Is it possible for a system to have more than one solution? Explain your answer

Answers

Answer 1

A linear system can have infinite solutions if both systems represent the same line. if a linear system down not represent the same line then it can only have one or no solutions. No solution is if the system is representing parallel lines and one solution represents an intersection of the two lines. in a nonlinear system you can have infinite or up to a maximum of intersections as the highest degree of the systems.

Related Questions

Please help me asap!!!

Answers

rewrite (1st) equation
-x - 2y = - 9
multiply the (1st) equation by 3
-3x - 6y = -27

now you have
-3x - 6y = -27
3x - 6y = -15
-----------------------add
-12y = -42
y = 3.5

2(3.5) = -x + 9
7 = - x + 9
x = 2

answer
(2 , 3.5)

The width of Zorn’s patio is labeled in the diagram below. If the perimeter of the patio is (30x + 26) feet, what is the length of the patio?

Answers

Correct Option:
4th option is the correct answer

Solution:

The shape of Zorn's Patio is rectangular, as shown in the given image/ The perimeter of rectangle is calculated as:

Perimeter = 2 (Length + Width)

Width is given to be = (7x+4) feet
Perimeter is given to be = (30x+26) feet

Using the formula of perimeter we can write:

30x+26 = 2(Length + 7x+4)

Taking out 2 common from left hand side, we get:

2(15x+13) = 2(Length + 7x + 4)

Cancelling the common 2 from both sides, we get:

15x + 13 = Length + 7x + 4
⇒
Length = 15x + 13 - 7x -4
Length = 8x + 9

Therefore, the length of Zorn's Patio is (8x+9) feet

Width = 7x + 4
Perimeter = (30x + 26)

Perimeter = 2( Length + Width)
30x + 26 = 2(Length + 7x + 4)

[Divide by 2 through]
15x + 13 = Length + 7x + 4

[Minus 7x on both sides]
15x + 13 - 7x = Length + 7x + 4 - 7x
8x + 3 = Length + 4

[Minus 4 on both sides]
8x + 13 - 4 = Length + 4 - 4
8x - 1 = Length

Length = 8x + 9 (Answer D)

Jensen wants to hang a mirror in his boat and put a frame around it. The mirror and frame must have an area of 19.75 square feet. The mirror is 4 feet wide and 5 feet long. Which quadratic equation can be used to determine the thickness of the frame, x? (2 points)

2x2 + 6x − 19.25 = 0

3x2 + 5x − 19.25 = 0

4x2 + 18x + 0.25 = 0

4x2 + 18x + 20 = 0

Answers

The third choice, 4x²+18x+0.25=0, is correct.

The frame will have the same thickness on both sides of the mirror. Therefore we add 5+x+x to get the total length, and we have 4+x+x to get the total width.

The area is found by multiplying the total width and total length:

A=(5+x+x)(4+x+x)
A=(5+2x)(4+2x)

Multiplying the binomials, we have:
A=5*4+5*2x+2x*4+2x*2x
A=20+10x+8x+4x²
A=20+18x+4x²

We know that the area is 19.75:
19.75=20+18x+4x²

We need quadratics set equal to 0, so subtract 19.75 from each side:
19.75-19.75 = 20+18x+4x²-19.75
0=0.25+18x+4x²

In standard form, it will be:
4x²+18x+0.25=0

Sandra can type 180 words in 3 minutes. At this rate, how many words can she type in 5 minutes?
_____MInutes
(FREE ANSWER> I WILL MARK BRAINLIEST AND RATE AND SAY THANKS)

Answers

180 divided by 3 = 60

60 x 5 = 300

she can type 300 words in 5 minutes

180/3 = 60 she can write 60 words per minute. 60 x 5 = 300 She can type 300 in five minutes.

Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.

Answers

sum of the angles of any quad =360
then y+(x+2)+(x-2)+(x-10) = y +3x -10 =360 (by adding both sides by 10)
y + 3x =370 ;.... eq 1
the sum of each two opposite sides in a quad inscribed in a circle =180
then (x+2)+(x-2)=180
therefore 2x =180
therefore x=90 (sub in eq 1)
y+3*90 =y +270 = 370 (subtracting both sides by 270)
therefore y=100
then measure angle B=100 degrees
A=92 degrees
C=88 degrees
D=80 degrees

HOLA FELLOW AMERICANS I AWAIT YOUR ASSISTANCE

Answers

the answer is d x=3 and y=2

Answer:

Step-by-step explanation:

PLEASE HELP ME ASAP
PLEASE

Answers

Answer
Choice D
Company 2 is greater in avg rate of change by $750

=======================================

Explanation:

Average rate of change is the same as slope through two points. The two points are the endpoints of the interval.

The x values we'll use is x = 0 and x = 12 since it constitutes the first 12 years (12-0 = 12)

For company 1, if x = 0 and x = 12, then y = 12000 and y = 30000 respectively. The two points (0,12000) and (12,30000) are on the graph for company 1
The slope of the line through these two points is
m = (y2-y1)/(x2-x1)
m = (30000-12000)/(12-0)
m = 18000/12
m = 1500
Over the first twelve years, the average rate of change for company 1 is 1500

For company 2, the points (0,15000) and (12,42000) are on the graph
The slope of the line through these two points is
m = (y2-y1)/(x2-x1)
m = (42000-15000)/(12-0)
m = (27000)/(12)
m = 2250
Over the first twelve years, the average rate of change for company 2 is 2250

Now find the difference in the slopes
2250-1500 = 750

Company 2's rate of change is larger by $750
So that's why the answer is choice D. Over this timespan, company 2 is growing faster on average compared to company 1

Please help asap!!! 16 points ):

Answers

This is a line on the x axis because it does not intersect with the y axis at all. The line is at x=3 and is a vertical line. If the line was x=-3, it would be to the left of (0,0), but it is positive to the right of the x and y intersection.

ANSWER: D) x=3

Hope this helps! :)

Andy is trying to determine the correlation between the number of math homework assignments he completes and his test score. Which is the BEST estimate for the correlation coefficient of the data? A) r = 1.5 B) r = 0.5 C) r = 0.96 D) r = −0.90

Answers

Answer option C:
The model is close to being linear. Therefore, there is a strong positive correlation.

Answer:

Option C

Step-by-step explanation:

It is really obvious that whenever the number of homework assignments he completes increases, his knowledge in the subject increases. This will increase automatically his test score in Maths.

Thus we can expect a perfect linear association between number of assignments done and his test score.

The correlation coefficient which is a measure of linear association between two variables always lies between -1 and +1.

Hence Option a cannot be correct since the value is greater than 1.

b) r=0.5 gives a positive but not very strong association. This is wrong as there is a strong association between the two variables

c) r=0.96 seems to be a correct answer as the positive and near to 1 r value confirms the linear strong positive association between the two variables.

D) r =-0.90 is wrong since there cannot be a negative association.

So only option right is option C

8.9 – 1.4x + (–6.5x) + 3.4

Answers

8.9 + 3.4 -1.4x - 6.5x = 12.3 - 7.9x

Answer:

12.3 – 7.9x

Step-by-step explanation:

the product of + and - is -

Therefore,

8.9 – 1.4x + (–6.5x) + 3.4

= 8.9 – 1.4x –6.5x + 3.4

collect like terms

= – 1.4x – 6.5x + 3.4 + 8.9

= –7.9x + 12.3

= 12.3 – 7.9x

Choose the polynomial that is written in standard form. (1 point)

−3x5y2 + 4x3y + 10x2

−8xy2 + 4x4y2 + 3x3

x4y2 + 4x3y5 + 10x4

x6y2 + 4x3y8 + 10x7

Answers

Standard form is where the degree of each monomial decreases from left to right. Degree can be found by adding the exponents on each variable.

The only one where this is true is the first one.
The degree goes from 7 to 4 to 2

Answer:

[tex]-3x^5y^2+4x^3y+10x^2[/tex]

Step-by-step explanation:

A polynomial in two variables is in standard form if its monomial from left to right are arrangerd in descending order. We say that a monomial [tex]x^ay^b[/tex] is greater than a monomial [tex]x^{a^{\prime}}y^{b^{\prime}}[/tex] if [tex]a+b > a^{\prime} + b^{\prime}[/tex] or [tex]a+b=a^{\prime}+b^{\prime} \quad \text{and} \quad (a,b)>(a^{\prime},b^{\prime}})[/tex] in the alphabetical order.

For example

[tex]x^2y>xy \quad \text{since} \quad 2+1>1+1 \\\\x^2y>xy^2 \quad \text{since} \quad 2+1=1+2 \quad \text{and} \quad 2>1[/tex]

The polynomial [tex]-3x^5y^2+4x^3y+10x^2[/tex] is in standard form, since [tex]x^5y^2 > x^3y >x^2[/tex]. On the other hand, the polynomial [tex]-8xy^2+4x^4y^2+3x^3[/tex] is not in standard form since [tex]x^4y^2>xy^2.[/tex]

The number 1,054 is?
< 1,045
= 1,045
> 1,045
Or none of these is correct

Answers

>1045 because 1054 is greater than 1045

The number 1054 > 1045

We are learning polynomials in algebra one. Can anyone help explain trinomials like- n^3 - 5n^2 - 50n

Answers

Prefixes you will see in math (and other places) include mono-, bi-, tri-, quadri-, hexa-, poly- and others. Respectively, they mean 1, 2, 3, 4, 6, many. So, a "trinomial" is a 3-term expression. Yours has terms (n^3), (-5n^2), (-50n).

If you examine these terms, you can see that n is a factor of all of them.

There are a few things we like to do with polynomials (or trinomials, in this case). We like to perform arithmetic operations on them (addition, subtraction, multiplication, division). There is generally nothing tricky about this. The usual rules apply, and polynomial math is easier than multi-digit arithmetic in many ways.

We also like to factor polynomials. Binomials and trinomials are generally the easiest, so these are the ones you see most often. It can help to be familiar with the way binomials multiply.
.. (x +a)*(x +b)
.. = x*(x +b) +a*(x +b) . . . . . use the distributive property
.. = x^2 +bx +ax +ab . . . . . use the distributive property twice more
.. = x^2 +(a +b)x +ab . . . . . collect terms

Here, when we say "collect terms", we mean we want to combine the coefficients of "like" terms, that is, terms that have the same constellation of variables. Here, the only "like" terms are terms that have a constant multiplying the variable x. We add the terms bx and ax to get (a+b)x. (Again, the distributive property is involved. Know it backward and forward.)

When we factor out n from your trinomial, we have
.. = n(n^2 -5n -50) . . . . . . using the distributive property

Comparing this to the product of binomials above, we could factor this to binomial terms if we could find "a" and "b" such that ab = -50 and (a+b) = -5. Sometimes it helps simply to list factor pairs of a number to check for possiblities.
.. -50 = -50*1 = -25*2 = -10*5
The sums of these factor pairs are -49, -23, and -5. This last one matches what we are looking for as a coefficient of the linear term, so we could choose a=-10, b=5 and write your trinomial in factored form as
.. = n(n -10)(n +5)

Factoring is a little trickier if the coefficient of the squared term is not 1, but it generally follows the same pattern.

_____
In summary:
a trinomial is a 3-term polynomial
the unusal rules for multiplying and dividing arithmetic expressions apply
the process of factoring a trinomial can be helped by remembering the pattern for the product of binomials

Molly can either take her lunch or buy it at school. It cost $1.95 to buy lunch. If she wants to spend no more than $30 each month, how many lunches can she buy at most?

Answers

Final answer:

Molly can purchase a maximum of 15 school lunches per month with a budget of $30, considering each lunch costs $1.95.

Explanation:

The question asks how many school lunches Molly can buy if each lunch costs $1.95 and she wants to spend no more than $30 each month. To find out how many lunches Molly can buy, we divide her monthly budget by the cost of one lunch.

So, we perform the calculation: $30 ÷ $1.95 ≈ 15.38. Since Molly cannot buy a fraction of a lunch, we round down to the nearest whole number, which means Molly can buy 15 lunches at most in a month without exceeding her budget.

Express the ratio of a's to n's in the word banana, in simplest form.

Answers

2:3 3:2 1:2 2:1 theres your answer.

The ratio of A's to N's in the word BANANA is 2:1. This means that there are twice as many A's as there are N's in the word. Therefore, the correct answer is D: 2:1.

To find the ratio of A's to N's in the word BANANA, we need to count the number of A's and N's in the word.

1. Count the occurrences of A and N:

In the word BANANA, there are 3 A's and 1 N.

2. Express the ratio:

The ratio of A's to N's is 3:1.

3. Simplify the ratio:

To simplify the ratio, we can divide both parts by their greatest common divisor (GCD), which is 1 in this case, because 3 and 1 have no common divisor other than 1.

[tex]\[ \text{Ratio} = \frac{3}{1} = 3:1 \][/tex]

4. Check the given options:

Now, let's compare the simplified ratio 3:1 with the given options.

A. 2:3 - This doesn't match the simplified ratio.

B. 3:2 - This doesn't match the simplified ratio.

C. 1:2 - This doesn't match the simplified ratio.

D. 2:1 - This matches the simplified ratio.

Therefore, the correct answer is D: 2:1.

The ratio of A's to N's in the word BANANA is 2:1. This means that there are twice as many A's as there are N's in the word.

The complete question is:

Express the ratio of A's to N's in the word BANANA, in simplest form.

A: 2:3

B: 3:2

C: 1:2

D: 2:1

I will give brainliest.
What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (2, 5)? y + 5 = x + 2 y − 2 = x − 5 y − 5 = −(x − 2) y + 2 = −(x + 5)

Answers

Answer:

You are requested to kindly provide the equation of line to which our to be found line is perpendicular.

Step-by-step explanation:

***WILL GIVE MEDAL TO WHOEVER HELPS***
Question:
Sherri has 23 pieces of jewelry to sell. She sells the bracelets for $2 and the necklaces for $3, and earns a total of $55. If the bracelets are represented by x and the necklaces are represented by y, which of the following systems of equations can be used to calculate the number of bracelets and necklaces sold?

Answer choices:
x + y = 23, 3x + 2y = 55
x + y = 55, 3x + 2y = 23
x + y = 23, 2x + 3y = 55
x + y = 55, 2x + 3y = 23,

Answers

x+y = 23 and 2x+3y=55; The wording of the answer choices were confusing, but both of these come together to make the correct answer. First, you need x (number of bracelets) + y (number of necklaces) to determine how many of each were sold. Then, you add 2x (cost of each bracelet x bracelets sold) and 3y (same as bracelets but for necklaces). This results in the total amount sold.

If x and y are positive integers, what is the value of x + y ? x+y=15 xy=6

Answers

The answer is 9+6= 15

How do you find a scale factor?

Answers

Look in the legend area or title block on the map or mechanical drawing.

Determine the ratio of corresponding linear dimensions of geometrically similar figures.

Read the problem statement.

___
The method is determined by the nature of the information you are given to work from.

Can Someone Please Help Me Factor (x^(2)+6x+58)

Answers

The last term is 58. List out the ways to multiply two whole numbers to get to 58

1*58 = 58
2*29 = 58
(-1)*(-58) = 58
(-2)*(-29) =58

Then go through those factors and see which two values add to 6 (which is the middle number in the given expression)

1+58 = 59
2+29 = 31
-1+(-58) = -59
-2+(-29) = -31

None of those sums are 6, so the original expression cannot be factored. It is said to be prime.

Roman stands across from a flag pole.

What is the distance from Roman's feet to the base of the flag pole?

Round only your final answer to the nearest tenth.

https://learning.k12.com/d2l/common/viewFile.d2lfile/Database/MTM5NDQzMDQ/test%20-%20quest%205.JPG?ou=373236

Answers

The answer is 13.2 m.
Because we are only given the hypotenuse, adjacent, and theta measurements.
the opposite side is always opposite theta. In this case, theta is 39 degrees. The hypotenuse is always the slant of the triangle, so it is 17 m. And adjacent is obviously the only one left, in this case, it is x.

You have to use sin, cos, or tan for this problem. You would use cos because cos = adjacent /hypotenuse (x/17)

so you would do cos(39) times 17
x = cos(39) * 17
x = .777 * 17
x = 13.21

And it says round to the nearest tenth, so it is 13.2 m.
Hope this helps.

The distance from Roman's feet to the base of the flag pole 13.2 m.

What is Trigonometry?

It is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given:

Angle of elevation= 39.

Hypotenuse = 17 m

Using Trigonometry

cos 39 = adjacent side /hypotenuse

cos 39= base/17

0.777= base/17

base= 0.777*17

base= 13.21m

base= 13.2 m.(rounding off)

Hence, the distance from Roman's feet to the base of the flag pole 13.2 m.

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How do you find the x intercept, y intercept, and M

Answers

You can divide your equation by 12 to put it into intercept form. Then read the intercepts from the equation.
.. (2x/12) + (-3y)/12) = 1
.. x/6 + y/-4 = 1

The x-intercept is 6
The y-intercept is -4

The "slope triangle" is 4 units high and 6 units wide, so ...
.. the slope is m = 4/6 = 2/3.

There are 514 children in all at both Peter’s and Nada’s schools. Nada’s school has 185 children. About how many children go to Peter’s school?

Answers

When there are 514 children in total and 185 go to Nada's school, there are
514 - 185 = 329 children left.
Therefore, 329 (about 330) children go to Peter's school.

Please help aassssaaaapppp

Answers

go to symbolab.com its really helpful

B
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The standard form of an exponential growth or decay equation is

f(x) = a(b)^x

What do each of the variables in this equation (a,b,x) represent?

Answers

a: represents the initial amount (before the growth or decay starts).

b: represents the factor of growth or decay (e.g. 0.75 or 1.32).

x: represents the variable. This can be an amount of time (which is mostly true), or (sometimes) the other meaning of the variable is given.

The exponential function, which means as you increase in x , y increases exponentially.

It is required to represent the variable.

What is Exponential functions?

Exponential functions are patterns that get continuously multiplied by some number. It's exponential growth when the base of our exponential is bigger than 1, which means those numbers get bigger. It's exponential decay when the base of our exponential is in between 1 and 0 and those numbers get smaller.

Given that:

The standard form of an exponential growth or decay equation is

f(x) = a(b)^x

This is an exponential function, which means as you increase x , y increases exponentially. The initial amount is given by the value a , which is easy to see (just let x=0 and you have y=a left). The growth factor is the value b .

If you restrict b such that 0<b<1 , the function will decay (represented below) and if b>1 , the function will grow.

Therefore, the exponential function, which means as you increase in x , y increases exponentially.

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Simplify algebraic fraction

Answers

You can get common denominator in the denominator of the original fraction so it would look like:
[tex] \frac{4}{ \frac{1}{4}- \frac{10}{4} } = - \frac{1}{ \frac{9}{4} } [/tex]

You can reciprocalize and then multiply:
[tex]4* -\frac{4}{9} = -\frac{16}{9} [/tex]

So, your answer is C.

the sum of two fractions is three times their difference.six times the smaller fraction exceeds the larger fraction by 3/2.find the fractions

Answers

Let a and b represent the fractions.
.. a +b = 3(b -a)
.. 6a -b = 3/2
Rewriting the first equation, we have
.. 4a -2b = 0
or
.. 2a -b = 0
Subtracting this from the second equation gives
.. 4a = 3/2
.. a = 3/8
.. b = 2a = 3/4

The two fractions are 3/8 and 3/4.

A cone is inscribed in a regular square pyramid. If the pyramid has a base edge of 6" and a slant height of 9", find the volume of the cone. 12√2 18√2 27

Answers

check the picture below.

so, a cone inscribed in a square pyramid, like the blue one there, will have the a diameter that is the length of the base of the pyramid, as you can see there, is 6, now, since the radius is half of the diameter, that means r = 3.

we know the slant height is 9, since the slant height and the height segment make a right-triangle with the base's segment, then we use the pythagorean theorem to get the height "h".

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\quad \begin{cases} r=radius\\ h=height\\ -----\\ r=3\\ h=6\sqrt{2} \end{cases} \implies V=\cfrac{\pi (3)^2(6\sqrt{2})}{3}[/tex]

Final answer:

The volume of the cone inscribed in the pyramid, calculated using the formula for the volume of a cone and the Pythagorean theorem, is 18√2π cubic inches.

Explanation:

In this question, we're asked to find the volume of the cone inscribed in a regular square pyramid. The volume V of a cone can be calculated using the formula V = 1/3 * pi * r^2 * h, where r is the radius of the base and h is the height of the cone. Since the cone is inscribed in the pyramid, its height and base radius would be the same as those of the pyramid.

However, the pyramid is a square pyramid with a base edge of 6 inches and a slant height of 9 inches. The height of the pyramid (and thus the cone) can be calculated using the Pythagorean theorem as √(9^2 - (6/2)^2), which is √(81 - 9) = √72 = 6√2.

The radius of the base of the cone is half of the base edge length of the pyramid, or 3 inches. So the volume of the cone is V = 1/3 * pi * 3^2 * 6√2 = 18√2π cubic inches.

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Which tasks are performed by individuals in the Science and Math pathway? Select all that apply.

research human behavior

design and test machinery

develop scientific theories

interpret designs and documents

perform calculations and make predictions

maintain lab equipment to perform experiments

Answers

design and test machinery
develop scientific theories
perform calculations and make predictions
maintain lab equipment to perform experiments

Tasks that are performed by individuals in the Science and Math pathway are design and test machinery, develop scientific theories, perform calculations and make predictions, and maintain lab equipment to perform experiments. They involve Science and Math tasks, and while they may not all apply to a single course, they are related in the same department.

Answer:

design and test machinery develop scientific theories perform calculations and make predictions maintain lab equipment to perform experiments

Step-by-step explanation:

Although science is quite broad, it may involve all or almost all of the alternatives, I suppose you are referring to the exact sciences, as you also want to know which of these options are studied by mathematicians.

Science is a term popularly used to refer to the natural and formal sciences, which use rigorous scientific research methods and benchmarking. In science there are quantitative, mathematical or logical-formal proofs. The sciences are those that encompass a range of various areas of knowledge, some of which are mathematics, computation, statistics, physics, chemistry, engineering, aeronautics, as well as parts of biology, psychology and economics. Generally, these sciences are closely linked to calculations and numbers, which are present in almost all of these fields.

Based on this conceptualization, we can say that the tasks that are performed by individuals in the path of science and mathematics are: design and test machinery, develop scientific theories, perform calculations and make predictions and maintain lab equipment to perform experiments.

#16 ) BRAINLIEST + POINTS !!!!!

Answers

B is the answer hope this helps and please give me brainliest

Answer:

b is correct

Step-by-step explanation:

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