What is the equation of the line of the best fit for the following data? Round to the slope and y-intercept of the line to three decimal places

The correct answer is option 1: x = -4y+19

Step-by-step explanation:

Given equations are:

[tex]3x+2y=17\ \ \ Eqn1\\x+4y=19\ \ \ \ Eqn2[/tex]

When we have to solve a system of equations using substitution method we look for a variable in both of equations that is without any co-efficient as it is easy to isolate that variable in the equation and then using substitution method to solve it

We can see that in equation 2, x is without any co-efficient

So,

[tex]x+4y = 19[/tex]

Subtracting 4y from both sides

[tex]x+4y-4y = 19-4y\\x = 19-4y\\[/tex]

Can also be written as:

[tex]x = -4y+19[/tex]

Hence,

The correct answer is option 1: x = -4y+19

Keywords: Linear equations, variables

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Answer:

The correct answer is option 1: x = -4y+19

Step-by-step explanation:

The equation y=0.02x+250 gives the weekly income y in terms of sales x.

Step-by-step explanation:

Given,

Weekly salary of real estate agent = $250

Commission rate = 2%

Let,

x be the sales per week.

y be the total weekly income.

Amount of commission = 2% of sales per week

Amount of commission = [tex]\frac{2}{100}*x[/tex]

Amount of commission = 0.02x

Total weekly income = Amount of commission + Weekly salary

[tex]y=0.02x+250[/tex]

The equation y=0.02x+250 gives the weekly income y in terms of sales x.

Keywords: equation, percentage

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The weekly income y of a real estate agent can be calculated using the equation y = 250 + 0.02x where 'y' is the weekly income, 'x' is the sales amount, '250' is the fixed salary and '0.02x' is the commission on sales.

The weekly income y of a real estate agent is comprised of a fixed salary and a variable part which is a commission based on the amount of sales done. Given the fixed salary is $250 and the commission is 2% of sales, we can represent this as a mathematical equation:

y = 250 + 0.02x

Here, 'y' represents the weekly income, 'x' represents the amount of sales and '250' is the fixed salary. The term '0.02x' is the 2% commission of sales. So, for a given sales amount 'x', the weekly income 'y' can be computed using this equation.

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The number Fred thinks of is 111

Solution:

Given that, Fred thinks of a number that is greater than 110 and less than 120

He can make his number with same number of hundreds,tens and ones

To find: Fred's number

Given that the number is greater than 110 and less than 120

The possible numbers are:

111 , 112, 113, 114, 115, 116, 117, 118, 119

But he can make his number with same number of hundreds,tens and ones

So the numbers in ones, tens and hundreds place are same

So the only possible number is 111

Thus the number Fred thinks of is 111

Final answer:

Fred's number is 111, as it is the only number that is greater than 110 and less than 120 and has the same number of hundreds, tens, and ones.

Explanation:

The number Fred thinks of must be greater than 110 and less than 120. Additionally, it must have the same number of hundreds, tens, and ones. To meet these conditions, the only number that fulfills this is 111. This is because it's the only number between 110 and 120 that has the same digit in the hundreds, tens, and ones place.

Fred's number is unique in this range because it is represented with three identical digits, showcasing an interesting property of numbers in our base-ten system where a digit's value depends on its position. Hence, 111 is the number Fred is thinking of, which consists of one hundred, one ten, and one one.

Answer:

T_12 = 5(T_3)

Step-by-step explanation

T_17 = 13(T_2)

T_n = a + (n-1)d; where a=first term and d=common difference

T_17 = a + 16d

T_2 = a + d

Therefore,

a + 16d = 13(a + d)

a + 16d = 13a + 13d

16d - 13d = 13a - a

3d = 12a

d = 4a

To prove that T_12 = 5(T_3)

a + 11d = 5(a + 2d)

a + 11d = 5a + 10d

since d = 4a

a + 11(4a) = 5a + 10(4a)

a + 44a = 5a + 40a

45a = 45a

Since  LHS = RHS

Therefore; T_12 = 5(T_3)

Answer:

Step-by-step explanation:

First, parallel lines have the same slope, so the slopes should be the same , and then you use the given point to find the y intercept

EX:

y=x+1

find equation of line the is parallel and passes through (1, 1)

Same slope, so y=x+b

then plug in the point

1=1+b

b=0

our line would be y=x

To write the equation of a line when you know a point on the line and have the equation of a line parallel to it, use the point-slope form of a linear equation. Substitute the values and simplify to get the equation.

To write the equation of a line when you know a point on the line and have the equation of a line parallel to it, you can use the point-slope form of a linear equation. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is the known point and m is the slope of the parallel line. Substitute the values into the equation and simplify to get the equation of the line.

For example, if you know a point on the line is (2, 5) and you have the equation of a line parallel to it as y = 2x + 3, the slope of the parallel line is 2. Substitute the values of the known point and the slope into the point-slope form: y - 5 = 2(x - 2). Simplify the equation to get the equation of the line: y - 5 = 2x - 4.

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Answer:

3 cases

Step-by-step explanation:

Total Money Needed = $850

Each Golf Ball = $2

Total Balls needed = 850/2 = 425 balls

Case = 24 Pack

Pack = 6 balls

So a Case has:

24 * 6 = 144 balls

They need 425 balls to sell and each case has 144 balls, so number of case needed would be:

425/144 = 2.95

We can't have 2.95 cases, so we round up to 3 cases

Answer:

8,535,300

Step-by-step explanation:

the answer is 41,464,700 + 8,535,300 = 50,000,000

Answer:

2/3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(5-3)/(4-1)

m=2/3

Answer:

First of all, before writing the y-intercept you need to make sure that the equation is in slope intercept form.

x + 3y = 14

3y = 14 - x

y = 14/3 -x/3

y= -x/3 + 14/3

                         14/3 is the y-intercept

The y-intercept of the line with equation x + 3y = 14 is 4.67.

The equation of the line is in the form x + 3y = 14. To find the y-intercept, we need to set x = 0 and solve for y. Plugging in x = 0, we get 0 + 3y = 14. Simplifying the equation gives us 3y = 14. Dividing both sides by 3, we find that y = 4.67. Therefore, the y-intercept of the line is 4.67.

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Answer:

1/3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(3/4-2)/(1-19/4)

m=(3/4-8/4)/(4/4-19/4)

m=(-5/4)/(-15/4)

m=(-5/4)(-4/15)

m=20/60

m=2/6

m=1/3

Answer:

1/3

Step-by-step explanation:

Answer:

3x6+7x4=46 it’s correct

we can rewrite it this way : (3x6)+(7x4)=46

Answer:

[tex]\large\boxed{(h\circ g)(x)=6x-16}[/tex]

Step-by-step explanation:

[tex]h(x)=3x-1\\\\g(x)=2x-4\\\\(h\circ g)(x)=h\bigg(g(x)\bigg)\\\\\text{Substitute instead of x the expression (2x - 4) to h (x):}\\\\(h\circ g)(x)=3(2x-4)-4\qquad\text{use the distributive property}\\\\(h\circ g)(x)=(3)(2x)+(3)(-4)-4\\\\(h\circ g)(x)=6x-12-4\\\\(h\circ g)(x)=6x-16[/tex]

Answer:

75%

Step-by-step explanation:

42/56 = [tex]\frac{42}{56}[/tex]

Convert to decimal form:

42÷56 = 0.75

= 75%

Darren got 75% of the questions correct on his test, as 42 out of 56 simplifies to 3/4 or 75%. This percentage might place him in a higher percentile, indicating good performance.

Darren scored 42 out of 56 questions correctly on his test. To find what percent of the questions he got correct, you set up a fraction of correct answers over the total number of questions and then convert it to a percentage. The fraction for Darren's test is 42/56, which simplifies to 3/4 or 0.75 when divided. To convert this to a percentage, you multiply by 100, giving Darren a score of 75% correct on his test.

Some students might be interested in how this compares to percentile ranks. For example, if the 70th percentile for a test is 16 correct answers out of 20, this means that 70% of the students answered 16 or fewer questions correctly. Darren's score of 75% would likely place him in a higher percentile since he got a larger proportion of the questions correct, which is generally considered good.

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45 adult tickets and 80 children tickets were sold

Solution:

Let "a" be the number of adult tickets sold

Let "c" be the number of children tickets sold

Cost of 1 adult ticket = $ 6

Cost of 1 children ticket = $ 3.50

They sold a total of 125 tickets

Therefore,

a + c = 125

c = 125 - a --------- eqn 1

They made a total of $550. Therefore, frame a equation as:

number of adult tickets sold x Cost of 1 adult ticket + number of children tickets sold x Cost of 1 children ticket = 550

[tex]a \times 6 + c \times 3.50 = 550\\[/tex]

6a + 3.50c = 550 ----------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

6a + 3.50(125 - a) = 550

6a + 437.5 - 3.50a = 550

2.5a = 112.5

Substitute a = 45 in eqn 1

c = 125 - 45

Thus 45 adult tickets and 80 children tickets were sold

Answer:

[tex]DC=\frac{8}{3}\ units[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The triangle ABD is an isosceles triangle

because

AB=BD

The segment BM is a perpendicular bisector segment AD

so

In the right triangle ABM

Applying the Pythagorean Theorem

[tex]BM^2=AB^2-AM^2[/tex]

we have

[tex]AB=5\ units\\AM=x\ units[/tex]

substitute

[tex]BM^2=5^2-x^2[/tex]

[tex]BM^2=25-x^2[/tex] -----> equation A

In the right triangle BMC

Applying the Pythagorean Theorem

[tex]BM^2=BC^2-MC^2[/tex]

we have

[tex]BC=7\ units\\MC=AC-AM=(9-x)\ units[/tex]

substitute

[tex]BM^2=7^2-(9-x)^2[/tex]

[tex]BM^2=49-(81-18x+x^2)[/tex]  

[tex]BM^2=49-81+18x-x^2[/tex]

[tex]BM^2=-x^2+18x-32[/tex] ----> equation B

equate equation A and equation B

[tex]-x^2+18x-32=25-x^2[/tex]

solve for x

[tex]18x=25+32\\18x=57\\\\x=\frac{57}{18}[/tex]

Simplify

[tex]x=\frac{19}{6}[/tex]

Find the length of DC

[tex]DC=AC-2x[/tex]

substitute the given values

[tex]DC=9-2(\frac{19}{6})[/tex]

[tex]DC=9-\frac{19}{3}\\\\DC=\frac{8}{3}\ units[/tex]

Given AB = 4x + 5, BC = 3x - 2 and AC 9x -5

The sum of the length of any two sides of a triangle is greater than the length of third side.

Case I

AB + BC > AC

⇔4x +5 +3x -2 > 9x -5

⇔7x + 3 >9x - 5

⇔ 7x -9x > -5 -3

⇔-2x > -8

⇔x <4

Case II

if AB+AC > BC

4x +5 +9x -5> 3x -2

⇔13x >3x -2

⇔ 13x -3x> -2

⇔10x > -2

⇔x >[tex]-\frac{1}{5}[/tex]

Case III

AC+BC > AB

⇔9x - 5 +3x - 2 > 4x +5

⇔6x -7 > 4x +5

⇔6x -4x >5+7

⇔2x > 12

⇔x > 6

Answer: a. 10%

Step-by-step explanation:

Girls in the class = 40%

Girls play tennis = 25%

Percentage of class play tennis = 40%*25% = 0.4*0.25 = 0.1

Percentage of class play tennis = 10%

The percentage of the class that plays tennis is 70%.

The percentage means the required value out of 100.

It is calculated by dividing the required value by the total value and multiplying by 100.

The percentage change is also calculated using the same method.

In percentage change we find the difference between the values given.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We

If 40% of a class is girls, then 60% of the class must be boys.

Let's say there are 100 students in the class, so 40 of them are girls, and 60 are boys.

If 25% of the girls play tennis, that means 25% of 40, which is 10 girls, play tennis.

Therefore, the total number of students who play tennis is 10 girls + some number of boys.

We don't know how many boys play tennis, but we can find out what percentage of the whole class plays tennis by dividing the total number of tennis players by the total number of students:

(10 girls + X boys) / 100 total students

We know that 40% of the class is girls, so:

X boys = 60% of 100 total students = 60 students

So the total number of students who play tennis is:

10 girls + 60 boys = 70 students

And the percentage of the class that plays tennis is:

70 students / 100 total students = 70%

Therefore,

The percentage of the class that plays tennis is 70%.

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Answer: m = 1

Step-by-step explanation: Use the slope formula to find the slope m.

Hope this helps you out! ☺

Answer:

m = 1

Step-by-step explanation:

refer to attached picture for reference

we are given 2 points

(x₁, y₁)  = (5,7)

(x₂,y₂) = (-4,-2)

simply substitute these into the given equation for slope

m = (y₂ - y₁)/(x₂-x₁)

= (-2 -7) / (-4 - 5)

= -9 / -9

= 1

Answer:

you need 4 1/3 cups of flower

Answer:

the probability answer will be 8/49.

Step-by-step explanation:

the answer probability would be equal to multiplication of the odd cases of the given probabilities.Therefore,for him to playin both the halves of the game would be 8/49.

Using Bayesian probability, we find that the probability of Patrick playing in the first half given that he played in the second half is 3/4 or 75%.

This was determined by calculating intermediate probabilities and applying Bayes' theorem.

Therefore, the probability that Patrick played in the first half given that he played in the second half is 3/4 or 75%.

Answer:

$3,750

Step-by-step explanation:

1.5% of 250,000 is 3,750

The question does NOT ask for the total price. It is just asking for commission.

Answer:

it’s 92 on edge

Step-by-step explanation:

Answer:

5.8

Step-by-step explanation:

Answer:

Step-by-step explanation:

he has 120 bucks...burritos are 6 and sodas are 4

the largest number of burritos a person can afford to purchase....

120/6 = 20....he can purchase 20 burritos....but then he doesn't get any soda because thats gonna take all his money

The largest number of burritos a person can afford to purchase is 20.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

It is given that:-

The largest number of burritos a person can afford to purchase:-

120  /  6  =  20.

He can purchase 20 burritos....but then he doesn't get any soda because that's gonna take all his money.

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Answer:

see explanation

Step-by-step explanation:

To find the terms of the sequence substitute n = 1, 2, 3, 4, 10 into the rule.

n = 1 → 2(1)² = 2(1) = 2

n = 2 → 2(2)² = 2(4) = 8

n = 3 → 2(3)² = 2(9) = 18

n = 4 → 2(4)² = 2(16) = 32

n = 10 → 2(10)² = 2(100) = 200

The first 4 terms are 1, 8, 18, 32 and the 10 th term is 200

Answer:

2, 8, 18, 32.

10th term =  200.

Step-by-step explanation:

The first 4 terms of 2n^2 are

2(1)^2,  2(2)^2,   2(3)^2, 2(4)^2

= 2, 2*4, 2*9, 2*16

= 2, 8, 18, 32.

The 10th term = 2(10)^2

= 200.

Answer:

The solved expression is [tex]x=3+\sqrt{2}[/tex] and [tex]x=3-\sqrt{2}[/tex]

Therefore [tex]x=3\pm\sqrt{2}[/tex]

Step-by-step explanation:

Given quadratic equation is [tex]x^2-6x+7=0[/tex]

To solve the given equation by using completing the square :

[tex]x^2-6x+7=0[/tex]

Rewritting the above equation as below :

[tex]x^2-6x+7+2-2=0[/tex]

[tex](x^2-6x+7+2)-2=0[/tex]

[tex](x^2-6x+9)-2=0[/tex]

[tex](x^2-6x+3^2)-2=0[/tex]

[tex](x^2-2(x)(3)+3^2)-2=0[/tex]  ( it is of the form of [tex](a-b)^2=a^2-2ab+b^2[/tex]  heere a=x and b=3 )

[tex](x-3)^2-2=0[/tex]

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

Taking square root on both sides we get

[tex]\sqrt{(x-3)^2}=\pm\sqrt{2}[/tex]

[tex]x-3=\pm\sqrt{2}[/tex]

[tex]x=\pm\sqrt{2}+3[/tex]

[tex]x=3\pm\sqrt{2}[/tex]

Therefore [tex]x=3+\sqrt{2}[/tex] and [tex]x=3-\sqrt{2}[/tex]

Answer:

y=ax+b

Step-by-step explanation:

i got it right on TTM

Answer:

C

Step-by-step explanation: