Which expression is equivalent to 30 ÷ ( 3 + x)?

Answer:

slope = \(\frac{9}{4}\)

Step-by-step explanation:

Equation to find slope: \(\frac{y1-y2}{x1-x2}\)            (-3, 4) (-7, -5)

\(\frac{4+5}{-3+7}\) = \(\frac{9}{4}\)

To find the length of the original painting, we need to use the given information that the print is 5/8 the length of the original painting, and the length of the print is 35 cm.

To calculate the length of the original painting, we can set up a proportion:

Let x be the length of the original painting.

We can set up the following equation:

35 cm / x = 5/8

To solve for x, we can cross-multiply:

35 cm * 8 = 5 * x

280 cm = 5x

Dividing both sides of the equation by 5:

280 cm / 5 = x

x = 56 cm

Therefore, the length of the original painting is 56 cm.

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An interior decorator bought a print of a famous painting for a home he was decorating. the print had a length of 35 cm and was 5/8 the length of the original painting. The length of the original painting is 56 cm.

The length of the original painting can be found by multiplying the length of the print by the reciprocal of the fraction given.
The length of the print is 35 cm and it is 5/8 the length of the original painting, we can set up the following equation:
35 cm = (5/8) * length of the original painting

To find the length of the original painting, we need to isolate the variable on one side of the equation. To do this, we can multiply both sides of the equation by the reciprocal of the fraction (8/5):
35 cm * (8/5) = (5/8) * length of the original painting * (8/5)

After simplifying, we have:
56 cm = length of the original painting
Therefore, the length of the original painting is 56 cm.'

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In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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14  triangles with exactly two equal sides can be formed

The triangles will be isosceles as there have to be 2 equal sides.

The possible triangles are :

2 2 3      3 3 2        5 5 2       7 7 2         11  11  2

             3 3 5        5 5 3       7 7 3         11  11  3

                             5 5 7       7 7 5         11  11  5

                                            7 7 11       11  11  7

So 14   triangles are possible

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On simplifying the given algebraic expression, we get -

(x¹⁰y²z)⁴ = (x⁴⁰y⁸z⁴).

An algebraic expression is a combination of terms, both constants and variables. For example, we can write the algebraic expressions as -

2x + 3y + z

4x + 5

Given is the algebraic expression as -

(x¹⁰y²z)⁴

The given expression is -

(x¹⁰y²z)⁴

We can simplify the given expression as -

(x¹⁰y²z)⁴ = (x¹⁰⁽⁴⁾y²⁽⁴⁾z⁴)

(x¹⁰y²z)⁴ = (x¹⁰⁽⁴⁾y²⁽⁴⁾z⁴)

(x¹⁰y²z)⁴ = (x⁴⁰y⁸z⁴)

Therefore, on simplifying the given algebraic expression, we get -

(x¹⁰y²z)⁴ = (x⁴⁰y⁸z⁴).

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Daniel's method is incorrect, as the interquartile range is given by the difference between the third quartile and the first quartile.

The interquartile range of a data-set is by the difference of the 75th percentile(Q3) by the 25th percentile(Q1) of the data-set.

The quartiles are described as follows:

From this, we get that the quartiles are related to the median of the set, that is, neither is given by the highest and by the lowest values, hence the interquartile range is given by the difference between the third quartile and the first quartile.

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Answer: 10

Step-by-step explanation:

6-5 = 1

-2 x 1 = -2

-2 x -5 = 10

The correct answer is: III only. Variance investigation is typically based on a cost-benefit analysis.

Statement I is incorrect because the relative size of a variance, in comparison to other variances, can be important in understanding its significance.

Statement II is incorrect because variance investigation does not focus solely on unfavorable variances. Both favorable and unfavorable variances are considered during the investigation.

Statement III is true. Variance investigation is typically based on a cost-benefit analysis, where the potential benefits of investigating and addressing variances are weighed against the associated costs.

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Answer:

84

Step-by-step explanation:

7*[(9+8)-(12-7)]

= 7*[17-5]

= 7*12

= 84

Answer:

20

Step-by-step explanation:

Number of paperback books = 4

Percentage of total books that were paperbacks = 20%

Let total number of books = x

Hence,

20% of total books = paperback books

20% of x = 4

0.2 * x = 4

0.2x = 4

0.2x / 0.2 = 4 / 0.2

x = 20

Total number of books = 20

The amount of liters that is equivalent to 12 quarts is 11.37.

The unit of measurement is a term that make us to understand which of the  quantities that have been measured. Examples are kilogramms, meters, Coulomb's, Liters etc.

In the given question, we have;

1 quart = 0.25 gallon

12 quart = x

So that;

x = 12 * 0.25

  = 3

x = 3 gallons

Then,

1 gallon = 3.79 liters

3 gallons = y

y = 3*3.79 liters

  = 11.37

y = 11.37 liters

The amount of liters that is equivalent to 12 quarts is 11.37.

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The cross sectional area of the cargo trailer floor, which is a composite figure consisting of a square and an isosceles triangle, indicates that the volume of the inside of the trailer is about 3,952 ft³.

A composite figure is a figure comprising of two or more regular figures.

The possible cross section of the trailer, obtained from a similar question on the internet, includes a composite figure, which includes a rectangle and an isosceles triangle.

Please find attached the cross section of the Cargo Trailer Floor created with MS Word.

The dimensions of the rectangle are; Width = 6 ft, length = 10 ft

The dimensions of the triangle are; Base length 6 ft, leg length = 4 ft

Height of the triangular cross section = √(4² - (6/2)²) = √(7)

The cross sectional area of the trailer, A = 6 × 10 + (1/2) × 6 × √(7)

A = 60 + 3·√7

Volume of the trailer, V = Cross sectional area × Height

V = (60 + 3·√7) × 6.5 = 3900 + 19.5·√7

Volume of the trailer = (3,900 + 19.5·√(7)) ft³ ≈ 3952 ft³

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I will write out the procedure to draw the isosceles triangle;

- Using the straight edge, measure the length of the base and draw a straight line congruent to the base length.

- Measure the length of the legs.

- Using the compass, set the compass to the same length as the length of the legs.

- From each edge of the base line drawn, Use the compass (already set to the length of the legs) to draw an arc each at the top of the base line;

- Then join each edge of the base line to the point at which the two arcs meet.

- Then you'll have an isosceles triangle, with base and legs as shown above.

Answer:

f(g(x))=3x^2-30x+75

Step-by-step explanation:

We want to find the value of f(x) when x is equal to g(x)

So we can substitute the value of g(x) into the f(x) equation

f(g(x))= 3(5-x)^2

f(g(x))= 3(25-10x+x^2)

f(g(x))=3x^2-30x+75

Completely simplified version: 3(x-5)^2

Answer:

987 ft.

Step-by-step explanation:

We can solve this with an equation.

Since she has 5 rolls of 99 feet long blue streamer, then she has 5*99=495 feet of blue streamer

Since she has 9 rolls of 88 feet long blue green, then she has 9*88=792 feet of blue green

To find the total, we can add them up and get 495+792=987

Unit conversion is a way of converting some common units into another without changing their real value. The value of (3π/4) radian converted to a degree is 135°.

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimeter is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.

Since π radian is equal to 180°. Therefore, the value of (3π/4) radian is equal to,

1 radian = 180°/π

(3π/4) radian = (3π/4) × (180°/π) = 135°

Hence, the value of (3π/4) radian converted to a degree is 135°.

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Answer:

option 2

Step-by-step explanation:

Laplace transforms are an essential mathematical tool used to solve differential equations. These transforms transform differential equations to algebraic equations that can be solved easily.

To solve the differential equations given in the question, we will use Laplace transforms. So let's start:Solution:a) y" – y = t y(0) = 1, y'(0) = 1First, we take the Laplace transform of the given differential equation.L{y" - y} = L{ty}

Taking the Laplace transform of both sides gives:L{y"} - L{y} = L{ty}Using the formula, L{y"} = s²Y(s) - s*y(0) - y'(0), and L{y} = Y(s) then we get:s²Y(s) - s - 1 = (1/s²) + (1/s³)Rearranging the above equation, we get:Y(s) = [1/(s²*(s² + 1))] + [1/(s³*(s² + 1))]Now, we apply the inverse Laplace transform to find the solution.y(t) = (t/2)sin(t) + (cos(t)/2)

The solution of the differential equation y" – y = t, with initial conditions y(0) = 1, y'(0) = 1 is y(t) = (t/2)sin(t) + (cos(t)/2).

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Answer:

S=540

140+33+x+75+x+2x=540

173+x+75+x+2x=540

x+75+x+2x=367

x+x+2x=292

4x=292

x=73

2x=146

Answer: D) $221.93

Step-by-step explanation: that's the answer on edge.

The solution is, the minimum monthly payment is $221.93. Among the choices, the answer is D.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

Solving for the future values of the credit card balances:

1260(1 + 0.12/12)^24

= 1599.8656571502122308900(1 + 0.18/12)^24

= 1286.55253073612259711290(1 + 0.09/12)^24

= 1543.37345291648033351200(1 + 0.16/12)^24

= 1649.0625893406018547

Adding the future balances to obtain total bill:

1599.8656571502122308 + 1286.5525307361225971 + 1543.3734529164803335 + 1649.0625893406018547

= 6078.85

Solving for the annuity A (monthly payments for each account):

1599.87 = A [(((1 + 0.12/12)^24) - 1) / (0.12/12)] A = 59.31

1286.55 = A [(((1 + 0.18/12)^24) - 1) / (0.18/12)]A = 44.93

1543.37 = A [(((1 + 0.09/12)^24) - 1) / (0.09/12)]A = 58.93

1649.06 = A [(((1 + 0.16/12)^24) - 1) / (0.16/12)]A = 58.76

Adding the annuities together to obtain the minimum monthly payment:59.31 + 44.93 + 58.93 + 58.76 = 221.93

Therefore, the minimum monthly payment is $221.93. Among the choices, the answer is D.

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The indefinite integral of 9sec²(x)tan(x) dx is 9tan²(x)/2 + C, where C is the constant of integration.

The indefinite integral of 9sec²(x)tan(x) dx can be found using the substitution method.

Let u = tan(x), then du/dx = sec²(x)dx.

Rearranging to get like terms on one side, we have dx = du/sec²(x).

Substituting these values in the given integral, we get

∫9sec²(x)tan(x) dx = ∫9u du

Integrating the equation obtained above, we get

= 9(u²/2) + C

= 9tan²(x)/2 + C

Therefore, the antiderivative of 9sec²(x)tan(x) dx is equal to 9tan²(x)/2 + C, where C is the constant of integration, obtained using the substitution u=tan(x).

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Answer:

$82.50

Step-by-step explanation:

Given that the unit rate is $13.75 per hour,

1 hour -----> $13.75

6 hours -----> $13.75 x 6 = $82.50

The area of the triangle is 14 square cm

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

Base = 7 cm

Height = 4 cm

The area formula is given as

Area = 0.5 *  Base * Height

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

Area = 0.5 * 7 * 4

Evaluate

Area = 14

Hence, the area is 14 square cm

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Complete question

The expression 1/2bh gives the area of a triangle where b is the base of the triangle and h is the height of the triangle. What is the area of a triangle with a base of 7 cm and a height of 4 cm?

Answer:

it will be 12:00 when they get there

Answer:

12.00 pm

Step-by-step explanation:

3 hours after 9.00 am is 12.00 pm

The values are: -9, 7, -2, Undefined, Undefined, 8, Undefined, Undefined.

Let's match each expression with its corresponding value:

Expression: -9

Value: -9

Expression: 7

Value: 7

Expression: -2

Value: -2

Expression: Undefined

Value: Undefined

Expression: h(3.999)

Value: Undefined

Expression: h(4)

Value: 8

Expression: h(4.0001)

Value: Undefined

Expression: h(9)

Value: Undefined

Now let's explain the reasoning behind each value:

The expression -9 represents the number -9, so its value is -9.

Similarly, the expression 7 represents the number 7, so its value is 7.

The expression -2 represents the number -2, so its value is -2.

When an expression is labeled as "Undefined," it means that there is no specific value assigned or that it does not have a defined value.

For the expression h(3.999), its value is undefined because the function h(x) is not defined for the input 3.999.

The expression h(4) has a value of 8, indicating that when we input 4 into the function h(x), it returns 8.

Similarly, the expression h(4.0001) has an undefined value because the function h(x) is not defined for the input 4.0001.

Lastly, the expression h(9) also has an undefined value because the function h(x) is not defined for the input 9.

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Answer:The answer is very easy its..........

Step-by-step explanation:This is the step by step explanation ...............

Answer:

6h 45 min.

Step-by-step explanation:

\(\frac{4}{3} x=9\)

\(x=\frac{9}{\frac{4}{3} } =\frac{(9)(3)}{4} =\frac{27}{4} =6.75\)

= 6h 45m

Hope this helps.

The required solution of the expressions is (a) 7x⁵ + 13³ - 11x⁴ - x, (b) 5p² - 7p + 1.

Given that,
To arrange the like terms in columns and add them. - a) 2x³ - 7x⁴ + 7x⁵ and 11x³ - 4x⁴ – x b) -2p - 3p² and 1 - 5p + 8p²​.

The algebraic expression consists of constant and variable. eg x, y, z, etc.

Here,
(a)
= 2x³ - 7x⁴ + 7x⁵ + 11x³ - 4x⁴ – x
= 7x⁵ - 7x⁴  - 4x⁴+ 2x³ + 11x³– x
=  7x⁵ + 13³ - 11x⁴ - x,

(b)
=  -2p - 3p² +  1 - 5p + 8p²
= 1  -2p - 5p -3p² + 8p²
=  1 - 5p + 8p²​

Thus, the required solution of the expressions is (a) 7x⁵ + 13³ - 11x⁴ - x, (b) 5p² - 7p + 1.

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The required solutions to the given polynomials are 13x³- 11x⁴+ 7x⁵  – x and - 7p + 5p²​+ 1.

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers.

The polynomials are given in the question :

2x³ - 7x⁴ + 7x⁵, and 11x³ - 4x⁴ – x

-2p - 3p² and,1 - 5p + 8p²​

According to the question,

⇒ 2x³ - 7x⁴ + 7x⁵ + 11x³ - 4x⁴ – x

Rearrange the terms and apply the arithmetic operation,

⇒ 2x³ + 11x³- 7x⁴- 4x⁴ + 7x⁵  – x

⇒ 13x³- 11x⁴+ 7x⁵  – x

⇒ -2p - 3p² + 1 - 5p + 8p²​

Rearrange the terms and apply the arithmetic operation,

⇒ -2p - 5p - 3p²  + 8p²​+ 1

⇒ - 7p + 5p²​+ 1

Thus, the required solutions to the given polynomials are 13x³- 11x⁴+ 7x⁵  – x and - 7p + 5p²​+ 1.

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If a party gaining 25% of vote out of 100 seats in a pure proportional representation system would mean that the party got 25 seats.

We can compute it as,

100 × 25% = 25

A group of electoral systems used to choose candidates in multi-member electorates are referred to as proportional representation (PR). PR allows for the proportional representation of parties, organisations, and independent candidates in the selection of members of Parliament. Systems that use proportional representation have some advantages over the winner-takes-all principle.

The essence of such systems is that they provide mixed, balanced representation that reflects how votes are cast and that all votes cast, or nearly all votes cast, contribute to the outcome and are genuinely used to help elect someone. Due to the fact that seats are distributed based on the number of votes each party receives, few votes are "wasted," more parties can win seats in the legislature, and justice is prioritised.

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