Determine the value of A so that x-1 is a factor of 2x^3 +x^2+2Ax+4

Answer:

The third side is 4cm

Step-by-step explanation:

[tex] {3}^{2} + {a}^{2} = {5}^{2} [/tex]

a=25-9

a=16

a=4

Answer:

3√2

Step-by-step explanation:

We have an isoceles right triangle, so the length of the hypotenuse is √2 the length of each leg.

[tex]y \sqrt{2} = 6[/tex]

[tex]y = \frac{6}{ \sqrt{2} } ( \frac{ \sqrt{2} }{ \sqrt{2} } ) = \frac{6 \sqrt{2} }{2} = 3 \sqrt{2} [/tex]

Answer:

Hamid's original weight was 80 kgs

Morgan will score 150.7 points in 11 season

The first step is to calculate the number of point that Morgan will score in one season

41= 3

x= 1

cross multiply both sides

3x= 41

x= 41/3

x= 13.7

The number of points he will score in 11 game season can be calculated as follows

= 13.7 × 11

= 150.7

Hence Morgan will score 150.7 points in 11 game season

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b. Division property of equality justifies going from the first statement: 5x = 20 to the second statement: x = 4.

Division property is a type of property of equality that states that if both sides of an equation are divided by the same number except 0, then that equation will remain true.

This property can be proved for the given statements as follows;

5x = 20

According to the division property of equality, we divide both sides by the same number which in this case is 5. Therefore;

5x = 20

5x/5 = 20/5

x = 4

As x = 4 is the second statement, therefore property of equality that justifies going from the first to the second statement is the division property of equality.

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so the answer is x=2

Answer:

x=2

Step-by-step explanation:

2(x-4)+7=3

First, multiply the 2 to x-4.

2x-8+7=3

Simplify.

2x-1=3

Add x on both sides.

2x=4

Divide 2 on both sides.

x=2

Answer:

4

Step-by-step explanation:

[tex]\frac{(-6) - (-3)}{s - 5} = -3\\-3(s-5)=-3\\s-5=-1\\\\s=4[/tex]

Answer:

first one (2*2*2*3*3)

Step-by-step explanation:

2*2*2*3*3=72

Answer:

2.4

Step-by-step explanation:

tan(theta) is defined as: [tex]tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}[/tex]

in the given diagram we only have the opposite and hypotenuse, but we can use the Pythagorean Theorem to solve for the other two missing sides.

Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex], where c is the hypotenuse.

Plugging in known values we get the following:

[tex]a^2+12^2=13^2[/tex]

in this case the missing side, or the adjacent side is simply "a"

from here we simplify the bases with exponents

[tex]a^2+144=169[/tex]

now subtract 144 from both sides

[tex]a^2=25[/tex]

take the square root of both sides

[tex]a=5[/tex]

So now we know the adjacent side so we can plug it into the tan equation

[tex]tan(z)=\frac{12}{5}\\\\tan(z)=2.4[/tex]

The maximum profit which this company can expect to earn is $11,650.

The maximum value of a function can be defined as a point on the graph where the function reaches its highest point. This ultimately implies that, the maximum value of a function simply refers to its vertex on a graph.

In order to determine the maximum profit which this company can expect to earn, we would differentiate the given function as follows:

f(x) = y = -10x² + 700x - 600

y' = -20x + 700

-20x + 700 = 0

20x = 700

x = 700/20

x = 35.

Substituting the parameter into the formula, we have;

f(x) = -10x² + 700x - 600

f(35) = -10(35)² + 700(35) - 600

f(35) = -12250 + 24,500 - 600

f(35) = $11,650.

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Answer:

the farmer can sell 55 cartons

Step-by-step explanation:

1 carton = 12 eggs

660 decided by 12 = 55

The x and y intercepts are (7/5, 0) and (0, -7/2) respectively.

Given equation is 5x-2y = 7.

To find the x-intercept substitute y = 0 in the equation and then solve,

5x - 0 = 7

x = 7/5

So the x-intercept is (7/5, 0).

Similarly, to find the y-intercept substitute x = 0 in the equation and then solve,

0 - 2y = 7

y = -7/2

So the y-intercept is (0, -7/2).

Now, graph the intersections of (7/5, 0) and (0, -7/2).

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There are 6 customers in the barber shop on an average.

What is average in ?

As per the Little's law, the average number of costumers or individuals in a system (L) can be calculated by multiplying the average arrival rate (λ) and the average time each customer spends in the system (W).

The algebraic expression, is as follows:

L = λW

Here,

L=inventory or average number of customers in the system.

λ=arrival rate = 10

W=flow time average customer spends in the system = 0.6

L = 0.6 * 10 = 6

Thus, there are 6 customers in the barber shop on an average.

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The relation that is a function from the given option is Graph A.

In mathematics, a relation is a group of ordered pairs that expresses the relationship between two sets.

Function contains both domain and codomain which are also known as dependent and independent variables

For the relation to be a function, two or more of the coordinates must not lie on the same line.

From the given graphs, the relation that is a function is Graph A since two points does not lie on the same vertical line.

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The interquartile range of the number of jumps of the 10 students during the competition is 38.

The interquartile range is the difference between the third quartile and the first quartile. The interquartile range is used to determine the variation of a data set.

Th first step is to determine the median of the first half of the dataset. The median of the first half is the first quartile.

First half of the data set: 30, 36, 38, 45, 57

Median = first quartile =  38

The next step is to determine the median of the second half of the dataset. The median of the second half is the third quartile.

Second half of the data set: 60, 77, 86, 88, 88

Median : third quartile =  86

Interquartile range = third quartile - first quartile

86 - 38 = 48

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The shortest total distance for the route from Anglemouth to Doncatry is 15 units.

On the table, we can see that there is a dash in the section of:

"Anglemouth to Doncatry"

So there is not a direct route, so we need to try another way.

If we go from Anglemouth to Covenham, we have a distance of 10 units.

If now we go from Covenham to Doncatry, we have a distance of 5 units.

Adding these two distances we get:

Total distance = 10 + 5 = 15 units.

This is also the shortest total distance between the two towns.

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Option C is the next step to construct a congruent angle.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Given Data

R makes the same angle with PQ and QR.

Option C is the next step to construct a congruent angle.

Steps to construct congruent triangle:

1) Each of the three sides is equal (SSS: side, side, side)

2) A comparable side and two angles are the same (ASA: angle, side, angle)

3) Both the angle between the two sides and the two sides' dimensions are equal (SAS: side, angle, side)

4) The hypotenuse, the corresponding side, and a right angle are all equal (RHS, right angle, hypotenuse, side).

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Initial temperature T₀ = 13°c

second Temperature T₁= 10°c

Change in Temperature  T₂ =  T₀ - T₁   = 13°c - 10°c   = 3°c

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After solving percent equation ,the number of red pins from the set of red and yellow pins that Pam ordered is 910 red pins out of 1000 pins.

Eventually, we'll run into a problem that requires us to calculate a percentage of something. The percent equation is the formula we'll employ and it goes like this: part = percent x whole.

The symbol for percent (%) denotes a percentage of one hundred.

You'll need to convert between a percent and a decimal to express these numbers, so let's take a moment to go over that. When you see a percentage, it means 40 out of 100, or 40/100, and that is our fraction. When you divide 40 by 100, you get the decimal 0.40. Remember that 0.40 is the same as 40/100, which means 40%, when converting a decimal to a percent.

Pam ordered a set of red and yellow pins. She received 1,000 pins, and 91% of them were red, so the amount of red pins is

red pins = 91/100  ×  1000

red pins = 910

Thus, the number of red pins from the set of red and yellow pins that Pam ordered is 910 red pins out of 1000 pins

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Answer:

56.4 degrees

Step-by-step explanation:

You can make a right-angle triangle from the isosceles triangle, with height 2.5cm and hypotenuse 3cm.

You have the opposite side to the angle and the hypotenuse, so you use sin x = Opposite/Hypotenuse

sin x = 2.5/3

x = [tex]sin^{-1}[/tex] (2.5/3)

x = 56.44269024

Therefore the base angle of the triangle is 56.4 degrees (3sf)

Answer: The answer is 279

Step-by-step explanation:

12 x 24=288

288-9=279

12(24)-9=279

The expression to represent the equation is given by  y = x + 3 .

An algebraic expression is one that was created in mathematics utilizing integer variables, constant, and algebraic procedures (accumulation, deletion, multiplication, separation, and exponentiation by a rational exponent).

The required expressions are :

y₁ = x + 3

y₂ = 3x²

y₃ = 3ˣ

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Answer:

Step-by-step explanation:

x=0.83

Answer:

b, c

Step-by-step explanation:

a) 32=18 - not true

b) 32=18+14 - true

c) 18+32=50 - true

d) 32=-18/16 - not true

If  x and y vary directly, than the relationship between y and x will be →

y = (16/9)x

Direct proportion or direct variation is the relation between two quantities where the ratio of the two is equal to a constant value.

Given is x and y vary directly and y = 32 when x = 18.

Since x and y vary directly, this means that -

y/x = K [constant]

Now, we have -

x = 18

y = 32

Substituting values -

32/18 = K

K = 32/18 = 16/9

y/x = 16/9

y = (16/9)x

Therefore, if  x and y vary directly, than the relationship between y and x will be → y = (16/9)x

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The daily rate charged to the client for each associate is $800 and the daily rate for each partner is $1800.  The equations that could be used to determine the number of associates assigned to the case and the number of partners assigned to the case is: 800 x + 1800 y = 17600.

Let variable x = number of associates, assigned to the case

Let variable y = number of partners assigned to the case.

The system of equations to describe this are:

800 x + 1800 y = 17600

y = x + 2

Plugging equation 2 in equation 1, we get,

800 x + 1800(x+ 2) = 17600

2600 x + 3600 = 17,600

Collect like terms

2400 x = 14,000

Divide both side by 2400x

x = 14,000 / 2400

x = 5.8

x = 6 (Approximately)

So,

y = x + 2

y = 5.8 +3

y = 7.8

y = 8 (Approximately)

Therefore the number of associates assigned to the case were 6, and the number of partners associated to the case were 8.

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The probability that the amount dispensed per box will have to be increased is 0.0062.

Consider the provided information.

Sample of 16 boxes is selected at random.

If the mean for 1 hour is 1 pound and the standard deviation is 0.1

1 Pound = 16 ounces , then 0.1 Pound = 16/10 = 1.6 ounces

Thus: μ = 16 ounces and σ = 1.6 ounces.

Compute the test probability

z= x−μ/σ/[tex]\sqrt{n}[/tex]

z= 15-16/ 1.6/4

z= -1/ 0.4

z= -2.5

By using the table.

Probability p value = P(Z<-2.50) = 0.0062

Thus, the probability that the amount dispensed per box will have to be increased is 0.0062.

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The equation that models the balance y after x months is;

y = 1,700 - 130x

What is Equation of line?

The equation of line with slope m and y intercept at point b is given as;

y = mx + b

Given that;

Zachary purchased a computer for $1,700 on a payment plan.

Seven months after he purchased the computer, his balance was $790.

Eight months after he purchased the computer, his balance was $660.

Now, Let months is represented by x and models the balance is represented by y.

So, We get;

For 0 months, balance is $1,700.

For 7 months, Balance is $790

For 8 months, balance is $660.

So, Slope = (1,700 - 790) / 7

               = 910/7

               = 130

And, Slope = (1,700 - 660) / 8

                = 1,040/8

                = 130

So, The equation with slope 130 and starting balance $1,700 will be;

y = 1,700 - 130x

Thus, The equation that models the balance y after x months is;

y = 1,700 - 130x

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