Ben drinks tea at an incredible rate. He drinks 3.5 loiters of tea every 2/3 of an hour. How many of liters of tea does he drink in one hour?

Final answer:

To subtract two polynomials, change the sign of the second polynomial and combine like terms. The result of subtracting (5x^2-3x-2) and (-2x^2-x+10) is 7x^2 - 2x - 12.

Explanation:

To subtract the given polynomials, (5x^2−3x−2) and (−2x^2−x+10), we need to change the sign of each term in the second polynomial and then combine like terms with the first polynomial. This is similar to subtracting negative numbers, where subtraction turns into addition when the number being subtracted is negative.

The subtraction process step-by-step is as follows:

Change the signs of the second polynomial: +2x^2 + x - 10

Add the results to the corresponding terms in the first polynomial:

5x^2 + 2x^2 = 7x^2

−3x + 1x = −2x

−2 − 10 = −12

So the answer to the subtraction in standard form is 7x^2 − 2x − 12.

The cost of the video game system is $144 and the cost of the games is $432.

Determining the costs of the video game system and the games:

Let the cost of the video game system be x, and the cost of the games be 3x since the games cost 3 times as much as the system.

The total cost is $576, so we can set up the following equation:

x + 3x = 576

Combining like terms:

4x = 576

Solving for x:

x = 576/4

​

x = 144

Now, we find the cost of the games:

The cost of the system is x = 144 dollars.

The cost of the games is 3x = 3 × 144 = 432 dollars.

Answer:

It is 30 exactly um. yes or no

Final answer:

With a daily budget of $98 for car rental, where the rental costs $35 per day plus 21 cents per mile, Jorge can drive a maximum of 300 miles per day.

Explanation:

If Jorge has $98 to spend for the daily car rental, where the cost comprises a fixed charge of $35 and 21 cents per mile, we use the equation 35 + 0.21x = 98 to find the maximum number of miles he can travel per day, with x representing the number of miles. Subtracting 35 from both sides of the equation gives us 0.21x = 63. Dividing both sides by 0.21 yields x = 300. Therefore, Jorge can drive a maximum of 300 miles per day within his budget.

9x+4 +32 = 90

9x+36 = 90

9x=54

x = 54/9 = 6

x = 6

Answer:

[tex]\frac{A1}{A2}[/tex]

Step-by-step explanation:

We are give that the distance travelled by the bird is A1.

And the time taken to fly this distance is A2.

Now we will find the speed with the formula mentioned below:

[tex]Speed=\frac{Distance}{time}[/tex]

Replacing Distance as A1 and Time as A2. We get speed of the bird as

[tex]\frac{A1}{A2}[/tex]

The required equation is x - 1/2 .

It is required to find the equation.

A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

Given:

According to given question we have,

The difference of a number x and 1/2 is

x - 1/2

Therefore, the required equation is x - 1/2 .

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To identify a segment congruent to segment AB based on the scenarios provided, one should look for shared lengths or properties of geometric figures that indicate congruence such as equal markings or vector properties.

The question appears to be discussing congruent segments within geometrical diagrams, likely in the context of triangles or vectors. In geometric terms, congruent segments are segments that have the same length. From the information provided, several scenarios involving congruent segments are described. For example, when two triangles within different mediums share a segment, such as AB', or when judgment is required to determine congruence, as in Asch's conformity study.

In order to determine which segment is congruent to segment AB without the accompanying diagram, one would need to look for indications of shared lengths, parallel lines, or properties of similar triangles or figures. Typically, one would look for notation such as 'equals' marks on the segments or use the properties of the specific geometric shapes given (like the properties of triangles or the rules pertaining to vectors) to identify congruent segments.

In the diagram, segment AB is congruent to the segment on the surface AB' which is shared by both the triangle ABB' and AA'B'.

In the given diagram, segment AB is congruent to the segment on the surface AB', which is shared by both the triangle ABB' inside medium 1 and the triangle AA'B' inside medium 2. This is because the angles

Becky bought 6 dried apples and 4 dried apricots if Becky bought seven more packages of dried apples than dried apricots. If she bought fifteen of these two fruits altogether.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Becky bought seven more packages of dried apples than dried apricots.

Let x be the number of dried apples

Let y be the number of dried apricots

x = y + 7

She bought fifteen of these two fruits all together

x + y = 15

The above two equation represents the linear equation in two variables, solving the linear equation in two variables by the substitution method:

y + 7 + y = 15

2y = 15 - 7

2y = 8

y = 8/2

y = 4

x = 4 + 2 = 6

Thus, Becky bought 6 dried apples and 4 dried apricots if Becky bought seven more packages of dried apples than dried apricots. If she bought fifteen of these two fruits altogether.

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Answer:

The solution for [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex] is [tex]\(y = 7 - 2x\).[/tex]

Explanation:

To solve the equation [tex]\(2x + y = 7\)[/tex] for [tex]\(y\)[/tex], we isolate [tex]\(y\)[/tex] by moving [tex]\(2x\)[/tex] to the other side of the equation. Subtracting [tex]\(2x\)[/tex] from both sides gives [tex]\(y = 7 - 2x\).[/tex]This expression represents [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex], indicating that [tex]\(y\)[/tex] is equal to [tex]\(7\)[/tex]minus twice the value of [tex]\(x\)[/tex]. Thus, for any given value of [tex]\(x\)[/tex], we can find the corresponding value of [tex]\(y\)[/tex] using this equation.

To solve the system of equations [tex]\(2x + y = 7\) for \(y\)[/tex], you can follow these steps:

1. Subtract [tex]\(2x\)[/tex] from both sides of the equation:

[tex]\[y = 7 - 2x\][/tex]

So, the solution for [tex]\(y\)[/tex] in terms of [tex]\(x\)[/tex] is [tex]\(y = 7 - 2x\).[/tex]

Answer:

D. $991.19

Step-by-step explanation:

He starts with $1,234.56 in his account. He has to pay for plumbing supplies, so he writes a check for $115.12 and we have to subtract that amount from his account.

Now he has $1,234.56 - $115.12 = $1,119.44

After that, he has to pay a loan so he writes a check for $225.00.

Now he has $1,119.44 - $225.00 = $894.44

Finally, he deposits $96.75 in his account, so we have to add that amount to the amount he had before.

That's $894.44 + $96.75 = $991.19

divide total distance by the number od descents they want to do it in

100 / 5 = 20

 so each one should be 20 feet

The relationship between parallel lines is that they have the same slope. The equation of the line that is parallel to [tex]2x = 1 - 3y[/tex] and passes through (9,4) is [tex]y=\frac 23x -2[/tex]

Given that:

[tex]2x = 1 - 3y[/tex]

First, we make y the subject

[tex]2x - 1 = 3y[/tex]

Divide both sides by 3

[tex]y = \frac 23x - \frac 13[/tex]

A linear equation is represented as:

[tex]y = mx + b[/tex]

Where:

[tex]m \to slope[/tex]

So, by comparison:

[tex]m = \frac 23[/tex]

Parallel lines have the same slope.

So the slope of the line that passes through (9,4) is [tex]m = \frac 23[/tex]

The equation is then calculated as:

[tex]y = m(x - x_1) + y_1[/tex]

Where:

[tex]m = \frac 23[/tex]

[tex](x_1,y_1) = (9,4)[/tex]

So, the equation becomes:

[tex]y = m(x - x_1) + y_1[/tex]

[tex]y = \frac 23(x - 9) + 4[/tex]

Expand

[tex]y = \frac 23x - 2 \times 3+ 4[/tex]

[tex]y=\frac 23x - 6 + 4[/tex]

[tex]y=\frac 23x -2[/tex]

Hence, the equation of the line that is parallel to [tex]2x = 1 - 3y[/tex] and passes through (9,4) is [tex]y=\frac 23x -2[/tex]

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