This graph shows the solutions to the inequalities y> x+2 and y< x-3.
Does the system of inequalities have solutions? If so, which region contains
the solutions?
A
B
C
O There are no solutions.
OB. There are solutions, and they are the points in region C.
OC. There are solutions, and they are the points in region B.
OD. There are solutions, and they are the points in region A.

Quotient of x⁴ - 13x² + 36 ÷ x-3 = x³+3x²-4x-12

Factored form of x⁴ - 13x² + 36 = (x+3)(x+2)(x-2)(x-3)

Zeros of  x⁴ - 13x² + 36 = -3, -2, 2, 3

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable).

Given,

f(x) = x⁴ - 13x² + 36 and its factor (x-3)

Using synthetic division

x⁴ - 13x² + 36 ÷ (x-3) = x³+3x²-4x-12

Quotient = x³+3x²-4x-12

= (x³+3x²)-(4x-12)

= x²(x + 3) - 4 (x + 3)

= (x+3)(x² - 4)

= (x+3)(x+2)(x-2)

x⁴ - 13x² + 36 = (x³+3x²-4x-12) (x-3)

Factored form

x⁴ - 13x² + 36 = (x+3)(x+2)(x-2)(x-3)

By factors, zeros are:

x+3 ⇒ x = -3

x+2 ⇒ x = -2

x-2 ⇒ x = 2

x-3 ⇒ x = 3

Hence, x³+3x²-4x-12 is the quotient of x⁴ - 13x² + 36 ÷ x-3 .

(x+3)(x+2)(x-2)(x-3) is the factored form of x⁴ - 13x² + 36.

x⁴ - 13x² + 36 has zeros = -3, -2, 2, 3

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The amount of red blood cells contained in 40 cubic millimeter is 1.08×10⁸

A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

For example If Mary is paid for a job $50 per day.

How much will she earn in 10 days.

She will earn 50×10 = $ 500 in 10 days

Similarly, 1 cubic millimeter contains 5.2× 10⁶ red blood cells

then, 40 cubic millimeter will contain 40× 5.2×10⁶

= 108×10⁶ = 1.08 × 10⁸ red blood cells

Therefore the amount of red blood cells contain in 40cubic millimeter of blood is 1.08× 10⁸

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Answer:13/5

Step-by-step explanation:The answer would be 13/5 because that is the trigonometric ratio.

Answer:

s(5+7)

Step-by-step explanation:

Since 's' is the Highest Common Factor that will go outside the brackets.

[tex]s(5+7).[/tex]

[tex]5s+7s[/tex]

As you can tell, a common term between "5s" and "7s" is variable "s". Hence, we may factorize using that variable.

[tex]s(\frac{5s+7s}{s} )\\\\s(\frac{5s}{s} +\frac{7s}{s} )\\ \\s(5+7)[/tex]

Final answer: [tex]s(5+7)[/tex].

Gina sold more than twice as many TVs as Ethan, because 19 > (2 * 8)

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Ethan sold exactly eight TVs this quarter.

Ethan TV = 8

Gabriel sold more TVs than Ethan, hence:

Gabriel TV (G) > 8

Gabriel TV > 8

Gina sold exactly three more TVs than Gabriel and Ethan combined

Gina TV = Gabriel TV + 8 + 3

Gina TV > 8 + 8 + 3

Gina TV > 19

Frank sold exactly twice as many TVs as Gina, hence:

Frank TV = 2 * Gina TV

Frank TV > 2 * 19

Frank TV > 38

Gina sold more than twice as many TVs as Ethan.

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Team Tackle's score was 28 points. And team Sack's score was 9 points.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

During the 2005 football season, Team Tackle beat Team Sack by 19 points. If their combined scores totaled 37.

Let 'x' be the Tackle's score and 'y' be the Sack's score. Then the equations are given as,

x + y = 37        ...1

x = y + 19        ...2

From equations 1 and 2, then we have

y + 19 + y = 37

2y = 18

y = 9

Then the value of 'x' is given as,

x = 9 + 19

x = 28

Team Tackle's score was 28 points. And team Sack's score was 9 points.

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Step-by-step explanation:

annual interest = 1650

10

= 165

[tex] \frac{165}{8000} \times 100 = 2.0625\%[/tex]

Since George can build a laptop twice as fast as Kurt and working together takes them 3 hours, an equation which you would use to determine how long it will take Kurt working alone is: D. 1/t + 1/2t = 1/3.

In order to determine the amount of time it would take Kurt working alone, we would have to assign variables to the amount of time taken by George to build a laptop and the amount of time taken by Kurt to build a laptop, and then translate the word problem into an algebraic equation (expression) as follows;

Since George can build a laptop twice as fast as Kurt, an equation which models this situation is given by;

g = 2t     .....equation 1.

Next, we would write an algebraic equation (expression) that models the combined work rate;

1/c = 1/t + 1/g     .....equation 2.

Substituting equation 1 into equation 2, we have the following:

1/3 = 1/t + 1/2t

1/t + 1/2t = 1/3.

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The number of seniors that are on academic watch than freshman will be 868.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.

In this case, since there are there are 2435 seniors and 1567 freshmen on academic watch. The number of seniors that are on academic watch than freshman will be:

= 2435 - 1567

= 868

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Complete question

In a school, there are 2435 seniors and 12567 freshmen on academic watch. How many more seniors are on academic watch than freshman

The sum of numbers 4 and - 9 is, - 5.

And, A weather station is a collection of instruments that measure atmospheric conditions to help study the weather and climate of a specific location.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

The numbers are,

⇒ 4 and - 9

Now, Sum of the numbers 4 and - 9 as;

⇒ 4 + (-9)

⇒ 4 - 9

⇒ - 5

Thus, The sum of numbers 4 and - 9 is, - 5.

And,  A weather station is a collection of instruments that measure atmospheric conditions to help study the weather and climate of a specific location.

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The solution is Option A.

The coordinate of the triangle after the translation is given by A' ( 0 , -3 ) with 4 units right and 4 units down

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the coordinate of the triangle be represented as A

Now , the coordinate A = A ( -4 , 1 )

Now , the coordinate of the triangle after translation is A' ( 0 , -3 )

when there is a translation of the coordinate A by 4 units to the right , we get

A to 4 units right = A ( -4 + 4 , 1 )

The new coordinate of A = A ( 0 ,  1 )

Now , A to 4 units down , we get

The coordinate of A' = A' ( 0 , 1 - 4 )

The coordinate of A' = A' ( 0 , -3 )

Hence , the translated coordinate is A' ( 0 , -3 )

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Answer:

[tex]f \left( g \left( f \left( 1 \right) \right) \right)=45[/tex]

[tex]g \left( f \left( g \left( 0 \right) \right) \right)=3[/tex]

We had to use the equation on the first problem as the graph does not show the value of function f(x) when x = -6.

Step-by-step explanation:

When calculating composite functions, work from the inside out.

Given composite function:

[tex]f \left( g \left( f \left( 1 \right) \right) \right)[/tex]

First use the graph to find f(1):

[tex]\implies f \left( g \left( f \left( 1 \right) \right) \right)= f \left( g \left(-4\right)\right)[/tex]

Now use the graph to find g(-4):

[tex]\implies f \left( g \left(-4\right)\right)=f(-6)[/tex]

As the graph does not show the value for f(x) when x = -6, we need to use the equation:

[tex]\implies f(-6)=(-6)^2-2(-6)-3=45[/tex]

Therefore:

[tex]f \left( g \left( f \left( 1 \right) \right) \right)=45[/tex]

------------------------------------------------------------------------------

Given composite function:

[tex]g \left( f \left( g \left( 0 \right) \right) \right)[/tex]

First use the graph to find g(0):

[tex]\implies g \left( f \left( g \left( 0 \right) \right) \right)=g \left( f \left( -2 \right) \right)[/tex]

Now use the graph to find f(-2)

[tex]\implies g \left( f \left( -2 \right) \right)=g \left(5 \right)[/tex]

Finally, use the graph to find g(5):

Therefore:

[tex]g \left( f \left( g \left( 0 \right) \right) \right)=3[/tex]

We had to use the equation on the first problem as the graph does not show the value of function f(x) when x = -6.

The vectors generated by means of operations with canonical vectors:

Herein we find three canonical vectors, one for each orthogonal axis, from which we need to perform operations to generate new vectors. There two fundamental operations:

Vector sums

(a, b, e) + (c, d, f) = (a + c, b + d, e + f)

Vector multiplication by a scalar

α · (a, b, c) = (α · a, α · b, α · c)

Where:

If we know that U = (5, 0, 0), V = (0, 5, 0) and W = (0, 0, 5), then the following operations are below:

Case 1

U + V + 2 · W

(5, 0, 0) + (0, 5, 0) + 2 · (0, 0, 5)

(5, 0, 0) + (0, 5, 0) + (0, 0, 10)

(5 + 0 + 0, 0 + 5 + 0, 0 + 0 + 10)

(5, 5, 10)

Case 2

U + T = V

T = V - U

T = (0, 5, 0) - (5, 0, 0)

T = (0 - 5, 5 + 0, 0 + 0)

T = (- 5, 5, 0)

Case 2b

R = U + V + W

R = (5, 0, 0) + (0, 5, 0) + (0, 0, 5)

R = (5 + 0 + 0, 0 + 5 + 0, 0 + 0 + 5)

R = (5, 5, 5)

Case 3

T - 2 · R

(- 5, 5, 0) - 2 · (5, 5, 5)

(- 5, 5, 0) + (- 10, - 10, - 10)

(- 5 - 10, 5 - 10, 0 - 10)

(- 15, - 5, - 10)

Case 3b

S = U + W

S = (5, 0, 0) + (0, 0, 5)

S = (5 + 0, 0 + 0, 0 + 5)

S = (5, 0, 5)

Case 4

U + V + W + R + S + T

(5, 0, 0) + (0, 5, 0) + (0, 0, 5) + (5, 5, 5) + (5, 0, 5) + (- 5, 5, 0)

(5 + 0 + 0 + 5 + 5 - 5, 0 + 5 + 0 + 5 + 0 + 5, 0 + 0 + 5 + 5 + 5 + 0)

(10, 15, 15)

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Answer:

The domain of a function is the set of all input values (x-values) for which the function produces a valid output (y-value). In the case of the function H(x) = x+2/x^2+4x+4, we need to find the values of x for which the denominator x^2+4x+4 is not equal to zero.

x^2+4x+4 = 0

(x+2)^2 = 0

The denominator is always non-zero as the square of any real number is always positive. Therefore, the function H(x) = x+2/x^2+4x+4 is defined for all real values of x. Therefore, the function H(x) does not have any values that are not in its domain.

Step-by-step explanation:

By using the fact that the sum of the interior angles must be 180°, we wil see that:

x = 110°.

First, remember that the sum of the interior angles of a triangle is alway equal to 180°.

We also can see that the interior angle that is adjacent to x can be written as:

a = 180° - x

Then the sum of the interior angles will give:

30° + 80° + (180° - x) = 180°

30° + 80° - x = 0

110° - x = 0

110° = x

That is the value of x.

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Answer: first one is D 15 1/2

second one is B 11 2/8

Third one is C (already had the correct answer)

fourth answer would be A 3 2/12

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

To calculate how long it will take John to recover his investment, we need to divide the cost of the degree by the difference in income between the two options.

$10,000 / ($35,000 - $20,000) = $10,000 / $15,000 = 0.67 years or 0.67*12 = 8 months.

So, it will take John 8 months to recover his investment if he goes to school.

Please note that this is a simplified calculation as it does not take into account the cost of living, taxes, and other expenses.

The denominator of the fraction at point Y is equal to 24.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

Let the variable d represent the denominator of the fraction at point Y and since point Y is the same distance from 0 as point X, which is at 2/3 on a number line, this can be modeled by this mathematical expression:

8/d = 1 - 2/3

8/d = 1/3

Cross-multiplying, we have:

d = 8 × 3

d = 24.

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3y = 4x + 2 is a linear equation that satisfies the graph.

A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph.

Given, Few coordinates of a linear function to make the equation of line we need only two coordinates.

general formula for linear equation is y = mx + c

where, m = slope

c = constant

General formula for slope m = (y₂ - y₁)/(x₂ -x₁)

Since graph passes through the points(3, 6) and (0, 2)

Slope m = (2 - 6)/ (0 - 3)

m = -4/-3 = 4/3

Thus, equation of line will be

y = 4/3x + c

Since the Line passes through (0, ,2 ) these point will satisfy the above equation

2 = 4/3 * 0 + c

=> c = 2

substitute the values

y = 4/3x + 2

3y = 4x +6

Therefore, equation of line that relates with the graph is 3y = 4x + 6.

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The given expression (3p)³ without exponents is 27×p×p×p.

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

The given exponential expression is (3p)³.

Here, (3p)³=3p×3p×3p

= 27×p×p×p

Therefore, the given expression (3p)³ without exponents is 27×p×p×p.

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Answer:

-----------------------------------------

To find the remaining credit plug in the value of x = 30 into equation and calculate:

Based on the graph of this quadratic function with vertex (-1, -4), the domain and the range are as follows;

Domain = {-3, 0.5}.

Range = {-4, ∞}.

In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

Note: The vertex of any quadratic function represents the minimum of the given function.

By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following:

Domain = -3 < x < 0.5 or [-3, 0.5].

Range = -4 < y < ∞ or [-4, ∞].

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Answer: An obstacle course is a series of challenging physical obstacles that must be completed in order to finish the course. To find out how many kilometers long the obstacle course is, you need to add up the distance that Caleb runs, jumps crawls, and dribbles.

First, we need to convert the 500 meters to kilometers by dividing it by 1000.

500 meters / 1000 = 0.5 kilometers

Then, we need to add the distance that Caleb crawls through the tunnel, which is 20 meters.

20 meters = 0.02 kilometers

Finally, we need to add the distance that Caleb dribbles the soccer ball, which is 100 meters.

100 meters = 0.1 kilometers

To find the total distance of the obstacle course, we need to add the distance that Caleb runs, jumps, crawls, and dribbles:

0.5 + 0.02 + 0.1 = 0.62 kilometers

So the obstacle course is 0.62 kilometers long.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To convert minutes to hours, we divide by 60, since there are 60 minutes in an hour.

So 4 hours is equal to 4 * 60 = 240 minutes

Charise can pick 1/3 pound of berries in 15 minutes. This is her unit rate. To find out how many pounds of berries she can pick in 4 hours, we need to multiply this unit rate by the number of 15-minute intervals in 4 hours.

240 minutes / 15 minutes = 16 (four-hour intervals)

So the amount of berries Charise can pick in 4 hours is:

1/3 pound/15 minutes * 240 minutes = (1/3) * 16 = 16/3 = 5.333 pounds of berries.

Answer:

----------------------------------

Charise can pick 1/3 pound of berries in 15 minutes.

There are 4 of 15 minutes in an hour and we need to calculate it for 4 hours.

She picked:

Answer:

1734

Step-by-step explanation:

We can simply solve the volume of the 2 different cubes. The bigger cube's volume is 15*12*8 = 1440. The volume of the small cube is 6*7*(15-4-4)=294.

So the total volume should be 1734

Answer:

1944 cm³

Step-by-step explanation:

Two rectangular parallelepipeds:

Upper: 12 x 7 x 6 = 504 cm³

Lower: 12 x 15 x 8 = 1440 cm³

Total: 504  + 1440 = 1944 cm³

Answer:

Step-by-step explanation:

Yes, Monica is correct. When dealing with simple interest, the amount of interest earned is determined by the principal amount, the interest rate, and the time the money is invested. Since Monica and Paul both have different principal amounts and interest rates, the amount of interest each of them earns in one year will be different. Monica's account has a higher interest rate of 3.4%, so she will earn more interest in one year compared to Paul's account, which has a lower interest rate of 2.6%.

Answer: 5/8 "=" 10/16

Step-by-step explanation: To compare the fractions 5/8 and 10/16, we need to find a common denominator. In this case, the least common multiple of 8 and 16 is 16.

So, we can write the fractions as:

5/8 = (52)/(82) = 10/16

So the fractions are equal, therefore, the symbol that correctly compares them is = (the equal sign).

Answer: =

Step-by-step explanation:

In order to compare the fractions, we must make sure that the fractions have common denominators. Because 8 is a factor of 16, we will convert 5/8 into a fraction that has a denominator of 16. To do this, we need to multiply the numerator and denominator by the same number, in this case, 2 since that is what multiplies by 8 to get 16. (5/8) * (2/2) = 10/16 (you can just multiply across the top and bottom to solve). Now, we can compare. 10/16 is the same as 10/16, so an = would be the appropriate symbol. Hope this helps!

Answer: 3 x y (2 x + 5 y)

Step-by-step explanation:

im not really sure but i gave it a try

Answer:

16pi =2pi r

pi are cancelled

r=16/2

r=8m

area of circle =pi r²

22/7×64

area=201.15m²

Step-by-step explanation:

circumference of circle is 2pie radius

area of circle is pi r²