Make x the subject:

y = 6x-7 / 3x-8

Answer:

C

Step-by-step explanation:

The total number of bowls that the assistant help prepare is 192.

"A theorem based on the topic of proportions permits a faster way to carry out the calculations and cut down the count of expansions required. It is helpful in situations involving equations with fractions or rational functions."

Given ,

The chef can make 3 pots of soups.

And the assistant use = 1/16 cup on 1 cup of soup

Total number of serving in 1 cup is 16 soups

So, In 12 cups, total number of soup that can be prepared is 16*12 = 192.

Hence, the total number of bowl of soup can the assistant help prepare are 192.

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Answer:

51.984

Step-by-step explanation:

45.6*1.14

Answer:

around 7.00 ft

Step-by-step explanation:

tan(35 degrees)=x/10

x/10=tan(35 degrees)

x=10*tan(35 degrees)

x=7.0020753821

x= around 7.00 ft

Answer:

1085

Step-by-step explanation:

100 - 69 =31%

3500 /100 =35

35 x 31 = 1085

Answer: you would pay 1085

Answer:

Given that the graph is not provided, I will answer the question in general terms.  

To know if a relationship is or is not a function you have to check if for every value of the dependent variable there is associated only one value of the dependent variable.

The domain of a function is composed of all the possible values that variable x (the independent variable) can take.

The range of a function is  composed of all the possible values that variable y (the dependent variable) can take. That is, all the values that f(x) can assume (see picture attached).

there is no real solutions.

Answer:

The area of rectangle A is length x breadth

= 3x5

= 15 units^2

The area of square B is side x side

= 3x3

= 9 units^2

Therefore,

The area of the rectangle is not double of the area of the square because 9x2 is not equal to 15. Steven isn't correct.

Answer:

a) Steven is incorrect.

b) Steven is incorrect, because he claims that, in other words, 15 units squared = 18 units squared. 18 > 15, so the statement that 15 = 18 is false. 15 does not equal 18.

Step-by-step explanation: Steven claims that the area of rectangle A is double the area of square B. The area of rectangle A is 15 units squared, because you get a product of 15 when you multiply the side lengths 5 and 3. The area of square B is 9 units squared, because you get a product of 9 when you multiply the side lengths 3 and 3. In other words, Steven is claiming that the area of rectangle A is not 15 units squared, but 18 units squared (this is double the area of square B, as 18 is the product of 9 and 2), and that statement is false, because we know that 18 > 15. Therefore, 18 cannot equal 15; the figure that is made from the value of double the area of square B (18 units squared) is larger than rectangle A (15 units squared) - this reinforces the fact that 18 > 15, and hence cannot be equal to 15.

Answer: C

Step-by-step explanation:

You can write each term into a fraction.

[tex]\sqrt[5]{x^4}[/tex] becomes [tex]x^4^/^5[/tex]

When you multiply 2 terms with the same base, you add the exponents.

[tex]x^4^/^5*x^4^/^5=x^4^/^5^+^4^/^5=x^8^/^5[/tex]

[tex]x^8^/^5[/tex] is also the same as [tex]x\sqrt[5]{x^3}[/tex]

You get this because [tex]\sqrt[5]{x^8} =\sqrt[5]{x*x*x*x*x*x*x*x}[/tex]. When you pull out 5 os x, you are left with x³ on the inside.

Answer:

The probability that a coin flip is a head or a tail is 0.5. The probability that a coin flip is either a head or a tail is 1. The probability that a three-coin-flip is two heads and a head or a tail is 0.25.

Step-by-step explanation:

Answer:

a)The constant of proportionality is 6.

b)The equation for this relationship is y=6x.

Step-by-step explanation:

a) 6/1=6

b)if apples is "x" and slices is "y," substitute y for 6 and x for 1

so 6=6(1) which is y=6x

The required constant of proportionality is 6 and the equation for this relationship is y=6x.

A table of data is given which describe the relationship between number of apples and number of slices. Blank space in statement to be filled.

The equation is a function of the relation between two or more values contains equal sign.

Here, from table the equation can be calculated as
Number of apples(x) is directly proportional to the number of slices(y). i.e.
y ∝ x
Now,
y=kx  ----(1)  (where k is proportionality constant)
for 1 apple the number of slices is 6 so,
6 = k*1
k = 6
Put k is equal to 6 in the equation (1).
y = 6x.

Thus, the required constant of proportionality is 6 and the equation for this relationship is y=6x.

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Answer:

B. Figure B

Step-by-step explanation:

We have the phrase "If it is not warm, then it is not hot".

Chronologically and logically, it has to not be warm in order to not be hot. "Not warm" will have to encompass "not hot". Therefore, choice B is correct as the diagram shows "not warm" encompassing "not hot".

Answer:

Figure A

Step-by-step explanation:

Ap*x

Answer:

B. $185,600

Step-by-step explanation:

80/20 mortgage means pay 20% down payment and 80% finance amount of home value.

Home value = $232,000

Now, we need to find finance amount from this hone value of $232,000

Let's calculate the 80% of $232,000 as finance amount;

Finance amount = 80% of 232000

Finance amount  = 0.80 x 232000

Finance amount = 185,600

Answer:

Step-by-step explanation:

Let the number of children = c

The number of adults = a

Total people = 528

c + a = 528   ------------------------(I)

Total price  = $ 985

1.25c + 2.25a = 985 ---------(II)

Multiply equation (I) by (-1.25).

(I)*(-1.25)      -1.25c - 1.25a =  - 660

(II)                1.25c + 2.25a = 985  {add, c will be eliminated}

                                       a =  325

Number of adults = 325

Plugin the value of a in equation (I)

c + 325 = 528

         c = 528 - 325

         c = 203

Number of children = 203

Answer:

B.

Step-by-step explanation:

(x-1)2+(y+2)2=4.

because the equation is shown in the graph

the equation of the circle with a center at (-1, 2) and a radius of 2 is:

(x + 1)² + (y - 2)² = 4

From graph er can see that center of circle is (-1,2) and radius is 2

The equation of a circle with its center at point (h, k) and radius r is given by:

(x - h)² + (y - k)² = r²

In this case, the center of the circle is (-1, 2), and the radius is 2. Plugging these values into the equation, we have:

(x - (-1))² + (y - 2)² = 2²

Simplifying further:

(x + 1)² + (y - 2)² = 4

Expanding the square terms:

x² + 2x + 1 + y² - 4y + 4 = 4

Combining like terms:

x² + y² + 2x - 4y + 1 + 4 - 4 = 0

Simplifying:

x² + y² + 2x - 4y + 1 = 0

Therefore, the equation of the circle with a center at (-1, 2) and a radius of 2 is:

(x + 1)² + (y - 2)² = 4

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Answer:

The least common multiple, but you can use the greatest common factor, but at the end you have to simplify for it to be correct. 1 3/30

Step-by-step explanation: 4/15+5/6

Change 15 into a 30 by multiplying 2 to both sides.

Change 6 into a 30 by multiplying 5 to both sides.

so the new fractions are 8/30+25/30=33/30

The final fraction is 1 3/30.

Answer:

Step-by-step explanation:

Angles 153 and QRP are straight angles, and thus Angle QRP is

180 - 153, or 27 degrees.

The interior angles of the triangle must sum up to 180 degrees:

27 + (3y + 5) + (2y - 7) = 180.

combining like terms, we get:

5y - 25 = 180, or 5y = 155, or y = 31

Then Angle Q is 3(31) + 5, or 93

Angle P is 2(31) - 7, or 55, and

Angle QRP is 27 degrees (found earlier).

Answer:

1/18

Step-by-step explanation:

there are 18 combination choices and cookies 'n cream is one of the 18

Answer:

1/2x = 3*(27-12)

Step-by-step explanation:

Let x be the number

Is means equals

Difference means subtract

1/2x = 3*(27-12)

Answer:

[tex]$\frac{1}{2} x = 3(27-12)$[/tex]

or

[tex]$\frac{x}{2} = 3(27-12)$[/tex]

Step-by-step explanation:

Half of a number is equal to three times the difference between 27 and 12.

Half of a number ([tex]x[/tex]): [tex]$\frac{1}{2}x=\frac{x}{2} $[/tex]

Three times the difference between 27 and 12: [tex]3(27-12)[/tex]

[tex]$\frac{1}{2} x = 3(27-12)$[/tex]

By the way, we can find the value of [tex]x[/tex]

[tex]$\frac{x}{2} = 3(27-12)$[/tex]

[tex]$\frac{x}{2} = 3(27-12)$[/tex]

[tex]$\frac{x}{2} = 45 $[/tex]

[tex]$x = 90 $[/tex]

Answer:

[tex]25=10+\frac{1}{3}n[/tex].

Step-by-step explanation:

It is given that the sum of 10 and one-third of a number  is 25.

Let as consider n be the unknown number.

One-third of a number [tex]=\frac{1}{3}n[/tex]

Sum of 10 and one-third of a number [tex]=10+\frac{1}{3}n[/tex]

The sum of 10 and one-third of a number  is 25. It can be written as

[tex]25=10+\frac{1}{3}n[/tex]

Therefore, the required equation is [tex]25=10+\frac{1}{3}n[/tex].

Answer:

A

Step-by-step explanation:

Answer:

- 3/2            This matches Answer C

Step-by-step explanation:

The midpoint of the segment connecting (2,4) and (2,-7) is (2, y), where

       4 - 7

y = ---------- = - 3/2            This matches Answer C.

          2

Answer:

The answer we be is D.980

Answer:

A. Parallelogram

This is because all sides of a parallelogram are parallel to each other, it is also a quadrilateral.

Answer:

It is a parallelogram

Step-by-step explanation:

Answer:

15.5x+7=100

15.5x = 93

x=6 people

Answer:

6 people

Step-by-step explanation:

let x = amount of people Mr. Donovan brings

7 + 15.50x = 100

-7                 -7

15.50x = 93

/15.50      /15.50

x = 6

6 people

Answer:

x =  ± sqrt(43)

Step-by-step explanation:

2x^2 - 28 = x^2 + 15

Subtract x^2 from each side

2x^2-x^2 - 28 = x^2-x^2 + 15

x^2 -28 = 15

Add 28 to each side

x^2 - 28 +28=  15+28

x^2 = 43

Take the square root of each side

sqrt(x^2) = ± sqrt(43)

x =  ± sqrt(43)

Answer:

The Hotel charge without tax in first city is $3500 and The hotel charge before tax in the second city is 2000

Step-by-step explanation:

Let x be the hotel charge without tax in first city

We are given that The hotel charge before tax in the second city was $1500 lower than in the first.

So, Hotel  charge without tax in second city =x-1500

Tax% in first city = 10%

So, tax in first city = 0.1x

Tax% in second city =5%

So, tax in second city = 0.05(x-1500)

We are given that The total hotel tax paid for the two cities was $600.

So,0.1x+0.05(x-1500)=600

0.1x+0.05x+75=600

0.15x=600-75

[tex]x=\frac{600-75}{0.15}[/tex]

x=3500

Hotel charge without tax in first city = $3500

The hotel charge before tax in the second city =x-1500=3500-1500=2000

Hence The Hotel charge without tax in first city is $3500 and The hotel charge before tax in the second city is 2000

Answer:

D,C

Step-by-step explanation:

Answer:

The value of x is 12.

Step-by-step explanation:

Given that the area of triangle formula is A = 1/2×b×h where b represents base which is the x and h is height, 10 inches. So you have to substitute the following values into the formula :

[tex]area = \frac{1}{2} \times base \times height[/tex]

Let area = 60,

Let base = x,

Let height = 10,

[tex]60 = \frac{1}{2} \times x \times 10[/tex]

[tex]60 = 5 \times x[/tex]

[tex]5x = 60[/tex]

[tex]x = 12 \: inches[/tex]

Answer:

12 inches

Step-by-step explanation:

The area of a triangle can be found using the following formula.

a=(b*h)/2

We know that the triangle has an area of 60 inches squared. We also can see from the picture that the height is 10 inches, and the base is x inches.

a=60 inches^2

b= x inches

h= 10 inches

Substitute these values into the formula

60=(x*10)/2

Now, solve for x. To do this, get x alone. Perform the opposite of what is being done to the equation. Remember to perform everything to both sides of the equation.

x*10 is being divided by 2. The opposite of division is multiplication, so multiply both sides by 2.

2(60)=(x*10/2)2

2(60)=x*10

120=x*10

x is being multiplied by 10. The opposite of multiplication is division. Divide both sides by 10.

120/10=x*10/10

120/10=x

12=x

The base, or x, is 12 inches.

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1) 4x + 9 = 2x - 6

Subtract 9 from both sides

4x = 2x - 15

Subtract 2x from both sides

2x = -15

Divide both sides by 2:

x = -15/2 or -7.5

2) 2(x - 5) = 5x + 23

Expand the brackets:

2x - 10 = 5x + 23

Subtract 23 from both sides

2x - 33 = 5x

Subtract 2x from both sides

3x = -33

Divide both sides by 3

x = -11

3) 7x + 3 = 2x + 13

Minus 3 from both sides

7x = 2x + 10

Subtract 2x from both sides

5x = 10

Divide both sides by 5

x = 2

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