Solve the following system of equations.

The equation [tex]y = x^2 + 4x - 12[/tex] represents a parabolic curve in a 2D coordinate system.

What is graph?

A graph is a concept in mathematics and computer science that involves a set of nodes or vertices, linked together by edges to depict the interconnections between objects. Graphs are a powerful method for examining complex relationships within diverse systems, including communication networks, transportation systems, and social networks.

To graph this equation, you can follow these steps:

Choose a range of values for x that you want to plot. For example, you might choose x values from -6 to 2.

For each x value, calculate the corresponding y value by plugging it into the equation. For example, if x = -6, then y = [tex](-6)^2[/tex] + 4(-6) - 12 = 0.

Plot each (x, y) pair on the graph.

Connect the plotted points with a smooth curve to represent the parabolic shape of the equation.

Using these steps, you can graph the equation [tex]y = x^2 + 4x - 12[/tex] to visualize its shape and better understand its behavior.

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The given statement "  to calculate the value of the 50th term, you could assume 5 is g(1). then, using the growth factor of 3, use g(n) = 5*3^n-1 with n = 50 to find g(50)" is true. Assuming that 5 is g(1), we can use the growth factor of 3 to find the value of g(50) using the formula g(n) = 5*3^(n-1).

Assuming that 5 is the first term of the sequence g(n), we can use the formula g(n) = 53^(n-1) to find any term of the sequence. This formula gives us the value of the nth term in the sequence, where n is any positive integer.

For example, if we want to find the 50th term of the sequence, we simply substitute n = 50 into the formula and calculate g(50) = 53^(50-1) = 5*3^49. Therefore, we can use this formula to find any term of the sequence, given the first term and the growth factor. so, the given statement is true.

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--The given question is incomplete, the complete question is given

" true or false: to calculate the value of the 50th term, you could assume 5 is g(1). then, using the growth factor of 3, use g(n) = 5*3^n-1 with n = 50 to find g(50)."--

Net WPM is a better formula than Gross WPM to calculate typing speed because it provides a more comprehensive and accurate measure of a person's typing abilities

Speed is a measure of how fast an object or person is moving. It is usually expressed in units of distance per unit of time, such as miles per hour (mph), kilometers per hour (km/h), or meters per second (m/s).

Net WPM is a better formula than Gross WPM to calculate typing speed because it takes into account the number of errors made during typing.

Gross WPM (Words Per Minute) is calculated by dividing the total number of characters typed by 5 (the average number of characters in a word) and then dividing the result by the time taken to type those characters in minutes.

However, Gross WPM does not account for any mistakes made during typing.

On the other hand, Net WPM calculates the typing speed by subtracting the number of errors made during typing from the total number of words typed and then dividing the result by the time taken to type.

This formula provides a more accurate measure of the typing speed, as it takes into account the accuracy of typing as well as the speed.

Therefore, Net WPM is a better formula than Gross WPM to calculate typing speed because it provides a more comprehensive and accurate measure of a person's typing abilities

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Answer:

Samuel will need 614 2/3 feet of material to build eight of his standard fences. To find this answer, we simply need to multiply 76 2/3 feet (the perimeter of one fence) by 8 (the number of fences he wants to build). Thus, 76 2/3 feet x 8 = 614 2/3 feet.

The value of f is -10.

What is an inverse function?

An inverse in mathematics is a function that "undoes" another part. In other words, if f(x) produces y, y entered into the inverse of f producing x. An invertible function has an inverse, and the inverse is represented by the symbol f1.

Here, we have

Given: If f varies inversely as g, and when g = -6, f = 15.

We have to find the value of f.

f ∝ 1/g

f₁ ×g₁ = f₂ ×g₂

Let the required value of f = x

Inserting in equation (1) and we get

15 × (-6) = x × 9

-90/9 = x

x = -10

Hence, the value of f is -10.

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$30.21  is the total amount, in dollars, the customer pays for the discounted book.

If the original price of the book was $38, and it was discounted by 25%, then the discounted price of the book would be:

Discounted price = Original price - Discount

Discounted price = $38 - 0.25 x $38

Discounted price = $28.50

Now, the customer must pay a 6% sales tax on the discounted price of the book. The sales tax can be calculated as:

Sales tax = 0.06 x Discounted price

Sales tax = 0.06 x $28.50

Sales tax = $1.71

Therefore, the total amount the customer pays for the discounted book is the sum of the discounted price and the sales tax:

Total amount = Discounted price + Sales tax

Total amount = $28.50 + $1.71

Total amount = $30.21

So, the customer pays $30.21 for the discounted book

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The ratio representing the sine of angle ∠M in triangle MNO, where ∠O = 90°, MO = 8, ON = 15, and NM = 17, is 17/8.

In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this problem, we are given a right triangle MNO, with a right angle at O. The side opposite angle M is MN, and the hypotenuse is MO.

To find the sine of angle M, we use the formula sin(M) = opposite/hypotenuse, where the opposite side is MN and the hypotenuse is MO.

Using the Pythagorean theorem, we can find the length of side MN:

[tex]MN^2 = MO^2 + ON^2[/tex]

[tex]MN^2 = 8^2 + 15^2[/tex]

[tex]MN^2[/tex] = 289

MN = 17

Therefore, the sine of angle M is:

sin(M) = MN/MO

sin(M) = 17/8

The ratio that represents the sine of angle M is 17/8.

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Answer: 17

Step-by-step explanation:

First, you would subtract 30 from 120 to see how much money is left over for the classes, which is 90. Now you would divide 90 by 5 to see how many classes you can go to with the leftover money, which is 18. But since this is the same as the 120, just take away one lesson so it's sum would be less than 120, which would be 17. Hope this helps

Answer:

The sisters will spend a total of $240 on their mom for Christmas.

Step-by-step explanation:

$60 x 4 (sisters) = $240

The required sample size is 108, to estimate the population mean with a 98% confidence level.

The following formula can be used to determine the required sample size.

n = ((z*σ) / E)^2

where:

n = sample size

z = z-score corresponding to desired confidence level (98% = 2.33 for two-sided test)

σ = population standard deviation (specified in the problem)

E = tolerance (2 for the problem)

After plugging in the values ​​it looks like this:

n = ((2.33*) / 2)^2

n=107.13

Rounding up to the nearest integer, the required sample size is 108.

Therefore, a sample size of at least 108 is required to estimate the population mean with a 98% confidence level and a margin of error of 2, taking the population standard deviation as approximate.

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Two equations that represent the line that is parallel to 3x - 4y = 7 and passes through the point (-4,-2) are [tex]y + 2 = (\frac{3}{4})(x + 4)[/tex] and [tex]y = (\frac{3}{4})x - 5[/tex]. So, option A and D are correct.

We know that a line parallel to 3x - 4y = 7 will have the same slope as the given line. So, we can rearrange the equation 3x - 4y = 7 into slope-intercept form y = mx + b to find the slope:

3x - 4y = 7

-4y = -3x + 7

[tex]y = (\frac{3}{4}) x - \frac{7}{4}[/tex]

Therefore, the slope of the line is 3/4.

Now, we can use the point-slope form of the equation of a line to write the equations of the line that is parallel to 3x - 4y = 7 and passes through the point (-4,-2):

[tex]y - (-2) = \frac{3}{4} *(x - (-4))[/tex] or [tex]y - (-2) = \frac{3}{4} x - 3[/tex]

Simplifying these equations, we get:

[tex]y + 2 = (\frac{3}{4})(x + 4)[/tex] or [tex]y = (\frac{3}{4})x - 5[/tex].

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The total distance of the trip is 600 km if a train meet with an accident and then proceed further with its former speed.

Normal time be x for remaining distance, but time taken = 4x/3

Difference in time = (1+1/2+4x/3)−(1+x)=72

x=9

2nd case of going further 90 km which lessens the difference by 1/2

If it loses 90 km in 1/2 hr.

Total difference was 3 + 1/2 out of which 1/2 was for repair

Difference in travelling is 3+1/2-1/2=3 hrs

It will lose 3 hrs in 90 x 6=540 km

Now it travelled for 10 hr hours, which is 1 hr + 540 km

So 540 in 9hr

So 60 km per hour

Total distance = 540+60=600km

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-- The given question is incomplete, the complete question is

"A train, an hour after starting, meet with an accident which delays it for half an hour and after this, it proceeds at 3/4th of its former rate and arrives 3.5 hrs late. Had the accident happened 90 km farther along the line, it would have arrived only 3 hour late. What is the length of trip in km?" --

5) The measure of arc BC is 1.14π radians and the length of arc BC is 2.86π units.

6) The measure of arc ABC is 1.99π radians and the length of arc ABC is 3.14π units.

An arc is a curved line that is a portion of a circle.

It is formed by connecting two points on the circumference of the circle with a curve.

5) BC: To find the measure of arc BC, we need to find the measure of angle BAC.

angle BAC = angle AOC

angle BAC = 129 degrees

Therefore, the measure of arc BC is:

arc BC = (129/360) x (2π x 4)

arc BC = 1.14π radians

To find the length of arc BC, we need to find the measure of angle BAC.

angle BAC = angle AOC

angle BAC = 129 degrees

Therefore, the length of arc BC is:

arc BC = (129/360) x (2π x 4)

arc BC = 2.86π

6) ABC:  To find the measure of arc ABC, we need to find the measure of angle BOC.

angle BOC = 360 - angle AOB - angle AOC

angle BOC = 360 - 51 - 83

angle BOC = 226 degrees

Therefore, the measure of arc ABC is:

arc ABC = (226/360) x (2π x 4)

arc ABC = 1.99π radians

To find the length of arc ABC, we need to find the measure of angle BOC.

angle BOC = 360 - angle AOB - angle AOC

angle BOC = 360 - 51 - 83

angle BOC = 226 degrees

Therefore, the length of arc ABC is:

arc ABC = (226/360) x (2π x 4)

arc ABC = 3.14π

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The complete question is -

Answer:

Step-by-step explanation:

1/4 divided by 3/2 as a fraction

1/4 : 3/2 =  (flip 3/2 and change the sign from division to multiplication)

1/4 × 2/3    (semplify)

1/2 × 1/3 =  (solve)

1/6

Answer:

= 1/6

Step-by-step explanation:

(1/4) ÷ (3/2) = (1*2) ÷ (4*3) = 2/12

= 1/6

The curve described by these parametric equations is the graph of the Cartesian equation: x = 2e^[(1 - y)/5]

To eliminate the parameter t, we need to find a way to express t in terms of x and y, and then substitute that expression into one of the equations to eliminate t.

x(t) = 2e^t

y(t) = 1 - 5t

Let's start by solving the second equation for t:

y = 1 - 5t

Adding 5t to both sides, we get:

5t = 1 - y

Dividing both sides by 5, we get:

t = (1 - y)/5

Now we can substitute this expression for t into the first equation:

x = 2e^t

x = 2e^[(1 - y)/5]

This is the Cartesian equation in terms of x and y. We have eliminated the parameter t and expressed the equation solely in terms of x and y.

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Angles are measured in degrees and radians, and can be created by joining the extremities of two rays. The joint vertex is the common terminal of the two beams. Thus, ∠SRT = 38.16°.

An angle is the result of the intersection of two lines.

An "angle" is the length of the "opening" between these two beams.

Angles are commonly measured in degrees and radians, a measurement of circularity or rotation.

In geometry, an angle can be created by joining the extremities of two rays. These rays are intended to represent the angle's sides or limbs.

The two primary components of an angle are the limbs and the vertex.

The joint vertex is the common terminal of the two beams.

According to our question,

6x-66°+5x-26°+70°+x+70°=360°

6x+5x+x+ 66°+140°=360°

12x+ 206°=360°

12x=360°-206°

12x=  154°

x= 154/12°

Hence, ∠SRT = 5x - 26°

                       = 5 * 154/12° - 26°

                       = 770/12° - 26°

                       = 64.16° - 26°

                       = 38.16°

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It has been proved from the given equation that (2 + -7 + 2 = -3)

A rational equation is defined as an equation that containins at least one fraction whose numerator and denominator are polynomials. These fractions may be on one or both sides of the equation.

Now, we are given the rational expression as:

√(2 + -7 + 2 = -3)

In order words, we want to prove that:

(2 + -7 + 2 = -3)

The left hand side, when we multiply + and - sign, we have negative sign and as such we will have:

2 - 7 + 2

= 4 - 7

= -3

This is same as the right hand side of the original equation

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The expression  [tex]^3\sqrt {27x} + ^3\sqrt{x}[/tex] is equivalent to 0 when x=0.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

If x=0, then the expression [tex]^3\sqrt {27x} + ^3\sqrt{x}[/tex] becomes:

And we are given that x=0. So, we can substitute x=0 into the expression:

[tex]^3\sqrt{ 27 * 0} + ^3\sqrt{0}[/tex]

= 0 + 0 = 0

The first term simplifies to ∛(0), which is 0, because any number raised to the 1/3 power and multiplied by 0 is equal to 0.

The second term also simplifies to ∛(0), which is 0, because any number raised to the 1/3 power and multiplied by 0 is equal to 0.

Therefore, the sum of the two terms is 0.

Hence, the expression  [tex]^3\sqrt {27x} + ^3\sqrt{x}[/tex] is equivalent to 0 when x=0.

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To find out how many games the soccer team won, we need to multiply the total number of games they played by the percentage of games they won.

25% of 32 games can be calculated as:

0.25 x 32 = 8

Therefore, the soccer team won 8 games out of 32.

Step-by-step explanation:

30% of 500 voted for Sycamore

30% x 500   =   .30  * 500 = 150  votes

Fox Glen got the most votes

Step-by-step explanation:

give atleast 2 situations,in which you would store the data on cloud storage

Relationship between the area and the circumference of the circle is that they are proportional to each other.

The relationship between the area and the circumference of a circle with a radius of 5 units that has an area of 78.5 units² and a circumference of 31.4 units can be expressed as follows:

Area = πr²

where r is the radius of the circle.

Area = π(5)² = 78.5 units²

Therefore, the area of the circle is 78.5 units².

Circumference = 2πr,

where r is the radius of the circle.

2πr = 31.4 units

Therefore, 2π(5) = 31.4 units

Therefore, the circumference of the circle is 31.4 units.

Since the radius is the same, the relationship between the area and the circumference of the circle is that they are proportional to each other.

Area : Circumference

πr² :  2πr

r : 2

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Answer:

Tony is not correct because 3(x^2-25) can be factored further. The final answer is 3(x+5)(x-5)

Step-by-step explanation:

Reasons to include an interaction term in our model include (1) to estimate context-specific effects of some predictor variable on the outcome (y) and (2) if the joint effect of two variables on the outcome cannot be correctly modeled as the sum of the main effects associated with each variable. So, the correct answers are (1) and (2).

Including an interaction term can be useful to estimate the context-specific effects of some predictor variable on the outcome (y) when the effect of that predictor on the outcome may depend on the value of another predictor variable.

Additionally, including an interaction term can be necessary if the joint effect of two predictor variables on the outcome cannot be correctly modeled as the sum of the main effects associated with each variable.

This is because the effect of one predictor variable on the outcome may depend on the value of the other predictor variable, and this dependency cannot be captured by the main effects alone.

So, the correct options are (1) and (2).

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Step-by-step explanation:

The decrease from 212 to 198 is   14 degrees

14 degrees is what percent of 212 degrees?

     14 / 212  x 100% = 6.6 % decrease

The area of the space devoted to paintings is: 600 ft²

The formula for the area of a triangle is expressed as:

A = ¹/₂ * b * h

where:

A is area

b is base

h is height

From the 7th grade painting, we see that each box of 1 unit represents 10 ft actually.

Thus, area of space devoted to paintings is:

Area = ¹/₂ * 40 * 30

= 600 ft²

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According to the problem, the amount of petrol in the second tank is twice that in the first tank, which means the amount of petrol in the second tank is 2x liters.

If we draw out 25 liters from the first tank and add it to the second tank, the amount of petrol in both tanks will be the same. Therefore, the total amount of petrol in both tanks after the transfer is (x - 25) + (2x + 25) = 3x.

Since the amount of petrol in both tanks is the same after the transfer, we can set up an equation:

x - 25 = (2x + 25) / 2

Simplifying this equation, we get:

2x - 50 = 2x + 25

2x - 2x = 25 + 50

x = 75

Therefore, the amount of petrol in the first tank is 75 liters, and the amount of petrol in the second tank is 2x = 2*75 = 150 liters.