Examine the system of equations. –2x + 3y = 6 –4x + 6y = 12 Answer the questions to determine the number of solutions to the system of equations. What is the slope of the first line? What is the slope of the second line? What is the y-intercept of the first line? What is the y-intercept of the second line? How many solutions does the system have?

Answers

Answer 1

Answer:

Examine the system of equations.

–2x + 3y = 6

–4x + 6y = 12

Answer the questions to determine the number of solutions to the system of equations.

What is the slope of the first line?  

✔ 2/3

What is the slope of the second line?  

✔ 2/3

What is the y-intercept of the first line?  

✔ 2

What is the y-intercept of the second line?  

✔ 2

How many solutions does the system have?  

✔ infinitely many

Answer 2

The equations are a multiple of the other, therefore, by the multiplicative

property of equality, the equations are equivalent.

Response:

The slope and y-intercept of the first equation are [tex]\underline{\dfrac{2}{3} \ and \ 2}[/tex] respectivelyThe slope and y-intercept of the second equation are [tex]\underline{\dfrac{2}{3} \, and \, 2}[/tex]

The system of equations have infinitely many solutions.

Methods used to obtain the above response.

The given system of equations are;

-2·x + 3·y = 6

-4·x + 6·y = 12

Required:

The slope of the first line.

Solution:

The slope of the first line is given by the coefficient of x when the equation is expressed in the form; y = m·x + c.

Therefore, from -2·x + 3·y = 6, we have;

3·y = 2·x + 6

[tex]y = \dfrac{2}{3} \cdot x + \dfrac{6}{3} = \dfrac{2}{3} \cdot x + 2[/tex]

[tex]y =\dfrac{2}{3} \cdot x + 2[/tex]

[tex]\underline{The \ slope \ of \ the \ first \ equation \ is \ \dfrac{2}{3}}[/tex]

Required:

The slope of the second line;

Solution:

The equation of the second line, -4·x + 6·y = 12, can be expressed in the form;

[tex]y =\dfrac{4}{6} \cdot x + \dfrac{12}{6} = \dfrac{2}{3} \cdot x + 2[/tex]

[tex]y = \mathbf{\dfrac{2}{3} \cdot x + 2}[/tex]

[tex]\underline{The \ slope \ of \ the \ second \ equation \ is \ therefore \ \dfrac{2}{3}}[/tex]

The y-intercept of the first line = 2The y-intercept of the second line = 2

Given that the equation have the same slope and the same y-intercept, the equations are equations of the same line, therefore;

The equations have an infinite number of solutions

Learn more about the solutions of a system of equations here:

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Related Questions

Jane exchanged £100 for 216 Swiss francs. After buying a meal and a present to take home,she had 70 francs left.How much is this in £?​

Answers

Answer:

£32.4

Step-by-step explanation:

£100 = 216 Swiss francs

x        =  70 francs

70 x 100=7000/216=32.4

I need help!!! Please Help!!​

Answers

Answer:

Step-by-step explanation:

If you aren't supposed to do this on your calculator, then you'd have to figure out a way to get the bases of 10 to have the same power somehow in order to use the properties of exponents. This is the problem (you multiply the 2 dimensions together to find area, remember):

[tex](5.5*10^5)(4.2*10^4)[/tex]You cannot simply add the exponents on the 10's and say your power is 9...cuz it's not. It needs to be rewritten so that there is a power of 4 on the 10 in the parenthesis on the left. Do that this way:

[tex](5.5*10^4*10^1)(4.2*10^4)[/tex] Now you've got a common power of 4 between the 2 sets of parenthesis. 10 to the first is the same as 10, so multiplying that into the 5.5 gives us

[tex](55*10^4)(4.2*10^4)[/tex]

55 * 4.2 is 231 and 10 to the 4th times 10 to the 4th is 10 to the 8th.

[tex]231*10^8[/tex] But that's not in correct scientific notation. If we move the decimal to places to the left, we have to add 2 to the exponent of 8, giving us, finally,

[tex]2.31*10^{10}m^2[/tex]

Next use the hint to convert that to kilometers:

[tex]2.31*10^{10}m^2*\frac{1km^2}{1*10^6m^2}[/tex]

Dividing like bases means we subtract the lower exponent from the upper. 10 - 6 = 4, so the equivalent number of km squared is

2.31 × 10⁴ km²

Kilometers are comparable to miles, which is how we measure large things, like pieces of land. So it would be better to measure the forest in kilometers squared instead of meters squared.

The graph of f(x) = 2x3 – 19x2 + 57x – 54 is shown below.

On a coordinate plane, a graph of a function is in quadrants 1 and 4. The function goes through the x-axis at (2, 0), (3, ), and (4.5, 0).

How many roots of f(x) are rational numbers?
0
1
2
3
Mark this and return

Answers

Answer:

it'd be 3! :)

Step-by-step explanation:

took quiz

to be sure, the graph goes like

/ ,  then a hill like shape, then goes U, and then goes up

The number of rational roots of the equation are 3.

What is the root of an equation?

The root of an equation are the solutions to an equation. The equation as shown is a cubic equation hence will have three roots shows as  (2, 0), (3, 0), and (4.5, 0).

It thus implies from the foregoing that the number of rational roots of the equation are 3.

Learn more about root of an equation:https://brainly.com/question/12029673

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Please help me with this question.

Answers

Answer:

75% (I think)

Step-by-step explanation:

1/4 of babies have no hair

2/4 of babies have little hair

1/4 of babies have a lot of hair

Miguel is playing a game in which a box contains four chips with numbers written on them. Two of the chips have the number 1, one chip has the number 3, and the other chip has the number 5. Miguel must choose two chips, and if both chips have the same number, he wins $2. If the two chips he chooses have different numbers, he loses $1 (–$1).

Let X = the amount of money Miguel will receive or owe. Fill out the missing values in the table. (Hint: The total possible outcomes are six because there are four chips and you are choosing two of them.)





Answers

Answer:

[tex]P(X_i=2) =\dfrac{1}{6}[/tex]

[tex]P(X_i=-1) =\dfrac{5}{6}[/tex]

Step-by-step explanation:

Given the numbers on the chips = 1, 1, 3 and 5

Miguel chooses two chips.

Condition of winning: Both the chips are same i.e. 1 and 1 are chosen.

Miguel gets $2 on winning and loses $1 on getting different numbers.

To find:

Probability of winning $2 and losing $1 respectively.

Solution:

Here, we are given 4 numbers 1, 1, 3 and 5 out of which 2 numbers are to be chosen.

This is a simple selection problem.

The total number of ways of selecting r numbers from n is given as:

[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]

Here, n = 4 and r = 2.

So, total number of ways = [tex]_4C_2 = \frac{4!}{2!\times 2!} = 6[/tex]

Total number of favorable cases in winning = choosing two 1's from two 1's i.e. [tex]_2C_2 = \frac{2!}{2! 0! } = 1[/tex]

Now, let us have a look at the formula of probability of an event E:

[tex]P(E) = \dfrac{\text{Number of favorable ways}}{\text{Total number of ways}}[/tex]

So, the probability of winning.

[tex]P(X_i=2) =\dfrac{1}{6}[/tex]

Total number of favorable cases for -1: (6-1) = 5

So, probability of getting -1:

[tex]P(X_i=-1) =\dfrac{5}{6}[/tex]

Please refer to the attached image for answer table.

Answer:

two = 1/6

and -1 =  5/6

Step-by-step explanation:

if x= y^2/y^3 +1, what is the value of y in terms of x?

Answers

Answer:

1/(x-1)

Step-by-step explanation:

here,x=y^2/y^3 +1

x-1=y^2-3

x-1=y^-1

y=1/(x-1)

So, the value of y in terms of x is 1/(x-1)

I Hope this will be helpful for you

Find the value of f(-1)g(-1)

Answers

Answer:

  4

Step-by-step explanation:

f(-1) = (-1)^2 +1 = 1 + 1 = 2

g(-1) = 3(-1) +5 = -3 +5 = 2

f(-1)g(-1) = (2)(2) = 4

Which sign makes the statement true?
11
20
? 61%
>
<
Submit
ASAP

Answers

11/20 < 61%

11/20 =.55
61% = .61
.55<.61

find the value of x in the triangle shown below ​

Answers

Answer:

46°

Step-by-step explanation:

We can tell that this triangle is an isosceles triangle because 2 of it's sides are the same, therefore, two of it's angles are the same.

Looking at it, we can assume that the two angles not defined (x and the other one) are the two angles that are the same because they look similar.

Now, the angles of all triangles add up to 180°. So, we can subtract 88° from 180 to see what the two angles add up to.

[tex]180-88=92[/tex]

So both of these angles add up to 92 degrees. Since there are two, we divide 92 by 2.

[tex]92 \div 2 = 46[/tex]

Hope this helped!

Jeff's sister drives 14 miles to her collage his brother only drives 5/7/10 miles to his collage how much farther does Jeff's sister drive than his brother

Answers

Answer:

8.3miles

Step-by-step explanation:

Here Jeff's sister drives 14 miles

his brother only drives 57/10 miles then the question is only asking the difference between their distance of driving to school knowing fully well that Jeff's sister drive farther than his brother, then we find the difference between their drives which is done bow

14miles -57/10 miles

= 83/10

= 8.3miles

Therefore, Jeff's sister drive 8.3miles farther than his brother

what is the initial value for g(x) = 3(1/4)^(x-2) - 3

Answers

Answer: g(1) = 9

Step-by-step explanation:

g(x) = 3(1/4)^(x-2) - 3

g(1) = 3(1/4)^(1-2) - 3

g(1) = 3(1/4)^(-1) - 3

g(1) = 3(4) - 3

g(1) = 12 - 3

g(1) = 9

Hope is the coach of the Wilson High School girls' soccer team. There are 3 minutes left in the game they are currently playing, and they are losing by 1 goal. In the past, when losing by 1 goal, Hope has pulled a defender out of the game and replaced her with a forward a total of 9 times. When in the same position, she has left the defender in the game 10 times. In the situations when Hope has pulled her defender, the team has lost 4 times, tied 2 times, and won 3 times. In situations when she has left her defender in the game, the team has lost 1 time, tied 3 times, and won 6 times. Based on the information above, if the goal is to either tie or win the game, should Hope pull the defender or leave her in the game?

Answers

Answer:

Hope should not pull her defender.

Step-by-step explanation:

When Hope has pulled her defender:

The team had lost 4 times, tied 2 times, and won 3 times.

Hence, the total number of times she meets her goal is:

6 times (Since the goal is to either tie or win the game )

Hence, the probability that she meets her goal is =   6/9=2/3=0.66

When she  left her defender in the game:

The team has lost 1 time, tied 3 times, and won 6 times.

Hence, the total number of times she meets her goal is: 9

Hence, the probability that she meets her goal is: 9/10=0.9

As the probability of meeting her goal is more when she left her defender in the game is more.

 Hence, Hope should not pull her defender.

Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions: 2ab-6a+5b+___ Please include an explanation too!

Answers

Answer:

[tex]2ab - 6a + 5b - 15[/tex]

Step-by-step explanation:

Given

[tex]2ab - 6a + 5b + \_[/tex]

Required

Fill in the gap to produce the product of linear expressions

[tex]2ab - 6a + 5b + \_[/tex]

Split to 2

[tex](2ab - 6a) + (5b + \_)[/tex]

Factorize the first bracket

[tex]2a(b - 3) + (5b + \_)[/tex]

Represent the _ with X

[tex]2a(b - 3) + (5b + X)[/tex]

Factorize the second bracket

[tex]2a(b - 3) + 5(b + \frac{X}{5})[/tex]

To result in a linear expression, then the following condition must be satisfied;

[tex]b - 3 = b + \frac{X}{5}[/tex]

Subtract b from both sides

[tex]b - b- 3 = b - b+ \frac{X}{5}[/tex]

[tex]- 3 = \frac{X}{5}[/tex]

Multiply both sides by 5

[tex]- 3 * 5 = \frac{X}{5} * 5[/tex]

[tex]X = -15[/tex]

Substitute -15 for X in [tex]2a(b - 3) + 5(b + \frac{X}{5})[/tex]

[tex]2a(b - 3) + 5(b + \frac{-15}{5})[/tex]

[tex]2a(b - 3) + 5(b - \frac{15}{5})[/tex]

[tex]2a(b - 3) + 5(b - 3)[/tex]

[tex](2a + 5)(b - 3)[/tex]

The two linear expressions are [tex](2a+ 5)[/tex] and [tex](b - 3)[/tex]

Their product will result in [tex]2ab - 6a + 5b - 15[/tex]

Hence, the constant is -15

Which of the points listed is the same distance from the y-axis as the point (−4, 7.5)?


Answers

Answer:

(-4, y) and (4, y), where y is any real number.

Step-by-step explanation:

The point (-4; 7.5) is 4 units from the y axis.

All points that lie on the line x = -4 and the line x = 4 have the same distance from the y-axis of 4 units.

Which of the following is the product of the rational expressions shown
below?

Answers

Answer:

The answer is b

Step-by-step explanation:

since 2*9=18 and (x)(2x+3)=2x^2+3x

Answer: B

Step-by-step explanation:

a box of tickets has an average of 100, and an SD of 20. Four hundred draws will be made at random with replacement from this box. a) Estimate the chance that the average of the draws will be in the range 80 to 120. b) estimate the chance that the average of the draws will be in the range 99 to 101

Answers

Answer:

(a) The probability that the average of the draws will be in the range 80 to 120 is 1.

(b) The probability that the average of the draws will be in the range 99 to 101 is 0.6827.

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.  

Then, the mean of the sample means is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the sample means is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

As the sample selected is quite large, i.e. n = 400 > 30, then the sampling distribution of sample means will be approximately normally distributed.

Compute the mean and standard deviation of sample mean as follows:

[tex]\mu_{\bar x}=\mu=100\\\\\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{20}{\sqrt{400}}=1[/tex]

So, [tex]\bar X\sim N(100, 1)[/tex]

(a)

Compute the probability that the average of the draws will be in the range 80 to 120 as follows:

[tex]P(80<\bar X<120)=P(\frac{80-100}{1}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{120-100}{1})[/tex]

                            [tex]=P(-20<Z<20)\\\\=P(Z<20)-P(Z<-20)\\\\=(\approx1)-(\approx0)\\\\=1[/tex]

Thus, the probability that the average of the draws will be in the range 80 to 120 is 1.

(b)

Compute the probability that the average of the draws will be in the range 99 to 101 as follows:

[tex]P(99<\bar X<101)=P(\frac{99-100}{1}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{101-100}{1})[/tex]

                            [tex]=P(-1<Z<1)\\\\=P(Z<1)-P(Z<-1)\\\\=0.6827[/tex]

Thus, the probability that the average of the draws will be in the range 99 to 101 is 0.6827.

Determine if the function is a polynomial function. If the function is a polynomial function, state the degree and leading coefficient. If the function is not a polynomial, state why. f(x)=x^4(2-x^3)+1

Answers

Answer:

The correct option is

This is a polynomial function of degree 7 with a leading coefficient of -1

Step-by-step explanation:

Functions that consist of a variable such as x raised to positive integer powers which are equal to or larger than zero added together to make the function are known as polynomial functions

Therefore, the function in the question which is f(X) = x⁴ × (2 - x³) + 1

Which can be expanded as follows

f(x) = 2·x⁴ - x⁷ + 1, which is the same as given as follow equation;

f(x) = -x⁷ + 2·x⁴ + 1

Which is  polynomial function with a leading coefficient of -1 as it consists of only whole number positive powers of x including the powers of x 4 and 7  

Therefore, the correct option is that f(x) is a polynomial function of degree 7 with a leading coefficient of -1.

6) Which expressions are equivalent to 12x + 36y? Choose ALL that apply.
12(x + 3y)
9(3x + 4y)
6(2x + 6y)
4(3x + 9y)
2(6x + 24y)
3(4x + 12y)

Answers

the 1st one

third one

fourth one

the last one

each of the equation has one of the common factor out

12(x + 3y),  6(2x + 6y),  4(3x + 9y) and 3(4x + 12y) are the equivalent expressions of 12x + 36y.

What is Expression?

An expression is combination of variables, numbers and operators.

Equivalent expressions are expressions that work the same even though they look different.

The given expression is 12x + 36y.

Twelve times of x plus thirty six times of y.

When we solve each expression we have to get 12x + 36y.

1. 12(x + 3y)- Equivalent expression

By distributive property

=12x+36y

2. 9(3x + 4y)- Not Equivalent expression.

27x+36y

3. 6(2x + 6y)- Equivalent expression

12x+36y

4. 4(3x + 9y)-Equivalent expression

5. 2(6x + 24y)- Not Equivalent expression.

12x+48y

6. 3(4x + 12y)-Equivalent expression

12x+36y

Hence, 12(x + 3y),  6(2x + 6y),  4(3x + 9y) and 3(4x + 12y) are the equivalent expressions of 12x + 36y.

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using the order of operations, which operation should be performed first? 3(7+2²) - 5 A:7+ 2 B: 2² C: 3 x 7 and 3 x 2 D: 11 - 5

Answers

Answer:

B: 2²

Step-by-step explanation:

3(7+2²) - 5

PEMDAS says parentheses first

Then we do the order of operations inside the parentheses

Exponents are the first thing inside the parentheses

Which relation is a function of x? {(1, 2), (7, 6), (3, 2), (1, 0), (5, 6)} A 2-column table with 4 rows. Column 1 is labeled x with entries 0, 0, 0, 0. Column 2 is labeled y with entries 2, negative 6, 9, negative 7. x = 3 y squared minus 7 On a coordinate plane, a graph curves up, then curves down, and then curves up again. please comment i cant see answers thank you! :)

Answers

Answer: The answer is D . The graph

Step-by-step explanation: It was the answer given on Edge.

Answer:

d

Step-by-step explanation:

A line contains the points (3,1) and (−6,4). A line contains the points (3,1) and (−6,4). What is the equation for this line in slop-intercept form? What is the equation for this line in slop-intercept form?

Answers

Answer:

y = -1/3 x + 2

Step-by-step explanation:

The equation of  a line in slope-intercept form is expressed as y = mx+c

m is the slope of the line

c is the intercept

m = Δy/Δx = y₂-y₁/x₂-x₁

Given the points on a line to be  (3,1) and (−6,4);

x₁ = 3, y₁ = 1, x₂ = -6 and y₂ = 4

m = 4-1/-6-3

m = 3/-9

m = -1/3

To get the intercept c, we will substitute any of the points given and the value of the slope into the equation y = mx+c. Using the point (3, 1) and m = -1/3

1 = -1/3(3)+c

1 = -1+c

c  = 1+1

c =2

Substituting m = -1/3 and c = 2 into the sllpe intercept form of the equation will give;

y = -1/3 x + 2

Hence the  equation for the line in slope-intercept form is y = -1/3 x + 2

What is 3.41 (where the .41 is repeating) written as a fraction?
Please help!!

Answers

Answer:

41/99

Step-by-step explanation:

There are two types of non terminating decimals. These are: Simple and Mixed

The one that you wrote up here is Simple, Since 41 is the only number that goes on repeating itself.

And mixed non terminating decimal is like 0.352 whereas 52 keeps repeating itself.

So when you change a non terminating decimal the denominator is always 9. But it depends on the decimal whether it is simple or mixed.

Since the decimal you wrote is simple and 2 digits keep on repeating themselves the denominator will be 99.

And the numerator will be the decimal number that keeps repeating itself without the repeating bar.

Therefore, the answer is 41/99.

Hope it helps ;) ❤❤❤

Please help me i give 40 points and five more to who say me the answers

Answers

Answer:

Step-by-step explanation:

A frequency table can be used to group a raw data. It shows the quantity of each variable in the data.

The required answers to the question can be found in the attachments to this answer.

At a central train station, there are 4 different train routes with trains that leave every 6 minutes, 10 minutes, 12 minutes, and 15 minutes. If each train can hold up to 200 passengers, what is the maximum number of passengers who can leave the station on a train in one hour?

Answers

Answer:

5,000 passengers

Step-by-step explanation:

1. Find out how many trains leave each hour.

6 min – 60/6 = 10 x 200 passengers = 2000

10 min – 60/10 = 6 x 200 passengers = 1200

12 min – 60/12 = 5 x 200 passengers = 1000

15 min – 60/15 = 4 x 200 passengers = 800

2. Add it all up.

2000 + 1200 + 1000 + 800 = 5000 passengers

Answer:

5000

Step-by-step explanation:

6 minute train leaves 10 times

10 x 200 = 2000 passengers

10 minute train leaves 6 times

6x200 = 1200

12 minute train leaves 5 times

5x200 =1000

15 minute train leaves 4 times

4x200 =800

2000+1200+1000+800=5000

assuming more than 1 train can be at the station at once

A group conducted a poll of 2022


likely voters just prior to an election. The results of the survey indicated that candidate A would receive 49

​%

of the popular vote and candidate B would receive 46

​%

of the popular vote. The margin of error was reported to be 5

​%.

The group reported that the race was too close to call. Use the concept of a confidence interval to explain what this means.

Answers

Answer:

Step-by-step explanation:

number of likely voters = 2022

candidate A = 49%

candidate B = 46%

margin of error = 5%

using the concept of a confidence interval to explain

from the result of the poll conducted candidate A scored 49% of the votes while Candidate B scored 46% therefore the difference between the two voters is 3%.

also the margin of error is 5% which is higher than the 3% difference between the candidates. this margin error means that the 5% can vote for either candidate A or candidate B .which makes the results TOO CLOSE TO CALL




pls help !!!! i do not know or understand this at all

Answers

Answer:

(3, -3)

Step-by-step explanation:

Given functions:

f(x)= x² - 5x + 3

and

f(x)= -3

Solution is the Intersect which is found by equalizing the two functions:

x² - 5x + 3= -3

Solving for x:

x² - 5x + 6=0x² - 2x -(3x -6) =0x(x-2) - 3(x-2)=0(x-2)(x-3)= 0x= 2 and x= 3

As both values of x for the first function reveal f(x) = -3, the pairs are:

(2, -3) and (3, -3)

Which values for h and k are used to write the function f of x = x squared + 12 x + 6 in vertex form?

h=6, k=36
h=−6, k=−36
h=6, k=30
h=−6, k=−30

Answers

Answer:

h=−6, k=−30

Step-by-step explanation:

did on edge

Considering the equation of the parabola, the coefficients of the vertex are:

h=−6, k=−30

What is the vertex of a quadratic equation?

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](h,k)[/tex]

In which:

[tex]h = -\frac{b}{2a}[/tex]

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

In this problem, the equation is:

[tex]f(x) = x^2 + 12x + 6[/tex]

Hence the coefficients are a = 1, b = 12, c = 6, thus:

[tex]h = -\frac{12}{2} = -6[/tex]

[tex]k = -\frac{120}{4} = -30[/tex]

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PLEASE HELP I WILL REWARD BRAINLY. PLEASE ONLY ANSWER IF YOU KNOW HOW TO SOLVE THIS PROBLEM. PLEASE INCLUDE INSIGHTFUL EXPLAINATION AND THOUGHT PROCESS: A woman and her two children are playing on a seesaw. This seesaw has seats that can move to different distances from the fulcrum. Riders can also add seats to the seesaw. The woman weighs 145lb, her son weighs 95lb, her daughter weighs 70lb, each seat weighs 5 pounds. Question: The woman is on the left side of the seesaw, 60 inches from the fulcrum. The daughter and son both get on the right side. The son sits 60 inches from the fulcrum. Where should the daughter sit to balance the seesaw. Please explain your process and give correct answer.

Answers

Answer: 40 inches

Step-by-step explanation:

The woman weight and the seat will be: 145lb + 5lb = 150lb,

her son weight and the seat will be: 95lb + 5lb = 100lb

her daughter weight and the seat will be: 70lb + 5lb = 75lb

Given that the woman is on the left side of the seesaw, 60 inches from the fulcrum. The moment of the woman will be 150 × 60 = 9000

The daughter and son both get on the right side.

If the son sits 60 inches from the fulcrum, his moment will be:

100 × 60 = 6000

The sum of the moment of the son and daughter must be equal to the moment of their mother.

Let the position of the daughter = X

The moment of the daughter will be:

75 × X = 75X

Equate the moment of the mother to the sum of the moment of her children

9000 = 6000 + 75X

Collect the like terms

75X = 9000 - 6000

75X = 3000

X = 3000/75

X = 40

The position the daughter should sit to balance the seesaw is 40 inches away from seasaw to the right.

what is the value of y in the figure below? (Picture provided)

Answers

Since it is a 30, 60, 90 triangle theN y would be 7.
30 degrees= x
60 degrees= x root 3
90 degrees= 2x
In this case since you know 90 degrees is 14 then you would have to find c which is 7 when you divide it by 2

factor the equation using zero product property. x2+7x=-6

Answers

Answer:

x = -6    x = -1

Step-by-step explanation:

We want to solve using the zero product property

x^2+7x=-6

Add 6 to each side

x^2 +7x +6 = 0

Factor

What 2 numbers multiply to 6 and add to 7

( x+6) (x+1) =0

Using the zero product property

x+6 =0          x+1 =0

x+6-6 =0-6    x+1-1 = 0-1

x = -6    x = -1

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