La ganancia obtenida después de t años de
haber realizado una inversión inicial de
$1.000.000 está dada por la expresión:
1.000.000 × 2t
¿Qué representa el número 2 en la
expresión anterior?
A)las ganancias obtenidas en el segundo año
B)las ganancias obtenidas en el último año
C) que cada nuevo año las ganancias se reducen a la mitad
D) que cada nuevo año las ganancias se duplican con respecto al año anterior

Answer:

x = -6 and y =5

Step-by-step explanation:

2x + 5y = 13    (call this equation '1')

-4x - 3y = 9    (call this '2')

multiply '1' by 2

4x + 10y = 26       (call this '3')

eliminate by adding '2' and '3':

(-4 + 4)x + (-3 + 10)y = 9 + 26

7y = 35

y = 5

sub that into '1':

2x + 5(5) = 13

2x + 25 = 13

2x = 13 - 25 = -12

x = -6

sub both x = -6 and y =5 into '2' to make sure everything adds up:

-4(-6) - 3(5) = 24 - 15 = 9

so x = -6 and y = 5

The length of B'C' from the given quadrilateral A'B'C'D' is 3 units. Therefore, option D is the correct answer.

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.

Here, AB = A'B' = 7 units

AD = A'D'= 6 units

DC = D'C'= 4 units

BC = B'C' = 3 units

Therefore, option D is the correct answer.

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Answer:L*W

Step-by-step explanation:

if you look at the pattern you will see that

Answer:

d)  171.8°

e)  72

f)  60°

Step-by-step explanation:

The Polygon Interior Angle Theorem states that measure of the interior angle of a regular polygon with n sides is [(n - 2) · 180°] / 2.

The number of sides of a 44-gon is n = 44. Therefore, the measure of its interior angle is:

[tex]\begin{aligned}\textsf{Interior angles of a 44-agon}&=\dfrac{(44-2) \cdot 180^{\circ}}{44}\\\\&=\dfrac{42\cdot 180^{\circ}}{44}\\\\&=\dfrac{7560^{\circ}}{44}\\\\&=171.8^{\circ}\;\sf(nearest\;tenth)\end{aligned}[/tex]

Therefore, the interior angle of a 44-gon is 171.8°.

[tex]\hrulefill[/tex]

The Polygon Interior Angle Theorem states that measure of the interior angle of a regular polygon with n sides is [(n - 2) · 180°] / 2.

Given the interior angle of a regular polygon is 175°, then:

[tex]\begin{aligned} \textsf{Interior angle}&=175^{\circ}\\\\\implies \dfrac{(n-2) \cdot 180^{\circ}}{n}&=175^{\circ}\\\\(n-2)\cdot 180^{\circ}&=175^{\circ}n\\\\180^{\circ}n-360^{\circ}&=175^{\circ}n\\\\5^{\circ}n&=360^{\circ}\\\\n&=72\end{aligned}[/tex]

Therefore, the number of sides of the regular polygon is 72.

[tex]\hrulefill[/tex]

According the the Polygon Exterior Angles Theorem, the sum of the measures of the exterior angles of a polygon is 360°.

Therefore, to find exterior angle of a regular hexagon, divide 360° by the number of sides:

[tex]\begin{aligned}\sf Exterior\;angle&=\dfrac{360^{\circ}}{\sf Number\;of\;sides}\\\\&=\dfrac{360^{\circ}}{6}\\\\&=60^{\circ}\end{aligned}[/tex]

Therefore, the exterior angle of a regular hexagon is 60°.

Answer:

4. a. 171.818°

b. 72 sides

c. 60°

Step-by-step explanation:

d. The interior angle of a regular polygon with n sides can be calculated using the formula:

[tex]\bold{Interior Angle =\frac{ (n-2) * 180\°}{n}}[/tex]

For a regular 44-gon, the interior angle would be:

[tex]\bold{Interior Angle =\frac{ (44-2) * 180\°}{44}=171.818^o}[/tex]

[tex]\hrulefill[/tex]

e. The number of sides in a regular polygon with an interior angle of 175° can be found using the formula:

[tex]\bold{n = \frac{360\° }{180\° - Interior \:Angle}}[/tex]

For an interior angle of 175°, the number of sides would be:

substituting Value,

[tex]\bold{n =\frac{ 360\° }{ 180\° - 175\°} = \frac{360\° }{ 5\° }= 72 \:sides}[/tex]

[tex]\hrulefill[/tex]

f.

The sum of the exterior angles of any polygon is always 360°.

Since a regular hexagon has six sides,
n=6

exterior angle would be [tex]\bold{\frac{360\° }{ n}}[/tex]

substituting value,

exterior angle=[tex]\bold{\frac{360\° }{ 6}=60\°}[/tex]

[tex]\hrulefill[/tex]

In "f(3)", we are told to use an x-value of 3.

Looking at the function, we can either pick a formula that is used when x≤0 or x>0.

Since 3 > 0, we need to use the formula paired with x > 0:

    f(x) = x + 1  if  x>0

So f(3) = 3 + 1 = 4.

To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).

Assuming the height of the rectangular prism is h inches.

According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.

The total surface area of the rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we have:

576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)

576 = 8h² + 4h² + 4h²

576 = 16h² + 4h²

576 = 20²

h² = 576/20

h² = 28.8

h = √28.8

h = 5.37

The height of the prism is approximately 5.37 inches.

The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.

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Answer:

a = 4

b=2

x=18

QR =16+1=17

Angle QRS =59

Step-by-step explanation:

4a+1 = 2a + 9

2a = 8

a = 4

6b = 11b-10

-5b=-10

-b= -2

b=2

6x+13 = 7x - 5 (opposite angles are equal)

-x=-18

x=18

QR =16+1=17

Angle QRS = 180 - 18•6+13 =59 (PQR + QRS = 180)

keeping in mind that the sum of all exterior angles in a polygon always add up to 360°, then

[tex]58+39+50+48+59+x+x~~ = ~~360\implies 254+2x=360 \\\\\\ 2x=106\implies x=\cfrac{106}{2}\implies x=53[/tex]

Answer:

X is 53 because 106 divide by 2 is equal to 53

Given: The equation x² = 5x + 4

We have to draw the the graph for the given equation.

Consider the given equation,

x^2 - 5x - 4 = 0  

The vertex of the parabola of the form f(x) = ax^2 + bx + c   is given by x = -b/2a

Here,

a= 1

b= -5

c= -4

vertex = x = 5/2= 2.5

Also, the y coordinate at x = 2.5 is,

y = (2.5)^2 -5(2.5)-4

y = -10.25

Thus the vertex of parabola is (2.5 , -10.25)

y - intercept is the point where x = 0

put x = 0 in given equation

f(x) = 0 - 0 -4

f(x) = -4

hence y intercept is at (0, -4).

Now, we calculate x- intercept

x- intercept is where y is equal to 0.

Put f(x) = 0

We have,

x^2 - 5x - 4 = 0

by using quadratic formula,

x = -b ±√b² - 4ac/2a

x=5 ±√-5² - 4 (1)(-4)/2

x= 5±√41/2.

Hence with the obtained values the graph of the equation is obtained.

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Answer:

140

If that's wrong, try 147

Step-by-step explanation:

With this brief sequence of numbers, we can see that the function is linear, and increases by 7 each term, with the first term at -21, and therefore, the "0th" term, or the y-intercept, at -28. With this information we can create a function in slope intercept form (y=mx+b):

[tex]y=7x-28\\[/tex],

where our m (slope) is 7, and our b (y-intercept) is -28.

If this doesn't make sense, then the easiest way is to just keep adding seven to the previous number until you get to the 24th term.

Hope this helps!

The number that belongs in the green box is 57.8 degrees.

We are given that;

The triangle sides 11 12 20

Now,

The interior angles of a triangle always add up to 180 degrees. To find the interior angles of a triangle whose sides are 11 cm, 12 cm and 20 cm, we can use the law of cosines1.

Let’s call the angle opposite the side of length 11 cm as A, the angle opposite the side of length 12 cm as B, and the angle opposite the side of length 20 cm as C. Using the law of cosines, we can find that:

[tex]cos(A) = (b^2 + c^2 - a^2) / (2bc) = (12^2 + 20^2 - 11^2) / (2 * 12 * 20) = 0.55cos(B) = (a^2 + c^2 - b^2) / (2ac) = (11^2 + 20^2 - 12^2) / (2 * 11 * 20) = 0.6cos© = (a^2 + b^2 - c^2) / (2ab) = (11^2 + 12^2 - 20^2) / (2 * 11 * 12) = -0.45[/tex]

We can then use inverse cosine function to find the angles:

[tex]A = cos^-1(0.55) ≈ 57.8 degreesB = cos^-1(0.6) ≈ 53.1 degreesC = cos^-1(-0.45) ≈ 129.1 degrees[/tex]

The interior angles of this triangle are approximately 57.8 degrees, 53.1 degrees, and 129.1 degrees.

Therefore, by the angle answer will be 57.8 degrees.

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Answer: Factor the problem

Step-by-step explanation:

Take out the common factor (-16), it will leave you with (t^2 - t - 30)

Factor (t - 6) (t + 5)

t - 6 = 0 or t + 5 = 0

t = 6 seconds

The volume of the cylinder with a height of 12 cm and a diameter of 8 cm is approximately 602.19 cm³.

To calculate the volume of a cylinder, you can use the formula:

Volume = π * (radius²) * height

Given that the diameter of the cylinder is 8 cm, the radius (r) can be calculated by dividing the diameter by 2:

radius (r) = 8 cm / 2 = 4 cm

The height (h) of the cylinder is 12 cm.

substitute these values into the formula:

Volume = π * (4 cm)² * 12 cm

Volume = π * 16 cm² * 12 cm

Volume ≈ 602.19 cm³ (rounded to two decimal places)

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Answer:

Step-by-step explanation:

To determine whether y is a function of x in the equation x+4y=8, we can solve for y in terms of x:

x + 4y = 8

4y = 8 - x

y = (8 - x)/4

Copy

Since every value of x corresponds to exactly one value of y, y is a function of x.

Answer:

664

Step-by-step explanation:

6x17

6x17

10x6

10x6

10x17

10x17

add them all up and u get 664

The required outputs of the given rule are 6, 10, 14, 18, 22.

Given inputs are 3, 5, 7, 9, 11 and the rule is 2x.

To find the outputs by applying the given rule to the inputs.

Let x be the input, then the output is 2x.

That implies,

x = 3 then output = 2× 3 = 6.

x = 5 then output = 2× 5 = 10.

x = 7 then output = 2× 7 = 14.

x = 9 then output = 2× 9 = 18.

x = 11 then output = 2× 11 = 22.

Hence. the required outputs of the given rule are 6, 10, 14, 18, 22.

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Answer:

  15.  f(-2) = 2

  17.  f(x) = 1 for x = ±1.7

Step-by-step explanation:

You want various values of the function and its inverse relation for f(x)=x²-2.

The value of f(x) is found by locating the value x on the x-axis and following the vertical line until it intersects the graph. Find the y-coordinate of that point.

The value of x for f(x) = k is found by locating k on the y-axis and following the horizontal line to the points of intersection with the graph. The x-coordinates of the points are the values of interest. Interpolation is often required.

The graph intersects the vertical line at x=-2 where y = 2.

  f(-2) = 2

The horizontal line at y=1 intersects the graph in two places, located symmetrically about the y-axis. The leftmost point is approximately (-1.7, 1). The rightmost point is approximately (1.7, 1).

  x ≈ -1.7 or +1.7

__

Additional comment

The instructions are to use the figure to answer the question. We interpret that to mean that you are to read the answers from the graph.

You can also use the figure to determine the equation for the graph (part of our problem statement, above). Then you can find the solutions by using the equation.

  f(x) = 1

  x² -2 = 1

  x² = 3

  x = ±√3 ≈ ±1.732 . . . . the values for problem 17

<95141404393>

Answer:

x = 17

Step-by-step explanation:

KL + LM = KM

x+8+12 = 3x-14

or, x+20 = 3x-14

or, 3x-x=20+14

or, 2x = 34

x = 17

Answer:

Step-by-step explanation:

3x-14=x+8+12

3x-x=8+12+14

2x=34

x=17

then

KL=(17)+8=25

The percentage is 26%, so the number is 26.

Here we know that the x% of the number 800,000 is equal to 208,000.

Remember that the x% of a number N, is given by the product:

(x%/100%)*N

So in this case we can solve the equation:

(x%/100%)*800,000 = 208,000

Solving that equation for the percentage, we will get:

x% = 100%*(208,000/800,000)

x% = 26%

That is the missing number.

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The quadrant of the terminal side for 15) is fourth quadrant.

To change from radians to degrees, you need to the multiple the number of radians by 180/π.

Multiple the number of radians by 180/π.

15) 5 radians = 5 * (180/π)

16) 11π/6 = (11*180)/6 = 330.

19) 3.5 = 3.5*(π/180) degree.

20) 1 = 1*(π/180) degree.

therefore, terminal side for 15) is fourth quadrant.

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Using calculator, the quadratic regression function that models the data is

f(x) = -290.6x² + 7127.4x - 43447.5.

the profit ≈  582.43

To find the profit for a selling price of $18.75, we substitute x = 18.75 into the equation.

f(18.75) = -147.30(18.75)² + 3231.00(18.75) - 8213.66

= -147.30 x 351.5625 + 60581.25  - 8213.66

=582.43375

f(18.75) ≈ 582.43

Therefore, the profit for a selling price of $18.75 is approximately $ 582.43

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I can guide you on how to perform the dilation with a scale factor of 3 for the figure.

To perform a dilation with a scale factor of 3, you would multiply the coordinates of each point of the original figure by 3. This will result in the figure being enlarged by a factor of 3.

Let's assume the coordinates of the original figure ABCDEFGH are as follows:

A: (1, 1)

B: (4, 1)

C: (4, 4)

D: (1, 4)

E: (2, 2)

F: (3, 2)

G: (3, 3)

H: (2, 3)

To obtain the image of the figure after dilation with a scale factor of 3, multiply each coordinate by 3:

A': (3, 3)

B': (12, 3)

C': (12, 12)

D': (3, 12)

E': (6, 6)

F': (9, 6)

G': (9, 9)

H': (6, 9)

These new coordinates (A', B', C', D', E', F', G', H') represent the image of figure ABCDEFGH after the dilation with a scale factor of 3. You can plot these new coordinates on a graph or use a drawing tool to visualize the enlarged figure.

Answer: The value of P(2) is equal to 26

Step-by-step explanation:

To find P(2) for the given polynomial P(x) = -x^3 + 3x^2 + 6, we can use the remainder theorem by dividing the polynomial by (x - 2).

        -x^2 + 5x - 4

__________________________

x - 2 | -x^3 + 3x^2 + 0x + 6

        (x^3 - 2x^2)

        ___________

                5x^2 + 0x

                (5x^2 - 10x)

                ____________

                         10x + 6

                         (10x - 20)

                         __________

                                 26

The quotient is -x^2 + 5x - 4, and the remainder is 26.

Therefore, the value of P(2) is equal to the remainder, which is 26.

The function is a good model for the data.

The retail sales in the U.S. in 2016 is estimated to be 282.24 billion dollars.

The year that corresponds to retail sales of $241 billion is 2020.

The function F(t)= 9.44 t +84.182 is a linear model for the data. This means that the graph of the function is a straight line.

The scatter plot shows that the data points are close to a straight line. This means that the function is a good model for the data.

To estimate the retail sales in the U.S. in 2016, we need to find the value of F(11). F(11) = 9.44 * 11 + 84.182

= 282.24.

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Answer: B 102

Step-by-step explanation: The perpendicular sides of the room tells us that it is a right triangle.

To find our the area of the triangle you use the formula [tex]\frac{base*height}{2}[/tex]base*height/2

We plug in 12feet and 17 feet for the base and height

We get [tex]\frac{12*17}{2}[/tex]

12 and 2 cancel out so our new equation is 6*17 squared feet

So our answer is 102 square feet