Consider the given quadratic equations. Equation A Equation B Equation C Equation D y = 3x2 − 6x + 21 y = 3x2 − 6x + 18 y = 3(x − 1)2 + 18 y = 3(x − 1)2 + 21 Complete the following statement. Equations are equivalent, and of those, equation is in the form most useful for identifying the extreme value of the function it defines.

Answer:

2

Step-by-step explanation:

count how many more

Answer:

The point (2 - d, y) is on the graph of f(x)

The line x = 2 is the axis of symmetry of the graph of f(x)

Step-by-step explanation:

* Lets explain how to prove that a point lies on a graph Algebraically

- Substitute the value of the x-coordinate of the point in the equation

 of the graph the answer must be equal the y-coordinate of the point

- The function is a quadratic because the greatest power of x is 2,

  then it represented by parabola

- The parabola has a vertex point (h , k), where h is the x-coordinate

  and k is the y-coordinate

- This vertex divides the parabola into two equal parts, then the axis

 of symmetry of the parabola is a vertical line passing through it

∴ The equation of the axis of symmetry is x = h

- The vertex of the parabola could be minimum point if the parabola

  opened upward or maximum if it opened downward

- The minimum value and the maximum value are the value of k

# Look to the attached figures for more understand

* Now lets solve the problem

∵ f(x) = x(x - 4)

∵ Point (2 + d , y) is on the graph of f(x)

- Replace each x in f(x) by 2 + d

∴ f(2 + d) = (2 + d)(2 + d - 4) ⇒ add 2 and -4

∴ f(2 + d) = (2 + d)(-2 + d)

∵ f(2 + d) = y

∴ y = (2 + d)( -2 + d)

* Multiply them to simplify

∴ y = 2(-2) + 2(d) + d(-2) + d(d) = -4 + 2d - 2d + d²

∴ y = -4 + d²

* Lets do these steps again with point (2 - d , y)

- Replace each x in f(x) by 2 - d

∴ f(2 - d) = (2 - d)(2 - d - 4) ⇒ add 2 and -4

∴ f(2 - d) = (2 - d)(-2 - d)

∵ f(2 - d) = y

∴ y = (2 - d)( -2 - d)

* Multiply them to simplify

∴ y = 2(-2) + 2(-d) - d(-2) - d(-d) = -4 - 2d + 2d + d²

∴ y = -4 + d²

- The value of y of the point (2 - d , y) = the value of y of the point on

  the graph

∵ f(2 + d) = f(2 - d)

∵ The point (2 + d , y) is on the graph of f(x)

∴ The point (2 - d , y) is on the graph of f(x)

* It is true the point (2 - d, y) is also on the graph.

* To find the relation between the line x = 2 and the graph of f(x)

  lets find the vertex of the parabola

- If f(x) = ax² + bx + c in the general form, where a, b , c are constant

 then h = -b/2a, where h is the x-coordinate of the vertex point, a is

 the coefficient of x² and b is the coefficient of x

∵ f(x) = x(x - 4) ⇒ multiply the bracket by x to put it in the general form

∴ f(x) = x² - 4x

- Find the value of a and b to find h

∵ a = 1 and b = -4

∵ h = -b/2a

∴ h = -(-4)/2(1) = 4/2 = 2

∴ The x-coordinate of the vertex point = 2

∵ The axis of symmetry of the parabola passing through the

   vertex point

∴ The equation of the axis of symmetry of the parabola is x = 2

* The line x = 2 is the axis of symmetry of the graph of f(x)

Answer:

Step-by-step explanation:

AYOOO

Cash flow from operating activities is $43,000. Calculated by adjusting net income for changes in working capital items.

To calculate the cash flow from operating activities using the indirect method, we start with net income and adjust for changes in working capital.

Net Income = $50,000

Changes in Working Capital:

1. Accounts Receivable increased by $30,000, so we subtract $30,000.

2. Inventory decreased by $20,000, so we add $20,000.

3. Amounts Payable increased by $4,000, so we add $4,000.

4. Salaries Payable decreased by $1,000, so we subtract $1,000.

Now, let's calculate the cash flow from operating activities:

Cash flow from operating activities = Net Income + Changes in Working Capital

= $50,000 - $30,000 + $20,000 + $4,000 - $1,000

= $50,000 - $7,000

= $43,000

So, the amount of cash flow from continuing operating activities under the indirect method is $43,000.

Answer is letter A

it is the answer

For this case we must find the difference of the following expressions:

[tex]0.00067\\2.3 * 10 ^ {- 5}[/tex]

For the second expression we must run the decimal 5 times to the left, because the exponent is negative, that is:

[tex]0.000023[/tex]

We subtract:

[tex]0.00067-0.000023 = 0.000647[/tex]

Represented in scientific notation we have:

[tex]6.47 * 10 ^ {- 4}[/tex]

Answer:

Option A

Answer:

  2. area = 504 cm^2

  3. x = 30°

Step-by-step explanation:

2. The figure can be divided across the middle into a rectangular bottom part and a triangular top part. The triangle will have a base length of 21 cm and a height of 32 -16 = 16 cm. Its area is ...

  triangle area = (1/2)bh = (1/2)(21 cm)(16 cm) = 168 cm^2

The area of the rectangle is the product of its base (21 cm) and height (16 cm). Its area is ...

  rectangle area = bh = (21 cm)(16 cm) = 336 cm^2

Then the total area of the figure is the sum of the areas of its parts:

  total area = triangle area + rectangle area

  = (168 cm^2) + (336 cm^2) = 504 cm^2

A plane figure has no volume. The volume is zero.

__

3. The angle whose measure is 4x is supplementary to the angle marked 60°, so is 180° -60° = 120°. That means ...

  4x = 120°

  x = 120°/4 = 30° . . . .  divide by the coefficient of x

The value of x is 30°.

Answer:

(a) 110 mm Hg

(b) 70 mm Hg

(c) 3/4 second

(d) see the attachment

Step-by-step explanation:

(a) The sine function has a maximum value of +1, so the maximum value of p is ...

pmax = 20·(+1) +90 = 20+90 = 110 . . . . . mm Hg

__

(b) The sine function has a minimum value of -1, so the minimum value of p is ...

pmin = 20·(-1) +90 = -20+90 = 70 . . . . . mm Hg

__

(c) The period of the sine function is 2π, so the value of t that makes the argument be 2π will be the period.

8π/3·t = 2π

t = 2π·3/(8π) = 3/4 . . . . . . multiply by the inverse of the coefficient of t

The period of her heartbeat cycle is 3/4 seconds.

__

(d) a graph is attached.

The domain is the input values, which are the X- values.

The domain would be -6, -1 , 0, 3

The first answer is the right one.

For this case, we have that by definition, the domain of a function is given by all the values of "x" for which the function is defined. The values of the domain are represented in the starting point.

Then, it is observed in the figure that the values of the domain are:

[tex]{x | x = -6, -1,0,3}[/tex]

ANswer:

Option A

Answer:

Step-by-step explanation:

So we're looking at a rectangle split into 5 smaller rectangles.  If the height of each rectangle is y and the width of each rectangle is x, then the amount of fencing is:

P = 6y + 10x

And the area of the large rectangle is:

A = 5xy

We know that P = 780:

780 = 6y + 10x

10x = 780 - 6y

5x = 390 - 3y

If we substitute this into our area equation:

A = (390 - 3y) y

A = -3y² + 390y

This is a vertical parabola pointing down, so we know the maximum is at the vertex, which is at -b/(2a).  Or, we can use calculus to take the derivative and set to 0.

dA/dy = -6y + 390

0 = -6y + 390

y = 65

Solving for x:

5x = 390 - 3y

5x = 390 - 3(65)

5x = 195

x = 39

So each part will have a width of 39 feet and a height of 65 feet.

5 x tan 66 = 7.140

your welcome :)

Answer:

Step-by-step explanation:

Answer:

The vertices are (3 , -5) , (-5 , -5)

The foci are (4 , -5) , (-6 , -5)

Step-by-step explanation:

* Lets study the equation of the hyperbola

- The standard form of the equation of a hyperbola with  

  center (h , k) and transverse axis parallel to the x-axis is

  (x - h)²/a² - (y - k)²/b² = 1

- The length of the transverse axis is 2 a

- The coordinates of the vertices are  (h  ±  a  ,  k)

- The coordinates of the foci are (h ± c , k), where c² = a² + b²

- The distance between the foci is  2c

* Now lets solve the problem

- The equation of the hyperbola is (x + 1)²/16 - (y + 5)²/9 = 1

* From the equation

# a² = 16 ⇒ a = ± 4

# b² = 9 ⇒ b = ± 3

# h = -1

# k = -5

∵ The vertices are (h + a , k) , (h - a , k)

∴ The vertices are (-1 + 4 , -5) , (-1 - 4 , -5)

* The vertices are (3 , -5) , (-5 , -5)

∵ c² = a² + b²

∴ c² = 16 + 9 = 25

∴ c = ± 5

∵ The foci are (h ± c , k)

∴ The foci are (-1 + 5 , -5) , (-1 - 5 , -5)

* The foci are (4 , -5) , (-6 , -5)

Answer:

Vertices: (3,-5) (-5,-5)

Foci: (-6,-5) (4,-5)

Step-by-step explanation:

(x+1)^2/16-(y+5)^2/9 =1

formula: (x-h)^2/a^2 -(y-k)^2/b^2=1

in this case...

a^2=16      b^2=9

h=-1 k=-5

a=4           b=3

v=(h+/-a,k)

v1=(-1+4,-5)=

v1=(3,-5)

v2=(-1-4, -5) =

v2=(-5,-5)

Foci=(h+/-c,k)

F1=(h-c,k)

=(-1-5,-5)

f1=(-6,-5)

F2=(h+c,k)

=(-1+5, -5)

F2=(4,-5)

Hope this helps! :)

Answer:

a. 215.6 in^3

b. 1.51 lb

Step-by-step explanation:

The area of each hand grip hole is that of a circle of radius 0.6 in together with a rectangle 2 in long and 1.2 in wide. So, that area is ...

π·(0.6 in)^2 + (2 in)(1.2 in) = (0.36π +2.4) in^2

The area of the kickboard before the hand grip holes are put in is that of a semicircle of radius 5.5 in together with a rectangle 12 in long and 11 in wide. So, that area is ...

(1/2)·π·(5.5 in)^2 + (12 in)(11 in) = (15.125π +132) in^2

Taking the hand grip holes out, the top area of the board is ...

((15.125π +132) -2(0.36π +2.4)) in^2

= (14.405π + 127.2) in^2

___

a. The volume is the product of the area and the thickness, so is ...

((14.405π +127.2) in^2)·(1.25 in) ≈ 215.568 in^3

__

b. The weight of the kickboard is the product of its volume and its density:

(215.568 in^3)(0.007 lb/in^3) ≈ 1.509 lb

To find the volume of the foam kickboard, its length, width, and height are needed. The weight is then calculated by multiplying the volume by the weight per cubic inch. Without specific dimensions, we cannot provide exact answers for the volume and weight.

To find the volume of the foam kickboard, we would need its dimensions such as length, width, and height. If we had these measurements, the volume (V) can be calculated using the formula V = length × width × height. Unfortunately, the question does not provide specific dimensions, so we cannot calculate an exact volume without this information.

To calculate the weight of the kickboard, once the volume is determined, you would multiply the volume by the weight per cubic inch of the foam. Assuming we had a volume of V cubic inches, the weight (W) of the kickboard can be found with W = V × 0.007 lb/in3.

For example, if the kickboard's volume was 100 cubic inches, then the weight would be 100 × 0.007 lb/in3 = 0.7 lb.

A is at -8 and C i5 at 5

-8 to 0 is 8 units and 0 to 5 is 5 units.

8 +5 = 13

AC is 13 units long.

For this case, we have that by definition, the distance between two points any A and B will be the absolute value of the subtraction of their coordinates in the order that is preferred. (the distances can not be negative)

So:

We find the distance from A to a point x located at 0. ENtonces:

[tex]| -8-0 | = | -8 | = 8[/tex]

Now we add the distance from x to C. From point x (located at zero) to point C there are 5 spaces, then:

[tex]8 + 5 = 13[/tex]

Thus, the distance from A to C is 13

Answer:

13

See the attached picture for the solution.

Answer:

X-intercept: (0,4)

Y-intercept: (-4,0)

Answer:

  c)  110°

Step-by-step explanation:

Arc FP is twice the measure of the marked angle, so is 70°. If FD is supposed to be a diameter, then arc FPD is a semicircle (180°) and arc PD is 180° -70° = 110°.

Answer:

y = -2(x -1)^2 -2

Step-by-step explanation:

My "work" consists of providing a table of values to a calculator and asking it for a quadratic model. The result is ...

y = -2(x -1)^2 -2

__

If you like to do these "by hand", you can write the model, then solve for its parameters using the given points.

We observe that the first and third points have the same y-coordinate. Then the vertex of the quadratic will be halfway between the corresponding x-values, at ...

h = (-2 +4)/2 = 1

So, one of the parameters of the model is found already. Using the second point and one other, we can find the remaining parameters for our model:

y = a(x -1)^2 +k

for (4, -20) ...

-20 = a(4 -1)^2 +k = 9a +k

for (0, -4) ...

-4 = a(0 -1)^2 +k = a + k

Subtracting the second equation from the first, we get

-16 = 8a

-2 = a . . . . . divide by 8

Substituting this value of a into the second equation, we have ...

-4 = -2 +k

-2 = k . . . . . . add 2

So, our model is ...

y = -2(x -1)^2 -2

Answer:

401 people per square mile

Step-by-step explanation:

First find the number of people per square mile in Detroit by dividing people by square miles:

672,800/142.9 = 4708.18754374

Then do the same for Grand Rapids:

195,100/45.3 = 4306.84326711

Subtract:

4708.2-4306.8 = 401.4

Round to the ones place:

401

The number of more people per square mile living in Detroit compared to Grand Rapids is approximately 400.45 people per square mile.

To find the number of more people per square mile living in Detroit versus Grand Rapids, we need to find the population density for each city. Population density is calculated by dividing the population by the area. Let's do the calculations:

Detroit population density = Detroit population / Detroit area = 672,800 / 142.9 = 4,706.42 people per square mile

Grand Rapids population density = Grand Rapids population / Grand Rapids area = 195,100 / 45.3 = 4,305.97 people per square mile

To find the difference in the number of people per square mile, we subtract the population density of Grand Rapids from the population density of Detroit. Therefore, the number of more people per square mile living in Detroit compared to Grand Rapids is approximately 400.45 people per square mile.

Answer:

a. 20.5

Step-by-step explanation:

because this will form a right triangle we can use tan (opposite over adjacent) so an equation we could set up would be tan(70)=25/x

therefore we can just solve the equation which would give us 20.45. so if we round it the answer would be a

Answer:

The correct answer option is a. 20.5 feet.

Step-by-step explanation:

We are given that the angle of elevation of the ladder is 70° and the height of the ladder is 25 feet from the ground.

We are to find the distance of the building from the base of the ladder.

For this, we will use tan:

[tex] tan 70 = \frac { 2 5 } { x } [/tex]

[tex] x = \frac { 2 5 } { tan 7 0 } [/tex]

x = 20.5 feet

Answer:4(3y-5)

Yes. 4(3y-5) is the factored version

Answer:

Step-by-step explanation:

Segment

A segment is a line that has 2 end points. We can measure the segment length. A segment is represented by [tex]\overline{AB}\\[/tex] where A and b are the two end points of the segment.

Ray

A ray is an line that has one end point and one point goes in infinity. We cannot measure ray as it's one end goes to infinity. A ray is represented by [tex]\overrightarrow{AB}[/tex] where A is the end point and B is the infinite point.

Figures of ray and segment are attached.

The answer is 30.

if 7=a and 2(a+8)

all you need to do is replace a with 7

so the formula would then be 2(7+8)

next you would solve in the parentheses.

2(15)

and 2(15) is the same as 2 x 15

so the answer would be 30

Answer: E. 30

Step-by-step explanation:

Cause a=7 and the equation is 2 (a+8) and it the same as 2 × (7+8) which if you use PEMDAS it's 2 × 15 =30

Final answer:

To find the total fraction of the lawn mowed by Melvin before his first break, one would add the additional 3/10 to the already mowed fraction represented by the shaded model.

Explanation:

The student's question is about calculating the fraction of the lawn that will be mowed by Melvin before he takes his first break. Initially, the question does not specify what fraction of the lawn is already mowed, but indicates that Melvin will mow an additional 3/10 of the lawn. Assuming that the shaded model represents the fraction already mowed (let's say x), the total fraction mowed before Melvin's first break would be x + 3/10. Without the specific value of the initially mowed fraction, we cannot provide the exact answer; however, generally, the operation would involve adding the given fraction to Melvin's progress before he mows the additional 3/10.

ANSWER

See attachment.

EXPLANATION

The given equation is

-3y=5x-7

when y=0,

-3(0)=5x-7

0=5x-7

5x=7

[tex]x = \frac{7}{5} [/tex]

we plot (7/5,0)

when x=0

-3y=5(0)-7

y=7/3

we plot (0,7/3)

when x=1,

-3y=5(1)-7

-3y=-2

y=2/3

we plot (1,2/3)

Answer:

Step-by-step explanation:

Unless I'm reading this incorrectly, he throws 155 6's.

There are 1000 throws altogether (according to the table)

So the experimental probability is 155/1000 = 0.155

The answer is B. It is a bit tricky to read.

Answer:

Part 1) The commission is $35.6 and the total salary for week 1 is $285.6

Part 2) The commission is $45.04 and the total salary for week 2 is $295.04

Part 3) The commission is $39 and the total salary for week 3 is $289

Part 4) The commission is $32.96 and the total salary for week 4 is $282.96

Step-by-step explanation:

Let

x-----> the amount in sales

y----> Cindy Nelson’s salary

we know that

4%=4/100=0.04

so

The linear equation that represent this situation is

y=250+0.04x

case 1) week 1

Sales  $890

For x=890

substitute in the linear equation

y=250+0.04(890)

y=250+35.6=$285.6

therefore

The commission is $35.6

The total salary for week 1 is $285.6

case 2) week 2

Sales  $1,126

For x=1,126

substitute in the linear equation

y=250+0.04(1,126)

y=250+45.04=$295.04

therefore

The commission is $45.04

The total salary for week 1 is $295.04

case 3) week 3

Sales  $975

For x=975

substitute in the linear equation

y=250+0.04(975)

y=250+39=$289

therefore

The commission is $39

The total salary for week 1 is $289

case 4) week 4

Sales  $824

For x=824

substitute in the linear equation

y=250+0.04(824)

y=250+32.96=$282.96

therefore

The commission is $32.96

The total salary for week 1 is $282.96

Answer:

1/2

Step-by-step explanation:

The ratio of corresponding side lengths of the dilation are 1/2 those of the original, so the scale factor is 1/2.

___

For example, A'C'/AC = 9/18 = 1/2.

Answer:

f(-3) = -5

Step-by-step explanation:

Put -3 where x is and evaluate the expression:

f(-3) = -5

_____

The function describes a horizontal line. It doesn't matter what x is, the value of the function is -5.

Answer:

a=4/5y

Step-by-step explanation:

Answer:

See the attached photo for the calculations and answers

Step-by-step explanation:

The calculations and explanations are shown in the 3 attached photos below.

The answer to the given question will be a) P(flush) = 0.0019 b) P(one pair) = 0.4225 c) P( two pairs) = 0.475 d) P(three of a kind) = 0.211 e) P(four of a kind) = 0.00024

What is probability?

It's a field of mathematics that studies the probability of a random event occurring. From 0 to 1, the value is expressed.

The probability of being dealt a flush:

For a suit there are 4 choices and 13C₅ choices for a card in that suit

Probability of flush = 4.( 13C₅)/52C₅

Probability of flush = 0.0019

The probability of being dealt one pair:

There are 13 possible values of a, 4C₂ choice for suit of a, 12C₃ value for b, c, d and 4 choices each for choosing the suit of b, c, d.

P(one pair) = (13.4C₂.12C₃.4.4.4)/52C₅

P(one pair) = 0.4225

The probability of being dealt two pairs:

There are 13C₂ possibility for the value of a and b, 4C₂ choices for suits of both a and b and 44 possibilities for c from the remaining cards.

P(2 pairs) = (13C₂.4C₂.4C₂.44)/(52C₅) = 0.475

The probability of being dealt three of a kind:

There are 13 possibilities for the value of a and 4C₃ choices for the suits of a, 12C₂ possibilities for both b and c and 4 choices of suits for both b and c.

P( three of a kind) = (13.4C₃.12C₂.4.4)/52C₅ = 0.211

The probability of being dealt four of a kind:

There are 13 possibilities of a and 4C₄ values for the suit of a and 48 choices of b from the remaining cards.

P(four of a kind) = (13.4C₄.48)/52C₅ = 0.00024

Learn more about probability on:

https://brainly.com/question/24756209

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Answer:

$162

Step-by-step explanation:

Discount = percentage discount ÷ 100 × original cost

Discount = [tex]\frac{40}{100}[/tex] × $405 = $162