Describe the system of equations
How many solutions does this system have.

Describe The System Of Equations How Many Solutions Does This System Have.

Answers

Answer 1

Answer:

Step-by-step explanation:

One solution, at the point of intersection, (3,3)


Related Questions

Test for symmetry and then graph the polar equation.
r=3−5sinθ

Answers

Answer:

Symmetric with respect to the x-axis

Symmetric with respect to the y-axis

Symmetric with respect to the origin

What is the chance of getting 3 of the same cards in a row in a 52 cards deck?

Answers

Answer:

1/425

Step-by-step explanation:

The first card can be any card, so we don’t have to evaluate the probability.

Now we can suppose that the exit card is a two

- For the second card we have 3/51 of possibilities that is a 2 = 1/17

- For the third card we have 2/50 of possibilities that is a 2 = 1/25

1/17 * 1/25 = 1/425

Scores on the SAT are approximately normally distributed. One year, the average score on the Math SAT was 500 and the standard deviation was 120. What was the score of a person who did better than 85% of all the test-takers

Answers

Answer:

The score of a person who did better than 85% of all the test-takers was of 624.44.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

One year, the average score on the Math SAT was 500 and the standard deviation was 120.

This means that [tex]\mu = 500, \sigma = 120[/tex]

What was the score of a person who did better than 85% of all the test-takers?

The 85th percentile, which is X when Z has a p-value of 0.85, so X when Z = 1.037.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.037 = \frac{X - 500}{120}[/tex]

[tex]X - 500 = 1.037*120[/tex]

[tex]X = 624.44[/tex]

The score of a person who did better than 85% of all the test-takers was of 624.44.

what is the length of a rectangular solid with a volume of 180 cu ft, if it is 9 ft high and 4ft wide?

Answers

Answer:

5 ft

Step-by-step explanation:

The formula for Volume is V=lwh, or Volume = length x width x height.

The equation would be:

[tex]180=l(4)(9)[/tex]

or

[tex]180=36l[/tex]

To find the answer, divide by 36.

[tex]\frac{180}{36} =\frac{36l}{36}[/tex]

[tex]5=l[/tex]

Choose the correct solution for the given equation x^2-6x=40

Answers

Answer:

10,-4

Step-by-step explanation:

not sure where the options are but if you were to solve this equation first bring everything to one side.

x^2 - 6x - 40 = 0

factor it

(x-10)(x+4) = 0

set each part to 0

x-10 = 0 and x+4 = 0

solutions are 10 and -4

Help! Given that tanθ=-1, what is the value of secθ, for 3π/2<θ<2π?

Answers

Answer:  Choice B)  [tex]\sqrt{2}[/tex]

Work Shown:

[tex]\sec^2(\theta) = \tan^2(\theta) + 1\\\\\sec^2(\theta) = (\tan(\theta))^2 + 1\\\\\sec^2(\theta) = (-1)^2 + 1\\\\\sec^2(\theta) = 2\\\\\sec(\theta) = \sqrt{2}\\\\[/tex]

Note: secant is positive in quadrant Q4, when theta is between 3pi/2 radians and 2pi radians (270 degrees and 360 degrees). So that's why we don't consider the minus form of the plus minus.

Help with solving this Functions problem

Answers

Answer:

See answers below

Step-by-step explanation:

Given the following functions:

r(x) = x - 6

s(x) = 2x²

r(s(x)) = r(2x²)

Replacing x with 2x² in r(x) will give;

r(2x²) = 2x² - 6

r(s(x)) = 2x² - 6

(r-s)(x) = r(x) - s(x)

(r-s)(x) = x - 6 - 2x²

Rearrange

(r-s)(x) = - 2x²+x-6

(r+s)(x) = r(x) + s(x)

(r-s)(x) = x - 6 + 2x²

Rearrange

(r-s)(x) = 2x²+x-6

Consider the function z(x,y) describing the paraboloid \[z = (2x - y)^2 - 2y^2 - 3y.\]Archimedes and Brahmagupta are playing a game. Archimedes first chooses $x.$ Afterwards, Brahmagupta chooses $y.$ Archimedes wishes to minimize $z$ while Brahmagupta wishes to maximize $z.$ Assuming that Brahmagupta will play optimally, what value of $x$ should Archimedes choose?

Answers

Answer: -3/8

Step-by-step explanation:

Expanding z we get  

z = 4x^2 - 4xy + y^2 - 2y^2 - 3y

  = -y^2 - (4x + 3) y + 4x^2.

After Archimedes chooses x, Brahmagupta will choose

y=-(4x+3/2) in order to maximize z

Then  

z=-((-4x+3)/2)^2 -(4x+3)(-4x+3)/2)^2)+4x^2

z=8x^2+6x+9/4

To minimize this expression, Archimedes should choose x=-3/8

Find the solution(s) of the system of equations. y = x2 + 4x y + x2 = –4x Question 7 options: A) (–4, 0) and (0, 0) B) (0, 0) C) (–4, 0) and (4, 0) D) (0, 0) and (4, 0)

Answers

Answer:

Hello,

Answer A (-4,0) and (0,0)

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}y&=&x^2+4x\\y+x^2&=&-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&x^2+4x\\y&=&-x^2-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}y&=&x^2+4x\\x^2+4x&=&-x^2-4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}2*x^2+8*x&=&0\\y&=&x^2+4x\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}x(x+4)&=&0\\y&=&x^2+4x\\\end{array} \right.\\\\\\[/tex]

[tex]\left\{\begin{array}{ccc}x&=&0 \\y&=&0\\\end{array} \right. \ or\ \left\{\begin{array}{ccc}x&=&-4 \\y&=&0\\\end{array} \right.[/tex]

A human resources office is working to implement an increase in starting salaries for new
administrative secretaries and faculty at a community college. An administrative secretary
starts at $28,000 and new faculty receive $40,000. The college would like to determine the
percentage increase to allocate to each group, given that the college will be hiring 8
secretaries and 7 faculty in the upcoming academic year. The college has at most $5,000 to
put towards raises. What should the percentage increase be for each group?​

Answers

Answer:

Step-by-step explanation :

Let % increase in administrative secretary be = x

Let % increase in new faculty receive be = y

Administrative secretary salary = 28,000

New faculty receive Salary = 40,000

(8)*(x/100)* (28000) + (7)*(y/100)*(40000) = 5,000

2240x +2800 y = 5,000

224x +280 y = 500

56x +70y = 125

Therefore, x and y should be chosen such that it satisfy the above equation.

Translate To An Algebraic Expression:

S% of 1/r

Answers

Answer:

S/100r

Step-by-step explanation:

S% of 1/r = (1/r x S) : 100

(1/r x S) : 100

S/r : 100

S/100r

S/100r







Have a great day! Stay safe. Hope it helped

You are dividing a rectangular garden into 2 equal sections by
placing a wooden plank diagonally across it, from one corner to
the opposite comer. The garden measures 4 feet by 6 feet. What
length diagonal plank should you buy, and why?
Diagonal planks are available in 1-foot increments (you can
buy a 1-foot board, or a 2-foot board, or a 3-foot board, and
so on...)
• You can cut the plank down from the size you buy to the
exact size, but you want to waste as little wood as possible.

Answers

Answer:

You can cut the plank down from the size you buy to the

exact size, but you want to waste as little wood as possible.

Use the figure to find u.

Answers

Answer:

u = 2

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj side / hypotenuse

cos 45 = sqrt(2) / u

u cos 45 = sqrt(2)

u = sqrt(2) / cos 45

u = sqrt(2) / 1/ sqrt(2)

u = sqrt(2) * sqrt(2)

u =2

u=2

Answer:

Solution given:

Relationship between base and hypotenuse is given by cos angle.

Cos 45°=base/hypotenuse

[tex]\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{u}[/tex]

doing crisscrossed multiplication

[tex]\sqrt{2}*\sqrt{2}=1*u[/tex]

u=2

Kenji simplifies 3^5 x 4^ 5and gets the result 12^10, but Darlene is not sure. Is Kenji correct? Justify your answer.

Answers

That's a question about exponentiation.

Answer:

Kenji is wrong because he does not aply the porperty correctly.

Step-by-step explanation:

A exponetiation has this form:

[tex]\boxed{a^b}[/tex]

a is the base

b is the power or exponent

To understand that situation it's important to know a property about exponentiation. When we have a multiplication with the same exponent and diferent bases, the result is the multiplication of the bases with the same exponent. Let's see this above, in mathematical language:

[tex]\boxed{a^b \cdot c^b = (a\cdot c) ^b}[/tex]

Examples:

[tex]2^3 \cdot 8^3 = (2 \cdot 8) ^3 = 16^3[/tex][tex]10^9 \cdot 23^9 = (10 \cdot 23) ^9 = 230^9[/tex]

Now, we can say why Kenji is wrong. It's easy simplify [tex]3^5 \cdot 4^5[/tex]! We know that the result is [tex](3 \cdot 4) ^5 = 12^5[/tex], but Kenji multiplied the bases and added the exponents, that's why he is wrong.

I hope I've helped. ^^

Enjoy your studies! \o/

3-6÷12
simplyfication​

Answers

hope this helps! feel free to clarify

An alarm clock is slow. It falls behind 4 minutes every 24 hours. If the clock was showing the correct time at 6:00 this morning, how many seconds ahead was the clock at 10:00 last night?

Answers

Answer:

80 Seconds

I dont really want to type the whole thing out, just think about it again, or go to a tutor website, you should be able to get it, you have to use these, multiplication of three numbers, and multiplication and division by factorization of numbers.

What is the difference of the two polynomials? (NineX squared plus 8X) minus (twoX squared plus 3X)

Answers

Answer:

[tex]7x {}^{2} + 5x[/tex]

Step-by-step explanation:

[tex]9x {}^{2} + 8x - (2x {}^{2} + 3x) \\ \\ = 9x {}^{2} + 8x - 2x {}^{2} - 3x (remove \: brackets) \\\ \\ = 7x {}^{2} - 5x [/tex]

PLEASE HELP ANSWER THISS!!! I NEED THIS PLEASE!!! AND NO LINKS EITHER PLSS!!

Answers

It doesn't change because to add fractions, you need a common denominator. To find it, they multiplied 1/3 by 2 to make 2/6, to add to the 3/6.

Which statement is true about the parts of this expression?

StartFraction 5 over 6 EndFraction + one-fourth x minus y
The constant is StartFraction 5 over 6 EndFraction.
The only coefficient is One-fourth.
The only variable is y.
The terms StartFraction 5 over 6 EndFraction and One-fourth x are like terms.

Answers

Answer:

The constant is StartFraction 5 over 6 EndFraction

Step-by-step explanation:

StartFraction 5 over 6 EndFraction + one-fourth x minus y

5/6 + 1/4x - y

A. The constant is StartFraction 5 over 6 EndFraction.

True

B. The only coefficient is One-fourth.

False

There are two coefficients: the coefficient of x which is 1/4 and the coefficient of y which is 1

C. The only variable is y

False

There are 2 variables: variable x and variable y

D. The terms StartFraction 5 over 6 EndFraction and One-fourth x are like terms.

False

5/6 and 1/4x are not like terms

The only true statement is: The constant is StartFraction 5 over 6 EndFraction

Answer:

It's A if you don't want to read. A). The constant is 5/6

Step-by-step explanation:


What are the zeros of f(x) = (x - 2)(x + 7)? Select all that apply.
A. X= -7
B. X = -2
C. X = 2
D. X = 7

Answers

Answer:

2 = x          -7 = x

Step-by-step explanation:

f(x) = (x - 2)(x + 7)

y  = (x - 2)(x + 7)

Set y = 0

0 = (x - 2)(x + 7)

Using the zero product property

0 = x-2    0 = x+7

2 = x          -7 = x

Answer:

Zeros happen when f(x) = 0. There are two zeros in the given function:

when (x - 2) = 0when (x + 7) = 0

Therefore solve both equations above and you'll get:

Zero #1 = 2Zero #2 = -7

Solve the following system of equations by using the inverse of a matrix.
Give your answer as an ordered triple (x , y , z)

Answers

Answer:

(x, y, z) = (-8,4,-2)

Step-by-step explanation:

.......................................

Remember the dataset of alligators which was about the length and weight of several aligators in Florida. The variable X is the length of aligator and the Y variable is the weight of them. A researcher decided to use decision tree and designed two steps: X<4, X>4. What is the name of this method of splitting?A. Multi-way splitting.B. Entropy classification.C. Binary splitting.D. Gini index.

Answers

Answer:

A. multi-way split.

Step-by-step explanation:

Multi way split consists of internal at decision tree branches. Gini index measures probability of impurity in the random variables chosen. Entropy is measure of uncertainty in the sample selected. Binary splitting is used to speed up numerical evaluation.

Lakisha wants to buy some bitcoins. The exchange rate is $1 USD to 0.004 bitcoin. How many bitcoins can she buy with $400?

Answers

Answer:

1.6 Bitcoins

Step-by-step explanation:

Given data

We have the rate as

$1 USD to 0.004

Hence $400 will buy x bitcoins

Cross multiply to find the value of x

1*x= 400*0.004

x=1.6

Hence $400 will get you 1.6 Bitcoins

factor 9-x^2 completely

Answers

Answer:

-(x + 3)(x - 3)

Step-by-step explanation:

Using the difference of squares we can factor this expression.

[tex](9 - x^2)\\= (3^2 - x^2)\\= (3 + x)(3 - x)\\= -(3 + x)(-3 + x)\\= -(x + 3)(x - 3)[/tex]

How many spaces does it move over

Answers

Answer:

The point at the bottom has to move over 2 to the left to be aligned with the point at the top however they will have a 3 space in between the 2 same for the point at the top, the top point moves over 2 to the right to be aligned with the bottom point, then they will have a 3 square space between each other.

Answer:Around 3 spaces between?

Step-by-step explanation:

Please look at the file below. (No links will give brainiest)

Answers

Answer:

3.564 m^2

Step-by-step explanation:

The area of the original garden is

A = 5.4 * 1.5 = 8.1

The new garden is

5.4*1.2 = 6.48 by 1.5*1.2 =1.8

The area is

A = 6.48*1.8=11.664

The increase in area is

11.664-8.1=3.564

The given information is,

To find the increase in area of the garden.

Formula we use,

→ Area = Length × Width

Area of the real garden is,

→ 5.4 × 1.5

→ 8.1 m

The new garden will be,

→ 5.4 × 1.2 = 6.48 m

→ 1.5 × 1.2 = 1.8 m

The area of the new garden is,

→ 6.48 × 1.8

→ 11.664

Then the increase in area of the garden,

→ 11.664 - 8.1

→ 3.564 m²

Hence, 3.564 m² is the increase in area.

Based on a​ poll, among adults who regret getting​ tattoos, 24​% say that they were too young when they got their tattoos. Assume that six adults who regret getting tattoos are randomly​ selected, and find the indicated probability.

a. Find the probability that none of the selected adults say that they were too young to get tattoos.
b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.
c. Find the probability that the number of selected adults saying they were too young is 0 or 1.

Answers

Answer:

a) 0.1927 = 19.27% probability that none of the selected adults say that they were too young to get tattoos.

b) 0.3651 = 36.51% probability that exactly one of the selected adults says that he or she was too young to get tattoos.

c) 0.5578 = 55.78% probability that the number of selected adults saying they were too young is 0 or 1.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they say they were too young to get tattoos, or they do not say this. The probability of a person saying this is independent of any other person, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

24​% say that they were too young when they got their tattoos.

This means that [tex]p = 0.24[/tex]

Six adults

This means that [tex]n = 6[/tex]

a. Find the probability that none of the selected adults say that they were too young to get tattoos.

This is P(X = 0). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{6,0}.(0.24)^{0}.(0.76)^{6} = 0.1927[/tex]

0.1927 = 19.27% probability that none of the selected adults say that they were too young to get tattoos.

b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.

This is P(X = 1). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{6,1}.(0.24)^{1}.(0.76)^{5} = 0.3651[/tex]

0.3651 = 36.51% probability that exactly one of the selected adults says that he or she was too young to get tattoos.

c. Find the probability that the number of selected adults saying they were too young is 0 or 1.

This is:

[tex]p = P(X = 0) + P(X = 1) = 0.1927 + 0.3651 = 0.5578[/tex]

0.5578 = 55.78% probability that the number of selected adults saying they were too young is 0 or 1.

Find the total surface area of this square based pyramid. 10ft 10ft (in the image)​

Answers

Answer:

300ft^2

Step-by-step explanation:

Surface Area = 2bs + b^2 where s = height of each triangular surface and b = base

Surface Area = 2(10)(10) + 10^2
Surface Area = 2(100) + 100
Surface Area = 200 + 100
Surface Area = 300ft^2

Which function below has the following domain and range?
Domain: {-7, - 5,2, 6, 7}
Range: {0, 1,8}

Answers

Answer:

{(2,0),(-5,1),(7,8),(6,0),(-7,1)

If the total income generated from Gasoline for AER was $408 millions, how much would be the cost for a barrel of gasoline

Answers

Answer:

$20 per gallon

Step-by-step explanation:

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