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White raven [17]
2 years ago
6

Given that x+1 is a factor of 3x³-14x²-7x+d, show that d= 10

Mathematics
1 answer:
Alja [10]2 years ago
8 0

Answer:

3x³ - 14x² - 7x + d = (x + 1)(ax² + bx + c)

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

  (x + 1)(ax² + bx + c)  

= ax³ + bx² + cx + ax² + bx + c

= ax³ + (a + b)x² + (b + c)x + c

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

ax³ + (a + b)x² + (b + c)x + c = 3x³ - 14x² - 7x + d

=> a = 3

    a + b = -14

    b + c = -7

    c = d

=> a = 3, b = -17, c = 10, d = 10

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Of the total number of people on a cruise ship, 1/4 or child passengers. 2/5 of the remaining people were crew. There were 1320
Nuetrik [128]
<h2>462</h2>

Step-by-step explanation:

       Total number of people on the cruise ship was 1320.

\frac{1}{4}^{th} of the people were child passengers. Number of child passengers = \dfrac{1}{4}\times (\text{Total number of people})=\dfrac{1}{4}\times 1320=330

\frac{2}{5}^{th} of the people were crew. Number of people that were crew = \dfrac{2}{5}\times (\text{Total number of people})=\dfrac{2}{5}\times 1320=528

       Remaining people in the ship constitute the adult passengers.

       Number of adult passengers = (\textbf{Total number of people})-(\textbf{Total number of children})-(\textbf{Total number of crew})=1320-330-528=\textbf{462}

∴ Number of adult passengers = 462

5 0
2 years ago
The table and the graph show the relationship between the edge length, x, of a cube and its surface area, y. Is the relation a f
d1i1m1o1n [39]

Answer:

Yes, the relationship between x and y is a non-linear function.

Step-by-step explanation:

Given the table

Edge Length, x            Surface Area, y

1                                             6

2                                            24

3                                            54

4                                             96

  • The table values clearly represent a function, because each input value has one and only one output value. i.e. there is no repetition of x values.

  • Also from the table values and the graph, it is clear that the function is not a linear function, because the graph is not a straight line. Also, In a cubic function, the highest power over the x variable(s) is 3. So, it is not a linear function.

Hence, we conclude that Yes, the relationship between x and y is a non-linear function.

Therefore, the 'last option' is correct.

4 0
1 year ago
Explain why the graphing calculator cannot be used to solve or approximate solutions to all polynomial equations.
Triss [41]

Did your explanation include the following?

Some polynomial equations have complex solutions.

Therefore, complex solutions cannot be found by graphing the related system or function in the Cartesian (x-y) plane.

Polynomial functions with all complex solutions do not have x-intercepts, and the related system of equations will not intersect.

6 0
2 years ago
Read 2 more answers
6 points Emily’s family needs to rent a moving truck to move their belongings to a different house. The rental cost for Trucks-A
Alexxx [7]

Answer/Step-by-step explanation:

Equation to represent the daily rental cost for each type of truck can be written as follows:

Daily rental cost for Trucks-A-Lot = 42 + 0.72m

Daily rental cost for Move-in-Truckers = 70 + 0.12m

Where, m = Emily's mileage

To determine the number of miles for which the truck cost the same amount, set both equations equal to each other and solve for m.

42 + 0.72m = 70 + 0.12m

Collect like terms

0.72m - 0.12m = 70 - 42

0.6m = 28

Divide both sides by 0.6

\frac{0.6m}{0.6} = \frac{28}{0.6}

m = 46.7

At approximately 47 miles, both trucks would cost the same amount.

Check:

Daily rental cost for Trucks-A-Lot = 42 + 0.72m

Plug in the value of x = 47

= 42 + 0.72(47) = $75.84 ≈ $76

Daily rental cost for Move-in-Truckers = 70 + 0.12m

Plug in the value of x = 47

= 70 + 0.12(47) = $75.64 ≈ $76

7 0
2 years ago
Jody bought 20 shares of amazon at the close price of $121.00. She bought 20 more shares a year later at the price of $127.00. T
hjlf

Answer:

Jody made $210 after all of these transactions.

Step-by-step explanation:

Jody bought 20 shares of amazon at the price of $121.00

= 121.00 × 20 = $2,420

After one year she bought 20 more shares at the price of $127.00

= 127.00 × 20 = $2,540

Her broker charges $50.00 for each transaction = 50 × 2 = $100

Total cost of all shares = 2,420 + 2,540 + 100 = $5,060

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= 133 × 40 = $5,320

She gave broker charge for this transaction = $50.00

Total selling amount  = 5,320 - 50 = $5,270

Profit = Selling amount - cost

Profit = 5,270 - 5,060 = $210

Jody made $210 after all of these transactions.

8 0
2 years ago
Read 2 more answers
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