2x^2 + 2y^2 + 16x + 16y + 32 = 0 is the equation of a circle with center (h, k) and radius r for: h= ____ and k= ____ and r= _____

sin(30°) = ½

Sin(30°) have the value of √1/2 which gives ½

Based on the given information, the cost of a pound of pistachios and a pound of cashews is $7.875 and $5.50, respectively.

To find the cost of a pound of pistachios and the cost of a pound of cashews, we can use a system of equations.

Let's let P represent the cost of a pound of pistachios and C represent the cost of a pound of cashews.

Then we can write two equations based on the information given:

4P + 1C = 37

3P + 3C = 48

Now we can use the elimination method to solve for one of the variables.

Let's multiply the first equation by -3 to eliminate the P variable:

-12P - 3C = -111

3P + 3C = 48

Adding these two equations together gives us:

-8P + 0C = -63

Simplifying gives us:

P = 63/8

This means that the cost for a pound of pistachios is $63/8 or $7.875.

Substitute the value of P to any of the two equations so we can have the value of C.

4(63/8) + 1C = 37

C = 11/2 = 5.5

Therefore, the cost of a pound of pistachios is $7.875 while the cost of a pound of cashews is $5.50.

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Therefore , expression problem solution is during the run, the adults covered a distance of 24 metres, and it took them 8 seconds to catch up to the children.

There is a need for mathematical operations like multiplying, splitting, combining, and now even deleting. If they were combined, it would be said that: A mathematical formula, some data, and an equation A declaration of truth is composed of values, elements, and mathematical operations like additions, subtractions, missteps, algebraic formulas, and divisions. It is possible to evaluate and analyse words and phrases.

Here,

Distance is determined by rate and duration.

for the distances that children and adults travel, two equations should be made up:

=> (d - 16) = 1t (for the youngsters) (for the kids)

=> d = 3t (for the males) (for the adults)

where "t" represents the amount of time that has elapsed since the competition began.

We can set the distances between the children and adults to be equal because we know that they were side-by-side at some time during the race:

=> d - 16 = 3t - 16

When we simplify this solution, we obtain:

=> d = 3t

When we add this to the prior solution, we obtain:

=> 3t - 16 = 1t

To solve for "t," we obtain:

=>  t = 8 sec.

Now that we know how far the grownups travelled:

D=3t=3x8=24 metres.

As a result, during the run, the adults covered a distance of 24 metres, and it took them 8 seconds to catch up to the children.

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The probability of rolling a triangle is 9 out of 15, or 60%.

Its essential vision is that an individual will nearly certainly happen.

Then the probability is given as,

P = (Favorable event) / (Total event)

As per the given data:

Total sides is a die = 15

triangles = 9

circles = 4

squares = 2

The probability of rolling a triangle is 9 out of 15, or:

For probability in % = (Favorable outcomes/Total outcomes) × 100

= (9/15) × 100

= 60%

Hence, The probability of rolling a triangle is 9 out of 15, or 60%.

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The maximum number of days she can drive the car is approximately 4 days.

A rental car company charges $61.79 per day to rent a car and $0.13 for every mile driven.

She plans to drive 50 miles. She has at most $230 to spend.

Therefore, the maximum number of days that Tallulah can rent the car while staying within her budget can be computed as follows:

Using equations,

y = 0.13a + 61.79b

where

Therefore, she has a budget of 230 dollars and she wants to ride for 50 miles.

230 = 0.13(50) + 61.79b

230 - 6.5 = 61.79b

223.5 = 61.79b

b = 223.5  / 61.79

b = 3.61709014404

Therefore,

b = 4 days

Hence, she can ride maximum of 4 days.

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B is the right response: (6 + 4) 2 = 20.

We must analyse each expression and compare them in order to determine which number statement is correct.

starting with the formula A (6 + 4 2 = 6 + 8 = 14)

Let's now assess expression B:

(6 + 4) × 2 = 10 × 2 = 20

Expression in C: 6 + 4 2 = 6 + 2 =

The final expression is D (6 + 4) 2 = 10 2 = 5.

The values of the expressions can now be compared to determine which number sentence is correct.

As can be seen, expression B is the real number sentence because it has the highest value of all the expressions. As a result, B is the right response: (6 + 4) 2 = 20.

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By answering the above question, we may state that Hence, [tex]xy{(-4)}[/tex]is x exponents divided by y raised to the power of 4.

The mathematical process of exponentiation, frequently referred to as "b raised to the nth power," is symbolised by the symbol bn and includes two numbers: a base number, b, and an exponent, or power, n. Exponents demonstrate the number of times that a number has been multiplied by itself. For example, 2-3 (written as 23) means: 2 x 2 x 2 = 8. 2 + 3 does not equal 6, nor does 23. Remember that an integer whose power is one is equal to itself. Exponents can be used as a way to express large numbers as powers. Therefore, the exponent is the measurement that shows how many times a number has been multiplied by itself. For instance, multiplying 6 by 4 results in the values 6 x 6 x 6.  .

Considering that the phrase is:

[tex]xy^{-4}[/tex]

We may simplify the case when x and y both have positive exponents as follows:

[tex]xy^{(-4)} = x / y^4[/tex]

This is due to the negative exponents rule, which claims that y(-n) = 1/yn, which indicates that [tex]y(-n) = 1/yn.[/tex]

Hence, [tex]xy{(-4)}[/tex]is x divided by y raised to the power of 4.

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Step-by-step explanation:

We can solve for x in terms of y from the equation 3x - y = 12 as follows:

3x - y = 12

3x = y + 12

x = (y + 12)/3

Similarly, we can solve for y in terms of x:

3x - y = 12

-y = -3x + 12

y = 3x - 12

Now, we can substitute these expressions for x and y into the expression 8x/2y to get:

8x/2y = 4x/y

Substituting (y + 12)/3 for x, we get:

4x/y = 4((y + 12)/3)/y = 4(y + 12)/3y

Simplifying the numerator, we get:

4(y + 12) = 4y + 48

Substituting 3x - 12 for y, we get:

4y + 48 = 4(3x - 12) + 48 = 12x

Therefore, 8x/2y = 4x/y = 12x/4y = 12x/(3x - 12)

We cannot simplify this expression further without additional information. Therefore, the answer is (D) The value cannot be determined from the information given.

The account will be growing by $741.87 per year 11 years from now.

To find the answer, we need to use the formula for compound interest, which is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

In this case, P = $2000, r = 0.03, n = 1, and t = 11. Plugging these values into the formula gives us:
A = $2000(1 + 0.03/1)^(1*11)
A = $2000(1.03)^11
A = $2741.87
To find out how fast the account will be growing 11 years from now, we need to subtract the principal amount from the final amount:
$2741.87 - $2000 = $741.87

Therefore, the account will be growing by $741.87 per year 11 years from now.

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The interpretation of the 1001 measurements in the third set of data vary due to reasons are as follow,

Measurement error, Random variation and Sampling error.

Measurement error: The measurand being measured may have inherent variability, but measurement error can also contribute to variation in the data set.

Random variation: Even if the same measurand is being measured under the same conditions, there may be random fluctuations in the system or the environment that can cause variation in the data.

Sampling error: If the 11 measurements were not taken at random from the population of interest, then the variation could be due to sampling error.

For the 1001 measurements in the second and third data sets, some possible explanations for the variation could be measurement error, systematic variation, changes in the measurand and Sampling error.

Thus, variation in data can have many different causes, and it is important to carefully consider the context and specific factors that may be contributing to the variation when interpreting the results.

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Yes, the equation y = 3/4(x) represent a proportional relationship because its line passes through the origin.

In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Generally speaking, the graph of any proportional relationship such as the linear equation is characterized by a straight line that passes through all the points and the origin, which is denoted by the ordered pair (0, 0).

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The 6th term of the sequence is -97.65625

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

A(n) = -2.5^(n-1)

In the sixth term, we have

n = 6

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

A(6) = -2.5^(6-1)

Evaluate

A(6) = -97.65625

Hence, the 6th term is -97.65625

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The calculated system of inequalities shown in the graph of inequalities is x  > -2 and y < 4

A system of inequalities is a set of two or more inequalities involving one or more variables.

The variables can take on different values that satisfy the given inequalities simultaneously.

By the above analysis, the inequalities shown in the graph is x > -2 and y < 4

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Answer:

A: 24, B: 12, C: 28, D: 24. Hope this helps

Step-by-step explanation:

Part A:

168/3 = 56

Therefore, Chad is driving the car in 56 mph.

672/56 = 12

Therefore, Chad drives 672 miles in 12 hours.

308/11 = 28

Therefore, Chad drives 28 miles per gallon of gas.

672/28 = 24

Therefore, Chad uses 24 gallons of gas to drive 672 miles.

Part B:

12 hours, you can use proportions, miles/hours.

[tex]\frac{56}{1}[/tex]= [tex]\frac{672}{x}[/tex]

x = 12

Part C:

divide the miles driven by Chad (308 miles ) by the number of gallons used (11 gallons).

308 miles / 11 gallons =28 miles per gallon

Chad's car gets 28 miles per gallon.

Part D:

[tex]\frac{28}{1} = \frac{672}{x} \\[/tex]

28x = 672

x = 672/28 = 24

24 gallons

Answer: A=56 B=12 C=28 and D=24

Step-by-step explanation:

A. Chad drove 168 miles in 3 hours

    In 1 hour he drove          168÷3

                                          = 56 Miles

B. We know,

    Covering 56 miles takes 1 hour

    So, It will take to cover 672 miles
                                           = 672÷56

                                           = 12 Hours

C. We know,

    Chad drove 308 miles with 11 gallons of gas

    So, miles per gallon chads car gave him 308÷11

                                                                       = 28 Miles Per Gallon.

D. We know,

   Chad car gives him 28 miles per gallon

   So, To cover 672 miles

   Chad needs                                            = 672÷28

                                                                    = 24 Gallons.

NOTE: Its simple math kiddo, do better in school

an = 2*an-1 + an-2 is the sequence's recursive rule, and the seventh term is 268.

A formula that explains how to move from one word in a sequence to the next is known as a recursive rule for a sequence.

The variable typically serves as a symbol for the concept of a number.

In other words, takes on the values 1, 2, 3, etc. for the first, second, third, etc. terms.

A recursive sequence is one in which terms are defined by reference to one or more previously defined terms.

The recursive formula an+1=an+d can be used to find the (n+1)th term of an arithmetic series if you know the nth term and the common difference, d.

So, we know that:
2 = 2 * 1 + 0

3 = 2 * 1 + 1

8 = 2 * 3 + 2

19 = 2 * 8 + 3

46 = 2 * 19 + 8

The sequence's nth term is as follows after the preceding sequence:

a7 = 2*an-1 + a7 - 2

For, a7:
a7 = 2*a7-1+a7-2

a7 = 2*a6+a5

a7 = 2*a6+46

a6 = 2*a5+a4

a7 = 2*(2*46+19)+46

a7 = 268

Therefore, an = 2*an-1 + an-2 is the sequence's recursive rule, and the seventh term is 268.

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Answer:

80%

Step-by-step explanation:

96.3 - 53.5 = 42.8

42.8 / 53.5 = 0.8

0.8 × 100 = 80%

By the squeeze theοrem, lim f(x) = 0 as x apprοaches -5.

The squeeze theοrem, alsο knοwn as the sandwich theοrem, is a theοrem in calculus that allοws us tο find the limit οf a functiοn using the limits οf twο οther functiοns that "squeeze" the οriginal functiοn between them.

We have the inequality:

-2x² - 20x - 51 ≤ f(x) ≤ 2x² + 20x + 49

We can rewrite this inequality as:

-2(x+5)(x+4.5) ≤ f(x) ≤ 2(x+5)(x+4.5) + 1

Nοte that we have factοred -2x² - 20x - 51 as -2(x+5)(x+4.5) and 2x² + 20x + 49 as 2(x+5)(x+4.5) + 1.

As x apprοaches -5, we can see that (x+5) and (x+4.5) apprοach 0, sο we have:

-2(0)(0) ≤ lim f(x) ≤ 2(0)(0) + 1

0 ≤ lim f(x) ≤ 1

Therefοre, by the squeeze theοrem, we have:

lim f(x) = 0 as x apprοaches -5.

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Step-by-step explanation:

remember, sine is the up/down leg, cosine is the left/right leg.

the Hypotenuse is the radius of the circle around the trigonometric triangle.

so,

sin(R) = 5/13

cos(R) = 12/13

tan(R) = sin(R)/cos(R) = 5/13 / 12/13 = (5×13)/(13×12) =

= 5/12

The volume of the cylinder is 42080.87 cubic yd

Cylinder is a 3-dimensional solid shape that consists of two identical and parallel bases linked by a curved surface.It has two curved edges, one curved surface, and two flat faces.

Volume of a cylinder = π * r^2 * h

Where π = 3.14

r = 17.2 td

h = 45.3 yd

Volume of a cylinder = 3.14 * (17.2)^2 * 45.3

Volume = 3.14 * 295.84 * 45.3

Volume = 42080.87 cubic yard

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So, the coefficient of the x^(2) term in the expression 5x-4x^(2)+2 is -4.

The coefficient of the x^(2) term in the expression 5x-4x^(2)+2 is -4.

A coefficient is the number that is multiplied by a variable in an expression. In this case, the x^(2) term is -4x^(2), so the coefficient is -4.

To find the coefficient of a specific term in an expression, you can simply look at the number that is directly in front of the variable and its exponent. For example, in the term 5x, the coefficient is 5, and in the term 2, the coefficient is 2 (since there is no variable, the coefficient is simply the number itself).

In the expression 5x-4x^(2)+2, the x^(2) term is -4x^(2), so the coefficient is -4. This means that the x^(2) term is being multiplied by -4 in the expression.

So, the coefficient of the x^(2) term in the expression 5x-4x^(2)+2 is -4.

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    The angles of a triangle equal 180 degrees when added together. We will use this logic to solve all three for x. We will use inverse operations and combine like terms to solve.

[30] Answer: x = 36

    Step-by-step explanation:

2x + 2x + x = 180

5x = 180

x = 36

[31] Answer: x = 9

    Step-by-step explanation:

* the little box represents 90 degrees

7x + 3x + 90 = 180

10x = 90

x = 9

[32] Answer: x = 45

    Step-by-step explanation:

2x + x + x = 180

4x = 180

x = 45

The values of 'x' in |3x + 4| > 6, is, x > 3/2 or x < - 10/3.

We know the absolute value function of the modulus function always outputs a positive value irrespective of the sign of the input.

In piecewise terms  | x | = x for x ≥ 0 and | x | = - x for x < 0.

We know, If |x| > a, Then x > a or x < - a.

Given, |3x + 4| > 6.

Therefore,

3x + 4 > 6 or 3x + 4 < - 6.

3x > 2 or 3x < - 10.

x > 3/2 or x < - 10/3.

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The requried measure of the PQ in the triangle PQT is 16 in.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
A figure of triangles has been shown, ΔPQT and ΔORS.
We have to determine the measure of side PQ.

Since the given triangle is similar to one another, we can apply the property of proportionality between the similar triangles. By which:

PR/PQ = RS/QT
PQ + 4 / PQ = 10/8
8PQ + 32 = 10PQ
2 PQ = 32
PQ = 16 in

Thus, the requried measure of the PQ in the triangle PQT is 16 in.

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The completely factored expression by pulling out the 15x^(7)+3x^(4)+21     is  3(5x^(7)+x^(4)+7).

A factored expression is an algebraic expression that has been broken down into its prime factors. This is usually done to simplify the expression and make it easier to solve for a particular variable or to factor out a common factor from multiple terms.

To factor the given expression, we need to find the greatest common factor (GCF) of the terms and then divide each term by the GCF to get the simplified expression.

The GCF of 15x^(7), 3x^(4), and 21 is 3. So, we can factor out 3 from each term to get the simplified expression:

15x^(7)+3x^(4)+21 = 3(5x^(7)+x^(4)+7)

Therefore, the completely factored expression is 3(5x^(7)+x^(4)+7).

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Answer:

[tex]\left(x-\frac{5}{2}\right)^2=\frac{25}{2}[/tex]

Step-by-step explanation:

I am not completely sure if you just wanted me to write it in square form, so I will show the process of writing it in square form and how to find the solution.

[tex]-4x^2+20x=-25[/tex]    start by moving 25 to the right side

[tex]\frac{-4x^2+20x}{-4}=\frac{-25}{-4}[/tex]         divide both sides by -4

= [tex]x^2-5x=\frac{25}{4}[/tex]    

Now we rewrite the equation in the form [tex]\:x^2+2ax+a^2[/tex]

= [tex]x^2-5x+\left(-\frac{5}{2}\right)^2=\frac{25}{2}[/tex]  apply perfect square formula: [tex]\left(a-b\right)^2=a^2-2ab+b^2[/tex]

= [tex]\left(x-\frac{5}{2}\right)^2=\frac{25}{2}[/tex]   -- square form

Solutions to the quadratic equation:

Possible solutions: [tex]x=\frac{5}{\sqrt{2}}+\frac{5}{2}[/tex]    and [tex]\:x=-\frac{5}{\sqrt{2}}+\frac{5}{2}[/tex]

Answer:

Step-by-step explanation:

12/13=0.92307692307

We can use the proportion (1000 grams )/(1 kilogram ) = (x grams )/(5 kilograms ) to convert 5 kilograms into grams.

The right proportion to use to convert 5 kilograms to grams is (1,000 grams)/(1 kilogram) = ( x grams)/(5 kilograms). This is because there are 1,000 grams in 1 kilogram, so we can use this ratio to find the number of grams in 5 kilograms. To solve for the unknown value, we can cross multiply and then divide.

The proportion is solved as:

So, the answer is 5,000 grams. Therefore, 5 kilograms is equal to 5,000 grams.

In conclusion, the correct proportion is (1000 grams )/(1 kilogram ) = (x grams )/(5 kilograms ).

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Answer:

Step-by-step explanation:

Answer:Price of the table yesterday is x.

Price of the table today is $513.

$513 is 76% of yesterday's price x. 76% can be also written down as 76 divided by 100 (percentage) or 76/100 = 0.76.

Formula we can set up now is: x= 513 / 0.76 (To get the price of yersterday's table we need to divide the price of today's table with percentage in decimal form).

x= 675

The price of yesterday's table was $675 since 76% of that price (675 times 0.76) equals 513 dollars.

Step-by-step explanation:

Standard form of a polynomial expression is a way of writing the expression in descending order of the powers of the variable, starting with the highest power and ending with the constant. In this case, the polynomial expression is - 6 - 7x ^ (2) + 8x ^ (5).

In standard form, this expression can be written as 8x ^ (5) -7x ^ (2) - 6. This expression indicates that 8 is the coefficient of the highest power, x ^ (5). The coefficient of the second highest power, x ^ (2) is -7, and the coefficient of the constant, the term with no variable, is -6.

Standard form is useful for simplifying polynomial expressions, as it helps to clearly illustrate the coefficients of each term. It is also useful for graphing polynomials, as the order of the terms can be clearly seen.

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