6. Sal is selling two types of printed socks. He sells type a at R45 a pair. He sells type b at R30. If he sold 16 pairs in total, and had a total income of R585, how many pairs of sock b did Sal sell?​

The solution set of the inequality for R is given by [tex]-\frac{1172}{85} \leq x\leq \frac{1228}{55}[/tex] .

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.  It is frequently used to compare two numbers on the number line based on their sizes. Different types of inequalities are represented by a variety of notations such as < ,> ,≤ and ≥.

The modulus function takes the absolute value of a function.

To solve the given inequality we have simplify the inequality first.

[tex]x-\frac{7}{9} |(\frac{12}{5} -6x)|+50\ge -30[/tex]

[tex]or, x-\frac{7}{9}\times \frac{6}{5} |(2-5x)|+50\ge -30\\or,x-\frac{14}{15}|2-5x|\ge-80\\[/tex]

Now we separate the inequalities:

[tex]x-\frac{14}{15}(2-5x)\ge-80[/tex]  for 2x-5 ≥ 0

[tex]x-\frac{14}{15}(-(2-5x))\ge-80[/tex]  for 2x-5 ≤ 0

Now we will solve the two inequalities separate and find the intersection.

[tex]x-\frac{14}{15}(2-5x)\ge-80\\or,15x-28+70x\ge-1200\\or,x\ge -\frac{1172}{85}[/tex]

Again

2x-5 ≥ 0

or, [tex]x\le\frac{2}{5}[/tex]

hence [tex]-\frac{1172}{85}\le x\le\frac{2}{5}[/tex]

Similarly solving the other inequality we get

[tex]\frac{2}{5}\le x\le\frac{1228}{55}[/tex]

Now we find the intersection of the two inequalities:

[tex]-\frac{1172}{85}\le x\le\frac{1228}{55}[/tex]

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Answer: -4x²-11x-7

Step-by-step explanation:

[tex]-3x^2-3x-7-(x^2+8x)=\\-3x^2-3x-7-x^2-8x=\\-4x^2-11x-7[/tex]

Answer:

Quadratic Formula

Step-by-step explanation:

x^2-11x+10=

x^2-x-10x+10=

x(x-1)-10(x-1)=(x-10)(x-1)

Answer:

HELP WITH WHAT?

Step-by-step explanation:

Answer:

Step-by-step explanation:

x + x + 16 = 90

2x +16 = 90

2x = 74

x = 37

Answer: 15

Explanation:

The length of the segment is 10 plus 5 which is fifteen because you need to know how long it is. Just ignore the negatives.

Answer:

Step-by-step explanation:

-9x - 45 = -7x - 15  (Distribute -0.75 to (12x+60))        (x-8x = -7x)

-30 = 2x   (add 15 to both sides and add 9x to both sides)

-15 = x (divide both sides by 2)

After juggling for several minutes i.e., 2.5 minutes and [tex]1\frac{1}{3}[/tex] minutes (mixed fraction), the total number of bowling pins by clown is 37 pins

As per the question statement, a clown juggles 12 bowling for the first 2.5 minutes then he bump it up to an average of 18 bowling pins per minute for the last [tex]1\frac{1}{3}[/tex]  minute (Mixed Fraction form)

We are supposed to find the total number if pins by the clown.

Let's calculate the total time first that will be 2.5 minutes + [tex]1\frac{1}{3}[/tex] minutes

[tex]1\frac{1}{3} =\frac{3*1 +1}{3} =\frac{4}{3} =1.34[/tex] minutes.

Therefore total time = 3.84minutes

Given that he bumps it up to an average of 18 bowling pins per minute for the last [tex]1\frac{1}{3}[/tex]  minute so, the number of pins in the last  [tex]1\frac{1}{3}[/tex]  minute will be = [tex]18*1.34 = 24.12 = 25[/tex] (approx.)

So total number of bowling pins = [tex]12+25 = 37[/tex] pins

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The value of the functions f(6), f(- 10), f(0) are 9, 7 and 3 respectively.

A function can be defined as an expression, rule or law that shows the relationship between a dependent and an independent variable.

Given the function;

f(x) = |x+3|

To determine f(6)

Substitute the value of x as 6

We have;

f(6)  = | 6 + 3 |

f(6) = 9

To determine f(-10)

Substitute the value of x as - 10

We have;

f(-10) = | -10 + 3 |

f(-10) = | -7|

f(-10) = 7

To determine f(0)

Substitute the value of x as 0

We have;

f(0) = | 0 + 3|

f(0) = 3

Thus, the value of the functions f(6), f(- 10), f(0) are 9, 7 and 3 respectively.

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Answer: 207936 millimeters squared

Step-by-step explanation:

57 * 57 = 3249

3249 * 64 = 207936

Answer: 207936 millimeters^2

Step-by-step explanation: 57*57=3249

3249 64 times is 207936.

The cost of each hamburger is $8, the cost of each French fry is $5 while the cost of each Soda is $3.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the cost of hamburger, y represent the cost of french fries and z represent the cost of soda, hence:

x + y = 13   (1)

Also:

x + 2z = 14    (2)

And:

x + y + z = 16    (3)

From the three equations:

x = 8, y = 5, z = 3

The cost of each hamburger is $8, the cost of each French fry is $5 while the cost of each Soda is $3.

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Answer:

1728

Hope this helps :)

The turning point of the equation of the graph f(x) = |x - 4| is (4, 0)

The equation of the graph is given as

f(x) = |x - 4|

The above equation is an absolute value function

An absolute value function is represented as

f(x) = a|x - h| + k

Where the vertex is

Vertex = (h, k)

The vertex also represents the turning point of the absolute value function

From the given equation, we have

(h, k) = (4, 0)

Hence, the turning point of the graph is (4, 0)

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Part a: Resulting mixture: 92.2 milliliters.

Part b: Percentage of acid in the resulting mixture = 36.88%.

Part a: Find the both values from the given percentage;

225 millilitres of a solution contains is 39% acid.

39% of 225 = (39×225)/100 = 87.75 millilitres.

Now, 25 milliliters of a solution contains is 19% acid.

19% of 25 = (19×25)/100 = 4.75 millilitres.

Mixture solution = 87.75 + 4.75

Mixture solution = 92.2 milliliters of acid.

Part b: percentage of the resulting mixture is acid.

92.2 milliliters of the total 250 milliliters is acid.

= 92.2/250 × 100

= 36.88 %

Thus, 36.88% of the the resulting mixture contains acid.

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Answer:

The equation in slope-intercept form is: [tex]y=5x+32[/tex]

Step-by-step explanation:

To calculate the slope, [tex]m[/tex], we use the formula [tex]\frac{y_{2} -y_{1}}{x_{2}-x_{1} }[/tex] where [tex]y[/tex] are the [tex]y[/tex]-values of the points and [tex]x[/tex] are the [tex]x[/tex]-values.

Pugging our numbers into the formula, we get [tex]\frac{(-3)-12}{-7-(-4)}[/tex]. This simplifies to 5.

To calculate the [tex]y[/tex]-intercept, we first substitute one of our points into the formula. Substituting -4  and 12, we get [tex]12=5(-4)+b[/tex].

Then we can solve for [tex]b[/tex].

[tex]12=5(-4)+b[/tex]

[tex]12=-20+b[/tex]

[tex]32=b[/tex]

So, our slope is 32.

We can then plug these values into the slope-intercept form [tex]y=mx+b[/tex]

Answer:

area of the arrow is 36inches^2

Step-by-step explanation:

Area of rectangle= lw

10x3=30

Area of triangle = bh/2

3x4=12/2=6

30+6=36 inches^2

[tex]\cfrac{12}{16}\implies \cfrac{4\cdot 3}{4\cdot 4}\implies \cfrac{4}{4}\cdot \cfrac{3}{4}\implies 1\cdot \cfrac{3}{4}\implies \boxed{\cfrac{3}{4}}~\hfill \cfrac{8\cdot 3}{8\cdot 4}\implies \boxed{\cfrac{24}{32}}[/tex]

The INEFFICIENT point of production in the given graph is represented by Point A , the correct option is option (a).

The given graph is for skateboards vs Bikes .

We need to find the point representing the Inefficient Point of Production.

The Production Possibility Curve points are said to be Inefficient when the resources are not utilized to the fullest.

In the given Production Possibility Curve between Skateboards and Bikers the point A is the inefficient point of production .

Therefore , the Inefficient point of production in the given curve is represented by Point A , the correct option is option (a)

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The amount to  report for Plant Assets in the Classified Balance Sheet of the company is $24,600

What are plant assets?

Plant assets are long-term fixed assets used to manufacture or sell products and services for Adventure Travel. These assets are of tangible nature and of monetarily benefits to the company for more than one accounting year.

The only plant assets in this case is the office equipment bearing in mind that it has a contra entry, in other words, the $29,600 is the cost of the office equipment , we need to deduct the accumulated depreciation on it so as to determine its current book value

plant assets=$29,600-$5,000

plant assets=$24,600

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Answer:

Here's an answer to part of your question.

Step-by-step explanation:

The older the kids get, the less you have to change their diapers. Therefore, that is why the graph is going down

The area of the polygon is approximately 24.497 square units.

In accordance with the statement, we have a polygon with three vertices set on Cartesian plane, that is, a triangle. We need to find the side lengths first and later to calculate the area by Heron's formula. First, determine the lengths of each line segment by Pythagorean theorem:

JK = √[[4 - (- 3)]² + (4 - 4)²]

JK = 7

KL = √[(3 - 4)² + (- 3 - 4)²]

KL = √[(- 1)² + (- 7)²]

KL = 5√2

JL = √[[3 - (- 3)]² + (- 3 - 4)²]

JL = √85

Second, calculate the area of the triangle:

s = (JK + KL + JL) / 2

s = (7 + 5√2 + √85) / 2

s ≈ 11.645

A = √[s · (s - JK) · (s - KL) · (s - JL)]

A = √[11.645 · (11.645 - 7) · (11.645 - 5√2) · (11.645 - √85)]

A ≈ 24.497

The area of the polygon is approximately 24.497 square units.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$1024\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{half-yearly, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &3 \end{cases}[/tex]

[tex]A=1024\left(1+\frac{1}{2}\right)^{2\cdot 3} \implies A=1024(1.5)^6\implies A = 11664~\hfill \underset{earned~interest}{\stackrel{11664~~ - ~~1024}{10640}}[/tex]

The angle of depression of the meat from the top of the table is 40°

This situation makes a right-angle triangle with the height of table being the perpendicular to the right-angle triangle and the distance of meat from the foot of the table becomes the base of the imaginary right-angle triangle

to know the angle of depression of the meat from the top of the table

we need to find the ratio between the perpendicular and the base of the triangle to use trigonometry.

Tan  is the ratio of perpendicular and base of the triangle

which is = 96/114.4

          tan Ф=0.8392

To solve for Ф , a tan would move from the left-hand side to the right-hand side and would become tan inverse.

            Ф  = tan-1 0.8392

             Ф = 40°

 The correct question is a cat on a table 96cm views a piece of meat on the ground 114.4cm away from the foot of the table. find the angle of depression of the meat from the top of the table.

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The required radius and error in radius is 13.8 cm and ± 0.12cm

Given that,
A machinist is required to manufacture a circular metal disk with an area of 600cm².
(a) What radius produces such a disk is to be determined
(b) If the machinist is allowed an error tolerance of ±5cm2 in the area of the disk, how close to the ideal radius in part is to be determined.

The area of a circle is given by the pie times square of the radius.

Area of circle = πr^2

Here,
a) The given area of disk = 600 cm²
   πr² = 600
   r = √600/3.14
   r = 13.8 cm

b) an error tolerance of ± 5 cm² in the area of the disk,
So the percentage of error is 0.84%
Now, 0.84% of radius = 0.84 *13.8/100 = 0.12
The required error in radius will be ±0.12 cm

Similarly,
c) limx→a f(x) = L
Where a is the area of the disk and L is length, and f(x) is function of area.

Thus, the required radius and error in radius is 13.8 cm and ± 0.12cm.

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Part A  The quadratic expression in factored form is 2t(19 - 8t)

Part B The height of the soccer ball 1.25 seconds after Callie kicks it is 22.5 ft

Since Callie kicks a soccer ball from the ground. The height of the ball, in feet, above the ground t seconds after the ball is kicked can be represented by the expression 38t- 16t².

So, the expression is a quadratic expression, we have that h(t) = 38t- 16t².

To write the expression in factored form, we find the common factors of both terms and factor them out.

So,  h(t) = 38t- 16t²

= 2 × 19 × t - 2 × 8 × t × t

Factoring out 2 and t, we have

= 2 × t × (19 - 8 × t)

= 2t(19 - 8t)

So, the quadratic expression in factored form is 2t(19 - 8t)

Since the quadratic expression h(t) = 38t- 16t² represents the height of the ball above the ground in feet, to find the height of the ball after 1.25 second,we substitute t = 1.25 s into the expression.

So, h(t) = 38t- 16t²

h(1.25) = 38(1.25) - 16(1.25)²

h(1.25) = 47.5 - 16(1.5625)

h(1.25) = 47.5 - 25

h(1.25) = 22.5 ft

So, the height of the soccer ball 1.25 seconds after Callie kicks it is 22.5 ft

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The work in process(Job C) is $14,250

The finished goods(job B) is $23,000

The cost of goods sold(job A) is $31,500

What are work in process, finished goods and cost of goods sold in this case?

The work in process refers to the total costs incurred on Job C, since it was not completed at the end of the month, the finished goods refers to the costs incurred on job B which has been completed but not yet sold and cost of goods sold means the cost incurred on Job A which has been sold since it has been completed.

Job A:

Cost of job in process=$12,000

direct materials used=$2,000

direct labor=$10,000

number of direct labor hours=direct labor cost/ direct labor rate

number of direct labor hours=$10,000/$20=500 hours

Applied Manufacturing Overhead=labor hours*predetermined overhead rate per direct labor hour

Applied Manufacturing Overhead=500*$15=$7,500

cost of goods sold=$12,000+$2,000+$10,000+$7,500

cost of goods sold=$31,500

Job B:

Cost of job in process=$1,000

direct materials used=$8,000

direct labor=$8,000

number of direct labor hours=direct labor cost/ direct labor rate

number of direct labor hours=$8,000/$20=400 hours

Applied Manufacturing Overhead=labor hours*predetermined overhead rate per direct labor hour

Applied Manufacturing Overhead=400*$15=$6,000

finished goods=$1,000+$8,000+$8,000+$6,000

finished goods=$23,000

Job C:

Cost of job in process=$0

direct materials used=$9,000

direct labor=$3,000

number of direct labor hours=direct labor cost/ direct labor rate

number of direct labor hours=$3000/$20=150 hours

Applied Manufacturing Overhead=labor hours*predetermined overhead rate per direct labor hour

Applied Manufacturing Overhead=150*$15=$2,250

work in progress=$0+$9,000+$3,000+$2,250

work in progress=$14,250

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Answer:

h=sqrt2*5i, h=-sqrt 2*5i

Step-by-step explanation:

Answer:

DNE

No real solutions

Step-by-step explanation:

This Quadratic Equation: 2h² + 100 = 0

The quotient of the given problem using laws of exponents is; 6 * 10⁰

We want to express the quotient of the quantity 30 times ten raised to the negative twenty fourth power end quantity divided by the quantity 5 times ten raised to the negative twenty fourth power end quantity.

This is;

(30 * 10⁻²⁴)/(5 * 10⁻²⁴)

Now, we can break this down into like terms to get;

(30/5) * (10⁻²⁴/10⁻²⁴)

= 6 * 1

Now, 1 can also be written as;

10⁰ = 1

Thus, the solution of the given problem is; 6 * 10⁰

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[tex]76000\times1.08=\boxed{82,080}[/tex]

Answer:

82,080

Step-by-step explanation:

To increase a number by it's percentage, you must first extract what 8% of 76,000 is (6080). Then, you must add the original number to what is 8% of it, to get 82,080, and that, is the final answer.