Write and graph an equation in two variables that shows the relationship between the time and distance traveled

The cost of the flour per ounce will be $0.06 per ounce. Then the correct option is A.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

A 5-pound of flour costs $4.80.

We know that in one pound, there are 16 ounces. Then the number of ounces in 5 pounds is calculated as,

⇒ 5 x 16

⇒ 80 ounces

Then the cost of the flour per ounce will be given as,

⇒ $4.80 / 80

⇒ $0.06 per ounce

The cost of the flour per ounce will be $0.06 per ounce. Then the correct option is A.

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Answer:

17 heartbeats in 15 seconds as a unit rate is-

1.13 over 1

hope it is clear to you

length= 93 width=31

248=2L+2w

L=3w

248=2x3w+2w

248=6w+2w

248=8w      (248/8=31)

31=w

L=3 x 31

L=93

check answer: 248= 2x93 + 2x31

                       248=186+62

                         248=248

The matching of the given numbers to there standard notation is given as follows:

     232,000,000------ 2.32E8

     0.00000431 ------  4.31E-6

 2,320,000,000 ----- 2.32E9

 0.000000000000431 ----- 4.31E-13

We know that the standard  notation of a number is given by:

There must be only one digit before the decimal and rest after that.

Also, it there is a shift of the decimal to the right then the power goes to negative and positive if shift is to the left.

1)

        232,000,000

Here we have to take the decimal 8 digits from the left and the number in standard notation will be given by:

              [tex]2.32\times 10^8[/tex]

which is written as:  2.32E8

2)

      0.00000431

Here we have to shift the decimal 6 digits to the right.

Hence, the number is expressed as:

           [tex]4.31\times 10^{-6}[/tex]

which is written as: 4.31E-6

3)

       2,320,000,000

Here the decimal is to be put 9 digits from the left and hence the number is represented as:

           [tex]2.32\times 10^9[/tex]

which is given by: 2.32E9

4)

         0.000000000000431

Here we will shift the decimal 13 places to the right and hence the number is given by:

            [tex]4.31\times 10^{-13}[/tex]

which is given by:  4.31E-13

Final answer:

The solution to the system of equations y = -1/5x + 1 and y = x + 4 is found by setting the equations equal to each other, solving for x, and then substituting back to find y. The solution is the ordered pair (-5, -1).

Explanation:

The student is asking to find the ordered pair that represents the best estimate for the solution to a system of linear equations. The given system of equations is: y = −1/5x + 1 and y = x + 4. To find the solution, we need to determine where the two lines intersect, which will give us the coordinates (x, y) of the solution.

To find the intersection, we can set the two equations equal to each other since they both equal y: −1/5x + 1 = x + 4. Then, we would solve for x:

Add 1/5x to both sides to get 1 = 6/5x + 4

Subtract 4 from both sides to get −3 = 6/5x

Multiply both sides by 5/6 to get x = −3 × (5/6)

Which simplifies to x = −5

Now we substitute x back into either of the original equations to find y. For instance, using the second equation y = x + 4, we find that:

y = (−5) + 4 = −1

Therefore, the ordered pair that is the solution to the system of equations is (-5, -1).

The height of Mel in the air is decreasing at a faster rate than victor's height in the air.

Given information:

Mel slides down water-slide A and Victor slides down water-slide B.

After 1 second, height achieved by [tex]\rm{Mel}= 50\; \text{Ft}[/tex]

After 5 seconds, the height remained is 35 feet.

In another case,

Now, the expression is used for evaluating the slope of the equation are formulated below:

[tex]\bold{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Where, [tex]m[/tex] is the slope and [tex]x[/tex] and [tex]y[/tex] are respective coordinates.

Hence, for Mel's case, apply the formula of slope and solve it further:

[tex]\begin{aligned}m_1&=\dfrac{35-50}{5-2} \\m_1&=-5 \end{aligned}[/tex]

So, the rate of change of Mel's height is 5 feet per second.

And for victor's case, slope will be:

[tex]m_2=\dfrac{50-60}{4-1} \\\\m_2=-3.33[/tex]

The rate of change of victor's height is 3.33 feet per second.

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Final answer:

The hyperbolas' equations are analyzed to find the values of a² and b². For the first equation, a² is 9 and b² is 16; for the second, a² is 4 and b² is 16; and for the third, a² is 3 and b² is 2.

Explanation:

To identify the required elements for each of the hyperbolas, we need to look at the equations of the hyperbolas and determine the values of a and b, which are the square roots of the denominators of the x-squared and y-squared terms when they are in the standard form for a hyperbola, x²/a² - y²/b² = 1 for horizontal hyperbolas, and y²/a² - x²/b² = 1 for vertical hyperbolas.

1. For the hyperbola x²/9 - y²/16 = 1, the required elements are a² and b². Hence, a² = 9 and b² = 16, leading to the answers being c and d respectively.

2. The hyperbola 4x² - y² = 16 can be rearranged to x²/4 - y²/16 = 1. Here, a² = 4 and b² = 16, making the answers c and d respectively.

3. For hyperbola 2y² - 3x² = 6, it rearranges to y²/3 - x²/2 = 1. In this case, a² = 3 and b² = 2, so the answers are d and a respectively, since we are looking for a and b, not a² and b².

The total time for two game is 32 minutes. The time for each game can be determine using system equation.

The time for game is 10 minute and 22 minute respectively.

Given:

Total time to complete two game is 32 minutes.

Let [tex]x[/tex] is the time took to complete one game.

Write the system equation for the given condition.

[tex]\begin{aligned}\\ x+x+12=32\\2x=32-12\\x=10 \:\rm min\\\end{aligned}[/tex]

As per the question, one game took 12 minutes longer than other. So the time for second game is,

[tex]x+12=10+12=22 \:\rm minutes[/tex]

Thus, the time took to complete game is [tex]10\:\rm minutes[/tex] and [tex]22\:\rm minutes[/tex] respectively.

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Use formula for the length of the arc:

[tex] \text{Arc Length} = (\theta\cdot \dfrac{\pi}{180^{\circ}}) \cdot r [/tex], where [tex] \theta [/tex] is central angle.

Substitute [tex] \theta [/tex] and r=3 into formula:

[tex] \text{Arc Length} = (\theta\cdot \dfrac{\pi}{180^{\circ}}) \cdot r=(70^{\circ}\cdot \dfrac{\pi}{180^{\circ}})\cdot 3=\dfrac{7}{6}\pi [/tex].

Answer: [tex] \text{Arc Length} =\dfrac{7}{6}\pi [/tex].

Answer:

its 3.7

Step-by-step explanation:

To compare Sandra's unit rate with Terrance's and Jesse's, we must calculate their speeds in mph. Terrance runs at 12 mph, Jesse at 8 mph, and Sandra at 10.67 mph. Therefore, Sandra is faster than Jesse but slower than Terrance.

To compare Sandra's unit rate to Terrance's and Jesse's, we need to determine the speed at which each person runs in miles per hour (mph). The given information is:
Terrance runs 6 miles every half hour.
Jesse runs 2 miles every 15 minutes.
Sandra runs 8 miles in 45 minutes.

First, we calculate each person's running speed:

Terrance: 6 miles in 0.5 hours (30 minutes), so we multiply by 2 to find his speed per hour: 6 miles ÷ 0.5 hours = 12 mph.

Jesse: 2 miles in 0.25 hours (15 minutes), so we multiply by 4 to find his speed per hour: 2 miles ÷ 0.25 hours = 8 mph.

Sandra: 8 miles in 0.75 hours (45 minutes), so we divide her distance by the time in hours: 8 miles ÷ 0.75 hours = 10.67 mph.

Therefore, compared to Terrance and Jesse, Sandra's running speed is:

Faster than Jesse's (10.67 mph > 8 mph)

Slower than Terrance's (10.67 mph < 12 mph)

The product of (6x - y)(2x - y + 2) is 12x² + y² -8xy + 12x -2y

The required table to multiply (6x - y)(2x - y + 2) is shown below.

"It is a mathematical statement that consists of constants, variables and some mathematical operations."

For given question,

We have been given an expression (6x - y)(2x - y + 2)

The product of above expression is,

(6x - y)(2x - y + 2)

= 6x(2x - y + 2) - y(2x - y + 2)

= 12x² - 6xy +12x - 2xy + y² - 2y

= 12x² + y² -8xy + 12x -2y

The required table to multiply (6x - y)(2x - y + 2) is shown below.

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