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65x + y = 455

A grocery store receives a shipment of oranges and consistently sells the same number of oranges each day. The equation above models the number of oranges, y, that remain x days after the shipment is received. What does it mean that (7, 0) is a solution to the equation?

A. It takes 7 days after the shipment until none of the oranges are remaining.

B. There are 7 oranges in the shipment.

C. It takes 7 days for orange to be sold to 455 customers.

D. After the shipment, 7 oranges are sold each day.

is a hope this helped

Answer:

answer is d

Step-by-step explanation:

Answer:

graph c is the correct answer hope this helps you get an A.

The way to decide which variable to isolate in order to use the substitution method to solve a system of linear equations is;

to look for the variable with no coefficient or least coefficient and then isolate it and use substitution to solve the simultaneous equation.

       A system of linear equations can be solved by three major methods which are;

- Elimination method

- Substitution method

- Graph method

     Now, in this question we want to know how substitution method is done.

Let us say we have two simultaneous equations which are;

2x + 3y = 8   ----(eq 1)

x + 5y = 11     ----(eq 2)

      Now, in this method, we need to first isolate a variable in one of the equations by making it the subject of formula there. Usually, we go with the variable that has no coefficient first.

In this case, it is x that has no coefficient in eq 2 and as such, we will isolate it to get;

x = 11 - 5y

    In conclusion, the way we decide which variable to isolate in substitution method of simultaneous equations is to look for the variable with no coefficient or least coefficient.

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Simple Interest can be calculated using the formula I=Pr t

Here I= interest earned ,P= Principal ,R= rate of interest ,t= time in years.

It is given Principal P=$7,064

Rate r=6.5% =0.065

Time t= 8 months =[tex] \frac{8}{12} =\frac{2}{3} [/tex] years

Substituting these values in I = P r t

I =(7064)(0.065)([tex] \frac{2}{3} [/tex])

Solving for I

I=306.11

interest earned on $7,064 at 6.5% for 8 months is $306.11

The operation in the equation, (r + s)(r2 - rs + s2), is solved by distributing the multiplication of the binomial across each term in the trinomial. When the multiplications are complete and the terms are added, the resulting solution is r3 + s3.

The indicated operation in the question is the multiplication of the binomial, (r + s), and the trinomial, (r2 - rs + s2). This can be performed by using the distributed property of multiplication over addition. In this case, you would multiply each term in the binomial by each term in the trinomial, then add the products. So the solution will be:

r3 - r2s + rs2 + r2s - rs2 + s3 = r3 + s3

Note: the terms -r2s and r2s cancel each other out, as do the terms rs2 and -rs2, which is why the final result is r3 + s3.

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Final answer:

The best initial step in solving the equation 3 + 3√(6x) = 5 is to subtract 3 from both sides, simplifying the equation to 3√(6x) = 2, which lays a clear path towards isolating and solving for x.So,option A.)Subtract 3 from both sides. is correct.

Explanation:

The best first step in solving the equation 3 + 3√(6x) = 5 is to simplify the equation by isolating the square root term. This can be done by following option A: Subtract 3 from both sides of the equation. This action makes the equation easier to manage step-by-step as you move toward isolating x, which is the ultimate goal of solving for x. The resulting equation after subtracting 3 from both sides is 3√(6x) = 2. This simplified equation can then be further manipulated to solve for x, primarily by squaring both sides to eliminate the square root, and then solving the resulting simple algebraic equation.

Answer:

usa test prep its B

Step-by-step explanation:

Final answer:

Comparing a 4ft by 6ft rectangular table and a circular table with a 6ft diameter, the circular table can seat more people (approximately 9) due to more efficient use of its perimeter, compared to the rectangular table which can seat 6 people.

Explanation:

The question asks which table would seat more people: a 4ft by 6ft rectangular table or a circular table with a diameter of 6ft. To answer this, we need to compare the arrangements and sizes of the two tables.

The rectangular table measures 4 feet by 6 feet. Typically, a person needs about 2 feet of space at a dining table to sit comfortably. Therefore, on the longer sides (6 feet), you can seat 3 people on each side, for a total of 6. On the shorter sides (4 feet), it's not practical to seat anyone due to space constraints and leg room. So, the rectangular table can seat 6 people.

The circular table has a diameter of 6 feet. Placing chairs around a circle often allows for more efficient use of space. If we assume each person requires the same 2 feet of space, roughly, the circumference of the table (which is π * diameter) dictates how many people can sit around it. The circumference of a 6-foot diameter table is about 18.85 feet (π * 6). Dividing this by 2 feet per person, you can seat approximately 9 people around the circular table.

In conclusion, a circular table with a diameter of 6 ft would seat more people, approximately 9, compared to a 4ft by 6ft rectangular table, which would seat 6 people. This is due to the circular table's ability to more efficiently use the perimeter for seating.

The width of the roped off area around the museum display is 4 feet.

To find the width of the roped off area around the museum display of Native American artifacts, we need to solve for x in the area equation. The area of just the display is 4 feet by 6 feet, which is 24 square feet. Since we know the combined area of the display and the roped-off area is 120 square feet, the equation is:

Area of display + Area of roped-off region = Total Area

(4)(6) + ((4 + 2x)(6 + 2x) - (4)(6)) = 120

24 + (24 + 4x + 12x + 4x2) - 24 = 120

Simplifying, we get:

4x² + 16x - 96 = 0

Divide by 4:

x² + 4x - 24 = 0

Factor the quadratic equation:

(x + 6)(x - 4) = 0

Setting each factor equal to zero gives us two potential solutions:

x + 6 = 0
or
x - 4 = 0

Therefore, x can be -6 or 4. Since a width can't be negative, the only logical solution is:

x = 4 feet

The width of the roped-off area is 4 feet.

Given is [tex] 2*cos^{2} (x)=sin(2x) [/tex]

We can use following formulas to solve this problem :-

1. [tex] \frac{sin\;\theta}{cos\;\theta} = tan\;\theta [/tex]

2. sin(2∅) = 2·sin(∅)·cos(∅)

Solving the given equation :-

[tex] 2*cos^{2} (x)=sin(2x) \\\\2*cos^{2} (x)=2*sin(x)*cos(x) \\\\2*cos^{2} (x)-2*sin(x)*cos(x)=0 \\\\2*cos^{2}(x)*(1-\frac{sin(x)}{cos(x)}) =0 \\\\2*cos^{2}(x)*(1-tan(x)) =0 \\\\cos^{2}(x) = 0 \;or\; (1-tan(x)) =0 \\\\cos(x) = 0 \;or\; tan(x) =1 \\\\x = cos^{-1}(0) \;or\; x=tan^{-1}(1) \\\\x=\frac{\pi}{2} \;or\; x=\frac{\pi}{4} [/tex]

Hence, final answer is [tex] x=\frac{\pi}{2} \;or\; x=\frac{\pi}{4} [/tex].

The best estimate for the solution of the system of equations is (-4.5, 1.5).

The system of equations given is:

y = -34x - 2

y = x + 6

To find the best estimate for the solution, we can substitute the x-coordinate from each ordered pair into the second equation and solve for y.

Let's check each option:

For (-4.25, 1.5):

1.5 = -4.25 + 6

1.5 = 1.75 (not equal)

This is not a solution for the system.

For (-4.75, 1.75):

1.75 = -4.75 + 6

1.75 = 1.25 (not equal)

This is not a solution for the system.

For (-4.5, 1.5):

1.5 = -4.5 + 6

1.5 = 1.5 (equal)

This is a solution for the system.

For (-4.5, 1.75):

1.75 = -4.5 + 6

1.75 = 1.5 (not equal)

This is not a solution for the system.

Therefore, the best estimate for the solution of the system of equations is (-4.5, 1.5).

The explicit rule for the sequence is [tex] a_{n}=14-9n [/tex]

Let us put n=1, we get

[tex] a_{1}=14-(9 \times 1)=5 [/tex]

Now let n=2,

[tex] a_{2}=14-(9 \times 2)=-4 [/tex]

Let n=3,

[tex] a_{3}=14-(9 \times 3)=-13 [/tex]

Similarly, in this manner we obtain a sequence as

5, -4, -13, -22,.....

Since we can clearly observe that the first term is '5' and common difference is '-9'.

So, we get recursive rule for the sequence as:

[tex] a_{n}=a_{n-1}-9 [/tex] , where [tex] a_{1}=5 [/tex].