Write “$4,915 for 72 shares of stock” as a unit rate. Round to the nearest hundredth if necessary.

Final answer:

The given equation has no solution, as simplifying both sides leads to the false statement -6 = -11. The number of solutions is zero, and the Distributive Property was used to solve the equation.

Explanation:

To solve the equation 4x + 2(x – 3) = 4x + 2x – 11, follow these steps:

Expand the left side of the equation: 4x + 2x - 6.

Combine like terms: 6x - 6.

Since the left and right side both have 4x, we can cancel out 4x from both sides, leaving 2x - 6 = 2x - 11.

Subtract 2x from both sides to get -6 = -11, which is a contradiction.

There is no solution to this equation because we arrived at a false statement. Therefore, the number of solutions is zero.

Part B: The property I used to solve this equation is the Distributive Property when expanding 2(x - 3).

radius = diameter/2

so 28/2=14

 using 3.14 for PI

2*3.14*14 = 87.92 = 88 inches

Answer:

The answer is:

D. -3/5

Answer:

x = + 0.85 , -0.85

Step-by-step explanation:

Given : 11x² = 8.

To find : use any method to solve the equation. If necessary, round to the nearest hundredth.

Solution : We have given that : 11x² = 8.

First we divide both sides by 11,

x² = [tex]\frac{8}{11}[/tex].

Now taking square root both sides .

x = [tex]\sqrt{\frac{8}{11}}[/tex].

x =± 0.8528.

Therefore, x = + 0.85 , -0.85

Answer:(x+1)/9x

Step-by-step explanation: Hope this helps

The cost to rent each chair is $5, and the cost to rent each table is also $5.

This problem can be solved using the method of substitution in solving systems of linear equations. We can set up two equations based on the information given: 5C + 3T = 25 and 2C + 6T = 40 where C represents the rental cost of each chair and T represents the rental cost of each table.

When we simplify the second equation, we get C + 3T = 20. We can then substitute this into the first equation, which gives us 5(C + 3T) = £25. Solving these equations gives us the cost to rent each chair (C) as $5 and each table (T) as $5.

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Answer:

The correct answer is B. 110.

3/4 divided by 3 

3/4 *1/3 = 3/12 = 1/4

Final answer:

To determine where the tangent line to a function is horizontal, find the derivative of the function, set it equal to zero, and solve for 'x'. This value of 'x' is where the slope is zero, indicating a horizontal tangent line.

Explanation:

How to Find Where the Tangent Line is Horizontal

To find where the tangent line to a curve is horizontal, you need to determine where the slope of the tangent (which is the derivative of the function) is zero. This involves calculating the derivative of the given function and solving for the value of 'x' where this derivative equals zero.

For example, if we have a function y = 4x - x², we first find its derivative: dy/dx = 4 - 2x. Setting this derivative equal to zero gives us 4 - 2x = 0. Solving for x gives us x = 2. This is the value of x where the tangent line is horizontal.

If we are given a graph, like in a velocity-time graph, a horizontal tangent indicates a moment where the velocity is zero, signifying a change in direction of the particle. At such points, we can see that the slope of the tangent line is zero, meaning it is a horizontal tangent.

Answer: 15²=225

225-(7.5²•3.14)=48.375 or to the nearest form 48.38.

Step-by-step explanation: In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the equals sign "=".

Answer:

4 deaths per hour

Step-by-step explanation:

We have been given that approximately 31,000 citizens of the country died in automobile accident in 2015.

Since we know that 1 year = 365 days,

1 day = 24 hours

In one year there are total hours = 365 × 24 = 8,760 hours

Death per hour = [tex]\frac{31000}{8760}[/tex] = 3.5388 ≈ 4

Therefore, the toll in deaths per hour is approximately 4 in 2015.

This problem states that the sum of 3 consecutive integers is 63 and it asks us to find the largest integer.

Three consecutive integers can be represented as followed.

X → first integer

X + 1 → second integer

X + 2 → third integer

Since the sum of our three consecutive integers is 24, we can write an equation.

X + X + 1 + X + 2 = 63

We can simplify our equation on the left and it will read...

Answer:

[tex]y\geq \frac{1}{3}x -1[/tex]

Step-by-step explanation:

To find linear inequality, first we find the equation of the line.

LEts pick two points (3,0)  and (0,-1)

To get equation of a line [tex]y=mx+b[/tex], use slope formula to find slope m

[tex]m=\frac{y_2-y_1}{x_2-x_1} =\frac{0+1}{3-0} =\frac{1}{3}[/tex]

y intercept is (0,-1) . so b=-1

The equation of the line becomes

[tex]y=\frac{1}{3}x -1[/tex]

now we look at the shaded region.

the graph is shaded at the top and also we have solid line . so we use >= symbol

[tex]y\geq \frac{1}{3}x -1[/tex]

area = 1/2 * b * h=

1/2 * 2 * 1 1/4 = 1 1/4 square meters each

Answer: area = 1/2 * b * h=

1/2 * 2 * 1 1/4 = 1 1/4 square meters each

The dimes are 28 dimes

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

Given:

total coins = 57

So,

D + Q = 57

D= 57 - Q....(1)

0.10D + 0.25 Q = 10.05

Using (1), we get

0.10(57 - Q) + 0.25Q= 10.05

5.7 - 0.10Q + 0.25Q = 10.05

0.15Q = 4.35

Q= 29

So, dimes = 57- 29= 28 dimes

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The solution is, the dimensions of the field if the length of the field is 8 feet more than the width is:

width = 51,047

length = 51,055

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

Here, we have,

given that,

A fence is to be installed around a rectangular field.

the​ field's perimeter is 204204 feet.

now, we have,

204204 - 16 = 204188

we get,

204188 / 4 = 51,047

so, we get,

width = 51,047

length = 51,055

Hence, The solution is, the dimensions of the field if the length of the field is 8 feet more than the width is:

width = 51,047

length = 51,055

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The formula for K in terms of F is [tex]K = \frac{5}{9} (F - 32) + 273.15[/tex]

The given expression:

[tex]F = \frac{9}{5} (K - 273.15) + 32[/tex]

To find:

The formula for K is obtained by making K the subject of the formula as shown below;

[tex]F = \frac{9}{5} (K - 273.15) + 32\\\\subtract \ 32 \ from \ both \ sides \ of \ the \ equation\\\\F - 32 = \frac{9}{5} (K - 273.15)\\\\multiply \ both\ sides \ by \ 5\\\\5(F - 32) = 9(K - 273.15)\\\\divide \ both\ sides \ by \ 9\\\\\frac{5}{9} (F - 32) = K - 273.15\\\\add \ 273.15 \ to \ both\ sides \ of \ the \ equation\\\\\frac{5}{9} (F - 32) + 273.15 = K\\\\[/tex]

Thus, the formula for K in terms of F is [tex]K = \frac{5}{9} (F - 32) + 273.15[/tex]

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Answer:

3:1 or 3/1

Step-by-step explanation:

We have the next information:

Gallons of Milk             Cost

           2                  ⇒     $6

dividing both quantities by two, we get the price for a single gallon of milk:

Gallons of Milk             Cost

           1                  ⇒     $3

We are asked for the ratio of dollars to gallons of milk (the order is important since dollars go first than gallons) so we will have the following:

dollars:gallons or dollars/gallons

and since $3 dollars pay for 1 gallon of milk, the ratio is:

3:1 or 3/1