prove that y=2x^2-6x+7 and y=x^2-2x+3 touch each other and find the point of contact

Answers

Answer 1

Answer:

See below ~

Step-by-step explanation:

We need to prove they are equal.

Equate the values to each other.

2x² - 6x + 7 = x² - 2x + 3x² - 4x + 4 = 0(x - 2)² = 0x = 2

Now input the x-value in the 1st equation.

y = 2(2)² - 6(2) + 7y = 8 - 12 + 7y = -4 + 7y = 3

Now input the same in the 2nd equation.

y = (2)² - 2(2) + 3y = 4 - 4 + 3y = 3

Since the same x-value, on inputting in both equations, give the same y-value, it is proved they touch each other.

Point of Contact

(x, y)(2, 3)

Related Questions

A teacher has been given £35 to spend on pencils and rulers.
A packet of 12 pencils costs £2.15.
A pack of 30 rulers costs £6.00.
She buys 4 packs of rulers and spends the rest on packets of pencils.
How many packets of pencils can she buy?

Answers

Packet of 12 pencils = p
Packet of 30 rulers = r

p = £2.15
r = £6.00

£35 = 4r + xp
£35 = 4(£6.00) + x(£2.15)
£35 = £24 + £2.15x
£11 = £2.15x
x = 5.12

Since she can buy 5.12 packets of pencils, it is equal to 5 packets of pencils.

The value of 4,576 x (2,480 + 3) is 3 more than the value of 4,576 x 2,480

Answers

This is false

It would be true if it said (4576 * 2480) + 3 is 3 more

But this is actually ~13728 more

This due to the fact that the 3 is also being multiplied by 4576

A, B & C form a triangle where Z BAC = 90°.
AB = 4.2 mm and CA = 1.5 mm.
Find the length of BC, giving your answer rounded to 1
DP.
mm
BC =

Answers

Answer:

Step-by-step explanation:

Nothing further can be done with this topic. Please check the expression entered or try another topic.

A, B, C, ZBAC=90°

AB=4.2mm

CA=1.5mm,

DP

mm

BC

hope this helps

Answer:

BC = 4.5 (1 dp)

Step-by-step explanation:

Pythagoras’ Theorem

[tex]a^2+b^2=c^2[/tex]

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

a = AC = 1.5b = AB = 4.2c = BC

Substituting these into the formula and solving for BC:

[tex]\implies 1.5^2+4.2^2=BC^2[/tex]

[tex]\implies 2.25+17.64=BC^2[/tex]

[tex]\implies BC^2=19.89[/tex]

[tex]\implies BC=\pm\sqrt{19.89}[/tex]

As distance is positive,

⇒ BC = 4.5 (1 dp)

Bryan and Jadyn had barbecue potato chips and soda at a football party. Bryan ate 5oz of chips and drank 1 cup of soda for a total of 650mg of sodium. Jadyn ate 1oz of chips and drank 5 cups of soda for a total of 250mg of sodium. How much sodium is in 1oz of chips and how much is in 1 cup of soda?

Answers

Answer:190 mg of sodium in 1 oz of chips and 40 mg for 1 cup soda.

Step-by-step explanation:

Find the surface area and volume, GIVING BRAINLY

Answers

[tex]\bold{ANSWER:}[/tex]
1040.91 mm^2

[tex]\bold{EXPLANATIONS:}[/tex]

what is the area of 10in circle

Answers

Answer:

Step-by-step explanation:

going by the assumption tha the radius is 10inches.

area would be pi r^2

which would be pi(10)^2 = 100pi =314.16 (rounded)

Five gallons of gasoline cost \$ 22. 80$22. 80. ​
​What is the price per gallon?

Answers

Answer:

$4.56

Step-by-step explanation:

22.80/5 = 4.56

number story for 4 divided by 1/8

Answers

Answer:

32

Step-by-step explanation:

4 ÷ 1/8

4/1 · 8/1 = 32/1

32

I hope this helps & God bless!

Is a triangle with the side lengths 4 feet, 7. 5 feet, and 8. 5 feet a right triangle? Why or why not? ​

Answers

Answer:

Yes

Step-by-step explanation:

You can test if a triangle is right-angled by using Pythagoras' Theorem.

So:

[tex]4^2 + 7.5^2 = 8.5^2[/tex]

16 + 56.25 = 72.25

They do in fact add up so this triangle is right angled.

Given circle E with diameter CD and radius EA. AB is tangent to Eat A.
If AD = 14 and CD = 26, solve for AC. Round your answer to the nearest
tenth if necessary. If the answer.cannot be determined, click "Cannot be
determined."

Answers

The hypotenuse is equal to the square of the other two sides. The length of AC from the diagram is 21.9feet

Application of pythagoras theorem

The theorem states that the square of the hypotenuse is equal to the square of the other two sides

Given the following

Hypotenuse = 26 feet = CD
Base side = AD = 14ft

Required

Length AC

Use the theorem

26^2 = 14^2 + AC^2

AC^2 =  676 - 196
AC^2 = 480
AC = 21.9feet

Hence the length of AC from the diagram is 21.9feet

Learn more on pythagoras theorem here: https://brainly.com/question/343682

Answer:

Given circle E with diameter CD and radius EA. AB is tangent to E at A. If
CD = 8, solve for AD. Round your answer to the nearest tenth if necessary. If the
answer cannot be determined, click "Cannot be determined.

Step-by-step explanation:

WILL GIVE BRAINLIEST

Answers

Distance formula: distance = sqrt((x2-x1)^2 + (y2-y1)^2)


distance = sqrt((-2 - -9)^2 + (-2 - -6)^2)

Distance = sqrt( 7^2 + 4^2)

Distance = sqrt(49+ 16)

Distance = sqrt(65)

Answer is c. Sqrt(65)

Answer: the answer is c which square root 65

Step-by-step explanation: hope it is correct .

please help me find the same denominator

Answers

Answer:

[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

let us first start with some basic information ~

A fraction can be represented as [tex]\frac{x}{y}\\[/tex] where ,

x is the numerator and y is the denominator !

the question asks us to do something that will help us get same denominator for both the terms !

so let's see what we should do in such a case ~

[tex] \frac{9}{10} \: and \: \frac{7}{8} \\ \\ \\ lets \: make \: the \: denominator \: of \: both \\ the \: terms \: reach \: 80 \: , \\ \\ \bold\orange{ \implies \: \frac{9}{10} \times \frac{8}{8} = }\bold\red{ \frac{72}{80}} \\ \\\bold\orange{ \implies \: \frac{7}{8} \times \frac{10}{10} =}\bold\red{ \frac{70}{80}} [/tex]

and we're done !

let's add some more info to be lil more clear ~

while converting the denominator of both the terms , we must multiply the same number ( this number refers to the one we'll have to multiply to the denominator to obtain the desired result ) with the denominator as well as with the numerator !

hope helpful :D

Answer:

Step-by-step explanation:

you have to multiply first fraction with '8' and second fraction with '10' :

the fractions will become 72/80 and 70/80 then you can compare it

Suppose a town has a population of 5,000 residents but that the population is decreasing by 200 people each year. Write a linear function to represent the population of the town in terms of the numbers of years. After how many years will the town have a population of 1,800? When will the town have only 400 residents?

Answers

Answer:

it will take 16 years to reach a population of 1800 and in 23 years the population will be 400.

Step-by-step explanation:

population: 5000

population decreasing: 200x

y=5000-200x

(1800-5000)/-200

(400-5000)/-200

find the Perimeter and area

Answers

Answer:

perimeter = 22 + 3π

area = 48 + (9/2)π

Step-by-step explanation:

perimeter = 8 + 6 + 8 + (1/2)(6π) = 22 + 3π

area = 8(6) + (1/2)(3^2)π = 48 + (9/2)π

If Emily walks to school at 3 miles per hour, the walk takes 20 minutes. If she rides her bike to school at 5 miles per hour, how long will the trip take her?​

Answers

Answer:

40 minutes

Step-by-step explanation:

I think this is the correct answer

I hope I helped you

sorry if I got it wrong btw

Solve using the Elimination Method

x - 2y = 4
3x + 4y = 2​

Answers

Answer: x=2, y=-1

Step-by-step explanation:

Step 1) Make both equations have the same coefficient

What I mean by this is make either y or x have the same number multiplied to them so that we can eliminate. We can do this by multiplying everything in the first equation by 2.

[tex](2)x - (2)2y = (2)4\\2x-4y=8[/tex]

Step 2) Add the equations together to eliminate y

[tex]2x - 4y = 8\\+3x + 4y = 2\\5x+0=10\\5x=10[/tex]

Step 3) Solve for x

[tex]\frac{5x}{5} =\frac{10}{5} \\x=2[/tex]

Step 4) Sub the value of x into an equation and solve for y

[tex]x-2y=4\\2-2y=4\\2-2-2y=4-2\\-2y=2\\\frac{-2y}{-2} =\frac{2}{-2} \\y=-1[/tex]

How to multiply a ratio then divided by 3.

Answers

Answer:

Heres the answer

Step-by-step explanation:

To calculate the ratio of an amount we divide the amount by total number of parts in the ratio then multiply the answer by original ratio.

3 1/8 x 90 please help me thank you everyone ! :)

Answers

Answer:

[tex]2248\frac{1}{4}[/tex]

Step-by-step explanation:

given: [tex]3\frac{1}{8} * 90[/tex]

now, we turn both into improper fractions:

25/8 * 90/1 :: [tex]\frac{25}{8} * \frac{90}{1}[/tex]

now we multiply across

[tex]\frac{25}{8} * \frac{90}{1} = \frac{2250}{8}[/tex]

now turn into a mixed number:

[tex]\frac{2250}{8} = 2248\frac{2}{8}[/tex]

simplify! :

[tex]2248\frac{1}{4}[/tex]

The diagram shows a prisim
Draw the front elevation and the side elevation of the prism on the grids.
use a scale of 2 squares to 1m​

Answers

Because 2 squares equal a meter u have to do four up down one. (Front elevation)
Then just four by one square on second row down(side elevation)

Ms. Upton spends a total of $42 for 3 sweaters for her children. Each sweater costs the same amount. How much does each sweater cost?

Which equation can be used to find the answer?



Group of answer choices

42 + S= 3

S= 423

S=42*3

S-42=3

Answers

Answer:

The answer would be $14 a sweater.
And S=42*3 (If * is a divide by sign)

Step-by-step explanation:

Step 1. Find the equation. If $42 is total then we know to to divide that number by three getting the equation S=42*3.
Step 2. Do the math. 42 divided by 3 is 14, meaning 14 dollars per sweater.
I hope this helps! :)

what is the area of a 14cm square?

Answers

Answer:

196

Step-by-step explanation:

the area of a square is simple its just a=length time width, so you just plug in youre length which is 14 and a square side are all the same size so the width is also 14, so your equation is a=14 times 14= 196. ;) hope that helped.

11 What is the value of k if the mid-point of the line joining (1 – k, 4) and (2, k + 1) is (-k, k)? ​

Answers

Answer:

k = -3

Step-by-step explanation:

Given

(-k, k) is the midpoint of the line joining (2, k + 1) and (1 - k, 4)

Solving

Equate the midpoint and endpoints using the Midpoint FormulaLet's equate the x parts-k = 2 + 1 - k / 2-2k = 3 - k-k = 3k = -3

The parabola in the image has its focus at (4,3).Its directrix is the line y=1.The point (8,6) is on the parabola.

Answers

The true statements for the parabola in the image are:

C. The point (8, 6) is the same distance from the point (4, 3) as it is from the line y = 1.Option D.

How to determine the equation of the directrix?

Mathematically, the standard equation of the directrix lines for a parabola is given by y = a(x - h)² + 2.

Given the following data:

Vertex (h, k) = (4, 3).

Point (x, y) = (8, 6).

Next, we would determine the distance where point (8, 6) lies on the parabola:

y = a(x - h)² + 2

6 = a(8 - 4)² + 2

6 = a(4)² + 2

6 = 16a + 2

16a = 6 - 2

16a = 4

a = 4/16

a = 1/4.

Therefore, the equation becomes:

y = 1/4(x - 4)² + 2

When x = 2, we have:

y = 1/4(2 - 4)² + 2

y = 1/4(-2)² + 2

y = 1/4(4) + 2

y = 1 + 2

y = 3.

In conlusion, the true statements regarding the parabola in the image are:

The point (8, 6) is the same distance from the point (4, 3) as it is from the line y = 1.The point (2, 3) is on the parabola.

Read more on directrix here: https://brainly.com/question/2346582

#SPJ1


Please help me I’ve asked this questions several times and I really need help with this I do not understand it at all

Answers

Answer:

(-5,-2)

(-4,-3)

(-6,-1)

Step-by-step explanation:

-5(x)-2(y)=-7

-4(x)-3(y)=-7

-6(x)-1(y)=-7

3 cm
Find the surface area of the above solid.
O A. 56 cm2
• B. 40 cm2
• C. 48 cm2
D. 36 cm2
Help quickly please

Answers

area is 36...............

Given that a student is in 10th grade, what is the probability that the student is also not involved in after-school activities? 0.43 0.45 0.55 0.57

Answers

Answer:D

Step-by-step explanation:

Math 50 points Please Help

Answers

Answer:

Step 3

Step-by-step explanation:

-4(3)(-1)

Will be equal to a positive 12

The step that was wrong was step 3; multiplying -4(3)(-1) will equal to 12 and not “-12” so overall it would be square root of 28 and not 4

A greenhouse owner wants to test the effectiveness of a new fertilizer on African violets. She has 60 violet
seedlings that were grown for 8 weeks. She wants to test the new fertilizer on 10 of the plants, and decides to use
a simple random sample to select them. Which of the following statements is true?
She needs to select the 10 biggest plants to test the new fertilizer.
She needs to select the 10 smallest plants to test the new fertilizer.
She needs to number each plant 1-60 and randomly select 10 plants.
She needs to put the plants in 6 groups of 10 and randomly select 1 of the groups.

Answers

Answer:

1 - 60

Step-by-step explanation:

She needs to number each plant 1-60 and randomly select 10 plants.

formular for area of a circle

Answers

Answer:

Tr2

Step-by-step explanation:

pie * radius * radius

Answer:

πr²

Step-by-step explanation:

The circumference of a circle is given to be 2πr, and its radius to be r.

Area = 1/2 x circumference x radiusArea = 1/2 x 2πr x rArea = πr²

ou earn $17.50/hr and work 40 hr/wk. Your deductions are FICA (7.65%), federal tax withholding (12.3%), and state tax withholding (6.2%). Your housing and fixed expenses are 30% of your realized income per month. You want to save 5 months' worth in an emergency fund within a year. How much do you need to save per month to fund the emergency fund?

Answers

Step-by-step explanation:

MARK A BRAINLESS THIS ANSWER IS CORRECT

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