A landscape supply business charges $35

Answer:

The solution set of x^2 + 4x - 21 ≤ 0 is (-7, -3)

Step-by-step explanation:

To solve this inequality, we first set x^2 + 4x - 21 = 0 and factor it to get (x + 7)(x - 3) = 0. This gives us x = -7 and x = 3 as the solutions.

To find the solution set of x^2 + 4x - 21 ≤ 0, we need to determine the values of x that make the expression on the left-hand side non-positive. Since x^2 + 4x - 21 is a quadratic function, it is non-positive when x is less than -3 or x is greater than -7.

Therefore, the solution set of x^2 + 4x - 21 ≤ 0 is the set of all x such that x ∈ (-7, -3).

The FOIL method to find the product (x + 5)(x² - 3x) is x³ + 2x² - 15

You should note the following about FOIL method

It stands for "First, Outer, Inner, Last"

It is the sum of:

· multiplying the First terms,

· multiplying the Outer terms,

· multiplying the Inner terms, and

· multiplying the Last terms

That is  (a+b)(c+d) = ac + ad + bc + bd

Use FOIL (First, Outside, Inside, Last)

The give expression is

x(x²) = x³

x(-3x) = -3x²

5(x²) = 5x²

5(-3x) = -15x

Combine like terms:

x³ - 3x² + 5x² - 15x

x³ + 2x² - 15

Therefore the FOIL method is x³ + 2x² - 15

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For the graph of the function F(x), when x goes from 0 to 1, F(x) is a negative number with large absolute value. Option D is correct.

A function that wraps an algebraic expression in absolute value symbols is known as an absolute value function. Remember that a number's distance from 0 on the number line represents its absolute value.

When the value of x goes from 0 to 1 the function shifts and the value is decreased gradually, thus giving F(x) as negative number with a large absolute value.

Hence, option D is the correct answer.

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The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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Answer:

Step-by-step explanation:

Using Squeeze theorem, the limit of the function is 0

The Squeeze Theorem states that if f(x,y) <= g(x,y) <= h(x,y) for all x,y in a region around (x0,y0) and lim (x,y)->(x0,y0) g(x,y) = L, then lim (x,y)->(x0,y0) f(x,y) = lim (x,y)->(x0,y0) h(x,y) = L.

We can use the Squeeze Theorem to find the limit of the given function by finding two other functions that bound it and have known limits as (x,y) approaches (0,0).

We can see that

(x^2+y^2)/(x^2+y^2) <= 3x^2y/(x^2+y^2) <= (3xy)/(x^2+y^2)

As x,y approaches 0, the first inequality approaches 1 and the second one approaches 0, so the limit of the given function is also 0.

Therefore, lim [(x,y) -> (0,0)] (3 . x^2 . y / (x^2 + y^2)) = 0.

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Answer:

y = -x - 3

Step-by-step explanation:

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Given that the point (-8,5) lies on the line and the slope of the line is m=-1, we can use the point-slope form of a linear equation to write the equation of the line.

The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line.

So substituting the given point (-8,5) and slope m=-1 into the point-slope form, we get:

y - 5 = -1(x + 8)

Simplifying, we get:

y = -x - 3

This equation is the slope-intercept form of the line that passes through the point (-8,5) and has a slope of -1.

Average rate of change of reading = [tex]\frac{7034 - 6852}{3.5} = 52[/tex] miles per hour

The equation representing t in hrs and odometer reading after noon in y is

y = 6852 + 52t

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.

The reading in odometer =6852 miles at 12:00

The reading in odometer = 7034 miles at 3 :30 pm

Average rate of change of reading = [tex]\frac{7034 - 6852}{3.5} = 52[/tex] miles per hour

An equation representing t in hrs and odometer reading after noon in y is

y = 6852 + 52t

The point is (5,7112)

for t = 5

y = 6852 + 52*5 = 7112 (proved)

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Answer:

  -0.155

Step-by-step explanation:

You want the slope of Bob's descent when he descends 3200 feet in a horizontal distance of 3.9 miles.

To find the slope of Bob Dean's descent, we can use the formula:

  slope = (change in elevation) / (change in horizontal distance)

In this case, the change in elevation is 3200 feet and the change in horizontal distance is 3.9 miles.

  slope = -3200 feet / (3.9 miles)

To convert the horizontal distance to feet, we multiply by 5280 (the number of feet in a mile)

  slope = -3200 feet / (3.9 * 5280 feet)

  slope = -3200 / 20,592

  slope ≈ -0.1554

The slope of Bob Dean's descent is about -0.155.

__

Additional comment

As a percent grade, this is a 15.5% grade, very steep. He will need to check his brakes before he starts down.

By solving a linear equation we will see that the polygon has 19 sides.

Remember that for a polygon of n sides, the sum of the interior angles is equal to:

(n - 2)*180°

Here we also know that 3 angles are:

136°, 138°, and 146°

And the rest of the angles (n - 3) angles are of 165° each.

Then the sum of the interior angles gives:

136° + 138° + 146° + (n - 3)*165°

And that must be equal to the expression above, so we can write the linear equation:

136° + 138° + 146° + (n - 3)*165°  = (n - 2)*180°

420° + n*165° - 495° = n*180° - 360°

n*165° - 75° = n*180° - 360°

360° - 75° = n*180 - n*165

285° = n*15°

285°/15° = n

19 = n

That is the solution.

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Answer:

Amount = $ [tex]2080[/tex]

Step-by-step explanation:

Given ,

To Find : The Amount

We can derive the SI i.e the Simple Interest by the formula,

[tex]SI = \frac{PRT}{100}[/tex]

Applying the values into the given equation we get,

[tex]SI = \frac{2000X8X5}{100}[/tex]

Substituting we get,

[tex]SI = 80$[/tex]

[tex]Amount =[/tex] [tex]SI + Principal[/tex]

[tex]Amount = 80 + 2000[/tex]

[tex]Amount = $2080[/tex]

Therefore , to calculate the  average AVC, use the formula: TC at 0 output is 5, which equals fixed cost (FC) of 5.

The fixed cost per unit of output is known as the AFC, and the variable cost per unit of output is known as the AVC. We previously stated that Bob's Bakery can produce 100 loaves with FC = 40, VC = 500, and TC = 540. ATC = TC/Q = 540/100 = 5.4 as a result. Additionally, AVC = 500/100 = 5 and AFC = 40/100 = 0.4.

Here,

Total cost is equal to total fixed cost plus total variable cost, or TC.

In order to obtain the VC at each output, we must first subtract 5 from the TCs for all subsequent output levels.

AVC is now equal to VC divided by Q.

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Answer:

Step-by-step explanation:

You want to use the graph to evaluate the compositions ...

where f(x) = x² -2x -3, and g(x) = x -2.

To find the value of a graphed function, locate the function argument on the x-axis and find the point of intersection of that vertical line with the graph. The y-coordinate of that point is the function value.

Here, we're asked to read the graph to find f(1), use that value to find g(f(1)), then use that value to find f(g(f(1))). This last value is f(-6), which is off the top of the graph. We need to use the equation to find the value:

  f(x) = (x -2)x -3

  f(-6) = (-6 -2)(-6) -3 = 48 -3 = 45

The value of f(g(f(1))) is 45. The equation must be used for this.

Reading the graph for g(0), we find the value to be -2. Then f(-2) is 5, and g(5) is 3.

The value of g(f(g(0))) is 3.

__

Additional comment

A suitable calculator or spreadsheet can evaluate these expressions for you.

19.63

Step-by-step explanation: area of circle=pi*r^2

3.14*2.5^2

3.14*6.25

=19.625 rounded to nearest tenth is 19.63

Answer:I think being honest with them just tell them how you really feel not because just they ask and you just say I am fine how are you just tell how you really feel about that day. Be honest ...

Step-by-step explanation:

How I've been today? Quite magnificent. Thank thou for your generosity.

Answer:

The equation that this graph corresponds to is y -3/4x + 8

Step-by-step explanation:

The answer choice you chose is correct.

The  age of the older brother is 21 years

Two or more expressions with an Equal sign is called as Equation.

Six years ago, the sum of the ages of two brothers was 22

x+y=22

The product of their ages is 21

xy=21

y=21/x

x+21/x=22

x²+21=22x

x²-22x+21=0

Factorize the equation

x²-21x-x+21=0

x(x-21)-(x-21)=0

(x-1)(x-21)=0

x=1 and x=21

21+y=22

y=1

Hence, the  age of the older brother is 21 years

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Answer:

3.25

Step-by-step explanation:

To find the arithmetic mean of a set of data, you add up all of the values in the set and then divide by the total number of values.

In this case, the set of data is {6, 1, 5, 1} and the total number of values is 4.

To find the arithmetic mean, we add up all the values:

6 + 1 + 5 + 1 = 13

then divide by the total number of values:

13 / 4 = 3.25

So the arithmetic mean of the set of data {6, 1, 5, 1} is 3.25.

For the local salesman to have a monthly income of $3,000, using mathematical operations, he would need to sell $20,045 worth.

The sales revenue that the local salesman should generate to reach his monthly income target is determined by working backward with the mathematical operations of subtraction, division, multiplication, and addition.

Firstly, the base salary is deducted from the expected monthly earnings to obtain the amount of the sales commission.

The sales commission is equated to its commission percentage through division and multiplication operations.

The result is added to $500 to arrive at the expected sales revenue.

The monthly base salary = $850

Commission = 11% on sales above $500

Needed monthly income = $3,000

Sales commission = $2,150 ($3,000 - $850)

11% = $2,150

100% = $19,545 ($2,150/11% x 100%)

$19,545 = Sales above $500

Total target sales = $20,045 ($19,545 + $500)

Thus, if the salesman expects a monthly income of $3,000, he must generate monthly sales revenue of at least $20,045.

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The trigonometric ratios as fractions in simplest terms are sin X= 8/17 and cos W= 8/17.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

In the given triangle WVX, WV=24, WX=51 and VX=45

We know that, sinθ = Perpendicular/Hypotenuse and cosθ = Base/Hypotenuse

Here, sin X= 24/51

sin X= 8/17

cos W= 24/51

cos W= 8/17

Therefore, the trigonometric ratios as fractions in simplest terms are sin X= 8/17 and cos W= 8/17.

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The square root of a number is only defined for non-negative numbers, since the square root of a negative number is not a real number.

For the expression sqaure root of -(6-x) to make sense mathematically, the expression inside the square root must be non-negative.

So, we need to find the values of x that make -(6-x) non-negative.

-(6-x) is non-negative when -(6-x) ≥ 0

Simplifying this inequality, we get 6-x ≤ 0

x ≤ 6

So, for x ≤ 6, the expression sqaure root of -(6-x) is defined and makes sense mathematically. This is the domain of the expression.

In summary, the domain of the expression sqaure root of -(6-x) is x ≤ 6.

The given system of equations has infinitely many solutions. Option A is correct.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
Given equation,
- 6x - 2y = 10 - - - -1

y = - 3x - 5  - - - -2

From equation 1
-6x - 2y = 10
Reform the equation,
-2y = 6x + 10

Divide the above equation by -2,
y = -3x - 5

Since the above equation is equivalent to equation 2, therefore the system of equations has infinitely many solutions.

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Answer : 165/2

To do this, we just have to add 82 and 1/2. However, the question asks for an improper fraction, so we turn 82 into 164/2. Now, we add 1/2 to 165/2 which equals 164+1/2 = 165/2.

The required system of equation has no solution.

The more physical interpretation of the idea of two linear equations having a linear equation is that it will always have a singular solution regardless of whether the lines are parallel or coinciding.

We have,

4x + 10y = 57---------------(1)

2x + 5y = 38

Multiply 2

4x + 10y = 76----------(2)

So, above equation (1) and (2) has no solution.as values of x and y are not same for both the equation.

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Answer: 360

Step-by-step explanation:

If 10% of people were 55 or older, than 90% of people were younger than 55.

This is 9 times the number of people that were 55 or older.

Therefore, the answer is 360.

The age of the older brother is 13

From the information given, let their ages by x and y

This is represented as;

x + y = 22

(x - 6) (y -6) = 21

From equation (1), make x, the subject of formula

x = 22 - y   (3)

Substitute equation (3) in equation (2), we get;

(22 - y- 6)(y - 6) = 21

expand the brackets

(16 - y)(y-6) = 21

16y - 96 - y² +6y = 21

collect iike terms

-y² + 22y - 96 - 21 = 0

subtract like terms

-y² + 22y - 117 = 0

y²- 22y + 117 = 0

Find the pairs factors of 117 and substitute the values

y² - 13y - 9y + 117 = 0

(y² - 22y) - (9y + 117) = 0

factorize

y(y - 22) - 9(y - 22) = 0

Then y = 9 and y = 22

The older brothers age = x = 22 - y = 22- 9 = 13

Hence, the value is 13

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The complete question:

The sum of the ages of two brothers is 22 years. Six years ago, the product of their ages was 21 years. What is the age of the elder brother?

Answer:  True. In an elastic collision, both momentum and kinetic energy are conserved. This means that the total momentum and total kinetic energy of the system before the collision is equal to the total momentum and total kinetic energy of the system after the collision.

Step-by-step explanation:

To answer this, you get to pick any x-value and then solve for y OR you can pick any y-value and solve for x.

For this one, let's pick x = 3.  We'll then substitute 3 in for x in the equation:

       - (3) + 2y = 7

and then solve for x:

       -3 + 2y = 7

Add 3 to both sides:
              2y = 10

Divide by 2 on both sides:
                y = 5

This shows that (3,5) is a solution for the equation.

Again, you could pick any x-value and solve for y OR pick any y-value and solve for x.  There are an infinite number of solutions.

Answer:

B

Step-by-step explanation:

A quadratic function is a polynomial function which has a degree of 2, and is generally expressed in standard form: [tex]ax^2+bx+c\text{ where }a\ne 0[/tex]. The degree of a polynomial function can be determined by looking at which term has the largest exponent.

By looking at both options, B would be the correct option as it is a polynomial function with degree 2, while option A is a polynomial function with degree 1, also known as a linear equation.