Write the equation of the line with slope -2/3 and y-intercept 3.

Write the answer in slope-intercept form.​

The solution to the nonlinear system of equations is (x, y) = (-3, -2) and (x, y) = (1, 6). These points represent the coordinates where the two equations intersect and satisfy both equations simultaneously.

To solve the nonlinear system of equations:

Equation 1: \(y = -x^2 + 7\)

Equation 2: y = 2x + 4

We can equate the right sides of both equations since they both represent y.

\(-x^2 + 7 = 2x + 4\)

To simplify the equation, we can rearrange it to be in the standard quadratic form:

\(x^2 + 2x - 3 = 0\)

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

(x + 3)(x - 1) = 0

From this equation, we get two possible solutions:

x + 3 = 0 => x = -3

x - 1 = 0 => x = 1

Now, we substitute these x-values back into either equation to find the corresponding y-values.

For x = -3:

y = 2(-3) + 4

y = -6 + 4

y = -2

For x = 1:

y = 2(1) + 4

y = 2 + 4

y = 6

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True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.

In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.

To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.

It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.

In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

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The solution is:  (A) y+4=-3(x+6), is the equation of the line in point-slope form.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

here, we have,

The point-slope form of the equation of a line whose slope is m and passes through the point (x1,y1) is:

y-y1 = m (x-x1)

Given the point:

(x1,y1) = (-6, -4)

Slope, m= -3

x1 = -6,

y1 =-4

Substituting these values into: y-y1 = m (x-x1) , we obtain the point slope form of the equation:

we get,

y+4=-3(x+6)

The correct option is A.

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complete question:

The graph of a line has a slope of -3 and passes through the point (-6,-4).

What is the equation of the line in point-slope form?

Oy + 4 = -3(x + 6)

y + 6 = -3(x + 4)

y-4 = -3(x-6)

y-6 = -3(x – 4)

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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The two cars must be approximately 177.34 feet apart from each other for Spiderman to have different depression angles to each car.

To find the distance between the two cars, we can use trigonometry and the concept of similar triangles. Let's denote the distance between Spiderman and the nearest car as d1 and the distance between Spiderman and the farther car as d2.

In a right triangle formed by Spiderman, the height of the hotel, and the line of sight to the nearest car, the tangent of the depression angle (52 degrees) can be used:

tan(52) = 600 / d1

Rearranging the equation to solve for d1:

d1 = 600 / tan(52)

Similarly, in the right triangle formed by Spiderman, the height of the hotel, and the line of sight to the farther car, the tangent of the depression angle (46 degrees) can be used:

tan(46) = 600 / d2

Rearranging the equation to solve for d2:

d2 = 600 / tan(46)

Using a calculator, we can compute:

d1 ≈ 504.61 feet

d2 ≈ 681.95 feet

The distance between the two cars is the difference between d2 and d1:

Distance = d2 - d1

Plugging in the values, we have:

Distance ≈ 681.95 - 504.61

Distance ≈ 177.34 feet

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Answer:

51

Step-by-step explanation:

Use an online calculator

Answer:

The son has washed most of the laundry.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To multiply 4×5⅜, the mixed number can be broken down into a whole number and a fraction. In this case, that whole number would be 5 and the fraction would be three-eighths. Each of these parts are then multiplied by 4 and the products are added together.

4×5⅜ = 4×(5+⅜)

= 4×5 + 4×⅜

= 20 + 3/2

= 20 + 1½

= 21½

Answer:

I think its 40

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

Got it right on the assignment.

Hope this helps!!

Answer:

It might have convinced European nations to align with the South.

Step-by-step explanation:

i did this one twice

After 24 years, the amount will be $40,000

What is annual interest rate?

An annual percentage rate is expressed as an interest rate. It calculates what percentage of the principal you'll pay each year by taking things such as monthly payments into account.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

Formula:

a(t) = p*2^(t/8)

given, t=24 , p =5000

a(24) = 5000*2^(24/8)

a(24) = 5000*2^3

a(24) = 5000*8

a(24) = $40,000

Thus, after 24 years, the amount will be $40,000

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Answer:

Step-by-step explanation:

Answer:

9%=9/100=0.09 is in decimal

Answer:

0.09 = 9%

Step-by-step explanation:

9%= \(\frac{9}{100}\)

move the decimal twice left.

0.09

The arrow is at a height of 48 ft after approx. 3 - √6 s and after 3 + √6 s.

To find the time it takes for the arrow to reach a height of 48 ft, we can use the formula for the height of the arrow:

s = v0t - 16t^2

Here, s represents the height of the arrow, v0 is the initial velocity, and t is the time.

Given that the initial velocity, v0, is 96 ft/s and the height, s, is 48 ft, we can set up the equation:

48 = 96t - 16t^2

Now, let's solve this equation to find the time it takes for the arrow to reach a height of 48 ft.

Rearranging the equation:

16t^2 - 96t + 48 = 0

Dividing the equation by 16 to simplify:

t^2 - 6*t + 3 = 0

We now have a quadratic equation in the form of at^2 + bt + c = 0, where a = 1, b = -6, and c = 3.

Using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values:

t = (6 ± √((-6)^2 - 413)) / (2*1)

t = (6 ± √(36 - 12)) / 2

t = (6 ± √24) / 2

Simplifying the square root:

t = (6 ± 2√6) / 2

t = 3 ± √6

Therefore, the arrow reaches a height of 48 ft after approximately 3 + √6 seconds and 3 - √6 seconds.

In summary, the arrow takes approximately 3 + √6 seconds and 3 - √6 seconds to reach a height of 48 ft, assuming an initial velocity of 96 ft/s.

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Note the complete question is

The height of an arrow shot upward can be given by the formula s = v0*t - 16*t², where v0 is the initial velocity and t is time.How long does it take for the arrow to reach a height of 48 ft if it has an initial velocity of 96 ft/s?  

Solve (t-3)^2=6

The arrow is at a height of 48 ft after approx. ___ s and after ___ s.

Answer:

a=10

Step-by-step explanation:

use a^2+b^2=c^2

(a+2)^2+(a-5)^2=(a+3)^2

a^2+4a+4+a^2-10a+25=a^2+6a+9

2a^2-6a+29=a^2+6a+9

a^2-12a=-20

a^2-12a+20=0

quadratic formula→(12+/-8)/2

a=10 or 2

2 is not an option because 2-5=-3 which isn't possible in this case.

so a=10

Apply Pythagorean theorem

There is a side a-5 so 2 is not a answer

The production schedule for maximum profit is; X = 3 and Y = 6 with a maximum profit of $960

We are told that  two products X and Y, has a total production capacity of 9 tones per day, X and Y requiring the same production capacity

The firm has a permanent contract to supply at least 2 tones of X and at least 3 tones of Y per day to another company.

Let product A be x and product B be y. Therefore we have the following inequalities and constraints as;

x + y ≤ 9

x ≥ 2

y ≥ 3

Now, we are told that each tonne of A requires 20 machine hours of production time and each tonne of B requires 50 machine hours of production time. The daily maximum possible number of machine hours is 360. Thus, we have;

20x + 50y ≤ 360

Wea re told that all the firm's output can be sold and the profit made is $80 per tonne of A and $120 per tonne of B. Thus, we have the inequality as;

Z = 80x + 120y  maximize

The solution from the graph attached is;

x = 3, y = 6

Thus, the maximum profit is;

Z = 80(3) + 120(6)

Z = 960

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\(x\geq \frac{17s}{3}-8\).

\(17s-3x+2\leq 26\)

\(-3x\leq 26-17s-2\)

\(-3x\leq 24-17s\)

\(3x\geq 17s-24\)

\(x\geq \frac{17s-24}{3}\)

\(x\geq \frac{17s}{3}-\frac{24}{3}\)

\(x\geq \frac{17s}{3}-8\).

Answer:

D

Step-by-step explanation:

ANSWER:

A) 120 miles

STEP-BY-STEP EXPLANATION:

We can determine at a distance through the graph, just like this:

This means that at 4 hours they have driven 120 miles.

Therefore, the correct answer is: A) 120 miles

Answer:

$5 + 2.50k ≤ $20

6 kilometers

Step-by-step explanation:

Puedes viajar con $15 porque gastaste 5 en la tarifa base. 15 dividido por 2,5 es 6, por lo que puedes viajar 6 kilómetros con $20.

The two numbers that have a negative sum are the ones in option D.

-(2+ 2/3) and 2.2

Two numbers have a negative sum if:

Here we need to look at the last option, we have the two numbers:

-(2 + 2/3) and 2.2

If we write the mixed number as a decimal, we will get:

2 + 2/3 = 2 + 0.66 = 2.66

Then:

-(2 + 2/3) = -2.66

Now we can add the two numbers to get:

-2.66 + 2.2 = -0.46

The sum is negative.

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Answer:

95%: (3278.354 ; 3270.083)

99% : (3221.646 ; 3278.354)

Step-by-step explanation:

Given :

Sample size, n = 12

Mean, xbar = 3250

Sample standard deviation = √1000

The 95% confidence interval :

Mean ± Margin of error

Margin of Error = Tcritical * s/√n

Tcritical at 0.05, df=12-1 = 11 ;

Tcritical at 95% = 2.20

Hence,

Margin of Error = (2.20 * √1000/√12) = 20.083

Confidence interval : 3250 ± 20.083

Lower boundary = 3250 - 20.083 = 3229.917

Upper boundary = 3250 + 20.083 = 3270.083

2.)

The 99% confidence interval :

Mean ± Margin of error

Margin of Error = Tcritical * s/√n

Tcritical at 0.01, df=12-1 = 11 ;

Tcritical at 99% = 3.106

Hence,

Margin of Error = (3.106 * √1000/√12) = 28.354

Confidence interval : 3250 ± 28.354

Lower boundary = 3250 - 28.354 = 3221.646

Upper boundary = 3250 + 28.354 = 3278.354

Answer:

9.533

Step-by-step explanation:

1+(-2/3)-(-9.2)

1-2/3--9.2

1-2/3+9.2=9.533

Answer:

coefficient..........

The value of the vehicle after 12 years of purchase will be $13,500.

Here, we are given that a vehicle purchased for $25,000 depreciates at a constant rate of 5%.

Therefore, the value of the vehicle after 1 year will reduce by-

25,000 × 5/100

= 250 × 5

= 1250

Thus, the value after 1 year will become = 25,000 - 1250 = 23750

In the same manner, the value will keep on reducing every year. Thus, the value after 12 years will become-

25,000 \((1- 5/100)^{12}\)

= 25,000 \((1 - 0.05)^{12}\)

= 25,000 \((0.95)^{12}\)

= 25,000 × 0.54

= 250 × 54

= 13,500

Thus, the value of the vehicle after 12 years of purchase will be $13,500.

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The length of the arc KL in the given circle is 3.49 units

In a circle whose radius is R, the length of an arc defined by an angle x is given by:

Length = (x/360)*2*3.14*R

Here we know that the radius is 2 units, and the angle for the arc KL is 100°, then we can replace these values in the formula above so we get that the length of the arc is:

Length = (100/360)*2*3.14*2

Lenght = 3.49 units.

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Answer:

Step-by-step explanation:

Decrease in number:

Percent decrease:

Answer:

0 because 1-1=0 and that is the answer

Answer:

There are 60 dvds.

Step-by-step explanation:

72 - 3 - 9 = 60