Sam and Bethan share £54 in the ratio 5:4
Work out how much each person gets.

Answer:

k= 2

y = 32

Step-by-step explanation:

y is inversely proportional to x

y = 16, x = 8

find y when x = 16

k= 2 & y = 32

Step-by-step explanation:

Question 9:

Hypotenuse = 7

Leg = Hypotenuse / √2 = 7/√2 = 7√2 / 2.

Therefore x = y = 7√2 / 2.

Question 10:

Leg = 10

Since x is also a Leg, x = 10.

Hypotenuse = Leg * √2 = 10√2. => y = 10√2.

Question 11:

Leg = 7

Since x is also a Leg, x = 7.

Hypotenuse = Leg * √2 = 7√2, => y = 7√2.

$3.60 is the sales tax

After tax the price is $63.60

Answer

$63.60

Step-by-step explanation:

6% of 60 = 3.60

3.60+ 60= 63.60

Answer:

AB = BC = 4[tex]\sqrt{2}[/tex]

Step-by-step explanation:

This is a 45-45-90 triangle (right isosceles). This means that the side ratio is

1:1:[tex]\sqrt{2}[/tex], where AC is sqrt 2, and AB and BC are 1. Now, we need to plug this into our ratio. If sqrt 2 is 8, then 1 is x.

8/[tex]\sqrt{2}[/tex] = x/1 = x

x = 8/[tex]\sqrt{2}[/tex] = 4[tex]\sqrt{2}[/tex] (rationalized)

AB and BC are both 4 * sqrt 2

The answer is AB = BC = 4√2

Answer:

a

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

3 bouquets of 3$ is 3*3 = 3^2

4 bouquets of 2$ = 2 * 4

Answer:

Step-by-step explanation:

according to the question

the equation is

130+2x=180

2x=180-130

2x=50

x=25

Answer:

0

Step-by-step explanation:

The y-intercept of y = -3x is zero.

Answer:

0

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define

y = -3x

Step 2: Break Function

Identify Parts

Slope m = -3

y-intercept b = 0

*We assume that if the variable isn't there, it is 0 or being multiplied by 0.

Answer:

The three consecutive square numbers that added together give 149 are 6, 7 and 8.

Step-by-step explanation:

To determine which are the three square consecutive numbers that added together add up to 149, the following calculation must be performed:

1 x 1 = 1

2 x 2 = 4

3 x 3 = 9

4 x 4 = 16

5 x 5 = 25

6 x 6 = 36

7 x 7 = 49

8 x 8 = 64

9 x 9 = 81

10 x 10 = 100

Thus, we can see that 36 + 49 + 64 gives the result 149. Therefore, the three consecutive square numbers that added together give 149 are 6, 7 and 8.

9514 1404 393

Answer:

  23)  x = ±3i, ±√2

  26)  x = 4/3, (-2/3)(1 ± i√3)

Step-by-step explanation:

23) Put in standard form to make factoring easier.

  x^4 +7x^2 -18 = 0

  (x^2 +9)(x^2 -2) = 0 . . . . factors in integers

Using the factoring of the difference of squares, you can continue to get linear factors in complex and irrational numbers:

  (x -3i)(x +3i)(x -√2)(x +√2) = 0

  x = ±3i, ±√2

___

26) This will be the difference of cubes after you remove the common factor.

  81x^3 -192 = 0

  3(27x^3 -64) = 0

  (3x -4)(9x^2 +12x +16) = 0 . . . . . factor the difference of cubes

The complex roots of the quadratic can be found using the quadratic formula.

  x = (-12 ±√(12^2 -4(9)(16)))/(2(9)) = (-12 ±√-432)/18 = -2/3 ± √(-4/3)

Then the three solutions to the equation are ...

  x = 4/3, (-2/3)(1 ± i√3)

Answer:

Can you put a number line in the picture?

Step-by-step explanation:

That would really help

Answer:

I think its C but without the number line a cant tell.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The 1220 feet is positive because the plane is above her.

The 14 feet is negative because the tree is below her.

Because you're comparing distances, you need the absolute value of both distances.

The absolute value of 1220 is 1220 and the absolute value of -14 is 14, so the absolute value of 1220 is greater than the absolute value of -14. The answer is D.

Answer:

y = -3x + 30.

Step-by-step explanation:

The slope of line = (9- (-3)) / (7 - 11)

= 12/-4

= -3.

We use the point-slope form of a straight line:

y - y1 = m(x - x1)        where m = slope = -3 and (x1, y1) = (7, 9)

y - 9 = -3(x - 7)

y - 9 = -3x + 21

y = -3x + 21 + 9

y = -3x + 30.

You haven't supplied a list of possible answers so the correct answer might not  be in the above form but will be equivalent to it.

Answer:

line mo

Step-by-step explanation:

Because the triangle are congrument

RST and MNO are the triangle

RT is a line in the RST triqangle

it is equal to the MO line in MNO

Answer:

yes

Step-by-step explanation:

By ASA similarity;

<b=<a

<c=<e

DE=DC

Answer:help me

Step-by-step explanation:

Answer:

x3

Step-by-step explanation:

Step-by-step explanation:

The shaded area shows the region where it is enclosed in sample space S but does not include the subset B.

Hence it is the complement of B. (A)

If event B is a subset of the sample space S, hence the area represented by the shaded part is complement of B

The set is a collection of members and things.

According to the venn diagram given, the whole set including the set B is the universal set.

The part not shaded is not part of the universal set, hence, we name them the complement of a set.

If event B is a subset of the sample space S, hence the area represented by the shaded part is complement of B

Learn more on set here: https://brainly.com/question/2166579

#SPJ2

Answer:

11

Step-by-step explanation:

hope that helps out :)

Step-by-step explanation:

by collecting like terms =

7y - 12y = -38 - 17

-5y = - 55

by dividing both sides by -5

-5y/-5 = -55/-5

y = 11

Answer:

D

Step-by-step explanation:

Answer:

The maximum height the rocket reaches is 16.

Step-by-step explanation:

You know that a model rocket is launched in the air and the quadratic function is modeled by the equation y = -16*x² + 32*x where x is measuring time and y is the height of the model rocket.

A quadratic function or function of the second degree is a polynomial function defined by:

y= a*x² + b*x + c

A quadratic function has a maximum or a minimum and the vertex formula is used to get the highest or lowest value of the function. When a> 0, the vertex of the parabola is at the bottom of it, being a minimum (that is, the parabola opens "upward"), and when a <0 the vertex is at the top , being a maximum (that is, the parable opens "downward").

The value of the vertex on the x-axis can be calculated with the expression [tex]x=\frac{-b}{2*a}[/tex]

The value of the vertex on the y axis must be obtained by substituting the value of the vertex on the x axis in the function y= a*x² + b*x + c

In this case, a= -16, b=32 and c=0. Since a<0 the vertex will indicate the maximum of the function.

The value of the vertex on the x-axis is [tex]x=\frac{-32}{2*(-16)}=1[/tex]

The value of the vertex on the y axis  is:

y = -16*1² + 32*1

Solving:

y= -16*1 +32

y= -16 +32

y=16

The maximum height the rocket reaches is 16.

Answer:

-(135/31), 60/31

Step-by-step explanation:

y=60/31

x=-(135/31)

Answer:

79

Step-by-step explanation:

Supplementary are angles that will add up to 180. So to find the missing angle we do 180 - 101 and get 79.

hope this helps (:

Answer:

The zeroes are -1 and 13

Positive value: [tex]x = 13[/tex]

Step-by-step explanation:

Given

[tex]2x^2 - 24x = 26[/tex]

Solving (a): The zeros

[tex]2x^2 - 24x = 26[/tex]

Subtract 26 from both sides

[tex]2x^2 - 24x - 26= 26-26[/tex]

[tex]2x^2 - 24x - 26= 0[/tex]

Divide through by 2

[tex]\frac{1}{2}(2x^2 - 24x - 26) = \frac{1}{2} * 0[/tex]

[tex]x^2 - 12x - 13 = 0[/tex]

Expand

[tex]x^2 - 13x + x - 13 = 0[/tex]

Factorize:

[tex]x(x-13)+1(x-13)=0[/tex]

[tex](x+1)(x-13)=0[/tex]

Split:

[tex]x +1 =0\ or\ x-13=0[/tex]

[tex]x =-1\ or\ x=13[/tex]

Hence, the zeroes are -1 and 13

Solving (b): The positive value of x

In (a) above:

[tex]x =-1\ or\ x=13[/tex]

The positive value is:

[tex]x = 13[/tex]

Answer:

16.25% was spent on food

Step-by-step explanation:

Step one

given data

A family spends $520 every month on food

The family's income is $3200 Monthly

Required

We want to find the percentage of the income spent on food only

Step two

percentage spent on food= amount spent on food/income*100

percentage spent on food= 520/3200*100

percentage spent on food= 0.1625*100

percentage spent on food= 16.25%

=16.25%

Answer:

radio relationships?what do u mean?

Step-by-step explanation:

I think it will be 1.7

i am not sure