An artist mixes 25 ounce of blue paint with 115 ounce of green paint. Using the same ratio, how many ounces of green paint should she mix with 3 ounces of blue paint?

[tex]6 - 7(x + 1) = - 3(2 - x)[/tex]

[tex]6 - 7x - 7 = - 6 + 3x \\ - 1 - 7x = - 6 + 3x[/tex]

[tex] - 1 + 6 = 7x + 3x \\ 5 = 10x \\ \frac{5}{10} = x \\ \frac{1}{2} = x[/tex]

[tex]6 - 7( \frac{1}{2} ) - 7 = - 6 + 3( \frac{1}{2} ) \\ 6 - \frac{7}{2} - 7 = - 6 + \frac{3}{2} \Longrightarrow \sf{You \: \: can \: \: change \: \: sides \: \: to \: \: make \: \: it \: \: easier} \\ 6 - 7 + 6 = \frac{7}{2} + \frac{3}{2} \\ 5 = \frac{10}{2} \\ 5 = 5 \: \green{ \checkmark}[/tex]

The equation is true for x = 1/2.

[tex] \large \boxed{x = \frac{1}{2} } \: \: \: \: \green{ \checkmark}[/tex]

Answer:

14

Step-by-step explanation:

Answer:

9·x² - 36·x = 4·y² + 24·y + 36 in standard form is;

(x - 2)²/2² - (y + 3)²/3² = 1

Step-by-step explanation:

The standard form of a hyperbola is given as follows;

(x - h)²/a² - (y - k)²/b² = 1 or (y - k)²/b² - (x - h)²/a² = 1

The given equation is presented as follows;

9·x² - 36·x = 4·y² + 24·y + 36

By completing the square, we get;

(3·x - 6)·(3·x - 6) - 36 = (2·y + 6)·(2·y + 6)

(3·x - 6)² - 36 = (2·y + 6)²

(3·x - 6)² - (2·y + 6)² = 36

(3·x - 6)²/36 - (2·y + 6)²/36 = 36/36 = 1

(3·x - 6)²/6² - (2·y + 6)²/6² = 1

3²·(x - 2)²/6² - 2²·(y + 3)²/6² = 1

(x - 2)²/2² - (y + 3)²/3² = 1

The equation of the hyperbola  is (x - 2)²/2² - (y + 3)²/3² = 1.

Answer:

$5

Step-by-step explanation: 15/6 = 2.5 for each bunch. 2.5 x 2 = 5

Answer:

9 Litre of 100% acid, 27 Litre of 20% acid solution

Step-by-step explanation:

We know that 1 = 100% while

0.2 = 20%

We assume that x is volume of 100% solution, while y is volume of 20% solution.

x + 0.2y = (36×40/100)

x+0.2y= 14.4--------eqn(1)

x+y=36-------eqn(2)

x=36-y------eqn(3)

Input eqn(2) into 1 we have

(36-y)+0.2y= 14.4

-y+0.2y=14.4-36

-0.8y= 21.6

y=21.6/0.8

y=27

Hence, 27 Litre of 20% acid is required

From eqn(3) we can find value of x

x = 36-27

9 Litre of 100% acid is required

9 Litre of 100% acid, 27 Litre of 20% acid

Hence, the laboratory technician can combine a batch of 9 Litre of 100% acid, 27 Litre of 20% acid an acid solution that is pure acid with another that is ​20% to get the desired​ concentration

Answer:

360 degrees around a point. the angle opposite 125 is vertically opposite so will be 125. 125 X 2 = 250

360 - 250 = 110. 110/2 = 55 degrees.

the angle opposite X is vertically opposite and is also an alternate angle to the angle of 55 degrees.

X = 55 degrees

Answer:

24 degrees and 72 degrees

Step-by-step explanation:

4 EQUAL parts;

part 1, 2, and part 3 are all included in the bigger angle

part 4 is included in the smaller angle

96 (total) / 4 (parts) = 24 degrees

part 1 + part 2 + part 3 = 72 degrees

part 4 = 24 degrees

Your angle measures are 24 degrees and 72 degrees.

Answer:

Use the given functions to establish and reduce u (4)

x=x2+1=x=1+i√32,1−i√32

w=x=1+i√32,1−i√32

u(4)=4u

Step-by-step explanation:

Answer:

5, probably

Step-by-step explanation:

you are looking for the function w(u(4)). you need to find u(x) first when x=4 so solve for u(4)=-x+2 so u(4)=-4+2=-2. now plug this -2 value into the function w(x) so w(-2)=-2^2+1 so basically =4+1 and I think that is probably 5 maybe the value of w(u(4))=5

Answer:

1/5

Step-by-step explanation:

Hope it works

Answer:

4/20

Step-by-step explanation:

Given function:

Rewrite:

Therefore, the fraction that is equivalent to 20% would be 4/20..

Answer:

The annual profit is $6384, if the baker sells 240cupcakes

Step-by-step explanation:

Annual profit in dollars from selling cupcakes = [tex]p(n)=41n-0.06n^2[/tex]

where n is the number of cupcakes sold .

We need to find the annual profit if the baker sells 240cupcakes.

If baker sells 240 cupcakes, so we have n = 240

Putting value of n in the given equation and finding profit

[tex]p(n)=41n-0.06n^2\\Put\:n=240\\p(240)=41(240)-0.06(240)^2\\p(240)=9840-0.06(57600)\\p(240)=9840-3456\\p(240)=6384[/tex]

So, The annual profit is $6384, if the baker sells 240cupcakes

Answer:

-2 i think

Step-by-step explanation:

Answer:

Quotient: 5/6

Product: 8b.

Sum: 5/6 + 8b

Step-by-step explanation:

While translating the problems into mathematical expression or mathematical expression in English, Kind of Expression can be used. Mostly in the algebraic parts.

Quotient: It represents that one value is divided by the another value. It is also known as the ratio.

i.e: 5/6

Product: It means multiplying either a known value and unknown variables or both unknown variables.

i.e.: 8b.

Sum: It means adding either a known value and unknown variables or both unknown variables.

i.e. : 5/6+8b

Answer:

$8

Step-by-step explanation:

Given

Cost of fare from house to library

=$26

Let the fare to the airport be x

26=x-18

Solve for x

26-18=x

x=$8

Hence the fare is $8

Answer:

x=11 degrees,y=6

Step-by-step explanation:

Here, given ΔRWS ≅ ΔTUV

Two triangle are said to be congruent to each other it they have exactly the same three sides and exactly the same three angles.

So, here RW = UT, WS = UV and SR = VT

⇒ 25 = 3y + 7

or, 3y = 25 - 7 = 18

or, y = 18/3 = 6

⇒ y = 6

In ΔTUV

By Angle Sum Property:

∠ TUV + ∠ UVT + ∠ UTV = 180°

or, 90° + 29°+ ∠ UTV = 180°

⇒∠ UTV = 180° - 119 = 61°

Now, by congruence rule: ∠ WRS = ∠ UTV

⇒ (8x - 27)° = 61°

or, 8x = 27° + 61° = 88°

or, x = 88/8 = 11°

⇒ x = 11°

Answer:

the answer is c

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 32² = 48²

x² + 1024 = 2304 ( subtract 1024 from both sides )

x² = 1280 ( take the square root of both sides )

x = [tex]\sqrt{1280}[/tex]

  = [tex]\sqrt{256(5)}[/tex]

   = [tex]\sqrt{256}[/tex] × [tex]\sqrt{5}[/tex]

   = 16[tex]\sqrt{5}[/tex] → C

Answer:

they skided 242 feet

Step-by-step explanation:

Answer:

20x20)(20)20000)$yes

Answer: 30 feet

Step-by-step explanation: because 3 times 10 is 30 feet

Answer:

i'm not sure what you need help with.

Step-by-step explanation:

Answer: 19.4

Step-by-step explanation:

Given

Profit is given in terms of the selling price

[tex]y=-5x^2+194x-900[/tex]

to get the maximum price, differentiate y w.r.t x

[tex]\frac{\mathrm{d} y}{\mathrm{d} x}=-5\times 2x+194[/tex]

Put  [tex]\frac{\mathrm{d} y}{\mathrm{d} x}=0[/tex] to get maximum value

[tex]10x=194\\x=19.4[/tex]

Thus, the company must sell it at 19.4

Answer:

D

Step-by-step explanation:

-12 + 5 ≤ 4

-7 ≤ 4

this inequality is true

The answer to the question is D

Answer:

just buy 2 slurpies and 20 candies

Step-by-step explanation:

its not rocket science

Answer:

I think $800

Step-by-step

round 24 down to 20

and multiply it by 4

I got 800

24 ->20

20x4=800

Answer:

5ft= 60in

3/4 inch = 0.75 inch

=> 60/0.75 = 80 movies

Step-by-step explanation:

Answer:

ygjjjyc

Step-by-step explanation:

trzerxcgvjyu

Answer:

Hope this helps!

Step-by-step explanation:

12% of 75 would be 9

9

Step-by-step explanation:

12/ 100 × 75

3/ 25 × 75

75/ 25 = 3

3 × 3 = 9

hope it helps!

Answer:

Step-by-step explanation:

Number    Price per     Total            Commission                    Total cost

of Shares  Share                             (At 6% of total)        

100           $16.25          $1625         [tex]1625\times \frac{6}{100}=97.5[/tex]      1625+97.5 = $1722.5      

100           $11.31            $1131           [tex]1131\times \frac{6}{100}=67.86[/tex]    1131+67.86=$1198.86

40             $9.15             $366          [tex]366\times \frac{6}{100}=21.96[/tex]      366+21.96=$387.96

100           $15.27           $1527        [tex]1527\times \frac{6}{100}=91.62[/tex]    1527+91.62=$1618.62

100           $13.22           $1322        [tex]1322\times \frac{6}{100}=79.32[/tex]   1322+79.32=$1401.32

Answer:

x = 80

Step-by-step explanation:

All angles in a triangle add up to 180 degrees.

First, find the angle J:

60+40 = 100, J = 80 because 100+80= 180 degrees.

Now, the two angles on either side of J should also equal 180 degrees. We know that the inner angle is equal to 80 degrees. Thus, the outside angle must equal 100.

x + 20 = 100

x = 80 degrees.

Answer:

[tex]\huge\boxed{\text{1. }\$ 15}[/tex]

[tex]\huge\boxed{\text{2. } \$ 1200}}[/tex]

Step-by-step explanation:

By examining the different parts of this equation and what they mean in the context of this problem, we can use the equation to find out different pieces of information about the scenario.

An equation in the form [tex]y = mx+b[/tex] is set up in the way that m = slope, and b = y-intercept.

When starting on a graph, you start at x = 0. Plugging 0 into the equation as x leaves y as 1200. This shows that the base price to make a book is

$1200.

Also, the equation shows that the slope of the line is 15. If we were to put this on to a graph, then every time x (books) increases by 1, y (cost) would increase by 15. Therefore, books cost $15 per book to publish. This makes it the total cost for every book published.

Hope this helped!