CHALLENGE The sum of three consecutive terms of an arithmetic sequence is 6 . The product of the terms is -42. Find the terms.

Therefore, -3/5x + 4/5 is the expression that represents the outcome of applying the distributive principle to 1/5(3x+4).

An expression in mathematics is a grouping of digits, variables, and mathematical signs (like +, -, +, +, and =) that denote a mathematical relationship or computation. Expressions can be made up of a single number or variable or they can be intricate arrangements of different words and mathematical processes.

given

According to the distributive principle, a(b + c) = ab + ac. We can distribute the 1/5 to both terms inside the parentheses in order to apply the distributive principle to the expression 1/5(3x+4):

1/5(-3x + 4) = 1/5(-3x) + 1/5(4) (4)

If we simplify, we get:

1/5(-3x) + 1/5(4) = -3/5x + 4/5

Therefore, -3/5x + 4/5 is the expression that represents the outcome of applying the distributive principle to 1/5(3x+4).

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The exact solutions are x ≈ 0.590, x ≈ 2.552, and x ≈ 5.103.

The equation we are solving for exact solutions in the interval (0,2π) is Cos (2x) cos(x) - sin(2x)sin(x) = - √3 / 2.

First, let's use the double angle formula for cosine to simplify the equation:
cos(2x) = 1 - 2sin^2(x)
Substituting this into the equation, we get:
(1 - 2sin^2(x))cos(x) - sin(2x)sin(x) = - √3 / 2

Next, let's use the double angle formula for sine to simplify the equation further:
sin(2x) = 2sin(x)cos(x)
Substituting this into the equation, we get:
(1 - 2sin^2(x))cos(x) - 2sin^2(x)cos(x) = - √3 / 2

Combining like terms and rearranging, we get:
4sin^2(x)cos(x) - cos(x) = √3 / 2

Factoring out cos(x), we get:
cos(x)(4sin^2(x) - 1) = √3 / 2

Dividing both sides by (4sin^2(x) - 1), we get:
cos(x) = (√3 / 2) / (4sin^2(x) - 1)

Using the Pythagorean identity, sin^2(x) + cos^2(x) = 1, we can substitute for sin^2(x):
cos(x) = (√3 / 2) / (4(1 - cos^2(x)) - 1)

Multiplying both sides by (4(1 - cos^2(x)) - 1), we get:
cos(x)(4(1 - cos^2(x)) - 1) = √3 / 2

Expanding and rearranging, we get:
4cos^3(x) - 5cos(x) + √3 / 2 = 0

This is a cubic equation, which is difficult to solve algebraically. However, we can use a graphing calculator to find the approximate solutions. The solutions are x ≈ 0.590, x ≈ 2.552, and x ≈ 5.103.

Since all of these solutions are in the interval (0,2π), the exact solutions are x ≈ 0.590, x ≈ 2.552, and x ≈ 5.103.

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The percent of the clothe required to make doll outfit as per given cost price and selling price is equal to 59.91%.

Cost price of the material for one outfit = $9.38

Selling price of the outfit = $15

Selling price is greater than cost price

⇒Profit = Selling Price - Cost price

Substitute the value to get profit,

⇒ Profit = $15 - $9.38

⇒ Profit = $5.62

Percent Markup = (Profit / Cost price ) x 100

Substitute the value we get,

⇒Percent Markup = ($5.62 / $9.38) x 100

⇒Percent Markup = 59.9147%

⇒Percent Markup = 59.91

Therefore, the percent markup of the making doll outfit is approximately 59.91%.

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The above question is incomplete, the complete question is:

Keri is making a doll clothes for a holiday craft show. The wholesale cost of the materials for one outfit is $9.38. If she sells an outfit for $15, what is the percent of the markup?

Answer:

To find the answer / The result you get from adding numbers

Step-by-step explanation:

when you have a problem with two or more numbers being added your answer / result to the question would be called the Sum rather then an answer

Answer:

vertex = (2, - 10 )

Step-by-step explanation:

given a quadratic function in standard form

ax² + bx + c ( a ≠ 0 )

then the x- coordinate of the vertex is

[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]

x² - 4x - 6 ← is in standard form

with a = 1 and b = - 4 , then

[tex]x_{vertex}[/tex] = - [tex]\frac{-4}{2}[/tex] = 2

substitute x = 2 into the function for corresponding y- coordinate

2² - 4(2) - 6

= 4 - 8 - 6

= - 10

vertex = (2, - 10 )

Marco will need 2025 pounds of marble.

The ratio is defined as the relationship between two similar magnitudes in terms of the number of times the first includes the second.

Let's say that Marco mixes 1 bag of quartz with x pounds of marble. Then the ratio of quartz to marble in this bag is:

135 pounds quartz : x pounds marble

3 pounds quartz : x/45 pounds marble

Now we know that the ratio of quartz to marble in one bag is 3: (x/45). Since the ratio stays the same for every bag, we can set up a new proportion using the total amount of quartz and marble:

135 pounds quartz : x pounds marble = total pounds quartz : total pounds marble

We know the total pounds of quartz is 135. Let's call the total pounds of marble "m".

Substituting these values into the proportion, we get:

135 : x = 135 : m/45

To solve for x, we can cross-multiply and simplify:

135(m/45) = 135x

3m = 45x

m = 15x

So, Marco will need 15 times as many pounds of marble as he has of quartz, or:

m = 15 × 135 = 2025 pounds of marble.

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Answer:

Step-by-step explanation:

Make a model

Answer: The answer is 9/25. (36%)

Step-by-step explanation:

Since we know that 7/25 workers walk and 2/25 walk, we can do simple addition to find the total Percentage. This equals 9/25. To find the percentage, do the following:

Write 9/25 into a percentage: Divide

9 / 25 x (100%) = 36%

0.36 (100%) = 36%

Therefore 36% is your answer.

The formula for the nth term of the sequence is:

an = 1n^5 - 5n^4 + 9n^3 - 7n^2 + 3n + 3

To find the formula for the nth term of the sequence 4, 15, 44, 109, 228, 419,... using polynomial fitting, we need to follow the following steps:

1. Identify the degree of the polynomial: Since the sequence has 6 terms, the degree of the polynomial is 5.

2. Create a system of equations: Use the given terms of the sequence to create a system of equations with the polynomial coefficients as unknowns.

3. Solve the system of equations: Use any method to solve the system of equations to find the values of the polynomial coefficients.

4. Write the formula for the nth term: Use the values of the polynomial coefficients to write the formula for the nth term of the sequence.

The system of equations is:
a5n^5 + a4n^4 + a3n^3 + a2n^2 + a1n + a0 = an

Plugging in the values of the terms of the sequence, we get:
a5(1)^5 + a4(1)^4 + a3(1)^3 + a2(1)^2 + a1(1) + a0 = 4
a5(2)^5 + a4(2)^4 + a3(2)^3 + a2(2)^2 + a1(2) + a0 = 15
a5(3)^5 + a4(3)^4 + a3(3)^3 + a2(3)^2 + a1(3) + a0 = 44
a5(4)^5 + a4(4)^4 + a3(4)^3 + a2(4)^2 + a1(4) + a0 = 109
a5(5)^5 + a4(5)^4 + a3(5)^3 + a2(5)^2 + a1(5) + a0 = 228
a5(6)^5 + a4(6)^4 + a3(6)^3 + a2(6)^2 + a1(6) + a0 = 419

Solving this system of equations, we get:
a5 = 1
a4 = -5
a3 = 9
a2 = -7
a1 = 3
a0 = 3

Therefore, the formula for the nth term of the sequence is:
an = 1n^5 - 5n^4 + 9n^3 - 7n^2 + 3n + 3

So, the formula for the nth term of the sequence 4, 15, 44, 109, 228, 419,... using polynomial fitting is an = 1n^5 - 5n^4 + 9n^3 - 7n^2 + 3n + 3.

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d

2/3 is the same as 4/6 and 25/100 is the same as 1/4. -1.3 is transferred to the beginning of the equation

The scores of students were normally distributed.

a)Approximately 68% of the students scored between 40 and 62 .

b) The approximately 95% of the students scored between 29 and 73.

We have a nationwide test taken by high school students, Mean score, μ = 51

Standard deviations, s = 12

The scores were normally distributed, that is

X~ N(M= 51, s = 12)

Lower bound of confidence interval= 40

Upper bound of CI = 62

As we know according to empirical rule the percentage of data falls within one,two and three

standard deviations are 68%,95% and 99.7%

respectively.

a) Mean + standard deviations = 51 + 12 = 63 close to 62

= Upper bound

For 2 standard deviations, 51 + 2×12 = 75

Mean - standard deviations= 51 - 12 = 39 close to 40 = lower bound

For 2 standard deviations, 51 - 2×12 = 27

Thus, data falls within one standard deviation

that is under 68% and so, approximately 68% of students scored between 40 and 62.

b) Similarly, the empirical rule demonstrates that 95% of scores falls within two standard deviation.

mean - 2× standard deviations= 51 - 2× 11

= 51 - 22 = 29

mean + 2× standard deviations= 51 + 2×11

= 51 + 22 = 73

Therefore, approximately 95% of students scored

between 29 and 73.

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Complete question:

On a nationwide test taken by high school students, the mean score was 51 and the standard deviation was 11

The scores were normally distributed. Complete the following statements.

(a) Approximately ?% of the students scored between 40 and 62 .

(b) Approximately 95% of the students scored between ? and ?

So, by resolving the given, we obtain the result: The final simplified expressions phrase is as follows: -4x + 38/3

Mathematical operations include doubling, dividing, adding, and subtracting. A phrase is constructed as follows: Expression, monetary value, and mathematical operation Numbers, parameters, and functions make up a mathematical expression. It is possible to use words and terms in contrast. Every mathematical statement including variables, numbers, and a mathematical operation between them is called an expression, sometimes referred to as an algebraic expression. For example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

Let's start by condensing the first expression:

(2/3) (3x - 1) = 2x - 2/3

Now, we may reformat the phrase as follows:

(2x - 2/3) + 4x + 9 - 10x + 5

Mixing related concepts gives us:

-4x + 38/3

The final simplified phrase is as follows:

-4x + 38/3

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The expected value of consumption for each activity is $60 for Activity 1, $40 for Activity 2, and $50 for Activity 3.

The expected value of consumption for each activity can be calculated using the formula: E(x) = P(x) * X, where P(x) is the probability of an event occurring and X is the value of that event.

For Activity 1: Full time farming, the expected value of consumption is:
E(x) = (0.5 * $100) + (0.5 * $20) = $50 + $10 = $60

For Activity 2: Full time construction work, the expected value of consumption is:
E(x) = (1 * $40) = $40

For Activity 3: Part-time farming, the expected value of consumption is:
E(x) = (0.25 * $100) + (0.75 * $20) + (1 * $10) = $25 + $15 + $10 = $50

Therefore, the expected value of consumption for each activity is $60 for Activity 1, $40 for Activity 2, and $50 for Activity 3.

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Given:-

[tex] \: [/tex]

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps! :)

Answer: C

Step-by-step explanation:  8.95x2=17.9,  3/4x12.80=9.6,  17.9+9.6+5.85=33.35. 33.35+1.65=35

The correct answer is option C. Only Table 1 and Table 3 represent a function.

Each input value should be paired with only one output value, as stated in the definition of a function. Therefore, we must verify that each input value is paired with only one output value in order to determine which tables represent a function.

For each input value, Table 1 contains unique output values and unique input values. As a result, a function is represented by Table 1.

For the same input value (input 1), there are two distinct output values in Table 2. As a result, there is no function represented in Table 2.

For each input value, Table 3 contains unique output values and unique input values. As a result, a function is represented by Table 3.

For the same input value (input -2) in Table 4, there are two distinct output values. Subsequently, Table 4 doesn't address a capability.

Consequently, c is the correct response because Tables 1 and 3 only depict functions.

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Complete Question:

Which table(s) represent(s) a function? A. Table 1 only B. Table 2 only C. Tables 1 and 3 only D. Tables 1, 3, and 4 only

The rate of consumption of fuel of Matt's car is 37 miles per gallon (mpg).

Matt's car can travel a total distance of 555 miles.
The fuel required to travel the total distance is 15 gallons by Matt's car.
Hence the rate of consumption of fuel of Matt's car can be measured in mpg (miles per gallons) as = Total distance travelled / Total gallons required to travel that distance
(that is, total distance travelled divided by the total amount of gallons to travel the same)
Thus the mpg of Matt's car is = 555 miles / 15 gallons
= 37 miles per gallon
(that is 37 mpg)

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The distance across the river is approximately 597 feet.

The Law of Cosines is a formula that connects a non-right triangle's sides and angles. When the lengths of two sides and the angle between them, or the lengths of all three sides, are known, it is used to determine the length of a side or measure of an angle.

For the given figure:

Using trigonometry, we can find the length of PR as follows:

tan(43) = QR/PS

PS = QR/tan(43)

tan(68) = QR/RU

RU = QR/tan(68)

Since PS + RU = PR,

PR = QR/tan(43) + QR/tan(68)

Since triangle PQR is a right triangle, we can use the Pythagorean theorem:

QR² = PS² + RU²

Substituting the expressions for PS and RU gives:

QR² = (QR/tan(43))² + (QR/tan(68))²

QR ≈ 325.4 feet

Now we can substitute this value into the expression for PR to get:

PR ≈ 596.7 feet (rounded to the nearest foot)

Therefore, the distance across the river is approximately 597 feet.

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The complete question is:

Answer:821

Step-by-step explanation:773+32+7+9=821

The expressions ordered from least to greatest are: -2 < b < (a + c)

In maths, an expressiοn is a cοmbinatiοn οf numbers, variables, functiοns (such as additiοn, subtractiοn, multiplicatiοn οr divisiοn etc.)

Expressiοns can be thοught οf as similar tο phrases. In language, a phrase οn its οwn may include an actiοn, but it dοesn't make a cοmplete sentence.

According to the question:

-1 < a < 0

2 < b < 3

4 < c < 5

Now, we have the expression a + c

= (-1 < a < 0) + (4 < c < 5)

= (-1 + 4) < (a + c) < (0 + 5)

= 3 < (a + c) <  5

Thus, we have the expressions ordered from least to greatest are:

-2 < 2 < b < 3 < (a + c) <  5

-2 < b < (a + c)

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Complete question:

Answer: y = 5/6x

Step-by-step explanation:

It is a direct variation.

The vertex of the function is (-3, -20), the axis of symmetry is x = -3, the x-intercepts are (-8.44, 0) and (1.44, 0), the y-intercept is (-11), the range is (-∞, -20], and the domain is (-∞, ∞).

To find the vertex, axis of symmetry, x-intercept, y-intercept, range, and domain of the function f(x) = x² + 6x - 11, we can use the following formulas:

- Vertex: (-b/2a, f(-b/2a))

- Axis of symmetry: x = -b/2a

- X-intercept: Solve f(x) = 0

- Y-intercept: f(0)

- Range: All real numbers for a parabola that opens up or down

- Domain: All real numbers


Using these formulas, we can find the following:

- Vertex: (-3, -20)

- Axis of symmetry: x = -3

- X-intercept: (-8.44, 0) and (1.44, 0)

- Y-intercept: (-11)

- Range: (-∞, -20]

- Domain: (-∞, ∞)


Therefore, the vertex of the function is (-3, -20), the axis of symmetry is x = -3, the x-intercepts are (-8.44, 0) and (1.44, 0), the y-intercept is (-11), the range is (-∞, -20], and the domain is (-∞, ∞).

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The equation of the line in slope-intercept form is y = -x + 1

To write an equation for the line in point-slope form, we can use the formula y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is a point on the line.

Since the x-intercept and y-intercept are both 1, we know that the line passes through the points (1,0) and (0,1).

To find the slope of the line, we can use the formula m = (y2 - y1) / (x2 - x1). Plugging in the coordinates of the two points, we get:

m = (1 - 0) / (0 - 1) = -1

Now we can plug in the slope and one of the points into the point-slope form equation:

y - 0 = -1(x - 1)

Simplifying, we get:

y = -x + 1

This is the equation of the line in point-slope form.

To write the equation in slope-intercept form, we can use the formula y = mx + b, where m is the slope of the line and b is the y-intercept.

We already found the slope to be -1, and the y-intercept is given as 1. So we can plug these values into the slope-intercept form equation:

y = -1x + 1

Simplifying, we get:

y = -x + 1

This is the equation of the line in slope-intercept form.

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The exact value of cos(5π/12), using the cosine summation identity, is (√6 - √2)/4.

The exact value of cos(5π/12) can be found using the cosine sum identity, which is:

cos(a + b) = cosa · cosb - sina · sin b

In this case, we can rewrite 5π/12 as (π/4) + (π/6) and use the identity:

cos(5π/12) = cos[(π/4) + (π/6)] = cos(π/4) · cos (π/6) - sin(π/4) · sin (π/6)

Using the values of cos(π/4) = √2/2, cos(π/6) = √3/2, sin(π/4) = √2/2, and sin(π/6) = 1/2, we can plug them into the equation:

cos(5π/12) = (√2/2) · (√3/2) - (√2/2) · (1/2) = √6/4 - √2/4 = (√6 - √2)/4

Therefore, the exact value of cos(5π/12) is (√6 - √2)/4.

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Answer:

10 tonnes = 6 trucks, 5 tonnes = 2 trucks

Step-by-step explanation:

Total number of trucks = 8

Let number of trucks carrying 10 tonnes = x

then number of trucks carrying 5 tonnes = 8 - x

We can represent this situation as follows:

10x + 5(8 - x) = 70 tonnes

10x + 40 - 5x = 70

5x + 40 = 70

5x = 30

x = 6

Number of trucks with 10 tonnes capacity = 6

Number of trucks with 5 tonnes capacity = 2 (i.e; 8-x = 8-6)

Hope it helps.......

Answer:

36

Step-by-step explanation:

bbecause yes and because a put in my quiz and they put me a A

The value of x is approximately 2,04,582.80.

An expression is a mathematical phrase that can contain numbers, variables, operators, and functions. It can be a combination of terms and can include operations such as addition, subtraction, multiplication, division, and exponentiation.

Given,

Value of old car = 1,50,000

Price of new car = 6,50,000

Number of monthly installments = 20

Amount of each installment = 21,000

Rate of interest offered = 9% p.a.

Let x be the down payment amount.

The total amount to be paid by Madhu for the new car will be equal to the sum of the down payment and the total of 20 monthly installments.

Total amount = x + 20 × 21,000

Since the rate of interest is 9% p.a., the effective rate of interest for 20 months can be calculated as follows:

Effective rate of interest for 20 months = (1 + 0.09/12)^20 - 1 = 0.86118985

So, the total amount to be paid by Madhu for the new car can be expressed as follows:

Total amount = x + 20 × 21,000 × 0.86118985

According to the problem, Madhu exchanged her old car valued at 1,50,000 with the new car priced at 6,50,000. Therefore, the down payment x can be calculated as follows:

x + 20 × 21,000 × 0.86118985 = 6,50,000 - 1,50,00

x + 20 × 21,000 × 0.86118985 = 5,00,000

x= 5,00,000 - 20 × 21,000 × 0.86118985

x ≈ 2,04,582.80

Therefore, the value of x is approximately 2,04,582.80.

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The rational root theorem, as its name suggests, is used to find the rational solutions of a polynomial equation (or zeros or roots of a polynomial function). The solutions derived at the end of any polynomial equation are known as roots or zeros of polynomials.

A polynomial doesn't need to have rational zeros. But if it has rational roots, then they can be found by using the rational root theorem.

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