Suppose you go shopping for a new futon bed for your apartment/home. The model you really like happens to be on sale for $1100. It's original price is $1200. What percent of the original price will you save if you purchase it? Write your answer to the nearest tenth of a percent, but in decimal form. For example, if you saved 34.67%, you would round to 34.7% and enter .347 as your answer.

The  coordinates of d and e b. d = –2, e = 12.

To find the coordinates of points D and E, we need to remember that they are the same distance from point F, which has a coordinate of 5. This means D and E are equidistant from F on the number line. Let's check each option to see which one satisfies this condition:

Option a: d = -7, e = -1

The distance from -7 to 5 is 12.

The distance from -1 to 5 is 6.

Since the distances are not equal, this option is incorrect.

Option b: d = -2, e = 12

The distance from -2 to 5 is 7.

The distance from 12 to 5 is also 7.

Since the distances are equal, this option is correct.

Option c: d = 0, e = 5

The distance from 0 to 5 is 5.

The distance from 5 to 5 is 0.

Since the distances are not equal, this option is incorrect.

Option d: d = 8, e = 11

The distance from 8 to 5 is 3.

The distance from 11 to 5 is 6.

Since the distances are not equal, this option is incorrect.

Therefore, the correct answer is option b: d = -2, e = 12.

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 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.

Marc will need to work just over 4 hours of overtime each week at his new job, which pays $9.80 per hour and $14.70 per hour for overtime, to earn the equivalent of his previous monthly income of $1,650.

To determine the number of overtime hours Marc needs to work at his new job to earn the same monthly income he did at his previous job, we'll first calculate his weekly income at his old job, then use the overtime pay rates at the new job to find the equivalent number of hours needed.

Marc previously earned $1,650 per month. Assuming a standard 4-week month, his weekly income was:

$1,650 per month / 4 weeks per month = $412.50 per week.

At his new job, Marc earns $9.80 per hour with time and a half for all hours over 36 hours a week. This means his overtime pay is 1.5 times his hourly rate, which is:

$9.80 per hour x 1.5 = $14.70 per hour for overtime.

Marc's income for the first 36 hours at his new job would be:

36 hours x $9.80 per hour = $352.80

To earn the equivalent of his old weekly salary, we must make up the difference with overtime pay:

$412.50 (old weekly income) - $352.80 (new regular pay) = $59.70 needed from overtime.

To determine the overtime hours needed to make $59.70: $59.70 / $14.70 per hour = approximately 4.06 hours.

Therefore, Marc will need to work just over 4 hours of overtime each week to earn the same amount he did at his previous job.

The constant rate of change in the linear equation y=7-13x is -13, representing the slope of the line which remains constant for any value of x. This is different from nonlinear functions, where the rate can vary with x.

The constant rate of change in the equation y=7-13x refers to the slope of the line represented by this linear equation. In this case, the constant rate of change, or the slope, is -13. This means for every one unit increase in x, y decreases by 13 units. Since the equation is linear, this rate does not change regardless of the value of x, unlike in nonlinear functions where the rate of change can vary with x.

To elaborate, if we have a nonlinear function, the rate of change depends on the interval of x we are looking at. For a linear function like this one, the slope is the same over any interval, so there's no need to compute it over smaller ranges of x to understand the rate of change.

Moreover, in calculus, the derivative represents the rate of change, and for a linear function, the derivative is simply the coefficient of x. Hence, the derivative of y with respect to x is -13. The derivative is zero for any constant term in a function, such as the 7 in the given equation.

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

Answer:

A. (-13,-3)

Step-by-step explanation:

Solve the system of two equations:

[tex]\left\{\begin{array}{l}-2a+3b=14\\a-4b=3\end{array}\right.[/tex]

From the second equation:

[tex]a=3+4b[/tex]

Substitute it into the first equation:

[tex]-2(3+4b)+3b=14\\ \\-6-8b+3b=14\\ \\-8b+3b=14+6\\ \\-5b=20\\ \\5b=-20\\ \\b=-4[/tex]

So,

[tex]a=3+4b=3+4\cdot (-4)=3-16=-13[/tex]

The solution is (-13,-4)

Answer:

A

Step-by-step explanation:

Answer:

B) 2x - 5 ≤ 45

Step-by-step explanation:

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°.

To learn more about the angle measure;

brainly.com/question/14684647

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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

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