How many solutions does this linear system have?

y = x+ 2

6x – 4y = –10

one solution: (–0.6, –1.6)
one solution: (–0.6, 1.6)
no solution
infinite number of solutions

Answer:

the answer would be D

Step-by-step explanation:

The number of different selections possible when picking 6 numbers from a collection of 62 numbers for a LOTTO game is 62,891,499.

The question asks how many different selections are possible when picking 6 numbers from a collection of 62 numbers for a LOTTO game. Since the order of the selection does not matter, we can use the concept of combinations to solve this problem. The formula for combinations is given by C(n, r) = n! / (r! * (n-r)!), where n is the total number of items and r is the number of items selected. Plugging in the values, we have C(62, 6) = 62! / (6! * (62-6)!), which simplifies to 62! / (6! * 56!). Using a calculator or computer program to calculate the factorial, we find that C(62, 6) is equal to 62,891,499.

Final answer:

To find the number of different selections possible in a lotto where 6 numbers are chosen from 62, we use the combination formula: C(62, 6). This yields 45,057,474 possible selections.

Explanation:

Calculation of Different Selections in Lotto

To calculate the number of different selections possible when choosing 6 numbers from a set of 62 without regard to the order of selection, we use the combination formula:

The combination formula is C(n, r) = n! / (r! * (n-r)!), where C(n, r) is the number of combinations, n is the total number of items to choose from, r is the number of items to be chosen, and ! denotes factorial.

In this case, n = 62 and r = 6:

C(62, 6) = 62! / (6! * (62-6)!) = 62! / (6! * 56!)

Calculating the factorials and the division, we find that there are 45,057,474 possible selections.

Therefore, the probability of winning by correctly selecting all 6 numbers is 1 in 45,057,474, making lottery tickets a game of very low probability for individual success.

Answer:

300 cubic feet

Step-by-step explanation:

This isn't the only trick you'll need, but it will help you get these expressions in terms you'll be able to handle more easily. For example, for the cot example above: cot(-pi/2) = cos(-pi/2)/sin(-pi/2) = 0/-1 = 0

The exact values of the trig ratios are sqrt(2)/2, 0, and 2, for cos(13pi/4), cot(11pi/2), and sec(5pi/3) respectively.

To determine the exact value of the trig ratios, we can use the unit circle and trigonometric identities.

cos(13pi/4):

The angle 13pi/4 represents a full circle plus one revolution, so the cosine value is the same as cos(pi/4).

cos(pi/4) = sqrt(2)/2

cot(11pi/2):

The angle 11pi/2 represents 5 full circles plus a half revolution, so the cotangent value is the same as cot(pi/2).

cot(pi/2) = 0

sec(5pi/3):

The angle 5pi/3 represents 2 full circles plus two-thirds of a revolution, so the secant value is the same as sec(pi/3).

sec(pi/3) = 2

To subtract the polynomials, change the signs of the second polynomial and combine like terms. The result is -6m² + 11m - 6, which is option D.

To subtract the given polynomials, we need to subtract the second polynomial from the first one. We do this by changing the signs of the second polynomial and then combining like terms with the first.

(m² + 6m - 5) - (7m² - 5m + 1) becomes (m² + 6m - 5) + (-7m² + 5m - 1).

Now, combine the like terms:

So, the simplified form of the polynomial after subtraction is -6m² + 11m - 6, which corresponds to option D.

Answer:

it is c

Step-by-step explanation:

Answer:

Sometimes it is good to examine function analytically and sometimes it is good to examine function graphically it also depends on the nature of the function.

Moreover, when the function is examined graphically it does not shows the discontinuity of a single point, but it can be examined clearly by analytically.

Also, plotting the graph function is apparently clear by one view but it is not with examining the function analytically.

Final answer:

1 cm is a unit of length equal to [tex]10^{-2}[/tex],  meter while [tex]1 cm^2[/tex]is a unit of area equal to 10^{-4} square meters.

Explanation:

The difference between 1 cm and 1 cm2 is that 1 cm is a measure of length, while 1 cm2 is a measure of area. To clarify, 1 cm is equivalent to 10-2 meters (or 0.01 meters), and it represents a one-dimensional measurement. In contrast, 1 cm2 is the area of a square with 1 cm long sides. When converting to square meters (m2), remember that the conversion factor for area is the square of the conversion factor for length. Therefore, 1 cm2 equals (10-2 m)2 or 10-4 m2.

The intensity of a light bulb varies inversely as the square of the distance from the light bulb. To find the distance where the intensity is 40 w/m², use the inverse square law formula to solve for the distance.

The intensity of a light bulb varies inversely as the square of the distance from the light bulb. This means that as the distance increases, the intensity decreases.

If the intensity is 250 w/m² at a distance of 5 m, and we want to find the distance where the intensity is 40 w/m², we can use the inverse square law formula:

I₁d₁² = I₂d₂²

Plugging in the values, we get:

250 × (5)² = 40 × (d₂)²

Simplifying, we find that d₂² = 250 × (5)² / 40

d₂² = 312.5

Therefore, d₂ = √312.5 ≈ 17.68

So, it would be approximately 17.68 - 5 = 12.68 meters farther to a point where the intensity is 40 w/m².

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Sure, let's solve it step by step.

First, we know that the initial intensity (I1) is 250 w/m^2 and the initial distance (d1) is 5 m. We are asked to find a distance where the intensity is 40 w/m^2, which would be our final intensity (I2).

According to the inverse square law, the intensity of light is inversely proportional to the square of the distance from the source, i.e., I ∝ 1/d². Therefore, we can say that I1 * d1² = I2 * d2². This equation allows us to find the distance at which the intensity is I2.

So, substituting the given values in the equation, we have 250 * (5)² = 40 * d2².

Now, we can solve for d2. Rearranging terms, d2 = √((250 * (5)²) / 40), which will give us d2 = 12.5 m.

So, the distance at which the intensity of light is 40 w/m^2 is 12.5 m.

However, we have been asked to find the additional distance that needs to be traveled to reach a point where the intensity is 40 w/m^2. This additional distance is the difference between the final distance (d2) and the initial distance (d1), that is, distance_travelled = d2 - d1 = 12.5 - 5 = 7.5 m.

Therefore, you would need to travel an additional 7.5 m to reach a point with an intensity of 40 w/m^2.

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Answer:

[tex]y=(x-1)^{2}+4[/tex]

Step-by-step explanation:

To write this quadratic function in vertex form, which is the explicit form of the parabola, we have to complete the square in the expression.

First, we have to take the coefficient of the linear term and find the squared power of its half:

[tex](\frac{b}{2} )^{2}=(\frac{2}{2} )^{2}=1[/tex]

Then, we add and subtract this number in the quadratic expression:

[tex]y=x^{2}-2x+5+1-1[/tex]

Now, we use the three terms that can be factorize as the squared power of a binomial expression:

[tex]y=(x^{2}-2x+1)+5-1[/tex]

Then, we find the square root of the first term and third term, and we form the squared power:

[tex]y=(x-1)^{2}+4[/tex]

Now, this vertex form is explicit, because it says from the beginning what's the coordinates of the vertex, which is: [tex](1;4)[/tex], as minimum, because the parabola is concave up.

In vertex form, the quadratic equation is written as;

⇒ y = (x - 1)² + 4

An algebraic equation with the second degree of the variable is called an Quadratic equation.

We have to given that;

The quadratic equation is,

⇒ y = x² - 2x + 5

Now, We can write in vertex form as;

⇒ y = x² - 2x + 5

⇒ y = x² - 2x + 1 + 4

⇒ y = (x - 1)² + 4

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The volume V of a box with a square base of side a and a height that is three times its width is expressed as the function V(a) = 3a³.

To express the volume V of a box as a function of its base side length a, with the height being three times its width, we can use the formula for the volume of a rectangular prism, which is the product of its length, width, and height. As the base is a square with side a, both the length and the width of the base are a. Given that the box's height is three times its width (or length, since it is a square), the height will be 3a.

Therefore, the volume V of the box as a function of a is V(a) = a² × (3a) = 3a³.

Answer:

The area of shaded region is 45 square units.

Step-by-step explanation:

The length of the rectangle is 8 and the breadth is 6.

Area of rectangle is

[tex]A_R=l\times b[/tex]

[tex]A_R=8\times 6=48[/tex]

The area of rectangle is 48 square units.

Since the opposite sides of a rectangle are equal, therefore the legs of the right angled triangle are

[tex]l_1=8-5=3[/tex]

[tex]l_2=6-4=2[/tex]

The area of right angled triangle is

[tex]A_T=\frac{1}{2}\times l_1\times l_2[/tex]

[tex]A_T=\frac{1}{2}\times 3\times 2=3[/tex]

The area of triangle is 3 square units.

The area of shaded region is

[tex]A=A_R-A_L=48-3=45[/tex]

Therefore the area of shaded region is 45 square units.

The total time in minutes that he spent in reading is:

                                540 minutes.

We are asked to find the total number of minutes Jonathan spent on reading on Saturday.

It was given that he read for a total of 9 hours.

Hence, we will convert this time to minutes by using the conversion:

As 1 hour= 60 minutes.

Hence, 9 hours= 9×60 minutes= 540 minutes.

Hence, the total time Jonathan spent in reading on Saturday is:

                               540 minutes.