Factor x3 ‒ 11x2 ‒ 7x + 77 by grouping. What is the resulting expression?


a

(x2 ‒ 7)(x ‒ 11)


b

(x2 ‒ 7)(x + 11)


c

(x2 ‒ 11)(x + 7)


d

(x2 ‒ 11)(x ‒ 7)

Answer:

Explanation:

From the given figure:

• The base of the triangle, b = (4x-2) cm

• The perpendicular height, h = (2x+12) cm

The area of a triangle is calculated using the formula:

Substitute the given expressions:

Next, open the brackets:

The area of the triangle is:

Answer:

16 males and 9 females.

Step-by-step explanation:

If you subtract 7 from 25 you get 18. If you split 18 in half you get 9. Which means if you add 7 to 9 you get the number of males, which leaves you with 9 students left so the rest are females.

Answer:

16 males and 9 females

Step-by-step explanation:

To solve this we can use a system of equations.

Let's start by naming the number of females x.

The number of males would then be y.

Using these variables, we can set up 2 equations using info provided:

A french class has a total of 25 students, -> x+y=25

The number of males is 7 more than the number of females -> x+7=y

Use substitution to solve.

From the second equation:

x+7=y

Subtract 7 from both sides.

x=y-7

Substitute that into the first equation.

x+y=25

y-7+y=25

Combine like terms.

2y-7=25

Add 7 to both sides.

2y=32

Divide both sides by 2.

y=16

Substitute y=16 into equation 2.

x+7=y

x+7=16

Subtract 7 from both sides.

x=9

Therefore, there are 16 males and 9 females in the french class.

Answer:

92%

Step-by-step explanation:

Answer:

1,449

Step-by-step explanation:

Answer:

A = 0.5 × [ sqrt(17^2 - 15^2) ] × 15 + 0.5 × [ sqrt(25^2 - 15^2) ] × 15 = 210 in^2

The total cost if you buy 2 bottles of liquid soap and 3 sponges is $6.79.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=5x+6. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=5 and b=6.

First, you should convert the given text into an equation. See below.

From previous equations (1) and (2), you can find the unit cost. See below.

If 6b=9.12, you have:

    b=9.12/6

    b=$1.52

If 4s=5.00, you have:

    s=5.00/4

    s=$1.25

Since you know the unit cost for the bottles of soap and the sponges, you can find the total cost if you buy 2 bottles of liquid soap and 3 sponges.

2b + 3s =?

2*1.52+3*1.25

3.04+3.75=6.79

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Answer:

B

Step-by-step explanation:

You have to look at the second term to be sure of the meaning of t - 15n

What the given term says is that the total number of tickets sold (p) will decrease by 15 times the number of increases that there are.

The other term says that the cost of 1 ticket will increase that each ticket will increase by 2 dollars for each change in the ticket prices providing that change is 2 dollars.

C is out of the question. The information talks about 2 dollars per increase which is the first term.

A is not quite correct. It implies there is exactly 1 ticket increase. The crorect answer is the ticket increases can be a number of times (n)

The answer is B

Answer:

The answer is B

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

1+1 is 2

Answer: 6 - √35 < 0

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

The word PAYMENT has 7 letters. They can be arranged in groups of 4 like shown below:

PYNT, TA

Answer:

13

Step-by-step explanation:

1710/125 = 13.68

You need

125 x 13 = 1710

A student could take 13 credits.

Answer:

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

Formula for area of a rectangle with dimensions l and w is:

Substitute 10 for l and 4 for w:

The given line is parameterized by

x(t) = 1 + 7t

y(t) = 2 + 2t

z(t) = 3 + 4t

and points in the same direction as the vector

d/dt (x(t), y(t), z(t)) = (7, 2, 4)

So, the line we want has parameteric equations

x(t) = -1 + 7t

y(t) = -3 + 2t

z(t) = 5 + 4t

Solve for t when one of x, y, or z is equal to 0 - this will tell you for which value of t the line cross a given plane. Then determine the other coordinates of these intersections.

• x = 0, which corresponds to the y-z plane:

0 = -1 + 7t   ⇒   7t = 1   ⇒   t = 1/7

y(1/7) = -3 + 2/7 = -19/7

z(1/7) = 5 + 4/7 = 39/7

⇒   intersection = (0, -19/7, 39/7)

• y = 0 (x-z plane):

0 = -3 + 2t   ⇒   2t = 3   ⇒   t = 3/2

x(3/2) = -1 + 21/2 = 19/2

z(3/2) = 5 + 12/2 = 11

⇒   intersection = (19/2, 0, 11)

• z = 0 (x-y plane):

0 = 5 + 4t   ⇒   4t = -5   ⇒   t = -5/4

x(-5/4) = -1 - 35/4 = -39/4

y(-5/4) = -3 - 10/4 = -11/2

⇒   intersection = (-39/4, -11/2, 0)

Answer: 24 fl oz = 1 pt and 1 cup.

Step-by-step explanation: 24 fl oz is equivalent to 3 cups because 1 fl oz equals 8 cups and 8 x 3 is 24. There are 2 cups in a pint, so we have 1 pint and 1 cup left over which is our answer.

Answer:

-5 and -The zeros of a parabola are the points on the parabola that intersect the line y = 0 (the horizontal x-axis). Since these points occur where y = 0,

Answer:

A

False

Step-by-step explanation:

Answer:

1) increase

explanation: In most plants, the uptake of CO2 through photosynthesis is reduced by a side reaction called photorespiration. The research group has now found that the CO2 increase in the atmosphere over the 20th century has shifted the balance between photosynthesis and photorespiration toward photosynthesis.

2) think its false

Answer: (2 - 8x2 - 15) = -29/1 = -29

              (2 + 12x - 3x) = 0

(2 + 12•x - 3•x) = 0

9x = -2

x = -2/

9

≈ -0.222222

Step-by-step explanation:

Answer:

2+2 is 4-1=3 quick maths

Step-by-step explanation:

Answer:

2+(2) is the same to adding 2+2 because the "(" " )" just mean the you have to add the 2 + 2 just like----- 2+2

With the given percentages of discount, Cristobal need to spend at least

$138.81 in a year at the second bookstore to be the better value.

What is the percentage?

In mathematics, a percentage is a statistic or ratio that may be expressed as a fraction of 100. To find the percentage of a number, divide it by its total and multiply by 100. As a result, the percentage represents one part in a hundred. The phrase % stands for one hundred percent. It is represented by the symbol "%".

Here are some percentage examples:

Now,

Given annual membership charges and discount given on all purchases are

For First=$22.95, discount=15%

For second=$35.02, discount=25%

Then for second to be a better value its total cost should be less than first i.e. let x be the money Cristobal spent on both

22.95+x*85/100>35.02+x*75/100

x/10>12.07

x>120.7

So the greater value than $120.7 is $138.81.

Hence,

            Cristobal need to spend at least $138.81 in a year at the second bookstore to be the better value.

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Using linear functions, it is found that 4 movies would cause the two plans to have an equal monthly cost.

A linear function is modeled by:

y = mx + b

In which:

For the functions in this problem, we have that:

Hence the cost functions are given as follows:

The costs will be the same when:

C1(x) = C2(x).

Hence:

22 + x = 14 + 3x

2x = 8

x = 4.

4 movies would cause the two plans to have an equal monthly cost.

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The magnitude of the resultant force is approximately 9.07 lb.

We have,

To use the parallelogram rule to find the magnitude of the resultant force for the two forces, we first draw a diagram:

         B (11 lb)

        /|

       / |

      /  |

     /   |

    /    |

   /     |

  /θ     |

 /       |

A (7 lb)  |

 \       |

  \      |

   \     |

    \    |

     \   |

      \  |

       \ |

        \|

         C

where A and B are the magnitudes of the given forces, and θ is the angle between them.

Using the parallelogram rule, we draw a parallelogram with sides AB and BC:

         B (11 lb)

        /|

       / |

      /  |

     /   |

    /    |

   /     |

  /θ     |

 /       |

A (7 lb) D

 \       |

  \      |

   \     |

    \    |

     \   |

      \  |

       \ |

        \|

         C

The diagonal BD represents the magnitude and direction of the resultant force.

To find its magnitude, we use the Law of Cosines:

BD^2 = AB^2 + BC^2 - 2(AB)(BC)cos(θ)

BD^2 = (7 lb)^2 + (11 lb)^2 - 2(7 lb)(11 lb)cos(133 degrees)

BD^2 = 49 + 121 - 2(77)cos(133 degrees)

BD^2 = 170 - 154cos(133 degrees)

BD ≈ 9.07 lb (rounded to two decimal places)

Therefore,

The magnitude of the resultant force is approximately 9.07 lb.

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Answer:

34

Step-by-step explanation:

10-z=-24

-z=-24-10

-z=-34

z=34/-1

z=34

The solution of equation for z in the expression is,

⇒ z = 34

We have to given that,

An expression to solve is,

⇒ 2 + 8 - z = - 24

Now, We can simplify for z as,

⇒ 2 + 8 - z = - 24

Combine like terms,

⇒ 10 - z = - 24

Subtract 10 both side,

⇒ - z = - 24 - 10

⇒ - z = - 34

⇒ z = 34

Thus, The solution of equation for z in the expression is,

⇒ z = 34

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The probability of surveying 100 randomly selected households and getting 4 or fewer tuned to 60 minutes is only 0.02%.

P(X <= 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

P(X = k) = (100 choose k) * 0.078^k * (1 - 0.078)^(100-k)

P(X <= 4) = (100 choose 0) * 0.078^0 * (1 - 0.078)^(100-0) + (100 choose 1) * 0.078^1 * (1 - 0.078)^(100-1) + (100 choose 2) * 0.078^2 * (1 - 0.078)^(100-2) + (100 choose 3) * 0.078^3 * (1 - 0.078)^(100-3) + (100 choose 4) * 0.078^4 * (1 - 0.078)^(100-4)

Using a calculator or software, we can find that:

P(X <= 4) = 0.000203

This means that the probability is 0.02%.

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Charges for TV advertising on a TV show are based on the number of viewers, which is measured by the rating. The rating is the percentage of population of 110 million TV households.The CBS television show 60 minutes recently had a rating of 7.8, indicating that 7.8% of the household were tuned to that show.An advertiser conducts an independent survey of 100 households and finds that only 4 were tuned to 60 minutes. Assuming that the 7.8 rating is correct, find the probability of surveying 100 randomly selected households and getting 4 or fewer tuned to 60 minutes.Does the result suggest that the rating of 7.8 is too high?

Answer:

3 + 4 = 7

7 + 4 = 11

11 + 4 = 15

15 + 4 = 19

19 + 4 = 23

23 + 4 = 27

The mean value is 1.19

x           p(x)        x*p(x)        X^2p(x)
1           0.1            0.1               0.1
2           0.15         0.3               0.6
3           0.4          1.2                3.6
4          0.25          1                   4
5           0.1           0.5               2.5
Sum        1            3.1                 10.8

Mean =Σx * p(x)

u=3.1

Variance=σ^2

=Σx*p(x)-u^2

=10.8-(3.1)^2 =1 .19    

A probability distribution is a frequency distribution that has been idealised. A frequency distribution is a description of a particular sample or dataset. It is the number of times each possible variable value appears in the dataset.

The probability of occurrence determines how many times a value appears in a sample. Probability is a number between 0 and 1 that indicates the likelihood of an event occurring:


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Answer:

Step-by-step explanation:

take angle C as reference angle

using cos rule

cos C=adjacent/hypotenuse

cos C=21/75

cos C=0.28

C=\(cos^{-1}\)0.28

C=73.7 degree

Answer:

Selling Price = Cost + $3.00

c 1, 2, 3, 4, 5,

f(c) 4, 5, 6, 7, 8,

The merchant uses Selling Price = Cost + $3.00 to determine the selling price.

Addition is a process of combining two or more numbers.

A merchant adds $3.00 to his cost to determine his selling price.

The cost is denoted by c.

The selling price is given by f(c).

As there is given add in the sentence, it means we have to use the addition rule.

Selling price is the sum of cost plus three

Selling Price = Cost + $3.00

So the table becomes as below

c 1, 2, 3, 4, 5,

f(c) 4, 5, 6, 7, 8,

Hence, the merchant uses Selling Price = Cost + $3.00 to determine the selling price.

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Answer:

Step-by-step explanation:

15+5x=20x

   -5x  -5x  => Subtract 5x from each side

You get

15 = 15x

Divide both sides by 15

1=x

Answer:

$113.75

Step-by-step explanation:

First add 70.25 to 43.50 to get 113.75

Answer:

$113.75

Step-by-step explanation:

b-70.25=43.50

add 70.25 to each side ..

b-70.25=43.50

+70.25+70.25

simpilfy...b=113.75

Using Maxwell's equations, we can determine the magnetic flux density. One of the Maxwell's equations is:

\(\displaystyle \nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}}{\partial t}\),

where \(\displaystyle \nabla \times \mathbf{H}\) is the curl of the magnetic field intensity \(\displaystyle \mathbf{H}\), \(\displaystyle \mathbf{J}\) is the current density, and \(\displaystyle \frac{\partial \mathbf{D}}{\partial t}\) is the time derivative of the electric displacement \(\displaystyle \mathbf{D}\).

In this problem, there is no current density (\(\displaystyle \mathbf{J} =0\)) and no time-varying electric displacement (\(\displaystyle \frac{\partial \mathbf{D}}{\partial t} =0\)). Therefore, the equation simplifies to:

\(\displaystyle \nabla \times \mathbf{H} =0\).

Taking the curl of the given magnetic field intensity \(\displaystyle \mathbf{R} =2\cos( 10^{10} t-600x)\hat{a}_{z}\, \text{Am}\):

\(\displaystyle \nabla \times \mathbf{R} =\nabla \times ( 2\cos( 10^{10} t-600x)\hat{a}_{z}) \, \text{Am}\).

Using the curl identity and applying the chain rule, we can expand the expression:

\(\displaystyle \nabla \times \mathbf{R} =\left( \frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial y} -\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial z}\right) \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Since the magnetic field intensity \(\displaystyle \mathbf{R}\) is not dependent on \(\displaystyle y\) or \(\displaystyle z\), the partial derivatives with respect to \(\displaystyle y\) and \(\displaystyle z\) are zero. Therefore, the expression further simplifies to:

\(\displaystyle \nabla \times \mathbf{R} =-\frac{\partial ( 2\cos( 10^{10} t-600x)) \hat{a}_{z}}{\partial x} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Differentiating the cosine function with respect to \(\displaystyle x\):

\(\displaystyle \nabla \times \mathbf{R} =-2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z\).

Setting this expression equal to zero according to \(\displaystyle \nabla \times \mathbf{H} =0\):

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x)\hat{a}_{z} \mathrm{d} x\mathrm{d} y\mathrm{d} z =0\).

Since the equation should hold for any arbitrary values of \(\displaystyle \mathrm{d} x\), \(\displaystyle \mathrm{d} y\), and \(\displaystyle \mathrm{d} z\), we can equate the coefficient of each term to zero:

\(\displaystyle -2( 10^{10}) \sin( 10^{10} t-600x) =0\).

Simplifying the equation:

\(\displaystyle \sin( 10^{10} t-600x) =0\).

The sine function is equal to zero at certain values of \(\displaystyle ( 10^{10} t-600x) \):

\(\displaystyle 10^{10} t-600x =n\pi\),

where \(\displaystyle n\) is an integer. Rearranging the equation:

\(\displaystyle x =\frac{ 10^{10} t-n\pi }{600}\).

The equation provides a relationship between \(\displaystyle x\) and \(\displaystyle t\), indicating that the magnetic field intensity is constant along lines of constant \(\displaystyle x\) and \(\displaystyle t\). Therefore, the magnetic field intensity is uniform in the given medium.

Since the magnetic flux density \(\displaystyle B\) is related to the magnetic field intensity \(\displaystyle H\) through the equation \(\displaystyle B =\mu H\), where \(\displaystyle \mu\) is the permeability of the medium, we can conclude that the magnetic flux density is also uniform in the medium.

Thus, the correct expression for the magnetic flux density in the given medium is:

\(\displaystyle B =6\cos( 10^{10} t-600x)\hat{a}_{z}\).