Classify each system of equations as having a single solution, no solution, or infinite solutions. y = 11 − 2x 4x − y = 7 x = 12 − 3y 3x + 9y = 24 2x + y = 7 -6x = 3y − 21 x + y = 15 2x − y = 15 2x + y = 7 -4x = 2y + 14 x + 4y = 6 2x = 12 − 8y

Answers

Answer 1

Answer:

Let's analyze each system of equations and classify them based on the number of solutions they have:

1) y = 11 − 2x

  4x − y = 7

This system of equations represents two lines. The first equation is in slope-intercept form, and the second equation is in standard form. Since the equations have different slopes and different y-intercepts, they intersect at a single point. Thus, the system has a single solution.

2) x = 12 − 3y

  3x + 9y = 24

The first equation represents a line, and the second equation is a linear equation. Since the first equation can be rewritten as 3y = 12 - x or y = 4 - (1/3)x, it indicates that the slope-intercept form can't be satisfied. Both equations are equivalent and represent the same line. Therefore, the system has infinitely many solutions.

3) 2x + y = 7

  -4x = 2y + 14

The first equation represents a line, and the second equation is also a linear equation. If we simplify the second equation, we get y = -2x - 7, which is equivalent to the first equation. Thus, the system has infinitely many solutions.

4) x + y = 15

  2x − y = 15

Both equations are in standard form. By adding the equations, we eliminate y and get 3x = 30, which simplifies to x = 10. Substituting x = 10 into either equation, we find y = 5. Therefore, the system has a single solution.

5) x + 4y = 6

  2x = 12 − 8y

The first equation represents a line, and the second equation is a linear equation. By simplifying the second equation, we get x = 6 - 8y, which is equivalent to the first equation. Therefore, the system has infinitely many solutions.

To summarize:

- System 1: Single solution.

- System 2: Infinitely many solutions.

- System 3: Infinitely many solutions.

- System 4: Single solution.

- System 5: Infinitely many solutions.


Related Questions

What is 8.118 divded by 0.615

Answers

This is the answer

13.2

I need some help math

I need some help math

Answers

Answer:

ok I will help you please wait for some time

Answer:

23

Step-by-step explanation:

Add the total number of hours in the given situation

Solve by elimination
5x+6y= -10
3x-2y= -6

Answers

First equation:Solving for X.

\(x = - \frac{2(5 + 3y)}{5} \)

Solving for Y.

\(y = - \frac{5(2 + x)}{6} \)

Second equation:

Solving for X.

\(x = \frac{2(y - 3)}{3} \)

Solving for Y.

\(y = \frac{3(2 + x)}{2} \)

An insurance provider states that their customers save at least, on average, 300 dollars per year by switching to them, with a standard deviation of 150 dollars. Before we decide to switch to the new company and go through all of the hassle, we want to test the claim. So, we go out and sample 64 individuals who switched to the new insurance company and found them to have saved an average of 255 dollars per year. Do we have enough evidence at the α = 0.05 level to state that the insurance provider is false in their claim? Discussion Prompts Answer the following questions in your initial post: What are the hypotheses based on the words given in the problem? Should we use a Z or T distribution in this case? What is our Z or T statistic? What is the P-value? Based on your p-value and alpha, what conclusion will we make? Based on your results, would you switch to this company? Explain why or why not (Note: this can go beyond the use of statistics, but statistical analysis can help our decisions)

Answers

The solution to the question is mathematically given as

1)

H0: M \(\geqslant\) 300

H0: M \(\geqslant\) 300

2)

Z distribution.

3)

z=-2.4

4)

P=0.0082

5)

"H0" is rejected as a hypothesis with a level of significance of 0.05.

What is the hypothesis ?

Generally, the equation for is mathematically given as

Solutions

we have, \($u=300$$$\begin{aligned}& \sigma=150 \text { dollars } \\N &=64 \text { individuals } \\\bar{x} &=255 \text { dollare. } \\a=& 0.05 .\end{aligned}\)

(1):

H0: M \(\geqslant\) 300 dollars;  customers save at least 300 dollars per year by switching to them.

H0: M \(\geqslant\) 300 dollars:

(This is a left-tailed test)

(2):

when \(\sigma\) is known, we use the Z test. we use Z distribution.

(3):

\(\begin{gathered}z=\frac{\bar{x}-\mu}{6 / \sqrt{n}}=\frac{255-300}{150 / \sqrt{64}}=\frac{-45}{18.75}=-2.4 \\z=-2.4\end{gathered}\)

(4):

\(Pvalue $=P(z < -2 \cdot 4)$ $=0.0082 \quad\{$ wing $z$ tables $\}$ \\\\\text { Pvalue }=0.0082\)

(5):

In conclusion, Since p-value = 0·0082 <0.05

This is statistically significant at the 0.05 level.

We thus "Refect H0" using a threshold of significance of 0.05.

"H0" is rejected as a hypothesis with a level of significance of 0.05.

There is not enough data to support the assertion that consumers may save at least $300 annually by switching insurance providers.

Therefore, we would not consider making the transition to this firm.

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What’s the definition of the greatest common factor

Answers

Answer:

the largest common factor between 2 numbers

Step-by-step explanation:

Is it - or + 60 plz help me

Is it - or + 60 plz help me

Answers

+60 two negatives equal a positive

Use Newton's method with initial approximation x1 = 1 to find x2, the second approximation to the root of the equation x4 − x − 3 = 0. (Round your answer to four decimal places.) x2 =?

Answers

Answer:

\(x_{2} = 0.0000\)

Step-by-step explanation:

The formula for the Newton's method is:

\(x_{i+1} = x_{i} + \frac{f(x_{i})}{f'(x_{i})}\)

Where \(f' (x_{i})\) is the first derivative of the function evaluated in \(x_{i}\).

\(x_{i+1} = x_{i} + \frac{x_{i}^{4}-x_{i}-3}{4\cdot x_{i}^{3}-1}\)

Lastly, the value of \(x_{2}\) is determined by replacing \(x_{1}\) with its numerical value:

\(x_{2} = x_{1} + \frac{x_{1}^{4}-x_{1}-3}{4\cdot x_{1}^{3}-1}\)

\(x_{2} = 1.0000 + \frac{1.0000^{4}-1.0000-3}{4\cdot (1.0000)^{3}-1}\)

\(x_{2} = 0.0000\)

A bag contains​ pennies, nickels,​ dimes, and quarters. There are 50 coins in all. Of the​ coins, ​% are pennies and ​% are dimes. There are more nickels than pennies. How much money does the bag​ contain?

Answers

Answer:

5.26 dollars

the total turns out to be 5.26 dollars.

f(x)=3x−2, find f(−5).

Answers

Answer:

f(-5) = -17

Step-by-step explanation:

Given that,

→ x = -5

Then the value of f(-5) will be,

→ f(x) = 3x - 2

→ f(-5) = 3(-5) - 2

→ f(-5) = -15 - 2

→ [ f(-5) = -17 ]

Hence, the answer is -17.

The living room of Ann's house is a square with an area of 121 square feet. What is the length of each side of the foyer

Answers

Answer:

30.25

Step-by-step explanation:

121 divided by 4 is 30.25

find the value of x and the measure of angle axc

find the value of x and the measure of angle axc

Answers

Answer:

x = 4

m<AXC = 150

Step-by-step explanation:

m<1 + m<2 = m<AXC

102 + 10x + 8 = 6(6x + 1)

10x + 110 = 36x + 6

26x = 104

x = 4

m<AXC = 6(6x + 1)

m<AXC = 6(24 + 1)

m<AXC = 150

Factorise 5x + 10=

ᴘʟᴀʏɪɴɢ: Who Asked (Feat: Nobody did ) ───────────⚪────── ◄◄⠀▐▐⠀►:/:⠀───○

Answers

Answer:

5(x+2)

Step-by-step explanation:

5x + 10=

Factor out 5

5(x+2)

Answer:

\(5(x + 2)\)

Step-by-step explanation:

Get 5 out

\(5x + 10 \\ 5(x + 2)\)

Label 1/4 on the number line. Label 1/2 on the number line .

Answers

Answer:

it goes 0 then 1/4 in the first notch 1/2 in the second notch 3/4 in the third notch then the number 1 on the fourth

Step-by-step explanation:

Hope that helps.

The owner of a deli gathered data about the number of flavored bagels and plain bagels sold during the first hour of business for several days. He organized the data in a scatter plot, with x representing the number of flavored bagels and y representing the number of plain bagels sold. Then he used a graphing tool to find the equation of the line of best fit: y = 1.731x + 6.697. Based on the line of best fit, approximately how many flavored bagels can the deli expect to sell during an hour when 50 plain bagels are sold? A. 25 B. 33 C. 87 D. 93

Answers

The answer is A.) 25

The previous answer of 87 is wrong, and there is me to prove it below.

The owner of a deli gathered data about the number of flavored bagels and plain bagels sold during the

The deli can expect to approximately sell 25 flavored bagels during an hour when 50 plain bagels are sold.

What is a scatter plot?

A scatter plot is a plot containing points that are made using different cartesian coordinates. The line that passes approximately through these points is called the regression line.

The number of flavored bagels can be found as shown below:

To find the number of flavored bagels which is x, we have to substitute the value of y which is the number of plain bagels sold.

The equation is given as:

y = 1.731x + 6.697

Now substitute the value of y = 50:

50 = 1.731x + 6.697

43.303 = 1.731x

x = 43.303/1.731

= 25.016 ≈ 25 falvored bagels

Therefore, the deli can expect to approximately sell 25 flavored bagels during an hour when 50 plain bagels are sold. The correct answer is option A.

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Show that Sin3xCos3x is the same as Sin 6x

Answers

The solution to the trigonometric equation is sin( 6x ) = 2sin(3x)cos(3x)

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the equation be represented as A

Now , the value of A is

A = sin (6x)

From the trigonometric relations ,

The value of sin( 2x ) = 2sin(x)cos(x)

Now , when x is replaced by 6x

Substituting the values in the equation , we get

sin ( 6x ) = 2 sin ( 6x/2 ) cos ( 6x/2 )

On simplifying the equation , we get

sin ( 6x ) = 2 sin ( 3x ) cos ( 3x )

So , the value of the trigonometric relation is

sin(6x) = 2sin(3x)cos(3x)

Hence , the equation is sin(6x) = 2sin(3x)cos(3x)

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simplifying and expression (3xy)2x4y

simplifying and expression (3xy)2x4y

Answers

The simplification of the given expression  (3xy)²x⁴y / x³y² will be 9 x³y.

What is simplification of an expression?

Usually, simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.

WE have been given an expression as (3xy)²x⁴y / x³y²

First we need to solve the exponents;

= (3xy)²x⁴y / x³y²

= (3xy)²x⁴/ x³y

= 9 x²y²x⁴/ x³y

= 9 x²y²x⁴/ x³y

= 9 x³y

Therefore, the simplification of the given expression  (3xy)²x⁴y / x³y² will be 9 x³y.

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Both sets of values have an average of 13. Is Set A's standard deviation smaller, larger, or about the same as Set B's?
(Note: This question can be answered by knowing the concept of standard deviation, without actually computing the standard
deviation).
Set A: 1 2 3 23 24 25
Set B: 9 10 11 14 16 18
A Larger
B) About the same
Not enough information provided to tell
D) Smaller

Answers

The answer is D) Smaller  Set B's standard deviation is expected to be smaller than Set A's due to its tighter range.

To determine whether Set A's standard deviation is smaller, larger, or about the same as Set B's, we can analyze the spread of the values in each set. The standard deviation measures the dispersion or variability of a data set.

Looking at Set A, we can see that the values range from 1 to 25, with a progression that is relatively spread out. On the other hand, Set B has values ranging from 9 to 18, with a more limited range.

Based on this observation, we can infer that Set B's values are more tightly grouped together compared to Set A. Consequently, Set B is expected to have a smaller standard deviation since the values are less dispersed around the mean.

Therefore, the answer is D) Smaller. Set B's standard deviation is likely to be smaller than Set A's. However, to precisely determine the standard deviations and compare them, it would be necessary to calculate the actual values using the formulas for standard deviation or use statistical software.

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Need help asap it’s algebra 2

Need help asap its algebra 2

Answers

Answer:

sequence is 8,40,200

40/8=5

200/8=5

8*5*5*5*..... 10 times

Step-by-step explanation:

omg its

15625000

thats really big

Calculate the value for the for the following scores 20, 60, 30, 50 given:

begin inline style begin display style sum for blank of end style end style x squared =

Answers

The sum of the scores is equal to 160.

What is a mean?

In Mathematics, a mean is sometimes referred to as an average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

How to calculate the mean for a data set?

Mathematically, the mean for this set of scores can be calculated by using the following formula:

Mean = [F(x)]/n

For the total number of scores (data set), we have;

∑x = 20 + 60 + 30 + 50

∑x = 160.

Mean = [F(x)]/n = 160/4 = 40.

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Calculate the value for the for the following scores 20, 60, 30, 50 given: begin inline style begin display

Simplify this expression:2x + 3 – (5 – 6x).

Answers

Answer:

8x - 2

Step-by-step explanation:

2x + 3 - (5 - 6x) ← distribute parenthesis by - 1

= 2x + 3 - 5 + 6x ← collect like terms

= (2x + 6x) + (3 - 5)

= 8x + (- 2)

= 8x - 2

Suppose you have a bag with 10 red and 40 black marbles. You
put your hand in the bag and take out a single marble, record
its color, then put it back in the bag. Assume you repeat this
experiment 10 times. What is the probability of getting at least
5 red marbles?

Answers

Using the binomial distribution, there is a 0.0328 = 3.28% probability of getting at least 5 red marbles.

What is the binomial distribution formula?

The formula is:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

The parameters are:

x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.

For this problem, the values of these parameters are given as follows:

n = 10, p = 10/50 = 0.2.

The probability of getting at least 5 red marbles is given by:

P(X ≥ 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

In which:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 5) = C_{10,5}.(0.2)^{5}.(0.8)^{5} = 0.0264\)

\(P(X = 6) = C_{10,6}.(0.2)^{6}.(0.8)^{4} = 0.0055\)

\(P(X = 7) = C_{10,7}.(0.2)^{7}.(0.8)^{3} = 0.0008\)

\(P(X = 8) = C_{10,8}.(0.2)^{8}.(0.8)^{2} = 0.0001\)

\(P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} = 0\)

\(P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} = 0\)

Then:

P(X ≥ 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0264 + 0.0055 + 0.0008 + 0.0001 + 0 + 0 = 0.0328.

0.0328 = 3.28% probability of getting at least 5 red marbles.

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The perimeter of a rectangle is 52 inches, and the area is 160 square inches. Find the length and width of the rectangle.

Answers

Answer:16x16

Step-by-step explanation:

89% means 89 out of?

Answers

89% is equal to 89 out of 100 - your answer is 100

Answer:

100

Step-by-step explanation:

Help me with this
5x^ -8 = -3

Answers

Answer:

NO SOLUTION

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

Which of the following angles are shown in the drawing?

Which of the following angles are shown in the drawing?

Answers

The angle from the options given that is shown in the drawing is: D. <LIJ.

What is an Angle?

An angle is a geometric figure that is formed by two rays that share the same endpoint, called the vertex. The rays are called the sides of the angle, and the endpoint is called the vertex.

In the drawing given,  IJ and LI are two segments that have a common endpoint called vertex I.

Points L, I, and J forms an angle whose vertex is at I, as shown in the image given. Thus, the angle shown in the drawing is: D. ∠LIJ.

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Uhhhh If you need c and d ask me

Uhhhh If you need c and d ask me

Answers

Answer:

what are c and d?

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

john earns more than don

2x/5 + 5/8 = 1/4 help

Answers

\( \frac{2x}{5} + \frac{5}{8} = \frac{1}{4} \)

\( \frac{2x}{5} = \frac{1}{4} - \frac{5}{8} \)

\( \frac{2x}{5} = \frac{2}{8} - \frac{5}{8} \)

\( \frac{2x}{5} = \frac{2 - 5}{8} \)

\( \frac{2x}{5} = \frac{ - 3}{8} \)

\(2x = \frac{ - 3}{8} \times 5\)

\(2x = \frac{ - 15}{8} \)

\(x = \frac{ - 15}{8} \div 2\)

\( x = \frac{ - 15}{8} \times \frac{1}{2} \)

\(x = - \frac{ 15}{16} \)

Determine if the line segment YX is tangent to circle Z. 30 points

Determine if the line segment YX is tangent to circle Z. 30 points

Answers

Answer:

  XY is tangent to circle Z

Step-by-step explanation:

You want to know if segment XY, measuring 3.6 units, is tangent to circle Z at point X. Segment YZ has length 1.8 units outside the circle, which has radius 2.7 units.

Pythagorean relation

If the triangle XYZ is a right triangle, then we have ...

  XY² +XZ² = YZ²

  3.6² +2.7² = (1.8 +2.7)²

  12.96 +7.29 = 20.25 . . . . . true

Segment XY is a tangent.

Secant relation

If segment YZ is extended across the circle, the lengths of the segments from Y to the circle intersection points are 1.8 and (1.8 +2·2.7) = 7.2. The relation between the secant and the "tangent" will be ...

  3.6² = (1.8)(7.2) . . . . . true

This means XY is a tangent.

make e the subject
e-5=2f

Answers

Answer:

e-5=2f

take '-5' to the other side where '2f' is

e=2f+5

I need help asap please!!!

I need help asap please!!!

Answers

The values of the angles given are: 0,90,180,240,270,360,420,480,540,600,630,660,720 and

What is sine of angles?

he sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle.  It is defined as the length of the opposite side divided by the length of the hypotenuse

The given angles are: 0,30,45,90,120,135,180,210,225,240,270,300,315,330,360

2∅  2*∅ = 0, 90,180,240,270,360,420,480,540,600,630,660,720

sin 2∅ = sin0 = 0; Sin90=1;  sin180=0; sin240= -0.8660; sin270 = -1;

Each angle is multiplied by sine sine360 =1; sin420 = 0.8660; sin480= 0.9848; sin540=1; sin600=-0.8660; sin630=-1; sin660=0.8660; sin720= 0.9397

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