. Strengthening Vinegar: A food chemist has 200 gallons of
vinegar that is 4% acetic acid. How much acetic acid must be
added to get the acetic acid up to 5%?

Answer:

-7

Step-by-step explanation:

The line (y-1)=(2/3)(x+1) contains point (a,-3)

=> (-3-1) = (⅔)(a+1)

-4 = (⅔)(a+1(

(a+1)= -4 ÷ ⅔

a + 1 = -4 × 3/2

a+ 1 = -6

a = -6-1

a = -7

The value of 'a' will be;

⇒ a = - 7.

To find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The equation of line is,

⇒ (y - 1) = (2/3) (x + 1)

And, The point on the line = (a, - 3)

Now,

Since, The point on the line = (a, - 3)

Hence, It satisfy the equation of line.

Substitute x = a and y = - 3, we get;

⇒ (y - 1) = (2/3) (x + 1)

⇒ (- 3 - 1) = (2/3) (a + 1)

⇒ - 4 × 3 = 2a + 2

⇒ - 12 - 2 = 2a

⇒ 2a = - 14

⇒ a = - 7

Thus, The value of a = - 7

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Answer:

Option 1 is the correct equation.

Step-by-step explanation:

x = price of the student ticket.

One half price of x + $8 = adult ticket price ($15)

Answer:

The correct answer is A

Because taking the student ticket to be x

one half of x + 8 =15

Answer:

Step-by-step explanation:

Answer:

11. [tex]x^{5}[/tex]

12. 5*[tex]x^{2}[/tex]

13. x+21

14. 2x-8

Step-by-step explanation:

Patterns are set of rules that guide the creation of a dataset. The observation from the first three designs are as follows:

The pattern

The first three design show that, as the design number increases (i.e. 1, 2, 3), the number of tiles used also increases (i.e. 7, 12, 19)

The expressions for the number of tiles

The design number and the number of tiles is represented as follows

[tex]1 \to 7[/tex]

[tex]2 \to 12[/tex]

[tex]3 \to 19[/tex]

From the designs, we observe that some tiles are at the middle, while other tiles are at the sides.

Design 1 has 1 tile at the center and 6 tiles at either sides.

So, we have:

[tex]1 \to 1 + 6[/tex]

[tex]2 \to 4 + 8[/tex]

[tex]3 \to 9 + 10[/tex]

Expand

[tex]1 \to 1^2 + 6 \to 1^2 + 2 \times 3 \to 1^2 + 2 \times (1 + 2)[/tex]

[tex]2 \to 2^2 + 8 \to 2^2 + 2 \times 4 \to 2^2 + 2 \times (2 + 2)[/tex]

[tex]3 \to 3^2 + 10 \to 3^2 + 2 \times 5 \to 3^2 + 2 \times (3 + 2)[/tex]

Notice the pattern,

The number of tiles in design n will be:

[tex]Tiles = n^2 + 2 \times (n + 2)[/tex]

Open bracket

[tex]Tiles = n^2 + 2n + 4[/tex]

Hence, the expressions for number of tiles in design n are:

[tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex]

Technology to prove that both expressions are equivalent

To prove that [tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex] are equivalent using technology, the graphs of [tex]n^2 + 2(n + 2)[/tex] and [tex]n^2 + 2n + 4[/tex] can be plotted and then compared

The table and graph for the first 6 designs

The table entry for the first 6 designs is calculated as follows:

[tex]n = 1\ \ \ \ \ Tiles = 1^2 + 2 \times 1 + 4 = 7[/tex]        

[tex]n = 2\ \ \ \ \ Tiles = 2^2 + 2 \times 2 + 4 = 12[/tex]        

[tex]n = 3\ \ \ \ \ Tiles = 3^2 + 2 \times 3 + 4 = 19[/tex]        

[tex]n = 4\ \ \ \ \ Tiles = 4^2 + 2 \times 4 + 4 = 28[/tex]        

[tex]n = 5\ \ \ \ \ Tiles = 5^2 + 2 \times 5 + 4 = 39[/tex]        

[tex]n = 6\ \ \ \ \ Tiles = 6^2 + 2 \times 6 + 4 = 52[/tex]        

So, we have:

[tex]\begin{array}{cc}Design & {Tiles} & {1} & {7} & {2} & {12} & 3 & {19} & {4} & {28} & {5} & {39}& {6} & {52} \ \end{array}[/tex]

See attachment for the graph of the above table

All the points on the curve make sense in this scenario because all values are positive.

The pattern type

We have:

[tex]Tiles = n^2 + 2n + 4[/tex]

When an equation has a degree of 2, the equation is quadratic.

Hence, the pattern is quadratic.

The largest design that an empty sign of 10ft by 12ft can contain.

From the first three designs:

The number of tiles on a complete row and column are always the same.

Design 1 has 3 tiles in its complete row and column

Design 2 has 4 tiles in its complete row and column

Design 3 has 5 tiles in its complete row and column

The relationship between the design number (d) and the number of complete tiles (t) is:

[tex]d = t - 2[/tex]

For the 10ft by 12ft empty sign

[tex]t = 10[/tex] because [tex]10 < 12[/tex]

So, we have:

[tex]d = t - 2[/tex]

[tex]d = 10 - 2[/tex]

[tex]d = 8[/tex]

Hence, the largest design number is design 8

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Answer:

x > 2

Step-by-step explanation:

Distribute and cross-simplify 1/2 with parenthesis

4x + x + 2 > 12

Solve left side

5x + 2 > 12

Subtract 2 from both sides

5x > 10

Divide both sides by 5

x > 2

Answer:

1st box is "a 90°clockwise rotation about the origin

2nd box is "a 180° rotation about the origin

3rd box is "a 90° counterclockwise rotation about the origin

5^4 /5

Use the exponent rule x^a/x^b = x^a-b

5^4/5 = 5^4-1 = 5^3

Answer as a positive exponent is 5^3

Step-by-step explanation:

Answer-

b) 1

Answer:

x = -11

Step-by-step explanation:

To get to 49 by squaring, you need to square 7. Since x can only be negative, you need to get to -7.

-11 + 4 = -7

(-7)^2 = 49

Answer:

x = -11

Step-by-step explanation:

To get to 49 by squaring, you need to square 7. Since x can only be negative, you need to get to -7.

Answer: Yes, the set of real numbers is closed under addition.

Explanation:

Let x and y be two real numbers. Their sum x+y is some other real number. This is what it means when we say the set of real numbers is closed under addition. Taking any two numbers and adding them will get us some other real number.

There is no way to have x+y be nonreal while x,y are both real.

Answer:

7

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Ok, so we know 42 is the number of points added up, and we know that she threw 6 darts all scoring the same. Now, all we have to do is figure out what number(for example x) multiplied by 6 equals 42. Or in the form of an equation:

6x = 42

Now, to finish the equation, all we have to do is divide:

6x/6 = 42/6

42/6 = 7

x = 7

Answer:

12 miles in a day.

Step-by-step explanation:

Variable x = number of miles

Company A: 120 + 0.20x

Company B: 60 + 0.40x

Set up an equation:

120 + 0.20x = 60 + 0.40x

60 + 0.20x = 0.40x

60 = 0.20x

12 = x

Answer:

1/10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

x is the favorite number

x÷[tex]\frac{1}{x}[/tex] = 10x (flip the fraction and multiply)

[tex]x^{2}[/tex]=10x (divide both sides by x)

x=10

Answer:

the value of X is 3 and y is 6 .

Answer:

I think (x+4) (x+4) is right answer.

Step-by-step explanation:

here,

x2+8x+16

=x2+(4+4)x+ 16

=x2+4x+4x+16

=x(x+4)+4(x+4)

=(x+4)(x+4) Ans

Answer:

2x + 12

Step-by-step explanation:

6x + 36 / 3 =

(6x)/3 + (36)/3 = 2x + 12

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

Step-by-step explanation:

The probabilities for each point:

Required probability:

Correct choice is D

Answer:

B

Step-by-step explanation:

t=4x+c

Since we are looking for x,

t-c=4x

Divide through by the coefficient of x which is 4

4x/4=t-c/4

Therefore, x=t-c/4

Answer:

X should equal 12.

Step-by-step explanation:

I say this because we know TED= 30° bc 50°-20° = 30

then u have to think about what × 2 + 6 equals 30

sure enough 12 × 2 = 24 and 24 + 6 = 30

that's why I say X equals 12

Answer:

600

Step-by-step explanation:

since 1m=1000mm

Answer:

your answer is F

I hope it's helps you

Answer:

Step-by-step explanation:

6x + ( 14x - 5 ) + ( 17 - 3x )

= 17x + 12

- ( 2 - x ) -3 ( 6 + 8x ) -12,

= -23x - 32

( 4x - 9 ) + 8 ( 2x + 3 ) -7x

= 13x +15

hope this helps some