The graph of f(x) = x2 is shifted 3 units to the right to obtain the graph of g(x). Which of the following equations best describes g(x)?

a. g(x) = (x + 3)2

b. g(x) = x2 − 3

c. g(x) = x2 + 3

d. g(x) = (x − 3)2

Final answer:

A function that describes a student's distance from the finish line in a 3-km race, running 1 km every 2 minutes, is a linear function represented by the formula f(t) = 3 - 0.5t, where t is time in minutes. This function shows a direct and proportional decrease in distance as time progresses.

Explanation:

The question asks for a function that describes the student's distance from the finish line in a 3-kilometer race, given that they run at a constant pace of 1 kilometer every 2 minutes. To find this function, we can use the concept of a linear relationship between time and distance.

Since the student is 3 kilometers away from the finish line at the start and runs 1 kilometer every 2 minutes, we can set up the function f(t) = 3 - 0.5t, where t represents time in minutes. This function decreases linearly because for every increase of 2 minutes in time, the distance from the finish line decreases by 1 kilometer. After 6 minutes, the function will read f(6) = 0, indicating that the student has reached the finish line.

An example will make this clear: After 4 minutes, the student has run 2 kilometers (since 4 minutes is twice 2 minutes, and the student runs 1 kilometer every 2 minutes), so his distance from the finish line is 3 km - 2 km = 1 km. We use f(t) = 3 - 0.5t and substitute t = 4 to get f(4) = 3 - 0.5(4) = 1 kilometer from the finish line.

Final answer:

The probability of selecting a girl, then a boy, and then another girl from a class with 5 girls and 5 boys is 10.42%.

Explanation:

The probability of a specific sequence of students being selected in a random draw can be calculated by multiplying the probabilities of each event occurring in succession. Since there are five boys and five girls in the class, the probability of drawing a girl first is 5/10, or 1/2. After drawing one girl, there are now four girls and five boys left, so the probability of drawing a boy second is 5/9. Finally, with one girl and one boy already picked, there are three girls and four boys left, making the probability of drawing a girl third 3/8.

To find the overall probability, we multiply these individual probabilities:

Probability = (First girl drawn) × (Second boy drawn) × (Third girl drawn)
Probability = (1/2) × (5/9) × (3/8)
Probability = (1 × 5 × 3) / (2 × 9 × 8)
Probability = 15 / 144
Probability = 0.1042 or about 10.42%

Final answer:

The probability of the teacher randomly selecting a girl, a boy, and another girl from a class of 5 boys and 5 girls is 5/6.

Explanation:

To find the probability of the teacher randomly selecting three different students, we need to consider the number of possible outcomes and the number of favorable outcomes. In this case, there are 10 students to choose from and the teacher needs to select one girl, one boy, and another girl. To calculate the probability, we divide the number of favorable outcomes by the number of possible outcomes.

The number of favorable outcomes is 5 for the first girl, 5 for the boy, and 4 for the second girl (since the first girl has already been selected). So the total number of favorable outcomes is 5 x 5 x 4 = 100.

The number of possible outcomes is the total number of ways to choose 3 students from the 10 available. This can be calculated using the combination formula: C(10, 3) = 10! / (3!(10-3)!) = 120.

Therefore, the probability of selecting a girl, a boy, and another girl is 100/120 = 5/6.

answer is 2x+3, x not equal to 6

 see attached pic for steps

Answer:

2x + 3, x ≠ 6

Step-by-step explanation:

Answer:

Option 5th is correct

[tex]35x+120y = 500[/tex]

Step-by-step explanation:

Here, x represents only the clients that got a cut and y represent the clients that got a cut and color combo.

As per the statement:

Earyn owns French Twist Hair Salon. She charges $35 for a cut an $120 for a cut and color combo.

" Charges $35 for a cut" translated to 35x

"$120 for a cut and color combo" translated to 120y

It is also given that yesterday she had seven clients and earned $500.

⇒[tex]35x+120y = 500[/tex]

therefore, an  equations could be used to represent this situation is, [tex]35x+120y = 500[/tex]

Answer:

(0, 6)

Step-by-step explanation:

Since, when a points is reflected through the line y = 2,

Then, the rule will be,

[tex](x,y)\rightarrow (x, -(y-4))[/tex]

While, the points is reflected through the line x = 2,

Then, the rule will be,

[tex](x,y)\rightarrow (x-4, y)[/tex]

So, when (4,-2) is reflected over the line y = 2 is,

[tex](4,-2)\rightarrow (4, -(-2-4))[/tex]

Hence, the position of (4,-2) after reflection through line y = 2 is (4,6),

Now,  when (4,6) is reflected over the line x=2 is,

[tex](4,6)\rightarrow (4-4, 6)[/tex]

Hence, the position of (4,6) after reflection through line x = 2 is (0,6),

Third option is correct.

The volume of cone is 37,680 cubic inch.

Space is used by every three-dimensional object. This space is estimated concerning its volume. The volume of an object in three-dimensional space is the amount of space it occupies within its boundaries. The capacity of the object is another name for it.

An object's volume can help us figure out how much water is needed to fill it, like how much water is needed to fill a bottle, aquarium, or water tank.

Given radius of cone = r  = 30 inch

slant height = l = 50 inch

volume of cone = V = 1/3πr²h

relation between height, radius, and slant height is given by

l² = h² + r²

where l = slant height, h = height and r = radius

h = [tex]\sqrt{l^{2} - r^{2} }[/tex]

h = [tex]\sqrt{50^{2} - 30^{2} }[/tex]

h = √1600 = 40 inch

V = 1/3πr²h = 1/3π × (30)² × 40

V = (3.14 × 900 × 40)/3

V = 37,680 cubic inch

Hence the volume is 37,680 cubic inch.

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Answer:

Step-by-step explanation:

It’s A

The probability of choosing both yellow hats can be obtained as 1/5.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.

The number of yellow, green and blue hats are given as 7, 5 and 3.

Then, the total number of hats is 7 + 5 + 3 = 15.

Now, the probability for both hats to be yellow without replacement can be given as,

P(Both hats are yellow) = 7/15 × 6/14

⇒ P(Both hats are yellow) = 1/5.

Hence, the required value of probability is given as 1/5.

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it was 1091227 on APEX

To make the expression x + 108 equal to x, subtract 108 from both sides of the equation.

To make the expression x + 108 equal to x, we need to subtract 108 from both sides of the equation. This will give us:

x + 108 - 108 = x - 108

Simplifying the equation, we get:

x = x - 108

However, if we are not solving an equation and simply need to simplify the expression x + 108 to make it equal to x, then the answer is that nothing can be done. The expression cannot be simplified to make it equal to x without additional information or context.

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First let us assign the three positive integers to be x, y, and z.

From the given problem statement, we know that:

(1/x) + (1/y) + (1/z) = 1

Without loss of generality we can assume x < y < z.

We know that:

1 = (1/3) + (1/3) + (1/3)

Where x = y = z = 3 would be a solution

However this could not be true because x, y, and z must all be  different integers.  And x, y, and z cannot all be 3 or bigger than 3 because the sum would then be less than 1.  So let us say that x is a denominator that is less than 3.   So x = 2, and we have:

(1/2) + (1/y) + (1/z) = 1

Therefore

(1/y) + (1/z) = 1/2

We  also know that:

(1/4) + (1/4) = (1/2)

and y = z = 4 would be a solution, however this is also not true because y and z must also be different. And y and z cannot be larger than 4,  so y=3, therefore

(1/2) + (1/3) + (1/z) = 1

Now we are left by 1 variable so we calculate for z. Multiply both sides by 6z:

3z + 2z + 6 = 6z

z = 6

Therefore:

(1/2) + (1/3) + (1/6) = 1

so {x,y,z}={2,3,6} 

Final answer:

The product of Melissa's integers is 120.

Explanation:

The product of Melissa's integers is 120.

Let the integers be a, b, and c.

According to the given information, 1/a + 1/b + 1/c = 1.

By finding common denominators and simplifying, you can determine that a * b * c = 120.

The graph of the inequality 12 - 2x < 16 is represented by an open circle at -2 on a number line, with shading to the right, indicating all values greater than -2.

To describe the graph representing the inequality 12 - 2x < 16, we first need to solve for x. Subtracting 12 from both sides of the inequality, we get -2x < 4. Dividing both sides by -2 (and remembering to flip the inequality symbol when dividing by a negative), we have x > -2.

Graphically, this is represented on a number line with an open circle at -2 and a shaded area to the right of -2, indicating that x can be any number greater than -2.

Final answer:

To find when g(x) = 0 for the function g(x) = 6x² + 23x – 4, the quadratic formula is used, yielding the solutions x = 0.25 or x = −4.

Explanation:

The question asks for the values of x for which the quadratic function g(x) = 6x² + 23x – 4 equals zero. To find the values of x when g(x) = 0, one can use the quadratic formula, which is x = −(b ± √(b² ∔ 4ac)) / (2a) for a quadratic equation ax2 + bx + c = 0.

Here, a = 6, b = 23, and c = −4. Substituting these values into the quadratic formula gives:

x = −(23 ± √(23² ∔ 4 × 6 × (−4))) / (2 × 6)

After calculating the discriminant (√(b² ∔ 4ac)) and simplifying, we obtain the two solutions for x. Therefore, the correct answer is:

So, the correct answer, marked as (d) on Education 2020, corresponds to x = 0.25 or x = −4.

there is 1 gram per 1 milliliter so just divide them

5200/583.1 = 8.91785

you don't say if it needs to be rounded to a certain amount

 so since the mL has one decimal place

 round to 8.9mL

Answer:

C  (1, 1) is the solution to line K but not to line J..

There are two correct answers which are not techniques used in geometric constructions with paper folding and these are:

A. Creating arcs and circles work the compass

C. Measuring lengths of line segments by folding the paper and matching the endpoints

In geometric folding, a straight line becomes a crease or a fold. This is achieved by a person by folding a piece of paper and flattening the crease rather than drawing lines to make a guide. Therefore this means that shapes like arcs, curves, circles by using the compass, and measurement of line segments are not used. However, constructions using compass have a long history in Euclidean geometry.

The following are not techniques used in geometric constructions with paper folding:

A. Creating arcs and circles with the compass.

C. Measuring lengths.

A geometric construction can be defined as a process that is used to draw angles, lines, and other geometric figures (shapes), especially through the use of only a compass and straightedge such as a ruler without measurements.

In Geometry, the techniques that should be used in geometric constructions with paper folding include the following:

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