A company that manufactures bicycles has costs given by the equation below in which x is the number of bicycles manufactured and C is the cost to manufacture each bicycle. Complete parts a. through c.

What she approximated as 4.7 is not correct because the nearest perfect squares are 10 and 11 which are different from what she got.

We are told that Lauren is trying to approximate the solution to n² = 115.

Now, she has figured out that it lies between √100 and √121..

Now, √100 = 10 and √121 = 11. Thus, we can say that if she says it is between 4 and 5, then she is wrong because the nearest perfect squares are 10 and 11 which are different from what she got.

Thus, what she approximated as 4.7 is not correct.

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The circumference and area of the circular figure as given in the task content are; 31.4 and 78.5 respectively.

Since each unit on the graph measures one centimeter, it follows that the radius of the circle which is described by line PQ can be determined as; 5units = 5 centimetres.

On this note, the circumference of the figure; 2πr = 2 × 3.14 × 5

Circumference = 31.4 cm.

Also, the area of the circle in discuss can be determined from; πr² = 3.14 × 5²

Area = 3.14 × 25

Area = 78.5cm²

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Considering the expression of a line, they do not have the same value of m. So, the two lines are not parallel.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x1, y1) and (x2, y2) of a line, the slope m of said line can be calculated using the following expression:

m= (y2 - y1)÷ (x2 - x1)

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.

Parallel lines are two lines that are always at the same distance from each other and that prolonged towards infinity never touch.

Two lines are parallel if they have the same slope and different y-intercepts. That is, they have the same value of m and different value of b.

In this case, you can calculated the slope of the two lines as:

Being (x1,y1)= (-3,2) and (x2,y2)= (4, -1), the slope m can be calculated as:

m= (-1 -2)÷ (4 - (-3))

Solving:

m= (-3)÷ 7

m= -3/7

Being (x1,y1)= (1,3) and (x2,y2)= (-2,-4), the slope m can be calculated as:

m= (-4 -3)÷ (-2 -1)

Solving:

m= (-7)÷ (-3)

m= 7/3

You can observe that they do not have the same value of m. Finally, the two lines are not parallel.

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Answer:

(0, -3)

Step-by-step explanation:

.

Answer:

The answer is true!

Step-by-step explanation

Answer:

[tex]y=\frac{2}{5}x-3[/tex]

or

[tex]y+3=\frac{2}{5} (x-0)[/tex]

Step-by-step explanation:

We are given two points on Line A: (0,-3) and (5,-1). We can assign each integer to a variable in the slope formula (see above):

[tex]x_1=0[/tex]

[tex]y_1=-3[/tex]

[tex]x_2=5[/tex]

[tex]y_2=-1[/tex]

As we have identified point, we can now work to identify slope by substituting our points into the slope formula:

[tex]m=\frac{-1-(-3)}{5-0}=\frac{2}{5}[/tex]

Now that we have identified both point and slope for Line A, we can format these values in point-slope form. Substitute values into the formula:

[tex]y-(-3)=\frac{2}{5} (x-0)=y+3=\frac{2}{5}x[/tex]

Solve for [tex]y[/tex] to achieve an answer in slope-intercept form ([tex]y=mx+b)[/tex]:

[tex]y=\frac{2}{5} x-3[/tex]

Answer:

i the middle

Step-by-step explanation:

Answer:12.99+ 3.75x= total. therefore, 12.99+3.75(4)= 27.99

Step-by-step explanation:

tho

Answer:

1.25

Step-by-step explanation:

Answer:1.25

Step-by-step explanation:

The graph is attached below.

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50 guests were there at the party

Total champagne available = 15 litres

1 litre = 1000 ml

15 litres = 15000 ml

Total = 15000 ml

Each guest had 2 glasses of 150 ml = 300 ml, which means each guest was served 300 ml of champagne

Total no of guests = Total champagne  / champagne served to each

= 15000 / 300

= 50

50 guests were there at the party

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the graphed system of inequalities is:

y > − 2x − 4

y ≤ x + 1

Which is the first option.

On the image in the quesitonw e cans ee the graph of a system of inequalities. There we can see two lines.

One of the lines has a positive slope and we can see that it is a solid line, and we also can see that the region below that line is shaded, so one of the inequalities is of the form:

y ≤ line with positive slope.

The whole opposite happens for the other line, it has a negative slope, it is dashed (so this time we use the symbols > or <) and the region shaded is above the line, so this time we have an inequality of the form:

y > line with negative slope.

Then the system of inequalities is:

y ≤ line with positive slope.

y > line with negative slope.

By looking at the options, the only one with this form is:

y > − 2x − 4

y ≤ x + 1

Which is the first option

Finally, we conclude that the graphed system of inequalities is:

y > − 2x − 4

y ≤ x + 1

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The graphs of the functions and relations gives;

4. The graph of y(x) = x² represents a function and the graph of y² = x represents a relation

5. In equation, y² = x, the value x = 9, gives two y–values y = 3 or -3, therefore y² = x is a relation rather than a function.

6. The domain and range are both [-8, 8]

7. From the equation,x = √(8 - y²), each x– value gives two y–values, therefore x² + y² = 8 is a relation not a function

The given equations of the graphs are;

Where;

x = The input or independent variable

y = The output or dependent variable

In a function each input or value of x can give only one output or value of y, such that a vertical line drawn from each x–value crosses the graph only once.

Therefore;

The graph of y(x) = x², represent a function, given the each x–value has only one y–value, or the value of x determines the y–value.

The graph of y² = x represents a relation given that one x–value can give two y–values (a vertical line drawn at a point, x > 0, crosses the graph twice.

5. Let 9 represent the value chosen from the domain of both y(x) = x² and y² = x, we have;

y(9) = 9² = 81

Therefore, the equation, y(x) = x² is a function

In the relation, y² = x, we have;

y² = 9

y = ±3

Therefore, when x = 9, y = 3, or y = -3, which are two outputs or y–value for one input or x–value.

Which makes y² = x a relation rather than a function.

6. The equation of the graph is the equation of a circle, x² + y² = 8

Where;

8 = The square of the radius of the circle

(h, k) = (0, 0), the center of the circle is at the origin.

Therefore;

The coordinates of the edges of the circle on the x–axis are;

(-√8, 0), and (√8, 0)

The domain is therefore [-8, 8]

Similarly, the range, which are the possible y–values is also [-8, 8]

7. The equation x² + y² = 8, and therefore, the graph is not a function given that we have;

Given that y²y(x) = x²is always positive, each x - value gives two y-values, which does not conform with the mapping relationship of a function

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Answer:

18 degrees

Step-by-step explanation:

If <ABC and <DEF are complementary, m<ABC + m<DEF = 90 degrees. So M<DEF = 90 - 72 = 18 degrees.

Answer: 18

Step-by-step explanation: Complementary angles sum up to 90. (90 - 72 = 18)

Answer:

4600

Step-by-step explanation:

80000 is in 17001 and up category so the tax will be 5.75%. 80000/100 *5.75 = 4600

If a translation of T (2, -7) is applied to the triangle ABC as shown in the figure attached hereby for reference, and B (1, 5) gets repositioned to B', then the current coordinates of B' are (3, -2).

As per the question statement, a translation of T (2, -7) is applied to the triangle ABC as shown in the figure attached hereby for reference, and B (1, 5) gets repositioned to B'.

We are required to calculate the coordinates of B'.

To solve this question, we need to know what Translation (a, b) to (x, y) and (-a, -b) to (x, y) means. Translation (a, b) to (x, y) means the abscissa "x" is to be shifted to the right by "a" units while the ordinate "y" is to be shifted to the right by "b" units, i.e., after translation, the new coordinates become [(a + x), (b + x)]. On the other hand, Translation (-a, -b) to (x, y) means the abscissa "x" is to be shifted to the left by "a" units while the ordinate "y" is to be shifted to the left by "b" units, i.e., after translation, the new coordinates become [(a - x), (b - x)].

Here, as per the above mentioned concept, a translation of T (2, -7) if applied to the point B (1, 5), the new point B' will be at [tex][(1+2), (5+(-7)]=[3, (-2)][/tex].

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Answer: D (3,-12)

Step-by-step explanation:

Answer: 15. f(1)=3

16. g(3)=1

Step-by-step explanation:

15. (fog)(1)=

f(g(1))=

f(1)=3

16. (gof)(5)=

g(f(5))=

g(3)=1

According to the average rate, Heart can beat 140 times in = 2 minutes and Rate of heart beat= 70 beat per minute .

According to the statement

We have to find that the rate of the heart beat.

So, For this purpose, we know that the

Average rate is a measure of how much the function changed per unit, on average, over that interval.

From the given information:

In 10 minutes, a heart can beat 700 times. At this rate,in how many minutes will a heart beat 140 times?

Then

Heart can beat 700 times in = 10 minutes .

Heart can beat 140 times in = 10*140/700 minutes .

Heart can beat 140 times in = 1400/700 minutes .

Heart can beat 140 times in = 2 minutes .

Rate of heart beat : 140/2 beat per minute.

Rate of heart beat= 70 beat per minute .

Therefore, According to the average rate, Heart can beat 140 times in is 2 minutes and Rate of heart beat is 70 beat per minute.

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Answer: -20 yards

Step-by-step explanation:

Loss in 5 yards ==> -5 yards

-5*4=-20 yards

the 3 correct statements are:

For a function f(x), we define the inverse function f⁻¹(x):

This means that, if for a given value of x = x₀ we have:

f(x₀) = y₀

Then:

f⁻¹(y₀) = x₀

From this, we can conclude that the domain of f(x) is the range of the inverse, and the range of f(x) is the domain of the inverse.

Then the statements that are correct are:

These 3 are the 3 correct statements.

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The equation is 2.90 + 1.25m= 6.65

The number of miles in the taxi ride is 3 miles

The airport charged a pick up fee of $2.90

$1.24 was charged per mile

The total fare was $6.65

The equation can be expressed as

2.90 + 1.25m= 6.65

collect the like terms

1.25m= 6.65 - 2.90

1.25m= 3.75

divide by the coefficient of m which is 1.25

m= 3.75/1.25

m= 3

Hence the number of miles of the taxi ride is 3

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Answer:

x = 96

Step-by-step explanation:

[tex]\frac{x}{6} +4=20[/tex]

1. Isolate the variable 'x'.

1a. Subtract 4 so the equation becomes [tex]\frac{x}{6} =16[/tex]

2a. Multiply both sides by 6 to turn the fraction into a normal number, which becomes x=96.

Answer:

[tex] \sf \large \: x=96[/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

x/6+4=20

Step 1: Simplify both sides of the equation.

1/6x+4=20

Step 2: Subtract 4 from both sides.

1/6x+4−4=20−4

1/6x=16

Step 3: Multiply both sides by 6.

6*(1/6x)=(6)*(16)

x=96

The car's displacement according to the description given is; 0 meters while it's distance travelled is; 90 meters.

It follows from definition that, displacement which is a vector quantity is a measure of the change in position of a body after undergoing motion while the distance travelled which is a measure of magnitude only (scalar) is a measure of the space covered over the course of time.

Hence, the displacement is zero as the start position is same as the end position.

Also, the distance is the space covered= 25 +20 +20 +25 = 90 meters.

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In February, it will sell 420 skirts.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

A clothing store sells 300 skirts in January.

The number of skirts it sells in February is 40%,

that means,

the number of skirts,

= 300 x 1.4

= 420 skirts.

Therefore, It will sell 420 skirts.

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The Length of the rectangle is: B. 6 2/3.

The area of a rectangle is calculated as: Area = (length)(width). Therefore, if we known the area of a rectangle and its width, we can find the length of the rectangle using:

Length of rectangle = area of rectangle / width of rectangle.

Given the following:

Area of a rectangle = 21 and 2 over 3 square inches

Width = 3 and 1 over 4 inches

Length of the rectangle = 21 2/3 ÷ 3 1/4

Length of the rectangle = 65/3 ÷ 13/4

Length of the rectangle = 65/3 × 4/13

Length of the rectangle = 260/39 = 6 2/3.

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The simplest form of the ratios are not the same, hence, the ratios 6:4 and 18:8 are not equivalent ratios

In order to show why the given ratios are not equivalent ratios, we need to express them in their simplest form as shown:

For the ratio of 6:4

6:4 = 6/4

simplify.

= 3/2

= 3×2/2×2

= 3/2

= 3:2

For the ratio of 18:8

18:8 = 18/8

simplify.

= 9/4

= 9×2/4×2

= 9/4

= 9:4

Since the simplest form of the ratios are not the same, hence, the ratios 6:4 and 18:8 are not equivalent ratios.

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Answer:

12x + 9 = 4x + 7

Group likely terms

12x - 4x = 7 - 9

8x = -2

Now we need to isolate x

Therefore; Divide both side by the coefficient of x thus 8

Hence x = -1/4

Answer:

[tex]x = \bf -\frac{1}{4}[/tex]    

Step-by-step explanation:

We are given the following equation:

[tex]12x + 9 = 4x + 7[/tex]

In order to solve this equation, we have to rearrange it to make [tex]x[/tex] the subject of the equation:

[tex]12x + 9 = 4x + 7[/tex]

⇒ [tex]12x + 9 - 4x = 4x + 7 - 4x[/tex]       [Subtracting [tex]4x[/tex] from both sides]

⇒ [tex]8x + 9 = 7[/tex]

⇒ [tex]8x + 9 - 9 = 7 - 9[/tex]                     [Subtracting 9 from both sides]

⇒ [tex]8x = -2[/tex]

⇒ [tex]\frac{8}{8} x = -\frac{2}{8}[/tex]                                     [Dividing both sides by 8]

⇒ [tex]x = -\frac{2}{8}[/tex]

⇒ [tex]x = \bf -\frac{1}{4}[/tex]                                     [Simplifying the fraction]