Mathematics College

What can be used as a reason in a two-column proof?
Select each correct answer.
conjecture
postulate
definition
premise

Answers

Answer 1
Two column proofs are organized into statement and reason columns. Each statement must be justified in the reason column. The reason column will typically include "given", vocabulary definitions, and theorems.

Therefore, what can be used as a reason in a two-column proof are:

Postulates

Definitions
Answer 2

Answer:

Two column proofs are organized into statement and reason columns. Each statement must be justified in the reason column. The reason column will typically include "given", vocabulary definitions, and theorems.

Therefore, what can be used as a reason in a two-column proof are:

Postulates

Definitions

Related Questions

Why do you round 117290 up to 120000

Answers

because you round the 1 to the 7 and get 12 and everything that follows that number is 0.
bc its closest to that and not closest to 110000 or 10000

The three tools the Federal Reserve uses to enact monetary policy are:

Answers

Hey there! Hope this helps!

which algebraic expression represents the "phrase the quotient of -8 and the sum of a number and three"

A -8/g+3
B 8/g+3
C -8+g/3
D -8/g +3

Answers

"the quotient of -8 and the sum of a number and three," written symbolically, comes out to 

           -8
--------------------------     This most closely resembles answer choice "A."
        n + 3

I have used "n" instead of "g" here.


The algebraic expression represents the given phrase is -8/(g+3). Therefore, option A is the correct answer.

The given phrase is "the quotient of -8 and the sum of a number and three".

We need to identify which algebraic expression represents the given phrase.

What is an algebraic expression?

Algebraic expressions are the mathematical statement that we get when operations such as addition, subtraction, multiplication, division, etc. are operated upon on variables and constants.

Let the unknown number be g.

Now, the quotient of -8 and the sum of a number and three=-8/(g+3)

The algebraic expression represents the given phrase is -8/(g+3). Therefore, option A is the correct answer.

To learn more about an expression visit:

brainly.com/question/16804733.

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can someone please help with transformations of parent functions

Answers

[tex]\bf \qquad \qquad \qquad \qquad \textit{function transformations} \\ \quad \\\\ % left side templates \begin{array}{llll} f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}} \\ \quad \\ y=&{{ A}}({{ B}}x+{{ C}})+{{ D}} \\ \quad \\ f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}} \\ \quad \\ f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}} \\ \quad \\ f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}} \end{array}\\\\ --------------------[/tex]

[tex]\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]

[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{{{ B}}}[/tex]

that said, compressing vertical |x| by  a factor of 4, means A = 4, thus is 4|x|.

Please help badly I cannot answer

Answers

so, you asked 356 folks if they like drawing, 89 say they do.

now, if we take 356 as the 100%, what is 89 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 356&100\\ 89&x \end{array}\implies \cfrac{356}{89}=\cfrac{100}{x}\implies x=\cfrac{89\cdot 100}{356}[/tex]

What value of x is in the solution set of 2(3x – 1) ≥ 4x – 6?

Answers

It can be convenient to subtract the right side of the inequality from both sides.

... 2(3x -1) -(4x -6) ≥ 0

... 2x +4 ≥ 0 . . . . . . . . . collect terms

... x +2 ≥ 0 . . . . . . . . . . divide by the coefficient of x

... x ≥ -2 . . . . . . . . . . . . add the opposite of the constant

Any value of x that is at least -2 will be in the solution set.

Explain how to solve 2x + 7 = 15

Answers

The x would be 4 because if you multiply 2 times 4, that's 8, and 8+7=15
You would work backwards:15-7=8, because you will be adding this anyways later, and then you see that 2x = 8, then divide both sides by two, and you are left with the equation: x = 4, and there is your answer. x = 4.

What is the mean of the high temperatures, in degrees Fahrenheit, for the week? Show your work.

Answers

The mean is the average, so add all the numbers and divide by 7 (7 terms).

-14 is the sum, divided by 7 = -2

The mean is -2.

Write an equation of the line in the figure.

Answers

the slope is 6/5 and the y intercept is -1
Slope intercept y = 6/5x -1
Point slope form (y - 5) = 6/5 (x - 5)

what is 5.62 rounded to?

use all place values.

Answers

it could be rounded to 6.0 or 10 anything 5 or above gets rounded up to the nearest tenth
The answer could be 6 if you are rounding up to the nearest unit. If you are rounding to the nearest 10, it would be 10.

A backpack that normally sells for 39 is on sale for 34% off. Find the amount of the discount and the sale price.

Answers

Hello!

34% of 39 is 13.26 ( 34% = .34 × 39 = 13.26)

Subtract that from 39 to find the amount of the discount:

39 - 13.26 = 25.74

So, the amount of discount on the backback is 25.74%.

^ And that's your answer! I hope this was helpful! :)

Its number 15. Thank you

Answers

Going from step 1 to step 2, the person has factored out x. However, this is incorrect because there is no x to factor from the last term d.

Factoring like this is simply the distributive property in reverse. We can check if we did the factoring right by distributing the outer term x back into the inner terms

Let's multiply the outer x by each of the inner terms (a, b and d)

x times a = ax
x times b = bx
x times d = dx <--- the result should be d and not dx

-----------------------------------------------------------------------------

Here is the proper way to solve for x. We first need to move the d over, which is done by subtracting d from both sides. Once all of the x terms are on one side, we can finally factor out the x. Then after that we divide both sides by the quantity (a+b)

k = ax + bx + d
k - d = ax + bx + d - d
k - d = ax + bx
k - d = x(a + b)
(k - d)/(a + b) = x(a + b)/(a + b)
(k - d)/(a + b) = x
x = (k - d)/(a + b)

The final answer is
x = (k - d)/(a + b)
which can be written as 
[tex]x=\frac{k-d}{a+b}[/tex]
If you choose to use the first option, then make sure you use parenthesis as shown. The parenthesis are important to make sure that you divide all of "k-d" over all of "a+b" as one big fraction.

The formula f=5280m can be used to convert a measurement of f feet to an equivalent measurement m miles. If an airplane flies at 21,120 feet above the ground, how much is that in miles?

A. 4 miles
B. 5.3 miles
C. 111, 513, 600 miles
D. 132, 620, 600 miles

Answers

the answer is a
21,120/5280=4

Find the specified element in the inverse of the given matrix

Answers

what is the given matrix?
you didn't show a matrix.
the components of the matrix are the elements.
and the elements of the inverse matrix are the elements of the inverse matrix
1) 
so if matrix A is  1   4  1   
                          2   5  2
                          3   6  3
2)
14114
25225
36336

3)
15 24 12
15 12 24
4)
[A]=(15+24+12=51)-(15+12+24=51)
[A]=0
5)
    52    23   25
    63    23   36

    41    11   14 
    63    33   36

    41    12    14
    52    12    25
6)

    15-12   6-6   12-15

     12-6    3-3    6-12

      8-5     2-2     5-8


7) 
     3    0   -3

     6    0   -6

     3    0   -3
 8) 
     (+)3    (-)0   (+)-3

     (-)6    (+)0   (-)-6

     (+)3    (-)0   (+)-3
=

    3  0  -3
   -6  0   6
    3  0  -3

9)
        3 -6  3
N=   0  0  0
       -3  6 -3
10) the inverse of [A]= 1/|A|*[N]
which is in this case ⁻A= 0
because |A|=0

Unfortunately, arsenic occurs naturally in some ground water†. a mean arsenic level of μ = 8.0 parts per billion (ppb) is considered safe for agricultural use. a well in texas is used to water cotton crops. this well is tested on a regular basis for arsenic. a random sample of 36 tests gave a sample mean of x = 6.8 ppb arsenic, with s = 2.9 ppb. does this information indicate that the mean level of arsenic in this well is less than 8 ppb? use α = 0.01. (a) what is the level of significance? 0.01 state the null and alternate hypotheses. h0: μ = 8 ppb; h1: μ > 8 ppb h0: μ = 8 ppb; h1: μ < 8 ppb h0: μ > 8 ppb; h1: μ = 8 ppb h0: μ < 8 ppb; h1: μ = 8 ppb h0: μ = 8 ppb; h1: μ ≠ 8 ppb (b) what sampling distribution will you use? explain the rationale for your choice of sampling distribution. the standard normal, since the sample size is large and σ is known. the student's t, since the sample size is large and σ is unknown. the student's t, since the sample size is large and σ is known. the standard normal, since the sample size is large and σ is unknown. what is the value of the sample test statistic? (round your answer to three decimal places.) -2.483 (c) estimate the p-value. p-value > 0.250 0.125 < p-value < 0.250 0.050 < p-value < 0.125 0.025 < p-value < 0.050 0.005 < p-value < 0.025 p-value < 0.005 sketch the sampling distribution and show the area corresponding to the p-value. webassign plot webassign plot webassign plot webassign plot (d) based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? are the data statistically significant at level α? at the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. at the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. at the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. at the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. (e) interpret your conclusion in the context of the application. there is sufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb. there is insufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb.

Answers

Part A:

For a hypothesis test, the significant level is given by α. From the question, we were told that α = 0.01.

Therefore, the significant level is 0.01.

Our previous knowledge is that a mean arsenic level of μ = 8.0 parts per billion (ppb) is considered safe for agricultural use, we know want to know from a sample of 36 tests whether the mean level of arsenic in a particular well is less than 8 ppb.

Therefore, the null and the alternative hypothesis are:

[tex]H_0:\mu=8\ pbb \\ \\ H_a:\mu\ \textless \ 8\ pbb[/tex]



Part B:

The sampling distribution to be used is the student's t, since the sample size is large and σ is unknown.

The test statistics is given by:

[tex]t= \frac{\bar{x}-\mu}{s/\sqrt{n}} \\ \\ = \frac{6.8-8}{2.9/\sqrt{36}} \\ \\ = \frac{-1.2}{2.9/6} = \frac{-1.2}{0.4833} \\ \\ =-2.483[/tex]



Part C:

The p-value for a t-distribution test statistics of -2.483 with a degree of freedom of 35 is given by 0.0090

Thus 0.005 < p-value < 0.025



Part D:

Since the p-value is less that the significant level, we reject the null hypothesis and conclude the data are statistically significant.

i.e.
at the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.



Part E:

Therefore, we conclude that there is sufficient evidence at the 0.01 level to conclude that the mean level of arsenic in the well is less than 8 ppb.

Determine whether each of these sets is the power set of a set, where a and b are distinct elements.
a.∅
c.{∅,{a},{∅,a}}

Answers

a. [tex]\varnothing[/tex] cannot be the power set of any set. Consult Cantor's theorem, which says that the cardinality of the power set of any set (even the empty set) is strictly greater than the cardinality of the set.

(No part b?)

c. Also not the power set of any set, because any power set must have [tex]2^n[/tex] elements, where [tex]n[/tex] is the cardinality of the original set. The cardinality of this set is 3, but there is no integer [tex]n[/tex] such that [tex]2^n=3[/tex]. This set would be a power set if [tex]\{\varnothing\}[/tex] (that is, the set containing the empty set) were a member of it.

The sale price of an item is $45 after a 40% discount is applied. What is the original price of the item?

Answers

Diving the sales price by 60% (100-40) will obtain the original price. 
$45/60% = $75 was the original sales price. 

The original price of the item is $75.

Suppose the original price of the item =x

Discount =40%

What is the percentage?

The percentage is the value per hundred.

Given discounted price or sale price of the item =$45

This means [tex]x-\frac{x*40}{100} =45[/tex]

[tex]\frac{60x}{100} =45[/tex]

[tex]\frac{3x}{5} =45[/tex]

[tex]x=75[/tex]

So, the original price of the item =$75

Hence, the original price of the item is $75.

To get more about the percentage visit:

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Evaluate the line integral c y3 ds,
c.x = t3, y = t, 0 ≤ t ≤ 3

Answers

[tex]\displaystyle\int_{\mathcal C}y^3\,\mathrm dS=\int_{t=0}^{t=3}t^3\sqrt{1^2+(3t^2)^2}\,\mathrm dt=\int_0^3t^3\sqrt{1+9t^4}\,\mathrm dt[/tex]

Take [tex]u=1+9t^4[/tex] so that [tex]\mathrm du=36t^3\,\mathrm dt[/tex]. Then

[tex]\displaystyle\int_{\mathcal C}y^3\,\mathrm dS=\frac1{36}\int_{u=1}^{u=730}\sqrt u\,\mathrm du=\frac{730^{3/2}-1}{54}[/tex]

An omelet station uses 3 eggs to make each omelet. What is the cost for the total number of eggs in a single omelet if a case of 30 dozen eggs has an as-purchase cost of 32.40?

Answers

I think it's 0.27 (3*32.40/360)

The diagram shows a square of side 7 cm with two quadrants drawn inside. Find the area of the shaded region. (take pi= 22/7)

Answers

The area of the shaded region:
A = r ² π - a²
where: r = d/2 = 7√2 / 2
A = ( 7√2 / 2 )² · 22/7 - 7²
A = 49 · 2 / 4  · 22/7 - 49
A = 49/2 · 22/7 - 49
A = 7 · 11 - 49
A = 77 - 49
Answer: A (shaded) = 28 

will mark brainliest!!
solve this system of linear equations. separate the x- and y- values with a coma. 9x=27-9y
20x=71-9y

Answers

Solve the system

9x = 27-9y
20x=71-9y

Let's use the "elimination through addition/subtraction method.
Multiply the first equation by -1 so as to obtain +9y:

-9x = -27 + 9y
20x=  71-   9y
--------------------

Add these 2 equations together:

-9x = -27 + 9y
20x=  71-   9y
--------------------
 11x = 44

Solve this for x:  x = 44/11 = 4.

Now find y by subst. 4 for x in either of the original equations.

Using the second equation:     

20x=71-9y
20(4) = 71 - 9y
80-71 = -9y
9 = -9y.  Then y = -1.

The solution set is (4,-1).

Tickets for rides at the fair cost $0.75 each you can also buy a roll of 25 tickets for $15 what is the cost of each ticket if you buy a roll of tickets

Answers

You get 25 tickets for $15

all you need to do is take the cost and divide it by the number of tickets.

$15 ÷ 25 tickets = $0.60 per ticket

Final answer:

The cost per ticket when buying a roll of 25 tickets for $15 at the fair is $0.60, which is less than the single ticket price of $0.75.

Explanation:

The student has asked about the cost of each ticket if bought in a roll at a fair. To find the cost per ticket when purchasing a roll of 25 tickets for $15, you simply divide the total cost of the roll by the number of tickets in the roll.

Cost per ticket = Total cost of the roll / Number of tickets in the roll

Cost per ticket = $15 / 25

Cost per ticket = $0.60

Therefore, when buying a roll of tickets, the cost of each ticket is $0.60, which offers a saving compared to the single ticket price of $0.75.

James covers a distance of 8 meters in the first second of a 100 meter race. Then, he sprints at a speed of 9 meters per second. How far is James from the finish line 9 seconds after the race has started? a. 11 c. 28 b. 20 d. 80

Answers

so James covers 8 meters in the first second....then he sprints 9 meters per second......
9 seconds after the race....so there are 8 seconds that he is sprinting 9 meters per second.....(8 * 9) = 72 meters....plus the 8 meters for the 1st second = (72 + 8) = 80 meters....
and if it is 100 meter race, and he has ran 80 meters, then that leaves 20 meters from the finish line....answer is D

Answer:

Option b. 20 meters

Step-by-step explanation:

James covers a distance of 8 meters in the first second of 100 meter race.

Then, he sprints at a speed of 9 meters per second.

We have to find how far is James from the finish line 9 seconds after the start of the race.

James covers distance in first second = 8 meters.

Time remaining in 9 seconds after running 8 meter = 9 - 1 =  8 seconds.

In another 8 seconds James covers the distance = speed × time

 = 9 × 8 = 72 meters

Total distance covered in 9 seconds = 8 + 72 = 80  meters

Distance remaining in 100 meter race after 9 seconds = 100 - 80 = 20 meters.

James is 20 meters far from the finish line 9 seconds after the race has started.

Option b. 20 meters is the answer.

Find the probability that in a family of 4 children there will be
a.at least 1 boy
b.at least 1 boy and at least 1 girl
c.out of 2000 families with 4 children each how many would you expect to have 1 or 2 girls. assume that the probability of a male birth is 1/2.

Answers

It will be letter for family of 4 is letter c

Present 5 mixed numbers that add up to the whole number 10.

Answers

5 1/3 + 4 2/3 = 10
4 1/3 + 5 2/3 = 10
6 1/4 + 3 3/4 = 10
9 3/5 + 2/5 = 10
2 8/10 + 7 1/5 = 10

hope this helps

Sally's soccer team won 68% of the games they played.if they won 17 games, how many did they play?

Answers

Let the number of games played be x.  68% of x comes out to 17 games.

Then 0.68x = 17.  Mult. both sides by 100:  68x = 1700.

Divide 68 into 1700 to obtain x, the number of games played:  x = 25

The team plays in 25 games.

Answer: The total number of games played are 25

Step-by-step explanation:

Let the total number of games played be 'x'

We are given:

Number of games won = 17

Percentage of games won = 68 %

Calculating the total number of games:

[tex]68\% \text{ of x}=17[/tex]

So,

[tex]\frac{68}{100}\times x=17\\\\x=\frac{17\times 100}{68}=25[/tex]

Hence, the total number of games played are 25

A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?

Answers

a direct variation function, is just another way to word a "linear equation", and the slope will then be the "constant of variation".

so, in short, what's the equation of the line that runs through 2,14 and 4,28?

[tex]\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 2}}\quad ,&{{ 14}})\quad % (c,d) &({{ 4}}\quad ,&{{ 28}}) \end{array}[/tex]

[tex]\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{28-14}{4-2}\implies \cfrac{14}{2}\implies 7 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-14=7(x-2) \\\\\\ y-14=7x-14\implies y=7x[/tex]

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]\frac{y}{x}=k[/tex] or [tex]y=kx[/tex]

In this problem we have

Points [tex](2,14)[/tex] and [tex](4,28)[/tex]

so

Find the value of k

First point

[tex]\frac{14}{2}=k[/tex]

[tex]k=7[/tex]

Second point

[tex]\frac{28}{4}=k[/tex]

[tex]k=7[/tex]

the function is

[tex]y=kx[/tex] --------> substitute the value of k

[tex]y=7x[/tex]

therefore

the answer is

[tex]y=7x[/tex]

In this problem with a single point was sufficient to calculate the equation, since in a direct variation the line passes through the origin, it is not necessary to use the formula of the slope


Mary invests £12000 in a saving account. The account pays 1.5% compound interest per year. Work out the value of her investment after 2 years.

Answers

Final answer:

To find the value of Mary's investment after 2 years in a saving account with compound interest, we can use the compound interest formula. Substituting the given values into the formula gives us £12363.61.

Explanation:

To calculate the value of Mary's investment after 2 years, we can use the compound interest formula: A = P(1 + r/n)^(nt), where:

A is the final amountP is the principal amount (initial investment)r is the annual interest rate (as a decimal)n is the number of times the interest is compounded per yeart is the number of years

In this case, the principal amount is £12000, the annual interest rate is 1.5% (0.015 as a decimal), and the number of times the interest is compounded per year is 1. Plugging these values into the formula, we get:

A = 12000(1 + 0.015/1)^(1*2)

Simplifying this, we get:

A = 12000(1.015)^2

Calculating further, we get:

A ≈ 12000(1.030225) ≈ £12363.61

Therefore, the value of Mary's investment after 2 years is approximately £12363.61.

The sutton police department must write, on average, 6 tickets a day to keep department revenues at budgeted levels. suppose the number of tickets written per day follows a poisson distribution with a mean of 6.5 tickets per day. interpret the value of the mean.

Answers

The Poisson distribution defines the probability of k discrete and independent events occurring in a given time interval.
If λ = the average number of event occurring within the given interval, then
[tex]P(k \, events) = e^{-\lambda } ( \frac{\lambda ^{k}}{k!} )[/tex]

For the given problem,
λ = 6.5, average number of tickets per day.
k = 6, the required number of tickets per day
The Poisson distribution is
[tex]P(k \, tickets/day)=e^{-6.5} ( \frac{6.5 ^{k}}{k!} )[/tex]
The distribution is graphed as shown below.

Answer: 
The mean is λ = 6.5 tickets per day, and it represents the expected number of tickets written per day.
The required value of k = 6 is less than the expected value, therefore the department's revenue target is met on an average basis.

How many real solutions does the system have Y=-3x-3 Y=x^2-3x+5

Answers

Y = -3x-3 has one real solution.

Y= x^2 -3x + 5 has no real solutions because b^2 - 4ac, the discriminant, is less than zero.
To find the solutions to each equation, we'll first have to set Y to 0. We have:[tex]-3x-3 &=0\\ x^2-3x+5=0[/tex]

To obtain the solutions for both, you'll have to solve them for x. The first equation is linear, so obtaining a solution there is fairly straightforward, and you're guaranteed to get one real solution there. The second equation is a little more involved, and we'll need the quadratic formula to settle that one out. You might remember from earlier math classes that the quadratic formula gives you a way to quickly find the roots of a particular quadratic equation. Here's the full thing:

[tex]x= \frac{-b\pm\sqrt{b^2-4ac}}{2a} [/tex]

For the sake of this question, the only part we're concerned with is the [tex]b^2-4ac[/tex] bit, which is referred to as the descriminant of the quadratic. If [tex]b^2-4ac \geq 1[/tex], we'll have two real solutions, since we'll need to evaluate the square root of the term for both positive and negative outcomes. If [tex]b^2-4ac=0[/tex], we only have one real solution, since adding and subtracting 0 from the [tex]-b[/tex] term have the same effect. If [tex]b^2-4ac \ \textless \ 0[/tex], we have no real solutions; the discriminant is nested inside a square root, and taking the square root of a negative number only produces imaginary results.

With that in mind, let's look at the discriminant of [tex]x^2-3x+5[/tex].

Looking at the coefficients and constant, we have a=1, b=-3, and c=5, which makes our discriminant

[tex](-3)^2-4(1)(5) = 9-20=-11[/tex]

-11 is less than 0, so we have no real solutions to the second equation. This means that our first equation is the only one with a real solution, so the total number of real solutions for the system is 1.
Other Questions
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