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ivanzaharov [21]

3 years ago

13

A woman is now 30 years older than her son. 15 years ago, she was twice as old. What are the present ages of the woman and her s

on?

1 answer:

Paladinen [302]3 years ago

8 0

Answer:

75 and 45

Step-by-step explanation:

woman's age= w

son's age= s

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

w=s+30
w-15=(s-15)*2 ⇒ w-15=2s-30 ⇒ w=2s- 15

comparing the two above:

s+30=2s-15 ⇒ s= 45 ⇒ w= 75

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Find the length of AB

aniked [119]

FIRST QUESTION
Given points are:
A(2, -4) and B(6, 2)
Now, Use the distance formula.
distance formula = $\sqrt{ (x_{2}- x_{1})^{2} + ( y_{2} - y_{1} )^{2} }$

Now, plug the values into the formula, So,
distance = $\sqrt{ (6- 2)^{2} + ( 2 - (-4))^{2} }$

= $\sqrt{ (6- 2)^{2} + ( 2 +4))^{2} }$

= $\sqrt{ (4)^{2} + ( 6))^{2} }$

= $\sqrt{ 16+36}$

= $\sqrt{52}$

= $2 \sqrt{13}$

So, the length of AB is $2 \sqrt{13}$ .

<span>THIRD QUESTION
</span>Two points given are:
A(3, -2) and B(1, 1)
Also given that B is the midpoint of AC.

Let, the co-ordinates of C be C(a, b).
Now, using midpoint formula,
Midpoint = $(\frac{ x_{1}+ x_{2} }{2} , \frac{ y_{1}+ y_{2} }{2} )$

$(1, 1)=(\frac{ 3+ a }{2} , \frac{ -2+b }{2} )$

Now, equaling the ordered pair, we have,

$1=\frac{ 3+ a }{2}$ .............equation (1)

$1=\frac{ -2+b }{2}$ ................equation (2)

Now, taking equation (1)
$1=\frac{ 3+ a }{2}$

$1*2=3+a$

$2-3=a$

$a=-1$

Now, taking equation (2)
$1=\frac{ -2+b }{2}$

$1*2=-2+b$

$2+2=b$

$b=4$

<span>So, the co ordinates of C are (a, b) which is <u>(-1 , 4)

</u></span>
<span>SECOND QUESTION:
</span>Given equations are:
2x + 3y = 14.....................equation (1)
-4x + 2y = 4 .....................equation (2)
Taking equation (2)
-4x + 2y = 4
2y = 4 + 4x
y = (4 + 4x) / 2
y = 2 + 2x .......................equation (3)
Now, Taking equation (1)
2x + 3y = 14
Substituting the value of y from equation (3), we get,
2x + 3(2 + 2x) = 14
2x + 6 + 6x = 14
8x = 14 - 6
x = (14 - 6) / 8
x = 1

Taking equation (3)
y = 2 + 2x
Now, substituting the value of x in equation (3), we get,
y= 2 + 2 (1)
y = 2 + 2
y = 4

So, x=1 and y=4

6 0

3 years ago

I'll give you brainliest answer!! Help me. This diagram shows a smaller square inscribed within a larger square.

Veseljchak [2.6K]

Each side of the smaller square is the hypotenuse of the triangles with legs of 3 and 4. From the Pythagorean Theorem, we can calculate the hypotenuse:
hypotenuse^2 = 3^2 + 4^2
hypotenuse^2 = 9 + 16
hypotenuse^2 = 25
hypotenuse = 5
Therefore, the area of the smaller square is 5 * 5 = 25

8 0

3 years ago

Read 2 more answers

There are 8 employees on The Game Shop's sales team. Last month, they sold a total of g games. One of the sales team members, Ch

soldi70 [24.7K]

Answer:

g/8 - 17= C

Step-by-step explanation:

g/8 = A ( average game sales per employee)

A - 17 = C (amount of games Chris sold)

Chris sold C amount of games

I answered to the best of my ability

8 0

3 years ago

Is x-3 a factor of the polynomial p(x)=2x4-9x3+15x2-22x+12 and for waht reason

andre [41]

Yes, (x - 3) is a factor of the given polynomial.

If (x - 3) was a factor of the polynomial, then 3 would be one of the zeros of the function. That means if you input 3 into the function, you will get an output of zero.

In this case, inputting 3 does produce 0. Therefore, it is a factor.

3 0

3 years ago

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NNADVOKAT [17]

Answer:

The equation would be 2,250 - 120<em>m</em>

7 0

3 years ago