complete the square tov rewrite y=x^2+6x+2 in vertex form. then state whether the vertex is maximum or minimum and give its coordinates.

Answer:

[tex]\displaystyle [3\frac{1}{3}, -2][/tex]

Step-by-step explanation:

{2x + 3y = ⅔

{3x - 4y = 18

¾[3x - 4y = 18]

{2x + 3y = ⅔

{2¼x - 3y = 13½

____________

[tex]\displaystyle \frac{4\frac{1}{4}x}{4\frac{1}{4}} = \frac{14\frac{1}{6}}{4\frac{1}{4}} \\ \\[/tex]

[tex]\displaystyle x = 3\frac{1}{3}[/tex][Plug this back into both equations above to get the y-coordinate of −2]; [tex]-2 = y[/tex]

I am joyous to assist you anytime.

The system of equations is solved using the elimination method. By multiplying the equations to align the coefficients and adding them to eliminate y, x is found to be 3.3333. Plugging x back into one of the original equations then gives y as -2.0000.

To solve the system of equations:

we can use the method of substitution or elimination. Let's use elimination in this case:

First, we multiply the first equation by 4 and the second equation by 3 so that the coefficients of y have the same magnitude but opposite signs:

Next, we add the two equations together to eliminate y:

8x + 12y + 9x - 12y = 8/3 + 54

17x = 54 + 8/3

17x = 54 + 2.6667

17x = 56.6667

Now we divide both sides by 17 to solve for x:

x = 56.6667 / 17

x = 3.3333

With x found, we can now substitute it back into one of the original equations to find y. We'll use the first equation for this example:

2x + 3y = 2/3

Substitute x:

2(3.3333) + 3y = 2/3

6.6666 + 3y = 2/3

3y = 2/3 - 6.6666

3y = -6.0000

Now divide both sides by 3 to solve for y:

y = -6.0000 / 3

y = -2.0000

The solution to the system is x = 3.3333 and y = -2.0000.

Answer:

C. Both x is a function of y and y is a function of x

Step-by-step explanation:

A function is a relationship which assigns to each input (from the domain) value, a unique output (from the range).

y is a function of x means x is from domain, y is from range

x is a function of y means y is from domain, x is from range

1. Given [tex]y=16-x[/tex]

y is a function of x because for each x there is exactly one y corresponding to this x.

2. Rewrite [tex]y=16-x[/tex] expressing x in terms of y:

[tex]y-16=-x\\ \\-x=y-16\\ \\x=16-y[/tex]

x is a function of y because for each y there is exactly one x corresponding to this x.

Final answer:

In the equation y = 16 - x, both x and y are functions of each other since each variable can be expressed as having a unique output for each input of the other. The correct answer is c. both x is a function of y and y is a function of x.

Explanation:

To determine which statement is true regarding the equation y = 16 - x, we need to understand the concept of a function. A function, in mathematical terms, is a relationship between two sets that assigns to each element of the first set exactly one element of the second set. In simpler terms, for a variable to be a function of another variable, each input should give us exactly one output. This leads us to the vertical line test, which is a visual way to determine if a curve is a graph of a function of x.

Looking at the given equation, y is expressed in terms of x, implying that for each value of x, there is exactly one value of y. This satisfies the definition of a function, so y is a function of x. Conversely, if we solve the equation for x, we get x = 16 - y, which similarly means that for each value of y, there is exactly one value of x, so x is also a function of y.

Given these points, the correct answer is c. both x is a function of y and y is a function of x. This is because each variable can be expressed as having a unique output for each input of the other variable, therefore both variables are functions of each other.

Answer:

C. 1/2

Step-by-step explanation:

SOHCAHTOA

Cosine is adjacent over hypotenuse. For the angle that is 60 the adjacent is 1 and the hypotenuse is 2.

Ms. Brown has been reading for 18 weeks so far.

To find out how many weeks Ms. Brown has been reading so far, we can set up a proportion based on the rate at which she reads books.

Ms. Brown reads 2 books every 3 weeks, so we can write this as the ratio:

[tex]\[ \frac{2 \text{ books}}{3 \text{ weeks}} \][/tex]

Now, we can set up a proportion to find out how many weeks she has been reading to reach a total of 12 books.

Let ( x) represent the number of weeks she has been reading so far. So, we set up the proportion:

[tex]\[ \frac{2 \text{ books}}{3 \text{ weeks}} = \frac{12 \text{ books}}{x \text{ weeks}} \][/tex]

Now, we can solve for ( x ) by cross-multiplying:

[tex]\[ 2 \times x = 3 \times 12 \][/tex]

[tex]\[ 2x = 36 \][/tex]

Divide both sides by 2 to solve for ( x ):

[tex]\[ x = \frac{36}{2} \][/tex]

[tex]\[ x = 18 \][/tex]

So, Ms. Brown has been reading for 18 weeks so far.

complete question given below:

Ms. Brown is reading 2 books every 3 weeks. She has read 12 books so tar. How many weeks has she been reading so far?

The answer is $11200.

Answer:

$11,200 or its D

Step-by-step explanation:

got it right on edge

Answer:43%

Step-by-step explanation:

just finished test

Answer:

Step-by-step explanation:

The events describe is about picking a card, and placing it back into the deck. This means that the total number of event won't change in each trial.

We know that there are 4 queens of 52 cards. So, the probability of picking a card and be a queen is

[tex]P=\frac{4}{52}=\frac{1}{13}[/tex]

However, in this case, we have to apply the experimental probability definition, because we have several attempts. This experimental probability is defined as the ratio between the time the event occurs (4) and the total number of trials (7). That is

[tex]P_{exp}=\frac{4}{7}=0.57 \ (or \ 57\%)[/tex]

Therefore, the right answer is C.

Good evening ,

Step-by-step explanation:

we know that, x-1 = (-1)×(1-x) and 1-x=(-1)×(x-1)

then each of 1-x and x-1 is a multiple of the other one,

if x>1 then x-1>0 and 1-x<0 then x-1>1-x

therefore in this case the least common multiple of x-1 and 1-x is x-1.

if x<1 then x-1<0 and 1-x>0 Then 1-x>x-1

therefore in this case the least common multiple of x-1 and 1-x is 1-x.

:)

Answer:

y-1=-x+2

Step-by-step explanation:

m=-1

y-1=-1(x-2)

y-1=-x+2

Answer:

$3.60

Step-by-step explanation:

25+20=45 (because you need the tax of both)

0.8(45)=3.60 (finding the tax amount)

Final answer:

Juanita has 18 magazines and wants to divide them into 3 equal piles. By dividing the total number of magazines (18) by the number of piles (3), we find that there will be 6 magazines in each pile.

Explanation:

The question asked by the student is a simple division problem in which Juanita needs to organize her magazines into 3 equal piles, and she has a total of 18 magazines. To find out how many magazines are in each pile, we divide the total number of magazines by the number of piles.

To solve this, we perform the following calculation:

So, the calculation is 18 \/ 3 = 6 magazines per pile.

Answer:

The equation of the line in point slope form is equal to

[tex](y-4)=\frac{4}{3}(x+2)[/tex]

The graph in the attached figure

Step-by-step explanation:

we know that

The equation of a line in point-slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]3y-12=4x+8[/tex]

Convert to point slope form

Factor 3 left side and factor 4 right side

[tex]3(y-4)=4(x+2)[/tex]

Divide by 3 both sides

[tex](y-4)=\frac{4}{3}(x+2)[/tex]

In this equation

the point is (-2,4)

the slope is [tex]m=\frac{4}{3}[/tex]

using a graphing tool

The graph in the attached figure

Answer:

24:36:72

Step-by-step explanation:

multiply 2,3,and 6 by 12 and you got the ratio 24:36:72, which adds to 132

Answer: Option A, Option B, Option D.

Step-by-step explanation:

Let's check each option.

A. Substitute [tex]x=-7[/tex] into the equation and evaluate in order to find the value of "y". This is:

[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(-7) + 9\\\\y=7.25[/tex]

B. Substitute [tex]x=-8[/tex] into the equation and evaluate in order to find the value of "y". Then:

[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(-8) + 9\\\\y=7[/tex]

C. Substitute [tex]x=-4[/tex] into the equation and evaluate to find the value of "y":

[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(-4) + 9\\\\y=8[/tex]

D. Substitute [tex]x=5[/tex] into the equation and then evaluate in order to find the value of "y". You get that this is:

[tex]y=\frac{1}{4}x + 9\\\\y=\frac{1}{4}(5) + 9\\\\y=10.25[/tex]

Then, the correct options are: Option A, Option B, Option D.

Answer:

[tex]y\leq -\frac{1}{3}x+1[/tex]

Step-by-step explanation:

Given:

From the graph, the x and y intercepts are at the points (3, 0) and (0, 1) respectively.

Now, for a line with two points [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex], the slope is given as:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Here, [tex](x_1,y_1)=(3,0)\ and\ (x_2,y_2)=(0,1)[/tex]. Therefore,

[tex]m=\frac{1-0}{0-3}=-\frac{1}{3}[/tex]

Now, y-intercept is [tex]b=1[/tex]

Therefore, the standard form of a line is of the form: [tex]y=mx+b[/tex]. So, the equation of the line on the graph is:

[tex]y=-\frac{1}{3}x+1[/tex]

Now, from the graph, the region is below the line including all the points on the line. Therefore, the inequality used is less than or equal to. This gives,

[tex]y\leq -\frac{1}{3}x+1[/tex]

Answer:

The two numbers are -365 and -1825.

Step-by-step explanation:

5x=y

x-y=1460

--------------

x-5x=1460

-4x=1460

x=1460/-4

x=-365

-365-y=1460

y=-365-1460=-1825

Answer:

$79.20

Step-by-step explanation:

fixed charged of $19 x 4 months = $76.00

additional charged of $0.04 x 20 = $0.80 x 4 months = $3.20

Therefore, $76.00 + $3.20 = $79.20

Answer:

m∠NQP=74°

Step-by-step explanation:

we know that

The measure of the interior angles in a triangle must be equal to 180 degrees

In this problem

In the triangle NPQ

m∠N+m∠P+m∠Q=180°

we have

m∠N=(2x)°

m∠P=(34)°

m∠Q=(2x+2)°

substitute the values

[tex](2x)\°+(34)\°+(2x+2)\°=180\°[/tex]

solve for x

[tex](4x+36)\°=180\°[/tex]

[tex]4x=180-36[/tex]

[tex]4x=144[/tex]

[tex]x=36[/tex]

Find the measure of angle NQP

we know that

m∠NQP=m∠Q=(2x+2)°

substitute the value of x

m∠NQP=(2(36)+2)=74°

Answer:

9/20 yes, 4/15 not. See below

Step-by-step explanation:

Pick 9/20 and multiply numerator and denominator by 5:

9/20 = 45/100

We know that if we divide a number by 100 we need to move the coma as two places left, so:

9/20 = 45/100 = 0.45

And this is a terminal decimal as we know where it ends.

On the other hand if we pick 4/15 let try to divide it (here I will do it 'manually'):

4 |_ 15

we can divide 4 by 15, so we use 40 and begin with a comma

40 |_ 15

      0.

15 enters 2 times in 40 with a rest of 10, so:

40 |_ 15

  30  0.2

  100

100 divided by 15 is 6 and we have 10 as rest again, and again and again...

40 |_ 15

  30  0.266.....

  100

    100

      ....

So, we will have 0.266666666666666 infinitely. The decimal for 4/15 is non terminating and is 0.26666666666666666...

Answer:

40

Step-by-step explanation:

if 3/8 equals 15 that means 1/8 equals 5 because 15/3=5. now if we multiply 5 by 8 then we get 40 years

If jay has been working for his current company for 15 years, then his age is 40 years.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, jay spent 3/8ths of his life working for a company and he has been working for his current company for 15 years.

Assuming Jay's age to be x years.

∴ (3/8) of x is 15 years.

(3/8)x = 15.

x = 15×(8/3).

x = 40.

So, Jay's age is 40 years.

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Answer:

y=125x+75

Step-by-step explanation:

Y= 125x+B

700=125(5)+B

700=625+B

700-625=625-625+B

75=B

The initial value, or deposit, for the vacation home is $75. The rate of change, or the cost per day, is $125. This constitutes a linear relationship where the total cost increases by a constant daily fee as the number of rental days increases.

In this problem, the total cost of the vacation home equals the deposit plus (daily rental fee * number of days). The total cost came out to be $700 when the family rented the home for 5 days. Given that the daily rental rate is $125, that means that the cost of the rental alone was $125 * 5 = $625.

Subtract the cost of the rental from the total cost to find the deposit: $700 - $625 = $75. Therefore, the initial value is $75, which represents the deposit.

The rate of change, which is the cost per day, is $125. This means for every additional day the family rents the vacation home, they are charged an additional $125. So the relationship is linear because the total cost increases by a constant rate - the daily fee - as the number of days increases.

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This question is incomplete, here is the complete question:

On a recent day, 8 euros were worth $9 and 24 euros were worth $27. Write an equation of the form y = kx to show the relationship between the number of euros and the value in dollars.

The equation that represents the relationship between the number of euros and the value in dollars is y = 1.125 x

Step-by-step explanation:

On a resent day;

We need to write an equation of the form y = kx to show the relationship between the number of euros and the value in dollars

∵ The form of the equation is y = kx, where x is the number of

   euros and y is the value in dollars

∵  8 euros were worth $9

∴ (8 , 9) is an ordered pair belong to the equation

∵ 24 euros were worth $27

∴ (24 , 27) is another ordered pair belong to the equation

To find k substitute x and y in the equation by the coordinates of one of these two points

∵ x = 8 and y = 9

∵ y = kx

∴ 9 = 8k

- Divide both sides by 8

∴ 1.125 = k

- Substitute the value of k in the equation

∴ y = 1.125 x

To check the equation substitute x by the x coordinate of the 2nd point if it gives the same value of the y-coordinate of the point then the equation is true

∵ x = 24

∵ y = 1.125 x

∴ y = 1.125(24)

∴ y = 27 the same value of the y-coordinate of the point

∴ The equation is true

The equation that represents the relationship between the number of euros and the value in dollars is y = 1.125 x

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Answer:

k = 4

Step-by-step explanation:

Given that a varies directly as b then the equation relating them is

a = kb ← k is the constant of variation

To find k use the condition a = 8 when b = 2

k = [tex]\frac{a}{b}[/tex] = [tex]\frac{8}{2}[/tex] = 4

Answer:

K = 4

Step-by-step explanation:

Given that varies a directly as b then the equation relating them is

Simply implies that a is directly proportional to b, that is increase in a will cause increase in, and decrease in a will cause decrease in b, and vice versa, where k remains constant.

a α b

a = kb, where k is constant

To find k use the condition a = 8 when b = 2, we make k the subject of the formular

K = a/b

K = 8/2

K = 4

Answer:

Explanation:

1. Name the angle of inclination of the line joining p to the origin α.

2. Find the relation between the coordinates of the point (x,y)

When you draw a line from the origin to the parabola, the intersection point, p(x,y) will have coordinates (x,y).

As per the definition of the tangent trigonometric ratio you have:

From which you can clear y:

Which is the expression of the coordinates of p as a function of the angle of inclination of the line joining p to the origin.

Answer:

35.33 km/h.

Step-by-step explanation:

Given: Distance= 212 km.

           Times= 6 hours

Now, finding unit rate (speed) for the situation.

Formula; Speed= [tex]\frac{Distance}{time}[/tex]

Speed (rate)= [tex]\frac{212}{6} = 35.3333\ km/h[/tex]

Speed (rate)= 35.3333≅ 35.33 km/h (nearest hundredth).

∴ Rate of the unit is 35.33 km/h

The percent decrease in the mass of Finley's pumpkin after carving is approximately 40.55%.

To calculate the percent decrease in the mass of Finley's pumpkin after carving, use the following formula:

Percent Decrease = ((Original Mass - New Mass) / Original Mass) 100%

First, let's find the decrease in mass.

Decrease in Mass = Original Mass - New Mass = 6.56 kg - 3.9 kg = 2.66 kg

Then, calculate the percent decrease:

Percent Decrease = (2.66 kg / 6.56 kg) 100% = 40.55%

The percent decrease in the mass of the pumpkin after carving is approximately 40.55%.

Answer:

60 minutes

Step-by-step explanation:

There are 3 feet in a yard, so a football field is 300 feet long.

Dive 300 by 5 to find the total minutes.

300 / 5 = 60

Answer:

1 hour

Step-by-step explanation:

100 yards = 300 feet

300 / 5 = 60

60 min = 1 hour

Answer: It would take 1 hour for sloths to walk across a 100-yard football field.

Answer:

y = 0.5x

Step-by-step explanation:

Given that x and y vary directly then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition x = 1, y = 0.5

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{0.5}{1}[/tex] = 0.5

y = 0.5x ← equation of variation

Answer: 0.5

Step-by-step explanation:

Answer:

51

Step-by-step explanation:

add them altogether then times by 3