(a-3)*(6-a)
Make this easier.

To determine the equation that best describe the data in the table, let us substitute the value of x given on the table into each equation and check for the equation that gives us the corresponding values of y;

for x = -2, y=-4; substituting x= -2 into each equation, we have;

From the first substitution, only equation a and c gave us the corresponding value of y.

Secondly, let's substitute another value of x into the two right right equaabove to confirm the best;

At x=1, y= -7; substituting x=1 into equation a and c we have;

From the above only equation c gave us the corresponding value of y at x=1.

Since only equation c gave us the corresponding values of y for both substituttions. The equation that best describe the data on the table is equation cequatio

Answer:

x = 48.6°

Step-by-step explanation:

see photo for explanation

The quadratic equation will be; 3x² + 6x + 9

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Given that roots are x = -3 and x = - 1, and whose leading coefficient is 3.

The factors are; (x + 3) and (x + 1)

f(x) = a(x + 3)(x + 1)

As, a = 3.

Then we get;

f(x) = 3(x + 3)(x + 1)

= 3(x² + 2x + 3)

= 3x² + 6x + 9

The quadratic equation will be; 3x² + 6x + 9

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Answer:

-1 1/2, 3

Step-by-step explanation:

The multiplied form of the Algebraic expression is 10x -0.8\(x^{2}\)

An algebraic expression is a mathematical statement that contains a combination of numbers, symbols, variables and mathematical operators.

These expressions may be linear, quadratic or polynomials and the numbers in front of each term is called coefficient while the symbols or letters are called variable

2x( 5 - 0.4x)

we multiply each term in the bracket by 2x

2x  x 5  - 2x x 0.4x = 10x - 0.8\(x^{2}\)

In conclusion, 2x(5 - 0.4x) reduces to 10x - 0.8\(x^{2}\)

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Unfortunately, the question seems to be incomplete as it mentions "Consider the following two person game. (5)" without providing any details about the game, its payoff matrix, or any specific instructions. Without this information, it is not possible to draw the graphs or provide an analysis of Nash equilibria.

In general, to find the Nash equilibria of a game, one must analyze the players' strategies and payoffs. The Nash equilibrium is a situation in which no player has an incentive to unilaterally deviate from their chosen strategy. It is often identified by looking for stable points where the players' best responses intersect.

A common approach to finding Nash equilibria is through the analysis of strategic dominance, where strategies that are strictly dominated by others can be eliminated from consideration. This process reduces the strategic space and narrows down the possible equilibria.

However, without the specific game and its details, it is not possible to provide a diagram or analyze the Nash equilibria. It would be helpful to provide more information or the specific game setup to proceed with a meaningful analysis.

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Answer:

24,000 milliliters

Step-by-step explanation:

Because

1 liter = 1000 milliliters

so 24 liters would be 24,000 Milliliters

Answer:

Each additional cup is 1 centimeter.

Step-by-step explanation:

We know this because we can see the height on the graph. For each number of cups increased (y-axis), 1 centimeter in height increases as well.

Therefore, we can say that each additional cup is 1 centimeter.

On solving the given problem by help of mathematical operations, we got - After Ray poured 0.47L, he was left with 2.201L.

The term "operation" in mathematics refers to the process of calculating a value using operands and a math operator. For the given operands or numbers, the math operator's symbol has predetermined rules that must be followed.

In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Total amount of tea Ray has - 2.671L

Amount of tea Ray poured - 0.47

Therefore,

amount he was left with was  = 2.671- 0.47 = 2.201L

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Given the following data:

A residual value can be defined as a difference between the measured (given or observed) value from a scatter plot and the predicted value from a scatter plot.

Mathematically, the residual value of a data set can be calculated by using this formula:

Residual value = given value - predicted value

Next, we would determine the predicted value by using the given regression equation as follows:

Hgt = 24 + 2.72(Age)

Hgt = 24 + 2.72(12)

Hgt = 24 + 32.64

Predicted value, Hgt = 56.64 inches.

Now, we can determine the residual value as follows:

Residual value = given value - predicted value

Residual value = 60 - 56.64

Residual value = 3.36 inches.

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Answer:

60%

Step-by-step explanation:

If your commission is $1480, your total sales amount would be $22,500.

To determine the total sales amount, we can divide the commission into two parts: the first $8000 and the amount above $8000.

Let's calculate the commission earned on the first $8000:

Commission on the first $8000 = 8% of $8000

Commission on the first $8000 = 0.08 * $8000

Commission on the first $8000 = $640

Now, let's calculate the commission earned on the amount above $8000:

Commission on sales above $8000 = $1480 - Commission on the first $8000

Commission on sales above $8000 = $1480 - $640

Commission on sales above $8000 = $840

To find the sales amount corresponding to the commission on sales above $8000, we can use the formula:

Sales amount above $8000 = Commission on sales above $8000 / Commission rate

Sales amount above $8000 = $840 / 0.12 (since the commission rate is 12%)

Sales amount above $8000 = $7000

Now, to find the total sales amount, we add the sales amount above $8000 to the initial $8000:

Total sales amount = $8000 + Sales amount above $8000

Total sales amount = $8000 + $7000

Total sales amount = $15,000

However, we must note that this calculation assumes the commission is calculated based on the total sales amount, including the initial $8000. Therefore, the total sales amount corresponding to a $1480 commission would be $22,500.

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Step-by-step explanation:

18 2+6(4+1)-2

18 8(5)-2

18 40-2

18 38

18×38

multiply it to get your answer

Answer:

we conclude that:

If 4x - 6≠4, then 2x–5≠5 is the contrapositive of a conditional statement if 2x -5=5, then 4x-6=14.

Step-by-step explanation:

We know that the contrapositive of a conditional statement of the form "If p then q" is termed as "If ~q then ~p".

In other words, it is symbolically represented as:

' ~q ~p is the contrapositive of p q '

For example, the contrapositive of "If it is a rainy day, then they suspend the match" is "If they do not suspend the match, then it won't be a rainy day."

Given

p: 2x -5=5

q: 4x-6=14

As the contrapositive of a conditional statement of the form "If p then q" is termed as "If ~q then ~p

Thus, we conclude that:

If 4x - 6≠4, then 2x–5≠5 is the contrapositive of a conditional statement if 2x -5=5, then 4x-6=14.

Answer: A, C, D

Step-by-step explanation:

1) AD=BD must be true because the angle bisector drawn from the vertex angle of an isosceles triangle is the perpendicular bisector of the base.

2) AC=CD does not need to be true because angles ADC and CAD do not need to be congruent.

3) This must be true by the definition of an angle bisector.

4) This must be true because angles CDA and CDB are both right angles.

5) This does not need to be true because triangle ADC does not need to be isosceles.

Answer:

3:5:6

Step-by-step explanation:

because there are 3 sheep 5 vows and 6 pigs

Simplify both sides of the inequality.

\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{3x+6 < 3x-21 } \end{gathered}$} }\)

Subtract 3x from both sides.

Subtract 6 from both sides.

\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{0 < -27} \end{gathered}$} }\)

Answer:

0 < - 27

Step-by-step explanation:

1. Distribute

3x + 6 < 3(x-7)

3x + 6 < 3x - 21

2. Subtract 6 from both sides

3x + 6 <  3x - 21

3x + 6 - 6 < 3x - 21 - 6

3. Simplify

   subtract

    3x + 6 - 6 < 3x - 21 - 6

    3x <  3x - 21 - 6

   subtract

     3x < 3x - 21 - 6

     3x < 3x - 27

4. Subtract 3x from both sides

3x < 3x - 27

3x - 3x < 3x - 27 - 3x

5. Simplify

    combine like terms

     3x - 3x < 3x - 27 - 3x

     0 < 3x - 27 - 3x

     0 < 3x - 27 - 3x

      0 < -  27

And that is how you get your answer

LCD = 12

Equivalent Fractions with the LCD

11/12 = 11/12

1/2 = 6/12

Solution:

Rewriting input as fractions if necessary:

11/12, 1/2

For the denominators (12, 2) the least common multiple (LCM) is 12.

LCM(12, 2)

Therefore, the least common denominator (LCD) is 12.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

11/12 = 11/12 × 1/1 = 11/12

1/2 = 1/2 × 6/6 = 6/12

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If a distribution of scores is shown in a bar graph, it suggests that the scores were measured on an ordinal scale of measurement.

An ordinal scale is a type of measurement scale that categorizes and orders variables or data points based on their relative ranking or position. In this case, the bar graph represents the frequencies or counts of different categories or ranges of scores, indicating an ordered arrangement of the data. However, the bar graph alone does not provide information about the exact numerical differences between the scores or their precise magnitudes.

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Answer:

\((-\frac{2}{7},-\frac{65}{7} )\)

Step-by-step explanation:

By steps in the image:

Step 1:

To eliminate, you need one of the coefficients to be the same in both equations. We will use the term "-6x" found in the first equation.

To get this, multiply the entire second equation by 6 and simplify using the distributive property. The new equation is:

\(6x-6y=54\)

Step 2:

Now you need to subtract the first equation and the new version of the second equation. By doing this, the "-6x" in both equations will cancel each other out.

Step 3:

Solve for x in the given equation by:

Step 4:

Solve for y by:

Solution:

\((-\frac{2}{7},-\frac{65}{7} )\)

:Done

Answer:

life span ................

The traits affected by a change in the environment are:

Skin and life span.

Options A and C are the correct answer.

Environmental change is the change in the physical nature such as the climate, weather, biosphere, food chain, atmospheric contents, etc.

We have,

The traits getting influenced by the change in environment are:

1) Skin

We see that our skin color becomes dark when we get more sunlight.

2)

Life span

If there is a change in the environment that disrupts the food chain and the basic survival elements.

Thus,

Skin and lifespan are the traits affected by changes in the environment.

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Using the values provided and a derivative of the cone's volume formula, the result is 0.059 feet per minute.

In mathematics, the rate at which a function changes in relation to a variable.

A cone is a three-dimensional geometric structure that has a smooth transition from a flat base that is typically circular to the point at the top, which is also referred to as the apex or vertex.

The formula for cone volume is:

V=πr2h/3

yields the formula for cone volume:

dv/dt = 2r * h/3 * dr/dt dV/dt = 3 r=2 h=12

dr/dt = 0.059 feet per minute.

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Answer:

y=1x-5

Step-by-step explanation:

Answer:

x is equal to negative 1/4

Step-by-step explanation:

Answer:

Negative Quarter.

Step-by-step explanation:

Simply send the letters to one side (preferrably the left) and numbers on the other side... Remember to swutch signs when you pelting the number or letter across the equal sign. i.e negative will become positive and vice versa. lets go...

7 - 5x - 5 - 7x = 5

-5x - 7x = 5 + 5 - 7

-12x = 3

x = -3/12

x = -1/4

3 (hight) × 8 (base) = 24

24 ÷ 2 = 12 (area of triangle)

12 × 2 = 24 (because there are 2 triangles)

5 × 7 = 35 (because length times width)

35 × 2 = 70 (because there are 2 rectangles)

8 × 7 = 56 (because of the base)

24 + 12 + 24 + 35 + 70 + 56 = 221

Answer:

The person above is correct. the answer is D. I, III, II

Step-by-step explanation:

I just did the test and it was right

The corresponding angles formed by two parallel lines having the same  transversal are congruent.

The correct order of the statements are:

III m∠VQT + m∠ZRS = 180°

II m∠SQV + m∠VQT = m∠VQT + m∠ZRS

I m∠SQV + m∠VQT - m∠VQT = m∠VQT  m∠ZRS - m∠VQT

The two column proof is presented as follows;

Statements                                                           Reason

Segments UV is parallel to segment WZ            Given

Points S, Q, R, and T all lie on the same line       Given

m∠SQT = 180°                                                        Definition of a straight                                      

                                                                                angle

m∠SQV + m∠VQT = m∠SQT                                 Angle Addition Postulate

m∠SQV + m∠VQT = 180°                             Substitution Property of                       Equality

III m∠VQT + m∠ZRS = 180°                          Same-side interior angle theorem

II m∠SQV + m∠VQT = m∠VQT + m∠ZRS    Substitution Property of Equality

I m∠SQV + m∠VQT - m∠VQT = m∠VQT

+ m∠ZRS - m∠VQT                                       Subtraction Property of Equality

m∠SQV = m∠ZRS                                      

m∠SQV ≅ m∠ZRS                                        Definition of Congruency

Therefore, the correct order;

First

III m∠VQT + m∠ZRS = 180°,

Given that m∠VQT and  m∠ZRS are same side interior angles

Second; II m∠SQV + m∠VQT = m∠VQT + m∠ZRS,  

By Substitution Property of Equality given that both (m∠SQV + m∠VQT), (m∠VQT + m∠ZRS) are equal to 180°

Third; I m∠SQV + m∠VQT - m∠VQT = m∠VQT  m∠ZRS - m∠VQT,

The same value - m∠VQT is subtracted from both sides of the equation in Step II, therefore, both sides of the equation remains equal.

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1) To find the demand equation, we can use the information provided about the quantity sold at different prices. We have two price-quantity pairs: (100, 110) and (80, 135).

We can start by using the point-slope form of a linear equation:

(y - y1) = m(x - x1)

where (x1, y1) is a point on the line and m is the slope.

Using the first price-quantity pair (100, 110), we have:

(110 - y1) = m(100 - x1)

Simplifying, we get:

110 - y1 = 100m - mx1  ------ (Equation 1)

Similarly, using the second price-quantity pair (80, 135), we have:

(135 - y1) = m(80 - x1)

Simplifying, we get:

135 - y1 = 80m - mx1  ------ (Equation 2)

Now, we can subtract Equation 1 from Equation 2 to eliminate the y1 and mx1 terms:

(135 - y1) - (110 - y1) = (80m - mx1) - (100m - mx1)

Simplifying, we get:

25 = -20m

Dividing both sides by -20, we get:

m = -25/20 = -5/4

Now that we have the slope, we can substitute it back into Equation 1 to find y1:

110 - y1 = 100(-5/4) - (-5/4)x1

110 - y1 = -500/4 + (5/4)x1

110 - y1 = (-500 + 5x1)/4

To get rid of the fraction, we can multiply both sides by 4:

440 - 4y1 = -500 + 5x1

Rearranging the equation, we get:

5x1 - 4y1 = 940  ------ (Equation 3)

Therefore, the demand equation based on the given information is:

D(x) = 5x - 4y = 940

2) To find the demand equation based on the given information, we can use the price-quantity pairs provided. The first pair is (140, 40) and the second pair is (140 + 60, 40 - 25).

Using the point-slope form of a linear equation:

(y - y1) = m(x - x1)

Using the first price-quantity pair (140, 40), we have:

(40 - y1) = m(140 - x1)

Simplifying, we get:

40 - y1 = 140m - mx1  ------ (Equation 4)

Using the second price-quantity pair (200, 15), we have:

(15 - y1) = m(200 - x1)

Simplifying, we get:

15 - y1 = 200m - mx1  ------ (Equation 5)

Subtracting Equation 4 from Equation 5 to eliminate the y1 and mx1 terms:

(15 - y1) - (40 - y1) = (200m - mx1) - (140m - mx1)

Simplifying, we get:

-25 = 60m

Dividing both sides by 60, we get:

m = -25/60 = -5/12

Now, substitute the value of m into Equation 4 to find y1:

40 - y1 = 140(-5/12) - (-5/12)x1

40 - y1 = -700/12

+ (5/12)x1

40 - y1 = (-700 + 5x1)/12

Multiply both sides by 12 to eliminate the fraction:

480 - 12y1 = -700 + 5x1

Rearranging the equation, we get:

5x1 - 12y1 = 1180  ------ (Equation 6)

Therefore, the demand equation based on the given information is:

D(x) = 5x - 12y = 1180

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