The perimeter of a rectangle is 112 cm. if the length is 30 cm, how wide is the rectangle?

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:

B) 2x - 5 ≤ 45

Step-by-step explanation:

Answer:

|h − 100| less than or equal to 4

Step-by-step explanation:

We know the difference between h, the actual height, and the designed height, 100, is no more than 4.

This means that the actual height h could be up to 4 more than the designed height or up to 4 less than the designed height.  This is why we use an absolute value inequality; this considers just the distance of 4 regardless of direction.

Since it can be "no more than" 4, we use less than or equal to; this gives us

|h − 100| less than or equal to 4

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

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

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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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

Answer:

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

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

Final answer:

To write 230,000 in standard form, place the decimal point after the first non-zero digit. For 230,000, the standard form is 2.3 x 10⁵.

Explanation:

To express the number 230,000 in standard form, you simply write it as it is, moving the decimal point to the right until only one non-zero digit appears before the decimal. In this case, 230,000 in standard form is 2.3 x 10⁵.

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