What is the degree measure of r?

A) 27°

B) 32°

C) 37°

D) 64°

Final answer:

The domain of the function g(x) = -[x] + 3 is all real numbers because the floor function is defined for all real numbers.

Explanation:

The given function is g(x) = -[x] + 3. To determine the domain of g(x), we look for the set of all input values (x) that the function can accept.

The square brackets around x indicate that we are dealing with the floor function, which takes a real number and rounds it down to the nearest integer.

Since the greatest integer function is defined for all real numbers, the only restriction we have is when the function involves division by zero.

Since the process of rounding down to the nearest integer is defined for all real numbers, the domain of g(x) is all real numbers, which is expressed as ∞ < x < ∞ or –∞ < x < ∞.

Answer:

a.)The total 4-letters passwords when repetition of letters is allowed are 456976

b.)The total 4-letters passwords when repetition of letters is not allowed are 358800

Step-by-step explanation:

Some situations of probability involve multiple events. When one of the events affects others, they are called dependent events. For example, when objects are chosen from a list or group and are not returned, the first choice reduces the options for future choices.

There are two ways to sort or combine results from dependent events. Permutations are groupings in which the order of objects matters. Combinations are groupings in which content matters but order does not.

How many 4-letter passwords can be made using the letters A throught Z if...

a)Repetition of letters is allowed?

There are only 26 possible values for each letter of the password (The English Alphabet consists of 26 letters). The total 4-letters passwords when repetition of letters is allowed are [tex]26^{4} =456976[/tex]

b) Repetition of letters is not allowed?

If repetition of  letters is not allowed, we can only choose 4 letters out of 26. Using the permutation equation [tex]nP_{k} =\frac{n!}{(n-k)!}[/tex]

The total 4-letters passwords when repetition of letters is not allowed are [tex]26P_{4} =\frac{26!}{(26-4)!}=26.25.24.23=358800[/tex]

.

When repetition of letters is allowed, there are 456,976 possible 4-letter passwords that can be made using the letters A through Z. When repetition of letters is not allowed, there are 358,800 possible passwords that can be made.

a) When repetition of letters is allowed, we have 26 choices for each of the 4 positions in the password. Therefore, the number of 4-letter passwords that can be made is 26 * 26 * 26 * 26 = 456,976.

b) When repetition of letters is not allowed, the number of choices for the first position is 26. For the second position, there are 25 choices left, since we can't repeat the letter used in the first position. Similarly, for the third position, there are 24 choices, and for the fourth position, there are 23 choices. Therefore, the number of 4-letter passwords that can be made without repetition is 26 * 25 * 24 * 23 = 358,800.

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For this case we have that by definition of trigonometric relations that, the sine of an angle is equal to the opposite leg to the angle on the hypotenuse. So:

[tex]Sin (36) = \frac {5} {x}[/tex]

Clearing x:

[tex]x = \frac {5} {sin (36)}\\x =\frac {5} {0.58778525}\\x = 8.517887564 [/tex]

Rounding off we have to:

[tex]x = 8.51[/tex]

Answer:

Option D

Step-by-step explanation:

Shift to the right 5 units and down 2 units.

Answer:

Transactional service

Step-by-step explanation:

If Allison pays all her bills using her bank's online bill pay, it will be considered as transactional service which is a type of electronic banking service.

A transaction involves paying a supplier for its services provided or any goods delivered.

Here the services used will include electricity, water, internet, gas, etc for which the bills are paid. Therefore, the correct answer is transactional service.

Answer:

Transaction service

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

-2x+8=14

Subtract 8 from each side

-2x+8-8=14-8

-2x = 6

Divide by -2

-2x/-2 = 6/-2

x = -3

-2x + 8 = 14

Step 1: Bring 8 to the right side of the equation. To do this subtract 8 to both sides (this is the opposite of addition and will cancel 8 from the left side)

-2x + (8 - 8) = 14 - 8

-2x + 0 = 6

-2x = 6

Step 2: Isolate x by dividing -2 to both sides (division is the opposite of multiplication and will cancel -2 from the left side)

-2x/-2 = 6/-2

x = -3

Check:

Plug -3 where you see x and solve

-2(-3) + 8 = 14

6 + 8 = 14

14 = 14...............................Correct!

Hope this helped!

To find the slope, you should rearrange the equation into slope-intercept form, ie. y = mx + c, where m is the gradient.

y - 9 = 15(x - 5)

y = 15(x - 5) + 9 (Add 9 to each side)

y = 15x - 15*5 + 9 (Expand 15(x - 5))

y = 15x - 75 + 9

y = 15x - 66

Therefor, the slope of the equation is 15.

Answer:

Use the slope-intercept form  

y

=

m

x

+

b

 to find the slope  

m

.

m

=

15

Step-by-step explanation:

Cuz i know all that

Answer:  56 mph

Step-by-step explanation:

48 miles x 2 hours = 96 miles

60 miles x 4 hours =  240 miles

240 + 96 = 360 total miles

360 / 6 (hours) = 56 mph

Answer:

10q

Step-by-step explanation:

Answer:

tan e = -1

cot e = -1

sin e = √2/2

cosec e = √2

cos e = -√2/2

sec e = -√2.

Step-by-step explanation:

6/6-  is the tangent of e  so tan e = -1.

cot e = 1/tan e = -1.

The hypotenuse  of the triangle containing angle e = √(-6)^2 + (6)^2 ( By the pythagoras theorem) and = √72 =  6√2.

Therefore sin e =   6/6√2

= 1/√2

= √2/2

cosec e  = 1 ./ sin e = √2.

cos e = -6 / 6√2

= -√2/2.

sec e = 1/cos e = -√2.

Answer:

60cm^2

Step-by-step explanation:

5 * 12 = 60cm^2

Answer:

the answer is A.616.39

Step-by-step explanation:

Megan can withdraw $615.21 per month for 5 years from the new account.

Option B is the correct answer.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

To solve this problem, we need to use the formula for the future value of an annuity:

[tex]FV = P [(1 + r/n)^{n\times t} - 1]/(r/n)[/tex]

where:

P = payment per period

r = interest rate per period

n = number of compounding periods per year

t = number of years

FV = future value of the annuity

First, we can calculate the future value of Megan's semiannual payments after 10 years:

P = $1,624.13

r = 1.5%/2 = 0.0075 (semiannual interest rate)

n = 2 (semiannual compounding periods)

t = 10 years

So,

[tex]FV = 1,624.13 \times[(1 + 0.0075/2)^{2\times10} - 1]/(0.0075/2)[/tex]

= $21,070.58

Next, we need to calculate the future value of this amount when transferred to the new account:

r = 2.3% / 12 = 0.00191667 (monthly interest rate)

n = 12 (monthly compounding periods)

t = 5 years (60 months)

FV

[tex]= $21,070.58 \times (1 + 0.00191667)^{60}[/tex]

= $24,526.41

Finally, we need to calculate the monthly payment Megan can withdraw for 5 years from this account, assuming the balance is depleted at the end of the 5 years:

P = ?

r = 2.3% / 12 = 0.00191667 (monthly interest rate)

n = 12 (monthly compounding periods)

t = 5 years (60 months)

Using the formula for the present value of an annuity:

[tex]P = FV \times (r/n) / [(1 + r/n)^{n\timest} - 1][/tex]

[tex]= $24,526.41 \times (0.00191667) / [(1 + 0.00191667)^{60} - 1][/tex]

= $615.21

Therefore,

Megan can withdraw $615.21 per month for 5 years from the new account.

Learn more about equations here:

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Answer:

b

Step-by-step explanation:

using pythagoras theorem:

d=(5^2+4^2)^1/2

=6.4 units

Answer:

The approximate length of the diagonal of the rectangle = 6.4 units ⇒ B

Step-by-step explanation:

* Lets revise the properties of the rectangle

- The rectangle has 4 sides

- Each two opposite sides are parallel and equal in length

- It has for right angles

- Its two diagonals are equal in length

- The diagonal divide the rectangle into two congruent right triangles

* Now lets solve the problem

∵ The length of the rectangle = 5 units

∵ The width of the rectangle = 4 units

∵ The diagonal of the rectangle with the length and the width formed

  right triangle, the length and the width are its two legs and the

  diagonal is its hypotenuse

- To find the length of the hypotenuse use Pythagoras theorem

∵ Hypotenuse = √[(leg1)² + (leg2)²]

∴ The length of the diagonal = √[5² + 4²] = √[25 + 16] = √41

∴ The approximate length of the diagonal of the rectangle = 6.4 units

the last one on the right

Answer:

see explanation

Step-by-step explanation:

Given

f(x) = x² - p(x + 1) - c

     = x² - px - p - c ← in standard form

with a = 1, b = - p and c = - p - c

Given that α and β are the zeros of f(x), then

α + β = - [tex]\frac{b}{a}[/tex] and αβ = [tex]\frac{c}{a}[/tex], thus

α + β = - [tex]\frac{-p}{1}[/tex] = p , and

αβ = [tex]\frac{-p-c}1}[/tex] = - p - c

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

(α + 1)(β + 1) ← expand factors

= αβ +α + β + 1 ← substitute values from above

= - p - c + p + 1

= - c + 1 = 1 - c ← as required

Final answer:

By applying Vieta's formulas to the given polynomial, we can determine that the product (α + 1)(β + 1) equals 1 - c.

Explanation:

Given the polynomial f(x) = x2 - p(x + 1) - c, whose zeroes are alpha (α) and beta (β), we can use the relationship between the coefficients of a polynomial and its zeroes to find the value of (α + 1)(β + 1). According to Vieta's formulas for a second-degree polynomial ax2 + bx + c = 0, the sum of its roots (-b/a) is equal to α + β, and the product of its roots (c/a) equals αβ.

For this specific polynomial, a = 1, b = -p, and c = -c. Thus, we have:

α + β = p

αβ = -c

Now, let's calculate (α + 1)(β + 1):

(α + 1)(β + 1) = αβ + α + β + 1 = (-c) + (p - 1) + 1 = 1 - c

Answer:

Step-by-step explanation:

ΔQTR and ΔRTS are similar (AAA). Therefore the corresponding sides are in proportion:

[tex]\dfrac{RT}{TS}=\dfrac{TQ}{RT}[/tex]

We have

[tex]RT=x,\ TS=9,\ TQ=16[/tex]

Substitute:

[tex]\dfrac{x}{9}=\dfrac{16}{x}[/tex]              cross multiply

[tex]x^2=(9)(16)\\\\x^2=144\to x=\sqrt{144}\\\\x=12[/tex]

Answer:

Area: 135 ft^2

Perimeter: 50 ft

Step-by-step explanation:

area:

take the rectanle so length 12 x 9 = 108 so that is the length of the rectangle and now we need to find that of the triangle left over

subract 18 - 12 = 6 so that is the base of the trianle and we know the side length is 9 so plus it in A = (9)(6)/2

A = 54/2

A = 27

add 27 + 108 to get the total area

135

perimeter:

18 + 9 + 11 + 12 = 50

For this case we have that by definition, the perimeter of the trapezoid is given by the sum of its sides:

[tex]p = 9 + 18 + 11 + 12\\p = 50[/tex]

So, the perimeter is 50ft

On the other hand, the area is given by:

[tex]A = \frac {1} {2} (b_ {1} + b_ {2}) * h[/tex]

Where:

[tex]b_ {1}:[/tex] It is the largest base

[tex]b_ {2}:[/tex] It is the minor base

h: It's the height

Substituting the values:

[tex]A = \frac {1} {2} (18 + 12) * 9\\A = \frac {1} {2} (30) * 9\\A = \frac {1} {2} (270)\\A = 135[/tex]

So, the area of the trapezoid is [tex]135 \ ft ^ 2[/tex]

Answer:

the perimeter is 50ft

the area of the trapezoid is [tex]135 \ ft ^ 2[/tex]

All you have to do is divide 150 by 18 and that will get you how many meters Pete drives per second

150 ÷ 18

8.3333333333333333333

so...

8.3 m/s (B)

Hope this helped!

~Just a girl in love with Shawn Mendes

Speed is defined as quotient of distance and time.

[tex]

s=\frac{d}{t}=\frac{150}{18}=8.33\dots

[/tex]

Speed is a scalar value therefore we cannot determine its vector. Speed with vector is known as velocity and that is where we specify its vector because velocity is a vector value.

So the answer is 8.3 m/s.

Hope this helps.

r3t40

The answer is:

The correct option is:

A) $74.55

To calculate how much does Sonya pay for the four pairs altogether, we need to calculate the original price after the 50% discount and the taxes.

Calculating we have:

[tex]PriceAfterDiscount=35*50(percent)=35*\frac{50}{100}\\\\35*\frac{50}{100}=35*0.5=17.5[/tex]

We have that before the tax, the price of the shoes was $17.5, then, calculating the price after the taxes, we have:

[tex]AfterTaxes=17.5(1+6.5(percent))=17.5(1+\frac{6.5(percent)}{100})\\\\AfterTaxes=17.5(1+\frac{6.5(percent)}{100})=17.5*(1+0.065)\\\\AfterTaxes=17.5*(1+0.065)=17.5*1.065=18.637[/tex]

So, we have that the price after discount and the taxes is $18.637 per each pair of shoes.

Hence, the price for the four pairs of shoes will be:

[tex]TotalPrice=4*18.637=74.548=74.55[/tex]

Have a nice day!

No. You cannot use the Pythagorean theorem to find the missing side, because you can only use The Pythagorean theorem when you are dealing with a right triangle.

first off, let's recall that supplementary angles are just two sibling angles that add up to 180°.

so we have ∡T and ∡S, but we also know that ∡T = 3∡S, namely T = 3S.

[tex]\bf T+S=180\implies \stackrel{T}{3S}+S=180\implies 4S=180\implies S=\cfrac{180}{4}\implies S=45 \\\\\\ T=3S\implies T=3(45)\implies T=135[/tex]

Answer:

[tex]\large\boxed{Q1:\ x=2\ or\ x=5}\\\boxed{Q2:\ x=1-\sqrt{21}\ or\ x=1+\sqrt{21}}[/tex]

Step-by-step explanation:

[tex]\text{Use the quadratic formula:}\\\\ax^2+bx+c=0\\\\\text{If}\ b^2-4ac<0,\ \text{then the equation has}\ \bold{no\ solution}\\\\\text{If}\ b^2-4ac=0,\ \text{then the equation has one solution}\ x=\dfrac{-b}{2a}\\\\\text{If}\ b^2-4ac>0,\ \text{then the equation has two solutions}\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\==========================================[/tex]

[tex]\bold{Q1}\\\\x^2-7x+10=0\\\\a=1,\ b=-7,\ c=10\\\\b^2-4ac=(-7)^2-4(1)(10)=49-40=9>0\\\\\sqrt{b^2-4ac}=\sqrt9=3\\\\x_1=\dfrac{-(-7)-3}{2(1)}=\dfrac{7-3}{2}=\dfrac{4}{2}=2\\\\x_2=\dfrac{-(-7)+3}{2(1)}=\dfrac{7+3}{2}=\dfrac{10}{2}=5\\\\========================================[/tex]

[tex]\bold{Q2}\\x^2-2x=20\qquad\text{subtract 20 from both sides}\\\\x^2-2x-20=0\\\\a=1,\ b=-2,\ c=-20\\\\b^2-4ac=(-2)^2-4(1)(-20)=4+80=84>0\\\\\sqrt{b^2-4ac}=\sqrt{84}=\sqrt{4\cdot21}=\sqrt4\cdot\sqrt{21}=2\sqrt{21}\\\\x_1=\dfrac{-(-2)-2\sqrt{21}}{2(1)}=\dfrac{2-2\sqrt{21}}{2}=1-\sqrt{21}\\\\x_2=\dfrac{-(-2)+2\sqrt{21}}{2(1)}=\dfrac{2+2\sqrt{21}}{2}=1+\sqrt{21}[/tex]

Answer:

Step-by-step explanation:

x^2 - 7x + 10 = 0 can be factored as follows:  (x - 5)(x - 2).  Note that -5x -2x combine to -7x, the middle term of this quadratic, and that (-5)(-2) = +10, the constant term.  Setting each of these factors = to 0 separately, we get:

x = 5 and x = 2.

x^2 - 2x = 20 should be rewritten in standard form for a quadratic equation before you attempt to solve it:  x^2 - 2x - 20 = 0.  This quadratic is not so easily factored as was the previous one.  Let's use the quadratic formula:

      -b ± √(b²-4ac)

x = --------------------

             2a

Here, a = 1, b = -2 and c = -20, so the discriminant b²-4ac = (-2)^2 - 4(1)(-20), or 4 + 80, or 84.  84 has only one perfect square factor:  4·21.  Because the discriminant is +, we know that this equation has two real, unequal roots.

They are:

       -(-2) ± √(4·21)         2 ± 2√21

x = ----------------------  =  ----------------- =   1 ± √21

             2(1)                            2

Answer:

Step-by-step explanation:

Answer:

A. different probabilities

Answer:

Object from Catapult B

Step-by-step explanation:

The question is on time of flight in falling objects

Given catapult A: h(x)= -16x^2+64x+17, find the height the object will reach at time 2.0

substitute value x=2 in h(x)= -16x^2+64x+17;

h(2)= -16 × (2)² +64 ×2 +17

h(2) = -16×4 + 145

h(2)= 81

However with catapult B at t=2.0 the height reached will be 60

Solution

Catapult A object will attain h=81, when t=2.0

Catapult B object will attain h=60, when t=2.0

Thus Object from Catapult B will hit the ground first because it covered a lesser distance compared to the object from catapult A

Answer:

Average = 1

Step-by-step explanation:

Let us define the average first:

Average is calculated by adding up all the values and then dividing the sum by total number of values.

The formula for average may be written as:

[tex]Average = \frac{Sum}{count}[/tex]

In the following case,

Sum of numbers = -3-2+2+2+6 = 5

Count = 5

So,

Average = 5/5

=> Average = 1

Answer:

the answer is 1

Step-by-step explanation:

Sum of numbers = -3-2+2+2+6 = 5

Count = 5

So,  

Average = 5/5

=> Average = 1

C is the correct answer. Good luck!

Answer:

I think it’s 28 but I’m not sure

(sorry if it’s wrong)

Step-by-step explanation: