What is the value of y? A. 30° B. 60° C. 120° D. 40°​

Answer:

Yes

Step-by-step explanation:

12) 31.5

14) 36

The domain of the inverse of the function f(x) = 5e^x + 3 is found being all real numbers > 3. Or, we can write this symbolically as: D( f^(-1)(x)) = (3,∞)

Domain is the set of values for which the given function is defined.

Range is the set of all values which the given function can output.

Suppose that the given function is

[tex]f:X\rightarrow Y[/tex]

Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is

[tex]f^{-1}: Y \rightarrow X[/tex]

such that:

[tex]\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X[/tex]

(and vice versa).

It simply means, inverse of 'f' is undo operator, that takes back the effect of 'f'

The domain of the inverse of a function (if it exists) is the range of the function it is inverse of. Similarly range of the inverse of that considered function is the domain of that considered function.

The function given is:

[tex]f(x) = 5e^x + 3[/tex]

The domain of the inverse of this function is this function's range.

Assuming only real values are allowed, for any real number x, we have:

[tex]e^x > 0[/tex]

And therefore, we get:

[tex]5e^x > 0 \: \forall x \in \mathbb R\\5e^x + 3 > 3 \: \forall x \in \mathbb R\\[/tex]

Also, since the function [tex]f(x) = 5e^x + 3[/tex] is strictly monotonically increasing and continuous, it touches all the values as its output from any real number > 3 till any finitely large number.

Thus, its range is (3, ∞) (it is an interval consisting of all the real numbers > 3)

This is the domain of its inverse function.

Thus, the domain of the inverse of the function f(x) = 5e^x + 3 is found being set of all real numbers > 3. Or, we can write this symbolically as: D( f^(-1)(x)) = (3,∞)

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Answer:

x = -1/2.

Step-by-step explanation:

x^2 - 4 = (x - 2)(x + 2)  so if we multiply each term by x^2 -4 we get:

2 - 1(x - 2) = 3(x + 2)

2 - x + 2 = 3x + 6

2 + 2 - 6 = 3x + x

4x = -2

x = -1/2.

Answer:

[tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

1. Multiply both sides of the equation by the LCM (x - 2)(x + 2):

[tex]\frac{2}{x^{2} -4} (x-2)(x+2)[/tex]

factor x² - 4 by rewriting it as x² - 2²

x² - 2² = (x + 2)(x - 2)

now we have;

[tex]\frac{2}{(x+2)(x-2)} (x-2)(x+2)[/tex]

cancel the common factors (x - 2)(x + 2)

= 2

-------------------------------

[tex]\frac{-1}{x+2} (x-2)(x+2)[/tex]

cross cancel the common factor (x + 2)

[tex]\frac{-1}{x-2}=-(x-2)=-x+2[/tex]

-------------------------------

[tex]\frac{3}{x-2} (x-2)(x+2)[/tex]

cross cancel the common factor (x - 2)

3(x + 2)

distribute the 3

3x + 6

-------------------------------

combining all new values, we have;

2 + (-x) + 2 = 3x + 6

-x + 4 = 3x + 6

2. Isolate x:

-x + 4-4 = 3x + 6-4

-x = 3x + 2

-x-3x = 3x-3x + 2

-4x = 2

-4x/-4 = 2/-4

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

hope this helps!

Answer:

A

Step-by-step explanation:

Step-by-step explanation:

Answer:

x=8, y=1

Step-by-step explanation:

subtract them from each other, so it ends up as 4y=4. y=1

therefore, x is 8 when you plug it back in.

Answer:

Step-by-step explanation:

2x = 16

x = 8

8 + 2y = 10

2y = 2

y = 1

(8, 1)

The perimeter of the water wheel  [tex]8\sqrt{10}[/tex]

The correct option is (A)

The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. To derive the formula, let us consider two points in 2D plane A( x, a) and B(y, b).

So, the distance between two points be: [tex]\sqrt{(y-x)^{2}+(b-a)^{2}}[/tex]

As water wheel is designed in the shape of regular octagon.

To find the perimeter of the  water wheel.

Since the water wheel is in the shape of regular octagon all sides are equal.

Using Distance Formula,

D= [tex]\sqrt{(4-3)^{2}+(0-3)^{2}}[/tex]

  = [tex]\sqrt{10}[/tex]

So, the side of regular octagon will be [tex]\sqrt{10}[/tex].

Perimeter of Regular Octagon = 8 x side

                                                   = [tex]8\sqrt{10}[/tex]

Hence, the perimeter of the water wheel  [tex]8\sqrt{10}[/tex]

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Answer:

A

Step-by-step explanation:

Step-by-step explanation:

here AE = DE

AND BC = DC SO BY SAS IT IS CONGRUENT

I am going to assume that leg a:

  ⇒ is the horizontal distance between the house and the gas station

     ⇒ Distance for leg a: 6 miles

I am also going to assume that leg b

  ⇒ is the vertical distance between the house and gas station

     ⇒ Distance for leg b: 5 miles

Thus using the Pythagorean theorem: [tex]a^2+b^2=c^2[/tex]

   ⇒ (look at diagram attached for further explanation)

   [tex]a^2+b^2=c^2\\\\6^2+5^2=c^2\\c=\sqrt{6^2+5^2} \\c=\sqrt{61} =7.81[/tex]

Answer: 7.81

Hope that helps!

Answer:

-10(-9)+8 or 98

Step-by-step explanation:

If they are asking for the question formart for an answer then plug in like the first answer if they’re asking for the full simplified answer then simplify the first answer and then you’ll get 98

Answer: 48

Step-by-step explanation: i know

Answer:

Stem Leaf

1 9 9

2 1 4 9

3 2 2 6

4 2 2

Step-by-step explanation:

Answer:

-1/4 x 4 = -1

Step-by-step explanation:

:)

The triangles AEB and DEC are congruent by the SAA congruence theorem

The given parameters are:

The above parameters mean that:

Also, it means that two corresponding angles and one corresponding side on triangles AEB and DEC are congruent;

This represents the ASA congruence theorem.

Hence, ΔAEB and ΔDEC are congruent by the SAA congruence theorem

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The answer is 10.

2.5 + 1.5 + 4 + 2 = 10.

Answer:

option B Is correct

in the above angle F is the vertex and EG are the arm of angles

The name of the angle below is ∠EFG.

Option B is the correct answer.

The angles between two lines are the angles formed by two intersecting lines, measured in degrees or radians.

Several different types of angles can be formed between two lines, including acute angles, right angles, and obtuse angles.

We have,

From the figure,

There is only one angle.

i.e

∠EFG = ∠GFE

Thus,

The name of the angle below is ∠EFG.

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Answer:

12

Step-by-step explanation:

there are 12

between 23 and 35

Answer: y=5

Step-by-step explanation:

114+7y+y+26=180

8y+140=180

    -140   -140

8y=40

8     8

y=5

Answer:Here, a=3, b=-10 and c=2. Substitute the values, Therefore, the discriminant of is 76.

Step-by-step explanation:

I believe it’s C, convert 0.188 into a fraction

The situation involving the food establishment has a probability 2.08 percentage points higher than the situation involving the financial establishment

The question is incomplete, as the required table is not given.

From a more complete question, we have the following parameters:

Using the above values, the difference in the probabilities is

d = 10.59% - 8.56%

This gives

d = 2.03%

Hence, the true statement about the probability is (d)

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Answer:

4ft

Step-by-step explanation:

Answer:

4ft

Step-by-step explanation:

The surface area of the barn is 2040 square feet.

A rectangle is a plane shape with four sides and four right angles.

Analysis:

The barn is composed of:

Two straight  long rectangles with dimensions = 10ft x 40ft

Two slant rectangles with dimensions = 10.6ft x 40ft

Two short rectangles with dimensions = 10ft x 14ft

Two triangles, height 8ft and base 14feet

The surface area of barn = 2(10x40) + 2(10.6 x 40) + 2(1/2 x 14 x 8) + 2(10 x 40) = 800 + 848 + 112 + 280 = 2040 square feet

In conclusion, the surface area of the barn is 2040 square feet.

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Step-by-step explanation:

using indices..

(7.2x 10³)/(1.2x10^5)

7.2/1.2 = 6

10³/10^5 = 10-²

answer = 6x 10-2

(c)

The Venn diagram of each situation is a diagrammatic way of representing what the situation stands for

Diagram 1: A ∩ B ∩ C

This means that we shade all intersection points of the sets A, B and C

Diagram 2: (A ∩ B) ∪ C

This means that we shade the intersection points of the sets A and B and the whole of set C

Diagram 3: A ∩ (B ∪ C)

This means that we shade the where the set A intersects with the whole of sets B and C

Diagram 4: (A ∩ B) \ C

This means that we shade the intersection point of the sets A and B without shading any point on set C

Diagram 5: (A\B) ∪ (B\C) ∪ (A\C)

This means that we shade all set A without set B, all set B without set C and all set A without set C. In other words, we shade everything in the set without shading set C

See attachment for the diagrams

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Answer:

rate of change:

y-intercept:

Step-by-step explanation:

your equation is y=3.25x+30

Here, the y-intercept is 30

your rate of change is $3.25, since you get charged $3.25 per bouquet.

The rate of change is $3.25 and the y-intercept is $30.

A mathematical statement that relates two algebraic expressions by an equal sign.

The Tram fancy balloons has offered a down payment of $30

and the charge per bouquet is $3.25

Let x represent the number of bouquets

The equation for the total cost can be formed is

y = 30 + 3.25*x

On comparing this with the standard equation y =mx+c

Here m is the slope and the rate of change and c is the y intercept

So,

The rate of change is $3.25

the y-intercept is $30

Therefore, the rate of change is $3.25 and the y-intercept is $30.

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Using an exponential function, it is found that it takes 5.42 years for the car to halve in value.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem, the car depreciates 12% a year in value, hence r = 0.12 and the equation is given by:

[tex]A(t) = A(0)(0.88)^t[/tex].

It halves in value at t years, for which A(t) = 0.5A(0), hence:

[tex]A(t) = A(0)(0.88)^t[/tex]

[tex]0.5A(0) = A(0)(0.88)^t[/tex]

[tex](0.88)^t = 0.5[/tex]

[tex]\log{(0.88)^t} = \log{0.5}[/tex]

[tex]t\log{0.88} = \log{0.5}[/tex]

[tex]t = \frac{\log{0.5}}{\log{0.88}}[/tex]

t = 5.42.

It takes 5.42 years for the car to halve in value.

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Answer:

B. The system has no solution.

Step-by-step explanation:

[12x + 7y] = (20)

[12x + 7y] = (11)

The numbers in (parentheses) are both different while the numbers in the [brackets] are the same.

20=7y+12x

12x+7y=11

Slopes are

No solutions

Step-by-step explanation:

the first : e.g. a trapezoid

only 2 lines are parallel, but still it is a closed object with 4 vertexes and therefore 360° sum of internal angles. and 2 of the angles are smaller than 90°, and 2 are larger than 90°.

the second : a parallelogram, with all 4 sides having the same length. a square that is pushed e.g. on the top while the bottom stays.

the third : a rectangle. perpendicular means intersecting at 90°. but not a square. length and width must be different.

that's it, really. what was so confusing for you ?

Answer:

+1

Step-by-step explanation:

Positive 1