The area of rectangle RSTU is 36x2+25x−25. The length of the rectangle RSTU is 4x+5. Which expression describes the width of the rectangle RSTU?

Given:

Let's solve the equation in terms of p:

(1) x² - 2 x - 8 and Option (2) x² + 2 x - 8 are two polynomials which has been factored.

Given are the polynomials,

1) x² - 2 x - 8

Factors = (x+2)(x-4)

2) x² + 2 x - 8

Factors = (x-2)(x+4)

3) x²-2x-4 = There will be no integral root.

4) x²+2x-4 = There will be no integral root.

Hence the (1) x² - 2 x - 8 and Option (2) x² + 2 x - 8 are two polynomials which has been factored.

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The coefficient of x^7 when the expression is expanded by the binomial theorem (3x + 4)^10 is 16,796,160.

In the given question, we have to find the coefficient of the given term when the expression is expanded by the binomial theorem.

The given expression is (3x + 4)^10 coefficient of x^7.

The binomial expression

\((x+y)^n = x^n+^nC_{1}x^{n-1}y^1+^nC_{2}x^{n-2}y^2+\dots\dots+^nC_{k}x^{n-k}y^k+\dots\dots +y^n\)

where \(^nC_{k}=\frac{n!}{k!{(n-k)!}}\)

coefficient of x^7

T(4) = T(3+1)

T(4) = \(^{10}C_{3}(3x)^{10-3}(4)^3\)

Solving

T(4) = \(\frac{10!}{3!(10-3)!}\cdot(3x)^{7}\cdot64\)

T(4) = \(\frac{10!}{3!7!}\cdot2187x^{7}\cdot64\)

T(4) = \(\frac{10\times8\times7!}{3\times2\times1\times7!}\cdot2187x^{7}\cdot64\)

T(4) = 16,796,160 x^7

The coefficient of x^7 when the expression is expanded by the binomial theorem (3x + 4)^10 is 16,796,160.

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Answer:

  y = {-1/2x +7 for x < 6; 1/2x +1 for x ≥ 6}

Step-by-step explanation:

You want y = 1/2|x -6| +4 written as a piecewise function.

The absolute value function changes its definition when its argument is negative:

  y = |x|   ⇒   y = -x for x < 0, and y = x for x ≥ 0

This means our piecewise function will have one definition for (x-6) < 0 and another for (x -6) ≥ 0.

The argument is negated in this domain, so we have ...

  y = -1/2(x -6) +4

  y = -1/2x +3 +4

  y = -1/2x +7

The absolute value function is an identity function in this domain:

  y = 1/2(x -6) +4

  y = 1/2x -3 +4

  y = 1/2x +1

Combining these descriptions into one, we have ...

  \(\boxed{y=\begin{cases}-\dfrac{1}{2}x+7&\text{for }x < 6\\\\\dfrac{1}{2}x+1&\text{for }x\ge6\end{cases}}\)

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[~S & (R V S)] ≡ (Q ⊃ S) is true when A = T, S = F, R = F, and Q = T by substituting the propositional variables.

A truth table is a table used to determine the truth values of a compound proposition, which is a logical statement made up of simpler propositions using logical operators such as "and" (represented by "&"), "or" (represented by "V"), "not" (represented by "~"), conditional (represented by "⊃"), and biconditional (represented by "≡").

Let's substitute the given truth values for the propositional variables in the given statement:

[~F & (F V F)] ≡ (T ⊃ F)

Using the truth table for conjunction (represented by "&") and disjunction (represented by "V"), we can simplify the left-hand side of the equivalence:

[T & F] ≡ (T ⊃ F)

Using the truth table for conditional (represented by "⊃"), we can simplify the right-hand side of the equivalence:

F ≡ F

Since both sides of the equivalence have the same truth value, the statement is true.

Therefore, [~S & (R V S)] ≡ (Q ⊃ S) is true when A = T, S = F, R = F, and Q = T.

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Neither statement "E and F are always independent" nor "E and F are always dependent" is correct for mutually exclusive events E and F with positive probabilities p(e)>0 and p(f)>0.

Events that are mutually exclusive cannot occur at the same time. For example, if we have two events E and F such that E represents "rolling a 1 on a fair die" and F represents "rolling a 2 on a fair die", These events cannot occur simultaneously since a 1 and a 2 cannot be rolled.

In probability theory, two events E and F are considered independent if the occurrence of one event has no effect on the probability of the other event occurring. For example, if we have two events E and F such that E represents "rolling a 1 on a fair die" and F represents "rolling a 6 on a fair die", these events are independent because the occurrence of one event (rolling a 1) does not affect the probability of the other event (rolling a 6) occurring.

In the case where events E and F are mutually exclusive, their occurrence does affect each other, as the occurrence of one event makes it impossible for the other event to occur. Therefore, the statement "E and F are always independent" is not correct. Similarly, the statement "E and F are always dependent" is also not correct because dependence is a different concept from mutual exclusiveness.

Therefore, "Neither of the above statements is correct" is the appropriate response.

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The complete question is:

Which of the following statements is correct if e and f are mutually exclusive and p(e)>0 and p(f)>0?

a) E and F are always independent

b) E and F are always dependent

c) Neither of the above statement is correct

Using DeMoivre’s theorem, the answer in regular form would be (5 + 5√3i)⁷ = -5000000 + 8660254.03i

The De Moivre's Theorem is used to simplify the computation of powers and roots of complex numbers and is used in together with polar form.

Convert the complex number to polar form. The polar form of a complex number is z = r(cos θ + isin θ),

r = |z|  magnitude of z

it becomes

r = √((5)² + (5√3)²) = 10

θ = arg(z) is the argument of z.

θ = atan2(b, a) = atan2(5√3, 5) = π/3

(5 + 5√3i) = 10 × (cos π/3 + i sin π/3)

De Moivre's theorem to raise the complex number to the 7th power

(5 + 5√3i)⁷

= 10⁷× (cos 7π/3 + i sin 7π/3)

= 10⁷ × (cos 2π/3 + i sin 2π/3)

Convert this back to rectangular form:

Real part = r cos θ = 10⁷× cos (2π/3) = -5000000

Imaginary part = r sin θ = 10⁷ × sin (2π/3) = 5000000√3 = 8660254.03i

∴  (5 + 5√3i)⁷ = -5000000 + 8660254.03i

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Answer:10^7 (1/2 - √3/2 i)

Step-by-step explanation:

To use DeMoivre's theorem, we first need to write the number in polar form. Let's find the magnitude and argument of the number:

Magnitude:

|5 + 5√(3i)| = √(5^2 + (5√3)^2) = √(25 + 75) = √100 = 10

Argument:

arg(5 + 5√(3i)) = tan^(-1)(√3) = π/3

So the number can be written in polar form as:

5 + 5√(3i) = 10(cos(π/3) + i sin(π/3))

Now we can use DeMoivre's theorem:

(5 + 5√(3i))^7 = 10^7 (cos(7π/3) + i sin(7π/3))

To simplify, we need to find the cosine and sine of 7π/3:

cos(7π/3) = cos(π/3) = 1/2

sin(7π/3) = -sin(π/3) = -√3/2

Explanation:

So the final answer in rectangular form is:

10^7 (1/2 - √3/2 i)

Answer:

17

Step-by-step explanation:

PEMDAS

parentheses, exponents, multiply, divide, add, subtract

5(12-9)^2 -4×7

5(3)^2 -4×7

5(9)-4×7

45 -28

17

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Answer:

the vector result is 7.852 magnitude and the direction is 67.63

Answer:

the volume of the square pyramid is 2430 cubic cm

Answer:

1296 cm³

Step-by-step explanation:

V = a² x [√s²- (a/2)²] / 3

a = 18 cm

s = 15 cm

V = 18² x [√15²-(18/2)²] / 3 = 18² x [√225-81] / 3

V = 324 x (√144/3) = 1296 cm³

Answer:

d: x = -8

Step-by-step explanation:

40 + 65 + x + 83 = 180  (sum of internal angles of a triangle)

x = 180 - 40 - 65 - 83

x = -8

Answer:

y = 15 , x = 6

Step-by-step explanation:

you can easily find y from first equation

Move y to the other side of the equation and reverse its sign

so (-11) changes to (+11) and now we have this equation

y = 15

now you must replace 15 instead of y in second equation ,then we have this equation

15 = 2x + 3

now we have to find x

move (+3) to other side of equation and reverse its sign

(+3) changes to (-3)

we have this equation now

15 - 3 = 2x

12 = 2x

x = 12 ÷ 2 = 6

Answer:

Step-by-step explanation:

Square root 24

Real numbers. Irrational numbers. Nothing below that contains Sqrt(24)

-93 is in the integers, rational numbers, real numbers.

Answer:

Graph 2

Step-by-step explanation:

We are given the inequality x≤2

First off, with the inequality sign being ≤ rather than <, we know that 2 is also included. This means that x can be equal to 2 or less than 2.

Since 2 is included, we know we are looking for a solid line.

That said, we can eliminate the 1st and 4th graphs because there is a dotted line at 2, meaning that 2 is not included.

Next, based on the inequality sign, we know that values less than 2 satisfy it. So judging by the shaded region on each graph, we see that Graph 2 is the one that satisfies it.

For clarity's sake, one trick you can use is thinking of the inequality sign as an arrow. If it points left, values toward the left should be shaded and vice versa.

Lastly, I'll give you the inequality for each graph.

Graph 1: x<2

Graph 2: x≤2

Graph 3: x≥2

Graph 4: x>2

Hope that helps, let me know if you have any questions!

The difference in the maximum values of the functions ​g(x) ​and ​f(x)​ is 3

The functions are given as

f(x) = -(x - 3)² + 9

Table of g(x)

x    −3 −4 −2 0 −1  4

g(x) 0   8   1  12  2  8

The maximum value of f(x) is when the root expression is 0

i.e. -(x - 3)² = 0

So, we have

Max f(x) = 0 + 9

Max f(x) = 9

For the table of values, we have

Max g(x) = 12

The difference between these values is

Difference = 12 - 9

Evaluate

Difference = 3

Hence, the difference is 3

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Answer:

-10x + 2

Step-by-step explanation:

So in order simplify the equation you have to add all the variables together and all the numbers together in this equation:

-9x + 3 - x - 1

So we are going to add -9x and x together while adding 3 and -1 together:

-9x + (-x) = -10x

3 - 1 = 2

So that would make the equation look like this:

-10x + 2

Tada! You have simplified the equation!!! Hope this helps you!!!

The value of the equation that defines the function is f(x) = 3(5/3)ˣ

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

(0, 3) and (1, 5)

An exponential function is represented s

y = abˣ

Where,

a = y when x = 0

So, we have

y = 3bˣ

Using the other point, we have

3b = 5

This gives

b = 5/3

So, we have

f(x) = 3(5/3)ˣ

Hence, the equation defining f is f(x) = 3(5/3)ˣ

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y = 4x +8

Step-by-step explanation:

Just take the signs of the integers and switch them around! -4 becomes +4, and -8 becomes +8. Note that you should not switch multiplication to division, this only works for addition and subtraction signs.

Answer:

-6

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

3(-2)(-1)(-1)= -6

[RevyBreeze]

Answer:

b) 4

Step-by-step explanation:

4 times $0.05 = $0.20

4 times $0.30 = $1.20

then you add the both totals together

0.20 + 1.20= $1.40

Answer:

See below

Step-by-step explanation:

For the second step, \(\angle T\cong\angle R\) by Alternate Interior Angles. The rest of the steps appear to be correct.

Check the picture below, notice the whole at 5, meaning that value is not included in the set.

Answer:

I love algebra anyways

The ans is in the picture with the  steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

Soln: Formula for a²+b² can be given by two types.

(i). a²+b² = (a+b)² - 2ab

= a²+2ab+b²-2ab

= a²+b²

=> LHS = RHS

Therefore, hence proved!

(ii). a²+b² = (a-b)² + 2ab

= a²-2ab+b²+2ab

=> LHS = RHS

Therefore, hence proved!

Hence, a²+b² = (a+b)² - 2ab

'OR'

a²+b² = (a-b)² + 2ab

Thank you. ☺️

hope it helps

Answer:

Domain = (-∞, ∞) Range = (-∞, ∞)

End Behavior: As X -> -∞, Y -> -∞ | As X -> ∞, Y -> ∞

Inflection Point: (2,0)

Step-by-step explanation:

Answer:u cheating like a mfka lol

Step-by-step explanation:dwd

Answer:

C) 6 (6w +5)

Step-by-step explanation:

6w+5 ≠ 36w +30

66 ≠ 36w +30

6 (6w +5) -> 36w + 30 = 36w +30

66w ≠ 36w +30

This leaves us with the option of 6 (6w +5)

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

x = sqrt(39)

Step-by-step explanation:

Let y = common side of the two triangles.

Upper right triangle:

6^2 + y^2 = 10^2

y^2 = 100 - 36

y^2 = 64

y = 8

Lower left triangle:

5^2 + x^2 = 8^2

x^2 = 64 - 25

x^2 = 39

x = sqrt(39)

The value of 3¾ft in yards would be = 1 6/25 yard

A mixed number is the type of number that is made up of three parts such as the whole number, a numerator and a denominator.

To convert to yards;

1 ft = 0.33 yard

3¾ = X yards

make x yards the subject of formula;

X yards = 3¾ × 0.33

X yards = 3.75×0.33

X yards = 1.24 yards

X yards in mixed number= 124/100 = 31/25 = 1 6/25 yard.

Note that the final value which is 124/100 is reduce to the lower figure by dividing through with 4 to arrive at the mixed number 1⁶/25

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