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The top-left graph is the correct representation of the function[tex]\( f(x) = 0.75^x \)[/tex]. It shows a decreasing function as [tex]\( x \)[/tex] increases, and the y-intercept is at (0, 1).

The correct option is (A).

To determine which graph represents the function [tex]\( f(x) = 0.75^x \)[/tex], we should consider the key characteristics of an exponential function where the base is between 0 and 1:

1. As [tex]\( x \)[/tex]  increases, [tex]\( f(x) \)[/tex] should decrease because 0.75 raised to a higher power becomes smaller.

2. As [tex]\( x \)[/tex] decreases (becomes more negative), [tex]\( f(x) \)[/tex] should increase because 0.75 raised to a negative power becomes larger.

3. The graph will never touch the x-axis, as an exponential function does not cross the axis when the base is positive.

4. The y-intercept should be at [tex]\( f(0) = 0.75^0 = 1 \)[/tex] because any non-zero number to the power of 0 is 1.

Now let's evaluate the provided graphs with respect to these characteristics:

- Top-left graph:This graph shows a decreasing function as [tex]\( x \)[/tex] increases, and the y-intercept is at (0, 1), which matches the behavior of [tex]\( f(x) = 0.75^x \)[/tex].

- Top-right graph:This graph increases as [tex]\( x \)[/tex] increases, which is not correct for [tex]\( f(x) = 0.75^x \)[/tex].

- Bottom-left graph:This graph also increases as [tex]\( x \)[/tex] increases, which does not match the expected behavior.

- Bottom-right graph:This graph shows a decreasing function as [tex]\( x \)[/tex]increases, but the y-intercept is not at (0, 1), so it does not represent [tex]\( f(x) = 0.75^x \)[/tex].

Based on this analysis, the top-left graph is the correct representation of the function[tex]\( f(x) = 0.75^x \)[/tex]. It shows a decreasing function as [tex]\( x \)[/tex] increases, and the y-intercept is at (0, 1).

complete question given below:

Which graph represents the function f(x) =0.75^x

Answer:

ASA

Step-by-step explanation:

We're already given a pair of congruent angles and sides

∠DEA and ∠BEC are congruent because they are verticle angles

So we can use ASA to prove the triangle ADE and triangle CBE congruent

To prove that triangle ADE is congruent to triangle CBE, you can use the SSS, SAS, or ASA congruence theorems depending on the given information. The Pythagorean theorem or trigonometry can be used if applicable. You must match corresponding sides or angles to decide which theorem to use.

There are several congruence theorems for triangles including Side-Side-Side (SSS), Side-Angle-Side (SAS), and Angle-Side-Angle (ASA). To determine which theorem to use in order to prove that triangle ADE is congruent to triangle CBE, you need to determine what information is given in the problem. For example, if you know that corresponding sides and angles are equal, you might use the SSS postulate, the SAS postulate, or the ASA postulate respectively.

If right angles are involved, we could also factor in the Pythagorean theorem to help establish side lengths - this theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b), expressed as: a² + b² = c². Solving for c gives us c = √a² + b². Similarly, if vectors and trigonometry are relevant factors in deriving your triangle sides or angles, they can also be used in establishing congruence.

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Answer:

The equation you should solve to find b is:

Option D. sin 35° / 9 = sin 40° / b

Step-by-step explanation:

m<A=35°

m<B=40°

a=9

b=?

We can use the Law of sines:

sin A / a = sin B / b

Replacing the given values:

sin 35° / 9 = sin 40° / b

This is option D.

Answer: 0

Step-by-step explanation:

2^3+16/4-3*4

2*2*2=8

8+16/4-3*4

16/4=4

8+4-3*4

12-3*4

3*4=12

12-12=0

Answer:

y=2x-11

Step-by-step explanation:

Answer:

The student should have simplified the equation to have y + 8 on the left. Then, the student should have subtracted 8 from both sides of the equation. The value of b should be 4, not 20.

Step-by-step explanation:

edge 2021.

The equation representing a proportional relationship, which is defined by a constant ratio and passes through the origin, is option A) y = 3x.

The question which equation represents a proportional relationship refers to a type of linear equation in which the ratio of one variable to another is constant. The form of a proportional relationship is y = kx, where k is the constant of proportionality. Looking at the options provided:

Therefore, the equation representing a proportional relationship is option A) y = 3x.

Answer:

40 books

Step-by-step explanation:

36-16=20

20 is half her original collection

20*2=40

Answer: He began with 40 Comic Books.

Step-by-step explanation: First exclude the 16 he bought from the 36. This leaves 20. Then dubble it because he sold half so it brings it up to 40! Hope this helps! ;)

36 - 16 = 20

20 * 2 = 40

The answer is 40!

Answer: $12.15

Step-by-step explanation:

5.70 + 2.15 = $7.85

$20 - 7.85 = $12.15

Answer:

3 3/5

Step-by-step explanation:

3 fives go into 18 with a remainder of 3.

Answer:

3 3/5

Step-by-step explanation:

Answer:

h =  2A / (b1 + b2)

Step-by-step explanation:

A = 1/2h (b1 + b2)

Divide both sides by 1/2 (b1 + b2)

h  =  A / 1/2 (b1 + b2)

h =  2A / (b1 + b2)

Answer:

2A /  (b1+b2)  = h

Step-by-step explanation:

The formula for the area of a trapezoid is

A = 1/2 (b1+b2) *h

We want to solve for h

Multiply each side by 2

2A = 2*1/2  (b1+b2) *h

2A =  (b1+b2) *h

Divide each side by  (b1+b2)

2A /  (b1+b2)  =  (b1+b2) / (b1+b2) *h

2A /  (b1+b2)  = h

In one year, $ 9,000 with a profit of 7.75%, is $ 697.5

697.5 × 18 = 12555

After 18 years old, it is $ 15,222

Answer:

The answer is 34494.79

Step-by-step explanation:

Y=ab^x

A= starting value= 9000

r=rate = 7.75% = 0.0775

Exponential growth

Y= 9000(1.0775)^x

Plug in time for x

Y= 9000(1.0775)^18

Y=34494.7918323

ROUND the number and your answer will be Y= 34494.78

Answer:

The height of the statue is 21.4 feet

Step-by-step explanation:

We are given

A person is standing 50 ft from a statue

The person looks up at an angle of elevation of 16 degree when staring at the top of the statue

hen the person looks down at an angle of depression of 8 degree when staring at the base of the statue

Firstly, we will draw diagram

In triangle ABF:

FC=50

we can use trig formula

[tex]tan(16)=\frac{y}{50}[/tex]

[tex]y=50tan(16)[/tex]

[tex]y=14.33727ft[/tex]

now, we can find x

In triangle DEF:

we can use trig formula

[tex]tan(8)=\frac{x}{50}[/tex]

[tex]x=50tan(8)[/tex]

[tex]x=7.0270ft[/tex]

we can see that

height of statue =x+y

so, the height of statue is

[tex]=14.33727+7.0270[/tex]

[tex]=21.4ft[/tex]

The height of the statue to the nearest tenth of a foot is 21.4 ft and this can be determined by using the trigonometric properties

Given :

Refer to the diagram attached below.

From the diagram in triangle ABF:

[tex]\rm tan(16)=\dfrac{a}{50}[/tex]

a = 14.33 ft

From the diagram in triangle DEF:

[tex]\rm tan(8)=\dfrac{b}{50}[/tex]

b = 7.02 ft

Now, the height of the statue is given by:

[tex]\rm Height = a +b[/tex]

Height = 14.33 + 7.02

Height = 21.4 ft

The height of the statue to the nearest tenth of a foot is 21.4 ft.

For more information, refer to the link given below:

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Answer:

it has no solution

Step-by-step explanation:

Answer:

No solution

Step-by-step explanation:

Life

Answer:

D. The two triangles are congruent because a translation does not change size and shape.

Step-by-step explanation:

I'm pretty sure that D is the answer. It jut basically moved , didn't change anything.

Answer:

1. The equation of line is [tex]y=-\frac{1}{2}(x)+1[/tex].

2. The correct option is D.

Step-by-step explanation:

1.

The slope intercept form of a line is

[tex]y=mx+b[/tex]

Where, m is slope and b is y-intercept.

The given equation of a line is

[tex]y=2x+8[/tex]

The slope of line is 2 and y-intercept is 8.

The product of slopes of two perpendicular lines is -1.

[tex]m_1\times m_2=-1[/tex]

[tex]2\times m_2=-1[/tex]

[tex]m_2=-\frac{1}{2}[/tex]

The slope of required line is [tex]-\frac{1}{2}[/tex] and it passes through the point (6,-2).

The equation of required line is

[tex]y-y_1=m(x-x_1)[/tex]

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

[tex]y+2=-\frac{1}{2}(x)+3[/tex]

[tex]y=-\frac{1}{2}(x)+3-2[/tex]

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

Therefore the equation of line is [tex]y=-\frac{1}{2}(x)+1[/tex].

2.

Translation is a rigid transformation. It means if a figure translated then the image and preimage are congruent

It the given figure two triangles are congruent because a translation does not change size and shape.

Therefore the correct option is D.

Answer:

The answer is 7.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

9.75 divided by 1.3 equals 7.5

I used a calculator... :)

Answer:

find below

Step-by-step explanation:

it would either be -1 1/3 or -3/4 since that is the reciprocal of -1 1/3

Answer:

Set the two equations equal to each other if you want me to solve tell me.

So.... 15x+10=16x+3

-15                  -15

10=1x+3

-3

7=x

Answer:

Step-by-step explanation:

Set them equal bc they are vertical angles

15x+10=6x+3

-6x. -6x

9x=

I don't know the rest

The margin of error is 0.97849

we are given

mean=235

so,

[tex]n=235[/tex]

standard deviation =7.5

so,

[tex]\sigma=7.5[/tex]

we know that

ME=2*standard error

and

[tex]SE=\frac{\sigma }{\sqrt{n} }[/tex]

If confidence level is 95%, then we can multiply by 1.96

so, we can multiply by 2 to get ME

now, we can use marginal error formula

[tex]ME=\frac{2\sigma }{\sqrt{n} }[/tex]

now, we can plug values

and we get

[tex]ME=\frac{2\times 7.5 }{\sqrt{235} }[/tex]

[tex]ME=0.97849[/tex]

Answer: 15

Step-by-step explanation:

Answer:

44   You will get the 2x and 88 and divide 88 by 2x

Step-by-step explanation:

Answer:  The required value of x is 22.

Step-by-step explanation:  Given that B and F are the midpoints of the sides AC and AE of triangle ACE.

Also, BF = 2x  and  CE = 88.

We are to find the value of x.

Midpoint theorem :  If a line segment joins the midpoints of any two sides of a triangle, then it is parallel to the third side and its length is equal to half of the length of the third side.

From triangle ACE, we have

B and F are the midpoints of the sides Ac and AE respectively, so BF will be parallel to CE and its length will ne half of the length of side CE.

Therefore,

[tex]BF=\dfrac{1}{2}\times CE\\\\\Rightarrow 2x=\dfrac{1}{2}\times88\\\\\Rightarrow 2x=44\\\\\Rightarrow x=\dfrac{44}{2}\\\\\Rightarrow x=22.[/tex]

Thus, the required value of x is 22.

[tex]\left\{\begin{array}{ccc}2x-y=8&(**)\\y=x-3&(*)\end{array}\right\\\\\text{Substitute }\ (*)\ \text{to}\ (**):\\\\2x-(x-3)=8\\2x-x-(-3)=8\\x+3=8\qquad\text{subtract 3 from both sides}\\\boxed{x=5}\\\\\text{Put the value of x to}\ (*):\\\\y=5-3\\\boxed{y=2}\\\\Answer:\ \boxed{a.\ (5,\ 2)}[/tex]

Answer:

Solution for the given system of equations is (5,2)

Step-by-step explanation:

We have been given the system of equations

[tex]2x-y=8....(1)\\y=x-3...(2)[/tex]

On substituting the value of y from equation (2) in equation (1)

[tex]2x-(x-3)=8[/tex]

Now, we solve the equation for x

[tex]2x-x+3=8\\x+3=8\\x=5[/tex]

Substituting the value of x in equation (2)

[tex]y=5-3\\y=2[/tex]

Therefore, the solution for the given system of equations is (5,2)

a is the correct option.

Answer:

Yes, they are.

Step-by-step explanation:

Lets simplify both rates to the rate typer per minute.

(m is minutes)

3m = 96

Divide both sides by 3:

[tex]\frac{3m}{3} = \frac{96}{3}[/tex]

m = 32

So the rate is 32 words per minute.

5m = 160

Divide both sides by 5:

[tex]\frac{5m}{5} = \frac{160}{5}[/tex]

m = 32

Final answer:

Each term is matched with its correct concept, revealing the fundamental concepts of biological macromolecules and their formation and breakdown through dehydration synthesis and hydrolysis.

Explanation:

Let's match each concept with its correct term:

Macromolecules such as proteins, carbohydrates, and nucleic acids are essential for life and are composed of smaller organic molecules called monomers. When these monomers join together through dehydration synthesis, they release a water molecule and form covalent bonds to create larger structures known as polymers. The opposite process, hydrolysis, involves adding water to break down polymers into monomers.

Answer:

The sum of x and y is a rational number

Step-by-step explanation:

X+Y or 5+7=12

A rational number is any number that can be divided without going on and on forever.

Answer:

The correct answer is A) The sum of the two is a rational number.

Step-by-step explanation:

Since both 5 and 7 are rational numbers, we know that their sum is also a rational number. This is true for any value of rational numbers.

Answer:

The length of side BC is 18 units

Step-by-step explanation:

Perimeter of the rectangle: P=76 units

AB=4z

BC=3z+3=?

We need to determine z

The formula to calculate the perimeter of a rectangle is:

P=2(w+l)

Width: w=AB=4z

Length: l=BC=3z+3

Replacing in the formula:

76 = 2 [4z+(3z+3)]

Eliminating the parentheses:

76 = 2 [4z+3z+3]

Adding like terms:

76 = 2 (7z+3)

Solving for z: Dividing both sides of the equation by 2:

76 / 2 = 2 (7z+3) / 2

38 = 7z+3

Subtracting 3 both sides of the equation:

38-3 = 7z+3-3

Subtracting:

35 = 7z

Dividing both sides of the equation by 7:

35 / 7 = 7z / 7

Dividing:

5 = z

z = 5

Then:

BC=3z+3

Replacing z by 5 in the formula above:

BC = 3(5)+3

Multiplying:

BC = 15 + 3

Adding:

BC = 18 units

Answer:

It took Latisha 2 hours and 18 minutes to finish hiking the trail.

Step-by-step explanation:

Speed = Distance traveled / Time taken

Given:

Distance traveled = 9.66 miles

Speed = 4.2 miles/hour

Time taken = Distance traveled/Speed

                   = 9.66/4.2 =2.3 hours = 2 hours 18 minutes.

∴ It took Latisha 2 hours and 18 minutes to finish hiking the trail.

Answer:

4≥x

Step-by-step explanation:

The person has to be at least four feet (=) or he can be higher (>).

Answer:

The probability is 3/18 which you can simplify down to 1/6. :) Hope this helps! And if you don't mind please mark as brainliest :)

Step-by-step explanation:

Answer:

3 out of 18 or 3/18