plssss helppp this mathematics

Answer:

x = - 6 and x = - 8

Step-by-step explanation:

(1)

- 6(x - 3) = 54 ( divide both sides by - 6 )

x - 3 = - 9 ( add 3 to both sides )

x = - 6

(2)

- 7(x + 2) = 42 ( divide both sides by - 7 )

x + 2 = - 6 ( subtract 2 from both sides )

x = - 8

The lengths of RS and ST are 20 and 1 respectively

Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the International System of Units system the base unit for length is the metre.

here, we have,

to solve for RS and ST;

The given parameters are:

RS= 2x+10, ST= x−4, RT= 21

This means that

RT = RS + ST

So, we have:

2x + 10 + x - 4 = 21

Evaluate the like terms

3x = 15

Divide by 3

x = 5

Substitute x = 5 in RS= 2x+10 and  ST= x−4

RS= 2*5+10 = 20

ST= 5−4 = 1

Hence, the lengths of RS and ST are 20 and 1 respectively

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The product of the polynomials (4x-7)^(2) is 16x^(2)-56x+49. This is the final answer expressed as a single polynomial in standard form.

To multiply the polynomials using a special product formula, we can use the formula (a-b)^(2)=a^(2)-2ab+b^(2). In this case, a=4x and b=7. Plugging these values into the formula gives us:
(4x-7)^(2)=(4x)^(2)-2(4x)(7)+(7)^(2)

Simplifying the terms on the right side of the equation gives us:
(4x-7)^(2)=16x^(2)-56x+49

Simplifying, we have (4x-7)2 = 16x2 - 56x + 49, which is our answer expressed as a single polynomial in standard form.

Multiplying polynomials require only three steps.

First, multiply each term in one polynomial by each term in the other polynomial using the distributive law.

Add the powers of the same variables using the exponent rule.

Then, simplify the resulting polynomial by adding or subtracting the like terms.

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We can state this by responding to the provided question B, D, and E are expressions the expressions that have values of 1/6.

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.

We need to simplify each expression to see which ones are equivalent to 1/6:

6. 1/6 is not equivalent to 6/1.

B. 3÷18 = 1/6

C. 2/3 of 2 equals 6 (not equivalent to 1/6)

D. 1÷6 = 1/6

E. 1/3 ÷ 2 = 1/6

B, D, and E are the expressions that have values of 1/6.

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Answer:

1

Step-by-step explanation:

1 / 1 = 1

(a) We can use the identity cos(180° - θ) = -cos(θ) to rewrite cos(165°) as cos(180° - 15°) cos(165°) = cos(180° - 15°) = -cos(15°) To find cos(15°),

we can use the half-angle formula for cosine: cos(15°) = cos(30°/2) = sqrt((1 + cos(30°))/2) = sqrt((1 + sqrt(3)/2)/2) = (sqrt(2) + sqrt(6))/4

Therefore, cos(165°) = -cos(15°) = -(sqrt(2) + sqrt(6))/4 (b) Using the product-to-sum identity, we have cos(80°)cos(20°) + sin(80°)sin(20°) = cos(80° - 20°) = cos(60°) = 1/2 Therefore, cos(80°)cos(20°) + sin(80°)sin(20°) = 1/2.

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The median of the solutions to the equation 3x³ + 5x² − 6x − 10 = 0 is -√2. The correct answer is A.

To find the median of the solutions to the equation 3x³ + 5x² − 6x − 10 = 0, first find the solutions of the equation and then find the middle value of those solutions.

Group the terms and factor out (3x + 5).

(3x³ + 5x²) + (-6x − 10) = 0

(3x + 5)(x²) + (3x + 5)(-2) = 0

(3x + 5)(x² - 2) = 0

Factor (x² - 2).

(3x + 5)(x + √2)(x - √2) = 0

So the solutions of the equation are x = -5/3, x = -√2, and x = √2.

To find the median of these solutions, we need to order them from least to greatest:

-5/3 < -√2 < √2

The median of these solutions is -√2.

Therefore, the correct answer is (A) -√2.

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cos 59° = ±([tex]\sqrt{1 - sin^2 59}[/tex]) ≈ ±0.515 in terms of the sine function.

To express cos 59° in terms of the sine function, we can use the trigonometric identity:

[tex]sin^2[/tex]θ + [tex]cos^2[/tex]θ = 1

Rearranging this identity, we get:

[tex]cos^2[/tex]θ = 1 - [tex]sin^2[/tex]    θ

Taking the square root of both sides, we get:

cosθ = ±[tex]\sqrt{(1 - sin^2θ)}[/tex]

In the case of cos 59°, we know that sin 59° can be calculated using the sine function since sin 59° is the opposite side of a right triangle divided by its hypotenuse, where the angle opposite to the opposite side measures 59 degrees. Therefore:

sin 59° = 0.85717 (rounded to 5 decimal places)

Substituting sin 59° into the equation for cosθ, we get:

cos 59° = ±([tex]\sqrt{1 - sin^2 59}[/tex]) = ±[tex]\sqrt{(1 - 0.85717^2) }[/tex]≈ ±0.515

Note that since the angle 59° is in the first quadrant, cos 59° is positive. Therefore, we can write:

cos 59° ≈ 0.515 in terms of the sine function.

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Answer:

The quotient of (2x³ + x² - x - 4) ÷ (x + 4) is 2x^2 - 7x + 17, and the remainder is 27x - 4.

Step-by-step explanation:

     2x^2 - 7x + 17

x + 4 | 2x^3 + x^2 - x - 4

- (2x^3 + 8x^2)

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

-7x^2 - x

+ (-7x^2 - 28x)

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

27x - 4

Therefore, the quotient of (2x³ + x² - x - 4) ÷ (x + 4) is 2x^2 - 7x + 17, and the remainder is 27x - 4.

Answer:

Direct proportion and inverse proportion are two types of relationships between two variables.

Direct proportion is a relationship in which two variables increase or decrease together at the same rate. In other words, if one variable increases, the other variable also increases, and if one variable decreases, the other variable also decreases. The mathematical expression for direct proportion is:

y = kx

where y is the dependent variable, x is the independent variable, and k is a constant of proportionality.

On the other hand, inverse proportion is a relationship in which two variables change in opposite directions. In other words, if one variable increases, the other variable decreases, and if one variable decreases, the other variable increases. The mathematical expression for inverse proportion is:

y = k/x

where y is the dependent variable, x is the independent variable, and k is a constant of proportionality.

So, the main difference between inverse proportion and direct proportion is the direction of change between the two variables. In direct proportion, the two variables change in the same direction, while in inverse proportion, the two variables change in opposite directions.

Rearranging this equation gives a quadratic equation[tex]length^2 - 3 length - 75 = 0[/tex]

Let's start by using the formula for the volume of a rectangular prism:

Volume = length x width x height

We know that the volume is 900 cubic meters and the width is 12 meters. Let's substitute these values into the formula:

[tex]900 = length \times 12 \times height[/tex]

Now we need to use the information about the height. We know that the height is 3 meters shorter than the length, so we can write:

height = length - 3

Substituting this into the formula gives:

[tex]900 = length \times 12 \times (length - 3)[/tex]

Simplifying this equation gives:

[tex]900 = 12 length^2 - 36 length[/tex]

Dividing both sides by 12 gives:

[tex]75 = length^2 - 3 length[/tex]

Therefore, Rearranging this equation gives a quadratic equation:

[tex]length^2 - 3 length - 75 = 0[/tex]

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The equation 4(5r-15)=13+11+8r has a unique i.e., one solution.

The given equation is: 4(5r-15) = 13+11+8r.

Simplifying the left-hand side, we get 20r-60 = 32+8r.

Bringing all the r terms to the left-hand side and the constants to the right-hand side, we get:

20r - 8r = 32 + 60

12r = 92

r = 7.67

Therefore, we get a unique solution for the given equation, which is r = 7.67.

There are a few possible reasons why an equation may not have any solution or may have infinitely many solutions. In this case, since we obtained a unique solution, neither of these situations applies.

One common reason why an equation may not have any solution is that the equation may be inconsistent, meaning that the left-hand side and right-hand side of the equation cannot be made equal for any value of the variable. For example, the equation 2x + 3 = 2x + 4 has no solution since the two sides of the equation can never be equal for any value of x.

On the other hand, an equation may have infinitely many solutions if it is an identity, meaning that the left-hand side and right-hand side of the equation are always equal, regardless of the value of the variable. For example, the equation x + 1 = x + 1 is an identity since the left-hand side and right-hand side are always equal for any value of x.

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The composite functions f ∘ g and g ∘ f are:
domain of f = (-∞, ∞)
domain of g = (-∞, ∞)
domain of f ∘ g = (-∞, ∞)
domain of g ∘ f = (-∞, ∞)

The composite functions f ∘ g and g ∘ f are formed by plugging one function into the other. To find f ∘ g, we plug the function g into the function f:

f ∘ g = f(g(x)) = f(x2/3) = (x2/3)3 = x2

To find g ∘ f, we plug the function f into the function g:

g ∘ f = g(f(x)) = g(x3) = (x3)2/3 = x2

The domain of a function is the set of all possible values of x that make the function defined. The domain of f is all real numbers, since the function f(x) = x3 is defined for all values of x:

domain of f = (-∞, ∞)

The domain of g is also all real numbers, since the function g(x) = x2/3 is defined for all values of x:

domain of g = (-∞, ∞)

The domain of f ∘ g is the intersection of the domain of f and the domain of g, which is all real numbers:

domain of f ∘ g = (-∞, ∞)

The domain of g ∘ f is also the intersection of the domain of g and the domain of f, which is all real numbers:

domain of g ∘ f = (-∞, ∞)

Therefore, the answers are:

domain of f = (-∞, ∞)
domain of g = (-∞, ∞)
domain of f ∘ g = (-∞, ∞)
domain of g ∘ f = (-∞, ∞)

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We round up to the nearest whole number because we are unable to have half a player. As a result, the softball team is allowed to send 7 players to the competition.

The equal sign joins two expressions to create a mathematical formula called an equation. An illustration formula could be 3x - 5 = 16. By resolving this equation, we find that the value of the variable x is 7.

To begin, let's define a few variables:

x: The softball team's total roster size

y: the sum of the players' meal expenses

We can construct the equation shown below:

$1353 - $943.50 - $31.50x = y

Simplifying this equation, we get:

$409.50 - $31.50x = y

we can set up another equation:

y = $31.50x

Now we can substitute the second equation into the first equation to eliminate y:

$409.50 - $31.50x = $31.50x

Simplifying this equation, we get:

$409.50 = $63x

Dividing both sides by 63, we get:

x = 6.5

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Hannah will have $681.98 in her savings account after 3 years at 2.75% simple annual interest.

To calculate the amount of money Hannah will have in the account after 3 years, we can use the formula for simple interest:

Simple interest = principal x rate x time

where:

principal is the amount of money initially deposited

rate is the annual interest rate (expressed as a decimal)

time is the number of years

In this case, the principal is $630, the rate is 2.75% (or 0.0275 as a decimal), and the time is 3 years. Plugging these values into the formula, we get:

Simple interest = $630 x 0.0275 x 3 = $51.98

This means that after 3 years, Hannah will have earned $51.98 in simple interest. To find the total amount of money in her account, we need to add this interest to the original principal:

Total amount = principal + simple interest

Total amount = $630 + $51.98 = $681.98

Therefore, after 3 years Hannah will be having $681.98 in her account after 3 years at 2.75% simple annual interest.

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The complete question is :

Hannah deposits $630 in a savings account at 2. 75% simple annual interest. How much money will she have in the account after 3 years?

This statement is false. A right exact functor preserves exactness of short exact sequences at the right-hand side, but it does not necessarily preserve exactness at the left-hand side. An example of a right exact functor that is not left exact is the tensor product functor.

The following statements can be proved or disproved as follows:
(a) Every ring is an IBN ring.
This statement is false. A ring is said to be an IBN (Invariant Basis Number) ring if all of its finitely generated free modules have unique rank. However, not all rings have this property. For example, the ring of polynomials over a field F, F[x], is not an IBN ring.
(b) In a ring R, if for any a,b∈R,ab=0, then ba=0.
This statement is true. If ab=0, then b is a zero divisor in the ring R. Since zero divisors are symmetric, this implies that ba=0 as well.
(c) The characteristic of a finite field is a prime number.
This statement is true. The characteristic of a finite field is the smallest positive integer n such that n*1=0 in the field. Since a finite field is also an integral domain, it cannot have zero divisors, and therefore the characteristic must be a prime number.
(d) Every right exact functor is also left exact.
This statement is false. A right exact functor preserves exactness of short exact sequences at the right-hand side, but it does not necessarily preserve exactness at the left-hand side. An example of a right exact functor that is not left exact is the tensor product functor.

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Answer:

Step-by-step explanation:

i don’t know

Answer:i really don´t know hopefully you get thw\e answer correct.

Step-by-step explanation:

The formula for calculating the effective annual rate of interest with quarterly compounding is:

(1 + r/4)^4 - 1 = A/P

where r is the quarterly interest rate, A is the final amount, and P is the principal.

In this case, P = $2,000, A = $3,000, and the time period is 7 years or 28 quarters.

So we have:

(1 + r/4)^4 - 1 = 3000/2000

(1 + r/4)^4 = 1.5

1 + r/4 = (1.5)^(1/4)

r/4 = (1.5)^(1/4) - 1

r = 4[(1.5)^(1/4) - 1]

To get the effective annual rate, we need to convert the quarterly rate to an annual rate by multiplying by 4:

effective annual rate = 4[(1.5)^(1/4) - 1] ≈ 8.84%

Therefore, the effective annual rate of interest at which $2,000 will grow to $3,000 in seven years if compounded quarterly is approximately 8.84%, rounded to 2 decimal places.

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Therefore , the solution of the given problem of unitary method comes out to be 29 1/3 yards of fabric.

To finish the job using the unitary method, multiply the measures taken from this microsecond section by two variable. In a nutshell, when a wanted thing is present, the characterized by a group but also colour groups are both eliminated from the unit technique. For expression instance, 40 changeable-price pencils would cost Inr ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.

Here,

If 1 2/9 yards of cloth are required for each choir robe, then 24 choir robes will require:

=> 1 2/9 * 24 = (1*9+2)/9 * 24 = 11/9 * 24

We add the numerators and denominators together to multiply fractions:

=> 11/9 * 24/1 = (1124)/(91) = 264/9

264/9 yards of cloth will be required to make 24 choir robes. This can be stated simply as:

(Rounded to the closest 1/3 yard) 264/9 = 29 1/3 yards of fabric.

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Answer:

25/99

Step-by-step explanation:

If the tickets are numbered 1-100, half of the tickets will be even and half of the tickets will be odd

Number of even tickets = 50

Number of odd tickets = 50

Let A be the event =>  even ticket on first draw

Let B be the event => odd ticket on second draw

P(even on first draw) = P(A)
= Number of even tickets/total number of tickets

= 50/100

= 1/2

Once a ticket has been drawn and the second draw is without replacement,

Total number of tickets remaining = 100 - 1 = 99

Total number of odd tickets remaining given first ticket drawn is even
= 50

P(odd ticket second draw | first draw is even) = P(B | A)
= 50/99

P(A and B) = P(A) · P(B | A)

= 1/2 x 50/99

= 50 / (2 x 99)

= 50/198

= 25/99

Probability that it is an even number:

[tex] \tt \: P(E) = \frac{F.O.}{T.O.} [/tex]

[tex] \tt \: P(E) = \frac{50}{100} = \frac{1}{2} [/tex]

Pribability that it is an odd number:

[tex] \tt \: P(E) = \frac{F.O.}{T.O.} [/tex]

[tex] \tt \: P(E) = \frac{50}{99} = 0.505051[/tex]

Answer:

the greatest number of groups you can make is 4

Step-by-step explanation:

First we have to find the greatest number which can divide 8 and 12 exactly.

there is none but G.C.F is 4

That is, 8 U.S stamps can be displayed in 4 groups at 2 groups.

And 12 international stamps can be displayed in 4 groups at 3 groups

In this way, each of the 4 groups would have 2 U.S stamps and 3 international stamps. And all the 4 groups would be identical.

Answer:

30

Step-by-step explanation:

40/4=10

25%=10

40-10=30

Answer: 7

Step-by-step explanation:

The slope is the number being multiplied by x

Answer: 43.96 inches^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]-\frac{1}{2}[/tex] x ≤ 17

( [tex]-\frac{2}{1}[/tex] )( [tex]-\frac{1}{2}[/tex] ) x ≤ 17( [tex]-\frac{2}{1}[/tex] )

x ≥ - 34

Answer:

Rise and run

Step-by-step explanation:
Lets have it in slope intercept form
y=3/5x

Therefore our slope is 3/5 and y-intercept is (0,0)

Now we can start to graph. Start on our Y-intercept which is zero. Let's count 3 spaces up, which is our rise, then lets count 5 spaces to our right, which is our positive run, and plot a dot on our final point. You can do the same negative to graph our opposing points. Start on our 0,0 y-intercept, and count down 3 spaces. Then count 5 spaces to the left, and plot a dot on your final point. Now, let's draw a line through our points (-5, -3), (0,0), and (5,3)!

There are a total of 26 letters in the English alphabet and 10 digits (0-9). Therefore, the total number of car number plates that can be made if each plate contains 3 different letters followed by 3 different digits can be calculated as follows:

- For the first letter, there are 26 options.

- For the second letter, there are 25 options (since the first letter has already been used).

- For the third letter, there are 24 options (since the first and second letters have already been used).

- For the first digit, there are 10 options.

- For the second digit, there are 9 options (since the first digit has already been used).

- For the third digit, there are 8 options (since the first and second digits have already been used).

Therefore, the total number of car number plates that can be made is:

26 × 25 × 24 × 10 × 9 × 8 = 11,232,000

So, the answer is 11,232,000 car number plates can be made if each plate contains 3 different letters followed by 3 different digits.

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The value of angle XYZ is 0.020 degrees using the cosine function.

Simply put, inverse trigonometric functions are the opposites of the fundamental trigonometric functions sine, cosine, tangent, cotangent, secant, and cosecant. The terms arcus functions, antitrigonometric functions, and cyclometric functions are also used to describe them. To find the angle for any trigonometric ratio, apply these inverse trigonometric functions. The fields of engineering, physics, geometry, and navigation all heavily utilise the inverse trigonometry functions.

From the given right triangle we observe that:

cos y = 6 / 15 = adjacent side /hypotenuse

y = arccos(6/15)

y = 0.020 degrees

Hence, the value of angle XYZ is 0.020 degrees using the cosine function.

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The probability of escape for the guest is approximately 9 - √27/4.

This can be calculated using the principle of inclusion-exclusion. To calculate the probability of escape, we can calculate the probability of the guest being unable to move from Room 0 to any of the other rooms.

This is the probability of all doors from Room 0 being locked, which is equal to 1/3 x 1/3 = 1/9. Therefore, the probability of escape is 1 - 1/9 = 8/9.

Using the inclusion-exclusion principle, we can calculate the probability of the guest being able to move from Room 0 to any of the other rooms. The probability of the guest being able to move from Room 0 to any of the other rooms is equal to 1 - (1/3 + 1/3 - 1/9) = 9 - √27/4.

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So, by resolving the given, we obtain the result: Alexandria thus shells expressions out a total of $12.86 for the 14 tracks.

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 +.

Alexandria downloads 13 tracks at $0.99 each, for a grand total of $12.87 (13 x $0.99).

She also spends $1.49 downloading one song.

The price before the coupon is thus $12.87 + $1.49 = $14.36.

The final price is $14.36 - $1.50 = $12.86 after the coupon for $1.50 discount is applied.

Alexandria thus shells out a total of $12.86 for the 14 tracks.

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