The ratio of forks to spoons in the cafeteria is 15:6. If there are 45 forks, how many utensils are there altogether?

Step-by-step explanation:

2y - 4x + 6 = 0

2y = 4x - 6

y = 4x/2 - 6/2

y = 2x - 3

Answer:

[tex]y = 2x - 3[/tex]

Step-by-step explanation:

Simply make the y as the subject

[tex]2y - 4x + 6 = 0 \\ 2y - 4x = - 6 \\ 2y = - 6 + 4x \\ \frac{2y}{2} = \frac{ - 6 + 4x}{2} \\ y = - 3 + 2x \\ y = 2x - 3[/tex]

So,

[tex]y = mx + b \\ y = 2x - 3[/tex]

Hope this helps you.

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

30 is the length of the hypotenuse

24 is one of the bases

a^2+b^2 = c^2

where c is the hypotenuse (longest side)

24^2 + y^2 = 30^2

576 +y^2 = 900

y^2 = 324

y= √324 = 18

y =  18

Answer:

x=-13

Step-by-step explanation:

the line is on the x axis and cant change its x axis of -13

Answer:

The answer is definitelly B.(Area of 1) + (Area of 2) = (Area of 3)

Step-by-step explanation:

A because they are all surrounding the triangle

Answer:4(c+9)

Step-by-step explanation:

4+36

4(+9)

Solution

4(+9)

A magic square is a square containing a number of integers arranged in such a way that the sum of the numbers vertically, horizontally and diagonally is always the same number.

Hope it helps.

Do comment if you have any query.

A magic square is a large square that is divided into smaller squares. In a magic square, the smaller squares that make up the diagonal, horizontal and vertical magic square add up to the same value.

Popular magic squares include:

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Answer:

Step-by-step explanation:

(-1,-4)→(4,1)

Answer:

Step-by-step explanation:

HIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

Answer:

Slope Intercept form: y = mx + b

Step-by-step explanation:

mx: the slope

b: y- intercept

To find the slope, use this formula:

y₂ - y₁ / x₂ - x₁

Add in the numbers

1 - (-5) / 0 - 2

-6/2 (or -3) = slope

Use point-slope form to find the Y- intercept

y - y₁ = m (x - x₁)

y - (-5) = -3 (x - 2)

y + 5 = -3x + 6

Subtract 5 from both sides

y = -3x + 1 ← Slope intercept form

Graph the y- intercept at 1, and go down 3 and to the right 1. Your two coordinates will be (0 , 1) and (1, -2) .

Answer:

m=1/0 (undefined)

equation=y2-y1/x2-x1=y-y1/x-x1

since M is undefined and M=y2-y1/x2-x1

then the equation=y-y1/x-x1=1/0

y-3/x--1=1/0

cross multiplying

0 (y-3)=1 (x+1)

=x+1

Answer:

The proportion which represents the 65% of 90 is:

Step-by-step explanation:

Given information:

We need to find the proportion that can be used to find

65% of 90

Let us take :

% of

So,

Hence , the proportion which represents the 65% of 90 is

Answer:

The proportion [tex]\frac{65}{100} = \frac{x}{90}[/tex]

Step-by-step explanation:

[tex]\frac{65}{100} = \frac{x}{90}[/tex]

(65)(90) = 100x

5850/100 = x = 58.5

58.5 = 65% of 90

Alternatively, you can use the more direct approach:

[tex]\frac{65}{100} (90)[/tex]

= [tex]\frac{65 * 9}{10}[/tex] = 585/10 = 58.5

The law of sines can't only be applied to right triangles. Therefore, it's B. False.

The Law of Sines says that in any given triangle, the ratio of any side length to the sine of its opposite angle is the same for all the three sides of the triangle.

The law of sines is used to solve any triangle, when we know two angles and one side or two angles and one included side. So, it can be used on non-right triangle and right triangle as the case may be.

The sine law states that the ratio of a triangle's side length to the sine of the opposite angle is the same for all three sides. When we are given a) two angles and one side, or b) two sides and a non-included angle, we use the sine rule.

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Answer:

x is being multiplied by 7p so to find x you need to have it alone on one side of the problem, so you could divide both sides by 7p, making it look like 2n+3pm/7p=x (simplify if needed)

Step-by-step explanation:

The logarithmic property chosen here is:

[tex]log_{a}[/tex] m - [tex]log_{a}[/tex] n = [tex]log_{a}[/tex] [tex]\frac{m}{n}[/tex], and its validity is proven below:

The logarithmic properties are up to six, but one of it that is applicable here is:

[tex]log_{a}[/tex] m - [tex]log_{a}[/tex] n = [tex]log_{a}[/tex] [tex]\frac{m}{n}[/tex]

In the above expression, both the numerator and denominator have the same base number, but different powers. So in this case, dividing a number of power m by the same number but of power n would given an answer that is the same as the number to the power of the difference between m and n.

For example: Solve;

a. [tex]log_{10}[/tex] 6 - [tex]log_{10}[/tex] 3

b. [tex]log_{10}[/tex] 8 - [tex]log_{10}[/tex] 5

c. [tex]log_{b}[/tex] 6 - [tex]log_{b}[/tex] 2

Solutions:

a. [tex]log_{10}[/tex] 6 - [tex]log_{10}[/tex] 3 = [tex]log_{10}[/tex] [tex]\frac{6}{2}[/tex]

        = [tex]log_{10}[/tex] 2

        = 0.3010

b. [tex]log_{10}[/tex] 8 - [tex]log_{10}[/tex] 5 = [tex]log_{10}[/tex] [tex]\frac{8}{5}[/tex]

      = [tex]log_{10}[/tex] 1.6

       = 0.2041

c. [tex]log_{b}[/tex] 6 - [tex]log_{b}[/tex] 2 = [tex]log_{b}[/tex] [tex]\frac{6}{2}[/tex]

        = [tex]log_{b}[/tex] 3

The stated examples defend the validity of the specific logarithmic property.

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Step-by-step explanation:

1) 3 – 36i = 9a + 4bi

3 = 9a => a = 3/9 = ⅓

-36 = 4b => b = -36/4 = -9

2) a – 15i = -7 – (2b-3)i

a = -7

-15 = -(2b-3)

2b-3 = 15

2b = 18

b = 18/2= 9

Answer:

Step-by-step explanation:

Use distributive property: a*(b +c) =a*b + a*c

-3( 6 - 1.5n) = (-3)*6 - (-3)*1.5n

                  = -18 + 4.5n

Answer:

-18 + 4.5n

Step-by-step explanation:

-3(6 - 1.5n) = -3(6) -3(-1.5n)                  Distributive

                  = -18 + 4.5n                       Multiplication. Remember (-) (-) = +

Answer:

-3

Have a nice day

Answer:

7/12

Step-by-step explanation:

change in y / change in x

Answer:

Step-by-step explanation:

Area = 72 m^2

L = 12m

Formula

w = Area / L

Perimeter = 2L + 2W

Solution

72m^2 = 12 W      Divide both sides by 12

72/12 = 12W / 12

W = 6 m

Perimeter = 2L + 2W

Perimeter = 2*12 + 2*6

Perimeter = 24 + 12

Perimeter = 36 m

Answer:

I think you're looking at the wrong place my guy...

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

I did this test is 20

60 percent of 20 is 12 dollars

The original price of a pair of jeans would be; 30 dollar.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b% Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Given that a pair of jeans is only $12 after a 60% discount.

The original price in percentage terms = 100%

After the first discount, the price is : 100- 60% = 40%

The equation can be used to represent the price;

40% x original price = $12

0.40 x p = 12

where p = original price

Divide both sides of the equation by 0.40;

p= $30

Hence, The original price of a pair of jeans would be; 30 dollar.

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Answer:

Step-by-step explanation:

Equations for each

Johnny:

Darnel:

In order to get J(x) = D(x) we need to make right sides equal and solve for x:

Let's assume –

[tex]\qquad[/tex] According to the question :-

[tex]\qquad \pmb{\sf\longrightarrow 4 \times (28−x)+2 \times x=90}[/tex]

[tex]\qquad \pmb{\sf\longrightarrow 112−4x+2x=90}[/tex]

[tex]\qquad \pmb{\sf\longrightarrow 112−2x=90}[/tex]

[tex]\qquad \pmb{\sf\longrightarrow −2x=90−112}[/tex]

[tex]\qquad \pmb{\sf\longrightarrow −2x=−22}[/tex]

[tex]\qquad \pmb{\sf\longrightarrow 2 x=22}[/tex]

[tex]\qquad \pmb{\sf\longrightarrow x= \cancel{\dfrac{22}{2}}}[/tex]

[tex]\qquad \longrightarrow {\pink{\underline{\underline{\pmb{\sf{ x= 11}}}}}}[/tex]

Therefore –

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Answer: 11

Step-by-step explanation:

This is a problem of solving word problems using systems of equations.

Let's denote 2-seat tables by x and 4-seat tables by y. Therefore, their sum will be the total number of tables, which is 28. So, x + y = 28.

Now, let's concentrate on the number of customers. It says that 'when all tables are full, there will be 90 customers in the restaurant'. Therefore if we seat 2 people on each 2-seat table(x), their total number will be 2x and if we seat 4 people on each 4-seat number(y), their total number will be 4y. Hence, 2x + 3y = 90.

Now, we have a system with two equations:

[tex]\left \{ {{x + y = 28} \atop {2x + 4y = 90}} \right.[/tex]

Multiply the first line by -4.

[tex]\left \{ {{-4x -4y = -112} \atop {2x + 4y = 90}} \right.[/tex]

Now, by adding up these two equations, we get the following:

-2x = -22

x = 11

This means that the restaurant has 11 two-seat tables.

Answer: 4

Step-by-step explanation:

Answer:

Y=#x+Y

Step-by-step explanation:

I think this formula would be best to use as one of the numbers would keep on changing while the other stays the same.

Enjoy, Hope i get what i promised :D

Answer:

Y=#x+Y

Step-by-step explanation:

Answer:

Step-by-step explanation:

16, 48 , 144 ...... is a geometric sequence.

first term = a = 16

common ratio = r = 2 term ÷ first term = 48 ÷ 16 = 3

nth term = [tex]ar^{n-1}[/tex]

[tex]6th \ term = 16 * (3)^{6-1}\\\\\\= 16 * 3^{5}\\\\= 16 * 243\\\\= 3888[/tex]

Answer:

C

Step-by-step explanation:

To find which of the given choices are solutions for the system of equations, we need to:

-substitute x, and y with the given coordinates and

-check if they are solutions for both equations.

7x+y= 6

x+ 2y = -1

A. (x = -1, y = 0) ❌

7(-1)+0= 6; -7 =6 FALSE

-1+ 2*0 = -1; -1= -1 TRUE

B. (x = 1, y = 0)❌

7*1+ 0= 6; 7= 6 FALSE

1+ 2*0 = -1; 1 =-1 FALSE

C. (x =1, y= -1)✅

7*1 -1= 6; 6=6 TRUE

1+ 2(-1) = -1; -1=-1 TRUE

D. None of these choices are correct ❌

because one choice is correct