standard to slope intercept form

From the given parameter, the total amount that Lou spent on the gas is; $30.8

We are told that Lou​'s car had 6.2 gallons in the 15 gallons in the ​-gallon tank on the coldest day of the year.

Now, Lou filled the tank with gas that cost ​$ 3.50 per gallon.

Thus;

Amount of gas that Lou bought = 15 - 6.2

Amount of gas that Lou bought = 8.8 gallons

Since he bought these gallons at the cost of ​$3.50 per gallon, then it means that;

Total amount he spent = 8.8 * 3.5

Total amount he spent = $30.8

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Complete question is;

Some people advise that in very cold​ weather, you should keep the gas tank in your car more than half full. Some people advise that in very cold​ weather, you should keep the gas tank in your car more than half full. Lou​'s car had 6.2 gallons in the 15 gallons in the ​-gallon tank on the coldest day of the year.

Lou filled the tank with gas that cost ​$ 3.50 per gallon. How much did Lou spend on​ gas?

Answer:

31cm

Step-by-step explanation:

Add AC and BC together to get AB.

AC = 2x - 13 and

BC = 3x + 4 and

AB = 36 (this is all the given information)

The two smaller pieces can be combined to equal the whole segment.

AC + BC = AB

2x - 13 + 3x + 4 = 36

combine like terms.

5x - 9 = 36

Add 9

5x = 45

Divide by 5.

x = 9

But you're not done because they asked for BC.

BC = 3x + 4

substitute 9 for x.

BC = 3(9) + 4

BC = 27 + 4

BC = 31

BC is 31 cm.

The greatest common divisor (24,6) is 6 and the least common multiple (24,6) is 24.

As per the question statement, the greatest common divisor of two integers is (x+2) and the least common multiple x(x+2). It is given that one of the integers is 24.

Let us assume that "b" is the value of other one.

greatest common divisor(24,b) = (x+2)

least common multiple(24,b) = x(x+2)

Formula:

greatest common divisor(24,b)*least common multiple(24,b) = 24*b

24*b = (x+2)*x(x+2)

[tex]b = \frac{x(x+2)^{2} }{24} \\[/tex]

Hence, the smallest possible value of the other one is "6" and x = 4.

Hence, the greatest common divisor (24,6) is 6 and the least common multiple (24,6) is 24.

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Answer:

310000000

That’s the answer

Answer:

Answer down below!

Step-by-step explanation:

We can tell from ABC and A'B'C' that they are similar, but not alike

Segment AC = 6 and segment A'C' =4

They just subtracted two from the 6

Let's do the same thing for segment BC!

If BC = 3, then we know that B'C' = 1

y=2/3x-3 that is the slope intercept form

After adding interest the sum would be worth $657.51 .

Interest is the amount paid over and above the original amount to a lender or depositor by a borrower or deposit-taking financial institution at a predetermined rate in the domains of finance and economics (the amount borrowed).

Interest when the principal is $5 , time is 100 years and rate is 5%.

We know that from compound interest:

Amount = principal (1 + rate)ⁿ

Therefore

Amount = 5 (1 +0.05)¹⁰⁰

Amount = $657.5062...

Amount ≈ $657.51

Therefore adding interest the sum would be worth $657.51

The probability of the random item chosen that it is less than 16.4 inches long is 2.7%

Probability means ?

The likelihood of an event happening is calculated using the probability formula. To review, probability is the probability that an event will occur. What is the likelihood that a specific event will occur when a random experiment is considered? is one of the first queries that pops into our heads. A prediction's chance is expressed as a probability. If we suppose that, for example, x represents the probability that an event will occur, then (1-x) is the probability that the event will not occur.

Variance of sample mean =1.3^2/1= 1.69

S D of sample mean =1.69^(1/2)= 1.3

Z score for length of 16.4 is( 16.4-15.4)/1.3= 0.7692307

The p value for -1.67 in standard normal table is 0.04746

The required probability =0.02764

Only 2.7% of the time will the sample mean be shorter than 16.4 inches.

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Answer:

21 cups oil

14 cups soy sauce

7 cups orange juice

Step-by-step explanation:

Use 1 cup for 1 part. The original recipe as given with its small amounts would make a total of 3 + 2 + 1 = 6 parts, or 6 cups of sauce.

You want to make 42 cups.

42/6 = 7

The amount you want to make is 7 times the amounts in the ratio.

3 parts oil: 3 × 7 = 21: 21 cups oil

2 parts soy sauce: 2 × 7 = 14: 14 cups soy sauce

1 part orange juice: 1 × 7 = 7: 7 cups orange juice

Check: 21 + 14 + 7 = 42

The amounts above do make 42 cups in total.

Answer:

21 cups oil

14 cups soy sauce

7 cups orange juice

The equivalent expression for the given expression is 0.4υ - 3ω - 9.

The given expression is 0.4υ - (3ω + 9).

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The equivalent expression for the given expression can be written as follows:

0.4υ - (3ω + 9)=0.4υ - 3ω - 9

Therefore, the equivalent expression for the given expression is 0.4υ - 3ω - 9.

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The least number of main courses that the restaurant should offer is 8.

The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.

let m be  the number of main courses restaurant serves

so, 2m is the number of appetizers  

then the number of dinner combination is =  2m x m x 3 = 6m^2

since the customer wants to eat a different dinner in all 365 days of 2003,

we must have ,

[tex]6m^{2}[/tex] ≥  365

[tex]m^{2}[/tex]  ≥ 60.83.....

also the 2003 is not a leap year

because 2003 / 4 is not equal to an integer

the smallest integer value satisfies this is 8 .

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The output value of g( 3b ) in the function g( x ) = x² - x is 9b² - 3b.

A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.

Given the data in the question;

To determine the output value of g( 3b ), replace all the occurrence of x with 3b in the function and simplify.

g( x ) = x² - x

g( 3b ) = (3b)² - 3b

Apply product rule

g( 3b ) = 3²b² - 3b

Raise 3 to the power of 2

g( 3b ) = 9b² - 3b

Therefore, the output value of g( 3b ) is 9b² - 3b.

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Answer:

D. 22.50

Step-by-step explanation:

22.5 - 8 = 14.5

14.5 + 22.5 = 37

For x = 28, the value of [y] such that [x] is directly proportional to [y] will be 112.

Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value. Mathematically, direct proportionality is represented by a straight line and it equation is of the form -

y = kx

k = y/x

where [k] is the constant

Given is the value of [y], which is directly proportional to the value of [x], and when [x] = 3.5, the value of [y] is 14.

We have the following data -

[y] = 14 at [x] = 3.5

Now, since [y] is directly proportional to [x], we cam write -

y = kx

k = y/x

k = 14/3.5.            [1]

Now, for x = 28, we can write the relation as -

y/x = k

k = y/28            [2]

Now, equating equation [1] and [2], we get -

14/3.5 = y/28

y = (14 x 28)/3.5

y = (140 x 28)/35

y = (140 x 4)/5

y = 28 x 4

y = 112

Therefore, for x = 28, the value of [y] such that [x] is directly proportional to [y] will be 112.

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Answer:

a. -5x³ + 29x² - 56x + 15

b. 8x² + 9x + 5

c. 18t³ - 42t² - 14t - 30

d. x³ - 2x² - 5x + 6

e. -2b⁴ + a² + 6b² - 24a

Step-by-step explanation:

a. 3(x³ − x² + 5) − 8(x³ − 4x² + 7x)

3x³ - 3x² + 15 - 8x³ + 32x² - 56x

-5x³ + 29x² - 56x + 15

b. 7x² + 2x + 5 + x(x + 7)

7x² + 2x + 5 + x² + 7x

8x² + 9x + 5

c. 10(t³ − 4t² + 1) − t(2t + 6) + 8(t³ − t − 5)

10t³ - 40t² + 10 - 2t² - 6t + 8t³ - 8t - 40

18t³ - 42t² - 14t - 30

d. (x − 1)(x + 2)(x − 3)

(x - 1)(x + 2)

x(x + 2) - 1(x + 2)

x² + 2x - x - 2

x² + x - 2(x - 3)

x(x² + x - 2) - 3(x² + x - 2)

x³ + x² - 2x - 3x² - 3x + 6

x³ - 2x² - 5x + 6

e. (3a − 2b²)(3a + 2b²) − 3(4a − b²)2 + 2(−2a − b²)(2a − b²)

3a(3a - 2b²) + 2b²(3a - 2b²)

9a² - 6ab² + 6ab² - 4b⁴ - 3(4a − b²)2 + 2(−2a − b²)(2a − b²)

9a² - 4b⁴ - 24a + 6b² + 2(−2a − b²)(2a − b²)

                                                               (−2a − b²)(2a − b²)

                                                              -2a(2a - b²) - b²(2a - b²)

                                                               -4a² + 2ab² - 2ab² + b⁴

                                                                -4a² + b⁴

                                                                 2(-4a² + b⁴)

                                                                  -8a² + 2b⁴

9a² - 4b⁴ - 24a + 6b² - 8a² + 2b⁴

-2b⁴ + a² + 6b² - 24a

Answer:

Step-by-step explanation:

Answer: p= 6-0.5

solve 1.5m + 3p=18

p= 6-0.5m

there are two aircraft​ carriers, a and​ b, and carrier a is longer in length than the carrier b. then Carrier A is 2,104 feet and Carrier B is 2,094 feet.

Since there are two aircraft carriers, A and B, and carrier A is longer in length than the carrier B, and the total length of these two carriers is 4198 feet, while the difference of their lengths is only 10 feet, to determine the length of each aircraft carrier, the following calculation must be performed:

(4,198 - 10) / 2 = X

4.188 / 2 = X

2,094 = X

2,094 + 10 = 2,104

2,094 + 2,104 = 4,198

Therefore, Carrier A is 2,104 feet and Carrier B is 2,094 feet.

the complete question is

There are two aircraft carriers, A and B, and carrier A is longer in length than the carrier B. The total length of these two carriers is 4198 feet, while the difference of their lengths is only 10 feet.

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The transformation of rotating 90° around a point not on the line segment would make corresponding line segments between a pre-image and image not be parallel.

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Answer:

u shall simply divide 98290 by 365 bc there are 365 days in 1 year

Step-by-step explanation:

98280 divided by 365 and that makes..

The difference of the given expressions is 5.

The given expressions are -6x+3 and -6x+8.

To subtract an algebraic expression from another, we should change the signs (from '+' to '-' or from '-' to '+') of all the terms of the expression which is to be subtracted and then the two expressions are added.

Now, subtract -6x+3 from -6x+8

-6x+8 - (-6x+3)

= -6x+8+6x-3

= 5

Therefore, the difference of the given expressions is 5.

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Given the following question:

Rule one: + 3

Rude two: + 9

3, 6, 9, 12, 15

3 + 3 = 6 + 3 = 9

9 + 3 = 12 + 3 = 15

= 15

9, 18, 27, 36, 45

9 + 9 = 18 + 9 = 27

27 + 9 = 36 + 9 = 45

= 45

We are now given..

3, 6, 9, 12, 15

9, 18, 27, 36, 45

They are related because these terms also have a rule, if you mutlply 3, by 3 we get 9, if we multiply 6 by 3 we get 18. The second sequence is three times the corresponding term in the first sequence or the first option.

Your answer is the first option.

Answer:

2

Step-by-step explanation:

The number right after the decimal is the tenths place.

More in-depth example:

1.234

1 is your integer(regular number)

2 is your tenths

3 is hundreths

4 is thousandths

Answer:

[tex]15^{12}[/tex]

Step-by-step explanation:

assuming you mean

[tex](15^3)^{4}[/tex]

using the rule of exponents

[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , then

[tex](15^3)^{4}[/tex]

= [tex]15^{3(4)}[/tex]

= [tex]15^{12}[/tex]

According to the table, the value of the function f(2) is 3

Functions are equations, ordered pairs, tables and graphs that are used to represent a relation

From the question, the function is represented by the table of values given as

X: 0 1 2 3 4

f(x): 4 2 3 9 1

From the question, the function to calculate is given as

f(2)

This means that we calculate the value of the function, when x = 2

i.e.

We calculate f(x), when x = 2

So, we look at the table of values for this function value

From the table of values, we have

When x = 2, f(x) = 3

This means that

f(2) = 3

So, we can conclude that the value of the function f(2) based on the given table when x =2 is 3

Hence, the function f(2) has a value of 3

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Based on the median and the centroid theorem, the length of WI is 6 units.

The line that joins the vertex of a triangle to the midpoint of the side it is directly opposite is called the median of a triangle.

According to the centroid theorem, since J is the centroid of triangle XYW, then:

the length of IE is 1/3 of the length of segment EW.

Thus, the equation that relates the length of the segments is;

IE = 1/3(EW)

Given that:

IE = 3 units

Now Substitute the value of IE into the equation:

3 = 1/3(EW)

3(3) = EW

9 = EW

EW = 9 units

Therefore:

The Length of WI = the length of EW - the length of IE

Substitute;

Length of WI = 9 - 3

Length of WI = 6 units.

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The solutions for each statement are given below.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

The initial amount of the company = -$200,000

Earnings for selling one batch = $40,000

Now,

1.

The two quantities that are changing in this situation are:

The number of batches.

The amount of profit.

2.

The independent variable is the number of batches.

The dependent variable is the profit.

3

The number of batches = x

The amount of profit = y

The equation for the profit.

P = -200,000 + B x 40,000

Where B is the number of batches.

4.

Batches of tires   Profits

   B                        P

0                         -200,000

1                          -160,000

2                          -120,000

3                           -80,000

4                           -40,000

5                            0

5.

The unit rate of change.

= (-120,000 + 160,000) / (2 - 1)

= 40,000

Thus,

The statements are given above.

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The probability that a truck drives at least 125125 miles in a day is 0.6839.

Given

trucks in a delivery fleet travel a mean of 110110 miles per day

standard deviation of 2626 miles per day

To find

find the probability that a truck drives at least 125125 miles in a day

Solution :

μ  = 110

σ  =  26

P (  63 < x < 125   )

=  P [ ( 63 - 110 )  / 26  < ( x  -  μ )  / σ <  ( 125 - 110 )  / 26  ]

=  P ( - 1.81 < z < 0.58 )

=  P (  z <  0.58 )  -  P (  z < -1.81)

using  standard normal table

=  0.7190 -  0.0351

=  0.6839

Probability  =  0.6839 .

Hence the probability that a truck drives at least 125125 miles in a day is 0.6839

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By substituting the first equation into the second, we get:

2x + 5*(2x +3) = 3

The correct option is the second one.

Here we have the system of equations:

y = 2x + 3

2x + 5y = 3

You can see that the variable "y" is already isolated in the first equation, so we can just substitute it in the second equation:

2x + 5*(2x +3) = 3

This is what we can see in the second option, so we conclude that the second option is the correct one.

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Answer:

y=2x-5

Step-by-step explanation:

y - 2x = -5
add 2x to both sides.
y=-5+2x

Answer:

y = 2x - 5 is a line. determine the two points that this line intersects with the axes then connect these points to graph it.

Step-by-step explanation:

Given y = 2x -5 set y = 0 then solve for the abscissa

y = 2x - 5

0 =2x - 5

2x=5

x = 5/2

we now have the point (5/2,0)

set now x = 0 then solve for ordinate

y = 2x - 5

y = 2(0) - 5

y = -5

we now have the point (0, - 5)

we now simply draw a line passing thru the two points ( 5/2, 0) and (0, - 5)

kindly see the graph of y = 2x - 5 with points (5/2, 0) and (0, - 5)

Hope this helps

Answer:

(0, -5)

Explanation:

The function is represented by f(x), and the line graphed would be y= f(x). In slope-intercept form, the equation of a line is given by y= mx +c, where m is the slope and c is the y-intercept.

Since we know that the line is linear, any two points along the line would give us the same slope value. Since y-intercepts occur at x= 0, let the y-intercept be (0, y).

[tex]\boxed{ \text{slope} = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]

Slope between (-3, 1) and (1, -7)= slope between (-3, 1) and (0, y)

[tex] \frac{1 - ( -7 )}{ - 3 - 1} = \frac{y - 1}{0 - ( - 3)} [/tex]

[tex] \frac{1 + 7}{ - 4} = \frac{y - 1}{0 + 3} [/tex]

[tex] \frac{8}{ - 4} = \frac{y - 1}{3} [/tex]

[tex] - 2 = \frac{y - 1}{3} [/tex]

Multiply both sides by 3:

-2(3)= y- 1

-6= y -1

Add 1 to both sides:

y= -6 +1

y= -5

Thus, the y-intercept is (0, -5).

__________

Based on the image, however, we are to find the equation of the linear function in slope-intercept form.

The first step would be to find the slope between any two points, which would be -2. This is found using the slope formula, and we have calculated it above.

Substitute the value of the slope into y= mx +c:

y= -2x +c

The y-intercept can be found by substituting a pair of coordinates the line passes through.

When x= -3, y= 1,

1= -2(-3) +c

1= 6 +c

c= 1 -6

c= 5

Thus, the equation of the line is y= -2x +5.

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Answer:

y = - 2x - 5

The intercept is 5 because that is where the graph cuts the y axis.

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Step-by-step explanation:

y = mx + c;

The m equals the change in y divided by the change in x. If you choose left to right for y then you must do the same for x as well.

Δy = ( - 7 ) - ( - 15 ); Δx = 1 - 5;

Δy = - 7 + 15;

Δy = 8;

Δx = - 4;

m = 8 / - 4;

m = - 2;

y = - 2x + c;

Pick a point (x, y) and sub it into the equation. Make sure to use brackets when subbing.

- 7 = - 2( 1 ) + c;

- 7 = - 2 + c;

Add 2 to both sides.

- 7 + 2 = - 2 + 2 + c;

- 5 = c;

c = - 5;

The c is the intercept.

y = - 2x - 5