Complete the square and graph: 9y²−x − 18y +10=0 ​

Answers

Answer 1

Answer:

See below ~

Step-by-step explanation:

Completing the square :

9y² - x - 18y + 10 = 09y² - 18y + 9 - 9 - x + 10 = 0(3y - 3)² - x + 1 = 0

Graph :

Complete The Square And Graph: 9yx 18y +10=0
Answer 2

Answer:

x = 9(y - 1)² + 1

see attached for graph

Step-by-step explanation:

Completing the square

Given equation:

9y² - x - 18y + 10 = 0 ​

As there is a y² in the equation, this implies it is a sideways parabola.

To complete the square for a sideways parabola, collect the y variable terms on the left and everything else on the right:

⇒ 9y² - 18y = x - 10

Factor out the leading coefficient from the left side:

⇒ 9(y² - 2y) = x - 10

Take the coefficient of y, half it, then square it:  (-2 ÷ 2)² = 1

Add this inside the parentheses, and add the distributed value of this to the right side:

⇒ 9(y² - 2y + 1) = x - 10 + 9

Factor the parentheses and simplify the right side:

⇒ 9(y - 1)² = x - 1

Add 1 to both sides to make x the subject:

x = 9(y - 1)² + 1

Graphing the parabola

Conic form of a sideways parabola with a horizontal axis of symmetry:

x = a(y - k)² + h

(where (h, k) is the vertex and y = k is the axis of symmetry)

If a > 0, the parabola opens to the right, and if a < 0, the parabola opens to the left.

Therefore, for  x = 9(y - 1)² + 1

vertex = (1, 1)axis of symmetry:  y = 1a > 0 ⇒ the parabola opens to the right

To find the x-intercept, set y = 0 and solve for x:

⇒ x = 9(0 - 1)² + 1

⇒ x = 9(-1)² + 1

⇒ x = 9(1) + 1

⇒ x = 10

Therefore, the y-intercept is (10, 0)

As the axis of symmetry is y = 1, the other value of y when x = 10 is y = 2

Plot the vertex and points. Add an axis of symmetry to help draw the curve.  Draw the parabola opening to the right.

**graph attached**

Complete The Square And Graph: 9yx 18y +10=0

Related Questions

Which graph represents the solution set of y = x2 − 4 and x + y + 2 = 0?

A.
graph A

B.
graph B

C.
graph C

D.
graph D

Answers

Graph b i think im not fully sure

Answer:

its C

Step-by-step explanation:

I used something else for it for it

Stephen buys two cookies and one muffin for $5. Jacks buys one cookie and one muffin for $3. How much is a cookie? How much is a muffin?

Answers

Answer: Cookie=2$ and Muffin=1$

Step-by-step explanation: Cookie=x and Muffin =y

then, 2x+y=5...(1)

x+y=3...(2)

(1) -  (2)

2x+y-x-y=5-3

or, x=2

then y=1

Answer:

c = 2

m= 1

Step-by-step explanation:

Im guessing you will need to use simultaneous equations

Let 'c' be the cost of 1 cookie and 'm' be the cost of 1 muffin

1) 2c + 1m = 5 -

2) 1c + 1m = 3

c / = 2

So c is 2

1) Label the equations 1 and 2

2) Find a common term in both equations ( bold)

3) Eliminate 1m by subtracting equation (2) from equation 1

( To know if to subtract or add always follow this rule: If the common terms and the same sign subtract if they are a different sign add)

4) Substitute c in any of the equation ( 1 or 2) to find m

I will use equation 2 because I think its easier

2) 1c+1m = 3

2 + m = 3

m= 3-2

m= 1

For his phone service, Omar pays a monthly fee of $26, and he pays an additional $0.06 per minute of use. The least he has been charged in a month is
$108.74
What are the possible numbers of minutes he has used his phone in a month?
Use m for the number of minutes, and solve your inequality for m.
D
>
DO
20
х
5
?

Answers

Answer: m ≥ 1,379

Step-by-step explanation:

$26 monthly fee

$0.06/minute of use

$108.74 (least charged in a month)

m = number of minutes

26 + 0.06m ≥ 108.74

0.06m ≥ 108.74 - 26

0.06m ≥ 82.74

[tex]\frac{0.06m}{0.06}[/tex]  ≥  [tex]\frac{82.74}{0.06}[/tex]

m ≥ 1,379

CAN SOMEONE HELP ME PLS?

Answers

Answer:

x = 8

[tex]\overline{AC}[/tex] = 30

[tex]\overline{CD}[/tex] = 10

Step-by-step explanation:

Triangle [tex]\triangle ABC[/tex] and triangle [tex]\triangle DEC[/tex] are similar because they have 2 congruent angles. We can find the scale factor between them by comparing the length of [tex]\overline{BC}[/tex] and  [tex]\overline{EC}[/tex] in a fraction, resulting in us finding the scale is 3:1 from [tex]\triangle ABC[/tex] to [tex]\triangle DEC[/tex].

Now we can solve for x using a proportion.

[tex]\frac{3}{1} = \frac{x+22}{x+2}[/tex] | Cross multiply

3x+6 = x+22 | Subtract x from both sides

2x+6 = 22 | Subtract 6 from both sides

2x = 16 | Divide both sides by 2

x = 8

Now we can solve for [tex]\overline{AC}[/tex] and [tex]\overline{CD}[/tex] by substitution.

[tex]\overline{AC}[/tex] = x + 22 = 8 + 22 = 30

[tex]\overline{CD}[/tex] = x + 2 = 8 + 2 = 10

These are your answers

- Kan Academy Advance

Determine the period.

Acellus

Answers

Answer:  5

Explanation:

One root (aka x intercept) is at x = 0

The next root over isn't clear, but luckily we can skip over it and see the next root after that is x = 5

After this point, the curve repeats itself. This means the period is 5 units.

The graph repeats itself every 5 units, aka the cycle is 5 time units long.

For the function f(x) = x3
Find f(2) =

Find f(-2) =

Answers

Answer:

[tex]f(2) = 6[/tex]

Step-by-step explanation:

Substitute x=2 into f(x) x times 3

[tex]f(2) = 2 \times 3[/tex]

Calculate it

[tex]f(2) = 6[/tex]

Find the missing angle. 60° 80° 90° 200

Answers

Answer:

80

Step-by-step explanation:

140-60

Answer: 160°

140 + 60 = 200

360 - 200 = 160

Mrs. thomas wants to put a table in the corner of a room. she considers the measurements of these tables. table 1 length: 1.5 feet width: 2.4 feet diagonal: 3.0 feet table 2 length: 3.2 feet width: 2.8 feet diagonal: 4.0 feet table 3 length: 2.4 feet width: 3.2 feet diagonal: 4.0 feet table 4 length: 2.6 feet width: 1.8 feet diagonal: 3.0 feet the walls forming the corner meet at a 90º angle. which table will fit snugly in the corner? table 1 table 2 table 3 table 4

Answers

Table 3 will fit snugly in the corner of the room.

What is the Pythagorean theorem?

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides.

From the given data we will check the value of the diagonal by applying the Pythagorean theorem.

So by using the Pythagorean theorem:-

D ²  =    L²   +   W²

D²   =    ( 2.4 )²  +  ( 3.2 )²

D²   =    ( 5.76   +    10.24 )  =   16

D     =   √16   =  4  feet

Therefore table 3 will fit snugly in the corner of the room.

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Answer:

Table 3.

Step-by-step explanation:

Person above is correct, I'm takin the test!!

I need help asap please

Answers

Answer:

12.36

Step-by-step explanation:

the standard deviation is 12.36123 or 12.36 rounded.

Marcus had to drive to a job training workshop in a city 225 miles away from his home. He was paid $0.55 per mile each way and was also given a motel and meal allowance of $145 per day for the four-day training. How much was he paid for attending this workshop?

Answers

Marcus was paid $703.75 for attending the workshop based on calculations from his driving job and motel & meal allowance.

How to calculate allowance?

According to this question, Marcus had to drive to a job training workshop in a city 225 miles away from his home.

He was paid $0.55 per mile each way and was also given a motel and meal allowance of $145 per day for the four-day training.

This means that Marcus was paid as follows:

$0.55 × 225 miles = $123.75$145 × 4 = $580

Therefore, Marcus was paid $703.75 for attending the workshop based on calculations from his driving job and motel & meal allowance.

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ABCD is a parallelogram. Determine the measure of ∠B.

Answers

The measure of the ∠B of given parallelogram is 362 - 42x

In the above question, a figure which is known as Parallelogram is given, where the following angles are given :

Measure of ∠A = 6x + 14

Measure of ∠C = 9x - 7

Measure of ∠D = 17x + 5

We need to find, the measure of the ∠B

From the properties of a Parallelogram, we know that "The sum of all the interior angles of a parallelogram is equal to 360°". So using this property we'll find the measure of ∠B

Now,

∠A + ∠B +  ∠C + ∠D = 360

16x + 14 +  ∠B + 9x - 7 + 17x + 5 = 360

∠B + ( 16x + 9x + 17x ) = 360 - ( -14 + 7 -5)

∠B + 42x = 360 - (-2)

∠B = 362 - 42x

Hence, the measure of the ∠B is 362 - 42x

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Answer:

56 degrees

Step-by-step explanation:

Just did the Imagine Math

In general, 60 beats per minute (bpm) is a heart rate that is considered too slow for an adult when at rest and 100 bpm is considered too high. As one way of measuring the stress of Canadian air traffic controllers, heart rates of 173 randomly selected air traffic controllers were measured across Canada. Of this sample of air traffic controllers, 47 had a resting heart rate over 100 bpm. What is the true proportion of air traffic controllers in Canada with resting heart rates over 100 bpm

Answers

The true proportion of air traffic controllers in Canada with resting heart rates over 100 bpm is; 0.2717 or 27.17%

How to calculate true proportion?

We are given;

Sample size; n = 173

Number of people who had  a resting heart rate over 100 bpm = 47

Now, formula for true proportion is;

p' = x/n

where;

x represents the number of successes

n represents the sample size.

p′ is the sample proportion which is the point estimate for the true population proportion.

Thus;

p' = 47/173

p' = 0.2717

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Kelly plants 45 tulips in 30 minutes what is the unit rate?

Answers

Answer:

1.5 per minute

Step-by-step explanation:

unit rate is how many in 1 minute so 45 divided by 30 is 1.5 and if you want to check your answer do 1.5 x 30 which is 45

#3
the price of a watch was decreased by 35% and
sold for $75.99. what was the original price of the
watch in dollars?
a. $26.60
c. $116.91
b. $49.39
d. $217.11

Answers

Step-by-step explanation:

it means

$75.99 = original price × 0.65 ((100-35)/100)

original price = $75.99/0.65 = $116.9076923... ≈

≈ $116.91

a1 = 10 and an =an -1 +2

Answers

I assume you're asking to solve for the n-th term in the sequence, [tex]a_n[/tex].

From the given recursive rule,

[tex]a_n = a_{n-1} + 2 \implies a_{n-1} = a_{n-2} + 2[/tex]

and by substitution,

[tex]\implies a_n = a_{n-2} + 2\times2[/tex]

Similarly,

[tex]a_n = a_{n-1} + 2 \implies a_{n-2} = a_{n-3} + 2[/tex]

[tex]\implies a_n = a_{n-3} + 3\times2[/tex]

The pattern continues, so that we can write the n-th term in terms of the 1st one:

[tex]a_n = a_1 + (n-1)\times2 \implies a_n = 10 + 2(n-1) = \boxed{2n+8}[/tex]

So the first few terms of the sequence are

{10, 12, 14, 16, 18, 20, …}

use the dots for one and two. what is the difference between the ranges


a. 20 points
b. 5 points
c. 10 points
d. 35 points

Answers

Answer:

a. 20 points

Step-by-step explanation:

Range = Largest given value - Smallest given value.

Identifying the range of test 1

Looking at the dot plot the lowest test grade appears to be 50 while the highest is 90.

So range of test 1 = 90 - 50 = 40

Identifying the range of test 2

Looking at the plot the lowest test grade appears to be 40 while the highest appears to be 100

So range = 100 - 40 = 60

Identifying the differences between the ranges

Test 1 range : 40

Test 2 range : 60

Difference between the two : 60 - 40 = 20 points

help me please i need help

Answers

Answer:

if you want to, I can explain it to you in more details

The chance of winning based on the type of lottery tickets we purchase is 0.05, or 1 in 20. We will play each saturday until we win. What is the probability of winning on the fourth ticket?

a .05
b .0407
c .0475
d .04287

Answers

Answer:

Given that the probability of winning is = 0.05

So the probability of losing is = 1 - 0.05 = 0.95.

We are told we have a 1 in 20 chance

Success: 0.05

Failure: 0.95

P(X=4)= 0.95*0.95*0.95*0.05

So the chance is 0.04286 or Option D

Please help!!!! Find the value of x.

Answers

Answer: 84

Step-by-step explanation:

Based on the end behavior of the graph, which polynomial function is graphed here?

graph of f(x) = -3x^4 - 6x^3 - 2x^2 + x + 3

A.
f(x) = 3x4 − 6x3 − 2x2 + x + 3
B.
f(x) = -3x3 − 2x2 + x + 3
C.
f(x) = -3x4 − 6x3 − 2x2 + x + 3
D.
f(x) = 3x3 − 2x2 + x + 3

Answers

Answer:

C) [tex]f(x)=-3x^4-6x^3-2x^2+x+3[/tex]

Step-by-step explanation:

As the graph of the function has 3 turning points, then it cannot be options B or D because the function would've had 2 turning points at most.

Also, since the graph of the function opens downward, the leading coefficient must be negative, so C must be the correct answer.

What is the measure of E​

Answers

Step-by-step explanation:

Represent D and E as x because you don't know them

Now the sum of all these angles is 180

so,D+E+90(THE SIGN AT THE TOP)=180

D which is x the E which is also x

x+x+90=180

2x+90=180

2x=180-90

2x=90

[tex] \frac{2x}{2} = \frac{90}{2} [/tex]

cancel and you will get x as 45

therefore x is 45 degrees

Mia is traveling in a car at a speed of 52.8 miles per hour. How many miles will she cover in 2 hours?

Answers

Answer:

52.8*2=105.6

Step-by-step explanation:

52 I'm per hour means in two hour she travels double times that is 105.6 miles per hour

Help me find the angle P and FHR equals in the attachment. I am running out of time pls help quick​

Answers

Vertically opposite angles are the same so 124= p-117 so p= 241
so angle FHR is 241-117= 124°

Which measure of variability is the most appropriate for this set of values? OA range OB. interquartile range OC. mean absolute deviation OD. absolute deviation O E. either interquartile range or mean absolute deviation​

Answers

The most appropriate measure is absolute deviation, as we know absolute deviation can help us gain a more representative notion of spread option (D) is correct.

What is the standard deviation?

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

We have data shown in the picture.

As we know, Quartiles or ranges are useful, but they are limited because they skip a lot of data in the group.

For a data set like the one in this question, where the items are close in difference, absolute deviation can help us gain a more representative notion of spread.

Thus, the most appropriate measure is absolute deviation, as we know absolute deviation can help us gain a more representative notion of spread option (D) is correct.

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HELPPPP THIS IS 7TH GRADE MATH AND IM CONFUSED (it’s the Jessica one btw)

Answers

Answer: $2.25
Explanation: First, subtract 11.50 - 4.75 = 6.75
Then 6.75 / 3 = 2.25

If the ratio of iphones to total phones in a classroom is 5: 8 and there are 24 phones overall, how many iphones are there?

Answers

Answer:

The answer is 15

Step-by-step explanation:

Step-by-step explanation:

let the number of total phones be 8x and number of iPhones be 5x

now,

8x=24

or, x= 24/8 = 3

therefore

no. of iPhones = 5x = 5×3 = 15

i hope my answer is clear

Please answer Asapp (Will give brainliest)!

Answers

Answer:

There is no answer as there is no question.

Step-by-step explanation:

Answer:

I added the answer to your newest problem :D

Step-by-step explanation:

Hope it helped!

To the nearest square centimeter, how many square centimeters of the plate are covered by the napkin? 16 square centimeters 30 square centimeters 56 square centimeters 60 square centimeters

Answers

The area covered by the napkin is 56 square centimeters

How to determine the area covered by the napkin?

This is calculated using:

[tex]Area = \frac 12 ab\sin(C)[/tex]

Where:

a = 15, b = 5 and C = 30

So, we have:

[tex]Area = \frac 12 * 15 * 15 * \sin(30)[/tex]

Evaluate the product

Area = 56.25

Approximate

Area = 56

Hence, the area covered by the napkin is 56 square centimeters

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Answer: 56

Step-by-step explanation:

that’s c on 2023 edge

What is the total area of the following composite figure?



136.26 m 2
122.13 m 2
117.42 m 2
62.13 m 2

Answers

Step-by-step explanation:

there is a rectangle and an octagon within

area of rectangle = 8*9 = 72

there are 4 right angled triangles

area of one such triangle = .5 × 9 = 4.5

total area of triangles = 18

area of octagon = 72-18 = 54 m^2

a sheet of paper is 0.1mm thick

a) A ream of paper has 500 sheets. how thick would 1 ream of paper be?

Answers

Answer:

a) 50 mmb) 1 200 sheet of paper

Step-by-step explanation:

a) the thickness of one ream of paper :

= 0.1 × 500

= 50 mm

b) 12 cm = 12 × 10 = 120 mm

Then

the number of sheets that exist in a pile of papers that has a thickness of 12 cm :

= 120 ÷ 0.1

= 1 200 sheet of paper

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