A camper lights an oil lantern at 12 noon lets it burn continuously. Once the lantern is lit, the lantern burns oil at a constant tare of each hour. At 2 p.m., the amount of oil left in the lantern is 63 ounces. At 5 p.m., the amount of oil left in the lantern is 61 1/2 ounces. Based on the average rate of oil burning per hour, how much oil, in ounces, was in the lantern at 12 noon?
Show your work.

Answer: The slope for this line is not defined.

Step-by-step explanation: We can find the slope of a line using the formula m = y2 -y1/x2 - x1

here, (x1,y1) = (-7,4)

and, (x2,y2) = (-7,-8)

now, m= -8-4/-7+7

        m = -12/0

        So, the slope for this line is not defined as we are getting zero in the denominator.

Work Shown:

a = old price = 5000

b = new price = 2800

c = change in price

c = b-a

c = 2800-5000

c = -2200

The value of c is negative to indicate a price decrease.

d = percent change

d = (c/a)*100%

d = (-2200/5000)*100%

d = -44%

There is a 44% decrease or discount.

Answer:

3.95 + 0.50 + 4.50 × 2 = 13.45

13.45 × x = 124.70

x = 9

Therefore, she can make 9 shirts.

The sum of the given equation is 7[tex]\sqrt[5]{x^{2} y}[/tex].

Given data :

4 ([tex]\sqrt[5]{x^{2} y}[/tex].) + 3 ([tex]\sqrt[5]{x^{2} y}[/tex].)

Add similar elements

= 7[tex]\sqrt[5]{x^{2} y}[/tex].

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If the total length of the journey is 146 km and he maintain the same  speed, the longer time he will be using for driving  will be 65m.

The  total length of my journey is 146 km.

Then the remain of the journry to reach 146 km = 146- 48 = 98

Then the if the same speed is maintained the estimate of  longer time he will be using for driving  will be calculated as :

(32 * 98)/48

Then get the productor quotient = 196/3 = 65 minutes

Therefore, option E is correct.

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MISSING OPTIONS:

A. 32

B.40

C. 52

D. 60

E.65

Answer:

Step-by-step explanation: Total Cost: TC = $126.07

Base fee: B = $16.95

Rate per mile: r = $0.88/mile

Distance (miles) : d -->this is what we need to find

The general formula is:

TC = B + r*d

In this problem:

$126.07 = $16.95 + ($0.88/mile)*d

126.07 - 16.95 = 0.88d    (I dropped the units starting here)

d = (126.07 - 16.95)/0.88 = 124 miles  (notice the parentheses. subtraction has a lower precedence than division.  If you omitted them when using a graphing calculator you would get an incorrect answer)

So the answer is 124 miles.

The equation that represents the sentence is y ÷ 6₄¹ = 11₄³

The word quotient is the outcome when dividend is divided by a divisor.

The result that comes from a division process is termed as quotient. While writing an equation quotient is placed on the right-hand side of the equal sign.

The number that is divided by other number is called dividend and this other number is called divisor.

11³₄ is the quotient of a number y and 6¹₄.

47/4 is the quotient of a number y and 25/4

hence, y is the dividend and 25/4 is the divisor

y ÷ 25/4 = 47/4

y × 4/25 = 47/4

y = 1175/16

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Answer:

6.78

Step-by-step explanation:

Answer:

x^2 - 2 /3 (x+3)

Step-by-step explanation:

Answer:

The one with the vertex of (-4,4)

Step-by-step explanation:

A tank that is 80 cm tall and has a base that is 60 cm by 75 cm.

To find the volume of the tank, you can use the formula for the volume of a rectangular prism, which is:

Volume = length * width * height

Using the dimensions given, we can plug them into the formula as follows:

Volume = 60 cm * 75 cm * 80 cm = 4,500 cm^3

This means that the tank has a volume of 4,500 cubic centimeters, and it would take 4,500 cubic centimeters of water to fill it up

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Answer:

Step-by-step explanation:

To find the volume of water that will fill up a tank that is 80 cm tall, 60 cm wide, and 75 cm deep, you can use the formula for the volume of a rectangular prism. The formula for the volume of a rectangular prism is length x width x height, so in this case, the formula would be:

60 cm x 75 cm x 80 cm = 36,000 cm^3

So the volume of water that will fill up the tank is 36,000 cubic centimeters.

Alternatively this also can be written as 806075 cubic cms

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The equation of the linear function represented by the table in slope intercept form is y = -4x - 5.

What is slope-intercept form?

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

Given two points (x,y), the slope is the change in y divided by the change in x.

The points are (1,-9) and (3,-17) -

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

m = [-17-(-9)]/(3-1)

m = -8/2

m = -4

Then the slope equation will be -

y = -4x + b

Taking points (1,-9) and substituting in the equation to get the value of b -

-9 = -4(1) + b

-9 = -4 + b

-9 + 4 = b

b = -5

Therefore, the slope intercept form of equation is y = -4x - 5.

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Answer:

very long question

Step-by-step explanation:

Answer:

75%

Step-by-step explanation:

To find the percent of change that Target marks the shoes up for, you need to calculate the difference between the cost of the shoes to Target and the price at which they sell it to the public, and then divide that difference by the cost of the shoes to Target. Finally, you need to multiply the result by 100 to express the answer as a percentage.

Using this formula, the percent of change that Target marks the shoes up for is:

(35 - 20) / 20 * 100 = 15 / 20 * 100 = 0.75 * 100 = 75%

This means that Target marks the shoes up by 75% of their cost.

Answer:

To determine the number of students at the open house, you can use the fact that the ratio of students to adults is 9:7 and set up the following proportion:

students/adults = 9/7

You can then cross-multiply to find the value of "students":

7 * students = 9 * adults

7 * students = 9 * (832/(9+7))

7 * students = 832

students = 832 / 7

students = approximately 118.85714285714 students

To determine the number of students at the open house, you can use the fact that the ratio of students to adults is 9:7 and set up the following proportion:

Copy code

students/adults = 9/7

You can then cross-multiply to find the value of "students":

Copy code

7 * students = 9 * adults

7 * students = 9 * (832/(9+7))

7 * students = 832

students = 832 / 7

students = approximately 118.85714285714 students

Since the number of students must be an integer, the number of students at the open house is approximately 118 students.

Step-by-step explanation:

Answer:

m∠5+m∠6=180°

m∠2+m∠3=m∠6

m∠2+m∠3+m∠5=180°

Step-by-step explanation:

Verify each option

case A) we have

m∠5+m∠3=m∠4 ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary angles

m∠4=180°-m∠3 ----> equation B

substitute equation B in equation A

m∠5+m∠3=180°-m∠3

m∠5+m∠3+m∠3=180°

This equation is true when m∠2=m∠3

Therefore Is not always true

case B) we have

m∠3+m∠4+m∠5=180° ----> equation A

we know that

m∠3+m∠4=180° -----> by supplementary angles

m∠4=180°-m∠3 ----> equation B

substitute equation B in equation A

m∠3+(180°-m∠3)+m∠5=180°

m∠5=0°

This option is not true

case C) we have

m∠5+m∠6=180°

we know that

m∠5 and +m∠6 are supplementary angles

so

Their sum is always 180 degrees

Therefore this option is always true

case D) we have

m∠2+m∠3=m∠6 -----> equation A

we know that

m∠5+m∠6=180° ----> by supplementary angles

m∠6=180°-m∠5 ----> equation B

substitute equation B in equation A

m∠2+m∠3=180°-m∠5

m∠2+m∠3+m∠5=180°

Remember that the sum of the interior angles of a triangle must be equal 180 degrees

Therefore this option is always true

case E) we have

m∠2+m∠3+m∠5=180°

Remember that the sum of the interior angles of a triangle must be equal 180 degrees

This option is always true

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The equation of the line that passes through the points (- 6, - 3) and (4, 5) is y = (4 / 5) · x.

In this question we have the knowledge of two points, of which we must derive the equation of a line, whose definition is shown below:

y = m · x + b

Where:

The slope of the line can be determined by secant line formula:

m = Δy / Δx

Where:

First, determine the slope of the line:

m = [5 - (- 3)] / [4 - (- 6)]

m = 8 / 10

m = 4 / 5

Second, determine the intercept of the line:

b = y - m · x

b = 5 - (4 / 5) · 4

b = 5 - 5

b = 0

Third, write the equation of the line:

y = (4 / 5) · x

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On soloing the provided question we can say that - Area of the Circle - Area of the Triangle - Area of the Square is the area of the darkened area. A = 210-123 = 87 sq unit

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is a graphical representation of a triangle having vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.

the sum of the areas of the circle, the triangle, and the square.

Area of the Circle - Area of the Triangle - Area of the Square is the area of the darkened area.

A = 210-123 = 87 sq unit

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Answer:

Step-by-step explanation:

Can u give more detail as to what the question is asking pease

Answer: 18.1666666667

Step-by-step explanation:

Option A) In the graph for each value of x there is exactly one value of y

So the function is  a One to One function.

A function is a procedure or a relation that links each element of a non-empty set A, at least one element of another non-empty set B, to another element of the first non-empty set A. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain. For all values of a and b, f = (a,b)|

A function f is said to be injective if it maps different items in its domain to other elements; for example, f = f implies x1 = x2. Alternatively, every element of the function's codomain is at most one of its domain's elements.

If some function output value corresponds to more than one input value, the function is said to be many-to-one (sometimes written as "many-one"). If the domain of f contains two different values a and b such that f(a)=f, the function f is many-to-one in symbols (b).

In the graph for each value of x there is exactly one value of y

So the function is  a One to One function.

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40% of an hour is 24 minutes = 2/5 hours.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Given that,

there are 60 minutes in an hour,

we can multiply this by 0.4 to find that 24 minutes constitutes 40% of an hour.

i.e. 60*40%= 24 minutes

Hence, 40% of an hour is 24 minutes = 2/5 hours.

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Answer: 3/4 is right

Step-by-step explanation:

The number of tennis ball  fit in the machine are 305 balls.

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Finding an object's volume can help us calculate the quantity needed to fill it, such as the volume of water needed to fill a bottle, aquarium, or water tank.

given dimensions of  machine 15 x 15 x 14

volume of machine is 15 x 15 x 14 = 3150 cubic inches

and shape of ball is spherical,

with dia = 2.7 inches

radius of ball = 2.7/2 = 1.35 inches

volume of sphere is 4/3πr³

V = 4/3πr³

V = 4/3(3.14)(1.35)³

V = 4/3(3.14)(2.46)

V = 10.30 cubic inches

the area covered by 1 ball is 10.30 cubic inches

the number of ball in machine is 3150/10.30

the number of ball in machine  = 305.82 = 305 approx

Hence  305 balls can be fit in machine.

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Therefore , the solution to the given problem of equation comes out to be 1. circle, 2. parabola, 3. ellipse and 4. hyperbola.

Expressions that equal one another are the building blocks of an equation. The equation 4x²+3x = 22. A equation is an equation that has at least two variables and depicts the relationship between them.

Here,

are the definitions of each equation:

1. x^2 + y^2 - 4x + 6y - 5 = 0

 The x2 and y2 terms share the same scaling factor, despite the fact that this equation contains a bunch of other garbage (which is 1). This ought to be screaming "circle" to you.

2. x^2 - 6y = 0

 The x term is squared, but the y term is not, which is an important distinction to make. A parabola is clearly indicated by this fact.

3. 4x^2 + 9y^2 = 1

This is the result of adding an x-squared and a y-squared phrase. That kind of sounds circular, but the results are scaled by those two coefficients. Additionally, they vary. So, a closed curve that resembles a circle but is slightly stretched out is what we're searching for. An ellipsis appears there.

4. 7x^2 - 9y^2 = 343

 A few squared terms for x and y are present here. However, we are removing rather than adding to them. This denotes a hyperbola.

Therefore , the solution to the given problem of equation comes out to be 1. circle, 2. parabola, 3. ellipse and 4. hyperbola.

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Answer:

  (b)  No solution

Step-by-step explanation:

You want the solution to 0.5(-2+ 4d) - 2d = -13.

Eliminating the parentheses using the distributive property, we have ...

  -1 +2d -2d = -13

Collecting terms gives ...

  -1 = -13 . . . . . false

No value of d will make this true. There is No Solution.

The new transformation coordinates are B""(6, 15), C""(-3, 12), and Dilate k=3 by multiplying both x and y by 3.

When locating points or other geometrical objects precisely on a manifold, such as Euclidean space, a coordinate system is a technique that uses one or more integers or coordinates. Locating a point or item on a two-dimensional plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y coordinates are used to describe a point's location on a 2D plane. a collection of integers that represent specific locations. The figure often has two numbers. The first number denotes the front-to-back measurement, while the second number denotes the top-to-bottom measurement. For example, in (12.5), there are 12 units below and 5 above.

given

For point B,

B(1,2) → B'(1 , -2) → B"( 2, -5) → B""( 6 ,-15)

For point C,

C(-2,1) → C'( -2 , -1) → C"( -1 , -4 )→ C"" ( -3 , -12)

In order to reflect a point across the x-axis, keep the x coordinate constant while changing the y coordinate to its opposite.

<1, -3> the following translations: Add 1 to x, take 3 away from y.

Add 3 to both x and y to dilate k=3.

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The solution to the system of given inequalities is (-7, 0).

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given system of inequalities are y> 2x-4 and y≤ -x-7.

The solution of the system of inequalities is the intersection region of all the solutions in the system.

x<y/2 +2 and x≤-y-7

The solution of the system of inequalities is (-7, 0)

Therefore, the solution to the system of given inequalities is (-7, 0).

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