Ash is 4 years younger than Gary, and Oak is 5 times Gary's age. The sum of their three ages is 94. Find Gary's age. Show working out. Thanks!!

Answer:

The solution to the system of equations is:

[tex]x=10,\:y=4[/tex]

Step-by-step explanation:

Given the system of equations

[tex]\begin{bmatrix}5x-4y=34\\ -x+8y=22\end{bmatrix}[/tex]

Multiply -x+8y=22 by 5:  -5x+40y=110

[tex]\begin{bmatrix}5x-4y=34\\ -5x+40y=110\end{bmatrix}[/tex]

so adding the equations

[tex]-5x+40y=110[/tex]

[tex]+[/tex]

[tex]\underline{5x-4y=34}[/tex]

[tex]36y=144[/tex]

solve 36y = 144 for y:

[tex]36y=144[/tex]

divide both sides by 36

[tex]\frac{36y}{36}=\frac{144}{36}[/tex]

Simplify

[tex]y=4[/tex]

For 5x-4y=34 plug in y=4

[tex]5x-4\cdot \:4=34[/tex]

[tex]5x-16=34[/tex]

Add 16 to both sides

[tex]5x-16+16=34+16[/tex]

Simplify

[tex]5x=50[/tex]

Divide both sides by 5

[tex]\frac{5x}{5}=\frac{50}{5}[/tex]

Simplify

[tex]x=10[/tex]

Therefore, the solution to the system of equations is:

[tex]x=10,\:y=4[/tex]

Answer:

From the first bag the probability is 5 out of 15 or 1/3 simplified

The second bags probability is 4 out of 9

All the bags combined the probability is 9 out of 24

Step-by-step explanation:

The probability should be set up by putting the blue marbles as the numerator and the sum of all the marbles combined for the denominator

With everything said all you have to do is figure out the two steps an you’re good to go

Answer:

z= 2√2

x=2

y=2√2

Step-by-step explanation:

=x²-10x-24

=x²-4x+6x-24

=x(x-4)+6(x-4)

=(x-4)(x+6)

hope it helps.

Answer:

8/9

Step-by-step explanation:

I'm pretty sure after you make it a reciprocal you multiply it

Answer:

Step-by-step explanation:

Answer:

= 2 and 5

Step-by-step explanation:

( 4 - 7x ) + ( 2x - 2 ) = 0

4 - 7x = 2x - 2 = 0

-7x -2x - 2 + 4 = 0

  -5x   - 2   = 0

-5 x = 0                  or             -2 = 0

x = 5                                       x = 2

Answer:

y=-15

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Answer:

a)  constant of proportionality is 3/5

b)  3.5cm per 1 minute

c)  21 cm water in trough after 6 min

d)  70 cm

Step-by-step explanation:

d)  21 / 6 = x / 20

    7 / 3 = x / 20    

    2x = 140

    x = 70

Answer:

-100

Step-by-step explanation:

-4 * 5 * 5

Answer:

-100

Step-by-step explanation:

Answer:

The answer is C, 40.32

Step-by-step explanation:

If you put 6.25 in your calculator times 40.32% you get 2.52. Then you add the 2.52 to 6.25 to get 8.77.

Answer:

The answer is b

Step-by-step explanation:

hope it helped bye :)

Answer:

4y+29

Step-by-step explanation:

Collect like terms

3y + y = 4y

5 + 24 = 29

4y+29

Answer:

1374

Step-by-step explanation:

delta math

The length of the side k in the given triangle is 1,373.9 cm.

The law of Cosines, also known as Cosine Rule or Cosine Formula basically relates the length of the triangle to the cosines of one of its angles.

Given that, in ΔKLM, l = 820 cm, m = 560 cm and ∠K=169°, we need to find the length of side k,

Using the cosine law,

k² = l²+m² - lmCos169°

= 820²+560²-(820)(560)cos169°
= 1,373.9

Hence, the length of the side k in the given triangle is 1,373.9 cm.

Learn more about cosine law, click;

https://brainly.com/question/17289163

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Answer:

26x2,

52xπ

Step-by-step explanation:

The perimeter of this semi-circle with a radius of 26 cm will be 81.64 cm.

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

Let 'r' be the radius of the circle. The circumference of the circle will be

C = 2πr units

The radius of the semicircle is given as,

r = 26 cm

Then the circumference of the semicircle is half of the circle. Then we have

C = 1/2 x 2πr

C = πr

At r = 26 cm, then we have

C = 3.14 x 26

C = 81.64 cm

The perimeter of this semi-circle with a radius of 26 cm will be 81.64 cm.

More about the circumference of a circle link is given below.

https://brainly.com/question/27177006

#SPJ5

Answer:

Say you have y=2x. That is direct variation and will always pass through the origin when graphed. When x is multiplied by a number, the y value will also be changed by that number. If you add a y-intercept and change y=2x to, for example, y=2x+2, the x and the y will no longer be related by a constant ratio.

Step-by-step explanation:

Answer:

1 Question= 26

2 Question=41

3 Question= 57

4 Question= 15

5 Question = 20

Step-by-step explanation:

To find the equation of a perpendicular line, you first need to find the negative reciprocal of the slope given. The slope is -1/3, so the slope of the perpendicular line will be 3

Now we just need to find the y intercept using the point (3, 2) and you can plug the coordinates in and then solve for b. Let's see what that looks like.

y=3x+b

2=3*(3)+b

2=9+b

-7=b  So now we know the y-intercept and slope. We just put them together now

y=3x-7

Answer:

-2

Step-by-step explanation:

-4-(-2) = -2

-6-(-4) = -2

Answer:

A

Step-by-step explanation:

Answer:

Step-by-step explanation:

For the first one, I believe you would need to use a rotation matrix; to rotate 90º counterclockwise, the matrices would look like ; you would then multiply those out. A reflection across the x-axis would be changing the sign of f(x) (from negative to positive or positive to negative), a reflection across the y-axis would be changing the sign of x, translation a units to the right would be subtracting a from x, translation b units up would be adding b to x. Rotation of 180º about the origin would be the same format as the first matrix, except it would be cos180 and cos0 on the top and sin180 sin0 on the bottom. Reflection across the y-axis would be changing the sign of x again.

OR

1. We know that, 'Translation shifts the figure in any direction'.

As, the function f(x) is translated 'a' units to the right, the new form of function is f(x-a).

Again, the function is translated 'b' units up, the final form of the function is f(x-a)+b.

2 and 3. We know that, ' Reflection flips the image over a line'.

As the function g(x) is reflected over y-axis, the new form of the function is g(-x).

As the function h(x) is reflected over x-axis, the new form of the function is -h(x).

4 , 5 and 6. We know that, 'Rotation turns the image around a point to a certain degree'.

Let us assume the function to be a point (x,y).

As the function is rotated by 90° counterclockwise about the origin, the new function becomes ( y,-x ) i.e. R_{90}R

90

(x,y) = ( -y,x ).

As the function is rotated by 180° counterclockwise about the origin, the new function becomes ( y,-x ) i.e. R_{180}R

180

(x,y) = ( -x,-y ).

As the function is rotated by 2700° counterclockwise about the origin, the new function becomes ( y,-x ) i.e. R_{270}R

270

(x,

Answer:

B) 4

Step-by-step explanation:

Use the slope formula:

slope [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Let:

[tex](x_1 , y_1) = (1 , -2)\\(x_2 , y_2) = (2 , 2)\\[/tex]

Plug in the corresponding numbers to the corresponding variables:

slope:

[tex]m = \frac{2 - (-2)}{2 - 1} \\m = \frac{2 + 2}{2 - 1}\\m = \frac{4}{1} = 4[/tex]

B) 4 is your answer.

~

Answer:

x < 5

Step-by-step explanation:

[tex]5x - 1 < 24\\5x < 25\\x < 5[/tex]

Answer:

any number under 5

Step-by-step explanation:

5(5) -1 =24

so anything under that would equal fewer than 24

Is this what you're asking?

Answer:

225.24099

Step-by-step explanation:

249.99(0.15) = 37.4985

249.99 - 37.4985 = 212.4915

212.4915(0.06) = 12.74949

212.4915 + 12.74949 = 225.24099