Sera drove 450 miles (y) and his car used 18 gallons (x) of gas. How many gallons of gas will Sera use if she drives 875 miles?

1. Identify x:

2. Identify y:

3. Calculate k using k =y/x:

4. Write an equation for the proportional relationship using y =kx:

5. Solve the problem and show your work: How many gallons of gas will Sera use if she drives 875 miles?

The numbers that are exactly divisible by 7  are;

a) 525

b) 798

d) 3696

To solve this, what we will do is to quote the divisibility rule for 7 here which is that;

For a 3 digit number abc to be divisible by 7 then it means that ab - 2c must be divisible by 7. Thus;

A) 525;

52 - 2(5)

= 52 - 10

= 42

42 is divisible by 7 and as such 525 is divisible by 7

B) 798;

79 - 2(8)

= 63

63 is divisible by 7 and as such 79 is divisible by 7

C) 836;

83 - 2(6)

= 83 - 12

= 71

71 is not divisible by 7 and as such 836 is not divisible by 7

D) 3696;

369 - 2(6)

= 357

35 - 2(7)

= 21

21 is divisible by 7 and as such 3696 is divisible by 7

E) 5706;

570 - 2(6)

= 558

55 - 2(8)

= 39

It's not divisible by 7 and so  5706 is not divisible by 7

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Every output value for g is half the output value for f.

I would describe the transformation as a vertical compression by a factor of 1/2, since every y-value was cut in half.

g(x) = 1/2 · f(x)

The distance between where Jenna stopped and the park is 1 1/10 miles

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.

The word problems are interpreted into mathematics equation.

The distance between Jena's school and the park is 1⅘ miles = 9/5 miles

He stopped after walking for 7/10 miles .

The distance left to the park from where he stopped = 9/5 - 7/10

= (18-7)/10

= 11/10 miles

= 1 1/10 miles

Therefore Jena is 1 1/10 miles away from the park when she stopped.

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The expression from the statement is 2x - 1 = 14

From the question, we have the following parameters that can be used in our computation:

The product of 2 and the difference between 1 is 14

Represent the variable with x

So, we have

2x and the difference between 1 is 14

When the difference is expressed as an expression, we have

2x - 1 is 14

So, we have

2x - 1 = 14

Hence, the expression is 2x - 1 = 14

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Answer:4x - 2 = 12

Step-by-step explanation:

Answer:

[tex](3+\sqrt{7},7+2\sqrt{7})[/tex]

[tex](3-\sqrt{7},7-2\sqrt{7})[/tex]

Step-by-step explanation:

Given equations:

[tex]\begin{cases}y=2x+1\\y=x^2-4x+3\end{cases}[/tex]

Substitute the second equation into the first equation:

[tex]\implies x^2-4x+3=2x+1[/tex]

Rearrange so that the terms in x are on the left side of the equation and the constants are on the right:

[tex]\implies x^2-4x-2x=1-3[/tex]

[tex]\implies x^2-6x=-2[/tex]

Add the square of half the coefficient of the term in x to both sides:

[tex]\implies x^2-6x+\left(\dfrac{-6}{2}\right)^2=-2+\left(\dfrac{-6}{2}\right)^2[/tex]

[tex]\implies x^2-6x+9=-2+9[/tex]

[tex]\implies x^2-6x+9=7[/tex]

Factor the perfect square trinomial on the left side of the equation:

[tex]\implies x^2-3x-3x+9=7[/tex]

[tex]\implies x(x-3)-3(x-3)=7[/tex]

[tex]\implies (x-3)(x-3)=7[/tex]

[tex]\implies (x-3)^2=7[/tex]

Square root both sides of the equation:

[tex]\implies x-3=\pm \sqrt{7}[/tex]

Add 3 to both sides of the equation:

[tex]\implies x=3\pm\sqrt{7}[/tex]

To find the y-values, substitute the found x-values into the first equation:

[tex]x=3+\sqrt{7}\implies y=2(3+\sqrt{7})+1=7+2\sqrt{7}[/tex]

[tex]x=3-\sqrt{7}\implies y=2(3-\sqrt{7})+1=7-2\sqrt{7}[/tex]

Therefore, the solutions to the system of equations are:

Using linear equations, the cost of each t - shirt is $8.

Consider how (0,5), (1, 4), (2, 3), etc. are all possible answers to the linear equation x + y = 5 to illustrate the infinite number of solutions to a linear equation with two variables. One solution that satisfies both solutions can exist for systems of two linear equations with two variables.

The only way to solve x + y = 5 and 2x y = 1 is to combine two equations with two variables into one equation with one variable, which is what we do when solving a system of equations. The two equations in the system can be added or subtracted to cancel out, or eliminate, one of the variables as each equation in the system has two variables.

Given,

Kathy pays 30 for 3 shirts and 2 caps.

marc pays 23 for 1 shirt and 5 caps.

Let us assume cost of t - shirt = x

cost of cap = y

⇒ 3x + 2y = 30

⇒ x + 5y = 23

on solving the equations using elimination method,

Multiply 2 equation by 3,

⇒ 3x + 2y = 30

⇒ 3x + 15y = 69

Now, subtract both equation -

⇒ - 13y = -39

⇒ y = 3

x = 30 - 2 × 3 / 3

x = 8

cost of each t - shirt = $ 8

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, The fraction equivalent to 3/9 with denominator 3 is the proper fraction p=1/3

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given here: The fraction 3/9

Now we can simplify the fraction further by dividing both the numerator and denominator by 3

let p=3/9

then p=3/3 / 9/3

       p= 1/3

Hence, The fraction equivalent to 3/9 with denominator 3 is the proper fraction p=1/3

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The volume of the cylinder with a radius of 19 km and a height of 5 km is 5706 km³, using 3.14 for π.

What is the volume of a cylinder?

The cylinder's volume is given by the formula, πr²h, where r is the radius of the circular base and h is the height of the cylinder.

The formula for the volume of a cylinder is given by:

V = π * r²* h

Where r is the radius of the base and h is the height of the cylinder.

Given that the radius of the cylinder is 19 km and the height is 5 km, we can substitute these values into the formula:

V = π * 19² * 5

V = 3.14 * 361 * 5

V = 5706 km³

Therefore, the volume of the cylinder with a radius of 19 km and a height of 5 km is 5706 km³, using 3.14 for π.

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The solution to the linear equations are;

20. x = 3. 200

21. x = 4. 333

22. x = 11. 438

23. x = 1.417

24. y = 0. 223

25. 45%

From the information given, we have to solve the linear equations, we have;

20. -15x + 73 = 26

collect like terms

-15x = 26 - 74

-15x = -48

Make 'x' the subject

x = 3. 200

21. 1.5x + 7.4 = -1.8x - 6.9

collect the like terms

3.3x = 14.3

Make 'x' the subject

x = 4. 333

22. 14.1 - 0.3x = 1.3x - 4.2

collect like terms

1.6x = 18.3

Make 'x' the subject

x = 11. 438

23. 6.2x + 4.5 = 3.8x + 7.9

collect like terms

2.4x = 3.4

Make 'x' the subject

x = 1.417

24. 4.603y - 1.842 = -3.651y

collect like terms

8.254y = 1.842

Make 'y' the subject

y = 0. 223

25. The percentage is given as;

159/350 × 100/1

45%

Hence, the values are x = 3. 200, x = 11. 438, x = 1.417, y = 0. 223 and 45%

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Answer:

The original price of the item was $9.99 and it was discounted by 70%, which means the new price is $2.99.

Step-by-step explanation:

The coordinate points on the graph line of the function given represent the ordered pair that satisfy the equation.

An function in mathematics defines a relationship between one variable (the independent variable, x)  and another variable (the dependent variable, y). Example -

y = f{x} = ax + b

Given is a function as -

2x - 4y = 14

The given equation is -

2x - 4y = 14

Rewriting the function, we get -

4y = 2x - 14

y = (1/2)x - (7/2)

Plot the graph of the above function. All the coordinate points on the line represent the ordered pair that satisfy the equation.

Therefore, the coordinate points on the graph line of the function given represent the ordered pair that satisfy the equation.

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Note that where Will C. Lowe wishes to purchase an ordinary whole life insurance policy with a face value Of $50,000, his annual premium, if his age for insurance purposes is thirty-one is: $7,665.

The insured pays a premium to the insurer on a regular basis to cover his risk. The risk is transferred from the insured to the insurer under an insurance arrangement. The premium is the amount charged by the insurer for accepting this risk.

To compute the Premium Payable, you must apply the stipulated rate against the sum insured.

Since the Sum assured is $50,000; and

The applicable rate for a 31-year-old is 15.33%

Thus the Insurance Premium for an Ordinary Whole Life Insurance Policy is:

(50,000 * 15.33)/100

= 766500/100

=  $7,665.

Thus Lowe to be entitled to an annual Life Insurance cover of $50,000 must pay $ $7,665 every year.

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Answer:

Quadrant IV

In quadrant 4, the x-coordinate is positive, while the y-coordinate is negative.

Answer:

a) GH¢15x

b) GH¢15

Step-by-step explanation:

a) To find the cost function, C(x), given that it is linear, we need to find the slope and y-intercept of the line that represents the cost to produce x units of the product. We can use the point-slope form of a line to find the cost function: C(x) = mx + b, where m is the slope and b is the y-intercept.

We have two points: (100, GH¢1,500) and (0, GH¢0), which represents the cost to produce 100 units and 0 units, respectively. The slope can be found by dividing the change in y by the change in x:

m = (GH¢1,500 - GH¢0) / (100 - 0) = GH¢15

The y-intercept can be found by plugging in one of the points and solving for b:

GH¢1,500 = (GH¢15)(100) + b

GH¢1,500 = GH¢1,500 + b

b = GH¢0

So the cost function is C(x) = GH¢15x + GH¢0.

b) To find the average cost per item to produce 50 units and 300 units, we need to divide the total cost by the number of units produced.

For 50 units:

C(50) = GH¢15 * 50 + GH¢0 = GH¢750

Average cost = C(50) / 50 = GH¢15

For 300 units:

C(300) = GH¢15 * 300 + GH¢0 = GH¢4,500

Average cost = C(300) / 300 = GH¢15

The value of sin θ from the unit circle is sin θ = 0.9230769

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

The terminal side of angle θ intersects the unit circle in the first quadrant at ( 3√10/10,√10/10 )

So , the equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r²   be equation (1)

Substituting the values of x and y in the equation , we get

x = -5/13

And , y = 12/13

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

So , the value of cos θ = ( -5/13 ) and sin θ = ( 12/13 )

On simplifying the equation , we get

sin θ = ( 12/13 )

sin θ = 0.9230769

Hence , the value of sin θ = 0.9230769

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The number of buttons on each card from Elaine's grandmother is given as follows:

7 buttons.

The number of buttons on each card is obtained applying the proportions in the context of this problem.

Elaine sorted the buttons into 6 piles, putting 8 buttons in each pile, hence the total number is given as follows:

6 x 8 = 48.

Elaine had 6 buttons, hence the number donated is given as follows:

48 - 6 = 42.

6 cards were donated, hence the number of buttons in each card is given as follows:

42/6 = 7.

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Answer:

Step-by-step explanation:

The equation of the line with the given points is y = 6x - 4. This can be derived by calculating the slope of the line, which is 6, and then using the point-slope form of the equation of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, the given points are (x1, y1) = (1, 10), so the equation of the line is y - 10 = 6(x - 1) or y = 6x - 4.

Answer y == 3

+7

Step-by-step explanation:

The graph of a linear relationship contains the points (1, 10) and (3, 16).

Write the equation of the line in slope-intercept fo

Step-by-step explanation:

the general slope-intercept form is

y = ax + b

a is the slope, which is the ratio of "y coordinate change / x coordinate change" when going from one point to another on the line.

b is the y-intercept - the y value when x = 0.

for the slope we see

x changes by +2 (from 1 to 3)

y changes by +6 (from 10 to 16)

so, the slope a is +6/+2 = 3

and the semi-ready equation is

y = 3x + b.

now we use one of the points in the equation to solve for b. I picked (1, 10) :

10 = 3×1 + b = 3 + b

b = 7

so, the full equation is

y = 3x + 7

Answer:Can somebody also help me with this. i'm confused please hurry!

Step-by-step explanation:

A) An equation to represents your plan to afford the iguana is,

⇒ y = $12 + $9w

Where, y is total money after w weeks.

B) The amount of money you should save each week to buy the iguana in 6 weeks is, $66.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

You want to buy a pet iguana. You already have $12 and plan to save $9 per week.

Let w represents the number of weeks until you enough Money to buy the iguana.

Hence, An equation to represents your plan to afford the iguana is,

⇒ y = $12 + $9w

Where, y is total money after w weeks.

And, The amount of money you should save each week to buy the iguana in 6 weeks is,

⇒ y = $12 + $9w

⇒ y = $12 + $9 × 6

⇒ y = $12 + $54

⇒ y = $66

Thus, A) An equation to represents your plan to afford the iguana is,

⇒ y = $12 + $9w

Where, y is total money after w weeks.

B) The amount of money you should save each week to buy the iguana in 6 weeks is, $66.

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The total number of cards is 192 cards

From the question, we have the following parameters that can be used in our computation:

Initial number of cards = 144 cards.

Nicole pays for the:

9/27 = 1/3 of the set

so she gets proportional amount of cards:

1/3*144 = 48 cards

Total number of cards Nicole has now:

144 + 48 = 192

Hence, the total number of cards is 192

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Complete question

Nicole has 144 role-playing cards and $9

to buy more cards. She and her friends buy

another set that costs $27. They evenly

split the cost and the cards in the set. How

many cards does Nicole have after she buys

part of a set with her friends?

Answer:

Circles are round shapes that doesn't have points or perhaps angles it shape is considered no a point shape thanks to it having no points ofc or can be used in measurements,yards,etc

Variables expression is done as given below.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Variables are the values for a specific item.

Example:

Apple cost = $4 per kg

Banana cost = $6 per kg

Total cost = $60

To find the number of kg for each item we have to consider x as the number of kg of apple and y as the number of kg of banana.

Here,

x and y are the variables.

Now,

The expression with the variables x and y.

4x + 6y = 60

Thus,

The expression with variables is given above.

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The inverse function of f(x) = (x^2+1)^2 step by step is given below.

The inverse of f(x) is √(√x - 1).

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = (x² + 1)²

The steps for finding the inverse of a function.

Step 1:

Keep y = f(x)

y = (x² + 1)²

Step 2:

Interchange x and y.

x = (y² + 1)²

Step 3:

Solve for y.

x = (y² + 1)²

Square root on both sides.

√x = y² + 1

(√x - 1) = y²

Square root on both sides.

y = √(√x - 1)

Thus,

The inverse of f(x) is √(√x - 1).

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a) The continuous growth rate can be calculated using the formula:

r = (ln(B) - ln(A)) / t

where r is the continuous growth rate, A is the initial count (330), B is the count after 6 hours (1340), and t is the time elapsed (6 hours).

Substituting the values:

r = (ln(1340) - ln(330)) / 6

r = 0.3907

b) The model for the bacteria colony can be written as:

B = A * e^(rt)

where B is the number of bacteria after time t, A is the initial count (330), and e is the base of the natural logarithm.

c) To find the number of bacteria after 16 hours, substitute t = 16 and the values of A and r from above:

B = 330 * e^(0.3907 * 16)

B = 9581.57

The number of bacteria after 16 hours is approximately 9582.

Slope intercept form of equation is y = -3x + 5.

The graph of the linear equation y = mx + c is a line with m as slope and c as the y-intercept. This form of the linear equation is called the slope-intercept form, and the values of m and c are real numbers.

Given equation,

-5 = -y - 3x

Standard Slope intercept form of equation y = mx + c

Given equation can be written as

y = -3x + 5

Hence, y = -3x + 5 is the slope intercept form of given equation

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The required equation in the slope-intercept form is given as y = -3x + 5.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
The equation of line passes through points (x, y) and has a slope and intercept of m and c respectively is given as,
y = mx + c

The above expression is the standard slope intercept form of a line.

Trasform the given equation,

-5 = -y - 3x
y - 5 = -3x

y = -3x + 5

Thus, the required equation in the slope-intercept form is given as y = -3x + 5.

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