How can you write and
solve equations involving rational numbers?

Answer:

C. -2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Pre-Calculus

Calculus

Step-by-step explanation:

Step 1: Define

g(x) = cot(x)

g'(π/4) is x = π/4

Step 2: Differentiate

Step 3: Evaluate

A, b and c can do a piece of work in 24, 30 and 40 days respectively. the work is completed in 13 days.

Let's calculate the work done by each person per day:

A completes 1/24 of the work per day.

B completes 1/30 of the work per day.

C completes 1/40 of the work per day.

Let's assume the total work is represented by "W".

When all three, A, B, and C, work together, their combined work rate per day is:

1/24 + 1/30 + 1/40 = (5 + 4 + 3) / 120 = 12/120 = 1/10

This means that when all three work together, they complete 1/10 of the total work per day.

Now, let's calculate the number of days it takes for them to complete the work. Let's represent this number of days by "D".

Since C leaves 4 days before the completion of the work, the remaining work is 1 - 1/10 = 9/10.

We can set up the equation:

(D - 4) * (1/10) = 9/10

Simplifying the equation:

D - 4 = 9

D = 9 + 4

D = 13

Therefore, the work is completed in 13 days.

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Answer:

3200

Step-by-step explanation:

Answer:

84 km

Step-by-step explanation:

you times 7 by 4 and get 28 then you times 3 by 28 and get 84 km

Solution

Given a triangle XYZ on the graph

The coordinates of points X, Y and Z are

To find the approximate length of the sides, we apply the formula to find the distance, d, between two points which is

To find the approximate length of side XY, substitute the coordinates of points X and Y into the formula to find the distance, d, between two points

Hence, the approximate length of side XY is 3.16 units (option b)

The distance traveled in the first 5.2 seconds when the speed dropped from the rest as v(t) = 9.8t is equal to 132.496 meters.

'v' is the speed of the object in meter per second

't' is the time in seconds.

Speed dropped from rest 'v(t) = 9.8t '

Distance traveled in the first 5.2 seconds is equal to

= \(\int_{0}^{5.2}\)9.8t dt

= ( 9.8 / 2 )t² \(|_{0}^{5.2}\)

Substitute the lower and upper limit to get the required distance we have,

= 4.9 [ ( 5.2)² - 0² ]

= 4.9 × 27.04

= 132.496 meters

Therefore, the distance traveled for the given first 5.2 seconds is equal to 132.496 meters.

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The above question is incomplete, the complete question is:

Free fall the speed v of an object dropped from rest is given by v(t)=9.8t where v is meters per second and time 't' is in seconds.

(a) Express the distance traveled in the first 5.2 seconds as an integral.

The shoe seller sells about 110 shoes of size 40 daily.

To find the wages of the person who sells shoes, we need additional information. The given information does not provide any direct relationship between the number of pairs of shoes sold and the wages of the person. Please provide more details or clarify the information to help determine the wages of the person.

Regarding the shoe seller's order from the wholesaler, we can calculate the number of shoes he orders of a specific size based on the given information. Here's how:

The shoe seller sells 100 pairs of shoes every day on average, and out of those, 55 pairs are of size 40.

Since a pair consists of two shoes, we can calculate the total number of shoes sold of size 40 as follows:

Number of shoes sold of size 40 = 55 pairs x 2 = 110 shoes.

As a result, the shoe store sells roughly 110 pairs of size 40 shoes each day.

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In Coralbank $ 1,359,468.19 and In Bank of Munich $ 1,240,088.97

The fee you pay to borrow money or the fee you charge to lend money is called interest. The most common way to represent interest is as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.

Given:

Coralbank is providing him an interest rate of 3% on the first $500,000 he invests with them and 1% on whatever else he invests beyond that point.

So, After 15 years

First, convert R as a percent to r as a decimal

r = R/100

r = 3/100

r = 0.03 rate per year,

Then solve the equation for A

A = P\((1 + r/n)^{nt\)

A = 500,000.00\((1 + 0.03/1)^{(1)(15)\)

A = 500,000.00\((1 + 0.03)^{(15)\)

A = $778,983.71

and, for Another $500,000

A = P\((1 + r/n)^{nt\)

A = 500,000.00 \((1 + 0.00/1)^{(1)(15)\)

A = 500,000.00 \((1 + 0.01/1)^{(1)(15)\)

A = $580,484.48

Total he Invests= $ 1,359,468.19

and, Bank of Munich is willing to pay him an interest rate of 2% on up to $250,000 of his money, and 1.25% on everything beyond that point.

Then solve the equation for A

r = R/100

r = 2/100

r = 0.02 rate per year,

Then solve the equation for A

A = P\((1 + r/n)^{nt\)

A = 250,000.00\((1 + 0.02/1)^{(1)(15)\)

A = 250,000.00 \((1 + 0.02)^{(15)\)

A = $336,467.08

and, for Another $750,000 .

A = P\((1 + r/n)^{nt\)

A = 750,000.00\((1 + 0.0125/1)^{(1)(15)\)

A = 750,000.00 \((1 + 0.0125)^{(15)\)

A = $903,621.89

Total he Invests= $ 1,240,088.97

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The difference between the price of an electric razor in 1983 and the cost of an electric razor when the cpi is 207, to the nearest cent is given by: Option D: $6.88

The consumer price index is the new cost of market basket in terms of percentage of old cost of market basket.

Then, we have:

\(CPI_t = \dfrac{C_t}{C_0} \times 100\)

For this case, we're given that:

Let the base price of the razor in some base period be \(C_0\)  

Then, for year 1983, we get:
\(CPI_t = \dfrac{C_t}{C_0} \times 100\\\\185= \dfrac{57.81}{C_0} \times 100\\\\C_0 \approx 31.248 \: \text{(in dollars)}\)

Now for the year when CPI is 207, let the price of th razor be $x, then we get:

\(CPI_t = \dfrac{C_t}{C_0} \times 100\\\\207 \approx \dfrac{x}{31.248} \times 100\\\\x \approx 64.683 \: \text{(in dollars)}\)

The difference between the two prices is:

\(d \approx 64.683 - 57.81 = 6.87 \approx 6.88\: \text{(in dollars)}\)

Thus, the difference between the price of an electric razor in 1983 and the cost of an electric razor when the cpi is 207, to the nearest cent is given by: Option D: $6.88

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Answer:

D

Step-by-step explanation:

Good fiction keeps the audience guessing about what is going to happen next or what a solution may be. An author adds several elements in the text to do this.

First and foremost, suspense plays a crucial role. By creating a sense of uncertainty and tension, the author keeps readers on the edge of their seats, eagerly turning pages to discover what comes next. Suspense can be built through various techniques, such as foreshadowing, unexpected plot twists, and cliffhangers at the end of chapters or sections.

Another essential element is the effective use of red herrings. These are misleading clues or events that divert readers' attention from the true course of the story or the real solution to a problem. Red herrings add complexity and intrigue, forcing readers to question their assumptions and consider multiple possibilities.

Furthermore, well-developed and unpredictable characters contribute to the mystery and suspense. Complex characters with hidden motivations, conflicting loyalties, and enigmatic personalities keep readers guessing about their true intentions and actions. Unforeseen character revelations and transformations can also add layers of uncertainty.

Intricate and multi-layered plots are another key aspect. A well-crafted plot intertwines various storylines, subplots, and conflicts, creating a tapestry of possibilities. By introducing unexpected events, unresolved conflicts, and ambiguous outcomes, the author maintains an aura of unpredictability, leaving readers speculating about the eventual resolution.

Additionally, skillful pacing is crucial. By controlling the flow of information, alternating between moments of tension and relief, and strategically revealing or concealing crucial details, the author can manipulate the readers' expectations and keep them guessing about what lies ahead.

Finally, effective storytelling techniques such as vivid descriptions, immersive world-building, and evocative language further enhance the suspense and keep the audience engaged. By crafting a rich and immersive narrative, the author creates an atmosphere of intrigue, where readers are constantly seeking answers and eagerly anticipating the next revelation.

In summary, to keep the audience guessing about what is going to happen next or what a solution may be, an author incorporates elements such as suspense, red herrings, unpredictable characters, intricate plots, skillful pacing, and compelling storytelling techniques. These tools work together to create a sense of anticipation, curiosity, and engagement, making the reading experience enjoyable and enthralling for the audience.

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Answer:

1.54034×10^5

Step-by-step explanation:

Solution,

As we have,

⇒2SinACosB=Sin(A+B)+Sin(A-B)

Now,

\(2sin7\alpha .cos2\alpha =sin9\alpha +sin5\alpha \\\\LHS=2sin7\alpha .cos2\alpha \\\\LHS=sin(7\alpha +2\alpha )+sin (7\alpha -2\alpha )\\\\LHS=sin9\alpha +sin5\alpha\)

Hence, LHS=RHS

Based on the normal model N(100,15) describing IQ scores, we can use the standard normal distribution to answer these questions. To find the percentage of people with IQs over 80, we need to calculate the Z-score for 80: Z = (80-100)/15 = -1.33. Using a standard normal distribution table, we find that the area to the right of Z = -1.33 is 0.0918, which means about 9.18% of people have IQs over 80.

To find the percentage of people with IQs under 90, we calculate the Z-score for 90: Z = (90-100)/15 = -0.67. Using the same table, we find that the area to the left of Z = -0.67 is 0.2514, which means about 25.14% of people have IQs under 90.

To find the percentage of people with IQs between 112 and 123, we need to calculate the Z-scores for 112 and 123: Z1 = (112-100)/15 = 0.80 and Z2 = (123-100)/15 = 1.53. Using the table, we find the area to the left of Z1 is 0.7881 and the area to the left of Z2 is 0.9370. Therefore, the percentage of people with IQs between 112 and 123 is approximately 14.89%.

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Answer:-1

Step-by-step explanation:

Answer: -6

Step-by-step explanation:

the line pass through (-3,-6)

To solve the matrix equation [3x y-x] = [3 1][t + 1/2z t-z] [7/2 3], we can equate the corresponding elements on both sides of the equation. This gives us the following system of equations:

3x = 3(t + 1/2z)

y - x = t - z

7/2x = 7/2(t + 1/2z) + 3(t - z)

Simplifying each equation, we have:

3x = 3t + (3/2)z

y - x = t - z

7x/2 = (7/2)t + (7/4)z + 3t - 3z

From the first equation, we can solve for x in terms of t and z as:

x = t + (1/2)z

Substituting this into the second equation, we get:

y - (t + (1/2)z) = t - z

y - t - (1/2)z = t - z

y = 2t - (1/2)z

Finally, substituting the expressions for x and y into the third equation, we have:

7(t + (1/2)z)/2 = (7/2)t + (7/4)z + 3t - 3z

7t/2 + (7/4)z = (7/2)t + (7/4)z + 3t - 3z

Simplifying and canceling terms, we find:

0 = 7t/2 + 3t

0 = (17t)/2

Therefore, t must be equal to 0 for the equation to hold.

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Answer:

39.8°

Step-by-step explanation:

We know slope is rise over run. That would mean our right triangle would have a horizontal leg of 6 and a vertical leg of 5. From there we use tan∅ to help solve ∅:

tan∅ = 5/6

∅ = tan⁻¹(5/6)

∅ = 39.8056

Answer:

(d)

because there is only y value, hence no point on x-axis therefore no x-intercept

The sum of the interior angles of a 22-sided polygon is (d) 3600 degrees

From the question, we have the following parameters that can be used in our computation:

Shape = 22-sided polygon

Parameter to calculate = the sum of the interior angles

The sum of the interior angles is calculated using the following angle formula

The sum of the interior angles = ( n − 2 ) × 180 ∘ where is the number of sides

In this case

n = 22

Substitute the known values in the above equation, so, we have the following representation

The sum of the interior angles = (22 − 2) × 180∘

Evaluate

The sum of the interior angles = 3600∘

Hence, the angle is (d) 3600 degrees

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The value of x in the given triangle is 10.

Thales Theorem States that,

If a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.

Given is triangle, a line parallel to its base is cutting the other two sides, we need to find the value of x,

So, by Thales Theorem :-

x+5 / x = 6 / 4

x+5 / x = 3 / 2

2x + 10 = 3x

x = 10

Hence, the value of x in the given triangle is 10.

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1) Estimate value of the product of 2/3 and 0.55 is, 2/3.

2) The fraction part is, 55 / 100

3) The product of the two numbers is, 11/30

We have to given that,

Estimate the product of 2/3 and 0.55.

And, Convert the decimal 0.55 to a fraction.

And, The product of the two numbers.

Now,

Estimate the product of 2/3 and 0.55,

So, we can round 0.55 to the nearest whole number, which is 1.

Then, multiply 2/3 by 1 to get an estimate of the product.

so, The correct answer is 2/3.

Now, we can convert the decimal 0.55 to a fraction,

= 0.55

= 55/100

= 11/20

Thus,  The correct answer is, 55/100.

And,  the product of 2/3 and 0.55,

= 2/3 x 55/100

= 110/300

= 11/30.

Hence, The correct answer is, 110/300 or 11/30

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Length of PS= 3.99 units

Length of QS=2.08 units

Area of triangle PQR=14.12units²

Answer:

-------------------

The volume of a pyramid is 1/3 of the product of the base area and height.

Find the area of the base:

The base is the square, so each side is the square root of the base area:

The perimeter of the base is:

Answer: 48 inches

Step-by-step explanation:

480*3=1440

1440/10=144

each side: 12

12*4=48 inches

Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

Answer: -2.2

Step-by-step explanation:

-10 is the most possible that can be divided by 5, resulting in -2.

The leftover 1 is divided by 5, resulting in .2.

The decimal ends up being -2.2.

Answer:

-2.2 or -1.2

Step-by-step explanation:

When you want to write a decimal as a fraction, you simply divide the numerator with the denominator. So when you divide -11 by five that would be a -2.2. Or if it is -1 1/5 the answer would be -1.2. I cant really tell what that number is.

Answer:

Original Area : 48 square inches

Step-by-step explanation:

Let's say that the width of this rectangle is x, and the length of this rectangular is y. Remember that they are even consecutive integers as well, so let's make the length 2 greater than the width.

x = width,

x + 2 = length

And remember that the width decreases by 3 inches, to result in a rectangle of area 24. So the width will be x - 3, and the area will be (x - 3)(x + 2). Therefore we have the quadratic equation (x - 3)(x + 2) = 24, in which we can solve for x and y to determine the area of the original rectangle.

Step # 1 : Expand the expression (x - 3)(x + 2),

x² - x - 6 = 24

Step # 2 : Simplify and factor the expression x² - x - 6

x² - x - 30 = 0 ⇒ (x + 5)(x - 6) = 0

Step # 3 : Apply the Zero Factor Principle

x + 5 = 0, and x - 6 = 0

x = - 5, x = 6

Now remember that the width can't be negative, so it will be 6 inches long. That would make the length 6 + 2 = 8 inches. The area of the original rectangular will be 6 \(*\) 8 = 48 square inches.

Answer:

  48 square units

Step-by-step explanation:

Let L and W represent the length and width of the rectangle.

  L = W +2 . . . . . . assuming the length is more than the width

  L(W -3) = 24 . . . . the area after the reduction in width

__

  (W +2)(W -3) = 24

So, we're looking for factors of 24 that differ by 5. We know that 24=8·3, so we have ...

  W+2 = 8

  W = 6 . . . . . . . matches W-3=3, also

Then the length is ...

  L = W+2 = 8

and the area of the original rectangle is ...

  A = LW = (8 inches)(6 inches) = 48 square inches

Answer:

Step-by-step explanation:

24-hour time has 12 hours added for p.m. The time is written as HHMM, a 4-digit number of "hours." (The two right-most digits are minutes.)

1) 7:25 p.m.   ⇒   1925 hours

2) 9:10 a.m.   ⇒   0910 hours

__

12-hour time starts at midnight, 12:00 a.m. That corresponds to 0000 hours in 24-hour time. Anything beyond 1200 hours is afternoon, p.m.

1) 0010 hours   ⇒   12:10 a.m.

2) 1800 hours   ⇒   6:00 p.m.

Answer I blive is is 8

Step-by-step explanation: