x^2-x-12<0.

A• {-3}
B• (-♾,-3) U (4,♾)
C• (-3,4)
D• [-3,4]

Answer:

Lana: 4 / 14 = 3.5
Markus: 4 / 20 = 5

I'm not completely sure how they can have the same amount of marbles for both of them but... Markus does have 2.5 more than Lana in each bag.

Hope this helps <3

Step-by-step explanation:

Let's call the number of marbles in each bag "x". We can set up two equations based on the given information:

4x = 14 (for Lana)

4x = 20 (for Markus)

Solving for x in each equation, we get:

x = 14/4 = 3.5 (for Lana)

x = 20/4 = 5 (for Markus)

So Markus has 5 marbles in each bag, which is 1.5 more marbles per bag than Lana.

The quotient is 2x^2-5 and remainder is -4

The necessary steps are:

p(x)= 6x^3 + 4x^2 - 15x−14

∴ degree of p(x) is 3.

g(x)=3x+2

∴ degree of g(x) is 1.

∴ degree of quotient q(x)=3−1=2,

and degree of remainder r(x) is zero.

Let, q(x)=ax2+bx+c (Polynomial of degree 2) and r(x)=k (constant polynomial)

By using division algorithm, we have

p(x)=[g(x)×q(x)+r(x)]

=6x^3 + 4x^2 -15x−14 = (3x+2)(ax2 + bx +c)+k

=3ax^3 + 3bx^2 + 3cx + 2ax^2 +2bx+2c+k

∴6x^3 + 4x^2 - 15^x - 14 = 3ax^3 + (3b+2a)x^2 + (3c+2b)x + 2c+k

We have cubic polynomials on both the sides of the equation.

∴ Let us compare the coefficients of x^3, x^2 ,x and k to get the values of a,b,c.

6=a, it is the coefficient of x^3 on both sides

4=3b+2a, it is the coefficient of x^2 on both sides

-15=3c+2b, it is the coefficient of x on both sides

−14=2c+k, it is the constant term on both sides

∴ the quotient is 2x^2 - 5 and the remainder is -4.

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Answer:

56 times

Step-by-step explanation:

An exponent are a quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression (e.g. 3 in 23 = 2 × 2 × 2).

Answer:

Actually her answer is wrong because it's a quodratic equation.

The probability of the combined event that the next six days are all sunny is 1/4096

From the question, we have the following parameters that can be used in our computation:

Probability that it is sunny = 1/4

Probability that it is cloudy = 3/4

Number of days = 6

The probability for all six days, it is sunny is represented as

Probability = Probability that it is sunny^Number of days

Substitute the known values in the above equation, so, we have the following representation

Probability = (1/4)⁶

Express as decimal

Probability = (0.25)⁶

Evaluate the exponent

Probability = 1/4096

Hence, the probability is 1/4096

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The height of the can of cylinder shape is 9.14 cm.

What is a cylinder?

In mathematics, a cylinder is a three-dimensional solid that maintains two parallel bases separated by a curved surface at a specific distance. These bases frequently have a circular shape (like a circle), and an axis connects their respective centres.

We are given the diameter as 4 cm.

So, the radius is 2cm.

Also, it is given that the surface area of the can is 140 square centimeters.

So, using the surface area of cylinder, we get

⇒Area = 2πr (h + r)

⇒140 = 2π * 2 (h + 2)

⇒140 = 4π (h + 2)

⇒140 = 4 * 3.14 * (h + 2)

⇒140 = 12.56 * (h + 2)

⇒11.14 = h + 2

⇒h = 9.14

Hence, the height of the can of cylinder shape is 9.14 cm.

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Based on the information given, we can conclude that RM = 2, but we cannot determine the lengths of the other sides of the quadrilaterals without further information.

Given that quadrilateral YFGT can be mapped onto quadrilateral MKNR by a translation, we can use the information to determine the length of RM.

A translation is a transformation that moves every point of a figure by the same distance and in the same direction. In this case, the translation is such that the corresponding sides of the quadrilaterals are parallel.

Since TY = 2, and the translation moves every point by the same distance, we can conclude that the distance between the corresponding points R and M is also 2 units.

Therefore, RM = 2.

By the properties of a translation, corresponding sides of the two quadrilaterals are congruent. Hence, side YG of quadrilateral YFGT is congruent to side MK of quadrilateral MKNR, and side GT is congruent to NR. However, the given information does not provide any additional details or measurements to determine the lengths of these sides.

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1) The expression 2⁻ˣ⁺³ = 3 is matched with graph B.

2 The expression  3ˣ⁺¹=3 is matched with graph C.

3) The expression 4ˣ = 3 is matched with graph

4 ) The expression 1ˣ/4 = 3 is matched with graph

1) The graph of the expression 2⁻ˣ⁺³ = 3  represents an exponential function where the y-coordinate is 3 when the base 2 raised to the power of (-x+3).

2) The graph of the expression 3ˣ⁺¹=3represents an exponential function where the y-coordinate is 3 when the base 3 raised to the power of (x+1). This graph is a straight line with a slope of 1.

3)  The graph of the equation 4ˣ = 3 represents an exponential function where the base 4 raised to the power of x is equal to 3. This equation has a single solution, which can be determined using logarithms.

4) The graph of the expression 1ˣ/4 = 3 represents an exponential function where the base 1 raised to the power of (x/4) is equal to 3.

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Answer:

232.5 cm²

Step-by-step explanation:

232.5

The required area of the regular pentagon with an 8-cm apothem and 11.6-cm sides is 232 cm².

The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.

Here,
To find the area of a regular pentagon, we can use the formula:

Area = (1/2) x Apothem x Perimeter

where Apothem is the distance from the center of the pentagon to the midpoint of any side, and Perimeter is the sum of the lengths of all the sides.

In this case, the apothem is given as 8 cm, and the length of each side is given as 11.6 cm.

To find the perimeter, we can simply multiply the length of one side by 5:

Perimeter = 5 x 11.6 cm = 58 cm

Now, we can plug in these values into the formula:

Area = (1/2) x 8 cm x 58 cm

Area = 232 cm²

Therefore, the area of the regular pentagon with an 8-cm apothem and 11.6-cm sides is 232 cm².

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Answer:

-40

Step-by-step explanation:

-4(0) + 0 = 2 ??

That's not possible! See

-4(0)=0

-> 0=2

Suppose we want to find the value of y when x=0

-> -4(x=0)+y = 2

-> -4*(0) + y = 2

-> 0 + y=2

-> y=2

Now, what if y=0? What would the value of x be? Let's find out!

-4x + (y=0) = 2

-> -4x + 0 = 2

-> -4x=2

-> -4x (-1/4) = 2(-1/4)

-> x=-2/4

-> x= -1/2

Answer:

5,000

Step-by-step explanation:

I used a calculator:)

Answer: NOW

Step-by-step explanation:

According to the solution we have come to find that,  the salesperson will receive a commission of $15 for the week.

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain.

Probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. For example, if you roll a standard six-sided die, there are six possible outcomes, each with an equal chance of occurring. The probability of rolling a 3 is 1/6, because there is only one favorable outcome (rolling a 3) out of six possible outcomes.

If the salesperson gets a 5% commission on each pair of shoes they sell, we can calculate their commission by multiplying the total sales by 0.05 (which is 5% expressed as a decimal):

Commission = Total sales * 0.05

In this case, the total sales are $300, so we can plug that into the formula:

Commission = $300 * 0.05

Commission = $15

Therefore, the salesperson will receive a commission of $15 for the week.

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Step-by-step explanation:

the answer is

\( \frac{486}{8100} \times 100\% = 6\%\)

Answer:

Independent

Step-by-step explanation:

From the word independent, which means being able ot stand alone, that is the absence or presence of one has no impact on the outcome of each phenomenon. Two events A and B are said to be independent, if the occurence of one has no bearing on the probability or chance that B will occur. This means that each event occurs without reliance on the occurence of the other. This is different from mutually exclusive event whereby event A has direct bearing in the probability of the occurence of event B.

If we restrict the domain of the function to the portion of the graph with a positive slope, the domain of the inverse function will be the range of the original function for values of x greater than 4, and its range will be all real numbers greater than or equal to 4.

The given function f(x) = |x – 4| + 6 is a piecewise function that contains an absolute value. The absolute value function has a V-shaped graph, and the slope of the graph changes at the point where the absolute value function changes sign. In this case, that point is x=4.

If we restrict the domain of f(x) to the portion of the graph with a positive slope, we are essentially considering the piece of the graph to the right of x=4. This means that x is greater than 4, or x>4.

The domain of the inverse function, f⁻¹(x), will be the range of the original function f(x) for values of x greater than 4. This is because the inverse function reflects the original function over the line y=x. So, if we restrict the domain of f(x) to values greater than 4, the reflected section of the graph will be the range of f⁻¹(x).

The range of f(x) is all real numbers greater than or equal to 6 because the absolute value function always produces a positive or zero value and when x is greater than or equal to 4, we add 6 to that value. The range of f⁻¹(x) will be all real numbers greater than or equal to 4, as this is the domain of the reflected section of the graph.

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Answer:

13.6

Step-by-step explanation:

I got it right

The estimated sum of 7 83/84 is 8 to the nearest whole number.

Mixed fractions are fraction that has a whole number attached to an improper fraction. A mixed fraction can be added by first adding the real whole numbers together, then adding their improper fraction counterparts with it.

Also, we can add two mixed fractions together by first converting all the mixed fractions to improper fractions before adding them together.

Using the first process:

= 4 5/12 + 3 8/14

The whole number are 4 and 3, adding those two together, we have:

= 7 (5/12 + 8/14)

The L.C.M of 12 and 14 is 84.

= 7( (7×5)+ (6*8) )  /84

= 7 (35+ 48/84)

= 7 (83/84)

To decimal, we get 7.988. Therefore, the estimated sum of 7 83/84 is 8 to the nearest whole number.

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Answer:

∠P = 111°

Step-by-step explanation:

∠P = 84 + 27

      = 111

The correct value of 2f(a-1) is 2a^2 - 12a + 10.

To find the value of 2f(a-1), we need to substitute (a-1) into the function f(x) and then multiply the result by 2.

Given: f(x) = x^2 - 4x

Substituting (a-1) into the function:

f(a-1) = (a-1)^2 - 4(a-1)

Expanding and simplifying:

f(a-1) = (a^2 - 2a + 1) - (4a - 4)

f(a-1) = a^2 - 2a + 1 - 4a + 4

f(a-1) = a^2 - 6a + 5

Now, we multiply the result by 2:

2f(a-1) = 2(a^2 - 6a + 5)

Expanding:

2f(a-1) = 2a^2 - 12a + 10

Therefore, the value of 2f(a-1) is 2a^2 - 12a + 10.

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Answer:

$524.30

Step-by-step explanation:

70+60+25+350+30= 535

535*.02(20%)

10.7

535-10.7=

524.3

Answer:

$107

Step-by-step explanation:

First you have to add up the costs and you get a total of $535

Then you need to make 535 equivalent to 100 then divide by 20 to get 107

Hope that helps and have a great day!

Answer: 7a+3

Step-by-step explanation:

9a and 2a are two like terms that we can combine. Because there is a minus sign in front of the 2a, we should subtract 9a from 2a to get

7a. Then because the 3 has plus sign in front of it, we add 7a to 3. BUT because 3 a is NOT a like term, you don’t actually add it, so it looks like this: 7a+3. Hope this helped!

Answer:

\(\boxed{-\infty < y\leq 2}\)

Step-by-step explanation:

See the appendix.

The set of values ​​is the interval  \(y\in (-\infty , 2 >\) .

\(y\in (-\infty , 2 > ~~\Leftrightarrow ~~\boxed{-\infty < y\leq 2}\)

The only true statement about the domain of the given function is:

B. f(x) is negative for all x < -5

The domain of a function is defined as the set of values that we can possibly plug into our function. This set is the x values in a function such as f(x).

Now, we are given the function as:

f(x) = \(\frac{2}{x^{2} } + 3x - 10\)

When x < -5, we have:

f(-4) = \(\frac{2}{(-4)^{2} } + 3(-4) - 10\)

f(-4) = -21.875

This suggests that for all values below x = -5 will result in negative values

When x > 2

f(3) = \(\frac{2}{3^{2} } + 3(3) - 10\)

f(3) = -0.78

Thus, it will get positive for higher values but it can also be negative as seen here.

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The graph of the image of the polygon after a reflection in the line y = -x is (2, 2), (-2, -3), (1, -1), and (1, 4).

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

We are given that;

Points of polygon A(-3,2),B(1,-1),C(-2,-2) and D(-4,-1)

Now,

To reflect a polygon in a line, we reflect each of its vertices in the line and then connect the reflected points to form the reflected polygon.

The line y = -x is the line passing through the origin with slope -1, which means that any point (x, y) reflected in this line will be transformed to the point (-y, -x).

Let's reflect each of the vertices in the line and connect the reflected points to form the reflected polygon:

Reflecting point A(-3, 2): (-2, -3)

Reflecting point B(1, -1): (1, -1)

Reflecting point C(-2, -2): (2, 2)

Reflecting point D(-4, -1): (1, 4)

Now we can plot these points and connect them to form the reflected polygon.

So, the reflected polygon with given slope of line is ACBD, with vertices at (2, 2), (-2, -3), (1, -1), and (1, 4).

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Answer:

x = 14

Step-by-step explanation:

As we can see that the bottom side is equivalent to 3 of the smallest triangle and the side of the larger triangle is equivalent to the 9

This represents that it is dilated by 3 factor

So

= 3 × 3

= 9

Now the other side i.e. 5 of the smallest triangle also need to be dilated by a 3 factor

So the new side is 15

Also the largest triangle is x + 1

So,

15 = x + 1

x = 14

For the given distribution, the Expectation, E(2X² + 3X) is 28.9

Now here we see that we have the distribution given to us

We need to find

E(2X² + 3X)

Now we know that

E(X) = ∑xp(x)

Hence we get

E(2X² + 3X) = 2[1 X 0.2  +  4 X 0.3  +  9 X 0.2  +  16 X 0.4] + 3[1 X 0.2  +         2 X 0.3  +  3 X 0.2  +  4 X 0.4]

= 2[0.2 + 1.2 + 1.8 + 6.4] + 3[0.2 + 0.6 + 0.6 + 1.6]

= 2 X 9.6  +  3 X 3

= 19.2 + 9

= 28.9

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