The ratio of the ages of father and son is 5:2. The summation of their present ages is 49 years. After how many years, the age of the father will be triple the age of son?

Answer:

I can't read that..........

Answer:

55

Step-by-step explanation:

You multiply 5 on both sides of the ratio, and you get 40 children : 15 adults. Adding that up, you would get 55 people.

Answer:

Step-by-step explanation:

Write and solve an equation of ratios.  The given ratio is 8:3.  The number of children is 40 and that of adults is 40 - c.  Note that c + (40 - c) = 40.

Solve the following equation of ratios for c:         8        40

                                                                               ---- = ----------

                                                                                3          a

Cross multiplying, we get 8a = 120, of 15.  Then a = number of adults = 24.

Here a = 15 and c = 40.  Check the ratio 40/15; does it equal 8/3?  YES

The total number of people at the pool is 40 + 24, or 64

Answer:

y = 2(x-5)(x+2)

Step-by-step explanation:

First make points out of the number!

(5,0), (-2,0), and (0,-20)

Plug it into this, p and q being the roots

y=a(x-p)(x-q) ---> y=a(x-5)(x+2)

Now plug in x and y from our y-intercept

-20 = a(0-5)(0+2) --> -20 = -10a ---> 2 = a

Now plug in "a" in orginal equation

y = 2(x-5)(x+2)

Answer:

x = 20

Step-by-step explanation:

The 2 given angles are adjacent on a straight line and sum to 180° , then

123 + 2x + 17 = 180

140 + 2x = 180 ( subtract 140 from both sides )

2x = 40 ( divide both sides by 2 )

x = 20

Answer:

8 + 12 =20

Step-by-step explanation:

i think 20 the answer

Answer:

You only have yo flip it

Step-by-step explanation:

I did it before

Answer:

C. 2 and 6

Step-by-step explanation:

2 and 6 are the zeros because they are both on X

Answer:

18 = 2 x 3²

Step-by-step explanation:

Factors of 18: 1, 2, 3, 6, 9, 18

Prime factorization: 18 = 2 x 3 x 3

Step-by-step explanation:

1)

The rule is: (x, y) → (x + 4, y - 3)

This is the translation 4 units right and 3 units down.

2)

Since same rule applied to all three points A, B and C, they translate into same direction and same distance.

It means AA' and BB' are parallel and congruent. Same applies to segment CC', it is parallel to AA' and BB' and have same length.

Answer:

1)

The rule is: (x, y) → (x + 4, y - 3)

This is the translation 4 units right and 3 units down.

2)

Since same rule applied to all three points A, B and C, they translate into same direction and same distance.

It means AA' and BB' are parallel and congruent. Same applies to segment CC', it is parallel to AA' and BB' and have same length.

Step-by-step explanation:  i did this so you can brainlist the other person

Answer:

56

Step-by-step explanation:

Let the angle be " x ".

Complement of the angle = ( x - 22 )

To find : x = ?

x + x - 22 = 90

2x - 22 = 90

2x = 90 + 22

2x = 112

x = 112 / 2

x = 56

Therefore, the angle is 56.

Answer:

hot dog= $2.25

juice= $1.50

Step-by-step explanation:

Let the price of a hot dog be $H and that of a juice be $J.

H +J= 3.75 -----(1)

2H +3J= 9 -----(2)

(1) ×2:

2H +2J= 7.5 -----(3)

(2) -(3):

2H +3J -(2H +2J)= 9 -7.5

Expand:

2H +3J -2H -2J= 1.5

J= 1.5

Substitute J= 1.5 into (1):

H +1.5= 3.75

H= 3.75 -1.5

H= 2.25

∴ The price of a hot dog and a juice is $2.25 and $1.50 respectively.

Answer:

Step-by-step explanation:

g(3)= (3+1)/(3-1)= 4/2= 2

f(2)= 3(2)-7 = 6 - 7 = -1

answer is a. -1

Answer:

-4/9

Step-by-step explanation:

Answer:

A)

6x - y = 8

3x + 2y = 9

(Graph is attached for you⤴⤴⤴)

Step-by-step explanation:

Line m ordered pairs = (-4,-32), (2,4),

(5, 22)

Line n ordered pairs = (-5,12), (1,3), (5,-3)

Use this formula⤵⤵⤵

[tex] \frac{y _{2} - y _{1} }{x _{2} - x _{1} } [/tex]

For line m, we'll use (2,4) and (5,22):

22 - 4 = 18

5 - 2 = 3

18 ÷ 3 = 6

Slope of line m = 6

For line n, we'll use (1,3) and (5,-3):

-3 - 3 = -6

5 - 1 = 4

Slope of line n = -6/4 or -3/2

We'll turn all the options to slope-intercept form, so we can tell which has the slopes we need.

A) - Subtract 6x on both sides to get

-y = -6x + 8, then flip all the signs to get y = 6x - 8.

- Subtract 3x on both sides to get 2y = -3x + 9, then divide 2 on both sides to get y = -3/2 x + 9/2.

B)

- Subtract 6x on both sides to get

y = -6x - 8.

- Subtract 3x on both sides to get

-2y = -3x + 9, then divide -2 on both sides to get y = -3/2 x - 9/2.

C)

- Add 6x on both sides to get -y = 6x - 8, then flip all signs to get y = -6x + 8.

- Add 3x on both sides to get 2y = 3x + 9, then divide 2 on both sides to get

y = 3/2 x + 9/2.

D)

- Subtract 6x on both sides to get

-y = -6x - 8, then flip all signs to get

y = 6x + 8.

- Add 3x on both sides to get -2y = 3x + 9, then divide -2 on both sides to get

y = -3/2 x - 9/2.

Hope this helps :)

Answer:

kikjnknj

Step-by-step explanation:

Y-intercept - 4

Slope - 3

Slope intercept form - y=3x + 4

Hope it's correct and it helped:)

Answer:

Step-by-step explanation:

given A(-1, 2), B(-3, 4), C(-2, 5)

after translating by (4, 4)

points are A(-1 + 4, 2 + 4),  B(-3 + 4, 4 + 4), C(-2 + 4, 5 + 4)

A(3, 6), B(1, 8), C(2, 9)

to rotate 90° counter clockwise (x, y) ----> (-y, x)

now it is rotated around point A(3, 6).That means A remains same and we need to find new coordinates of B and C.  To find B and C let us make origin as A and find B ,C coordinates from it.

B'(1 - 3, 8 - 6) = (-2, 2)

C'(2 - 3, 9 - 6) = (-1, 3)

now it becomes (-y, x)

B'(-2, -2)

C'(-3, -1)

now we have to move origin from (3,6) to (0,0) again.

so B'(-2 + 3, -2 + 6) = (1, 4)

C'(-3 + 3 , -1 + 6) = (0, 5)

now reflection over y axis means (x, y) --> (-x, y)

A'(-3, 6)

B'(-1, 4)

C'(0, 5)

it is different from the options

but this is the process, tell me if you find any step different from the question

see the figure below

Answer:

what is it

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Well since 11 of the pirates had eyepatches, and 11 is greater than 9, all 9 of the pirates that had cutlasses had eyepatches as well. I don't know if this is completely correct but it's the only thing that makes sense to me.

9514 1404 393

Answer:

  n = 3

Step-by-step explanation:

In order for 3 × 3 = 9 to be a factor of both numbers, we must have ...

  n = 3

Answer:

5/16

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Answer:

9a+18=9

9a=-9

a=-1

Step-by-step explanation:

We know that f(x) = 12x + 12

f(1) = 12 * 1 + 12= 24

f(0) = 12*0 + 12 = 12

The formula of the average rate of change is : f(1) - f(0)  /  (1 - 0)

(24 - 12) / 1 = 12/1 = 12

So the average rate of change is 12

Good Luck

Answer:

[tex]a=60\\b=44\\c=76[/tex]

Step-by-step explanation:

You can write these equations to represent the problem:

[tex]a+b+c=180\\b+c=2a\\b=c-32[/tex]

Now, just solve it as a system of equations. I'll solve by substitution, starting from the bottom as b is already defined there.

[tex]b=c-32\\b+c=2a\\(c-32)+c=2a\\c+c-32=2a\\2c-32=2a\\a=c-16[/tex]

That's the middle equation done, now I'll do the top one:

[tex]b=c-32\\a+b+c=180\\a+(c-32)+c=180\\a+2c-32=180\\a+2c=212\\a=-2c+212[/tex]

Now we have just 2 equations with 2 variables. That's another system of equations, but this one is much easier to solve. Using substitution again:

[tex]a=c-16\\a=-2c+212\\c-16=-2c+212\\3c-16=212\\3c=228\\c=76[/tex]

Finally, we have one variable solved. Using the value of C, now we can solve for A:

[tex]c=76\\a=c-16\\a=76-16\\a=60[/tex]

Thats 2 done. Now, pick any equation that has all 3 variables and solve for B:

[tex]a=60\\c=76\\a+b+c=180\\60+b+76=180\\b+136=180\\b=44[/tex]

All 3 variables done.

[tex]a=60\\b=44\\c=76[/tex]

Now, we can confirm that they're correct by checking with the original equations:

[tex]a+b+c=180\\60+44+76=180\\180=180\\\\b+c=2a\\44+76=2(60)\\120=120\\\\b=c-32\\44=76-32\\44=44[/tex]

They all work fine.

Answer:

2b + 3n = £15.50

4b + 1n = £13.50

2 ( 2b + 3n =  15.50 )

4b + 6n = 31.00

    4b + 6n =  31.00

-    4b +  1n = 15.50

            5n  = 15.50

              n  =  3.1

subtitue n in to the equation

2b + 9.3 = £15.50

2b          = £6.20

b             = 3.10p

Step-by-step explanation:

both the bracelets and necklace cost £3.10

The cost of one bracelet is $2.50

b = cost of the bracelet

n = costs of necklace

⇒ 2b + 3n = 15.50

⇒ 4b+1n = 13.50

Multiply the first equation by -2

⇒ -4b - 6n = -31

⇒ 4b + n = 13.50

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

-5n = -17.50

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

Divide each side by -5

⇒ -5n / -5 = -17.5 / -5

⇒ n = 3.50

Now we can find b

⇒ 4b + n = 13.50

⇒ 4b + 3.50 = 13.50

⇒ 4b + 3.50 - 3.50 = 13.50 -3.50

⇒ 4b = 10

Divide by 4

⇒ 4b / 4 = 10/4

⇒ b = 2.50

The cost of one bracelet is $2.50.

A system of equations comprises two or more equations and seeks common solutions to the equations.

Learn more the system of equations about here: brainly.com/question/14323743

#SPJ2

Answer:

12.64

Step-by-step explanation:

cos 53 = Adjacent side/Hypotenuse

cos 53 = Adjacent side/21

21 * cos 53 = (Adjacent side/21) * 21

21 cos 53 = Adjacent side

Adjacent side (AB) ≈ 12.64

Adjacent angles will be same

[tex]\\ \sf\longmapsto <N=<P[/tex]

[tex]\\ \sf\longmapsto 6y=8y-16[/tex]

[tex]\\ \sf\longmapsto 8y-6y=16[/tex]

[tex]\\ \sf\longmapsto 2y=16[/tex]

[tex]\\ \sf\longmapsto y=8[/tex]

Answer:

[tex]y = 8[/tex]

Step-by-step explanation:

If two sides of a triangle is equal the opposite interior angles are also equal.

Therefore,

[tex]6y = 8y - 16 \\ 16 = 8y - 6y \\ 16 = 2y \\ \frac{16}{2} = \frac{2y}{2} \\ 8 \degree = y[/tex]

Hope this helps you.

Let me know if you have any other questions :-)