The expression 6(5x^2+3x+5) -4(7x^2+3x+4) equals?

Answer:

Quadrant V

Step-by-step explanation:

A co-ordinate graph only has 4 quadrants!

Answer:

Step-by-step explanation:

Statement                     Reason

PR ≅ TR                        Given

<PQR≅<TSR                 Given

<PRQ≅<TRS                Vertical Angles Theorem

PQR=TSR                      SAS  Theorem   (Side-Angle-Side)

Answer:

5.14 mi/h

Step-by-step explanation:

( sorry if wrong )

The revenue function is the sum of the profit and cost functions

The average rate of the revenue is 55.67

The revenue function is given as:

\(R(x) = 56x - 0.01x^2\)

The interval is given as:

(a,b) =(11,22)

The average rate of change over the interval (a,b) is calculated as:

\(R'(x) =\frac{R(b) - R(a)}{b -a}\)

This gives

\(R'(x) =\frac{R(22) - R(11)}{22 -11}\)

\(R'(x) =\frac{R(22) - R(11)}{11}\)

Calculate R(22) and R(11)

\(R(22) = 56*22 - 0.01*22^2\)

\(R(22) = 1227.16\)

\(R(11) = 56*11 - 0.01*11^2\)

\(R(11) = 614.79\)

So, we have:

\(R'(x) =\frac{R(22) - R(11)}{11}\)

\(R'(x) =\frac{1227.16 - 614.79}{11}\)

\(R'(x) =\frac{612.37}{11}\)

Evaluate the quotient

\(R'(x) =55.67\)

Hence, the average rate of the revenue is 55.67

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Answer:

25

Step-by-step explanation:

The first 5 terms of the sequence is given by A = { -4.8 , 1.92 , -0.768 , 0.3072 , -0.12288 }

Given data ,

Let the geometric sequence be represented as A

Now , the value of A is

A = 12 ( -2/5 )ⁿ

On simplifying , we get

when n = 1

A₁ = 12 ( -2/5 ) = -4.8

A₂ = 12 ( -2/5 )²

A₂ = 12 ( 4/25 ) = 1.92

A₃ = 12 ( -2/5 )³

A₃ = -12 ( 8/125 ) = -0.768

A₄ = 12 ( -2/5 )⁴

A₄ = 12 ( 16 / 625 ) = 0.3072

A₅ = 12 ( -2/5 )⁵

A₅ = -12 ( 32 / 3,125 ) = -0.12288

Hence , the geometric sequence is solved

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Answer:

55.25

Step-by-step explanation:

So, all you gotta do is get rid of the decimal, times them both, then add the decimal back into it, and how you do that is you see how many numbers are behind a decimal point in the first place, in this case, it's two (8.5, 6.5) and you got your answer!

Hope this helps! <D

Answer:

Disclaimer: I'm not sure because the numbers are too blurry. If my numbers don't match yours, just replace them in my work and recalculate them.

1) not tangent

2) tangent

3) not tangent

Step-by-step explanation:

If they are tangent, the triangles formed will be right triangles.

Check using the Pythagorean theorem:

1) 18² = 14.4² + 11.7²

324 = 207.36 + 136.89

324 ≠344.25       not tangent  

2) 7.5² = 4.5² + 6²

56.25 = 20.25 + 36

56.25 = 56.25     tangent

3) 20² = 12² + 12²

400 = 144 + 144

400 ≠ 288        not tangent

The percentage change will be 25%.

According to its definition, a percentage is any number relative to 100. It is shown with the sign %. "Out of 100" is what the percentage means. Consider dividing any quantity or item into 100 identical bits.

Using these estimates, we can calculate the per cent decrease in the time spent driving as follows:

The initial time spent driving was 0.5 hours.

The final time spent driving was 0.375 hours.

The decrease in time spent driving was 0.5 - 0.375 = 0.125 hours.

The per cent decrease in time spent driving is,

P = (0.125/0.5) x  100%

P  = 25%.

Therefore, we can estimate that the per cent decrease in the time Jack spent driving his car is 25%.

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The difference between Walter and Denise's gas usage is 0.83 - 0.75 = 0.08 gallons. Therefore, Walter uses 0.08 gallons more gas than Denise.

Number is a mathematical object used to count, measure, and label. It is an abstract concept that describes a quantity or amount. Numbers can be represented in various forms, including words, symbols, and numerals. Numbers are also used to measure distance, time, and weight, as well as to express amounts of money. Numbers play a vital role in many areas of life, from science and engineering to economics and finance.

To calculate how much more gas Walter uses than Denise, we need to find the difference between the amount of gas each person uses.

Denise uses 3/4 of a gallon of gas, so 3/4 of a gallon is equal to 0.75 gallons. Walter uses 5/6 of a gallon of gas, so 5/6 of a gallon is equal to 0.83 gallons.

The difference between Walter and Denise's gas usage is 0.83 - 0.75 = 0.08 gallons. Therefore, Walter uses 0.08 gallons more gas than Denise.

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Answer:

Linear equation: y=mx+b

The answer is: y=2x+1  (equation 1)

Hope that helps!!

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The equation with an infinite number of solutions is 12x-x+8+3x=14x+8.

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

12x-x+8+3x=14x+8

The equation so that it has infinitely many solution is 12x-x+8+3x=14x+8.

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Answer:

i-09 vhcgcdg hdc

Step-by-step explanation:

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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The percentage decrease will be equal to 99.30 %.

The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.

Given that:-

The percentage decrease will be calculated as:-

Percentage decrease = \(\dfrac{2.88 - 0.02}{2.88}\)

Percentage decrease = 0.9930 = 99.30%

Therefore the percentage decrease will be equal to 99.30 %.

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Answer:

140°

Step-by-step explanation:

Since we know that a circle is 360 degrees, and we are given three angles, we can subtract what we know from 360 to get ∠PTQ:

360 = 120 + 60 + 40 + ∠PTQ

360 = 220 + ∠PTQ

-220   -220

140 = ∠PTQ

∠PTQ = 140°

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Answer:

C = 2 x 4.5 x π

Step-by-step explanation:

The equation to find the circumference of the circle is

C = 2π · r

r = 4.5 in

Looking at the options, the answer is C = 2 x 4.5 x π

Answer:

Below

Step-by-step explanation:

radius = 4.5       diameter = 2 x 4.5  in

the circumference of a circle is given by the formula   p * d

  substitute in the underlined equation for 'diameter')

          circumference = 2 * 4.5 * pi    inches

Answer:

Step-by-step explanation:

So far, what you are given is     y= -3x + b

So the point is used to define b

x = 5

y = 2

2 = 5*-3 + b

2 = -15 + b             Add 15 to both sides

2 + 15 = b

b = 17

Answer

y = -3x + 17

(b2+4b+4)(-b+3)

(b2)(-b)+(b2)(3)+(4b)(-b)+(4b)(3)+(4)(-b)+(4)(3)

-b3+3b2-4b2+12b-4b+12

-b3-b2+8b+1

Answer:

76

Step-by-step explanation:

Flute players- 5

Trumpet player- 3 times flute players -15

Trombone players- 8 fewer than trumpet-7

Drummers- 11 more than trombone-18

Clarinet- 2 times flute- 10

Tuba-4 fewer than trombone-3

French horn- 3 more than trombone- 10

Band director- 1

Assistant-1

Volunteers- 6

5+15+7+18+10+3+10+1+1+6=76

The correct option is (a) ŷ = -1.34x+21.5 , that is the best model to fit the scatter plot.

A scatter plot (or scatter chart, scatter graph) uses dots to represent values for two(2) different numeric variables. The position of each dot on horizontal and vertical axis indicates values for an individual data point.

The model of the equation best for the plot is,

ŷ = -1.34x+21.5

At point (1,20),

ŷ  = -1.34x+21.5

20 = (-1.34 ×  1) + 21.5

20 ≈ 20.15

At point (3,19),

ŷ = -1.34x+21.5

19 = (-1.34 × 3) + 21.5

19 ≈17.45

At point (5,15),

ŷ = -1.34x+21.5

15 = (-1.34 × 5) + 21.5

15 ≈ 14.75

The model ŷ = -1.34x+21.5   is giving the best estimation.

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The polynomial function is  \(f(x) = x^3+(\sqrt3-3)x^2+(2-3\sqrt3)x+2\sqrt3\).

The standard polynomial is given by:

f(x) = a(x-p)(x-q)(x-r) ...

Where a is the leading coefficient and p and q are the zeros.

Here We are given that the zeros are x = 1,2,and −√3.

Now leading Coefficient a = 1, p=1 , q=2 and r=−√3

Then the function is,

=> f(x) = 1(x-1)(x-2)(x-(−√3))

=> f(x)=(x-1)(x-2)(x+√3)

=> f(x)=\((x^2-2x-x+2)(x+\sqrt3)\)

=> \(f(x)=x^2-3x+2(x+\sqrt3)\)

=>\(f(x)=x^3+\sqrt3 x^2-3x^2-3\sqrt3 x+2x+2\sqrt3\)

=> \(f(x) = x^3+(\sqrt3-3)x^2+(2-3\sqrt3)x+2\sqrt3\)

Hence the polynomial function is \(f(x) = x^3+(\sqrt3-3)x^2+(2-3\sqrt3)x+2\sqrt3\).

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Answer:

5 miles per hour

Step-by-step explanation:

15/3=5

For the functions y = f(x) following statements are true:

b. A function is always relation.

e. The x values comprise the domain and y values the range.

f. The x values are inputs and the y is the output.

As given in the question,

For the functions y = f(x) following statements are true:

a, A relation is always a function .

False. Not all relations are functions as there may be more than one output foe each input.

b. A function is always relation.

Function is always a relation as for each input there is a single output.

True statement.

c. The x values comprise the range and y values the domain.

False. x values represent the input which is the domain .y is the range.

d. The x value are output determined by a value inputs.

False. x is the input and y is the output.

e. The x values comprise the domain and y values the range.

True. x represent the input value  called domain.

y represents the output called range.

f.  The x values are inputs and the y is the output.

True. x values are inputs of f(x) as it is the independent variable and y represents the output as it is the dependent variable on x.

Therefore, for the functions y = f(x) following statements are true:

b. A function is always relation.

e. The x values comprise the domain and y values the range.

f. The x values are inputs and the y is the output.

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A two-sample z-test for a difference in population proportions is the appropriate method for analyzing the results.

Z-test is a statistical test often utilizes to find the difference in mean. It is coupled with variances and sample size to find the appropriate results. It is a hypothetical test where normal distribution is seen.

z-test holds numerous advantages such as it indicates difference in small size groups making it more usable. Moreover, it is also reliable in non-normal distribution of data and is efficient while taking multiple groups in a single analysis. The question has two different popular proportion and hence the two sample z-test will suitable to compare the means.

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9514 1404 393

Answer:

  A:  (b) 320 is what percent of 400

  B:  80%

Step-by-step explanation:

Part A:

This is a reading comprehension question. You are told that ...

  $320 is the amount needed

  $400 is the amount earned

and you are asked to find ...

  what percent of the amount earned is the amount needed?

The question can be rephrased as ...

  the amount needed is what percent of the amount earned?

Filling in the amounts you are told, the rephrased question becomes ...

  $320 is what percent of $400 . . . . . matches choice (b)

__

Part B:

If we let x represent "what percent", then we can write the above question as ...

  320 = x · 400

Dividing by 400 gives ...

  320/400 = x = 0.80 = 80%

That is, 320 is 80% of 400.

Answer:

-72x - 53y + 287 = 0.

Step-by-step explanation:

To find the equation of the image of the circle, we need to reflect each point on the circle in the given line mirror.

The line mirror equation is given as 4x + 7y + 13 = 0.

The reflection of a point (x, y) in the line mirror can be found using the formula:

x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)

y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)

where A, B, and C are the coefficients of the line mirror equation.

For the given line mirror equation 4x + 7y + 13 = 0, we have A = 4, B = 7, and C = 13.

Now, let's find the equations of the image of the circle.

The original circle equation is x² + y² + 16x - 24y + 183 = 0.

Using the reflection formulas, we substitute the values of x and y in the circle equation to find x' and y':

x' = (x - 2Ay - 2B(Ax + By + C)) / (A^2 + B^2)

= (x - 2(4)y - 2(7)(4x + 7y + 13)) / (4^2 + 7^2)

= (x - 8y - 8(4x + 7y + 13)) / 65

= (x - 8y - 32x - 56y - 104) / 65

= (-31x - 64y - 104) / 65

y' = (y - 2Bx + 2A(Ax + By + C)) / (A^2 + B^2)

= (y - 2(7)x + 2(4)(Ax + By + C)) / (4^2 + 7^2)

= (y - 14x + 8(Ax + By + C)) / 65

= (y - 14x + 8(4x + 7y + 13)) / 65

= (57x + 35y + 104) / 65

Therefore, the equation of the image of the circle is:

(-31x - 64y - 104) / 65 + (-57x + 35y + 104) / 65 + 16x - 24y + 183 = 0

Simplifying the equation, we get:

-31x - 64y - 57x + 35y + 16x - 24y + 183 + 104 = 0

-72x - 53y + 287 = 0

So, the equation of the image of the circle is -72x - 53y + 287 = 0.

Answer:

Mauna Kea has from the base that is to say the deepest 10 km of height that is to say 10,000 m which is equivalent to being higher than Mount Everest.jj

Step-by-step explanation:

 The main reason why we could say that Mauna Kea is the highest mountain, even surpassing Mount Everest, is because of its altitude if we compare them we see the difference; for example Mauna Kea from its base that is to say from the deepest the ocean measures 10,000 m of altitude, on the other hand the Mount Everest has an altitude of 8848 meters (29,029 ft) above sea level, that is to say from its base it measures 8848 m altitude.