Find the inverse of the function

y = log₂ (x-3)

As Convex polygon:

A polygon is called a convex polygon when no line segments between the points, goes inside. The boundaries of the convex polygon do not go inside and all the vertices are pointed outside away from the center. The

Convex Polygon:

A polygon is called a convex polygon when no line segments between the points, goes inside. The boundaries of the convex polygon do not go inside and all the vertices are pointed outside away from the center. The interior angles of a convex polygon are less than 180°.

Lets simplify the given problem,

If we try using 1070 degrees as the sum of the interior angles of a convex polygon, we get:

1070 =[n - 2] x 180, where n = number of sides

[tex]1070 =180n - 360180n =1070+360180n =1430n = 1430 / 180[/tex]

n = 7.94 number of sides. Since this is not a whole number, will simply round it up to 8.

Hence the number of sides is 8

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The dimensions of the enlarged rectangular picture is 15 x 10 inches.

When the  dimensions of the enlarged rectangular picture is enlarged by a scale factor of 5, it means that the dimensions would be five times larger what they were initially.

New dimensions : (3 x 5) x (2 x 5)

15 x 10 inches

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Answer:

I’m just adding so you can mark brainliest

Step-by-step explanation:

Answer:

The two triangles in group A are similar because two angles of one are congruent to two angles of the other.

The two triangles in group A are similar because two angles of one are congruent to two angles of the other.

The two triangles in group B are not similar. The ratio of the short sides of the two triangles is 10:4 or 2.5:1, and that is the same ratio as the two sides 24 and 9.6.

However, using the fact that an angle bisector in a triangle divides the opposite side into two segments in the same ratio as the lengths of the two sides that include the angle, the length of the third side of the left triangle can be found to be about 25.12; and 9.25 times 2.5 is not close to 25.12.

b. In group A, the third side of the first triangle, by the Pythagorean Theorem, is sqrt(306).

The scale factor between the two triangles is 3:5, so the length of the third side of the second triangle is 15*(5/3) = 25.

In both triangles, the third angle measure is 31 degrees, since the sum of the three angles is 180.

c. The scale factor, again, is 3:5 which means the ratio of the areas of the two triangles is 3²:5² or 9:25.

d. The first triangle can be carried onto the second with the following transformations:

(1) dilate by a factor of 5/3 to make it the same size;

(2) rotate 90 degrees counterclockwise;

(3) translate so the hypotenuses of the two triangles are the same line segment; and

(4) reflect on the hypotenuse.

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Answer:

two and a half to three and one third

Step-by-step explanation:

Frequency is a physical quantity that relates to the number of cycles made by a wave per second. Therefore the required expression for the frequency of the lower note is:  [tex]\frac{2}{3}[/tex] f

A wave is a phenomenon that propagates through a material medium without any permanent effect on the molecules of the medium. It transmits energy from one end of the medium to another. Examples are sound waves, light waves, electromagnetic waves, etc.

The propagation of a wave gives rise to frequency. Which can be defined as the number of cycles made by a wave per second. And it is measured in Hertz.

Let the frequency of the higher note be represented by f, and that of the lower note by [tex]f_{l}[/tex]. Thus, we have;

[tex]f_{l}[/tex] = [tex]\frac{2}{3}[/tex] f

Therefore, the expression for the frequency of the lower notes is   [tex]\frac{2}{3}[/tex] f.

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Answer:

5$

Step-by-step explanation:

it is 5 because the difference of 8 and 3 is 5

Answer:

[tex]y=\frac{96}{x}[/tex]

Step-by-step explanation:

So when x and y, vary inversely, it means that the product of x and y will remain constant such that: [tex]xy=c[/tex]. This means that the function can be defined as [tex]y=\frac{c}{x}[/tex] by dividing both sides by x. In this case x=12, and y=8, this means the constant is equal to 12 * 8 which is 96. So we have the equation:  [tex]xy = 96[/tex], which can be defined as [tex]y=\frac{96}{x}[/tex]

The input and output table for the linear function y = 3x is (-2, -6), (-1, -3), (0, 0), (1, 3) and (2, 6).

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the linear function y = 3x:

When x = -2; y = 3(-2) = -6

When x = -1; y = 3(-1) = -3

When x = 0; y = 3(0) = 0

When x = 1; y = 3(1) = 3

When x = 2; y = 3(2) = 6

The input and output table for the linear function y = 3x is (-2, -6), (-1, -3), (0, 0), (1, 3) and (2, 6).

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Answer: ( -6/ 6/ 9

Step-by-step explanation:

Answer:

x = 145°

Step-by-step explanation:

x and 35° are a linear pair and sum to 180° , that is

x + 35° = 180° (subtract 35° from both sides )

x = 145°

Answer:

32 km / hr

Step-by-step explanation:

930 to 1015 is   45 min =   .75 hr

24 km / .75 hr = 32 km /hr

The approximate arc length from the task content is; Choice C; 0.785 units.

Since the arc length is given mathematically by the formular;

Arc length = (A/360) × 2πr

Hence, since A = π/4 = 18/4 = 45.

Hence; Arc Length = (45/360) × 2 × 3.14 ×1

Arc length = 6.28/8 = 0.785 units.

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The correct answer is option B which is we need ∠L ≅ ∠R to prove congruency.

The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.

According to the SAS theorem which means Side Angle Side, The angle which is included between the two sides must be congruent.

Here we are given that

KL = NR

JL = MR

Now in the figure, we can clearly see that the angle included between JL & KL is L & the angle included between NR & MR is R.

So for the triangles to be congruent by SAS, angle L must be congruent to angle R.

∠L=∠R

Therefore the correct answer is option B which is we need ∠L ≅ ∠R to prove congruency.

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Answer:

B  

Step-by-step explanation:

L=R

Answer:

20 cents/minute

Step-by-step explanation:

We need to convert both units

1 dollar is 100 cents

12 dollars * 100 cents/1 dollar = 1200 cents

1 hour  = 60 minutes

1 hours * 60 minutes / 1 hour = 60 minutes

12 dollars/ hour  = 1200 cents / 60 minutes

Simplify

20 cents/minute

Answer: A. 20 cents per minute

Unit rate given: $12 per hour

Conversion:

$1 = 100 cents

$12 = 1200 cents

1 hour = 60 minutes

Solving steps:

amount in cents/time in minutes = 1200/60 = 20 cents per minute

The way to construct the equation in a graph is illustrated.

Converting the equation in slope-intercept form

2x-3y= -18

-3y= -2x-18

-3y= -(2x+18)

3y=2x+18

y=(2x+18)/3

And for equation 2

y= -5-3x

The points can be calculated by putting negative and positive values of x in both equations.

The graph is attached as a picture.

As we can see from the graph that two lines intersect at (-3,4) so it is the solution of the given system of linear equations.

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The speed (rate) of the plane in still air is 1100 kilometers per hour and the speed (rate) of the wind is 210 kilometers per hour.

We assume the speed (rate) of the plane in still air to be x kilometers per hour, and the speed (rate) of the wind to be y kilometers per hour.

Thus, flying against the wind, the acting speed (rate) for the plane will be x - y kilometers per hour.

Flying with the wind, the acting speed (rate) for the plane will be x + y kilometers per hour.

We are given that flying against the wind, the airplane travels 6230 kilometers in 7 hours.

Thus, speed (rate) = 6230/7 kilometers per hour = 890 kilometers per hour.

Equating this to the derived speed of the airplane flying against the wind, we get x - y = 890 ... (i).

We are given that flying with the wind, the airplane travels 10480 kilometers in 8 hours.

Thus, speed (rate) = 10480/8 kilometers per hour = 1310 kilometers per hour.

Equating this to the derived speed of the airplane flying with the wind, we get x + y = 1310  ... (i).

Now, on adding equations (i) and (ii), we get:

2x = 2200,

or, x = 1100.

Substituting x = 1100 in (ii), we get:

x + y = 1310,

or, 1100 + y = 1310,

or, y = 1310 - 1100 = 210.

Thus, the speed (rate) of the plane in still air is 1100 kilometers per hour and the speed (rate) of the wind is 210 kilometers per hour.

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Hello,

U (n +1) = Un + 6

Un = Uo + nr

U9 = 7 + 9 × 6 = 7 + 54 = 61

Answer:

nth term = 6n + 1.

Step-by-step explanation:

The first term a1 = 7 and the common difference d =  6.

nth term = a + d(n - 1)

= 7  + 6(n - 1)

= 6n + 1.

If the top is 8 feet above the ground and ladder is 5 feet away from bottom of wall then the angle between ladder and house is 58°.

Given top is 8 feet above the ground, ladder is 5 feet away from bottom of the wall.

Trigonometric ratios are the ratios of the sides of a right angled triangle. sin is the ratio of perpendicular and hypotenuse , cos is the ratio of base and hypotenuse, tan is the ratio of perpendicular and base, cosec is the ratio of hypotenuse and perpendicular, sec is the ratio of hypotenuse and base, cot is the ratio of base and perpendicular.

Here we use tan d where d is the angle between ladder and wall of the house.

tan d= P/B

tan d=8/5

tan d=1.6

[tex]d=tan^{-1} 1.6[/tex]

d=57.99

After rounding off it will be 58°.

Hence the angle between ladder and house is 58°.

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Hello,

a) Volume of the figure = Volume of light blue rectangular parallelepiped - volume of dark blue rectangular parallelepiped

Volume of rectangular parallelepiped = lengh × high × height

Volume of light blue rectangular parallelepiped :

V = (x + 2) × (x + 5) × (2x + 1)

V = (x² + 5x + 2x + 10) × (2x + 1)

V = (x² + 7x + 10) × (2x + 1)

V = 2x³ + 15x² + 27x + 10

Volume of dark blue rectangular parallelepiped :

V = x × 3 × (x + 5)

V = 3x(x + 5)

V = 3x² + 15x

Polynomial function, in standard form, to model the volume of this solid :

V = 2x³ + 15x² + 27x + 10 - (3x² + 15x)

V = 2x³ + 15x² - 3x² + 27x - 15x + 10

V = 2x³ + 12x² + 12x + 10

b) We have to solve 2x³ + 12x² + 12x + 10 = 208

⇔ 2x³ + 12x² + 12x - 198 = 0

⇔ 2(x - 3)(x² + 9x + 33) = 0

⇔ x = 3 or x² + 9x + 33 = 0

a = 1 ; b = 9 ; c = 33

Δ = b² - 4ac = 9² - 4 × 1 × 33 = -51 < 0 ⇔ Δ < 0 ⇒ no solution

So if the volume of the solid is 208 cubic inches, the value of x is 3

Answer:

Step-by-step explanation:

-4 [tex]\leq[/tex] x [tex]\leq[/tex] 6

x = {-4,-3,-2,-1,0,1,2,3,4,5,6}

Hope I helped...

Answer:

x⊥a

Step-by-step explanation:

If we draw this out, we see that x is perpendicular to a as well.

The simplest way to factor polynomials is to use the greatest common factor.

It should be noted that the polynomial simply means the expression of more than two algebraic terms.

In this case, the simplest way to factor polynomials is to use the greatest common factor. This simply had to do with the largest factor that the numbers share.

Other methods that can be utilized include the grouping method, the sum of the difference in cubes and in two squares.

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The fabric mill produce 1,807,845 meters of fabric in 365 days.

A fabric mill produces 4953 meters of fabric in a day.

operations and interpretations to function to make function simple or more understandable called simplify and the process is called simplification.

We have 4953 meter of fabric in a day.
So for 365 days
fabric = 4953 x 365
= 1,807,845

Thus, the fabric mill produce 1,807,845 meters of fabric in 365 days.

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Applying the vertical angles theorem, the measure of VU is determined as: 64°.

If two angles lie directly opposite each other, they are vertical nagles and are therefore equal.

13x = 15x - 8 [vertical angles theorem]

13x - 15x = - 8

-2x = -8

x = 4

Let y represent m(VU). Since m(RV) = m(VU), therefore:

13x + 2y = 180 [angles on a straight line]

Plug in the value of x

13(4) + 2y = 180

52 + 2y = 180

2y = 180 - 52

2y = 128

y = 64°

m(VU) = 64°.

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The slosh-out water is 29.9 cubic cm.

Volume is defined as the space covered by any solid body in the three-dimensional plane. For the cylinder, the parameters are height and radius.

The volume of the cone is calculated as:-

V = ⅓r^2h

V = ⅓r^2h

V = ⅓(3.5)^2(7)

V = ⅓(12.25)(7)

V = 1/3(85.75)

V = 85.75/3

1/3 cup of water is sloshed out:

Sloshed water = (85.75/3 )/3

Sloshed water = 29.9 cubic cm

Therefore, the sloshed-out water is 29.9 cubic cm.

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It's not an accurate value for the data based on the scatter plot, r = 0.01 is not an accurate value for this data, because 0.01 means practically no correlation, while the points on the graph are moderately correlated

1. Part A:

Since the points in the scatter plot shows a moderated upward trend, you must expect a correlation coefficient close to ± 0.5. A correlation coefficient of 0.01 is too close to 0, which would mean that the points are almost not correlated at all.

The correlation coefficients, r, measure the strength of the correlation of two variables and they can have values from - 1 to  1.

Here, r = - 1 is a perfect negative correlation as the points will adjust perfectly to a line with a negative slope.

r =  + 1 is a perfect positive correlation: the points will adjust perfectly to a line with a positive slope.

r = 0 means that the variables are not correlated at all.

Hence, the closer to zero, the worse the correlation is, and that is what r = 0.01 means, but the graph shows another thing.

Therefore, the calculated value of r = 0.01 is not accurate for this scatter plot.

2. Part B.

A causal relationship means that the explanatory variable (the independent variable) is the cause of the dependent variable.

Hence, you must find a reasonable variable that can be the cause of the number of strawberries picked.

Thus, the scenario could be:

Amount of rainfall in mm (x)         Number of strawberries picked (y)

      100                                                     20

        50                                                     40

        25                                                     80

        12.5                                                  160

        6.25                                                 320

The amount of rainfall is the cause of the number of strawberries picked, and you could find a model that relates both variables.

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The statement "The value of a is positive, so the vertex is a minimum" is correct.

Any function of the form [tex]\rm f(x) =ax^2+bx+c[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic function.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

From the table we can find the quadratic function:

f(x) = ax² + bx + c

Plug (x, y) on the above function.

a + b + c = 3 ...(1)

9a + 3b + c = -3 ...(2)

25a + 5b + c = -5 ...(3)

After solving the above equations:

a = 0.5

b = -5

c = 7.5

The value of a is positive.

Thus, the statement "The value of a is positive, so the vertex is a minimum" is correct.

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Answer: D

Step-by-step explanation: I just took the quiz

Answer: B) The function is decreasing

Step-by-step explanation:

As x increases, y decreases.