1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nonamiya [84]
3 years ago
10

Marco is 8 years younger than his brother Paolo. If their product of their ages is 105, how old is Marco? plz help

Mathematics
1 answer:
Nina [5.8K]3 years ago
4 0

Answer:

Marco's age is 7 years old

Step-by-step explanation:

Let

x ----> Marco's age

y ----> Paolo's age

we know that

x=y-8 ----> y=x+8 ----> equation A

xy=105 ----> equation B

substitute equation A in equation B

x(x+8)=105

x^2+8x-105=0

Solve the quadratic equation

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}

in this problem we have

x^2+8x-105=0

so

a=1\\b=8\\c=-105

substitute in the formula

x=\frac{-8(+/-)\sqrt{8^{2}-4(1)(-105)}} {2(1)}

x=\frac{-8(+/-)\sqrt{484}} {2}

x=\frac{-8(+/-)22} {2}

x=\frac{-8(+)22} {2}=7

x=\frac{-8(-)22} {2}=-15

Remember that the solution cannot be a negative number

so

The solution is x=7

therefore

Marco's age is 7 years old

You might be interested in
Answer Questions and show all of your work.
Dmitriy789 [7]

Answer:

X= 35

Z=90

Step-by-step explanation:

sorry I don’t know how else to help

6 0
2 years ago
How do you factor 125-x^3?
xz_007 [3.2K]

Step-by-step explanation:

We have

125 - x {}^{3}

First, 125 is a perfect cube because

5 \times 5 \times 5 = 125

and

x^3 is a perfect cube because

x \times  x \times x = x {}^{3}

so we can use the difference of cubes identity

( {x}^{3}  -  {y}^{3} ) = (x - y)( {x}^{2}  + xy +  {y}^{2} )

Let say we have two perfect cubes:

64 because 8×8×8=64

and 27 because 3×3×3=27 and let subtract

64 - 27

we know that

64 - 27 = 37

but using the difference of cubes identity we should get the same thing.

Remeber cube root of 64 is 4 and cube root of 27 is 3 so we have

(4 - 3)( {4}^{2}  + 4(3) + 3 {}^{2} )

1(16 + 12 + 9) = 1(37) = 37

So the difference of cubes works for real numbers. This is a good way to help remeber the identity using real numbers.

Back on to the topic,

we know that 5 is cube root of 125 and x is the cube root of x^3 so we have

(5 - x)( {5}^{2}  + 5x +  {x}^{2} ) =

(5 - x)(25 + 5x +  {x}^{2} )

3 0
2 years ago
Read 2 more answers
If i had 10 pound then i times that by 4 then divide by 2 then take 5 away what is it
Lemur [1.5K]
15 because 10x4 is 40 divided by 2 is 20 and 20-5 =15
3 0
2 years ago
Read 2 more answers
Could someone me please​
mariarad [96]

Answer:

I think is 11/90.

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
To determine the density of grains, a student uses a 50ml beaker graded by 5ml increments and a scale with 1g absolute uncertain
labwork [276]

Answer:

The mass of the grains = 120 ± 1 g

Step-by-step explanation:

we are given the following:

Total mass of container + grains = 185 grams

Mass of container = 65 grams

Therefore, mass of grains is calculated as follows:

Mass of grains = ( Mass of container + grains) - mass of container

= 185 - 65 = 120 grams.

since the scale has an absolute uncertainty of 1 g, the mass of the grains is written as 120 ± 1 g

8 0
3 years ago
Other questions:
  • Andy is kayaking on a river in Morgan County, moving down the river at a speed of 10 miles per hour. Meanwhile, Tatsu is on a je
    14·1 answer
  • What is the effective annual rate for an APR of 10.60 percent compounded quarterly?
    11·1 answer
  • At the Pleasant Valley Golf Course, the average player finishes 18 holes in 72 shots. Landon can complete the course in 64 shots
    5·1 answer
  • Rosita had 17 subtraction problems and 28 multiplication problems. If she ca finish five problems in 20 minutes, how long will i
    11·2 answers
  • What is 0.4 divided by 0.242? Divide and check your answer using multiplication. Show your work.
    9·2 answers
  • Find the volume of the cube (asap) (picture)
    7·2 answers
  • Y-4=3(x - 1) <br> Identify slope <br><br> and what is an “anchor point”
    10·2 answers
  • Create Write a real-world problem that can be<br> solved using the equation 9 + 4x = 21 - 2x
    6·1 answer
  • Part B
    14·1 answer
  • Which phrase best describes the translation from the graph y = 6x² to the graph of y = 6(x + 1)²?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!