\large\boxed{90^o\ and\ 270^o\implies\dfrac{\pi}{2}\ and\ \dfrac{3\pi}{2}}[/tex]

8.65 is the answer to this question.

Answer:

Option 3 - 8.65  

Step-by-step explanation:

Given : The arc intercepted by a central angle of 62° on a circle with radius 8.

To find : What is the length of the arc?

Solution :

The formula to find arc length is

[tex]l=2\pi r\times (\frac{\theta}{360^\circ})[/tex]

Where, l is the length of the arc

r is the radius of the circle r=8

[tex]\theta=62^\circ[/tex] is the angle subtended

Substitute the values in the formula,

[tex]l=2\times 3.14\times 8\times (\frac{62^\circ}{360^\circ})[/tex]

[tex]l=50.24\times 0.1722[/tex]

[tex]l=8.65[/tex]

Therefore, option 3 is correct.

The length of the arc is 8.65 unit.

ANSWER

Option A

EXPLANATION

The given product is

[tex]1.42 \times {10}^{7} \times 2.81 \times {10}^{1} [/tex]

[tex]1.42 \times 2.81 \times {10}^{7} \times {10}^{1} [/tex]

We multiply to get;

[tex]3.9902 \times {10}^{7} \times {10}^{1} [/tex]

Recall the product rule

[tex] {a}^{m} \times {a}^{n} = {a}^{m + n} [/tex]

We apply the product rule to get,

[tex]3.9902 \times {10}^{7 + 1} [/tex]

[tex]3.9902 \times {10}^{8} [/tex]

Correct to the nearest tenth, we have

[tex]3.99 \times {10}^{8} [/tex]

This can also be written as;

[tex]3.99 {e}^{8.00} [/tex]

The correct choice is A.

[tex]a = \frac{b \times h}{2} [/tex]

33.6 × 2 = b×h

67.2 = b×h

h=4

67.2÷4 =b

16.8=b

answer: b=16.8inches

Answer:

Inconsistent

Step-by-step explanation:

Consistent independent means that there is only one solution; ie one place where the 2 lines intersect.

Inconsistent means that the lines will NEVER cross because they are parallel

Consistent dependent means that the 2 lines, when solved for y, are the exact same line (same slope, same y-intercept)

In our system, one of the equations is already solved for y, so let's solve the other one for y:

[tex]x-2y=1[/tex] so

[tex]-2y=-x+1[/tex] and

[tex]y=\frac{1}{2}x-\frac{1}{2}[/tex]

The slopes of the 2 lines are the same; therefore, they are parallel and will never intersect.  Inconsistent system.

Answer:

inconsistent

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Euler's formula for polyhedra states that

F + V - E = 2

where F is faces, V is vertices and E is edges

Substitute the values given and solve for F, that is

F + 13 - 26 = 2

F - 13 = 2 ( add 13 to both sides )

F = 15 → B

The correct option is (B) 15

Euler's formula states the relationship between the number of Faces, Edges and Vertices of any polyhedron. It is given as

[tex]F+V=E+2[/tex]

where

[tex]F=\text{number of faces}\\V=\text{number of vertices}\\E=\text{number of edges}[/tex]

From the question

[tex]V=13,E=26[/tex]

so

[tex]F+V=E+2\\F+13=26+2\\F=26+2-13=15[/tex]

Learn more about Euler's formula here: https://brainly.com/question/12716048

The answer is:

The correct option is:

C) [tex]4^{3}*4^{4}=4^{7}[/tex]

To solve the problem, we need to remember the product of powers with the same base property, the property is defined by the following relation:

[tex]a^{m}*a^{n}=a^{m+n}[/tex]

If we are multiplying two or more powers with the same base, we must keep the base and add/subtract the exponents.

So, we are given the expression:

[tex]4^{3}*4^{4}[/tex]

We can see that both powers have the same base (4), so solving we have:

[tex]4^{3}*4^{4}=4^{4+3}=4^{7}[/tex]

Hence, we have that the correct option is:

C) [tex]4^{3}*4^{4}=4^{7}[/tex]

Have a nice day!

Answer:

The correct answer is option C

4^7

Step-by-step explanation:

Points to remember

Identities

xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾

xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾

x⁻ᵃ = 1/xᵃ

To find the correct option

It is given that,

4^3 * 4^4

⇒ 4³ * 4⁴

By using identities we can write,

4³ * 4⁴  = 4⁽³ ⁺ ⁴)

 = 4⁷

Therefore the correct option is option C.  4^7

Answer:488

Multiply 12.20 and 40

Answer:

9841

Step-by-step explanation:

Each time the number of shaded triangles is multiplied by 3.  So this is a geometric series:

an = 1 (3)ⁿ⁻¹

The sum of the first n terms of a geometric series is:

S = a₁ (1 - rⁿ) / (1 - r)

Here, a₁ = 1, r = 3, and n = 9.

S = 1 (1 - 3⁹) / (1 - 3)

S = 9841

Answer:

on e2020 its 1 option

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's calculate the probability of selecting a blue shirt from a total of 10 shirts:

It's 5/10, or 0.5, which stems from there being 5 blue shirts among the 10 Jeremy owns.  50/50 is not a standard way of expressing probability; 0.5 is proper.

Answer:

314 m³

Step-by-step explanation:

The volume (V) of a cone is calculated using the formula

V = [tex]\frac{1}{3}[/tex]πr²h

where r is the radius and h the perpendicular height

To find h use the right triangle from the vertex to the midpoint of the base and the radius.

Using Pythagoras' identity on the right triangle

where the slant height is the hypotenuse, then

h² + 5² = 13²

h² + 25 = 169 ( subtract 25 from both sides )

h² = 144 ( take the square root of both sides )

h = [tex]\sqrt{144}[/tex] = 12, hence

V = [tex]\frac{1}{3}[/tex]π × 5² × 12

   = π × 25 × 4 = 100π ≈ 314 m³

Answer:

B) 1452π units³

Step-by-step explanation:

To find the Volume of a cylinder, use this formula:

V (cylinder) = πr²h

Note that:

r = radius of the circle (base) = 11

h = height of the cylinder = 12

π = 3.14

Plug in the corresponding numbers to the corresponding variables.

V = (3.14)(11)²(12)

Remember to follow PEMDAS. First, solve for the power, then solve left -> right.

V = (3.14)(121)(12)

V = (379.94)(12)

V = 4559.28 units³

Note that the answer choices have π  in them, divide π from the answer, and add to the answer.

V = (4559.28)/3.14 = 1452π units³

B) 1452π units³ is your answer.

~

Answer: Second Option

[tex]P =0.00476[/tex]

Step-by-step explanation:

The probability sought is calculated by calculating the quotient between the number of possible ways to select 4 seniors from a group of 4 seniors among the number of ways to select 4 seniors from a group of 10 people.

So:

[tex]P =\frac{4C4}{10C4}[/tex]

Where

[tex]nCr = \frac{n!}{r!(n-r)!}[/tex]

is the number of ways in which a number r of people can be selected from a group of n people

Then

[tex]P =\frac{\frac{4!}{4!(4-4)!}}{\frac{10!}{4!(10-4)!}}\\\\\\P =\frac{1}{\frac{10!}{4!(10-4)!}}\\\\P =\frac{1}{210}\\\\P=0.00476[/tex]

Let y - x = height of sign

tan 31 = x/24

tan 31 • 24 = x

14.4206548567 = x

tan 42 = y/24

tan 42 • 24 = y

21.6096970631 = y

Now subtract x from y.

y - x = 21.6096970631 14.4206548567

y - x = 7.1890422064

Rounding off to the nearest tenth of a foot, we get 7.2 feet.

The sign for the roof is 7.2 feet.

The height of the sign is approximately 7.2 feet, calculated from the differences in elevation angles and distance.

To determine the height of the sign, we'll start by calculating the height of the roof and the height of the top of the sign from point P.

First, let's define the variables:

[tex]- \( h_1 \):[/tex]  height of the roof

[tex]- \( h_2 \)[/tex]: height of the top of the sign

[tex]- \( h_s \):[/tex] height of the sign itself

From point P, the angle of elevation to the roof is [tex]\( 31^\circ \)[/tex] and the angle of elevation to the top of the sign is [tex]\( 42^\circ \).[/tex]  The horizontal distance from point P to the base of the building is 24 feet.

Using the tangent of the angles of elevation, we have the following relationships:

[tex]\[\tan 31^\circ = \frac{h_1}{24}\]\[\tan 42^\circ = \frac{h_2}{24}\][/tex]

First, let's calculate [tex]\( h_1 \):[/tex]

[tex]\[h_1 = 24 \times \tan 31^\circ\]Using a calculator to find \( \tan 31^\circ \):\[\tan 31^\circ \approx 0.6009\]\[h_1 = 24 \times 0.6009 \approx 14.422\][/tex]

Next, let's calculate  [tex]\( h_2 \):[/tex]

[tex]\[h_2 = 24 \times \tan 42^\circ\][/tex]

Using a calculator to find [tex]\( \tan 42^\circ \):[/tex]

[tex]\[\tan 42^\circ \approx 0.9004\]\[h_2 = 24 \times 0.9004 \approx 21.610\][/tex]

The height of the sign [tex]\( h_s \)[/tex] is the difference between  [tex]\( h_2 \) a[/tex]nd [tex]\( h_1 \):[/tex]

[tex]\[h_s = h_2 - h_1\]\[h_s = 21.610 - 14.422 \approx 7.188\][/tex]

To the nearest tenth of a foot, the height of the sign is:

[tex]\[h_s \approx 7.2 \text{ feet}\][/tex]

Thus, the height of the sign is ( 7.2 ) feet.

Answer:

B. 3.

Step-by-step explanation:

At the limit we can take the numerator  to be √(9x^4) = 3x^2

The function is of the form ∞/ ∞ as x approaches ∞ so we can apply l'hopitals rule:

Differentiating top and bottom we have   6x / 2x - 3. Differentiating again we get 6 / 2 = 3.

Our limit as x  approaches infinity  is 3.

The limit of [tex]\(\sqrt{9x^4 + 1}/(x^2 - 3x + 5)\)[/tex] as x approaches infinity is 3, after comparing the highest powers of x in both the numerator and the denominator and simplifying.

To find the limit of the given function [tex]\(\displaystyle\lim_{x \to \infty} \frac{\sqrt{9x^4+1}}{x^2 -3x + 5}\)[/tex] as x approaches infinity, we can use the property of limits involving infinity. We need to compare the highest powers of x in both the numerator and the denominator. The highest power of x in the numerator under the square root is x⁴, and outside the square root, it will be x². In the denominator, the highest power is x². If we divide the numerator and the denominator by x², we get:

[tex]\[ \frac{\sqrt{9x^4+1}}{x^2 -3x + 5} = \frac{\sqrt{\frac{9x^4}{x^4}+\frac{1}{x^4}}}{\frac{x^2}{x^2} -\frac{3x}{x^2} + \frac{5}{x^2}} = \frac{\sqrt{9+\frac{1}{x^4}}}{1 -\frac{3}{x} + \frac{5}{x^2}} \][/tex]

As x approaches infinity, the terms [tex]\(\frac{1}{x^4}\), \(\frac{3}{x}\), and \(\frac{5}{x^2}\)[/tex] approach zero, and we are left with:

[tex]\[ \frac{\sqrt{9}}{1} = 3 \][/tex]

Therefore, the limit of the given function as x approaches infinity is 3, which corresponds to option (B).

The answer is:

Andre exchanged 450 dollars for pesos.

To solve the problem, we need to write two principal equations in order to establish a relation between the number of dollars before and after the trip.

So,

Before the trip, we have:

[tex]Dollars_{beforetrip}*rate=9000pesos\\\\Dollars_{beforetrip}*\frac{20pesos}{1dollar} =9000pesos\\\\Dollars_{beforetrip}=9000pesos\frac{1dollar}{20pesos}=450dollars[/tex]

We have that he exchanged 450 dollars for pesos.

Also, we can calculate how many pesos he had before he exchanged it back to dollars, so:

After the trip, we have:

[tex]Pesos{AfterTrip}*rate=\frac{1}{10}Dollars_{BeforeTrip}\\\\Pesos{AfterTrip}*\frac{1dollar}{20pesos}= \frac{1}{10}Dollars_{BeforeTrip}\\\\Pesos{AfterTrip}= \frac{1}{10}Dollars_{BeforeTrip}*\frac{20pesos}{1dollar}\\\\Pesos{AfterTrip}= \frac{1}{10}*450dollars*\frac{20pesos}{1dollar}=900pesos\\[/tex]

We have that he had 900 pesos before he exchanged it back to dollars.

Hence, we know that:

Andre exchanged 450 dollars for pesos.

Have a nice day!

Andre exchanged $500 for pesos at the beginning of his trip.

Let's denote the number of dollars Andre exchanged for pesos at the beginning of his trip as ( D ). According to the exchange rate, he would receive ( 20D ) pesos for ( D ) dollars.

 Andre then spends 9000 pesos while in Mexico. After spending, he has 20D - 9000 pesos left.

Upon returning, Andre exchanges the remaining pesos back to dollars at the same rate of 20 pesos per dollar. The number of dollars he gets back is [tex]\( \frac{20D - 9000}{20} \)[/tex].

 According to the problem, the amount of dollars he gets back is [tex]\( \frac{1}{10} \)[/tex] of the amount he started with, which is [tex]\( \frac{D}{10} \)[/tex].

We can now set up the equation:

[tex]\[ \frac{20D - 9000}{20} = \frac{D}{10} \][/tex]

To solve for ( D ), we multiply both sides of the equation by 20 to get rid of the denominator:

[tex]\[ 20D - 9000 = 2D \][/tex]

Subtract ( 2D ) from both sides to isolate the term with ( D ) on one side:

[tex]\[ 18D - 9000 = 0 \][/tex]

Add 9000 to both sides to solve for ( D ):

[tex]\[ 18D = 9000 \][/tex]

Divide both sides by 18 to find the value of ( D ):

[tex]\[ D = \frac{9000}{18} \] \[ D = 500 \][/tex]

Therefore, Andre exchanged $500 for pesos at the beginning of his trip.

The remainder theorem says [tex]x-c[/tex] is a factor of a polynomial [tex]p(x)[/tex] if [tex]p(c)=0[/tex]. So all you need to do is check the value of [tex]x^3+7x^2+4x-12[/tex] when [tex]x=-6[/tex]. We have

[tex](-6)^3+7(-6)^2+4(-6)-12=0[/tex]

so [tex]x+6[/tex] is indeed a factor.

Answer:

  ? = 14

Step-by-step explanation:

If ∆EFG ~ ∆CBA, we have the proportion

  FG/FE = BA/BC . . . . . any pairs of corresponding sides will have the same ratio for similar triangles. (It is convenient to put the unknown in the numerator.)

  ?/18 = 21/27 . . . . . . filling in the given numbers

Multiplying by 18, we have ...

  ? = 18·21/27

  ? = 14

_____

If the triangles are not designated as being similar, the problem is unworkable.