Simplify

to a single trig function with no fractions.

Answer:

  -5

Step-by-step explanation:

You want the minimum value of f(x) = x² +6x +4.

The line of symmetry of a quadratic function f(x) = ax² +bx +c is given by ...

  x = -b/(2a)

The line of symmetry passes through the extreme point. When a > 0, that extreme point is the minimum.

Here, we have a=1, b=6, so the line of symmetry is ...

  x = -6/(2·1) = -3

The extreme point (minimum) is ...

  f(-3) = (-3)² +6(-3) +4 = (-3 +6)(-3) +4 = -9 +4

  f(-3) = -5

The minimum value of f(x) is -5.

The radian measure for 315° is (7/4)π radians.

What exactly is a radian measure?

Radian measure is a unit of measurement for angles, where one radian is defined as the central angle subtended by an arc of a circle with a length equal to the radius of the circle. Therefore, to convert degrees to radians, we need to multiply the degree measure by pi/180.

Now,

To convert 315 degrees to radians, we can use the formula:

radians = degrees x π/180

So, we have:

radians = 315 x π/180

Simplifying this expression, we get:

radians = (7/4) x π

Therefore,

             315 degrees is equal to (7/4) π radians.

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Answer: 173 centimeters of ribbon left

Step-by-step explanation:

Antonio starts with 2 meters of ribbon, which is equal to 200 centimeters (since 1 meter = 100 centimeters). He cuts off 27 centimeters to decorate the gift, so he is left with:

200 - 27 = 173 centimeters

Therefore, Antonio has 173 centimeters of ribbon left.

Delia hikes [tex]\tfrac{137}{100}[/tex] in all her wοrk, we get this answer by adding his first day hike and next day hike.

Wοrk can be defined as tο achieve the purpοse, gοal οr result we use οur physical οr mental effοrt during the activity.

Their are mainly twο types οf wοrk οne is physical wοrk and οther is mental wοrk. Physical wοrk is sοmetime alsο refer as labοur wοrk and mental wοrk is usually denοtes as οffice wοrk.

Wοrk (W) = F * s

W = Wοrk, F = Fοrce And s = Displacement

Tοtal wοrk dοne by him = 7/10 + 67/100

[tex]\tfrac{137}{100}[/tex]

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Answer:

Let's assume Adrian worked for x hours. Then, Bryan worked for (x + 8) hours.

According to the problem, the total hours worked by both is 88, so we can set up the equation:

x + (x + 8) = 88

Simplifying the equation:

2x + 8 = 88

Subtracting 8 from both sides:

2x = 80

Dividing both sides by 2:

x = 40

So Adrian worked for 40 hours and Bryan worked for 48 hours (since Bryan worked 8 hours more than Adrian).

Answer:

Adrian: 40 hours

Bryan: 48 hours

Step-by-step explanation:

The height of the tower obtained from the 188 ft long tower's shadow, the 3.75 ft long pole's shadow, the 7 ft height of the pole, and the equivalent ratio of the corresponding sides of similar triangles is about 351 feet

Similar triangles are triangles that have the same shape but may have different sizes.

Height of the pole = 7 ft

Length of the shadow cast by the tower = 188 ft

Length of the shadow cast by the pole = 3.75 ft

The triangle formed by the length of the shadows of the tower and the pole the tower and the pole and the line of sight from the tip of the shadow to the top of the tower and the pole are similar triangles, therefore, the ratio of the corresponding sides are the same, which indicates;

[tex]\frac{3.75}{188} = \frac{7}{Height \ of \ the \ tower}[/tex]

Height of the tower × 3.75 = 7 × 188

The height of the tower = 7 × 188/3.75 ≈ 351

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Using the system of equations, we found that the amount to be invested in fund A is $180,000 and in fund B is $320,000.

What is meant by an equation?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. As we can balance this by deducting the right-side expression from both sides' expressions, this won't reduce the generality.

The amount in the IRA account = $500,000

Let the amount invested in fund A be x and fund B be y.

x + y = 500,000

The amount received annually for fund A = 0.052x

The amount received annually for fund B = 0.077y

This amount is given as:

0.052x + 0.077y = 34,000

Now we have a system of equations.

x + y = 500,000

0.052x + 0.077y = 34,000

Multiply the first equation by 0.052.

0.052x + 0.052y = 26,000

0.052x + 0.077y = 34,000

Subtracting,

-0.025y = -8000

y = 320,000

Then, x = 500,000 - y = 500,000 - 320,000 = 180,000

Therefore using the system of equations, we found that the amount to be invested in fund A is $180,000 and in fund B is $320,000.

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Answer:

First, let's find the fraction of people wearing green or red shorts:

1/4 + 1/6 = 3/12 + 2/12 = 5/12

This means that 5/12 of the people are wearing either green or red shorts. To find the fraction of people wearing blue shorts, we need to subtract this from 1 (since the three options are exhaustive):

1 - 5/12 = 7/12

So, 7/12 of the people are wearing blue shorts. To find out how many people this represents, we can multiply this fraction by the total number of people in the race:

7/12 x 24 = 14

Therefore, 14 people are wearing blue shorts.

Step-by-step explanation:

Answer:

To use a tape diagram, we can start by drawing a rectangle to represent the total number of people in the race. Then, we can divide it into four equal parts to represent the people wearing green shorts and into six equal parts to represent the people wearing red shorts.

Let's use the letter "B" to represent the number of people wearing blue shorts. We know that the total number of people is 24, so we can write:

4 parts + 6 parts + B parts = 24

Simplifying this equation, we get:

10 + B = 24

Subtracting 10 from both sides, we get:

B = 14

Therefore, 14 people are wearing blue shorts.

To double-check our answer, we can add up the number of people in each category:

4 parts out of 24 = 6 people wearing green shorts

6 parts out of 24 = 4 people wearing red shorts

B parts out of 24 = 14 people wearing blue shorts

6 + 4 + 14 = 24, which matches the total number of people in the race.

Answer: To subtract mixed numbers with different denominators, we need to convert them into like fractions first.

14 1/3 can be converted to an improper fraction as follows:

14 1/3 = (14 x 3 + 1) / 3 = 43/3

6 5/8 can be converted to an improper fraction as follows:

6 5/8 = (6 x 8 + 5) / 8 = 53/8

Now we can subtract the fractions:

43/3 - 53/8

To get a common denominator, we can multiply the denominators together: 3 x 8 = 24

43/3 x 8/8 = 344/24

53/8 x 3/3 = 159/24

Now we can subtract the numerators:

344/24 - 159/24 = 185/24

Therefore, 14 1/3 - 6 5/8 = 185/24 or 7 13/24 as a mixed number in simplest form.

Step-by-step explanation:

The simplified value of 14 1/3- 6 5/8 is 7 17/24.

Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.

To subtract 6 5/8 from 14 1/3, we need to have the same denominator.

Converting the mixed numbers to improper fractions, we get:

14 1/3 = 43/3

6 5/8 = 53/8

Now, we need to find a common denominator, which is 24.

Multiplying the numerator and denominator of 43/3 by 8 and 53/8 by 3, we get:

43/3 * 8/8 = 344/24

53/8 * 3/3 = 159/24

Now, we can subtract:

43/3 - 53/8 = (344/24) - (159/24) = 185/24

Therefore, 14 1/3 - 6 5/8 = 185/24 or 7 17/24 as a mixed number.

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Answer:

So the answer is 24.2

Step-by-step explanation:

Good luck to you!

according to the model, Marie's lowest time after 14 weeks of training will be 24.2 seconds.

What is a linear equation?

Based on the given linear model, we know that Marie's best 200 meter time (y) is a function of the number of weeks of training (x), and can be calculated using the equation:

y = -0.4x + 29.8

To find Marie's lowest time after 14 weeks, we simply need to substitute x = 14 into the equation and solve for y:

y = -0.4(14) + 29.8

y = -5.6 + 29.8

y = 24.2

Therefore, according to the model, Marie's lowest time after 14 weeks of training will be 24.2 seconds.

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Step-by-step explanation:

you can simply solve this question by simple division

Answer:

BE=15

Step-by-step explanation:

Since E is the center, BE=2x+1

And AC is 6x-12 with E being a midpoint.

Since AC is 2 segments and BE is only 1 then you multiply 2x+1 by 2 so that

you can find x. You multiply 2x+12 by 2 because E is the midpoint so that means ED is the same value as BE

6x-12=4x+2

BD=AC

6x-4x-12=2

2x=2+12

2x=14

x=7

BE= 2x+1

2(7)=14+1=15

Answer:

½(a+b)h

½(24+32)×18

504ft²

I might be wrong

The polynomial equation with the roots is P(x) = x^2 - 15x + 56

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

Roots: x = 8 and x = 7

Using the above as a guide, we have the following:

The equation can be represented as

P(x) = (x - root)

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

P(x) = (x - 8)(x - 7)

Evaluate the product

P(x) = x^2 - 8x - 7x + 56

This gives

P(x) = x^2 - 15x + 56

Hence, the equation is P(x) = x^2 - 15x + 56

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Answer:

Listed below.

Step-by-step explanation:

(Let y be the length of the room and x be the width of the room.)

Because the width of the room is 5 feet less than the length of the room, we have:

The area of the room can be solved by multiplying its length and width, so we have x × y or xy = 750.

Substituting x for y - 5 into this equation:

If we expand the left side of the equation, we get:

Subtracting 750 from both sides, we get:

The equation [tex]y^{2}[/tex] - 5y - 750 = 0 can be factored into:

Therefore, 3 equations you can use are:

Therefore , the solution of the given problem of speed comes out to be it will take 4 hours to travel the same distance at an average speed of 90 km/h.

We can determine something's speed by keeping a watch on it from a distance. The amount of distance an object can move in a specific amount of time depends on its speed. Velocity is calculated using the formula velocity = distance/time. The three most popular pace measurements are miles per hour (mile), kilometres per hour (kilometres), and metres for each second (m/s) (mph).

Here,

Applying the algorithm

Distance is determined by multiplying time and motion.

We can make the two equations equal because we know that the distance travelled in both scenarios is the same:

Distance = time + speed1

1 = time2 + speed2

where time1 is the first time (3 hours), speed1 is the first average speed (120 km/h), speed2 is the second average speed (90 km/h), and we're trying to determine time2.

Inputting the numbers provided yields:

Distance: 360 km at 120 km/h for three hours.

We can now determine the time2:

360 kilometres are equal to 90 kilometres per hour multiplied by two.

time2 = 360 km x 90 km/hr = 4 hours

Therefore, it will take 4 hours to travel the same distance at an average speed of 90 km/h.

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A balance sheet is a financial statement that presents a company's financial position at a specific point in time. It shows the company's assets, liabilities, and equity.

Here are the steps to compute a balance sheet:

List all the assets: Assets are what the company owns, and they can be classified as current assets or long-term assets. Current assets include cash, accounts receivable, inventory, and prepaid expenses. Long-term assets include property, plant, and equipment, investments, and intangible assets.

Calculate the total value of assets: Add up the value of all the assets listed in step 1.

List all the liabilities: Liabilities are what the company owes to others and can be classified as current liabilities or long-term liabilities. Current liabilities include accounts payable, short-term loans, and accrued expenses. Long-term liabilities include long-term loans and bonds.

Calculate the total value of liabilities: Add up the value of all the liabilities listed in step 3.

Calculate equity: Equity is the difference between the assets and liabilities. It can be calculated as Total Assets minus Total Liabilities.

List equity: Write down the equity value calculated in step 5.

Add up the total liabilities and equity: This should be equal to the total assets calculated in step 2.

The balance sheet formula is:

Assets = Liabilities + Equity

By following the above steps, you can compute a balance sheet for a company. It is important to note that the balance sheet is a snapshot of the company's financial position at a specific point in time and should be updated regularly.

P.S: An overview was given due to your incomplete information.

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Answer:

17,500

Step-by-step explanation:

The best hypothesis based on the given information is Option C: Megan will clear 5'6" on 80% or more of her jumps.

A hypothesis is an educated guess or tentative explanation for a phenomenon or observation that can be tested through further investigation and experimentation. It is a proposed explanation or prediction for an event or set of events that is based on limited evidence or observations, and which serves as the starting point for scientific inquiry.

Based on the given information, Megan cleared 5'6" for 80% of her jumps. To create a hypothesis for the probability of future jumps cleared at 5'6", we need to make an educated guess based on this data.

Option A, stating that Megan will clear 5'6" for 100% of her jumps, is too optimistic and doesn't take into account the possibility of error or difficulty in jumping.

Option B, stating that Megan will clear 5'4" for 100% of her jumps, is not relevant to the given information about Megan's performance at 5'6".

Option D, stating that Megan will clear 5'8" on 80% or more of her jumps, is also not supported by the given information and is too high of a goal for Megan to realistically achieve.

Therefore, the best hypothesis based on the given information is Option C: Megan will clear 5'6" on 80% or more of her jumps. This hypothesis is supported by the fact that Megan has already achieved this level of performance in the past, and it allows for the possibility of some variability or error in future jumps.

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The linear regression equation for the data given in the table is presented as follows:

y = 0.51x + 1.07.

To find the regression equation, which is also called called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are usually given in a scatter plot or in a table.

The points for the data-set in this problem are given as follows:

(4,2), (6, 5), (12, 8), (17,9).

Inserting these four points into a linear regression calculator, the linear regression equation for the data given in the table is presented as follows:

y = 0.51x + 1.07.

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The required answers are a) 6.5 m, b) Dimensions 8 m, 5 m c) square has the greater area.

(a) Let s be the length of a side of the square. The perimeter of a square is given by 4s. Since the piece of wire used to make the square has length 26 m, we have:

[tex]$\begin{align*}4s &= 26 \s &= \frac{26}{4} = 6.5 \text{ m}\end{align*}[/tex]

Therefore, the length of a side of the square is 6.5 m.

(b) Let l be the length of the rectangle. Then the width of the rectangle is l-3. The perimeter of a rectangle is given by 2(l+w). Since the piece of wire used to make the rectangle has length 26 m, we have:

[tex]$\begin{align*}2(l + (l-3)) &= 26 \2(2l-3) &= 26 \4l - 6 &= 26 \4l &= 32 \l &= 8 \text{ m}\end{align*}[/tex]

Therefore, the length of the rectangle is 8 m and its width is 8-3=5 m.

(c) The area of the square is given by [tex]$s^2$[/tex], which in this case is [tex]$6.5^2 = 42.25$[/tex] square meters. The area of the rectangle is given by lw, which in this case is [tex]$8\times5 = 40$[/tex] square meters. Therefore, the square has the greater area.

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Complete question;

A workman has two pieces of worse, each of length 26 m. One piece is to be bent into a square. The other piece is to be bent into a rectangle whose width is 3 m shorter than its length.

(a) What is the length of a side of the square?

(b) What are the dimensions of the rectangle?

(c) Which shape has the greater area?

Answer: 0.6

Step-by-step explanation:

3 2/5 + 0.6 = 4

a) The 8 in the number 24.387 is in the hundredths place, its value is 8/100 or 2/25.

b) One and three quarter million can be written in figures as 1,750,000.

c) 2/10 or 1/5.

d) 0.26 < 0.62 < 2.06 < 6.2

e) 13.4 > 13.390.33 = 1/38 = 2³

An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

a) The 8 in the number 24.387 is in the hundredths place.

Therefore, its value is 8/100 or 2/25.

b) One and three quarter million can be written in figures as 1,750,000.

c) The 2 in the number 48.52 is in the tenths place.

Therefore, its value is 2/10 or 1/5.

d) Ordering the numbers from smallest to largest:

0.26 < 0.62 < 2.06 < 6.2

e) Completing the statements using the symbols <, > or = :

13.4 > 13.390.33 = 1/38 = 2³

Hence, The answers to each question are:

a)  8/100 or 2/25.

b) 1,750,000.

c) 2/10 or 1/5.

d) 0.26 < 0.62 < 2.06 < 6.2

e) 13.4 > 13.390.33 = 1/38 = 2³

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The company's advanced degree holders make up 18% of the workforce.

A percentage, which is denoted by the number 100, is a proportion, fraction, or piece of a whole. The Roman phrase per centum, which meaning "by the 100" or "per one hundred," is where the term "percent" originates. A numerical value and the percentage symbol (%) can be used to express percentages.

Part A:

The following expression sums up the amount of company employees with advanced degrees:

0.40c(0.15) + 0.60c(0.20)

Explanation: First, we multiply the overall amount of workers (c) by the proportions of male and female employees, which are, respectively, 40% and 60%. The number of male workers (0.40c) is then multiplied by the percentage of men who have advanced degrees (15%), and the number for female employees (0.60c) is multiplied by the percentage of women who have advanced degrees (20%). In order to calculate the overall number of workers with advanced degrees, we must add these two numbers.

If we condense this phrase, we get:

0.06c + 0.12c = 0.18c

Part B:

The number of staff members with advanced degrees must be divided by the total amount of employees, and the result must be multiplied by 100% to determine the percentage of the business that holds advanced degrees:

(0.18c/c) × 100% = 18%

Therefore, 18% of the company has advanced degrees.

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Answer: To find (g∘f)(x), we need to first find the composite function g(f(x)):

g(f(x)) = g(2x - 2)

We can now substitute the expression for f(x) into g(x):

g(f(x)) = g(2x - 2) = 6(2x - 2)^2 - 3

Expanding the squared term, we get:

g(f(x)) = 6(4x^2 - 8x + 4) - 3

Simplifying and combining like terms, we get:

g(f(x)) = 24x^2 - 48x + 21

Therefore, (g∘f)(x) = 24x^2 - 48x + 21.

Step-by-step explanation:

Now we can add K² to k + I to get the final result: K² + k + I = (4 3) + (3 1) + (1 0) = (8 4) (8 15) (3 5).

A matrix is a rectangular array of numbers or other mathematical objects, such as symbols or expressions, arranged in rows and columns. Matrices are commonly used in mathematics, physics, engineering, computer science, and other fields to represent and manipulate data.

Given by the question.

To find the matrix K²+k+I, we need to first find the matrix K.

The matrix K is the given matrix:

K = (2 1)

(3 4)

To find K², we can simply multiply K by itself:

K² = K × K = (2 1) × (2 1) = (4 3)

(3 4) (8 15)

To find k + I, we need to add the identity matrix I to K:

k + I = K + I = (2 1) + (1 0) = (3 1)

(3 4) (0 1) (3 5)

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The subtraction of 3045 and 2572 by the column method has the result given as follows:

473.

When we subtract two amounts by the column method, we subtract digit by digit separately, hence:

3045

-2572

5 > 2, hence:

5 - 2 = 3.

4 is less than 7, and 0 is also less than 5, hence we must borrow from the last column, where 2 - 2 will be of zero, hence:

Hence the result of the subtraction is given as follows:

3045 - 2572 = 473.

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Answer:

1. 92 m²

2. 184 cm²

Step-by-step explanation:

1.

Look at the left triangle.

Imagine that the 8 m segment continues to the bottom, and you have a horizontal leg there.

The hypotenuse measures 15 m.

The vertical leg is 8 m + 4 m = 12 m.

a² + b² = c²

12² + b² = 225

b = 9

The horizontal leg is 12 m.

A = 2 × 12 m × 9 m / 2 - 4 m × 4 m

A = 92 m²

2.

Bottom rectangle: length = 20 cm; width = 7 cm

Upper trapezoid: bottom base = 20 cm - 13 cm = 7 cm; height = 15 cm - 7 cm = 8 cm; upper base = 4 cm

A = 20 cm × 7 cm + (1/2)(7 cm + 4 cm)(8 cm)

A = 184 cm²

The answer of the given question based on the constant of proportionality the answer is  constant of proportionality equal to 1.

Slope is  measure of  steepness of a line. It describes how much  vertical coordinate (y) changes for given change in  horizontal coordinate (x). In other words, it is  rate at which  line rises or falls as you move horizontally along it

To find the constant of proportionality between y and x, we need to calculate the slope of this line.

We can choose any two points on the line and use them to calculate the slope. Let's choose the points (2, 2) and (8, 8), which are the first and last points on the line. The slope of the line passing through these points is:

slope = (change in y)/(change in x) = (8 - 2)/(8 - 2) = 1

This means that for every increase of 1 in the x-coordinate, there is a corresponding increase of 1 in the y-coordinate. Therefore, the constant of proportionality between y and x is 1. We can write this as:

y = x

This means that y is directly proportional to x with a constant of proportionality equal to 1.

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