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if a function representing distance (feet) as a function of time (minutes), what does f(30) represent in terms of the situation?

The theorems or postulates for the given pair of angles are as follows:

2. ∠2 ≅ ∠8 → Alternate exterior angles are congruent;

3. ∠2 ≅ ∠4 → Vertically opposite angles are congruent;

4. ∠3 ≅ ∠5 → Alternate interior angles are congruent;

5. ∠3 is supplementary to ∠6 → Consecutive interior angles are supplementary;

6. ∠4 ≅ ∠8 → Corresponding angles are congruent;

Consider two lines m and n are parallel. A transversal t is intersecting the lines m and n.

So, it forms 8 angles with the lines m and n. They are ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7, and ∠8.

Based on their position, they are paired into different categories. Such as:

Interior angles: ∠3, ∠4, ∠5, ∠6

Exterior angles: ∠1, ∠2, ∠7, ∠8

Classifying the given pair of angles and their corresponding theorems:

2. ∠2 ≅ ∠8 → These angles belong to pair of Alternate exterior angles.

Theorem - "The alternate exterior angles are congruent"

3. ∠2 ≅ ∠4 → These belong to pair of vertically opposite angles.

Theorem - "The verticle angles are congruent"

4. ∠3 ≅ ∠5 → These belong to pair of alternate interior angles.

Theorem - "The alternate interior angles are congruent"

5. ∠3 is supplementary to ∠6 → These angles belong to pair of consecutive interior angles. Thus, they are supplementary.

Theorem - " The supplementary angles add up to 180°"

6. ∠4 ≅ ∠8 → These angles belong to pair of corresponding angles.

Theorem - " The corresponding angles are congruent".

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Given : Chords A C and B D intersect at point E.  Length of Different segments is given in terms of x

To find :  Length of chord BD

Solution:

Chords A C and B D intersect at point E.

=> AE * CE   = BE * DE

AE = x

CE = x + 12

BE = x + 2

D = x + 5

=> x(x + 12) = (x + 2)(x + 5)

=> x² + 12x  = x²  + 7x + 10

=> 5x = 10

=> x = 2

BD = BE + DE

= x + 2 + x + 5

= 2x + 7

putting x = 2

=> BD = 2 (2) + 7

Applying the intersecting chord theorem, the length of segment CE in is: 2.5 units.

In geometry, the intersecting chords theorem is the theorem that defines the relation of the four line segments formed when two chords of a circle intersect each other at a point in the circle.

According to the intersecting chords theorem, the products of the lengths of the line segments that are formed on each chord are congruent or equal to each other.

In the diagram given, we have chords AC and BD intersecting at point E to form the following line segments:

BE = BD - DE = 7 - 2 = 5 units

DE = 2 units

AE = 4 units

CE = ?

Based on the intersecting chord theorem, we have:

(BE)(DE) = (AE)(CE)

Plug in the values

(5)(2) = (4)(CE)

10 = 4(CE)

Divide both sides by 4

10/4 = 4(CE)/4

2.5 = CE

CE = 2.5 units

Thus, applying the intersecting chord theorem, the length of segment CE in the circle given is: 2.5 units.

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Answer:

x = 7

Step-by-step explanation:

since the points all lie on the same line then the slopes of adjacent points will have the same slope.

calculate the slope using R and S then equate to slope using R and T or S and T

calculate slope using slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = R (- 5, - 3 ) and (x₂, y₂ ) = S (- 1, - 1 )

[tex]m_{RS}[/tex] = [tex]\frac{-1-(-3)}{-1-(-5)}[/tex] = [tex]\frac{-1+3}{-1+5}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]

Repeat with (x₁, y₁ ) = R (- 5, - 3 ) and (x₂, y₂ ) = T (x, 3 )

[tex]m_{RT}[/tex] = [tex]\frac{3-(-3)}{x-(-5)}[/tex] = [tex]\frac{3+3}{x+5}[/tex] = [tex]\frac{6}{x+5 }[/tex]

equating [tex]m_{RS}[/tex] and [tex]m_{RT}[/tex]

[tex]\frac{6}{x+5}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

x + 5 = 12 ( subtract 5 from both sides )

x = 7

Answer:

Step-by-step Explanation:

The correct option is C.

The algebraic expression for "seven more than the product of three and some number = 3x + 7 = 0

An algebraic expression is one that is composed of variables, integer constants, and algebraic operations. An algebraic expression is, for instance, 3x² 2xy + c.

we can search for the product of 3 and "some number",

Let the number be x.

So, the product of x is 3 times = 3x

And now

7 more then the Product .

we add the 7 to the product .

3x + 7 = 0

So the equation will be 3x + 7 = 0

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I understand that question you are looking for is:

Which of these is the algebraic expression for "seven more than the product of three and some number?"

A. 7 + 3 + x

B. 3 + 10 ÷ x

C. 3x + 7

D. 3 + 7x

Each element in the range of g(x) is 3 less than the corresponding element in the range of f(x).

Answer:

See below.

In short, by having vertical shift will affect range from -1 ≤ y ≤ 1 to -1 + a ≤ y ≤ 1 + a

Step-by-step explanation:

Generally, a cosine function without vertical shift will always have range equal to -1 ≤ y ≤ 1

If there is given vertical shift, our range will change to -1 + a ≤ y ≤ 1 + a

An example is if we are given the function of cos(x), this always has range of -1 ≤ y ≤ 1 because there is no vertical shift.

But if we have cos(x) + 1, we have vertical shift which is 1. Then the range will be -1+1 ≤ y ≤ 1+1 which equals to 0 ≤ y ≤ 2.

Hence, the function of -5cos(2x) has only range of -1 ≤ y ≤ 1 but the function of -5cos(2x) - 3 will have range of -1-3 ≤ y ≤ 1-3 which equals to -4 ≤ y ≤ -2

Answer:

B) 57 is the answer

Step-by-step explanation:

Let's try to make the given figure a parallelogram by extending DE and BA to F.

So now we have a complete parallelogram.

<AEF = 180 - 112 Since they are linear pairs

so, <AEF = 68

Now,

<EAF = 180 - 125 = 55

So, <AFE = 180-68-55 (interior angles of triangle sum up to 180)

<AFE = 57

Opposite angles of parallelogram are equal so,

<AFE = <BCD = 57°

Answer:

give it a try

Step-by-step explanation:

Okay. I'm gonna flip five coins, but I'm told the first coin is Tell there's no choice there at all. It is certain the first coin shows a tail and then I want to have four heads in a row. Okay, so one for tell which means certain getting ahead is a half chance. Again a half chance again a half and again a half So that you work out and it's 1/16. That's the answer. There's no choice about the foreheads. It just has to be head every time I said.

The second tree is 56.4 ft tall.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are identical, their respective sides are equal in number and their corresponding angles are congruent.

Let the length of the tall tree be x. Thus by similarity of triangles we get,

Length of small tree/ Shadow Length of small tree =

Length of  Tall tree/ Shadow Length of tall tree

Substituting the values we get,

5.6/4.2 = x/42.3

x = 56.4

Thus the second tree is 56.4 ft tall.

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the volume of the hexagonal prism is 184. 75 cm^3

It is important to note that the volume of a hexagonal prism is given as;

V = (2/√3) × ap2 × h

Where

From the information given, we have the values of the following parameters;

height = 10cm

apothem = 4cm

base edge = 6cm

Now, let's  substitute the value of the parameters

Volume = (2/√3) × ap^2 × h

Volume = 2/√3 × 4^2 × 10

Multiply through

Volume = 1. 1547 × 16 × 10

Volume = 184. 75 cm^3

Thus, the volume of the hexagonal prism is 184. 75 cm^3

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Answer:

14m

Step-by-step explanation:

Please refer to the attached figure
B is the position where John is standing, His eyes are at point A, 2 meters from the ground

D is the base of the cliff and E is the top of the cliff

∠EAC is the angle at which John looks up to the cliff and is given as 45°

BD is the distance from the cliff given as 12m

So AC is also 12m

∠ACE is 90°

Therefore ∠AEC is 180-(45+90) = 45° since AEC forms a triangle and sum of angles in a triangle = 180°

In the ΔAEC, by the law of sines
12/sin(45) = EC/sin(45) . This means EC = 12 since the denominators cancel out

Since point C is 2 meters above ground(the base of the cliff) add 2 and we get the height of the cliff as 12+2 = 14m

Answer:

x = 2.4; y = 3.2

Step-by-step explanation:

y = 3x - 4

2x + y = 8

2x + 3x - 4 = 8

5x - 4 = 8

5x = 12

x = 12 / 5

x = 2.4

y = 3(2.4) - 4

y = 7.2 - 4

y = 3.2

Eduro's mistake of solving the inequality -4x > 120 is adding 4 to both sides instead of dividing both sides by -4

minus four x greater than 120

-4x > 120

x < 120/-4

There is a change in the inequality sign from greater than to less than because the inequality is been divided by -4

x < -30

Check:

-4x > 120

-4(-30) > 120

120 > 120

Therefore, Eduro's mistake of solving the inequality -4x > 120 is adding 4 to both sides instead of dividing both sides by -4

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Answer:

heat map is the answer

The inverse of function f(x) = 9x+7 is f-1(x) = x/9 - 7/9

The function is given as:

f(x) = 9x + 7

Express f(x) as y

y = 9x + 7

Swap the positions of x and y in the above equation

x = 9y + 7

Subtract 7 from both sides

9y = x - 7

Divide through by 9

y = x/9 - 7/9

Express as an inverse function

f-1(x) = x/9 - 7/9

Hence, the inverse of function f(x) = 9x+7 is f-1(x) = x/9 - 7/9

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Answer:

  2.57

Step-by-step explanation:

The mean absolute deviation is the mean of the absolute values of the differences from the mean.

The mean of the dataset is the sum of values, divided by their number:

  mean = (20 +16 +21 +16 +22 +16 +15)/7 = 126/7 = 18

The absolute values of the differences from 18 will have an average of ...

  mean(|differences|) = (2 +2 +3 +2 +4 +2 +3)/7 = 18/7

  mad(data) ≈ 2.57

__

Additional comment

Some calculators have the mad( ) function built-in. See the second attachment, for example.

The true statements about the functions are:

The function is given as:

f(x) = 25000 * 0.96^x

Set x = 0 to determine the initial value of the function

f(0) = 25000 * 0.96^0

Evaluate

f(0) = 25000

This means that the population of the city in 2010 is 25000 i.e. option (B) is correct

Also, we have:

f(x) = 25000 * 0.96^x

The rate at which the population decreases every year is calculated as:

r = 1 - 0.96

Evaluate the difference

r = 0.04

Express as percentage

r = 4%

This means that the rate at which the population decreases every year is 4% i.e. option (C) is correct

The population after 5 and 10 years are:

f(5) = 25000 * 0.96^5

f(5) = 20384

f(10) = 25000 * 0.96^10

f(10) = 16621

Divide these populations by the initial population in 2010

20384/25000 = 82%

16621/25000 = 66%

This means that the population decreased by 82% and 66% in 5 years and 10 years since 2010, respectively.

So, options (d) and (e) are false

Lastly, because the population function is an exponential decay function;

The function value would approach 0 as it decreases

This means that option (f) is correct

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Based on the calculations, the sum of this geometric series is equal to 9,990.

Mathematically, the standard form of a geometric series can be represented by the following expression:

[tex]\sum^{n-1}_{k=0}a_1(r)^k[/tex]

Where:

Also, the sum of a geometric series is given by this mathematical expression:

[tex]S=\frac{a_1(1-r^n)}{1-r}[/tex]

Given the following data:

Substituting the given parameters into the formula, we have;

[tex]S=\frac{9000(1-0.1^3)}{1-0.1}\\\\S=\frac{9000(1-0.001)}{1-0.1}[/tex]

S = 9000(0.999)/0.9

S = 8,991/0.9

S = 9,990.

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∑ k = 1 88 2.5 ⁢ ( 1.2 ) k  is this series written in sigma notation.

What is the series written in sigma notation?

Given:

2.5 + 2.5(1.2) + 2.5(1.2)2 + ⋯ + 2.5(1.2)87

If we look at the power it is always one less the term i.e., for first term the value of k=0.

So, the series in the form of summation can be written as

∑ k = 1 88 2.5 ⁢ ( 1.2 ) k

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Step-by-step explanation:

Yes, an positive average rate of change means that our endpoint of the interval is greater than the initial point of our interval. By definition, a function, f is increasing over an interval [a,b], if f(b)> f(a)

Yes, a positive average rate of change means that our endpoint of the interval is greater than the initial point of our interval.

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

Yes, a positive average rate of change indicates that the endpoint of our period is higher than the interval's starting point. A function f is rising over the range [a,b] by definition if f(b)> f. (a)

Therefore, the positive average rate of change over an interval must be increasing over that interval.

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28. 1.45l ÷ 0.32l = 4.53125

so approximately 5 glasses to leave the bottle empty

29. 5.6kg + 2.5kg = 8.1kg

8.1kg ÷ 0.48 = 16.875

he can make 16 complete doughs

there will be 0.875kg of flour left

Answer:

7

Step-by-step explanation:

You take the corresponding side that you know which is 10.5 and you multiply that by your scale factor of 2/3.

Another name for 10.5 is 10 [tex]\frac{1}{2}[/tex]  and that can be changed to [tex]\frac{21}{2}[/tex]

([tex]\frac{21}{2}[/tex])([tex]\frac{2}{3}[/tex])  The two's cancel out and we are left with [tex]\frac{21}{3}[/tex]  Which is the same as 7.

Answer:

Step-by-step explanation:

Congruent parts of congruent triangles are congruent, so we can easily demonstrate BD ≅ DF ≅ BF.

AB ≅ BC ≅ CD≅ DE≅ EF ≅ FA . . . . definition of regular hexagon

∠A ≅ ∠C ≅ ∠E . . . . definition of regular hexagon

ΔFAB ≅ ΔBCD ≅ ΔDEF . . . . SAS congruence

FB ≅ BD ≅ DF . . . . CPCTC

ΔBDF is equilateral . . . . definition of equilateral triangle

Answer:

  no solution

Step-by-step explanation:

The Law of Sines tells you the relationship between sides and angles of a triangle.

The Law of Sines tells you ...

  sin(A)/a = sin(B)/b = sin(C)/c

Using the given information, this would tell us ...

  sin(55°)/12 = sin(B)/b = sin(C)/27

Then angle C would be ...

  sin(C) = (27/12)sin(55°) ≈ 1.843

There is no angle whose sine is greater than 1. The triangle we seek does not exist. (Side BC is too short relative to side AB.)

The area is 97.211 sq units.

This part of the plane is a triangle. We can Call it δ. We can find the intercepts by setting two variables to 0 simultaneously; we'd find, for instance, that y=z=0 means 3x=15 i.e., x=3 , so that (3, 0, 0) is one vertex of the triangle. Similarly, we'd find that (0, 5, 0) and (0, 0, 15) are the other two vertices.

Next, we can parameterize the surface by

s(u,v)=[tex]\int\limits^a_b {3(1-u)(1-v),5u(1-v),15v} \, dx[/tex]

so surface element is

dS= IIsu*svII =15[tex]\sqrt{42}[/tex](1-v)dudv

Then the area of  is given by the surface integral

[tex]\int\limits^a_b {} \, \int\limits^a_b {dS} \, dx = 15\sqrt[n]{42} \int\limits^a_b {x} \, dx \int\limits^a_b {1-v} \, dudv[/tex]=97.211

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The y-intercept of the line is (0,7).

Given the pairs of a line in the coordinate plane are (x, y) (-72,25), (-54,13) and (-36,11).

First we will find the slope of the linear equation

The formula for calculating the slope between two points is equal to

m = (y₂-y₁) / (x₂-x₁)

take points (-54,13) and (-36.,11)

by substituting the values ​​in the above formula, we get

m = (11-13) / (- 36 - (- 54))

m = -2 / 18

m = -1 / 9

Now, we will find the equation for the line in point-slope form

y-y₁ = m (x-x₁)

we have m = -1 / 9 and (x₁, y₁) = (- 36.11)

Further, substitute the values ​​in the above equation, we get

y-11 = (- 1/9) (x + 36) ..... (1)

Convert the equation to the form of a slope intercept

y = mx + b

isolate the variable y in equation (1), we get

y-11 = (- x / 9) -4

y = (- x / 9) - 4 + 11

y = (- x / 9) +7

Here, b=7

Hence, the y-intercept of the line for the pairs of lines in the coordinate plane(x,y) is (-72,25), (-54,13) and (-36,11) is the point (0,7).

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Answer:

t ≥ 36

Step-by-step explanation:

took a while but i had to try a lot of the numbers. hope it helped, mark me brainleist.

The inequality to represent the times when the phone would have at least as much battery charge as the tablet is t ≥ 36.

We know that t is the time,  in minutes, since Marcel plugged in the phone and the tablet.

For phone:-

Initial battery charge = 13%.

Rate of charging = 2% points in 3 minutes = 2/3 % in 1 minute.

Thus, the total charge on the phone after t minutes = 13% + t(2/3)%.

For tablet:-

Initial battery charge = 25%.

Rate of charging = 1% points in 3 minutes = 1/3 % in 1 minute.

Thus, the total charge on the tablet after t minutes = 25% + t(1/3)%.

We are asked to complete the inequality to represent the times when the phone would have at least as much battery charge as the tablet.

Since the phone is required to have at least as much battery charge as the tablet, we can show this as:

The total charge on the phone after t minutes ≥ The total charge on the tablet after t minutes,

or, 13% + t(2/3)% ≥ 25% + t(1/3)%,

or, t(2/3)% - t(1/3)% ≥ 25% - 13%,

or, t(1/3)% ≥ 12%,

or, t ≥ 12%/(1/3)%,

or, t ≥ 36.

Thus, the inequality to represent the times when the phone would have at least as much battery charge as the tablet is t ≥ 36.

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Answer: 420 minutes in 7 hours. 2 minutes in 120 seconds.

Step-by-step explanation: Multiply 7x60, as there are 60 minutes per hour. Divide 120/60 to find how many minutes are within those many seconds.