A tub of water is emptied at a rate of 3 gallons per minute. The equation y –12 = –3(x – 1) models the amount of water remaining, where x is time (in minutes) and y is the amount of water left (in gallons). Analyze the work shown below to determine the initial amount of water. 1. Solve for the y-variable.     y – 12 = –3(x – 1) y – 12 = –3x + 3 y = –3x +15   2. Write the equation using function notation.  f(x) = –3x +15 The tub started with ____ gallons of water. 

Answer:

✅ triangle

✅ pentagon

✅ hexagon

✅ trapezoid

❌ octagon

Step-by-step explanation:

divide completions by percentage

345 / 0.60 = 575 pass attempts

The correct answer is:

7.8 × 10⁷

Explanation:

To write a number in scientific notation, we want the decimal behind the first non-zero digit in the number. The first non-zero digit in 78 is 7; this means we want 7.8. In order to have the decimal point behind the 7, we need to move the decimal 7 places. This is the exponent of 10 in our scientific notation, which gives us

7.8 × 10⁷

1 mile = 5280 feet

 5280 * 2/3 =

5280 *2 = 10560

10560/3 = 3520

 it is 3520 feet long

Answer:

4 inches

Step-by-step explanation:

1 foot = 12 inches

45 feet --- 6 inches

From this we can conclude that the scale of the Blueprint is:

1 foot in actual = 1/90 foot on blueprint

If the girder is actually 30 feet long, then

30 feet --- (1/90*30*12) inches

30 feet --- 4 inches

The equation of the line will be y = 4/3x + 3. The correct option is C.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The general form of the equation of the line:-

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

From the given graph the slope will be calculated as:-

Rise = 4

Run = 3

Slope = Rise / Run = 4 / 3

The y-intercept is 3.

The equation can be written as:-

y = mx + c

y = 4/3x + 3

Therefore, the equation of the line is y = 4/3x +3.

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Answer:

Look at the below steps.  

Step-by-step explanation:

We have been given two intersecting lines:

The given angles are vertically opposite angles:

[tex]2x+6=96[/tex]

On simplification we get:

[tex]2x=90[/tex]

On further simplification we get:

[tex]x=\frac{90}{2}[/tex]

[tex]x=45[/tex]

Hence proved that x=45.

Answer:

D. [tex]6\pi\text{ cm}[/tex].

Step-by-step explanation:

We are asked to find the circumference of a a circle with a diameter of 6 cm.

We will use circumference of circle to solve our given problem.

[tex]C=\pi\cdot D[/tex], where,

C = Circumference of circle,

D = Diameter of circle,

Upon substituting [tex]D=6\text{ cm}[/tex] in above formula we will get,

[tex]C=\pi\cdot 6\text{ cm}[/tex]

[tex]C=6\pi\text{ cm}[/tex]

Therefore, circumference of our given circle would be [tex]6\pi\text{ cm}[/tex] and option D is the correct choice.

In a standard deck of cards, there are a total number of 52 different card. From those 52 cards, 4 cards are numbered as five. Therefore the probability of selecting a card of five is:

Probability = 4 / 52 = 1 / 13

Assuming that no replacement is made, so the probability changes with each draw, since the total number of cards decreases from 52 to 51 to 50 and so on. Therefore this is not a simple event.

Answer: I’m just adding this to verify that the other answer was correct

Each side of [tex]49^{3x} = 343^{2x + 1}[/tex], expressed in terms of their bases, is: [tex]7^{2(3x)} = 7^{3(2x + 1)}\\\\[/tex].

To solve an equation, the bases can be made equivalent and cancelled out by creating exponents.

Given:

[tex]49^{3x} = 343^{2x + 1}[/tex]

First, express each side by simplifying their bases and make them equivalent. Let the base be 7.

Thus:

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

To solve, cancel the bases to have, 2(3x) = 3(2x + 1) and solve for x.

Therefore, each side of [tex]49^{3x} = 343^{2x + 1}[/tex], expressed in terms of their bases, is: [tex]7^{2(3x)} = 7^{3(2x + 1)}\\\\[/tex].

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Answer: 7 then B on edge

Step-by-step explanation:

Answer: it’s

Step-by-step explanation:

Answer:

An equivalent expression to 54+18x, using the distributive property is 18(3+x)

Step-by-step explanation:

In the problem we have the binomial (54+18x), and we are asked to use the distributive property, this means that we can find a factor wich is distributed in both terms of the binomial.

We know that any number, or in this case any polinomial (or binomial), can be multiplied times 1 and will stay the same number, and we only need to write this 1 in a way that could resolve our problem, in particular we can say that

[tex]1=\frac{18}{18}[/tex]

then we can distribute the denominator, so we calculate:

[tex](54+18x)=1(54+18x)=\frac{18}{18}(54+18x)=18(\frac{54}{18}+\frac{18x}{18})=18(3+x)[/tex]

And the equivalent expression to (54+18x) is 18(3+x).

Answer: [tex]1x^2+4x+3[/tex]

Step-by-step explanation: Given expression (x^3-x^2-17x-15)/(x-5).

We need to divide it x^3-x^2-17x-15 by x-5 using synthetic division .

In order to solve by synthetic division, we would write all the coefficients of given divisor polynomial:

And we divide them by 5 using synthetic division method.

             ______________          

      5    |     1   -1   -17   -15                       Getting first number down.

            |           5   20   -15                      Multiplying each down number by

           - - - - - - - - - - - - - - - -                    divisor 5.

                  1    4      3       0                     5×1=5  , 5×2=20, 5×2=15

                                                   Subtracting those products from coefficients.

Now, writing the final polynomial degree 1 less than 3, that is 2.

So, [tex]1x^2+4x+3[/tex] would be our quotient.                    

The average fuel efficiency rating, calculated by adding the mpg ratings and dividing by five, is 32.418 mpg, rounded to the nearest hundredth as 32.42 mpg. The answer is D. 32.42 mpg.

To find the average fuel efficiency rating of the top five models, we need to calculate the mean mpg rating. To do this, we add up all the mpg ratings and then divide by the number of models:

Add the fuel efficiency ratings together: 26.3 + 28.95 + 33.6 + 35 + 38.24.

The sum is 162.09 mpg.

Divide this sum by the number of cars, which is 5: 162.09 ÷ 5.

The average is 32.418 mpg.

To record the average to the appropriate degree of precision, we consider the place values of the original data provided. The given ratings include mpg values recorded to the nearest hundredth, as in 28.95 mpg and 38.24 mpg. This means the average should also be recorded to the nearest hundredth: 32.42 mpg. Therefore, the correct answer is D. 32.42 mpg.

The value of m in the equation [tex]13m +3 -56m = -15[/tex] is [tex]\frac{18}{43}[/tex]

Given: [tex]13m +3 -56m = -15[/tex]

To find: value of m

To find the value of m we need to move all the terms containing variables on LHS and the constants on RHS. This can be done as follows:

[tex]13m +3 -56m = -15\\13m -56m =-15-3\\[/tex]

Now we can solve for m as follows:

[tex]13m-56m =-15-3\\-43m = -18\\[/tex]

The negative sign on both LHS and RHS will cancel out and it will give us:

[tex]m = \frac{18}{43}[/tex]

Since 18 and 43 do not have any common multiples so the fraction cant be simplified further. So, [tex]m = \frac{18}{43}[/tex]

x = 24
y = 18
Length of Major Axis = a
Length of Minor Axis = b

Center (0, 0):

h = 0
k = 0

a = 1/2 x
a = 1/2 *(24)
a = 12
b = 1/2 y
b =1/2 (18)
b = 9
So, Equation of Ellipse:

General : (x - h)² / a² + (y - k)² / b² = 1

(x - 0)² / (12)² + (y - 0)² / (9)² = 1

x² / 144 + y² / 81 = 1


Focus = c:
        _____
c = √a² - b²
        _______
c = √(12)² - (9)²
        ______
c = √144 - 81 = sqrt63 = 7.9372

Focus : ( -7.9372, 0) and ( 7.9372, 0)

The correct answer is: a. 7.94 ft

Step 1

To find the distance from the center of the board to the foci of the ellipse that will result in the largest possible elliptical tabletop, we can use the formula:

[tex]\[ c = \sqrt{a^2 - b^2} \][/tex]

where:

- a is half the length of the major axis (which is half of the longer side of the rectangle)

- b is half the length of the minor axis (which is half of the shorter side of the rectangle)

Step 2

Given that the rectangle is 18 feet by 24 feet, [tex]\( a = \frac{24}{2} = 12 \)[/tex] feet and [tex]\( b = \frac{18}{2} = 9 \)[/tex] feet.

Step 2

Now, we can substitute these values into the formula:

[tex]\[ c = \sqrt{12^2 - 9^2} \]\[ c = \sqrt{144 - 81} \]\[ c = \sqrt{63} \][/tex]

Taking the square root of 63 gives us approximately 7.94 feet.

The value of "a" is 2.

To find the value of "a," we can use the formula for the equation of a line, which is y = mx + b.

First, we need to find the slope, represented by "m," using the given points (-1, -5) and (4, 5). The slope formula is (y2 - y1) / (x2 - x1).

Substituting the coordinates, we have:

m = (5 - (-5)) / (4 - (-1))
m = 10 / 5
m = 2

Now that we have the slope, we can substitute it into the equation of the line with the point (a, 1):

1 = 2a + b

To solve for "a," we need to find the value of "b." We can substitute one of the given points into the equation and solve for "b."

Using (-1, -5):

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

Now we can substitute the values of "b" and "a" into the equation:

1 = 2a - 3

To isolate "a," we add 3 to both sides:

1 + 3 = 2a
4 = 2a

Dividing both sides by 2, we find:

2 = a

Therefore, the value of "a" is 2.