The graph of y = f(x) is shown above. If
-4< x <10, for how many values of x does
f(x) = 2?
(A) None
(B) One
(C) Two
(D) Three

The correct standard form of the equation of the parabola is y = 1/4(x - 2)² - 5.

In Mathematics, the standard form of the equation of the directrix lines for any parabola is given by this mathematical expression:

y = a(x - h)² + k.

Where:

Since the directrix is horizontal, the axis of symmetry would be vertical. Based on the graph, we have the following points;

directrix y = -6

Vertex (h, k) = (2, -5)

Focus (h, k + 1/4a) = (2, -4)

k + 1/4a = -4

-5 + 1/4a = -4

1/4a = 1

a = 1/4.

Therefore, the quadratic function (equation) for this parabola is given by;

y = a(x - h)² + k.

y = 1/4(x - 2)² + (-5).

y = 1/4(x - 2)² - 5

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Answer:

A = 20

B = 12.5

C = 10.2

Step-by-step explanation:

A = (10 + 20 + 30)/3 = 20

B = (5 + 10 + 15 + 20) = 12.5

C = (1 + 5 + 10 + 15 + 20) = 10.2

it is proven that there are no integers x, y, z such that x² + y² = 8z + 3.

What is Integers?

A whole number is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+, and √2 are not. The set of integers consists of zero, positive natural numbers, also called integers or counting numbers, and their additive inverses.

To prove that there are no integers x, y, z such that x² + y² = 8z + 3, we can use the concept of modulo arithmetic.

First, let's consider the possible values of x² and y² modulo 8:

For any integer n, n² modulo 8 can only be 0, 1, or 4.

Now, let's examine the possible values of 8z + 3 modulo 8:

8z modulo 8 is always 0.

3 modulo 8 is equal to 3.

Therefore, the possible values of x² + y² modulo 8 can only be 0, 1, or 4, while 8z + 3 modulo 8 is equal to 3. Since 0, 1, and 4 are not equal to 3 modulo 8, there are no integers x, y, z that satisfy the equation x² + y² = 8z + 3.

Hence, it is proven that there are no integers x, y, z such that x² + y² = 8z + 3.

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Answer: 8?

Step-by-step explanation: you want one shirt

Answer:

8

Step-by-step explanation:

Step 1 Add 2 to both sides.

5x=3+2

Step 2 Simplify  3+23+2  to  55.

5x=5

Step 3 Divide both sides by 5.

x=1

Hoped this helped :)

Also if this answered your question you can maybe give me brainilest?

Answer:

The answer would be True

Step-by-step explanation:

Because your getting 35 bagels for $10 rather then getting 5$ for 18

Your getting a cheaper price for more.

I CALL THAT A WIN - WIN!!!!!!!

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Answer:

True

Step-by-step explanation:

Answer:

hi hi hi hi hi hi hi hihi hi hi hi hi hi

Answer:

3 students

Step-by-step explanation:

1. Multiply 27 students by 11.111....%

   That would look like:

    27 x 0.1111111111 = 3

2. The answer is 3 students know calligraphy.

Answer:

regular price is $22.50

Step-by-step explanation: 22.50*.20=4.5 (discount)

The digit the represent the variable A is equal to the value 7. The actual value is 3771.

Let the equation be 3AA1 = 9M

M must be an even number  > 0

So,

3 + 1 + 2A  = 9M

4 + 2A  = 9M

2A  = 9M - 4

M = 2, A = 7

And 3771 / 9  =  419

Therefore, the value of A from the given question is 7.

           (or)

3 + 2A + 1 = 9

4 + 2A = 9

Notice how a will NOT be an integer, so we try 18.

3 + 2A + 1 = 18

4 + 2A = 18

14 = 2A

A = 7

Therefore, digit the represent the variable A is equal to the value 7. The actual value is 3771.

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Answer:

The missing fraction is 6/12

(you can further simplify this but the question requires that you don't do that)

Step-by-step explanation:

To add fractions easily, their denominators should have the same value, so the denominator should be 12,

Then, to get 16 in the numerator, we need to find a number that on adding to 10, gives 16, or,

10 + x = 16

x = 16 - 10

x = 6

So, the numerator should be 6

so we get the fraction, 6/12

We can also solve it in an alternate way,

\(10/12 + x = 16/12\\x = 16/12 - 10/12\\x = (16-10)/12\\x = 6/12\)

73 kg is equivalent to approximately 160.937 pound (lbs).

Kilogram (kg) and pound (lb) are both units of mass commonly used in different parts of the world. Kilogram is the base unit of mass in the International System of Units (SI) and is defined as the mass of the International Prototype of the Kilogram, which is a platinum-iridium cylinder kept at the International Bureau of Weights and Measures in France.

Pound, on the other hand, is a unit of mass commonly used in the United States, the United Kingdom, and other countries, which is defined as exactly 0.45359237 kilograms. This value is based on the international avoirdupois pound, which is defined as exactly 0.45359237 kg.      

To convert kilograms to pounds, you can use the conversion factor of 2.20462 lbs/kg. To convert pounds to kilograms, you can use the conversion factor of 0.45359237 kg/lb.

To convert 73 kilograms (kg) to pounds (lbs), you can use the conversion factor of 2.20462.

So,

73 kg * 2.20462 lbs/kg = 160.937 lbs (rounded to three decimal places)

Therefore, 73 kg is equivalent to approximately 160.937 lbs.

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The results for the given composite functions are-

a) f(g(x)) = x

b) g(f(x)) = x

c) g(x) is an inverse function of f(x)

The given functions are:

f(x) = x + 1

and

g(x) = x - 1

Now, we can evaluate the composite functions as follows:

Part (a)f(g(x)) means f of g of x

Now, g of x is (x - 1)

Therefore, f of g of x will be:

f(g(x)) = f(g(x))

= f(x - 1)

Now, substitute the value of f(x) = x + 1 in the above expression, we get:

f(g(x)) = f(x - 1)

= (x - 1) + 1

= x

Part (b)g(f(x)) means g of f of x

Now, f of x is (x + 1)

Therefore, g of f of x will be:

g(f(x)) = g(f(x))

= g(x + 1)

Now, substitute the value of g(x) = x - 1 in the above expression, we get:

g(f(x)) = g(x + 1)

= (x + 1) - 1

= x

Part (c)From part (a), we have:

f(g(x)) = x

Thus, g(x) is called an inverse function of f(x)

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The function g(3)'s expression is 8, which is

The supplied function is defined by a single expression, as per the query. Calculate the value of the other function using the provided expression.

In light of this, g(r) = -5 + 13 = 8

Additionally, the computed value can also be used as the value of the function expression g(3).

Consequently, the value of the function provided is 8.

The relationship between the dependent and independent variables is explained by the function. For the functions, it has a collection of values that may be connected using the domain technique.

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Hence, the factors of \((10x+1)^2=100x^2+1+20x\).

What are the factorization?

Factorisation or factoring is defined as the breaking or decomposition of an entity into a product of another entity, or factors, which when multiplied together give the original number.

Here given expression is

\(100x^2+1\)

\((10x)^2+(1)^2\)

\((10x+1)^2\)

As we know that,

\((a+b)^2=a^2+b^2+2ab\)

Here

\(a=10x\\b=1\)

So,

\((10x+1)^2=(10x)^2+(1)^2+2(10x(1))\\\\(10x+1)^2=(10x)^2+(1)^2+20x\\\\(10x+1)^2=100x^2+1+20x\)

Hence, the factors of \((10x+1)^2=100x^2+1+20x\).

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The factors of the expression 100x² + 1 are (10x+i) (10x-i).

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

The given expression is 100x² + 1.

The given expression is a quadratic function.

The standard form of quadratic function:

ax²+bx +c, where a is not equals to zero.

Comparing with the standard form we get,

a = 100, b = 0 and c = 1

Simplifying,

100x² + 1

=  100x² - (-1)

= (10x)² - (-1)

= (10x)² - (i)²   ,{i² = -1}

= (10x+i) (10x-i)

Therefore, (10x+i) (10x-i) are the factors.

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It cannot be determined. At least one other point on the line is needed to determine if x is proportional to y

Given data ,

A point on a straight line has an x-coordinate of 3 and a y-coordinate of 6

Now , A single point on a straight line does not define the connection between x and y. We must evaluate the connection between x and y for several places on the line in order to establish if x is proportional to y.

As a result, the relationship between x and y cannot be inferred only from the supplied location (3, 6). To establish the proportionality between x and y, at least one more point on the line is required

Hence , the equation of line is solved

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The ratio of the volume of the cylindrical tank to its surface area will be r / 2.

A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.

Let r be the radius and h be the height of the cylinder.

Then the volume of the cylinder will be

V = π r²h cubic units

Then the surface area of the cylinder will be

SA = 2πrh square units

Then the ratio of the volume of the cylindrical tank to its surface area will be

V / SA = π r²h / 2πrh

V / SA = r / 2

The ratio of the volume of the cylindrical tank to its surface area will be r / 2.

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Answer:

-1/4

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-8-(-5))/(0-(-12))

m=(-8+5)/(0+12)

m=-3/12

simplify

m=-1/4

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Answer: $23.92

Step-by-step explanation:

First, we know that 6 bagels is $2.99.

48/6=8

This means that 6 is a multiple of 48, which makes it easier to solve.

$2.99 x 8 = 23.92

= $23.92

The first 3 terms of the sequence using the expression are -5, -4 and -1

From the question, we have the following sequence that can be used in our computation:

n(n – 2) – 4

This means that

T(n) =  n(n – 2) – 4

Set n = 1, 2 and 3

So, we have

T(1) =  1 * (1 – 2) – 4 = -5

T(2) =  2 * (2 – 2) – 4 = -4

T(3) =  3 * (3 – 2) – 4 = -1

Hence, the first 3 terms of the sequence using the expression are -5, -4 and -1

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Answer:

one solution

infinite number of solutions  

no solutions

Step-by-step explanation:

i hope this helps :)

Answer:

i think 18

Step-by-step explanation:

The missing terms in the sentence are "Inclination" and "Vertical."

Inclination is the angle of tilt below the imaginary horizontal plane oriented 90-degrees to the vertical direction. It refers to the angle at which an object or surface deviates from being perfectly horizontal or flat. It measures the slope or tilt of the object or surface in relation to the vertical direction.

The vertical direction is the imaginary line or axis that points directly up or down, perpendicular to the horizontal plane. It is oriented at a 90-degree angle to the horizontal direction, which is typically considered the direction parallel to the ground or any other reference plane.

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Answer:

37.916667%

Step-by-step explanation:

455/1200 = 0.37916667

0.37916667 * 100 = 37.916667%

The percentage of all the students who said that their favorite sport was hockey was 37.9%

There are 1,200 students in total and out of these, 455 claim that hockey is their favorite sport.

To find the percentage that this is, use the formula:

= Number of students who like hockey / Total number of students x 100%

= 455 / 1,200 x 100%

= 37.9%

In conclusion, 37.9% of the students have hockey as their favorite sport.

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According to the rectangle plot, the total length of fence that Farmer Ted will use can be expressed in terms of x as 2x + 432/x.

Now, the problem asks us to find the total length of fence that Farmer Ted will use to enclose the rectangle and divide it into two equal parts using another fence parallel to one of the sides. To solve this problem, we need to first visualize the rectangle and understand what's happening.

Next, we need to enclose the rectangle with a fence. This means we need to find the perimeter of the rectangle, which is the total length of all its sides. The perimeter of a rectangle can be found by adding up the lengths of all its sides:

Perimeter = 2x + 2y

Now we have two smaller rectangles with dimensions x by y/2. The total area of both rectangles is still 216 square meters, so we can set up an equation to solve for y:

(x)(y/2) + (x)(y/2) = 216

Simplifying this equation, we get:

xy = 216

We can now use this equation to solve for y in terms of x:

y = 216/x

We can substitute this value for y in the equation for the perimeter of the original rectangle:

Perimeter = 2x + 2y

Perimeter = 2x + 2(216/x)

Simplifying this equation, we get:

Perimeter = 2x + 432/x

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Answer:

AAS

Step-by-step explanation:

For 2 triangles to be congruent, they must meet 1 of the following relative to each other:

These two triangles share 2 of the same angles and 1 of the same sides.

Therefore, they meet the AAS criteria.

The solution of the equation 3z minus 2 is equal to 46 is 16.

The given equation '3z minus 2 is equal to 46' can be written as

    3z - 2  =   46

Now solving for z because the value of z will give the required solution of the given equation. So now finding the z from the equation:

   3z = 46  + 2

   3z =  48

   z = 48/3

   z = 16

The value of the z is 16 which represents the solution of the given equation i.e 3z minus 2 is equal to 46.

Therefore it is concluded that the solution of the equation 3z minus 2 is equal to 46 is 16.

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One number is multiple times the principal number. The numbers are 93, 837 and 193.

Given, one number is multiple times a first number.

A third number is 100 a greater number of than the primary number.

The amount of the three numbers is 1123,

We really want to track down the numbers.

allow the principal second and third numbers to be a, b, c respectively

According to given information, b = 9a - - - - (1)

c = 100 + a - - - - (2)

a + b + c = 1123 - - - - - (3)

presently substitute (1) and (2) in (3)

a + 9a + 100 + a = 1123

11a + 100 = 1123

11a = 1123 - 100

11a = 1023

a = 93

presently substitute a value in (1) and (2)

b = 9 x 93 = 837

c = 100 + 93 = 193

thus, the numbers are 93, 837, 193.

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