Homework: Section 6.1 Homework Given that sin 50°= 0.7660 tan 50° = 1.1918 cos 50° = 0.6428 cot 50°=0.8391 csc 50° = 1.3054 sec 50° = 1.5557 find the six function values of 40°. sin 40°= 0.642

Answer:

x = 8

Step-by-step explanation:

16 + 12x = 28 * 4

16 + 12x = 112

12x = 96

x = 8

hope this helps! <3

The largest possible range for G(x) is (-∞, 2) ∪ (2, ∞).

(a) Domain of F(x): (-∞, ∞)

   Range of F(x): [2, ∞)

(b) Domain of G(x): (-∞, 1/2) ∪ (1/2, ∞)

   Range of G(x): (-∞, 2) ∪ (2, ∞)

(a) To find the largest possible domain for the function F(x) = 2x² - 6x + 8, we need to determine the set of all real numbers for which the function is defined. Since F(x) is a polynomial, it is defined for all real numbers. Therefore, the largest possible domain of F(x) is (-∞, ∞).

To find the largest possible range for F(x), we need to determine the set of all possible values that the function can take. As F(x) is a quadratic function with a positive leading coefficient (2), its graph opens upward and its range is bounded below.

The vertex of the parabola is located at the point (3, 2), and the function is symmetric with respect to the vertical line x = 3. Therefore, the largest possible range for F(x) is [2, ∞).

(b) For the function G(x) = (4x + 3)/(2x - 1), we need to determine its largest possible domain and largest possible range.

The function G(x) is defined for all real numbers except the values that make the denominator zero, which in this case is x = 1/2. Therefore, the largest possible domain of G(x) is (-∞, 1/2) ∪ (1/2, ∞).

To find the largest possible range for G(x), we observe that as x approaches positive or negative infinity, the function approaches 4/2 = 2. Therefore, the largest possible range for G(x) is (-∞, 2) ∪ (2, ∞).

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Answer:

  (a)  T'(-3, 6) and V'(0, 3)

Step-by-step explanation:

You want the coordinates of T'V' after segment TV is dilated by a factor of 3/4 about the origin. Points are T(-4, 8) and V(0, 4).

The coordinates of the dilated segment can be found using the given transformation:

  (x, y) ⇒ (3/4x, 3/4y)

  T(-4, 8) ⇒ T'(3/4(-4), 3/4(8)) = T'(-3, 6)

  V(0, 4) ⇒ V'(3/4(0), 3/4(4)) = V'(0, 3)

The coordinates of segment T'V' are T'(-3, 6) and V'(0, 3).

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In algebra, RHS and LHS refer to the right-hand side and left-hand side of an equation, respectively. The RHS represents the expression or value on the right side of the equal sign, while the LHS represents the expression or value on the left side of the equal sign.

In an equation, both the RHS and LHS are separated by an equal sign (=), indicating that the two sides are equal to each other. The equation expresses a relationship or equality between the two sides, and it can be solved to find the value of the variables involved.

To determine which part of an equation is the RHS and which is the LHS, you can look at the position of the equal sign. The expression or value to the left of the equal sign is the LHS, and the expression or value to the right of the equal sign is the RHS.

In conclusion, RHS and LHS are terms used in algebra to refer to the right-hand side and left-hand side of an equation, respectively. The RHS represents the expression or value on the right side of the equal sign, while the LHS represents the expression or value on the left side of the equal sign. The equal sign in an equation separates the RHS and LHS, indicating that the two sides are equal to each other.

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Q9.1: To justify the proposal, we need to compare the benefits of the road expansion (in terms of reduced travel time) with its costs. The value of time represents the monetary value individuals place on their time spent traveling. In this case, the value of time is $1.5 per minute.

First, let's calculate the reduction in travel time resulting from the road expansion. We compare the two road performance functions: t1​ = 30 + 6×10−6q and t2​ = 20 + 3×10−6q. By subtracting t2​ from t1​, we can determine the time savings: Δt = t1​ - t2​ = (30 + 6×10−6q) - (20 + 3×10−6q)    = 10 + 3×10−6q Next, we multiply the time savings by the number of trips (q) to obtain the total time savings: Total Time Savings = Δt × q = (10 + 3×10−6q) × q Now, we can determine the monetary value of the time savings by multiplying the total time savings by the value of time ($1.5 per minute): Monetary Value of Time Savings = Total Time Savings × Value of Time                             

= (10 + 3×10−6q) × q × $1.5  If the monetary value of the time savings exceeds the construction cost of $9.6×107, then the proposal is justified. Q9.2: To determine the construction cost at which the proposal becomes justified, we set the monetary value of the time savings equal to the construction cost and solve for q: (10 + 3×10−6q) × q × $1.5 = $9.6×107 By solving this equation for q, we can find the corresponding construction cost at which the proposal becomes justified.

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Step-by-step explanation:

\( = 4x - 8y + 6 {x}^{2} + 3x - 5y\)

\( = 6 {x}^{2} + (4x + 3x) + ( - 8y - 5y)\)

\( = 6 {x}^{2} + 7x - 13y\)

The answer is B.

Answer:

b.) 6x² + 7x - 13y

Explanation:

Given Expression

= 4x - 8y + 6x² + 3x - 5y

collect like terms

= 6x² + 4x + 3x -8y - 5y

combine similar terms

= 6x² + 7x - 13y

Answer:

A triangle where the angles in the inside are 100 degrees, 40 degrees, and 40 degrees.

Step-by-step explanation:

The angles inside a triangle always add up to 180 degrees

And an obtuse triangle is a triangle whose biggest angle is bigger than 90 degrees

100 is biggest angle out of the three angles we're using to make the triangle and 100 is bigger than 90.

Adding the three angles we're using also makes 180 (100 + 40 + 40)

Answer:

b

Step-by-step explanation:

The congruency statement TS ≅ HG is true. So the required statement is option c.

According to the congruency theorem, two triangles are considered congruent when they have identical sides and they have the same size angles. This can be proved by conditions such as side-angle-side (SAS), side-side-side (SSS), angle-side-ange (ASA), and right angle-hypotenuse-one another side (RHS). Their orientation need not have to be the same also.

Even though the triangle is rotated, the corresponding part of ΔGHJ and ΔSTR are congruent. So the sides ST = GH, RT= HJ, and SR= GJ. And the angles ∠S= ∠G, ∠T=∠H, and ∠R=∠J. From the given, options, option TS ≅ HG is correct.

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The complete question is -

Triangle GHJ is rotated 90° about point X, resulting in triangle STR. Which congruency statement is true?

A. TR ≅ GJ

B. ∠S ≅ ∠H

C. TS ≅ HG

D. ∠R ≅ ∠G

The type directions that lie in the (110) plane are Crystal planes are equivalent planes that represent a group of crystal planes with a common set of atomic indexes.

Crystallographers use Miller indices to identify crystallographic planes. A crystal is a three-dimensional structure with a repeating pattern of atoms or ions.In a crystal, planes of atoms, ions, or molecules are stacked in a consistent, repeating pattern. Miller indices are a mathematical way of representing these crystal planes.

Miller indices are the inverses of the fractional intercepts of a crystal plane on the three axes of a Cartesian coordinate system.Let us now determine which of the type directions lie in the (110) plane.[101] is not in the (110) plane because it has an x-intercept of 1, a y-intercept of 0, and a z-intercept of 1. So, this direction does not lie in the (110) plane.[110] is in the (110) plane since it has an x-intercept of 1, a y-intercept of 1, and a z-intercept of 0.

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The slope of the new road is zero.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take points from the Graph (5, 0) and (5, 4).

Slope of a line = m = tanθ

where θ is the angle made by the line with the x−axis.

For a line parallel to y−axis ,θ= π/2.

​

∴m = tan π/2 = undefined

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

An horizontal line now has zero slope.

The new road has a zero slope as a result.

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Answer:

I have included a screenshot of my test. It shows I got it wrong but has the correct answer as well. Good luck I hope my mistakes help someone.

Step-by-step explanation:

The area of the rectangular picture frame that is 5/6 feet long and \(1\frac{2}{3}\) feet wide is  \(1\frac{7}{18}\) ft²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, Jackie bought a rectangular picture frame that is 5/6 feet long and \(1\frac{2}{3}\) feet wide.

We need to find its area,

We know that, the area of the rectangle = length × width

Here,

Length = 5/6 ft

Width =  \(1\frac{2}{3}\) ft

Area =  \(1\frac{2}{3}\)  × 5/6

= 5/3 × 5/6

= 25/18

= \(1\frac{7}{18}\) ft²

Hence, the area of the rectangular picture frame that is 5/6 feet long and \(1\frac{2}{3}\) feet wide is  \(1\frac{7}{18}\) ft²

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Yes, when multiplying an inequality by a negative, the inequality sign must be flipped.

This is because the negative number changes the direction of the inequality. For example, if the inequality is x > 4, and we multiply both sides by -2, the inequality becomes -2x < -8. The left side is now less than the right side, so the inequality sign must be changed to <. Mathematically, this can be shown as follows:

Let x > 4

Multiply both sides by -2:

-2x > -8

Flip the inequality sign:

-2x < -8

Therefore, when multiplying an inequality by a negative number, the inequality sign must be flipped.

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Answer:

4(3r-1)

Step-by-step explanation:

GCF is the highest number that divides exactly into two or more numbers. In this case, it would be 4 because it's the largest number that both 12 and 4 divide into.

Answer: b. The sample should be chosen at random so that it is fair.

Step-by-step explanation:

One of the most important things when selecting a sample is that the sample must be totally random if the sample is not random (for example, selecting only the youngest people in a group or things like that) there is a high probability that the sample will be biassed towards something, so the study may not be really accurate for all the population.

The correct option is b. The sample should be chosen at random so that it is fair.

In summary, the difference between the total number of customers and the total number of business cards is 109,500.

If we examine the pattern established in the initial days, we observe that the number of customers increases by 5 each day, starting from 0. Simultaneously, the number of business cards left increases by 3 more than the previous day's count. To determine the total number of customers over the course of a year, we can sum the arithmetic series, with the first term as 5, the common difference as 5, and the number of terms as 365. This yields a sum of 66,725 customers.

Next, we need to calculate the total number of business cards left. Using the same approach, we have a first term of 3, a common difference of 3, and 364 terms (since no business cards were left on the first day). The sum of this arithmetic series is 66,220 business cards.

Finally, to find the difference between the total number of customers and business cards, we subtract the sum of business cards from the sum of customers: 66,725 - 66,220 = 505. Therefore, the difference between the total number of customers and business cards is 505.

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Answer

y = 32

Step-by-step explanation:

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

0.3y+0.4(25−y)=6.8

Step 1: Simplify both sides of the equation.

0.3y+0.4(25−y)=6.8

0.3y+(0.4)(25)+(0.4)(−\(\frac{-0.1y}{-0.1} =\frac{-3.2}{-0.1}\)y)=6.8(Distribute)

0.3y+10+−0.4y=6.8

(0.3y+−0.4y)+(10)=6.8(Combine Like Terms)

−0.1y+10=6.8

−0.1y+10=6.8

Step 2: Subtract 10 from both sides.

−0.1y+10−10=6.8−10

−0.1y=−3.2

Step 3: Divide both sides by -0.1.

-0.1y/-0.1=-3.2/-0.1

y=32

I hope this helps?

(a) Yes, there is a smallest real number a for which x^26 is big-O of ax. To find this value, we can use the limit definition of big-O notation.

We want to find a value of a such that x^26 is less than or equal to ax multiplied by some constant C, for all x greater than some value N. Mathematically, we can write this as:

x^26 <= Cax, for all x >= N

Dividing both sides by x and taking the limit as x approaches infinity, we get:

lim x->inf (x^25 / a) <= C

This limit exists only if a is greater than zero, so let's assume that. Then we can simplify the left-hand side of the inequality as:

lim x->inf x^25 / a = inf

So for any value of C, we can always find a value of N such that x^26 is less than or equal to ax multiplied by C, for all x greater than or equal to N. Therefore, we can say that x^26 is big-O of ax, for any positive real number a, and there is no smallest such value of a.

(b) No, there is no smallest integer number a for which x^26 is big-O of ax. The proof is similar to part (a), but we need to show that for any positive integer a, there exists a constant C such that x^26 is not less than or equal to ax multiplied by C, for infinitely many values of x.

To do this, we can choose x to be a power of 2, say x = 2^k. Then we have:

x^26 = (2^k)^26 = 2^(26k)

ax = a * 2^k

So we want to find a value of a and a constant C such that:

2^(26k) > Ca * 2^k, for infinitely many values of k

Dividing both sides by 2^k, we get:

2^(25k) > Ca, for infinitely many values of k

But this is true for any value of a greater than 2^(25), since 2^(25k) grows faster than Ca for large enough values of k. Therefore, for any integer value of a greater than 2^(25), there exist infinitely many values of k for which x^26 is not less than or equal to ax multiplied by some constant C. Hence, x^26 is not big-O of ax for any integer value of a less than or equal to 2^(25), and there is no smallest such value of a.

(a) No, there isn't a smallest real number 'a' for which x^26x is big-O of ax. This is because x^26x has a higher growth rate than ax for any real number 'a'. As 'x' becomes larger, the term x^26x will always grow faster than ax, no matter the value of 'a'.

(b) Yes, there is a smallest integer number 'a' for which x^26x is big-O of ax. The smallest integer 'a' would be 1, because if we let 'a' be any integer smaller than 1, ax will have a lower growth rate than x^26x. When 'a' is equal to 1, we have x^26x = O(x), which means x^26x grows at most as fast as x, and there's no smaller integer 'a' for which this is true.

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Answer:

Step-by-step explanation:

You want the measure of the third angle in a triangle in which two of the angles are 108° and 33°. You also want the measure of x where consecutive exterior angles at a transversal are (2x -15) and (3x +5).

The sum of angles in a triangle is 180°, so the measure of the third can be found by subtracting the other two from 180°:

  x = 180° -108° -33° = 39°

The missing angle measure is 39°.

The two marked angles are "consecutive exterior angles" so have a sum of 180°. This can be used to write an equation.

  (2x -15) +(3x +5) = 180

  5x -10 = 180 . . . . . . . . . . . simplify

  x -2 = 36 . . . . . . . . . . . divide by 5

  x = 38 . . . . . . . . . . . add 2

__

Additional comment

The two angles are 2(38)-15 = 61°, and 3(38)+5 = 119°. They total 180°.

There are a number of relationships involving angles in various geometries. It is helpful to remember them, or at least keep a handy list.

Answer:

16+5w/4

Step-by-step explanation:

The answer is 143.90. We used the formula for the standard error of the mean to find the expected value of the sample mean, then added 1.5 standard deviations to that value to find the answer.

To begin, we can use the formula for the standard error of the mean to calculate the expected value of the sample mean. The formula is as follows:

standard error of the mean = standard deviation / √(sample size)

In this case, the standard deviation is 8 minutes and the sample size is 40, so we can plug those values into the formula:

standard error of the mean = 8 / √(40)
standard error of the mean = 1.2649

Next, we can use the formula for the mean of the means to find the expected value of the sample mean:
mean of the means = average

In this case, the average is given as 142 minutes, so the mean of the means is also 142 minutes.

Now we can find the value that is 1.5 standard deviations above the expected value of the sample mean:

1.5 standard deviations = 1.5 * standard error of the mean
1.5 standard deviations = 1.5 * 1.2649
1.5 standard deviations = 1.8974

Finally, we add this value to the mean of the means to find the answer:

\(\bar{X} + 1.5\; standard \; deviations = 142 + 1.8974\)

\(\bar{X} + 1.5 \;standard \;deviations = 143.8974\)

Rounding to 2 decimal places, the answer is 143.90.

In summary, we used the formula for the standard error of the mean to find the expected value of the sample mean, then added 1.5 standard deviations to that value to find the answer. This calculation helps us understand the range of values we might expect to see in a sample of runners in this category.

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Answer:

d.) 21

Explanation:

Rules:

Solve:

\(\rightarrow \sf \dfrac{4|a|}{2} + |a-3|\)

[insert a = -6]

\(\sf\rightarrow \dfrac{4|-6|}{2} + |-6-3|\)

[simplify the following]

\(\sf\rightarrow \dfrac{4(6)}{2} + 9\)

\(\sf\rightarrow 12 + 9\)

\(\sf\rightarrow 21\)

If P(t) is the size of a population at time t , the differential equation describes linear growth in the size of the population is \(\frac{dP}{dt}=200\)

The differential equation is is an equation that contains one or more functions with its derivatives. The derivatives of the function define the rate of change of a function at a point.

dy/dx = f(x)

Here “x” is an independent variable and “y” is a dependent variable

According to the question,

Size of population at t time = P(t)

Also given ,The differential equations have a linear growth in the size of the population.

So, The degree of the variable must be one. And the equation of the population will be quadratic.

Therefore , dP/dt = 200 tells us the rate change of population with respect to time.

A derivative of linear function is constant .

Hence , option B is correct.

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Lily, the cheer team's captain, is putting together a performance for a tournament. A routine may be no less than 3 minutes in length and no more than 5 minutes in total. For which the two solutions are the shortest and longest permitted lengths, write an absolute value.

The absolute value for 3 is 3 .

The absolute value for 5 is 5.

The two solutions are the shortest and longest permitted lengths, The absolute value |2x−5|+|2x−3|=2

Absolute value is the non-negative value of a real number x, independent of its sign, is its absolute value (or modulus), | x |.

For example, 5 has an absolute value of 5, and -5 has a value of 5. Another way to think about a number's absolute value is as its distance from zero on the real number line. In addition, the distance between two real numbers is the absolute value of their difference.

Given that,

A routine may be no less than 3 minutes in length and no more than 5 minutes in total.

By absolute value equation

we can get 2x−5|+|2x−3|=m

By solving we get 2 m values they are,

m={-8,2}

Here, -8 we can take but the answer will be in decimal soo we take 2.

|2x−5|+|2x−3|=2

We get

\(|4x-8|=2\\|x-2|=1\\|x|=3\\\)

If we take 2x =y

|y−5|+|y−3|=2

\(|2y-8|=2\\|y-4|=1\\|y|=5\)

Therefore,

The absolute value for 3 is 3 .

The absolute value for 5 is 5.

The two solutions are the shortest and longest permitted lengths, The absolute value |2x−5|+|2x−3|=2.

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Answer:

2025+18=2043

Step-by-step explanation:

Answer:

118

Step-by-step explanation:

4x^2 + 3y

4(5^2) + 3(6)

4 * 25 + 18

100 + 18

118

The orthogonal decomposition of v with respect to w is v = (-4/10, -4/10, 6/10) + (22/10, -16/10, 9/10) = (18/5, -24/5, 15/5) = (18/5, -24/5, 3).

To find the orthogonal decomposition of v with respect to the subspace w, we need to find a vector w in w and a vector u in w⊥ such that v = w + u.

Let's begin by finding a basis for the subspace w. We can do this by setting up the augmented matrix [w | 0] and row reducing:

[−1 −1 0 | 0]

[3 4 1 | 0]

Row reducing gives us:

[1 1/3 0 | 0]

[0 0 1 | 0]

So a basis for the subspace w is {(-1, -1, 0), (0, 0, 1)}. We can use the Gram-Schmidt process to find an orthonormal basis for w, but for simplicity, let's just choose (0, 0, 1) as our basis vector w.

To find u, we need to project v onto w⊥, which is the subspace spanned by the vectors orthogonal to w.

Since we only have one basis vector for w, we can find a basis for w⊥ by finding a vector orthogonal to w. Let's choose (1, -1, 0) as our basis vector for w⊥. Then we can compute:

proj_w(v) = ((v ⋅ w)/(w ⋅ w)) w = (-4/10, -4/10, 6/10)

u = v - proj_w(v) = (22/10, -16/10, 9/10)

Therefore, the orthogonal decomposition of v with respect to w is v = (-4/10, -4/10, 6/10) + (22/10, -16/10, 9/10) = (18/5, -24/5, 15/5) = (18/5, -24/5, 3).

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Answer:

x=-8, y=-1

Step-by-step explanation:

i aint in middle school no more so im not sure what operation ur doing, but this is my best guess.

Answer:

x=-8

Step-by-step explanation:

4(1/2x+7)=12

Divide each side by 4

4/4(1/2x+7)=12/4

(1/2x+7)=3

Subtract 7 from each side

1/2x+7-7=3-7

1/2x = -4

Multiply each side by 2

1/2x*2 = -4*2

x = -8

Answer:

-8

Step-by-step explanation:

Divide both sides by 4 which will give you 1/2x+7=3

Then multipy both sides by 2 which will then give you x+14=16

Then move the constant = x=6-14

6-14 is -8 which will give you x=-8

Therefore , the solution of the given problem of average comes out to be the average price of a pizza in 2000 was about $9 (or half of $18).

An organised collection's median value is the precise value that makes up the collection's mean. In this case, the ratio between the lowest and highest 50% of the data is a normal but rather probability measure. When finding the middle and mode, a variety of algorithms can be applied in order to identify any unusual or even amounts of values.

Here,

By dividing 72 by the interest rate, we can calculate how many years it will take an investment to double in value at a specific interest rate. This is known as the law of 72. In this instance

With an inflation rate of 3.25 percent, it takes roughly how many years for the price of a pizza to double as a result of inflation:

72 / 3.25 = 22.15 years

In light of this, we can calculate that a pizza cost $9 (half of $18) roughly 22 years ago, which corresponds to the following year:

2022 - 22 ≈ 2000

As a result of inflation running at an average of 3.25% for many years, the average price of a pizza in 2000 was about $9 (or half of $18).

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