What are the possible values of x for the following functions? F(x)= x-3 / 2x+6

Answer:

4/3

Step-by-step explanation:

There different types of wording that tells us that we have a rate of change.

For example, when talking about speed, or in general, when talking about any measure per unit of time (meters per second, gallons per minute, miles per hour) all these are rates of change.

Other example, not as common as the first one, is when the statement refers to a slope, which is in other words, a rate of change.

Similar to the first one, when the statement talks about amounts and/or growth over time, for example: On the first day the plant was 10 cm high, on the second day it was 15 cm high, on the fifth day...

Triangle ADC also has a right angle at D, making it a right-angled triangle.

The exact value of x be 2.25.

The hypotenuse's square is equal to the sum of its two other side squares of a right-angled triangle, according to the Pythagoras theorem.

Triangle ADB exists even a right-angled triangle with right-angle at D.

Therefore, Base of Triangle ADB = BD = 4,

Height of Triangle ADB = AD = 3,

Hypotenuse of Triangle ADB = AB

Using the Pythagoras Theorem, we get,

\($\left[(A D)^2+(B D)^2\right]=(A B)^2$\)

substitute the values in the above equation, we get

or,\($(A B)^2=\left[(3)^2+(4)^2\right]$\)

simplifying the equation, we get

or, \($(A B)^2=[9+16]$\)

or, \($(A B)^2=25$\)

or, \($\sqrt{(A B)^2}=\sqrt{25}$\)

or, AB = 25

Triangle ADC is also a right-angled triangle with right-angle at D.

Therefore, Base of Triangle ADC = DC = x

Height of Triangle ADC = AD = 3,

And, Hypotenuse of Triangle ADC = AC

Using the Pythagoras Theorem, we get,

\(& {\left[(D C)^2+(A D)^2\right]=(A C)^2} \\\)

simplifying the equation, we get

\(& \text { or },(A C)^2=\left[(3)^2+(x)^2\right] \\\)

\(& \text { or },(A C)^2=\left[9+x^2\right]\)

Triangle ABC is also a right-angled triangle with right-angle at A. Therefore, Base of Triangle ABC = AC,

Height of Triangle ABC = AB = 5,

And, Hypotenuse of Triangle ABC =  BC = (4 + x)

Using the Pythagoras Theorem, we get,

\(& {\left[(A C)^2+(A B)^2\right]=(B C)^2} \\\)

\(& \text { or, }(B C)^2=\left[(A C)^2+(A B)^2\right] \\\)

substitute the values in the above equation, we get

\(& \text { or, }(4+x)^2=\left[\left(9+x^2\right)+(5)^2\right] \\\)

simplifying the equation, we get

\(& \text { or, }\left[4^2+(2 \times 4 \times x)+x^2\right]=\left[9+x^2+25\right] \\\)

\(& \text { or, }\left[16+8 x+x^2\right]=\left[(9+25)+x^2\right] \\\)

\(& \text { or, }\left[16+8 x+x^2\right]=\left[34+x^2\right] \\\)

\(& \text { or, }\left[16+8 x+x^2\right]-\left[34+x^2\right]=0 \\\)

\(& \text { or, },(16-34)+8 x+\left(x^2-x^2\right)=0 \\\)

8x - 18 = 0

8x = 18

\(& \text { or, } x=\frac{18}{8} \\\)

\(& \text { or, } x=\frac{9 \times 2}{4 \times 2} \\\)

\(& \text { or, } x=\frac{9}{4} \\\)

Therefore, the value of x be 2.25.

To learn more about Pythagoras Theorem refer to:

https://brainly.com/question/343682

#SPJ1

The properties of quadratic functions cause this "death ray" effect is discussed below.

The "death ray" effect refers to the phenomenon where a quadratic function appears to have a sharp point or vertex that shoots off to infinity in a graph. This effect is caused by the properties of quadratic functions, specifically:

The degree of the quadratic function: Quadratic functions have a degree of 2, which means they have a leading term that is a squared variable (x²). This leads to a graph that is a parabola.

The coefficient of the squared term: The coefficient of the squared term in the quadratic function determines the shape of the parabola. If the coefficient is positive, the parabola opens upward, and if the coefficient is negative, the parabola opens downward.

However, when the coefficient of the squared term is negative (a < 0), the graph of the quadratic function opens downward, and the vertex represents the maximum point of the parabola.

Learn more about Death Ray here:

https://brainly.com/question/13448624

#SPJ1

Answer:

Yes

Step-by-step explanation:

(-2)^2 is the same as (-2)(-2)

-2^2 is the same as -2*-2

both (-2)^2 and -2^2 = 4

Answer: \(x=4\)

Step-by-step explanation:

\(2x-7+x=5\)

Group like terms:

\(\left(2x+x\right)-7=5\)

Simplify the arithmetic:

\(3x-7=5\)

Add 7 to both sides:

\(3x-7+7=5+7\)

Simplify the arithmetic:

\(3x=5+7\)

Simplify the arithmetic:

\(3x=12\)

Divide both sides by 3:

\(\frac{3x}{3}=\frac{12}{3}\)

Simplify the fraction:

\(x=\frac{12}{3}\)

Find the greatest common factor of the numerator and denominator:

\(x=\frac{4\cdot 3}{1\cdot 3}\)

Factor out and cancel the greatest common factor and the answer will be:

\(x=4\)

Reason:

Choices A through C all result in 8/3 = 2.667 approximately

In contrast, choice D becomes 2/3 + 4/3 = (2+4)/3 = 6/3 = 2; showing that choice D is not equivalent to choices A through C.

Answer:

Sarah ate 2, atil ate 2

Step-by-step explanation:

The total number of cookie Sara got = y

Atill got 2 more than Sara so his total cookies is = 2+y

Sarah ate half if hers = y/2

Atil ate 1/3 of his = 2+y/3

We have

Y/2 = 2+y/3

Then we cross multiply

3y = 2(2+y)

3y = 4 + 2y

3y - 2y = 4

Y = 4

Since y = 4,

Sara ate 4/2 cookies = 2

Then atil ate 2+4/3 = 6/3 = 2 cookies

The number of students who play chess, but not tennis is 3.

Given that there are 25 students on the Geoville Math Team and that 11 students play chess and 15 play tennis. Also, it's given that 3 students play neither chess nor tennis. Let's solve the problem using a Venn diagram as shown below:In the diagram, let's label the unknown part, i.e. the number of students who play chess but not tennis, as "x".Now, let's fill in the diagram with the given values.

The number of students who play chess is 11, so we write "11" in the chess circle. The number of students who play tennis is 15, so we write "15" in the tennis circle. And the number of students who play neither chess nor tennis is 3, so we write "3" outside of both circles.

To find the number of students who play chess but not tennis, we need to subtract the number of students who play both chess and tennis from the total number of students who play chess. From the diagram, we can see that 8 students play both chess and tennis (since 11 - 3 = 8). Therefore, the number of students who play chess but not tennis is:11 - 8 = 3 students.

For more such questions on number

https://brainly.com/question/24644930

#SPJ8

Answer:

I think you would have to multiply 1,500 by 12 and also by 18 to figure it out.

Step-by-step explanation:

" "

Answer:

-9

Step-by-step explanation:

f(-3) means that X = -3

f(-3) = 3*-3 = -9

Answer:

See below ~

Step-by-step explanation:

Unit Conversion :

1 quart = 2 pints

1 quart = 4 cups

He wants the 3 quart birdbath to be 3/4 filled.

Hence,

He can fill it with 4.5 pints and using cups :

Answer:

Question 1: The appropriate measures of center for this data set would be (1) Mean and (2) Median. There is no mode in this data set as there are no repeating values.

Question 2: To find the standard deviation, we first need to find the mean:

Mean = (513 + 490 + 496 + 380 + 490 + 513 + 503 + 513 + 500 + 492) / 10 = 494.0

Next, we find the difference between each data point and the mean:

(513 - 494.0), (490 - 494.0), (496 - 494.0), (380 - 494.0), (490 - 494.0), (513 - 494.0), (503 - 494.0), (513 - 494.0), (500 - 494.0), (492 - 494.0)

19, -4, 2, -114, -4, 19, 9, 19, 6, -2

Then we square each difference:

361, 16, 4, 12996, 16, 361, 81, 361, 36, 4

The sum of these squared differences is:

361 + 16 + 4 + 12996 + 16 + 361 + 81 + 361 + 36 + 4 = 14136

To find the variance, we divide the sum of squared differences by the number of data points minus one:

Variance = 14136 / 9 = 1570.7

Finally, we find the standard deviation by taking the square root of the variance:

Standard deviation = √1570.7 ≈ 39.6 (rounded to the tenths place)

Step-by-step explanation:

Answer:

okay, so we have a wall that is 60 ft. The area of the wall because the wall is a square is just side squared. So the area of the wall is \(60^{2}\), which is 30 600 square feet. The mirror is 20 ft by 60 ft. So the area of the mirror, because its a rectangle is length times width, so that's 20 a 60 so 20 x 60 is gonna give me 1200 square feet. So if we take the area of the mirror and put that over the area, the wall we get 1200 over 30 600, which reduces to one over three. So the mirror is one third the area of the wall.

Step-by-step explanation:

For a population rate of change r and a total capacity of the pond C, the logistic growth is given by:

For r = 2.3, P0 = 200 fish and C = 1100 fish, we have:

Answer:

Step-by-step explanation:

Answer:

Number 3 is -17 7/24 yards and Number 2 is -42 1/36 meters

Step-by-step explanation:

Number 3:

-7 2/3 + (-9 5/8)

Then you find common denominator.

-7 16/24 + (-9 15/24)

Add.

-16 31/24

Lastly, Simplify.

-17 7/24

Number 2:

-64 7/9 + 22 27/36

Then you find common denominator.

-64 28/36 + 22 27/36

Add.

-42 1/36

Answer:

1,2,3,4,6,8,9,12,18,24,36 and72

Answer:

Im pretty sure that the answer would be choice f.

Step-by-step explanation:

(a) {T, P, E}: Neither. These points are not collinear because they do not lie on the same line, and they are not coplanar because they are not contained within the same plane.

(b) {A, B, D, M}: Coplanar. These points lie on the same plane since they are contained within the drawing.

(c) {B, K, C}: Collinear. These points lie on the same line within the drawing.

(d) {A, K, E}: Neither. These points are not collinear because they do not lie on the same line, and they are not coplanar because they are not contained within the same plane.

(e) {M, K, T}: Neither. These points are not collinear because they do not lie on the same line, and they are not coplanar because they are not contained within the same plane.

(f) {A, Q, P, D}: Coplanar. These points lie on the same plane since they are contained within the drawing.

EM, P, B: Neither. These points are not collinear because they do not lie on the same line, and they are not coplanar because they are not contained within the same plane.

EM, P, B: Neither. These points are not collinear because they do not lie on the same line, and they are not coplanar because they are not contained within the same plane.

To know more about  "Coplanar."  here

https://brainly.com/question/24430176

#SPJ2

The value of f(x+h)-f(x)  = h.

Given function:

f(x) = x + 7

difference quotient = f(x+h) - f(x)

= (x+h) - 7 - (x - 7)

= x + h - 7 - x + 7

= x - x + 7 - 7 + h

= 0 + 0 + h

= h

Therefore the value of f(x+h)-f(x)  = h.

Learn more about the function here:

https://brainly.com/question/5975436

#SPJ1

Answer:

14.25°

Step-by-step explanation:

distance from middle of the net = 8 m

width of the net = 2 m

this is a case of a triangle with height 8 m, and base 2 m. We are required to find the angle facing the base.

We can get this angle by splitting the triangle into two right angle triangles with base of 1 m, and then solve for the angle facing the base.

We use the trigonometric function;   tan∅ = opp/adj

opp is the side facing the angle = 1 m

adj is the height of the triangle (usually, it is the side besides the opposite side and the longest side; the hypothenus)

adj = 8 m

tan∅ = \(\frac{1}{8}\) = 0.125

∅ = \(tan^{-1}\) 0.125 = 7.125°

Angle within which Lars must fire his shot = 2 x ∅

= 2 x 7.125° = 14.25°

Answer:

Given number = 0.44

Find how many times the value of the hundredths place digit to the value of the tenths place digit.

=> Since this is a decimal number, I believe, the value you mean is tenths and hundredths, not tens and hundreds.

Now, how many times is the value of each digit differs from each other:

The answer is 10 times

=> 4 hundredths x 10 = 4 tenths

=> 0.04 x 10 = 0.4, which is correct

Step-by-step explanation:

Step-by-step explanation:

directly proportional means

y = kx

with k being a constant factor for all values of x.

we get k by using the given data point (10, 15).

15 = k×10

k = 15/10 = 1.5

so, now for the other tree we know k and x and calculate y

y = 1.5×14.4 = 21.6 m

it is 21.6 m tall (its height is 21.6 m).

Answer: Consider me the brainiest. The answer is... Decimal form =4.083

Exact form= 49/12

The mixed number form=4 1/12

How do we solve fractions step by step?

Conversion a mixed number 2  1/3 to a improper fraction: 2 1/3 = 2  1/3 = 2 3 + 1/3 = 6 + 1/3 = 7/3

To find a new numerator

A;   Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3

b) Add the answer from the previous step 6 to the numerator 1. The new numerator is 6 + 1 = 7

c) Write a previous answer (new numerator 7) over the denominator 3.

Two and one-third are seven-thirds.

Conversion a mixed number 1  3/4 to a improper fraction: 1 3/4 = 1  3/4 = 1 · 4 + 3/4 = 4 + 3/4 = 7/4

To find a new numerator:

a) Multiply the whole number 1 by the denominator 4. Whole number 1 equally 1 * 4/4 = 4/4

b) Add the answer from the previous step 4 to the numerator 3. The new numerator is 4 + 3 = 7

c) Write a previous answer (new numerator 7) over the denominator 4. One and three quarters are seven quarters.

Add: 7/3 + 7/4 = 7 · 4/3 · 4 + 7 · 3/4 · 3 = 28/12 + 21/12 = 28 + 21/12 = 49/12 It

is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions.  The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 4) = 12.  It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the following intermediate step, it cannot further simplify the fraction result by cancelling.  In other words - seven thirds plus seven quarters is forty-nine twelfths.

Answer:

\(\frac{4}{5}\)

0.8

Step-by-step explanation:

Happy to help:)

Answer: $72

Step-by-step explanation:

x = money M had before he bought the hat

0.25x = 18

x = 18/.25 = 72

Answer:

Simplifying

25x + 50 = y

Reorder the terms:

50 + 25x = y

Solving

50 + 25x = y

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-50' to each side of the equation.

50 + -50 + 25x = -50 + y

Combine like terms: 50 + -50 = 0

0 + 25x = -50 + y

25x = -50 + y

Divide each side by '25'.

x = -2 + 0.04y

Simplifying

x = -2 + 0.04y

Answer:

We conclude that -1 = 0 is false, therefore the system of equations has no solution.

Step-by-step explanation:

Given the system of equations

y = – 4x + 6

y = – 4x + 5

solving the system of the equations

\(\begin{bmatrix}y=-4x+6\\ y=-4x+5\end{bmatrix}\)

Substitute y = -4x+5

\(\begin{bmatrix}-4x+5=-4x+6\end{bmatrix}\)

Refine – 4x + 5 = – 4x + 6

-1 = 0

FALSE!

NO SOLUTION!

We conclude that -1 = 0 is false, therefore the system of equations has no solution.