If f(x) is defined as follows, find (a) f(-3), (b) f(0), and (c) f(4).
x²
if x < 0
if x = 0
3x + 3 ifx>0
f(x) = 0
(a) f(-3)= (Simplify your answer.)
THE

The step in which the subtraction property of equality was applied to solve the equation is given as follows:

D. The subtraction property of equality was not applied to solve this equation.

The subtraction property of equality states that subtracting the same number from both sides of an equation does not affect the equality, and hence it is used to isolate a variable that is adding on a side of the expression.

For this problem, to remove the term -7, we add 7 to both sides of the expression, hence the addition property of equality was applied.

In the other step, the multiplication property was applied, hence option D is the correct option for this problem.

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Answer:

52%

Step-by-step explanation:

If 25% is the 100% only multiply 13 by 4 and thats it

Answer:

B

Step-by-step explanation:

factor the expression.

recheck: -5×4= -20

-5+4= 1 (which is a)

a×a=a²

Answer:

16

Step-by-step explanation:

is the the associated

Answer:

  37

Step-by-step explanation:

  2022 -1986 +1 = 37

The holiday has been celebrated 37 years.

_____

The number of years is 1 more than the difference between the first year and the last year. You can get the same result by subtracting 1985 from 2022. That is, you want the count of celebrations after 1985.

Answer:

Step-by-step explanation:

So in this example we'll be using the difference of squares which essentially states that: \((a-b)(a+b)=a^2-b^2\) or another way to think of it would be: \(a-b=(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b})\). So in this example you'll notice both terms are perfect squares. in fact x^n is a perfect square as long as n is even. This is because if it's even it can be split into two groups evenly for example, in this case we have x^8. so the square root is x^4 because you can split this up into (x * x * x * x) * (x * x * x * x) = x^8. Two groups with equal value multiplying to get x^8, that's what the square root is. So using these we can rewrite the equation as:

\(x^8-16 = (x^4-4)(x^4+4)\)

Now in this case you'll notice the degree is still even (it's 4) and the 4 is also a perfect square, and it's a difference of squares in one of the factors, so it can further be rewritten:

\(x^4-4 = (x^2-2)(x^2+2)\)

So completely factored form is: \((x^2-2)(x^2+4)(x^4+4)\)

I'm assuming that's considered completely factored but you can technically factor it further. While the identity difference of squares technically only applies to difference of squares, it can also be used on the sum of squares, but you need to use imaginary numbers. Because \(x^2+4 = x^2-(-4)\). and in this case a=x^2 and b=-4. So rewriting it as the difference of squares becomes: \(x^4+4 = x^4 - (-4) = (x^2-\sqrt{-4})(x^2+\sqrt{-4}) = (x^2-2i)(x^2+2i)\) just something that might be useful in some cases.

We can factor this into \((x^{4}+4)(x^{4} -4)\).

This is because we use  difference of two squares where \(x^{2} -y^{2} = (x+y)(x-y)\)

So we rewrite x^8-16 to x^8-4^2.

This can then be written to the equation I put at the start.

p.s. The reason its \(x^{4}\) is because \(x^{4} * x^{4} = x^{8}\)
(P.S.S I just found that the other helper did it fully so I stopped here, read his, its correct)

Answer:

nx^(n-1).

Step-by-step explanation:

d/dx (x^n)

We multiply by n than subtract 1 from the exponent (n):

= n x^(n-1)

Numerical examples:

d(x^3) dx = 3 * x^(3-1)

= 3x^2.

d(2x^5)/dx = 5*2 x^(5-1)

= 10x^4.

The ratio of the perimeter of the smaller to larger rectangle is 3:4

The dimension of the smaller rectangle = 3 by 9

The dimension of the larger rectangle = 5 by 11

The perimeter of a rectangle is given by the relation :

Perimeter = 2(Length + width)

Perimeter of smaller rectangle = 2(3+9) = 24 ft²

Perimeter of larger rectangle = 2(5+11) = 32 ft²

Ratio of smaller to larger rectangle

Smaller perimeter : larger perimeter

24 : 32

Reduce to simplest form

3 : 4

Hence, ratio of smaller to larger rectangle is 3:4

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Answer:

10x^9 - 4x? As x-> - infinity then y -> infinity and as x-> infinity then y -> infinity.

Step-by-step explanation:

Answer:

b or c i think

Step-by-step explanation:

not for sure just a guess

Think of a number line.

Option A has a big number then a little number.

Nope

B has a little number, a big number then a litlte number

Nope

C has a little number, a bigger number, then a bigger number. then a smaller number.

Nope

D has a little number, a bigger number, a bigger number, a bigger number, then a bigger number.

Yea

D)

Hope this helps,

Jeron

:- )

(p.s., maybe brainliest if I really helped??  :))))    )

Answer:

Tom: £166

Ben: £581

Step-by-step explanation:

     In the ratio 2 : 7 there are 9 portions total (2 + 7 = 9).

£747 / 9 = £83

     For Tom:

£83 * 2 = £166

     For Ben:

£83 * 7 = £581

Checking our work:

      Since the decimals are the same, this means the ratios are equal.

2/7 = 0.2857

166/581 = 0.2857

Answer:

degree 24.7

Radian 0.43

Step-by-step explanation:

To answer this question let's graph the parent function f(x)=x.

Now that we have the parent function we can compare both graphs.

We notice that the function given is translated 3 units up. Therefore the answer is B.

The triangle which could be drawn as per the given description is only option b. isosceles triangle with measure 20° and 80°.

An acute triangle with sides measuring 7, 4, and 2

In an acute triangle, the sum of the squares of the two shorter sides must be greater than the square of the longest side .

According to the Pythagorean Theorem.

Here, 7² is greater than (4² + 2²).

So this is not possible.

An isosceles triangle with angles measuring 20° and 80°

In an isosceles triangle, two angles are equal, so if two angle measures 20° and 80°,

Then the third angle measures is

180° - 20° - 80°= 80°

Two angles are congruent implies two sides are congruent.

It is possible to form isosceles triangle.

An obtuse triangle with sides measuring 5, 10, and 15

In an obtuse triangle, the longest side is opposite the largest angle.

Sum of squares of two shorter sides is less than square of longest side according to Pythagorean Theorem.

However, 15²is greater than (5²+ 10²),

so this is not possible.

A scalene triangle with angles measuring 110° and 35°

The sum of the angles of any triangle is 180°,

so the third angle must measure

180° - 110° - 35° = 35°.

Two angles are congruent so it is isosceles triangle.

It is not possible to form scalene triangle.

Therefore, the triangle possible to draw as per the given condition is only option b. isosceles triangle with measure 20° and 80°.

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Answer:  D is the answer. trust me.

Step-by-step explanation:

The problem that could be solved using the equation 10x+5=35 is option D: After a $5 discount, an order of 10 items cost $35. How much did each item cost?

To solve this problem, we can use the equation 10x + 5 = 35, where x represents the cost of each item. The $5 discount reduces the total cost of the 10 items by $5, so the total cost of the 10 items before the discount would be 10x. Therefore, we can set up the equation:

10x + 5 = 35

Subtracting 5 from both sides, we get:

10x = 30

Dividing both sides by 10, we get:

x = 3

So, each item cost $3 before the discount.

Answer:

A

Step-by-step explanation:

Answer:

m<1 = 142°

m<3 = 142°

Step-by-step explanation:

We are given two vertical angles, which are <1 and <3.

We know that m<1 = 2x + 26°, and m<3 = 3x - 32°.

We want to find the measure of each angle.

Recall that vertical angles are congruent by vertical angles theorem.

This means that <1 ≅ <3.

This also means that 2x + 26 = 3x - 32.

We can solve the above equation.

Subtract 2x from both sides.

2x + 26 = 3x - 32.

-2x           -2x

_________________

26 = x - 32

Add 32 to both sides.

58 = x

Now, substitute this value of x into the values given.

Substitute x as 58 in 2x+26 to find the value of <1.

m<1 = 2x + 26 =  2(58) + 26 = 116 + 26 = 142°

We can now substitute x as 58 in 3x - 32 to find the value of <3.

m<3 = 3x - 32  =  3(58) - 32 = 174 - 32 = 142°

Solving a system of equations we can see that each pound of trail mix costs $3.50, and each pound of jelly beans costs $1.50

Let's define the variables:

Then we can write a system of equations so we will get:

5x + 3y = 22

2x + 12y = 25

To solve this, we can subtract 4 times the first equation fom the second one:

2x + 12y - 4(5x + 3y) = 25 - 4*22

2x + 12y - 20x - 12y = -63

-18x = -63

x = -63/-18

x = 3.5

That is the cost of each pound of trail mix, and replacing that in one of the equations:

2*3.5 + 12y = 25

y = (25 - 2*3.5)/12

y = 1.5

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Account balance of Ginny after withdrawal = $ 20 .

Given : Ginny's account balance before withdrawal ie . $ 40

            Her withdrawal amount ie . $ 20

To find : account balance after withdrawal

Calculation : Opening balance = $ 40 ie . initially Ginny had $ 40 .

After withdrawal ( taking out ) of $ 20 ,

Ginny has 40 - 20 = $ 20 left .

After adjustment , final amount = $ 20 .

Therefore , account balance of Ginny after withdrawal = $ 20 .

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Answer:

it would be 11....................

Answer:

its 11

according to the BODMAS RULE

Answer:

108, 324, 972

Step-by-step explanation:

This sequence is multiplying by ✖️3.

4✖️3=12✖️3=36✖️3=108✖️3=324✖️3=972

Hope this helps!

Answer:

m = (1.9 - 2.14)/2 = -0.24/2 = -0.12

therefore, m = -0.12 or -3/25

Answer: 3.9%

Step-by-step explanation:

We can use the formula for continuous compounding to solve this problem:

A = P * e^(r*t)

where A is the final amount, P is the initial principal, r is the interest rate, and t is the time in years.

In this case, we know that P = $1,800, A = $2,400, and t = 6 years. We want to solve for r.

First, we can rearrange the formula to isolate r:

r = (ln(A/P)) / t

where ln represents the natural logarithm.

Plugging in the values we know, we get:

r = (ln(2400/1800)) / 6

r = 0.0392

The simplified equation is (π2 / 2) * ∫[0, ∞] (x(2x-1) * e(-x) / (Γ(x) * Γ(1 - x)) DX

a. To prove B(x+1, y) = x * B(x, y), proceed as follows.

Start with B(x+1, y) = [(x+1)! * y!] / ((x+y+2)!) (using the definition of B(x, y)).

Rewrite 1 / (x+1) to (x+y+2 - (y+1)) / (x+y+2) .

Using the formula above, express B(x+1, y) as (x+y+2) / (x+y+2) * [(x+1)! to rewrite. * y!] / ((x+y+2)!) - (y+1) / (x+y+2) * [(x+1)! * y!] / ((x+y+2) !).

Simplify the formula to (x+y+2) / (x+y+2) * B(x, y) - (y+1) / (x+y+2) * B(x, y) increase.

Simplify further to B(x, y) - (y+1) / (x+y+2) * B(x, y).

Note that B(x, y) can be expressed as (x / (x+y+1)) * B(x, y) .

Substitute this formula in the previous step to get,

x * B(x, y) - (y+1) / (x+y+2) * x * B(x, y).

x * B(x, y) - (y+1) / (x+y+2) * x * B(x, y)

= x * B(x, y)

You have now proved B(x+1, y) = x * B(x, y).

b. We wish to prove the identity Γ(2x) = ((2sin(πx))) * Γ(x) * Γ(x + 1/2).

Integrate ∫[0, ∞] (x(2x-1) * Start with dx.

Evaluating this integral using the permutation u = du is obtained.

Simplify the integral to (1/2) * Γ(x + 1/2).

Express sin(πx) as π / (Γ(x) * Γ(1 - x)).

Let the original integral be π * (2(2x-1) / π) * ∫[0, ∞] (x(2x-1) * e(-x) * (1/sin( πx) Rewrite.)) DX.

Substituting the equations,

The integral, π * (2(2x-1) / π) * ∫[0, ∞] (x(2x-1) *

We get * (π / (Γ(x) * Γ(1 - x)))) dx.

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