What is the quotient of (4x2 − 15x + 9) ÷ (x − 3)?

Plug -7 in for where ever you see the variable p if the final answer is equal to each other then -7 is a solution to the equation

4 × (-7) - (-7 + 9) = 5 × (-7) + 5

Use the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)

Parentheses

4 × (-7) - (-7 + 9) =  5 × (-7) + 5

4 × (-7) - 2 =  5 × (-7) + 5

There are no exponents so go to the next step

Multiplication (apply this from left to right)

4 × (-7) - 2 =  5 × (-7) + 5

-28 - 2 = 5 × (-7) + 5

-28 - 2 = 5 × (-7) + 5

-28 - 2 = -35 + 5

There is no division so go to the next step

Addition

-28 - 2 = -35 + 5

-28 - 2 = -30

Subtraction

-28 - 2 = -30

-30 = -30

-30 = -30

-7 is a solution to this equation because when evaluated both sides equals -30

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Approximately 7 deaths per minute.

Step-by-step explanation:

Answer:

A. y = 3 cos (1/2) x.

Step-by-step explanation:

The y-intercept is 3  so it will contain 3 cos x (because  y = cos x passes through (0, 1).

The graph of 3 cos x has been stretched horizontally  by a factor 2 ( 3 cos x would pass through (π/2, 0) whereas the given graph passes through  (π, 0).

So the equation is 3 cos(1/2) x

The function which represents the graph is  A. y = 3 cos (1/2) x.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The y-intercept is 3  so it will contain 3 cos x (because y = cos x passes through (0, 1).

The graph of 3 cos x has been stretched horizontally by a factor of 2 ( 3 cos x would pass through (π/2, 0) whereas the given graph passes through  (π, 0).

Therefore the function which represents the graph is  A. y = 3 cos (1/2) x.

To know more about graphs follow

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Ques 4)

The system is:

                      [tex]y=x-4[/tex]

                     [tex]y=\dfrac{x-4}{x+2}[/tex]

Ques 5)

The system is:

                         [tex]6x+y=-27[/tex]

             and     [tex]y=x^2+5x+3[/tex]  

Ques 4)

After looking at the graph we observe that :

The first graph is a line which passes through (4,0) and (0,-4)

Hence, the equation of such a line is:

                y=x-4

and the second graph is a curve such that the vertical asymptote is at x= -2

and also x= 4 is a root of the rational function.

Since, the graph passes through (4,0)

Hence, the system equation which best represents the graph is:

                           [tex]y=x-4[/tex]

                     [tex]y=\dfrac{x-4}{x+2}[/tex]

Ques 5)

One of the curve is :

a line that passes through (-5,3) and (-6,9)

Hence, the equation of line is given by:

[tex]y-3=\dfrac{9-3}{-6-(-5)}\times (x-(-5))\\\\i.e.\\\\y-3=\dfrac{6}{-6+5}\times (x+5)\\\\i.e.\\\\y-3=\dfrac{6}{-1}\times (x+5)\\\\i.e.\\\\y-3=-6(x+5)\\\\i.e.\\\\y-3=-6x-30\\\\i.e.\\\\y=-6x-30+3\\\\i.e.\\\\y=-6x-27[/tex]

i.e. Equation of line is:

[tex]6x+y=-27[/tex]

While the other graph is a upward facing parabola such that the vertex is in third quadrant this means that the coefficient of x^2 must be positive and that of x must also be positive.

Hence, the system in which the equation of line satisfies is:

                          [tex]6x+y=-27[/tex]

             and     [tex]y=x^2+5x+3[/tex]  

Answer:

  cos(A) = (4√97)/97

Step-by-step explanation:

The cosine is related to the sine by ...

  cos(A)² = 1 - sin(A)²

  cos(A)² = 1 - (9/√97)² = 1 - 81/97 = 16/97 . . . . substitute for sin(A), simplify

Make the denominator a square:

  cos(A)² = (16·97)/97²

  cos(A) = (4√97)/97 . . . . . square root

The exact value of cos A can be determined using the Pythagorean identity. In this case, cosA = 4√97/97, which is the exact value of cos A in simplest radical form with a rational denominator.

In mathematics, the exact value of cos A can be determined using the Pythagorean identity, sin²A + cos²A = 1.

According to the problem, sinA = 9/√97, which when squared gives 81/97. Using the Pythagorean identity, we can substitute the value of sin²A to get cos²A. Hence, cos²A = 1 - sin²A = 1 - 81/97 = 16/97. The exact value of cos A, then, is the square root of 16/97. As A is in Quadrant I where cosine is positive, this will be √(16/97).

In order to write this value with a rational denominator, multiply and divide by the square root of the denominator (√97). Hence, cosA = 4√97/97, which is the exact value of cos A in simplest radical form with a rational denominator.

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[tex] (2x^2 - x + 1)(x - 3) [/tex]

We multiply 2x^2 - x + 1 by x and by -3 and add it all up:

[tex] (2x^2 - x + 1)(x - 3) = 2x^3 - x^2 + x - 6x^2 + 3x - 3 [/tex]

[tex] = 2x^3 - 7x^2 + 4x - 3 [/tex]

Answer: A

Answer:

2x^3 - 7x^2 + 4x - 3.

Step-by-step explanation:

(2x^2-x+1)( x-3)

= x(2x^2 - x + 1) - 3(2x^2 - x + 1)

= 2x^3 - x^2 + x - 6x^2 + 3x - 3

= 2x^3 - 7x^2 + 4x - 3.

Answer: It moves the graph down by 1/4

Step-by-step explanation:

I used demos and the graph had a change making it lower coordinates by a fourth.

Answer:

9/4

Step-by-step explanation:

For a perfect square trinomial x² + bx + c, the value of c is the square of half of b.

c = (b/2)²

Here, b = 3.

c = (3/2)²

c = 9/4

Answer: 1/20, or 0.05

Step-by-step explanation: What we have to do is figure out how many times the blue shades area goes into the total area. Horizontally, it would be 5/10 squares, or 1/2. Vertically, it is 5/50 squares, or 1/10.  Multiplying 1/2 and 1/10 gives us 1/20, or 0.05 as your answer.

Answer:

Paula must sell at least 2,500 windows in a year to earn a profit of at least $48,000.

Step-by-step explanation:

Let [tex]x[/tex] be the number of windows that Paula sells in a year.

Paula's revenue is the number of windows that she sell times the price that she charge for each window. That is:

[tex]\text{Revenue} = \text{Price}\times \text{Quantity} = \$\;28x[/tex].

Paula's cost comes in two parts:

[tex]\begin{aligned}\text{Cost} = \text{Total Cost}&= \text{Fixed Cost} + \text{Marginal Cost}\\ & = \$\;12,000 +\$\; 4x \\ & = \$\;(12,000 + 4x)\end{aligned}[/tex].

Consider the inequality in the picture:

[tex]\text{Revenue} - \text{Cost} \ge \text{Profit}\\ \$\; 28x - \$\; (12,000 + 4x)\ge 48,000\\\$\; 24x \ge 60,000[/tex].

Multiply both sides with 1/24. It is important that this number is positive. Otherwise, the direction of the inequality operator will flip.

[tex]\displaystyle x \ge \frac{\$\;60,000}{\$\; 24}[/tex].

[tex]x\ge 2,500[/tex].

In other words, Paula must sell at least 2,500 windows in a year to earn a profit of at least $48,000.

Answer:

see below

Step-by-step explanation:

1.  y = mx+b where m is the slope

The first slope is -1/3

The second slope is 3

m1 = m2 means they are parallel  False

m1*m2 = -1  means they are perpendicular

-1/3 *3 = -1  True

2.  Squares and rhombi have all 4 sides with the same length.  Squares however, have 4 angles that must equal 90 degrees.  Squares are a special form of rhombi

3.  To find the slope

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

   = (2-11)/(-5-0)

   =-9/-5

   = 9/5

The distance is found by

d = sqrt( (x2-x1)^2 + (y2-y1)^2)

  = sqrt( (-5-0)^2 + (2-11)^2)

  = sqrt( 5^2 + (-9)^2)

  = sqrt( 25+81)

  = sqrt( 106)

Answer:

See below

Step-by-step explanation:

y = -1/3x + 2

y = 3x - 5

Slopes are -1/3 and 3, they are opposite-reciprocal, it means the lines are perpendicular

2. Difference between squares and rhombus:

3. points A(0,11)  and B(-5,2)

Slope:

m= (y2-y1)/(x2-x1)= (2-11)/(-5-0)= -11/-5= 11/5

Distance between points:

√(x2-x1)²+(y2-y1)²= √ 25+121= √146 ≈ 12

For this case we have that by definition, a direct variation is given by:

[tex]y = kx[/tex]

Where:

k: It is the constant of proportionality of the variables.

On the other hand, we have that the inverse variation is given by:

[tex]y = \frac {k} {x}[/tex]

Where:

k: It is the constant of proportionality of the variables.

In this way, the correct option is: [tex]y = \frac {9} {x}[/tex]

ANswer:

Option A

Answer: Option A

[tex]y = \frac{9}{x}[/tex]

Step-by-step explanation:

It is said that two variables x and y vary inversely if the increase of one of the variables causes the other to decrease.

This is represented by the following equation

[tex]y = \frac{k}{x}[/tex]

Where k is known as variation constant

To answer this question, identify among the options given that the form has

[tex]y = \frac{k}{x}[/tex]

The answer is the option A. with k = 9

Answer:

x < 7

Step-by-step explanation:

Simplify ...

6x -12 -4x +7 < 9

2x < 14 . . . . . . . . . . . add 5

x < 7 . . . . . . . . . . . . . divide by 2

The probability of drawing a second green marble, given that the first marble is green is:

                    [tex]\dfrac{3}{8}[/tex]

Let A denote the event that first marble is green.

B denote the event that the second marble is green.

A∩B denote the event that both the marbles are green.

Let P denote the probability of an event.

We are asked to find:

                      P(B|A) i.e. probability of drawing a second green marble, given that the first marble is green.

We know that:

[tex]P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}[/tex]

Probability of drawing one green marble is 2/5  i.e.

          [tex]P(A)=\dfrac{2}{5}[/tex]

The probability of drawing two green marbles from the urn without replacement is 3/20 i.e.

[tex]P(A\bigcap B)=\dfrac{3}{20}[/tex]

Hence, we have:

[tex]P(B|A)=\dfrac{\dfrac{3}{20}}{\dfrac{2}{5}}\\\\\\i.e.\\\\\\P(B|A)=\dfrac{3\times 5}{20\times 2}\\\\\\P(B|A)=\dfrac{3}{8}[/tex]

Answer:

3/50

Step-by-step explanation:

Answer:

10.4 cm

Step-by-step explanation:

In this question apply the formulae for volume of a pyramid

General formulae for volume of a pyramid is = l*w*h /3 where l is base length, w is base width and h is height.

In this question l=w= 6cm, v=120 cm³ and h=? ,

Apply the formulae

[tex]V= l*w*h /3\\\\120=6*6*h/3\\\\120=12h\\\\120/12 =h\\\\10cm=h[/tex]

Slant height

The length = 6cm-----------------divide by 2 to get half the legth

a=6/2=3cm

h=b= 10cm

c=?

apply the Pythagorean relationship

a²+b²=c²

3² + 10²= c²

9+100=c²

√109=c²

c=10.44

slant height =10.4 cm

Answer:

Slant height of pyramid = 10.4 m

Step-by-step explanation:

Points to remember

Volume of square pyramid = a²h/3

Where 'a' is the side of base and h is the height of pyramid

To find the height of pyramid

It is given that volume of square pyramid = 120 cm³ and

base a = 6 cm

a²h/3 = 120

h = (120 * 3)/a²

 = (120 * 3)/6²

 =10 cm

Therefore h = 10 cm

To find the slant height of pyramid

By using Pythagorean theorem we can write,

slant height ² = (base/2)² + height²

l² = (a/2)² + h²

 = (6/2)² + 10²

 = 3² + 10²

 = 9 + 100

 =109

l = √109 = 10.44 ≈ 10.4

Answer:

B. 2 m

Step-by-step explanation:

20 da is equal to 2 m.

Answer:

  about 8 cm

Step-by-step explanation:

The formula for the area of a regular polygon is ...

  A = 1/2Pa . . . . where P is the perimeter and "a" is the apothem, the distance from the center to a side

Filling in your numbers, we have ...

  20 cm^2 = (1/2)P(5 cm)

Dividing by the coefficient of P, we find ...

  2×(20 cm^2)/(5 cm) = P = 8 cm

The perimeter of the pentagon is about 8 cm.

_____

Comment on the problem

This calculation makes use of the area formula, as apparently intended. A regular pentagon with an apothem of about 5 cm will have an area of about 90.8 cm^2. The given geometry is impossible, as the pentagon is nearly 10 cm across. It cannot have a perimeter of only 8 cm.

Answer:

65.52 square feet

Step-by-step explanation:

to find area of a rhombus with the diagonals multiply them together and divide by two.

10.4 x 12.6 = 131.04

131.04/2 = 65.52 square ft

Answer:

  (-12, 5), (12, -5)

Step-by-step explanation:

Reflection across the origin is the transformation ...

   (x, y) ⇒ (-x, -y)

Look for coordinates that are the opposites of their counterparts. You will find the appropriate answer choice is ...

  (-12, 5), (12, -5)

Answer:

(-12, 5), (12, -5)

Step-by-step explanation:

Since, the rule of point symmetry with respect to the origin is,

[tex](x,y)\rightarrow (-x, -y)[/tex]

That is, the mirror image of the point (x, y) with respect to the origin is (-x,-y),

Thus, in the point symmetry with respect to the origin,

[tex](-12, 5)\rightarrow (-(-12), -5))[/tex]

So, the mirror image of point (-12,5) with respect to the origin is (12, -5),

Hence, the set of ordered pairs has point symmetry with respect to the origin is,

(-12, 5), (12, -5)

Second option is correct.

Answer:

Y= 19.86 - 0.42b

Step-by-step explanation:

Step 1: Write the formula

Regression Line: Y = a + bx

a=(Total Y) x (Total X^2) - (Total X) x (Total XY)

                    n x (total X^2) - (Total X)^2

b= n x (Total XY) - (Total X) x (Total Y)

             n x (total X^2) - (Total X)^2    

Step 2: Make a table to find all values

X  Y          X^2    Y^2               XY

5 17.19 25 295.4961       85.95

6 19.12 36 365.5744       114.72

7 16.75 49 280.5625      117.25

8 15.58 64 242.7364       124.64

9 16.21 81 262.7641        145.89

10 14.14 100 199.9396        141.1

11 14.97 121 224.1009        164.67

12 16.2         144 262.44            194.4

68 130.16     620  2133.614       1088.62              TOTAL

Step 3: Substitute all values in the equation to find a and b

a=(Total Y) x (Total X^2) - (Total X) x (Total XY)

                    n x (total X^2) - (Total X)^2

a= (130.16 x 620) - (68 x 1088.62)

                     8 x (620) - (68)^2

a = 80699.2 - 74026.16

                336

a = 19.86

b = n x (Total XY) - (Total X) x (Total Y)

             n x (total X^2) - (Total X)^2    

b = 8 x (1088.62) - (68 x 130.16)

             8 x (620) - (68)^2

b = 8708.96 - 8850.88

                336

b = -0.42

Step 4 : Apply values of a and b in the formula of the regression line.

Regression Line: Y = a + bx

Y= 19.86 + b (-0.42)

Y= 19.86 - 0.42b

The regression line is calculated using the 'least squares method'. The formula is Y=a+bX, where a is the Y-intercept and b is the slope. These are calculated from the X and Y data values using specific formulas.

To calculate the regression line from the given X (year) and Y (high temperature) values, we first need to know the specific data. Unfortunately, the data isn't provided in the question. However, I can explain the process to you.

A regression line, also known as the line of best fit, is a straight line that best represents the data on a scatter plot. This line can be calculated using the 'least squares method'. This method minimizes the sum of the squares of the residuals (the differences between the actual and predicted Y values).

The formula for the regression line is Y=a+bX, where:

You can plug in your X and Y data values into these equations to find your regression line.

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Answer:

[tex]8g+16h=8(g+2h)[/tex]

Step-by-step explanation:

The given expression is

[tex]8g+16h[/tex]

To factor this polynomial, we just need to extract the common factor. Or you can see as the greatest common factor.

What is the greatest common factor between 8 and 16?

16: 1, 2, 4, 8, 16.

8: 1, 2, 4, 8.

You can observe that the greatest common factor is 8, so we extract it from both numbers

[tex]8g+16h=8(g+2h)[/tex]

Notice that we placed the GCM in the front as a product, if we don't do that, it would be completely wrong, because we can change the equivalence of the expression. Now, notice that each variable have different coefficients, that is because if you extract the GCM, you need to placed its quotients as coefficients.

Therefore, the factor of the polynomial is

[tex]8g+16h=8(g+2h)[/tex]

Answer:

  $110

Step-by-step explanation:

Let a, b, and c represent the earnings of Alan, Bob, and Charles. The problem statement tells us ...

  a + b + c = 480 . . . . . . the combined total of their earnings

  -a + b = 40 . . . . . . . . . . Bob earned 40 more than Alan

  2a - c = 0 . . . . . . . . . . . Charles earned twice as much as Alan

Adding the first and third equations, we get ...

  (a + b + c) + (2a - c) = (480) + (0)

  3a + b = 480

Subtracting the second equation gives ...

  (3a +b) - (-a +b) = (480) -(40)

  4a = 440 . . . . . . . . simplify

  a = 110 . . . . . . . . . . divide by the coefficient of a

Alan earned $110.

_____

Check

Bob earned $40 more, so $150. Charles earned twice as much, so $220.

The total is then $110 +150 +220 = $480 . . . . as required

Answer:

$96.25

Step-by-step explanation:

I just got done with the test...

According to the SMART goals method, goals should be clearly defined, aligning with the "Specific" attribute of the SMART acronym. This means having a clear and direct aim for the goal, which is essential for effective goal-setting.

According to the SMART goals method, goals should be clearly defined. SMART is an acronym that stands for Specific, Measurable, Attainable, Relevant, and Time-bound. Each of these attributes plays a crucial role in the formulation of effective and actionable goals.

Specific means the goal should be clear and direct, detailing exactly what is expected to be achieved. A goal that is Measurable has quantifiable criteria to indicate progress or completion. Attainable refers to the goal being realistic and possible to achieve given current resources and constraints.

Being Relevant means the goal aligns with broader objectives and makes sense within the greater plan. Lastly, Time-bound means there is a specific deadline or period within which the goal should be accomplished.

Therefore, the correct choice is A. Clearly defined, as a SMART goal must be specific and this inherently means the goal should have a clear definition.

Answer:

  3 - (n -1) = (1/2)(3n -4)

Step-by-step explanation:

three minus the difference of a number and one: 3 - (n -1)

one-half of the difference of three times the same number and four: (1/2)(3n -4)

These two expressions are said to be equal, so the equation is ...

  3 - (n -1) = (1/2)(3n -4)

Answer:

Step-by-step explanation:

D

The cost for talking 3.1 minutes, according to the graph, would be  Option C) 4 cents due to rounding up to nearest minute.

1. Understanding the ceiling function: The ceiling function takes a number as input and rounds it up to the nearest whole number. For example, the ceiling of 2.3 is 3, because 3 is the next whole number greater than 2.3.

2. Analyzing the graph: The graph provided represents the cost of a long-distance phone call in cents based on the duration of the call in minutes. The x-axis represents the minutes of the call, and the y-axis represents the cost in cents.

3. Identifying the jumps: From the graph, we can observe that the cost increases in steps or jumps at specific points along the x-axis. These jumps indicate where the cost increases by 1 cent.

4. Determining the cost for 3.1 minutes: Since 3.1 minutes fall between 3 and 4 minutes on the x-axis, we need to find out which whole number the ceiling function would round 3.1 up to. Since it rounds up to the nearest whole number, 3.1 would be rounded up to 4.

5. Conclusion: Therefore, the cost of talking for 3.1 minutes would be the same as talking for 4 minutes according to the graph. Looking at the y-axis corresponding to the point where x = 4, we see that the cost is 4 cents.

So, to answer the question, the cost to talk for 3.1 minutes would be 4 cents. Option C)

Complete Question:

Answer:

The correct answer is last option

5/7

Step-by-step explanation:

It is given that, eight white balls and twenty black balls are in a bag

To find the probability

From the above data we get,

number of white balls = 8

Number of black balls = 20

total number of balls = 8 + 20 = 28

Probability of getting black ball = number of black ball/Total number of balls

 = 20/28 = 5/7

The correct answer is last option

5/7

Answer: 48cm2

Step-by-step explanation:

area = base x height

a = 8 x 6

a = 48

Answer:

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1.

[tex]|\Omega|=15^2=225\\|A|=5\cdot4=20\\\\P(A)=\dfrac{20}{225}=\dfrac{4}{45}[/tex]

2.

[tex]|\Omega|=15^2=225\\|A|=6\cdot5=30\\\\P(A)=\dfrac{30}{225}=\dfrac{2}{15}[/tex]