Consider the two equations, y=5(x-2)^2-6 and (y+2)^2=9
How many solutions are there to this system? Without solving, give a convincing argument explain why there are that many solutions to the system.

Answers

Answer 1

Answer:

One solution. A system of linear equations has one solution when the graphs intersect at a point.

1\small{1}

1

2\small{2}

2

3\small{3}

3

-1\small{\llap{-}1}

-

1

1\small{1}

1

2\small{2}

2

3\small{3}

3

-1\small{\llap{-}1}

-

1

yy

y

xx

x

No solution. A system of linear equations has no solution when the graphs are parallel.

1\small{1}

1

2\small{2}

2

3\small{3}

3

-1\small{\llap{-}1}

-

1

1\small{1}

1

2\small{2}

2

3\small{3}

3

-1\small{\llap{-}1}

-

1

yy

y

xx

x

Infinite solutions. A system of linear equations has infinite solutions when the graphs are the exact same line.

Step-by-step explanation:


Related Questions

6.
What is the value of x?




24


30


40


38

Answers

You must do pythagorean theorem:

a^2 + b^2 = c^2

a and b are the legs and c is the hypotenuse

In this triangle...

a = 16

b = x

c = 34

so...

16^2 + x^2 = 34^2

256 + x ^2 = 1156

x^2 = 900

Then to isolate x square root both sides. This will get rid of the square on the x value.

This will give you...

30

x is 30

Hope this helped!

Answer: second option

Step-by-step explanation:

You need to apply the Pythagorean theorem:

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

Where "a"  is the hypotenuse and "b" and "c" are the legs of the right triangle.

In the figure you can observe the value the hypotenuse of the right triangle and the value of one of this leg. Then, you need to solve for the other leg from [tex]a^2=b^2+c^2[/tex]:

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

[tex]b=\sqrt{a^2-c^2}[/tex]

Substituting values, you get that the value of "x" is:

 [tex]b=\sqrt{(34)^2-(16)^2}[/tex]

 [tex]b=30[/tex]

What questions can you ask yourself as you decide on a career field?
What do I love to do?
What brings me joy?
What am I naturally good at?
All of the above

Answers

Answer:

What do I love to do?

What brings me joy?

What am I naturally good at?

Answer is all of the above - last choice

All of the above ! This will help you in choosing a career and what field you would want to work in ! Remember do something you like

(25 points)


Mr. Price earns $350 per week working in an appliance store. In addition, he earns 3% commission on all of his sales.


Last week, he sold $3, 800 worth of appliances.


What was Mr. Price's total income for the week?


A) $114


B) $236


C) $464


D) $556

Answers

Answer:

c

Step-by-step explanation:

commission is basically 3 percent of what he sells he gets, sooooo 3 percent of 3800 is 114 (3800 × .03 because change the percent to decimal) and add it to his pay :)

Answer:

D

Step-by-step explanation:

Find the next term of the arithmetic sequence shown. 23, 28, 33, 38, . . .

A) 42
B) 43
C) 45
D) 48

Answers

ANSWER

B) 43

EXPLANATION

The given arithmetic sequence is 23, 28, 33, 38, . . .

We can observe the following pattern,

23+5=28

28+5=33

33+5=38

To obtain the subsequent terms, we add 5.

Therefore the next term is

38+5=43

Divide and write in simplest form

3 1/3 divided by 2 3/5

Answers

Answer:

Step-by-step explanation:

If we change those mixed fractions to improper we will have a much easier time with them:

[tex]\frac{\frac{10}{3} }{\frac{13}{5} }[/tex]

Now that looks horrible.  The rule for dividing fractions by fractions is a simple one, thankfully.  Bring the bottom fraction up next to the top fraction, then flip it upside down and change the sign to multiplication:

[tex]\frac{10}{3}[/tex]×[tex]\frac{5}{13}[/tex]

Multiply straight across the top and straight across the bottom to get

[tex]\frac{50}{39}[/tex]

Depending upon what your teacher calls "simplest form", this form may be the simplest, or the mixed fraction may be the simplest.  The mixed fraction equivalent to this improper is

[tex]1\frac{11}{39}[/tex]

It’s simple but my teacher has “33 ft” as an answer and Idk why...

Answers

Answer:

  33 ft

Step-by-step explanation:

The distance of interest is apparently not the straight-line distance from the top of the vertical ladder to the ground (20 ft), but the length of the arc the top of the ladder makes as it rotates. That arc length (s) is given by ...

  s = r·θ . . . . . where θ is the angle in radians subtended by the arc

Here, the radius is 20 ft, and the angle is the supplement of 85°, or 95° = (95/180)π radians.

  s ≈ (20 ft)·(1.65806 radians) ≈ 33.16 ft ≈ 33 ft

In a plane, if a line is _____ to one of two parallel lines, then it is perpendicular to the other.

a. parallel
b. perpendicular
c. skew
d. intersecting

Answers

Answer:

Perpendicular

Step-by-step explanation:

Think of a ladder.  It has 2 long sides that are parallel to each other.  If a step is perpendicular to one long side then it is perpendicular to the other long side BECAUSE the 2 long sides are parallel to each other.

In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

In a plane, two lines which are parallel exist in the same axis.

In essence, any line which is perpendicular to one of two parallel lines is also perpendicular to the other.

This concept is evident in the model of ladders, where each of the vertical lines are perpendicular to the parallel step lines(horizontal lines).

Read more;

https://brainly.com/question/17463500

You select a letter randomly from a bag containing the letters s, p, i, n, n, e, and r. find the probability of selecting an s. description

Answers

Answer:

1/7

Step-by-step explanation:

Answer:

i think it would be 1/7 also

Step-by-step explanation:

If Ruth contributed $10,000 toward the total group investment of $200,000 for the purchase of a seafood restaurant, what percentage of the company does she own?



Answers

Answer:

20 %

Step-by-step explanation:

10000/200000

The percentage of the company she owns is equivalent to 5%.

What is percentage?

In mathematics →

a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign "%".

Given is that if Ruth contributed $10,000 toward the total group investment of $200,000 for the purchase of a seafood restaurant.

Assume that the percentage of the company she owns is equivalent to [x] percent. So, we can write -

10000 = [x]% 0f 200000

10000 = [x]/100 × 200000

10000 = [x] × 2000

[x] = (10000/2000)

[x] = 5%

Therefore, the percentage of the company she owns is equivalent to 5%.

To solve more questions on percentage, visit the link below -

https://brainly.com/question/24159063

#SPJ5

Which shows reflection

Is it c?

Will give BRAINLIEST. Can't see these very well

Answers

Answer:

B

Step-by-step explanation:

You could take these images (if you can visualize it)

And paste it into SM paint, and then reflect it.

But, if you look closely, A is just the notes higher, but not reflected, or changed in any other way.

C the second note is lower in the reflection. The notes shouldn't change in a reflection. Just the order.

Gavin and Jack are practicing shots against their goalie. On their last 15 attempts, Gavin made 6 and Jack made 7. Based on this performance, what is the probability that they both make their next shot?

Answers

Answer:

[tex]\dfrac{14}{75}[/tex]

Step-by-step explanation:

Gavin made 6 out of 15 shots, so the probability that Gavin's next shot will be  successful is

[tex]\dfrac{6}{15}=\dfrac{2}{5}[/tex]

Jack made 7 out of 15 shots, so the probability that Jack's next shot will be  successful is

[tex]\dfrac{7}{15}[/tex]

The probability that they both make their next shot successfully is

[tex]\dfrac{2}{5}\cdot \dfrac{7}{15}=\dfrac{14}{75}[/tex]

Find the coordinates of the point on the directed segment from (3,2) to (6,8) that divides into a ratio of 1:3.

a. (4.5, 5.5)
b. (5.25, 6.25)
c. (3.75, 3.5)
d. (4,4)​

Answers

Answer:

c. (3.75, 3.5)

Step-by-step explanation:

Let's call the given segment AB, and the dividing point P. Then you want AP:PB = 1:3.

There are a couple of ways you can get there.

1. Recognize that when you subtract the coordinates of A from P, the difference will be 1/4 of the result of subtracting A from B. That is, ...

P-A = (1/(1+3))·(B-A)

We can see that B-A = (6,8) -(3,2) = (3, 6), so 1/4 of that is (3/4, 3/2) = (0.75, 1.5). Adding these values to the coordinates of A gives ...

P = A + (.75, 1.5) = (3.75, 3.5)

__

2. Finish working out the equation above to solve for P:

4(P -A) = B -A

4P = B + 3A

P = (3A + B)/4 . . . . . note the multiplier for A is the relative length of PB and vice versa

P = (3(3, 2) +(6, 8))/4 = (15/4, 14/4) = (3.75, 3.5)

_____

Comment on choosing an answer

You only need to determine one of the coordinates in order to pick the correct answer. Finding both coordinates can help give you assurance that you have worked it out correctly.

(3^2)^6 = _____

A) 3^-4
B) 3^4
C) 3^8
D) 3^12

Answers

Hello!

The answer is:

The correct option is:

D) [tex](3^{2})^{6}=3^{12}[/tex]

Why?

To solve the problem, we need to remember the power of a power property, it's defined by the following way:

[tex](a^{m})^{n}=a^{m*n}[/tex]

When we have a power of a power, we must keep the base and then, the new exponent will be the product between the two original exponents.

So, we are given the expression:

[tex](3^{2})^{6}[/tex]

Then, calculating we have:

[tex](3^{2})^{6}=3^{2*6}=3^{12}[/tex]

Hence, we have that the correct option is:

D) [tex](3^{2})^{6}=3^{12}[/tex]

Answer:

The correct answer is option D).  3^12

Step-by-step explanation:

Points to remember

Identities

(xᵃ)ᵇ = xᵃᵇ

xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾

xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾

It is given that (3^2)^6

To find the correct option

(3^2)^6 can be written as, (3²)⁶

By using above identities,  

(3²)⁶ = 3⁽² ˣ ⁶⁾

 = 3¹²

Therefore the correct answer is option D).  3^12

A rabbit and a turtle were to start a race at the same place. the rabbit was feeling very confident and slept for 8 hours before starting. the turtle ran at a pace of 1 mile per hour, and the rabbit ran at 5 miles per hour. the race was a distance of 10 miles. who won the race?

Answers

Answer:

Step-by-step explanation:

D=RT

10=1T

T=10 HOURS FOR THE TURTLE.

10=5(T-8)

10=5T-40

5T=10+40

5T=50

T=50/5

T=10 HOURS FOR THE RABBIT.

LOOKS LIKE A TIE .

Solve 8 sin ( 5 x ) = 3 for the two smallest positive solutions a and b, with a < b

Answers

The two smallest positive solutions, with a < b, are approximately

x ≈ 0.384 and x ≈ 1.64.

We have,

Isolate the sine function by dividing both sides by 8.

sin(5x) = 3/8

The inverse sine function (also called arcsin) is on both sides of the equation.

5x = arcsin(3/8).

Divide both sides by 5.

x = (1/5) arcsin(3/8)

Now,

arcsin(3/8) is approximately 0.4115.

So,

x = (1/5) * 0.4115

x = 0.384.

Since the sine function repeats itself every 2π radians, we add multiples of 2π/5 to the solution to find other valid values of x.

The second smallest positive solution

x = 0.384 + (2π/5) = 1.64.

Therefore,

The two smallest positive solutions, with a < b, are approximately

x ≈ 0.384 and x ≈ 1.64.

Learn more about trigonometric identities here:

https://brainly.com/question/14746686

#SPJ12

Final answer:

The equation 8 sin(5x) = 3 is solved by isolating the variable term, using inverse sine to get an angle, and considering the period of the sine function when finding additional solutions.

Explanation:

To solve the equation 8 sin (5x) = 3, we first isolate the term involving the variable 'x'. Start by dividing both sides by 8. We get sin(5x) = 3/8.

The inverse sine (also known as arcsin or sin^-1) is used to get the angle whose sine is 3/8. So we have 5x = sin^-1(3/8).

To solve for 'x', we then divide both sides by 5: x = sin^-1(3/8) / 5.

This value of 'x' is a solution, but sine function repeats every 2π intervals, so we add multiples of 2π/5 to 'x' to get additional solutions.

Learn more about Trigonometry here:

https://brainly.com/question/11016599

#SPJ3

There are 16 girls in a school club. The number of girls is four more than twice the number of boys. Find the number of boys

Answers

16-4=12/2=6 so there’s like 6 bois
Final answer:

The problem describes a situation with 16 girls who are four more than twice the number of boys. By setting up and solving the simple algebra equation 2x + 4 = 16, we find there are 6 boys in the club.

Explanation:

This is a word problem which can be solved using simple algebra. Given that there are 16 girls in the club and the number of girls is four more than twice the number of boys, we can set up the equation:

2x + 4 = 16

Where x stands for the number of boys. Solving this equation, we subtract 4 from both sides to get: 2x = 12. Dividing both sides by 2, we find that there are x = 6 boys in the club.

Learn more about Algebra here:

https://brainly.com/question/32436021

#SPJ2

Find a cubic function with the given zeros. 7, -3, 2 (1 point)

Answers

ANSWER

[tex]f(x) =x^3-6x^2-13x+42[/tex]

EXPLANATION

The zeros of the cubic function is given as:

x=7,x=-3,x=2

This implies that, x-7,x+3,x-2 are factors of the given cubic polynomial function.

We can write the completely factored form as a function of x to get:

[tex]f(x) = (x - 7)(x + 3)(x - 2)[/tex]

We expand to get:

[tex]f(x) = (x - 7)(x^2+ x-6)[/tex]

[tex]f(x) =x^3-6x^2-13x+42[/tex]

This is a cubic function because the highest degree is 3.

a candle maker has 301.59 cubic centimeters (cm3) of liquid wax to make cone shaped candles. Each Candle has a circular base with a diameter of 3 cm and a height of 5 cm. what is the maximum number candles that can be made from the liquid wax?


A. 6

B. 7

C. 25

D. 26

Answers

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=1.5\\ h=5 \end{cases}\implies V=\cfrac{\pi (1.5)^2(5)}{3}\implies V=\cfrac{11.25\pi }{3} \\\\\\ V= 3.75\pi \implies V\approx 11.78~cm^3\qquad \leftarrow \textit{for one candle} \\\\\\ \stackrel{\textit{how many times does 11.78 go into 301.59?}}{301.59\div 11.78\implies 26}\qquad \leftarrow \textit{rounded up}[/tex]

The volume of the cone is one-third of the product of its base area and its height. The maximum number of candles that can be made from the liquid wax is 25.

What is the volume of a cone?

The volume of the cone is one-third of the product of its base area and its height. It is given by the formula,

The Volume of Cone = (1/3) × π × (d/2)² × h

The volume of wax that is needed to make a single candle with a diameter of 3 cm and height of 5 cm is,

The Volume of Cone = (1/3) × π × (d/2)² × h

The Volume of Candle = (1/3) × π × (3/2)² × 5 = 11.78 cm³

The total wax available is 301.59 cm³, while the amount of wax needed to make a candle is 11.78 cm³, therefore, the number of candles that can be made with the total wax is,

The Number of candles = (301.59 cm³/ 11.78 cm³) = 25.5999

Since a half candle can not be produced, therefore, the maximum number of candles that can be made from the liquid wax is 25.

Learn more about the Volume of the cone:

https://brainly.com/question/1984638

#SPJ2

Which numbers are necessary to solve this problem? Franklin brought 4 jump ropes to the park. Each jump rope can be used by 3 people at a time. Fifteen friends came to the park to jump rope. How many friends could play jump rope if all of Franklin's ropes were being used? A. 4 jump ropes, 3 people B. 3 people, 15 friends C. 4 jump ropes, 15 friends D. 4 jump ropes, 3 people, 15 friends

Answers

Answer:

  D. 4 jump ropes, 3 people, 15 friends

Step-by-step explanation:

In order to answer the question how many friends could play, you need to be able to determine the smaller of ...

(number of ropes) × (friends per rope)number of friends

You can find the first of these numbers using the values of answer A, but if the number of Franklin's friends is smaller than 12, then you need to know that in order to properly answer the question. Hence, we believe you need to know ...

the number of jump ropesthe number of friends per ropethe number of friends

quadrilateral ABCD is located at A(-2,2) B (-2,4) C(2,4) D(2,2). The quadrilateral is then transformed using the rule (x-2, y+8) to form A’B’C’D’. Describe what characteristics you would find if the corresponding vertices were connected with line segments !!! HELP WILL MARK AS BRAINLIEST PLS HELP!!

Answers

Answer:

  Those line segments are parallel and all the same length.

Step-by-step explanation:

Translation modifies the coordinates of each point the same way, moving the point some distance in some direction. Hence the line segments connecting original to image points will all have the same length and direction.

_____

Comment on the question

The question is pretty open-ended. If it is multiple choice, perhaps there is a choice that more or less expresses the idea above. Otherwise, it is hard to tell what the question is driving at.


At the movie theatre, child admission is $5.70 and adult admission is $9.40. On Wednesday, 173tickets were sold for a total sales of $1345.00. How many child tickets were sold that day?

Answers

Answer: 76 child tickets were sold that day.

Step-by-step explanation:

You need to set up a system of equations.

Let be "c" the number of child tickets sold that Wednesday and "a" the number of adult tickets sold that Wednesday.

Then:

[tex]\left \{ {{a+c=173} \atop {9.40a+5.70c=1345.0}} \right.[/tex]

Using the Method of Elimination, you can multiply the first equation by -9.40, then add both equations and finally solve for "c":

[tex]\left \{ {{-9.40a-9.40c=-1626.2} \atop {9.40a+5.70=1345.0}} \right.\\..................................\\-3.7c=-281.2\\\\c=\frac{-281.2}{-3.7}\\\\c=76[/tex]

How do you evaluate the limit?

Answers

Answer:

Step-by-step explanation:

First of all the answer.

[tex]\lim_{n \to -\infty}2^x= 1/ \lim_{n \to \infty}1/2^x = 0[/tex]

[tex]\lim_{n \to -\infty} 1-2^x = 1[/tex]

This approaches 0/1 = 0

The graph is included to show that this is the answer I get.

the surface area of the figure below is 50.80m^2 True or False

Answers

For this case we have that by definition, the surface area of a cone is given by:

[tex]SA = \pi * r * s + \pi * r ^ 2[/tex]

Where:

A: It's the radio

s: It's the slant

Substituting according to the data we have:

[tex]SA = \pi * 2.1 * 5.6 + \pi * (2.1) ^ 2\\SA = 36.9264 + 13.8474\\SA = 50.7738 \ m ^ 2[/tex]

If we round:

[tex]SA = 50.8 \ m ^ 2[/tex]

Answer:

True

After a group of 24 parts were tested. 5 were found defective. About what percent of the parts were defective

Answers

Answer:

20.8%

Step-by-step explanation:

5/24= defective

^divide, and multiply by 100 to get percent

:)

The required percentage of defective parts is 20.8%.

What is the percentage?

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,

After a group of 24 parts was tested. 5 were found defective.
The required percentage of the defective parts is given as,
= 5 / 24 × 100%
= 0.208 × 100%
= 20.8%

Thus, the required percentage of defective parts is 20.8%.

Learn more about percentages here:

brainly.com/question/13450942

#SPJ1

A jewelry box contains two gold hoop earrings and two silver hoop earrings. You randomly choose two earrings. What is the probability that both are silver hoop earrings? Write your answer as a fraction or percent rounded to the nearest tenth. The probability that both are silver hoop earrings is .

Answers

Answer:

fraction is 2/4

Step-by-step explanation:

The population of California is approximately 3.8 × 107, and the population of Nebraska is approximately 1.9 × 106. Which state has the larger population, and by how many times is its population larger than the other state’s?

Answers

Answer:

california by 205.2

Step-by-step explanation:

3.8 times 107=406.6-California

1.9 times 106=201.4-Nebraska

205.2

Answer: The Population of California is larger than the population of Nebraska by 20 times

Step-by-step explanation:

Given

Population of California , [tex]P_C=3.8\times 10^{7}[/tex]

and population of Nebraska, [tex]P_N=1.9\times 10^{6}[/tex]

From above data it is clear that the population of California is larger than the population of Nebraska

And Ratio, [tex]\frac{P_C}{P_N}=\frac{3.8\times 10^{7}}{1.9\times 10^{6}}=\frac{38}{1.9}=20[/tex]

Thus the population of California is larger than the population of Nebraska by 20 times

Linda received the following scores on her essay tests.

64, 65, 63, 66, 60, 65, 66, 68, 69, 66, 63

What is the mean of her scores?

A.64.5
B.65
C.65.5
D.66

Answers

The answer to your question is B. 65

Answer:

b

Step-by-step explanation:

you add them all together and divide 11 because there are 11 numbers.

i used to have problem on mean, median, and mode too.

What is the smallest fractional portion of an inch that you can measure with the ruler shown in Exam Figure A1?

A. 1/32"
B. 1/16"
C. 1/8"
D. 1/64"

Answers

Answer:

The minimun portion of inches that can be measured with the ruler is 1/16''.

Step-by-step explanation:

The precision , what is the minimun measurement that can be aprecciated by the ruler can be determined counting the number of disivion within 2 units.  To this ruler we can count 16 division bwtween one unit and asecutive one.

On the first day of the month, John counted his money and found he had 28.35. Since then, he has received an additional 17.26 from the jobs he does after school. How much money does he have now

Answers

Answer: He has 45.61

Step-by-step explanation:The answer is 45.61 because you add the decimals, 28.35+17.26, then you aline the decimal points and add, then get 45.61

1 1

28.35

+ 17.26

45.61

Total money John has now is 45.61.

On the first day of the month, John had $28.35 and received an additional $17.26.

To find out how much money John has now, you need to add the initial amount to the additional money he received. Therefore, John now has

28.35 + 17.26 = 45.61 money

A science teacher needs to choose 12 students out of 16 to serve as peer tutors how many different ways can the teacher choose the12 students

Answers

He can ask the student to raise their hands and pick them

the teacher can ask them to pick the closest number. the teacher can choose the students with the highest grades.

Other Questions
Who is someone you think you have a positive relationship with? In 35 sentences, what role do you think openness and truthfulness have in making this relationship positive? I need help with number 4 I cant get an answer Suppose you increase your walking speed from 5m/s to 13m/s in a period of 3s what is your acceleration? What is WorldCat?A. An international database of libraries and their collections B. An internet archive that serves as one stop spot for researchC. A database of more than 72,000 documents for education professionalalsD. A source for library and information professionals Punctuate the sentence correctly My dog a collie always sleeps at the foot of my bed. Who can convene the PA legislature into a special session? Jack leaves his house and walks north for 30m. He turns left and walks west for 30m. He then turns left again and walks another 30m. What is the point of reference for Jacks motion? Name one branch or part of the government Solve 2x2 + 12x - 14 = 0 by completing the square Following World War I, nativists used eugenics to justify racialintolerance by attributing: Last one! I just need to know what the slope of the line in this graph is, ty! how many terms does the polynomial have? What are images to help the reader see or hear or feel things Select the sentence that uses a participial phrase.1. Christa chose to critique the novel Oliver Twist.2. The main character of this book does not change much.3. The student receiving the achievement award should represent his class.4. Earning money has been a difficult task lately.5. Choose your words with great care.6. My job is leading me to rethink my future plans. How did the decision in Dred Scott v Sandford overturned the Missouri Compromise? (GEOMETRY) What are three of the five ways to prove triangles are similar? Which tissue acts as a filter on the water absorbed by root hairs? Can you help me with the top one please thnx Why was the house of burgesses significant in colonial America A field test for a new exam was given to randomly selected seniors. The exams were graded, and the sample mean and sample standard deviation were calculated. Based on the results, the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 5% of 75%. Is the confidence interval at 90%, 95%, or 99%? What is the margin of error? Calculate the confidence interval and explain what it means in terms of the situation.Will Mark Branliest, Please Help ASAP Steam Workshop Downloader