Reduce to simplest form.

-1/3+(-7/4)

Answer:  There is a total of 900 seats in the auditorium.

Step-by-step explanation:

there is a formula for this

t - n = a + ( n - 1) d

It is called a Arithmetic Progression.

We use this to find the number of seats in the last row first.

a = initial value, 12

d = common difference for each successive term

n = is the number of terms in the sequence

t - 25 = 12 + (25 -1) * 2

We ignore the left side for now, just solve the right and we get 60.

Now we use the equation,

n / 2 (2a + n -1 * d)

So,

25/2 ( 24 + 24 * d)

The answer is 900

Answer:

(1) p(x) = 7x³ + 4x² + 6 - 9x⁴

(2) p(x) = 1 + 3x - 9x⁵

(3) y = 9x² - x³ + x⁹

(4) f(x) = (x +3)(x-2)(x+5)

Step-by-step explanation:

Standard form has terms arranged from the highest to the lowest power

Degree is the highest power

Leading coefficient is the coefficient of the highest term

Leading term is the term containing the highest power

(x + 3) (x - 2)(x + 5)

(x + 3) (x - 2) = x² + x - 6 using the FOIL method
(x² + x - 6)(x +5) = x³ + 6x² -x - 30

Step-by-step explanation:

come on, we explained this already in previous questions. if you understood the explanations there, you should have been able to some that here without any problems.

again, standard form is the sorted polynomial from highest variable exponent to the lowest (as the potential constant at the end represents the x⁰ term).

the leading term is the first term on the left (with the highest exponent).

the leading coefficient is the factor in this leading term.

degree is the highest exponent used in the polynomial (again, given by the leading term).

so, what is still the problem ?

i have a slight problem with your handwriting. it is unclear, if there is 7x³ or 17x³. or 13x or 3x.

1.

p(x) = 17x³ + 4x² + 6 - 9x⁴

now, just sort this from the highest to the lowest exponent.

p(x) = -9x⁴ + 17x³ + 4x² + 6

if it should be 7x³ instead of 17x³, please use 7x³ in the polynomial.

degree = 4

leading coefficient = -9

leading term = -9x⁴

2.

p(x) = 1 + 13x - 9x⁵

again sort from highest to lowest exponent

p(x) = -9x⁵ + 13x + 1

again, if it should be 3x instead of 13x, please use 3x in the polynomial.

degree = 5

leading coefficient = -9

leading term = -9x⁵

3.

y = 9x² - x⁵ + x⁹

remember, y = f(x)

that is the same thing, means the same thing. it just gives the result variable a specific name.

again sort by exponent.

y = f(x) or p(x) or ... = x⁹ - x⁵ + 9x²

degree = 9

leading coefficient = 1

leading term = x⁹

4.

f(x) = (x+3)(x-2)(x+5)

this is really like the other question I just answered.

so, we always multiply 2 terms. that result we multiply by the third term. and if they're are more, then that result with the fourth term, and that with the 5th term,...

I usually start at the left :

(x+3)(x-2) = x² - 2x + 3x - 6 = x² + x - 6

now

(x² + x - 6)((x+5) = x³ + 5x² + x² + 5x - 6x - 30 =

= x³ + 6x² - x - 30

so,

f(x) = x³ + 6x² - x - 30

degree = 3

leading coefficient = 1

leading term = x³

Answer:

152.6 hours

Step-by-step explanation:

Distance = Speed × Time

Time = Distance/Speed

Santa's sleigh covered a total distance of 5797 kilometres averaging a speed of 38 km/h in snow storm conditions

Hence: Time Santa spent in snow storms is calculated as:

5797km ÷ 38 km/h

= 152.55263158 hours

Approximately = 152.6 hours

The four second partial derivatives are:

∂²z/∂x² = 12x²

∂²z/∂y² = -24xy - 90xy⁴

∂²z/∂x∂y = -12y² - 90xy⁴

∂²z/∂y∂x = -12y² - 90xy⁴

We are given the function:

z = x⁴ − 6xy²y³

The first-order partial derivatives are:

∂z/∂x = 4x³ − 6y²y³

∂z/∂y = -12xy² - 18xy⁵

Differentiating these partial derivatives with respect to x and y again:

∂²z/∂x² = ∂/∂x (4x³  − 6y²y³ ) = 12x²

∂²z/∂y² = ∂/∂y (-12xy² - 18xy⁵) = -24xy - 90xy⁴

To find the mixed partial derivatives, we differentiate the first partial derivatives with respect to the other variable:

∂²z/∂x∂y = ∂/∂x (-12xy² - 18xy⁵) = -12y² - 90xy⁴

∂²z/∂y∂x = ∂/∂y (4x³ − 6y²y³) = -12y² - 90xy⁴

As observed, the second mixed partial derivatives, ∂²z/∂x∂y and ∂²z/∂y∂x, are equal to each other: -12y² - 90xy⁴

So, the four second partial derivatives are:

∂²z/∂x² = 12x²

∂²z/∂y² = -24xy - 90xy⁴

∂²z/∂x∂y = -12y² - 90xy⁴

∂²z/∂y∂x = -12y² - 90xy⁴

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An inequality that can be written in the form ax + by < c (where a and b are not both zero) is called a linear inequality in two variables.

An inequality that represents a line in a two-dimensional coordinate system is referred to as a linear inequality. The set of points that satisfies the inequality is a half-plane bounded by a line that may be dashed or solid.

In contrast to a linear equation, which represents a line, a linear inequality represents a half-plane. The points on one side of the line, rather than the points on the line, are solutions to the inequality.

The method of shading is used to graph a linear inequality in two variables. First, graph the boundary line, which is usually represented by a solid or dashed line, and then select a test point on one side of the line. Shaded regions of the half-plane containing the test point satisfy the inequality.

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Answer:

Concentrations can be calculated in several different ways that all give different answers. The most common types of concentrations are by moles, mass, and volume. If this is really the entire question, I would have to assume they want the volume answer because we can't determine the mass or the moles of alcohol without knowing the actual formula of the alcohol. So this is how you do volume concentration:

concentration% = volume of pure substance / total volume of combination * 100

                                        or

                    12% = .12(16)/16 * 100           (just a restatement of the given)

So starting with 16 ml of solution, we add x ml of water to get a total volume of (16+x). And the amount of pure alcohol is found from .12(16).

Now we calculate:    8% = .12(16)/(16+x) * 100            Solve for x.

.08 = 1.92/(16+x)

.08(16+x) = 1.92

16 + x = 1.92/.08 = 24

x = 24 - 16 = 8 ml

Step-by-step explanation:

we have to add 7775000 to make 7800000 from 25000 which is calculated by using Substraction method.

Subtraction in mathematics is the process of subtracting one integer from another. In other terms, the result of subtracting two from five is three. After addition, subtraction is usually the second process you learn in math class.Subtraction is the action or procedure of determining the difference between two quantities or figures. The phrase "taking away one number from another" is also used to describe the process of subtracting one number from another.

Distance to be covered altogether= 7800000 m
THE distance has covered= 25000 m.

We can calculate the thousands needs to be added in 25000 to make it 7800000 by using Substraction method:-

7800000-25000= 7775000m

hence, to make 7800000 from 25000 we have to add 7775000.

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Answer: the answer is yes, she does have enough because 7% is 0.07 in decimals so then you multiply the .07 by the 18 and then add that to 18 which = 19.26 so she can buy it and have 74 cents left.

Answer:

t = 6.3

Step-by-step explanation:

t = 13\(\frac{3}{4}\) - 7.45

t = \(\frac{55}{4}\)-7.45

t= 13.75 - 7.45

t = 6.3

Answer:

T would equal 6.3

Step-by-step explanation:

You can start out by converting 13 3/4 to a decimal, which would be 13.75.

Therefore leaving you with this equation:

t + 7.45 = 13.75

Next, you subtract.

t + 7.45 = 13.75

   -7.45    -7.45

---------------------------

Therefore leaving you with your answer of 6.3 or 6 3/10. I hope this helps!  :)

Answer:

128/2 = 64 which gives you the height

sq root 64 = 8 which gives you the diameter

8/2= 4cm which is the radius (answer)

Refer to the image for the graph of the lines.

The common form of the equation of a line is y = mx + c, where m is the slope of the line and c is a constant.

We need to draw any line with a slope m = 2, and

another line with a slope m = -2.

Disclaimer: Let us assume that the constant c = 0.

Then the equation to the line with a slope of "positive" 2 is given by

y = 2x

Then the equation to the line with a slope of "negative" 2 is given by

y = -2x

Refer to the attached image for the graph of the lines with the slope of "positive" 2 and "negative" 2.

f: green line indicates a line with a slope of "positive" 2.

g: blue line indicates a line with a slope of "negative" 2.

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The value of the angle cos(L)° will be 0.42.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is a fundamental area of study in mathematics, with applications in a wide range of fields such as physics, engineering, navigation, architecture, and more.

Given that in a triangle JKL the side KL is 15 and the side JK is 36. The value of cos(L)° is the ratio of the side JK and KL.

cos(L)° = JK / KL

cos(L)° = 15/36

cos(L)° = 0.42

Therefore, the value of the angle cos(L)° will be 0.42.

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Answer:

x3 - 2x2 - 4x - 10

         x      

Step-by-step explanation:

i think

If the engineers are planning a car design in which only 25 of adults fit , then this sitting height is 38.68 inches .

To find the sitting height for the tallest 2% of adults, we first find z-score for upper 2% of standard Normal Distribution ;

we know ; that z = (x - μ)/σ ;

where z is = z core, x is = sitting height , μ is = mean sitting height, and

σ is = standard deviation of sitting heights.

From the normal table : Upper 2% of standard normal distribution have a z-score of approximately 2.05 ;

So , 2.05 = (x - 35.4)/1.6 ;

Multiplying both sides by 1.6, we get ;

⇒ 3.28 = x - 35.4

On adding 35.4 to both sides, we get:

⇒ x = 38.68 ;

Therefore, the sitting height for the tallest 2% of adults is 38.68 inches .

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Answer:

2

Step-by-step explanation:

The money that Adrian would  have to pay for parking if he left his car in the lot for 3 hours is $13  and ther amount that Adrian has to pay if he left his car in the lot for t hours is $(2t + 7)

We are given;

Fee for entering the Parking Lot = $7

Fee for one hour of parking = $2

Thus;

Fee for three hours of parking = 2 * 3 = $6

Total fee if he parks his car for 3 hours = $7 + $6

Total fee if he parks his car for 3 hours = $13

Total fee if she left the car for t hours = $(2t + 7)

Finally we conclude that the money that Adrian would  have to pay for parking if he left his car in the lot for 3 hours is $13  and ther amount that Adrian has to pay if he left his car in the lot for t hours is $(2t + 7)

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Answer:

5/6 or 0.8333333333 (83%)

Step-by-step explanation:

So she landed 15 out of 18 so we are going to divide 15 by 18 (15/18) which gets us 5/6 or 0.8333333333 or 83%

Hopes this help ^-^

SOLUTION

Write out the equation

The first step in solving this equation is to multiply both sides by 2 this is called

MULTIPLICATION PROPERTY OF EQUALITY

Step1; MUltiply both sides by 2

The next step in solving this equation is to add 7 to both sides of

the equation this is called ADDITION PROPERTY OF EQUALITY

step2: Add 7 to both sides of the equation

Hence the solution to the equation is y=-15

The steps are

Step1; MULTIPLICATION PROPERTY OF EQUALITY

Step2: SIMPLIFYING

Step3: ADDITION PROPERTY OF EQUALITY

Step4: SIMPLIFYING

Answer:

80 pieces of wire.

Step-by-step explanation:

It may not come out evenly. If there is a remainder, it won't matter. Just throw it away and go with the integer answer.

Change 3 3/4 to a decimal

3.75

Change the 25 foot roll to inches.

25 feet * 12 inches / foot  = 300 inches.

Now how many pieces of wire do we get.

1 piece of wire/3.75 inches = x pieces of wire / 300 inches

3.75 * x = 300

3.75 * x / 3.75 = 300 / 3.75

x = 80

Answer:

1/ $ 4.08

2/ $675.92

Step-by-step explanation:

Take 68 times 0.06% = $4.08

680 - 4.08= 675.92

Answer:

Step-by-step explanation:

40.80 it told me the answer

Answer:

explination...

Step-by-step explanation:

so from how i’m understanding it, it would be 12(90) + 20(121).

so 12 x 90 is 1080. so that’s already a good amt, but then 20 x 121 is 2420. now if we add those together,

2420

+1080

-————

3500

so instead of there being more money than she spent, she actually gets the same amount back. so just rearange what’s you out to make sense in a way that matches the problem and you should be good (that was saying it nicely sorry if that seemed rude haha)

Answer:

Two mathematical terms are alike (not alike) , if they have same (different) variables & in same (different) mathematical treatment.

Step-by-step explanation:

Two mathematical terms are alike, if they have same variables & in same mathematical treatment.

Eg : 2 xy , 5 xy. These are alike, as they have product of x & y being multiplied with constants.

They can be added, subtracted by adding or subtracting their constants.

2 xy + 5 xy =  (2 + 5) xy = 7 xy

5 xy - 2 xy =  ( 5- 2 ) xy = 3 xy

Answer:

The percentage of the surveyed that preferred Lirt juice is 40%

Step-by-step explanation:

In this question, we are asked to calculate the percentage of beings that preferred Lirt juice

Let’s look at the survey presented in the question. 10 beings preferred out of a total of 25

The percentage that preferred Lirt juice will thus be;

10/25 * 100%

= 10 * 4 = 40%

Answer:

25°

Step-by-step explanation:

We know the opposite angles must be equal when two lines intersect, so 67 = 42+t. Subtracting 42 from both sides gives t=25, which is our answer

answer:

25 degrees

step-by-step explanation:

67=42+t so using that equation the answer can be determined. hope that helps!

The ratio of the original height of candle x to the original height of candle y is 13:8. This means that candle x is 13/8 times taller than candle y.

The ratio of the original height of candle x to the original height of candle y can be found by considering their burning rates and the time it takes for them to reach the same length. Based on the given information, candle x burns at a rate of 1/13 of its height per hour, while candle y burns at a rate of 1/24 of its height per hour. After burning for 9 hours, both candles have the same length.

Let's assume the original height of candle x is Hx and the original height of candle y is Hy. Candle x burns at a rate of 1/13 of its height per hour, so after burning for 9 hours, its remaining height would be (1 - 9/13)Hx = (4/13)Hx. Similarly, candle y burns at a rate of 1/24 of its height per hour, so after burning for 9 hours, its remaining height would be (1 - 9/24)Hy = (15/24)Hy.

Given that both candles have the same length after burning for 9 hours, we can equate their remaining heights:

(4/13)Hx = (15/24)Hy

To find the ratio of the original heights, we divide both sides of the equation by Hy:

(4/13)Hx / Hy = (15/24)

Simplifying the equation, we get:

Hx / Hy = (15/24) * (13/4) = 13/8

Therefore, the ratio of the original height of candle x to the original height of candle y is 13:8. This means that candle x is 13/8 times taller than candle y.

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The universal set U from which the subset was derived is; U = {keys on a keyboard }

We are told that S is a subset within a universal set, U.

Now, If S = {x, y, 4, 9, ?}  

Given S is a subset within a universal set U;

According to the question S = {x, y, 4, 9, ?}.

Now, we need to find among the given sets the one that describes the best set.

The best Universal set will be {keys on a key board } since the keys on a keyboard will have alphabets, numbers and punctuation marks mentioned in the set

Therefore, U = {keys on a keyboard }

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The mean, median, and mode are:

Mean = 10

Median = 8

Mode = 8

To find the mean, median, and mode of the given set of numbers: 5, 8, 18, 1, 14, 6, 8, 13, 8, 19, we can perform the following calculations:

Mean: The mean is calculated by summing up all the numbers and dividing by the total count of numbers.

Mean = (5 + 8 + 18 + 1 + 14 + 6 + 8 + 13 + 8 + 19) / 10

= 100 / 10

= 10

Therefore, the mean is 10.

Median: The median is the middle value when the numbers are arranged in ascending order. If there are an odd number of values, the median is the middle number. If there are an even number of values, the median is the average of the two middle numbers.

Arranging the numbers in ascending order: 1, 5, 6, 8, 8, 8, 13, 14, 18, 19

Since there are 10 numbers, the median is the average of the two middle numbers, which are the 5th and 6th numbers:

Median = (8 + 8) / 2

= 16 / 2

= 8

Therefore, the median is 8.

Mode: The mode is the number(s) that appear(s) most frequently in the set.

In this case, the number 8 appears three times, which is more than any other number.

Therefore, the mode is 8.

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The ratios and relative fractions of the shapes A and B and are as follows;

First part; Shape A is 3/5 of shape B

Second part; Shape A is 2/5 of shape B
Third part; The dimensions of the possible rectangles represented by shape A and B are;

Shape A, length and width = 4 cm each

Shape B, length = 6 cm, width = 4 cm

A ratio indicates the quantitative relationship that exists between two measures, showing the number of times the quantity of one is contained within the other.

The area of shape A = 15 cm²

Area of shape B = 25 cm²

The fraction of shape B that gives the area of shape A is therefore;

Shape A is \(\dfrac{15}{25} = \dfrac{3}{5}\) of shape B

The fraction of shape B that is shape A is \(\dfrac{3}{5}\) of shape B

Second part;

The width of shape A = 4 cm

The length = 3 cm

Therefore;

The area of shape A = 4 cm × 3 cm = 12 cm²

The width of shape B = 6 cm

The length of shape B = 5 cm

Therefore, the area of shape B = 6 cm × 5 cm = 30 cm²

The fraction of shape B that is shape A is therefore;

The fraction of shape B that is shape A = \(\dfrac{12}{30} =\dfrac{2}{5}\)

Shape A is 2/5 of shape B

Third part;

Shape A is 2:3 of shape B, using fractions, we have;

\(\dfrac{Area \, of \, shape \, A}{Area \, of \, shape \, B} =\dfrac{2}{3} =\dfrac{2 \times 8}{3 \times 8} = \dfrac{16}{24} = \dfrac{4 \times 4}{6\times 4}\)

The dimensions of shape A are;

Width = 4 cm

Length = 4 cm

The dimensions of shape B are;

Width = 4 cm

Length = 6 cm

Please find attached the drawing of two shapes that show what shape A and shape B could be

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