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Troyanec [42]
3 years ago
15

What is the value of the leading coefficient a, if the polynomial function P(x) = a(x + b)2(x − c) has a multiplicity of 2 at th

e point (−1, 0) and also passes through the points (7, 0) and (0, −14)?
2
Mathematics
1 answer:
kirill115 [55]3 years ago
6 0
If the polynomial function P(x) = a(x + b)^2(x-c) has a multiplicity of 2 at the point (−1, 0) then the factor (x-(-1))=(x+1) twice enters the polynomial representation. So, you have known one part of the left side of the polynomial function that is P(x) = a(x + 1)^2(x-c).

If polynomial function passes through the point (7,0), then 0 = a(7+ 1)^2(7-c) and since a\neq 0 you have that c=7.

At last, if polynomial function passes through the point (0,-14), then -14 = a(0+ 1)^2(0-7) and -14=-7a, so a=2.
Answer: a=2.



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Lian is paid for SR 75 per hour. Using p for her pay and h for the hours of work, which function rule represents
Andru [333]

Answer:

The function p = 75h represents  this situation.

Step-by-step explanation:

We know the equation of linear equation in the slope-intercept form is

y = mx+b

where

m = rate of change = slope

b = y-intercept

  • Let 'h' be the number of hours
  • Let 'p' be the pay

Given that Lian is paid SR 75 per hour.

so the rate of change of slope = m = 75

As there is no initial condition, so b = 0

as

y = mx+b

Now, mapping the information data into the slope-intercept form

  • p = y
  • m = 75
  • h = x
  • b = 0

Thus, the equation becomes

p = 75h

Therefore, the function p = 75h represents  this situation.

VERIFICATION:

Given the equation

p = 75h

for h = 1

p = 75(1)

p = 75

Thus, Liam is paid SR 75 per hour.

4 0
2 years ago
Describe the general properties of rotations.
Korolek [52]

A rotation maps a line to a line, a ray to a ray, a segment to a segment, and an angle to an angle.

A rotation preserves lengths of segments.

A rotation preserves measures of angles. Step-by-step explanation:

You Welcome :)!

5 0
3 years ago
which of these shows the result of using the first equation to substitute for y in the second equation, then combining like term
Furkat [3]

Answer:

C. \Rightarrow \bold{8x = 16}

Step-by-step explanation:

Given the two equations:

y=2x ........ (1)\\ 2x+3y=16.......(2)

To find:

The correct option when value of y is substituted to 2nd equation using the 1st equation.

Solution:

First of all, let us learn about the substitution method.

Substitution method is the method to provide solutions to two variables when we have two equations and two variables.

In substitution method, we find the value of one variable in terms of the other variable and put this value in the other equation.

Now, the other equation becomes only single variable and then we solve for the variable's value.

Here, we have two equations and value of one varible is:

y=2x

Let us put value of y in 2nd equation:

2x+3y=16\\\Rightarrow 2x + 3(2x) = 16\\\Rightarrow 2x + 6x = 16\\\Rightarrow \bold{8x=16}

So, the correct answer is option C. \Rightarrow \bold{8x = 16}

7 0
3 years ago
Zach is 4 years older than twice his sister maya’s age. maya is 5 years old. how old is zach?
SCORPION-xisa [38]
Zach is 14 bc...
-4 years older(+4) than twice (x2) Mayas age.
-Maya is 5
- the correct order is 5x2+4
-5x2=10, 10+4=14
4 0
3 years ago
Robin's bank account balance is --$25.00. She makes a deposit of cash, which brings her balance now to
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Answer:

The answer will be

87- 25=62

so the integer to represent the amount she deposited

is =$25+$62.

5 0
3 years ago
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