Find the minimum and maximum values of the function on the interval [11,27].

Given 2-(×+4)=10​, to find x, our 1st step will be to open the bracket;

The 2nd step is to add 2 to both sides of the equation, this will give us the below;

The final thing to do is to multiply both sides of the equation with -1;

Therefore. x

The most appropriate choice for properties of addition will be given by-

The correct option will be additive identity

What is addition and its properties?

To find the total of two or more numbers, addition is used

There are some properties of addition

Let a, b and c be three numbers

1) Commutative property

The value of a + b is same as the value of b + a

a + b = b + a

2) Associative property

On adding more than two numbers, changing of bracket is permissible.

(a + b) + c = a + (b + c).

3)Additive identity

There is a number called additive identity. If any number is added to the additive identity, we will get back the same number. Here, 0 is the additive identity

a + 0 = a

4) Additive Inverse

Every number has an additive inverse.

On adding a number with the additive inverse, the result will be additive identity.

-a is the additive inverse of a

a + (-a) = 0

Here,

[tex]-\sqrt{3}+0=-\sqrt{3}[/tex]

0 is the additive identity

So this is the case of additive identity.

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The output value of the function is 8 when the input value is -2

A relation's input value is its first value, and its output value is its second. A particular kind of relation called a function is one in which every input value has only one and only one output value.

The value of an input is the independent value, but the value of an output is dependent on the value of the input.

Only data flows, mining flows, and sub processes can use input variables. The variable value that was modified inside a sub process is output using output variables.

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1) If Rachel's garden is a square and the area is mentioned, let's use the area of the square.

S= l²

36 =l²

Flipping it:

l²=36

l=√36

l=6

2) So the length of Rachel's garden is 6 feet.

Answer:

[tex]x\sqrt{3x}[/tex]

Step-by-step explanation:

Given expression to simplify:

[tex]4x\sqrt{3x}-x\sqrt{3x}-2x\sqrt{3x}[/tex]

Factor out the common term [tex]\sqrt{3x}[/tex] :

[tex]\implies \sqrt{3x}(4x-x-2x)[/tex]

Carry out the operations inside the parentheses:

[tex]\implies \sqrt{3x}(3x-2x)[/tex]

[tex]\implies \sqrt{3x}(x)[/tex]

Therefore the simplified expression is:

[tex]\boxed{x\sqrt{3x}}[/tex]

Answer:

a) x√(3x)

Step-by-step explanation:

We have to simplify,

→ 4x√(3x) - x√(3x) - 2x√(3x)

Then the simplest form is,

→ 4x√(3x) - x√(3x) - 2x√(3x)

→ 4x√(3x) - 3x√(3x)

→ x√(3x)

Hence, option (a) is correct.

The correct option for the equation of line is; y ≥ x - 4.

For the given question;

Consider two points lying on the line.

(x₁, y₁) = (4, 0)

(x₂, y₂) = (0, -4)

The, the slope of the line is found using;

slope = m = (y₂ -y₁)/(x₂ - x₁)

m = (-4 - 0)/(0 - 4)

m = 1

Now, the standard form of equation of line is;

y - y₁ = m(x - x₁)

Put the values,

y - 0 = 1(x - 4)

y = x - 4

As, the origin of the coordinates axis and the shaded portion lies on the opposite side of the line, thus the inequality used is greater than equal to.

y ≥ x - 4

Thus, equation of line obtained for the given graph is y ≥ x - 4.

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rate = 12 laps/4 min = 3 laps/min

3 laps ------------------ 1 min

x ------------------ 9 min

x = (9 x 3) / 1

x = 27 laps in 9 min

Result 27 laps in 9 min

The probability of selecting blue, yellow and blue marble without replacement is 3/170

Number of red marbles = 7

Number of blue marbles = 4

Number of yellow marbles = 6

Total number of marbles = 17

Probability of selecting a red marble = 7/17

Probability of selecting a blue marble = 4/17

Probability of selecting a yellow marble = 6/17

Now the probability of selecting the first blue marble = Number of blue marbles/Total number of marbles. = 4/17

Probability of selecting the yellow marbles = Number of yellow marbles/Number of marbles left after the first draw = 6/16

Probability of selecting the third blue marble = Number of blue marbles/Total number of marbles left after the second draw = 3/15

So the probability of blue, yellow and blue marble is:

4/17*6/16*3/15 = 3/170

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The length of each segment ST = 63, TU = 63, SU = 126

The midpoint theorem states that “The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.”

From the given figure

ST = 9x

TU = 5x+28

According to midpoint theorem,

ST = TU

9x = 5x+28

9x-5x = 28

4x = 28

x = 7

It means,

ST = 9×7 = 63

TU = 5×7+28 = 35+28 = 63

SU = ST+TU

     = 63+63

ST = 126

Hence, The length of each segment ST = 63, TU = 63, SU = 126

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If the cost of making the dish is $6.75, and he wants to make a 33% profit on each dish he sells. adam's selling price is: $8.98.

Using this formula to find the selling price

Selling price = Cost price + (Cost price × Profit percentage)

Let plug in the formula

Selling price = $6.75 + ($6.75 × 33%)

Selling price = $6.75 + $2.2275

Selling price = $8.977

Selling price = $8.98 (Approximately)

Therefore the selling price is the amount of $8.98

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a) It's a linear function because if time increases, precipitation increases. I'll graph it. On the graph we observe that the points form a line.

b) Both intercepts have the same meaning.

It means the amount of water (rain) at time = 0, when it still does not started to rain.

Answer:

chose your top 3 flavors

As shown in the figure : we have a right angle triangle

We need to find the value of x

The hypotenuse of the triangle = 29

And x represents the opposite side of the angle 19

So,

rounding the answer to the nearest tenth

So,

Vertically opposite angles are equal

Therefore,

The vertex is the minimum/maximum point of the parabola.

This parabola has a dip, minimum point.

Looking at the coordinates, the vertex is at:

Vertex = (1,1)

The axis of symmetry is always the x-coordinate of the vertex coordinate.

That is x = 1.

So,

Axis of Symmetry:

x = 1

Now,

Since x = 1 (vertical line) is the axis of symmetry, we reflect the points P and Q about this line and find the points P' and Q'.

P' = (2,2)

Q' = (-1,5)

To solve the question, we can plot the two functions on the same graph as shown below

The blue graph is that for the function g(x)

While that of the red graph is that of the function f(x)

We can observe that the graph of g(x) is

Also,

Thus, we can see that

The graph of g(x) is shifted 6 units below and 11 units to the left of the graph f(x)

Thus, option C is correct

ANSWER:

13 years old

STEP-BY-STEP EXPLANATION:

Let x be Devaugn's age and y be Sydney's age.

We establish the following linear equation system:

We solve the first equation in the second equation:

Which means Sydney's age is 13 years old.

The Domain of the relation is: -∞ < x <  ∞

The Range of the relation is: -∞ < y ≤ -3

What are Domain and Range?

The Domain of the function is the set of x-values for which the function is defined, whereas the Range of the function is the set of y-values for which it is defined.

Let us first determine the Domain.

On the x-axis, the curve starts from x = -∞, and ends at x = ∞  

So, the domain of the relation is: -∞ < x <  ∞  

Next, let us now determine the Range.

On the y-axis, the curve starts from y = -∞, and it ends at y = -3

The Range of the relation is: -∞ < y ≤ -3

Hence the domain and the Range of the graph are: -∞ < x <  ∞ and -∞ < y ≤ -3

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The given equation is

First, we subtract 7x on each side.

Answer:

A

Step-by-step explanation:

f(x) - g(x)

= [tex]\sqrt{x}[/tex] - x - (2x³ - [tex]\sqrt{x}[/tex] - x) ← distribute parenthesis by - 1

= [tex]\sqrt{x}[/tex] - x - 2x³ + [tex]\sqrt{x}[/tex] + x ← collect like terms

= - 2x³ + 2[tex]\sqrt{x}[/tex]

ANSWER

EXPLANATION

The slope-intercept form of a line is,

In this case, we have an inequality but the steps to rewrite it in the slope-intercept form are similar to the ones we would use if we had an equality.

Step 1: subtract x from both sides of the inequality,

Step 2: divide both sides by 2,

Step 3: distribute the denominator and simplify the fractions if possible,

Hence, the inequality in slope-intercept form is,

Since both inequalities don't have the equal to symbol (≤) Both lines must be dashed lines.

So, the top right option can't be.

Now we have 3 options:

If we graph the inequality: y < -3/4x + 1

It has a slope of -3/4 and a y-intercept on 1.

The only available option that represents this inequality is the right bottom one.

The most appropriate choice for  linear equation will be given by -

Total cost of setting up their shop and creating pygmy puffs, as a function of the number of boxes of pygmy puffs produced, p

C(p) = 3p + 1000

Second option is correct

What is  linear equation?

Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Here,

Initial cost of  manufacturing Weasley's Wizarding Wheezes by the Weasley brothers = 1000 galleons

Cost of producing one pygmy puff = 3 galleons

Cost of producing p boxes of pygmy puffs = 3p galleons

Total cost of setting up their shop and creating pygmy puffs, as a function of the number of boxes of pygmy puffs produced, p

C(p) = 3p + 1000

Second option is correct

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Complete Question

The Weasley brothers estimate that they will need a thousand galleons just to set up their joke shop, Weasley's Wizarding Wheezes. The first products they are manufacturing are pygmy puffs, and they realize that the cost of making a single box of pygmy puffs is 3 galleons. The brothers would like to estimate the cost, in galleons, of setting up their shop and creating pygmy puffs, as a function of the number of boxes of pygmy puffs produced, p. Which of the following equations is the correct equation representing this scenario?

1) C(p) = 3p - 1000

2) C(p) = 3p + 1000

3) C(p) = 1000p - 3

4) C(p) = 1000p + 3

Answer:

5

Step-by-step explanation:

6*9= 54

54/7 = 7 with remain 5

The second equation already has the value of x isolated, so in order to solve the system by substitution, we can apply this value of x from the second equation in the first one:

Now that we have the value of y, we can find the value of x:

So we have that x = -25 and y = 5.

Answer:

what is the question?

Step-by-step explanation:

Please write the question so i can answer it.

Answer: 24

Step-by-step explanation:

{(-4,-9), (-4,4),(-2,2), (9,5)}

Because the x values of -4 occurs more than once, the set of ordered pairs is not a function.

What is cross multiplication?
To discover the unknown values in a mathematical equation, we cross multiply the numbers in the equation. The method of cross multiplication is frequently employed to identify the missing variable in an equation. We multiply both the numerator and denominator of the provided expression or fractions.
If w/e = r/t is the given expression, then the formula for cross multiplication can be given as: w*t = r*e

For 11, comparing numerators by multiplying the 'x' on right with 2.5 we get, x - y = 2.5x ⇒ 1.5x + y = 0, only possible if y = -1.5x
Therefore, the blank in 11 should be filled using (-1.5x).
For 12, comparing numerators by multiplying LHS with 6 and RHS with 4, we get, 6(h + y) = 4(h - 12) ⇒ 6h + 6y = 4h - 12 ⇒ 6y = -2h -12
⇒ y = (-1/3)h -2
Therefore, the blank in 12 should be filled using (-1/3)h -2.
Similarly, using cross multiplication and equating denominators for the next four, the blank spaces can be constructively filled.

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