Carl is boarding a plane. He has 2 checked bags of equal weight and a backpack that weighs 4 kg. The total weight of Carl's baggage is 35 kg. Write an equation to determine the weight, (w), of each of Carl's checked bags.

Answer:

x=1, y=4

P=6

Step-by-step explanation:

We are given that

[tex]3x+y\leq 7[/tex]

[tex]x+2y\leq 9[/tex]

[tex]x\geq 0[/tex]

[tex]y\geq 0[/tex]

Objective function

[tex]P=2x+y[/tex]

We have to values of x and y that maximize the P and maximum value of P .

First we change inequality equation into equality equation

[tex]3x+y=7[/tex]  (I equation )

[tex]x+2y=9[/tex]  (II equation)

Equation I multiply by 2 and then subtract from II equation

[tex]-5x=-5[/tex]

[tex]x=1[/tex]

Substitute x=1 in equation I

Then, we get

[tex]3(1)+y=7[/tex]

[tex]3+y=7[/tex]

[tex]y=7-3=4[/tex]

The two equation intersect at point (1,4).

Substitute x=0 in equation I

Then , we get y=7

Substitute y=0 then

[tex]3x=7[/tex]

[tex]x=\frac{7}{3}=2.3[/tex]

The equation I cut the x- axis at point (2.3,0)and y-axis at (0,7).

Substitute x=0 in equtaion II

[tex]2y=9[/tex]

[tex]y=\frac{9}{2}=4.5[/tex]

Substitute y=0

Then, we get

[tex]x=9[/tex]

Therefore, the equation II cut the x- axis at point (9,0) and y axis at point (0,4.5).

Substitute x=0 and y=0 in inequality Equation I

[tex]3(0)+0=0< 7[/tex]

It is true . Therefore, shaded region below the line.

Substitute x=0 and y=0 in inequality equation II

Then, [tex]0+2(0)=0 < 9[/tex]

It is true. Therefore, the shaded region below the line.

The feasible region is bounded.The feasible region bounded by (0,0),(0,4.5),(2.3,0) and (1,4).

At (0,4.5)

[tex]P=2(0)+4.5=4.5[/tex]

At (2.3,0)

[tex]P=2(2.3)+0=4.6[/tex]

At (1,4)

[tex]P=2(1)+4=6[/tex]

At (0,0)

[tex]P=2(0)+0=0[/tex]

Hence, maximum value of P is 6 at (1,4).

x=1 and y=4

Answer:

Option C. $22.85

Step-by-step explanation:

Arthur is treating his friends to a meal at Chez Rich.

The meals added up to = $152.30

He tips the waiter = 15% of the bill

The amount of the tip = 15% × 152.30

                                    = 0.15 × 152.30

                                   = 22.845 ≈ $22.85

The amount  of the tip would be $22.85.

Option C. $22.85

The greatest common factor of the expressions 4a^2b and 6ab^3 is 2ab.

The question seeks to determine the greatest common factor of the expressions 4a2b and 6ab3. To find this, one must look at the common factors of the numerical coefficients (4 and 6) and the variables raised to their respective powers (a2 and a, b and b3). The numerical common factor of 4 and 6 is 2. The lowest power of 'a' common to both terms is a1 and for 'b' is b1. On doing this we get 2ab.

Answer:

[tex]\texttt{Height of the prism}=1\frac{3}{4}[/tex]

Step-by-step explanation:

Volume of rectangular prism = Length x Width x Height

[tex]\texttt{Volume of rectangular prism =}\frac{21}{32}\\\\\texttt{Length =}\frac{3}{4}\\\\\texttt{Breadth =}\frac{1}{2}[/tex]

Substituting

      [tex]\frac{21}{32}=\frac{3}{4}\times \frac{1}{2}\times h\\\\h=\frac{7}{4}=\frac{4+3}{4}=1\frac{3}{4}[/tex]

    [tex]\texttt{Height of the prism}=1\frac{3}{4}[/tex]

if the line is on the positive side then your answer is "y=2^x+1 +2"

if the line is on the negative side your answer is "y=2^x-1 +2"

Positive  always goes with positive

We can find the quantity of 1/3 pound paperback books that weigh a total of 25 pounds by performing the calculation, 25 ÷ 1/3 or equivalently, 25 x 3, which equals 75. Therefore, we would need 75 of these books to total 25 pounds.

To find out how many 1/3

pound

paperback

books weigh a total of 25 pounds, we use division. Since each book weighs 1/3 of a pound, we divide the total weight we want (25 pounds) by the weight of each individual book (1/3 pound). So, our calculation would look like this:

25 ÷ 1/3

. In mathematics, dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of 1/3 is 3/1, or just 3. So, our calculation is now:

25 x 3

. Multiplying 25 by 3 gives us 75. So, we would need

75

of these paperback books to

weigh

a total of 25 pounds.

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Answer:

Point, (0,4) and (-4,5), just took the test

The angle measure of g is  ∠g = 105°.

The correct option is D.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

As per the information provided, it is given that the two parallel lines u and v are traversed by line g.

To find the angle measure of ∠g:

The angle measure of ∠g is equal to 105° by the alternate exterior angle theorem.

Therefore, ∠g = 105°.

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The complete question:

Two parallel lines are crossed by a transversal. What is the value of g? g = 75 g = 80 g = 100 g = 105

A) The slope of line that goes through the points (4, 1) and (2, 5) is -2.

B) The slope of line that goes through the origin and the point (10, 5) is              

   1 / 2.            

C) Vertical lines has undefined slope.

D) The slope of line that goes through the points (1, 6) and (10, 6) is 0.

What is Slope?

Slope is defined as the steepness of the line.

Since, Slope of line passes through points (x₁ , x₂) and (y₁ , y₂) is;

m = (y₂ - y₁) / (x₂ - x₁)

Now,

A) The slope of line that goes through the points (4, 1) and (2, 5) is;

m = 5 - 1 / 2 - 4

m = 4 / -2

m = - 2

B) The slope of line that goes through the (0, 0) and the point (10, 5) is;

m = 5 - 0 / 10 - 0

m = 5 / 10

m = 1 / 2

C) A vertical line that goes through the point (6,-5) has undefined slope.

Because the horizontal change is 0 and we cannot divide a number by 0.

D) The slope of line that goes through the points (1, 6) and (10, 6) is;

m = 6 - 6 / 10 - 1

m = 0 / 9

m = 0

Thus,

A) The slope of line that goes through the points (4, 1) and (2, 5) is -2.

B) The slope of line that goes through the origin and the point (10, 5) is              

   1 / 2.            

C) Vertical lines has undefined slope.

D) The slope of line that goes through the points (1, 6) and (10, 6) is 0.

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3m +7/2 = -2m +5/2

subtract 5/2 from each side

3m +2/2 = -2m

2/2 = 1

 3m+1 =-2m

subtract 3m from each side

1=-5m

divide both sides by -5

m = 1/-5 = -1/5

m = -1/5