Study these equations:

f(x) = 2x – 4

g(x) = 3x + 1

What is h(x) = f(x)g(x)?

h(x) = 6x2 – 10x – 4
h(x) = 6x2 – 12x – 4
h(x) = 6x2 + 2x – 4
h(x) = 6x2 + 14x + 4

No, the expression 3x + 5y - 2200 is not a quadratic expression.

A quadratic expression is an expression of the form ax² + bx + c, where a, b, and c are constants and x is a variable raised to the power of 2.

It is a second-degree polynomial, meaning that the highest power of the variable is 2.Quadratic expressions often have a graph that is a parabola.

"3x + 5y - 2" is a linear expression, not a quadratic expression.

In a quadratic expression, the highest power of the variable(s) is 2, whereas in this expression, the highest power is 1.

The expression 3x + 5y - 2200 is a linear expression since it does not contain a term with a variable raised to the power of 2.

It is a first-degree polynomial, meaning that the highest power of the variable is 1.

Linear expressions often have a graph that is a straight line.

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No. The expression, 3x + 5y - 2, is not quadratic.

The expression "3x+5y-2" is a linear expression, not quadratic.

Quadratic expressions contain a squared term, like "[tex]ax^2 + bx + c[/tex]." In the given expression, there are no squared terms, only linear terms with variables "x" and "y" raised to the power of 1.

The coefficients for "x" and "y" are 3 and 5, respectively, and there is a constant term of -2. Therefore, it represents a linear relationship between "x" and "y" rather than a quadratic one.

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The second pair of points representing the solution set of the system of equations is (-6, 29).

To find the second pair of points representing the solution set of the system of equations, we need to substitute the x-coordinate of the second point into one of the equations and solve for y.

Given the system of equations:

y = x^2 - 2x - 19

y + 4x = 5

Substituting the x-coordinate of the second point (-6) into equation 2:

y + 4(-6) = 5

y - 24 = 5

y = 5 + 24

y = 29

Therefore, the second pair of points representing the solution set of the system of equations is (-6, 29).

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Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

y = x2 − 2x − 19

y + 4x = 5

The pair of points representing the solution set of this system of equations is (-6, 29) and

_________.

The equation of the tangent line at the point (108, 6) on the curve y² = x²/(xy - 324) is: y = 6

The equation is given as:

y² = x²/(xy - 324) at (108, 6)

Differentiating implicitly with respect to x gives:

2y(dy/dx) = (2x(xy - 324) - x²(y - 324)(dy/dx)) / (xy - 324)²

Simplifying further using power rule and chain rule gives us:

[tex]\frac{dy}{dx} = \frac{x^{2}y - 648x }{2y(-324 + xy) +x^{3} }[/tex]

We can find the slope by plugging in x = 108 and y = 6 to get

[tex]\frac{dy}{dx} = \frac{(108^{2}*6) - 648(108) }{2(6)(-324 + (108*6)) + 108^{3} }[/tex]

dy/dx = 0

To find the equation of the tangent line, we use the point-slope form:

y - y₁ = m(x - x₁),

where:

(x₁, y₁) is the given point (108, 6) and m is the slope.

Substituting the values, we have:

y - 6 = 0(x - 108)

y = 6

This is the equation of the tangent line at the point (108, 6) on the curve y² = x²/(xy - 324).

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Mercury will travel approximately 10800 miles in 6 minutes.

To convert the speed of Mercury from miles per second to miles per minute, we need to multiply the given speed by the number of seconds in a minute, which is 60.

Speed of Mercury in miles per minute = 30 miles/second [tex]\times[/tex] 60 seconds/minute = 1800 miles/minute

Therefore, Mercury travels at a speed of 1800 miles per minute.

To calculate the distance Mercury will travel in 6 minutes at this speed, we can multiply the speed by the time.

Distance traveled by Mercury in 6 minutes = Speed [tex]\times[/tex] Time = 1800 miles/minute [tex]\times[/tex] 6 minutes = 10800 miles

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Answer:

πr^2 h

π(11)^2 (15)

= 1815π or = 5701

Answer:

6

Step-by-step explanation:

"The exponential function grows faster than the quadratic function over only one interval" best describes the growth rates of the functions.

A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero.

There are three commonly-used forms of quadratics:

Standard Form: y = a x 2 + b x + c y= [tex]ax^2+bx+c y=ax2+bx+c.[/tex]

Factored Form: y = a ( x − r 1 ) ( x − r 2 ) y= a(x-r_1)(x-r_2) y=a(x−r1)(x−r2)

Vertex Form: y = a ( x − h ) 2 + k y= [tex]a(x-h)^2+k y=a(x−h)2+k.[/tex]

Quadratic functions can be represented symbolically by the equation, y(x) = ax2 + bx + c, where a, b, and c are constants, and a ≠ 0. This form is referred to as standard form.

The statement "The exponential function grows faster than the quadratic function over only one interval" best describes the growth rates of the functions.

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Answer: The second one, 3×5

Step-by-step explanation:

We can use a factor tree to determine the prime factorization of 15. We first choose factors of 15, and the only factors we can use besides 1 and 15 are 3 and 5.

                                                             15

                                                            3×5

That is all, because the final numbers listed are prime and we cannot perform any further actions. The prime factorization of 15 is 3×5, or in exponential form, [tex]3^1[/tex]×[tex]5^1[/tex].

Note: You may notice with other numbers that there are several factors to choose from. That's okay, because in the end it will give you the same result.

Hope this helps!

Answer:

it is real or imaginary depending on what u are talking about.

An output value for (fog)(x) is 55/(x² + 2x).

Domain = (-∞, 1) U (-2, 0) U (0, ∞) or {x|x ≠ 0, -2}.

In this exercise, we would determine the corresponding composite function of f(x) and g(x) under the given mathematical operations in simplified form as follows;

(fog)(x) = 5/(x + 2) × 11/x

(fog)(x) = 55/x(x + 2)

(fog)(x) = 55/(x² + 2x)

For the restrictions on the domain, we would have to equate the denominator of the rational function to zero and then evaluate as follows;

x² + 2x ≠ 0

x² ≠ -2x

x ≠ -2

Domain = (-∞, 1) U (-2, 0) U (0, ∞) or {x|x ≠ 0, -2}.

In conclusion, we can reasonably infer and logically deduce that x must not be equal to 0 and -2.

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Answer: 2×2×5×7 or, in exponent form, [tex]2^2[/tex]×[tex]5^1[/tex]×[tex]7^1[/tex]

Step-by-step explanation:

We can use a factor tree to determine the prime factorization of 140. You may notice that there are several factors to choose from that will give us 140, but you can choose any because in the end it will give you the same answer!

                                                         140

                                                     14   ×  10

                                                   2×7      2×5

That is all, because the final numbers listed are prime and we cannot perform any further actions.

Hope this helps!

Answer:

V = (3.14)(4.25)²(6)

Step-by-step explanation:

Answer:

A.

3.25x + 13.50 ≤ 40

Step-by-step explanation:

Answer:im not sure

Step-by-step explanation:

The transformation used to show congruence between polygon ABCDE and its image is a translation of 6 units to the left and 1 unit down.

To show that polygon ABCDE and its image are congruent, we need to determine which transformation was used. In this case, the transformation that can be used to show congruence is a translation.

A translation is a transformation that moves every point of a figure by the same distance and in the same direction. Since the image of A' is at (-4, 2) and the image of D' is at (-2, 1), we can see that the polygon was shifted 6 units to the left and 1 unit down.

Therefore, the transformation used is a translation of -6 units in the x-direction and -1 unit in the y-direction. This translation preserves the shape and size of the polygon, making ABCDE congruent to its image.

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Answer:

Step-by-step explanation:

65x2-26x

The linear function for this case is:

f(x) = 5,000*x + 7,000

The general linear function is written as:

f(x) = a*x + b

Where a is the slope and b is the y-intercept.

Here we want a linear function for the given scenario, we know that the initial population is 7,000, then we can write:

f(x)= a*x + 7,000

Then we know that the population increases by 5,000 per year for 5 years, so the slope is 5,000, then we can write the function as:

f(x) = 5,000*x + 7,000

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Both triangles in the image are similar based on the AAA similarity theorem. The radius of the circle B is therefore calculated as: AB = 12.

Similar triangles are geometric figures that have the same shape but may differ in size. They have corresponding angles that are equal and corresponding sides that are in proportion to each other.

Since AD serves as a common tangent, angle BAE is equal to 90 degrees, which is also equal to angle CDE due to being opposite angles.

By the Angle-Angle-Angle (AAA) similarity criterion, triangles ABE and DCE are similar.

Therefore:

AB/EA = DC/ED

Substitute:

AB/18 = 4/6

Cross multiply:

AB = 18 * 4/6

AB = 12

Therefore, the radius of the circle B is: 12.

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The sample space for this experiment is the one in the last option.

The sample space is the set of the possible outputs that we can have for selecting two marbles.

For example, if first you get a yellow marble, and then a red one, the output will be:

yellow red,

And that is different to the output:

red yellow

Where in the second one you draw the red one first.

From the options, the one that shows the complete sample space is the last one:

"Yellow Yellow, Yellow Red, Yellow Clear, Yellow Green, Yellow Blue, Yellow

Red Yellow, Red Red, Red Clear, Red Green, Red Blue, Red

Clear Yellow, Clear Red, Clear Clear, Clear Green, Clear Blue, Clear

Green Yellow, Green Red, Green Clear, Green Green, Green Blue, Green

Blue Yellow, Blue Red, Blue Clear, Blue Green, Blue Blue, Blue"

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Answer:

The word "ENTERTAIN" has 9 letters, but it contains repeated letters. Specifically, it has 3 E's, 2 N's, and 2 T's.

To find the number of distinct permutations, we can use the formula for permutations with repeated elements.

The number of distinct permutations is given by:

n! / (n1! * n2! * ... * nk!)

where n is the total number of elements and n1, n2, ..., nk are the frequencies of each repeated element.

In this case, we have:

n = 9

n1 = 3 (for E)

n2 = 2 (for N)

n3 = 2 (for T)

Plugging these values into the formula, we get:

9! / (3! * 2! * 2!)

Calculating this expression gives us:

(9 * 8 * 7 * 6 * 5 * 4) / (3 * 2) =

(30240) / (12) =

2520

Therefore, there are a total of 2520 distinct permutations that can be formed using the letters of the word "ENTERTAIN".

a. The initial velocity of the marble is 0 cm/s.

b. The marble is rolling at a speed of 80 cm/s at 4 seconds.

c. The velocity is 50 cm/s at approximately t = 2√2 - 1 seconds.

d. The marble is rolling at a speed of 90 cm/s when it is 90 cm from its starting point at t = 9 seconds.

e. lim s(t) as t approaches infinity is 100 cm and lim v(t) as t approaches infinity is 0 cm/s; the model may not be valid for large values of t as it assumes the marble is rolling up an inclined plane without considering other factors such as friction.

a. To find the initial velocity of the marble, we need to calculate the limit of the function s(t) as t approaches 0:

lim (t->0) s(t) = lim (t->0) (100t / (t + 1))

By substituting 0 into the expression, we get:

lim (t->0) (0 / (0 + 1)) = 0 / 1 = 0.

Therefore, the initial velocity of the marble is 0 cm/s.

b. To find the speed of the marble at time 4 seconds, we substitute t = 4 into the expression for s(t):

s(4) = 100(4) / (4 + 1) = 400 / 5 = 80 cm/s

The marble is rolling at a speed of 80 cm/s at 4 seconds.

c. To find the time at which the velocity is 50 cm/s, we set s'(t) (the derivative of s(t)) equal to 50 and solve for t:

s'(t) = 50

[tex](100 / (t + 1))^2 = 50[/tex]

100 / (t + 1) = ±√50

100 = ±√50(t + 1)

±√50(t + 1) = 100

t + 1 = 100 / ±√50

t + 1 = ±2√2

Since time cannot be negative, we take t + 1 = 2√2:

t = 2√2 - 1

The velocity is 50 cm/s at approximately t = 2√2 - 1 seconds.

d. To find the speed of the marble when it is 90 cm from its starting point, we need to solve the equation s(t) = 90 for t:

100t / (t + 1) = 90

100t = 90(t + 1)

100t = 90t + 90

10t = 90

t = 9

The marble is rolling at a speed of 90 cm/s when it is 90 cm from its starting point, which occurs at t = 9 seconds.

e. The limit of s(t) as t approaches infinity (lim s(t) as t->∞) is calculated by considering the dominant term in the numerator and denominator:

lim (t->∞) (100t / (t + 1))

≈ lim (t->∞) (100t / t)

= lim (t->∞) 100

= 100

Therefore, lim s(t) as t approaches infinity is 100 cm.

Similarly, the limit of v(t) (velocity) as t approaches infinity (lim v(t) as t->∞) can be found by taking the derivative of s(t) and evaluating the limit:

[tex]v(t) = s'(t) = 100 / (t + 1)^2[/tex]

lim (t->∞) v(t) = lim (t->∞) (100 / [tex](t + 1)^2)[/tex]

≈ lim (t->∞)[tex](100 / t^2)[/tex]

= lim (t->∞) [tex](100 / t^2)[/tex]

= 0.

The limit of v(t) as t approaches infinity is 0 cm/s.

As for the validity of the model for large values of t, it is important to note that the given model assumes that the marble is rolling up an inclined plane.

However, without further information about the nature of the inclined plane (e.g., its slope, frictional forces), it is difficult to determine the accuracy.

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It would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

To calculate the time it would take to drive from Statesville, NC to Washington, DC, we can divide the distance of 389 miles by the average speed of 65 mph.

Time = Distance / Speed

Time = 389 miles / 65 mph

Time ≈ 5.98 hours

Therefore, it would take approximately 5.98 hours to drive from Statesville, NC to Washington, DC on interstates with an average speed of 65 mph.

To calculate the cost of driving to Washington, DC, we need to know the number of gallons of gas required for the trip. We can find this by dividing the distance by the car's mileage, which is 29 miles per gallon.

Number of gallons = Distance / Mileage

Number of gallons = 389 miles / 29 miles per gallon

Number of gallons ≈ 13.41 gallons

The cost of gas can be calculated by multiplying the number of gallons by the cost per gallon, which is $3.89.

Cost = Number of gallons * Cost per gallon

Cost ≈ 13.41 gallons * $3.89/gallon

Cost ≈ $52.18

Therefore, it would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

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Answer:

B. 0.00467

Step-by-step explanation:

This is a binomial probability problem. The probability of fewer than three adults watching prime-time TV live is the sum of the probabilities of 0, 1, and 2 adults watching prime-time TV live.

Let X be the number of adults watching prime-time TV live. The probability mass function of X is given by:

P(X=k)=(kn​)p^k(1−p)^n−k

where n is the number of trials (7 in this case), k is the number of successes, and p is the probability of success on a single trial (0.8 in this case).

So, the probability that fewer than three of the selected adults watch prime-time TV live is:

P(X<3) = P(X=0) + P(X=1) + P(X=2)

=(7  0)(0.8)^0(0.2)^7 + (7  1​)(0.8)^1(0.2)^6 + (7  2​)(0.8)^2(0.2)^5

=1/78125 + 28/78125 + 336/78125

=73/15625

=0.004672

The nth square number of the value given is the squared value of 19, which is 361

The nth square number , S is related by the formula :

Given that , n = 19

The nth square number , where n = 19 can be calculated thus:

S = -19² = 361

S = (-19) * (-19)

S = 361

Therefore, the 19th square number is 361

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The point on the number line that is 5/7 of the way from A = -4 to B = 17 is approximately -1.8571.

To find the location of a point on the number line that is a certain fraction of the way from one point to another, we can use the concept of linear interpolation.

In this case, we want to find the point that is 5/7 of the way from A = -4 to B = 17.

To calculate this point, we can use the formula:

Point = A + (Fraction × Distance)

where A is the starting point, Fraction is the desired fraction, and Distance is the total distance between the two points.

In this case, A = -4, B = 17, and the desired fraction is 5/7. The distance between A and B can be calculated as:

Distance = B - A = 17 - (-4) = 21

Plugging in these values, we have:

Point = -4 + (5/7 × 21)

Simplifying the expression, we get:

Point = -4 + (15/7) = -4 + 2.1429 ≈ -1.8571

Therefore, the point on the number line that is 5/7 of the way from A = -4 to B = 17 is approximately -1.8571.

Among the given options, none of them match the calculated value. However, the closest option is C. 9.

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The direction and degree of rotation used to create the image include the following: C. 90° clockwise rotation.

In Mathematics and Geometry, a rotation is a type of transformation that moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

By applying either a rotation of 90° clockwise or a rotation of 270° counterclockwise to the coordinate of triangle ABC, the coordinate of its image (triangle A′B′C′);

(x, y)                            →            (y, -x)

Point A = (-2, -7)          →     Point A′ (-7, 2)

Point B = (3, -2)          →     Point B′ (-2, -3)

Point C = (2, -10)          →     Point C′ (-10, -2)

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Complete Question:

Determine the direction and degree of rotation used to create the image.

90° counterclockwise rotation

270° clockwise rotation

90° clockwise rotation

180° clockwise rotation

The equation of the line parallel to the line passing through (1, -2) and (-4, 3) and passing through the point (-4, -5) is y = -x - 9 in slope-intercept form.

To find the equation of a line parallel to a given line, we need to determine the slope of the given line and then use it to construct the equation of the parallel line.

First, let's calculate the slope of the given line passing through points (1, -2) and (-4, 3). The slope, denoted as m, can be found using the slope formula:

m = (y2 - y1) / (x2 - x1)

Substituting the coordinates, we have:

m = (3 - (-2)) / (-4 - 1) = 5 / (-5) = -1

Now that we have the slope, we can use it to construct the equation of the parallel line.

We'll use the point-slope form of a linear equation, which is:

y - y1 = m(x - x1)

where (x1, y1) represents the coordinates of a point on the line.

We'll use the point (-4, -5) on the parallel line:

y - (-5) = -1(x - (-4))

y + 5 = -1(x + 4)

Simplifying further:

y + 5 = -x - 4

y = -x - 9

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Is not possible to define a radius  nor a diameter in a trapezium.

Radius and diameter are two measures defined for circles.

Radius is the distance between the center and any point in the circumference, and the diameter is the distance between two opposite points in the circumference (so it does not need to be 3D to have radius/diameter).

At the same time, a trapezium is not a circle, is a quadrilateral, so it can't have any of these.

To get the area use the formula:

Area = (base1 + base2)*height / 2

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The element 4 is an element of D ∩ (E ∩ F).

To find the intersection of sets D, E, and F, we need to determine the elements that are common to all three sets.

Set D consists of all whole numbers, so any whole number can be an element of set D.

Set E consists of perfect squares between 1 and 9. The perfect squares in this range are 1, 4, and 9.

Set F consists of even numbers greater than or equal to 2 and less than 9.

The even numbers in this range are 2, 4, 6, and 8.

Taking the intersection of sets E and F, we find that the common element is 4, as it is the only number that satisfies both conditions of being a perfect square and an even number in the given range.

Finally, taking the intersection of set D with the intersection of sets E and F, we find that the element 4 is also an element of set D ∩ (E ∩ F).

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