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USPshnik [31]
3 years ago
9

Raul’s grandfather is Miguel, and Raul’s sister is Paula. Raul’s age is the same as his grandfather’s age minus 60 times the age

of his sister. Miguel is 65 years old, write an equation to find Paula’s age, p (in years).
Mathematics
2 answers:
Cerrena [4.2K]3 years ago
4 0

Answer : P = (65 - R) / 60

Effectus [21]3 years ago
3 0

Answer:

P = (65 - R) / 60

Step-by-step explanation:

Raul's grandfather is Miguel

Raul's sister is Paula

We are given that Raul’s age is the same as his grandfather’s age minus 60 times the age of his sister. If we write this mathematically, we have that:

R = M - (60*P)

Where R = Raul's age, M = Miguel's age and P = Paula's age

We are then given that Miguel is 65 years old, this means that M = 65

=> R = 65 - 60P

To find Paula's age, we make P the subject of formula, hence:

60P = 65 - R

=> P = (65 - R) / 60

We can use this expression to find Paula's age.

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Anna truncated the decimal expansion of x to find the best approximation. On a number line, the location of x is between 10.9 an
podryga [215]

Answer:

Well to estimate a decimal the best option would be to round it to.

10 or 11 (For 10.9)

11 (For 11.1)

and since two of them equal 11. 

The estimation would be 11.

I hoped this helped.

3 0
2 years ago
The polynomial p(x)=x^3-19x-30 has a known factor of (x+2)
riadik2000 [5.3K]

Answer:

(x+2) (x+3) (x-5)

Step-by-step explanation:

x³-19x-30 = (x+2) (x²+ax-15)  ... x³=x*(1*x²)   while -30= (2)*(-15)

x³ +<u> 0</u>*x² - 19x -30 = x³ + (<u>2+a</u>)x² + (2a-15)x -30

2+a = 0

a = -2

x³-19x-30 = (x+2) (x²-2x-15) = (x+2) (x+3) (x-5)

8 0
3 years ago
Read 2 more answers
Find the equation, (f(x) = a(x - h)2 + k), for a parabola containing point (2, -1) and having (4, -3) as a vertex. What is the s
Nataliya [291]

Answer:

f(x)=\frac{1}{2}x^2-4x+5

Step-by-step explanation:

A parabola is written in the form

f(x)=a((x-h)^2+k) (1)

where:

h is the x-coordinate of the vertex of the parabola

ak is the y-coordinate of the vertex of the parabola

a is a scale factor

For the parabola in the problem, we know that the vertex has  coordinates (4,-3), so we have:

h=4 (2)

ak=-3

From this last equation, we get that a=\frac{-3}{k} (3)

Substituting (2) and (3) into (1) we get the new expression:

f(x)=-\frac{3}{k}((x-4)^2+k) = -\frac{3}{k}(x-4)^2 -3 (4)

We also know that the parabola  contains the point (2,-1), so we can substitute

x = 2

f(x) = -1

Into eq.(4) and find the value of k:

-1=-\frac{3}{k}(2-4)^2-3\\-1=-\frac{3}{k}\cdot 4 -3\\2=-\frac{12}{k}\\k=-\frac{12}{2}=-6

So we also get:

a=-\frac{3}{k}=-\frac{3}{-6}=\frac{1}{2}

So the equation of the parabola is:

f(x)=\frac{1}{2}((x-4)^2 -6) (5)

Now we want to rewrite it in the standard form, i.e. in the form

f(x)=ax^2+bx+c

To do that, we simply rewrite (5) expliciting the various terms, we find:

f(x)=\frac{1}{2}((x^2-8x+16)-6)=\frac{1}{2}(x^2-8x+10)=\frac{1}{2}x^2-4x+5

6 0
3 years ago
F(x) = -x^3+ 6x – 7 at x = 2
vodomira [7]

Answer:

f(2)= -4

Step-by-step explanation:

f(x)= -x^3 + 6x - 7

f(2) = -2^3 + 6*2 - 7

f(2)= -8 +12 -7

f(2)= 3-7

f(2)= -4

4 0
2 years ago
If the equation of the line is y=1/2x-3, find the x-coordinate of the Lundy whose y coordinate is 5.
Anna71 [15]

Y=1/2x -3 find the x coordinate of the point whose y

coordinate is 5

y = 5. Write the equation as:

1/2F2x - 3 = 5

multiply both sides by 2, and you have

x - 6 = 10

x = 10 + 6

x - 16


Check solution in original equation, replace x with 16

y = 1/2F2(16) - 3

y = 8 - 3

y = 5

5 0
3 years ago
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