How many solutions does this system have?

5x - y = 3
2y = 10x + 2

a.one
b.two
c.an infinite number
b.no solution

Answer:

2:5!

Step-by-step explanation:

Have a great day!

Answer:

[tex]6000x=135000[/tex]

23 fire extinguisher.

Step-by-step explanation:

Let x be the number of fire extinguishers.

We have been given that one fire extinguisher be available for every 6,000 square feet in a building. So the total area covered by x extinguisher will be 6,000x.

Since the building has an area of 135,000 square feet. This means that that total area covered by x extinguisher is 135,000 square feet. We can represent this information in an equation as:

[tex]6000x=135000[/tex]

Therefore, the equation [tex]6000x=135000[/tex] represents the number of fire extinguishers needed for a building that has 135,000 square feet.

Now we will solve for by dividing both sides of our equation by 6000.

[tex]\frac{6000x}{6000}=\frac{135000}{6000}[/tex]

[tex]x=\frac{135}{6}[/tex]

[tex]x=22.5[/tex]

Since we can not have 0.5 of a fire extinguisher, so we will round up our answer as:

[tex]x\approx 23[/tex]

Therefore, 23 fire extinguisher are needed for the building.

Answer:

1

Step-by-step explanation:

39 days would it take for the patch to cover half of the loaf of bread

We have given that on a loaf of bread, there is a patch of mold. Every day, the patch doubles in size.

Number of days for the patch to cover the entire loaf of bread = 40 days

if we go forward, the mold doubles in size in one day and if we go backwards the mold covers half the size in one less day.

So, number of days for the patch to cover the entire loaf of bread - 1

=40 — 1

= 39

Therefore, it would takes 39 days for the patch to cover half of the loaf of bread.

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Considering the mold's exponential growth, it doubles every day. Hence, the mold would have covered half of the loaf of bread one day before it covers the entire loaf, which is on the 39th day.

The subject of this question is a mathematical concept known as exponential growth, which is when a quantity increases by the same proportion over a given period of time. Here, on a loaf of bread, a patch of mold is doubling in size every day, which is a classic example of exponential growth.

In the scenario provided, it takes 40 days for the mold to cover the entire loaf of bread. Given the nature of exponential growth, if the size of the mold doubles every day, then the day before the whole loaf is covered, half of the loaf must be covered. Therefore, it would take 39 days for the patch to cover half of the loaf of bread.

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If line AB is parallel to line CD and line CD is perpendicular to line EF, we can conclude that line AB is also perpendicular to line EF.

If line AB is parallel to line CD and line CD is perpendicular to line EF, we can conclude that line AB is also perpendicular to line EF.

The reason for this is that if two lines are parallel to the same line, they are parallel to each other. In this case, we have line AB and line CD both parallel to line EF. Then, because line CD is perpendicular to line EF, line AB must also be perpendicular to line EF.

To find the number of cases of coffee ordered, we can set up a system of equations using the total cost and number of cases. The solution is 150 cases of coffee.

To solve this problem, we can set up a system of equations. Let's assume the number of cases of coffee ordered is represented by x. Since coffee costs $12 per case, the total cost of the coffee would be $12x. And since tea costs $8 per case, the total cost of the tea would be $8(250 - x), since the total number of cases is 250. We know that the total cost of the order is $2,600, so we can set up the equation:

$12x + $8(250 - x) = $2,600

Simplifying this equation, we get:

$12x + $2000 - $8x = $2,600

Combining like terms, we have:

$4x + $2000 = $2,600

Subtracting $2000 from both sides, we get:

$4x = $600

Dividing both sides by $4, we find:

x = 150

Therefore, 150 cases of coffee were ordered.

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Solution:

we have been asked to find the graph of the equation

[tex]f(x)=\frac{2x}{x^2-1}[/tex]

We can get the graph by simply taking some values for the variable x and working out the value of the variable y. Then we just need to put those values on the graph and connect.

when[tex]x=-3, y=f(-3)=\frac{2\times(-3)}{(-3)^2-1}=\frac{-6}{8}=-0.75[/tex]

when[tex]x=-2, y=f(-2)=\frac{2\times(-2)}{(-2)^2-1}=\frac{-4}{3}=-  1.33[/tex]

when[tex]x=0, y=f(0)=\frac{2\times(0)}{(0)^2-1}=0[/tex]

when[tex]x=2, y=f(2)=\frac{2\times(2)}{(2)^2-1}=\frac{4}{3}= 1.33[/tex]

when[tex]x=3, y=f(3)=\frac{2\times(3)}{(3)^2-1}=\frac{6}{8}=0.75[/tex]

Also function is not defined at [tex]x=\pm1[/tex]

Now put theses value on the graph and connect the points, we will get the graph as attached.

Answer:

640 m

Step-by-step explanation:

We can consider 4 seconds to be 1 time unit. Then 8 more seconds is 2 more time units, for a total of 3 time units.

The distance is proportional to the square of the number of time units. After 1 time unit, the distance is 1² × 80 m. Then after 3 time units, the distance will be 3² × 80 m = 720 m.

In the additional 2 time units (8 seconds), the ball dropped an additional

... (720 -80) m = 640 m

_____

Alternate solution

You can write the equation for the proportionality and find the constant that goes into it. If we use seconds (not 4-second intervals) as the time unit, then we can say ...

... d = kt²

Filling in the information related to the first 4 seconds, we have ...

... 80 = k(4)²

... 80/16 = k = 5

Then the distance equation becomes ...

... d = 5t²

After 12 seconds (the first 4 plus the next 8), the distance will be ...

... d = 5×12² = 5×144 = 720 . . . meters

That is, the ball dropped an additional 720 -80 = 640 meters in the 12 -4 = 8 seconds after the first data point.

The cost function is a linear function

The function is given as:

[tex]\mathbf{C(x) = 17.5x - 10}[/tex]

(a) The cost of 10 tickets

This means that: x= 10

So, we have:

[tex]\mathbf{C(x) = 17.5x - 10}[/tex]

[tex]\mathbf{C(10) = 17.5 \times 10 - 10}[/tex]

[tex]\mathbf{C(10) = 175- 10}[/tex]

[tex]\mathbf{C(10) = 165}[/tex]

Hence, the cost of 10 tickets is $165

(b) The number of tickets that costs $130

This means that C(x) = 130

So, we have:

[tex]\mathbf{C(x) = 17.5x - 10}[/tex]

[tex]\mathbf{130 = 17.5x - 10}[/tex]

Add 10 to both sides

[tex]\mathbf{140 = 17.5x}[/tex]

Divide both sides by 17.5

[tex]\mathbf{8 = x}[/tex]

Rewrite as:

[tex]\mathbf{x = 8}[/tex]

Hence, you can buy 8 tickets with $130

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The next thing Kevin should do is to write the result in standard form

The standard form of scientific notation is expressed as [tex]A \times 10^n[/tex] where:

Given the product of 3.2 × 10^4 and 3.6 × 10^2 as 11.52 × 10^6, the next thing Kevin should do is to write the result in standard form as shown:

[tex]11.52 \times 10^6 = 1.152 \times 10 \times 10^6\\ 11.52 \times 10^6 = 1.152 \times 10^7[/tex]

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Answer:

4/6 or 2/3

Step-by-step explanation:

Amount of bread Tom ate= Tom ate in morning + Tom ate in evening

                                          = 1/6 + 3/6

                                          = 3+1/6

                                          = 4/6

                                          = 2/3

In an isometric transformation, the preimage and image must not change size. Therefore, the correct option is A.

Answer:

Let A = (5, -1) (x1, y1)

Let B = (10, -1) (x2, y2)

Length AB =

[tex] = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]

[tex] = \sqrt{ {(10 - 5)}^{2} + {( - 1 + ( - 1))}^{2} } [/tex]

[tex] \\ = \sqrt{ {(5)}^{2} + {( - 2)}^{2} } [/tex]

[tex] = √25 - 4[/tex]

[tex] = √21[/tex]

Final answer:

Sine and cosine functions are limited to values between -1 and 1, as they represent ratios of sides in a right triangle and cannot exceed the length of the hypotenuse. The tangent function, however, can have values from negative to positive infinity since it represents the ratio of the sine to the cosine, and as the cosine approaches zero, the tangent value can approach infinity.

Explanation:

There are indeed limits to the values of sine, cosine, and tangent functions based on their definitions in a right triangle. For a right triangle, where x is the adjacent side, y is the opposite side, and h is the hypotenuse:

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. Therefore, the sine function has a value range between -1 and 1 because the length of a side of a triangle cannot exceed the length of the hypotenuse.

The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. Like sine, the cosine values are also confined between -1 and 1.

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. Unlike sine and cosine, tangent does not have a maximum finite value because as the angle approaches 90 degrees, the length of the adjacent side approaches zero, making the ratio infinitely large.

The magnitude of the sine and cosine functions are capped due to the properties of a circle (since all right triangles can be inscribed in a circle) and the Pythagorean theorem, which together imply that the hypotenuse will always be greater than or equal to the lengths of the other two sides. In contrast, the tangent function can grow without bound as it is the sine function divided by the cosine function, and as the cosine of an angle approaches zero, the division can tend toward infinity. This is why the tangent function can have a much larger range of values and includes infinity and negative infinity even though sine and cosine are limited to the range [-1,1].